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Processing, characterization and modelling of borosilicate glass matrix-particulate silicon nitride composites, containing controlled additions of porosity, for use in high speed electronic packaging

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Processing, characterization and modelling of borosilicate glass matrix-particulate silicon nitride composites, containing controlled additions of porosity, for use in high speed electronic packaging
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Randall, Michael S., 1963-
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English
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2 v. : ill. ; 29 cm.

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Subjects / Keywords:
Ceramic materials ( jstor )
Diameters ( jstor )
Dielectric materials ( jstor )
Electronics ( jstor )
Latex ( jstor )
Packaging ( jstor )
Porosity ( jstor )
Sintering ( jstor )
Size distribution ( jstor )
Surface areas ( jstor )
Dissertations, Academic -- Materials Science and Engineering -- UF
Materials Science and Engineering thesis Ph. D
Silver Springs (Marion County) ( local )
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bibliography ( marcgt )
non-fiction ( marcgt )

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Thesis:
Thesis (Ph. D.)--University of Florida, 1993.
Bibliography:
Includes bibliographical references (leaves 581-629).
General Note:
Typescript.
General Note:
Vita.
Statement of Responsibility:
by Michael S. Randall.

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Copyright [name of dissertation author]. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
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PROCESSING, CHARACTERIZATION AND MODELLING OF
BOROSILICATE GLASS MATRIX-PARTICULATE SILICON NITRIDE COMPOSITES,
CONTAINING CONTROLLED ADDITIONS OF POROSITY, FOR USE IN
HIGH SPEED ELECTRONIC PACKAGING




















By

MICHAEL S. RANDALL





















A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA

1993


UNIVERSITY OF FLORIDA LIBRARIES



































Copyright 1993

by

Michael S. Randall















ACKNOWLEDGEMENTS


This work would not have been possible without the skilled help of

many individuals. First and foremost, I would like to thank my wife,

Sara, for her unconditional love, understanding and support. None of

this would have been possible without her. I would also like to thank

my parents (Randalls and Elders) for their support, understanding and

encouragement. I would like to thank my brothers and sisters for their

moral support as well.

On the technical side, I would like to sincerely thank Mr. Gary

Scheiffele for his vast amounts of training and advice in the area of

materials processing. I would like to thank R. Raghunathan and A.

Bagwell for their advice and creative discussions as well. Other

training and advice, in the area of materials processing, by Dr. M.

Amini, Dr. C. Khadilkar, Dr. T.S. Yeh, Dr. S. Vora, Dr. H.W. Lee, Dr. P.

Bendale, and Mr. M. Springate, are also greatly appreciated.

Furthermore, I would like to gratefully acknowledge the advice of Dr.

H.K. Ober, of Cornell University, in the area of dispersion

polymerization.

Complex impedance measurements were made possible through the

equipment and advice of Dr. L.L. Hench, Dr. J.K. West, and Dr. S.

Wallace, at the Advanced Materials Research Center (AMRC). Solution

(ICP) and surface (FTIR) analysis was also most graciously provided by

Dr. L. Hench and Mr. G. LaTorre. Technical advice and support in the

area of electron microscopy (SEM and TEM) from Mr. W. Acree, Mr. R.

Crockett, Dr. Y.J. Lin and Dr. S. Bates is also acknowledged gratefully.

In addition, I would like to thank Mr. A. Cozzi and Dr. D. Clark for

advice and support in doing thermal oxidation experiments. Processing

equipment and support was provided by Dr. M.D. Sacks.








I would like to sincerely thank my advisor, Dr. J.H. Simmons, for

all of his input and support. I would also like to acknowledge the co-

chairman of my committee, Dr. M.D. Sacks for his advice and support. I

would like to thank the rest of my committee, Dr. P.H. Holloway, Dr.

L.L. Hench, and Dr. D.E. Burke for their assistance as well.

Finally, I would like to thank the Engineering Offices of Gould,

Lewis and Proctor, as well as AVX Corporation for providing me

employment so that I could pursue my degree during difficult financial

times.
















TABLE OF CONTENTS
Page

ACKNOWLEDGEMENTS ......................................... .... iii

ABSTRACT ....................................................... x

CHAPTER ONE: INTRODUCTION ...................................... 1

1.1 The Impact of Electronics on Modern
Civilization ......................................... 1

1.1.1 Economic and Political Aspects ......... 1
1.1.2 The Future of the Electronics Industry:
Impact and Limitations ................. 2
1.1.2.1 The Fourth Generation ...... 2

1.2 Fundamental Microelectronic Packaging
Limitations ........ ....... .......................... 5

1.2.1 Electron Light Speed Limit ............. 9
1.2.2 Conductor Spacing Limit ................ 9
1.2.3 Cooling Limitations ................... 13

1.3 Electronic Packaging: Overview of the Field ....... 18

1.3.1 History ..... ........... ............ .. 18
1.3.2 Importance of the Electronic Package ... 24
1.3.2.1 Economic ................... 24
1.3.2.2 Functional ................. 24
1.3.3 Properties Desired of Packaging
Materials ...... ....................... 27

1.4 Materials Solutions to Electronic Packaging
Problems ........................................... 40

1.4.1 Ceramics versus Polymers .............. 40
1.4.2 Methods and Materials .................. 43
1.4.2.1 Traditional ................ 43
1.4.2.2 Advanced .................. 44

1.5 Proposed Packaging Material System:
Statement of Thesis ............................... 51

1.5.1 Choice of Electronic Packaging Material
System ................................... 51
1.5.2 Topics of Investigation ................ 53








Page

CHAPTER TWO: THEORETICAL AND TECHNICAL REVIEW ................ 75

2.1 Overview ...... ..... ............................. .. 75

2.2 Synthesis and Processing of Uniform Polystyrene
Latex Microspheres (UPLMs) ......................... 75

2.3 Particle Packing ................................... 85

2.3.1 Monosized Spheres ...................... 85
2.3.1.1 Ordered Packing ............ 85
2.3.1.2 Random Packing ............. 85
2.3.2 Packing of Multimodal, Discrete
Distributions of Spheres .............. 88
2.3.3 Continuous Size Distribution Particles 105
2.3.3.1 Ideal Packing .............. 105
2.3.3.2 Hindered Packing ........... 110
2.3.4 Effects of Settling and Segregation .... 110

2.4 Clustering and Percolation Theory .................. 112

2.4.1 Clustering ............................ 115
2.4.2 Percolation .................. ........ 116
2.4.3 Application of Percolation to
Microstructure ......................... 123

2.5 Sintering ............. .......... ................... 134

2.5.1 General ................................ 134
2.5.2 Viscous Sintering ...................... 140
2.5.2.1 Viscous Sintering of
Real Systems ............... 149
2.5.2.1.1 Effects of
Microstructure ....... 149
2.5.2.1.2 Viscous Sintering of
Glass Matrix
Composites Having
Nonsintering
Inclusions ........... 153

2.6 Dielectric Theory .................................. 158

2.6.1 Dielectric Materials ................... 158
2.6.2 Measurement of Dielectric Properties ... 163
2.6.3 Dielectric Properties of Composite
Materials ............ ................. 170

2.7 Mechanical Properties ............................. 179

CHAPTER THREE: EXPERIMENTAL PROCEDURE ........................ 184

3.1 Overview .......... .............................. .. 184

3.2 Powder Synthesis and Treatment .................... 184

3.2.1 Overview ..................... ........ 184
3.2.2 Synthesis, Characterization and
Preparation of Polystyrene Microspheres 184
3.2.3 Milling and Preparation of Borosilicate
Glass Powder .......................... 199








Pace

3.3 Powder Characterization ........................... 202

3.3.1 Overview ................................ 202
3.3.2 Visual ....... ......................... 203
3.3.3 Density .................................. 204
3.3.4 Size Characterization of Ceramic
Powders ....... ... ..................... 206
3.3.5 Surface Area .......................... 209
3.3.6 Chemical .............................. 220

3.4 Suspension, Casting and Green Compact Studies ...... 224

3.4.1 Overview ........ .. ... ....... ......... 224
3.4.2 Wet Processing and Characterization .... 225
3.4.2.1 Selection of the Dispersion
System ........ ....... .... 225
3.4.2.2 Characterization and
Optimization of the
Suspension System .......... 228
3.4.2.2.1 Overview ............. 228
3.4.2.2.2 Rheology of Dispersed
Composite Components 228
3.4.2.2.3 Optimization of the
Suspension System ... 230
3.4.2.2.4 Effects of Sonication
and Aging Upon
Suspension Properties 232
3.4.2.2.5 General Rheology
Studies .............. 235
3.4.3 Slip Casting of Compact Samples ........ 236
3.4.4 Suspension Solids Loading Determination 242
3.4.5 Characterization of Green Compacts ..... 243
3.4.5.1 Visual ..................... 243
3.4.5.2 Hg Porosimetry ............. 243

3.5 Thermal Analysis: Oxidation and Pyrolysis Studies 249

3.5.1 Overview ............. ................. 249
3.5.2 Oxidation Studies ...................... 250
3.5.3 Pyrolysis Studies ..................... 251

3.6 Thermal Treatments ................................. 252

3.6.1 Furnace Calibration ................. 252
3.6.2 Pyrolysis and Presintering ............. 258
3.6.3 Sintering .................. ............ 259

3.7 Materials Characterization ......................... 261

3.7.1 Archimedes Density Characterization .... 261
3.7.2 Dielectric Properties Characterization 267
3.7.3 Microscopic Investigation of Composites 277
3.7.3.1 Overview ................... 277
3.7.3.2 Specimen Preparation ....... 277
3.7.3.3 Investigation of Segregation
of Included Porosity ....... 281
3.7.4 Mechanical Properties Data ............. 281


vii








Page

CHAPTER FOUR: RESULTS AND DISCUSSION ......................... 286

4.1 Precursor Powders .................................. 286

4.1.1 Visual ....................... .......... 286
4.1.2 Powder Density ........................ 295
4.1.3 Particle Size/Size Distribution ........ 298
4.1.3.1 Polystyrene Microspheres ... 298
4.1.3.2 Ceramic Powders ............. 315
4.1.4 Powder Surface Area .................... 323
4.1.5 Effect of Ball Milling On BS Glass ..... 326

4.2 Suspension and Green/Pyrolyzed Structure
Characterization ....................................... 337

4.2.1 Suspension Characterization .............. 337
4.2.3 Green/Pyrolyzed Structure
Characterization ...................... 349
4.2.3.1 Overview ................... 349
4.2.3.2 Structural Characteristics
of Polystyrene Latex
Compacts .................. 349
4.2.3.3 Structural Characteristics
of Green and Pyrolyzed
Composites ............ ..... 360
4.2.3.4 Effects of Aging and
Sonication Upon Green
Properties ................. 382
4.2.3.4.1 Sonication ........... 382
4.2.3.4.2 Aging ................ 386

4.3 Thermal Processing and Characterization ............. 395

4.3.1 Removal of Organics ................... 395
4.3.2 Evolution of BS Glass Surface Area ..... 399
4.3.3 Oxidation of Si3N, Powder ................ 404
4.3.4 Sintering .............................. 408

4.4 Characterization and Modelling of Processed
Materials .......................................... 450

4.4.1 Characterization of Microstructure ..... 450
4.4.2 Modelling of Included Porosity .......... 482
4.4.3 Characterization of Dielectric
Properties .................. ... ....... 499
4.4.4 Microhardness Characterization ......... 534

CHAPTER FIVE: SUMMARY AND CONCLUSIONS ......................... 542

5.1 Overview ............. ....... .. .................... 542

5.2 Powder Development and Characterization ............ 542

5.3 Green Processing and Characterization .............. 543

5.4 Thermal Processing and Characterization ............ 544

5.5 Characterization and Modelling of Densified Compacts 546


viii











CHAPTER SIX:

APPENDIX I:


APPENDIX II:



APPENDIX III


APPENDIX IV:


SUGGESTIONS FOR FUTURE WORK ......................

MANUFACTURER'S DATA FOR CERAMIC CONSTITUENT
POWDERS ...........................................

PARTICLE SIZE AND SIZE DISTRIBUTION DATA
OF UNSETTLED 4.6 pm REGIME (061990 SERIES)
UPLM SPHERES ................................. ....

LEAST SQUARES POLYNOMIAL REGRESSION DATA
CURVE FITTING PROGRAM (BASIC) ...................

LIST OF ACRONYMS .................................


REFERENCES .....................................................

BIOGRAPHICAL SKETCH ............................................


Page

549


553



564


576

579

581

630















Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy

PROCESSING, CHARACTERIZATION AND MODELLING OF
BOROSILICATE GLASS MATRIX-PARTICULATE SILICON NITRIDE COMPOSITES,
CONTAINING CONTROLLED ADDITIONS OF POROSITY, FOR USE IN
HIGH SPEED ELECTRONIC PACKAGING


By

Michael S. Randall

August 1993

Chairman: Dr. Joseph H. Simmons
Major Department: Materials Science and Engineering


Borosilicate glass matrix-particulate silicon nitride composites,

with controlled additions of porosity, are produced through suspension

processing and slip casting of nonaqueous, codispersed suspensions.

Controlled porosity is obtained via the addition and pyrolysis of

polystyrene latex microspheres. The effects of latex size and size

distribution upon controlled pore structure are investigated. The

largest (9.0 ym monosized) latex, at a concentration of 17.6 V%, is

found to give the largest amount of closed porosity (15.6 V%).

The borosilicate glass-silicon nitride binary is also investigated

in order to determine the effect of nonsintering inclusion concentration

upon processing factors as well as upon final composite properties.

Composites containing all three constituents (borosilicate glass, Si3N4,

and polystyrene latex) are also investigated.

Above the percolation threshold of latex addition (i.e. a filled

fraction of approximately 16 V% of total space), the pore structure is

observed to change rapidly, greatly affecting densification behavior as

well as the pore structure. Additions of latex below the percolation








threshold result in hermetic, densified structures subsequent to

processing. Silicon nitride additions are found to retard densification

kinetics at and above concentrations of 16 volume percent of total space

and to arrest sintering at and above Si3N4 concentrations of 36 volume

percent of total space, in accordance with viscous sintering theory.

Hermetic, porous borosilicate glass-particulate silicon nitride

composites are produced having maximum closed porosities of

approximately 15.6 volume percent (at approximately 16.0 V% total

porosity). The densified included pore structure is accurately modelled

using a modification of standard series clustering and percolation

models.

Corresponding minimum composite dielectric constants of

approximately 3.5 are observed. The dielectric constant of the

composites are found to be stable over the range of frequencies

measured. Dielectric loss values are found to agree well with analogous

literature values for the borosilicate matrix glass. Composite

dielectric constants are modelled using effective medium theory as well

as traditional dielectric mixing rules.

Microhardness evaluations of representative composites are also

discussed. The elastic moduli of the composite system are modelled

using MacKenzie, linear regression, Voigt and Reuss models. Stoke's

settling theory is also extrapolated to explain the lack of segregation

observed in this system.















CHAPTER ONE
INTRODUCTION


1.1 The Impact of Electronics on Modern Civilization

1.1.1 Economic and Political Aspects

The electronics industry is a $460 billion industry world wide

[88SCH1]. The American electronics industry accounts for 38.1% of this

amount, while Japanese and European electronics industries account for

37.7% and 24.2% of the world electronics industry, respectively

[88SCH1]. Domestically, the electronics industry accounts for 3.6% of

the gross national product (GNP) which amounts to approximately 170

billion dollars [88SCH1, 90WRI]. The electronics industry is currently

growing at an annual rate of 13% for Japan, and 11% and 6% for the

United States and Europe, respectively [88SCH1].

Demand for improved electronic devices (i.e. higher speed, smaller

size, and greater ability, etc.) has provided a driving force for

continuous improvements in microelectronic technology. Never have Ralph

Waldo Emerson's words, "If a man can write a better book, preach a

better sermon, or make a better mouse-trap than his neighbor, though he

builds his house in the woods, the world will make a beaten path to his

door," been more applicable to an industry [88CAR, p. 84.8].

The electronics industry has generally progressed from analog to

digital electronics. The workhorse of digital electronics is the

integrated circuit. The IC was simultaneously invented by Jack Kilby of

Texas Instruments and by Robert Noyce of Fairchild Industries in 1958

[88MAC). The field of IC technology has grown through three generations

of successively increasing integration (i.e. MSI for medium scale

integration, LSI for large scale integration, and VLSI for very large

scale integration, respectively), with more generations to come (i.e.










ULSI and WSI, for ultra large scale integration and wafer scale

integration, respectively). Furthermore, IC devices are available in

many configurations, as required by the exhaustive number of electronic

appliance applications. The general trend in these electronic devices

is toward maximization of circuit elements per unit volume. Figure 1.1

illustrates the evolution of circuit density for both field effect (FET)

and bipolar junction (BJT) transistor IC devices. The relative scale of

integration is also indicated in Figure 1.1



1.1.2 The Future of the Electronics Industry: Impact and Limitations

1.1.2.1 The Fourth Generation

The major goals influencing the evolution of electronic technology

is to increase performance and universality of application. Digital

microprocessor-based devices dominate the electronics industry.

Therefore, improvements in electronic technology will focus upon

advancement of microprocessor technology as well as in advances in

microprocessor interlinking and increasing the availability and amount

of memory accessible by microprocessors. Other goals include reduction

in power consumption, reduction in device size and weight, increased

device capability as well as increased device dependability and

environmental/thermal stability. Other important requirements are the

maximization of device output and quality, at minimized cost.

The methods that will be used in order to achieve the above goals

will be quite varied [see 89SER,89TUM3, etc.]. In order to increase

computing speed (i.e. electronics performance), non-traditional

technologies, which are currently in their infancy, will be applied.

Examples of these technologies include optical switching and

communication (including holography) [89SER,88YAN,88SRI,87COR1,

87COR2,83BER], electro-optical interfacing [88HUT,87JIN], advanced

semiconductor materials, parallel processing [92SKE], artificial

intelligence (AI), integrated services digital networking (ISDN)












a

oC


O
L_,


6- T
VLSI
5








1 1 Hybrids

-1
0 Transjstors
Tu bes

1965 1970 1975 1980 1985 1990 1995
Year








re 1.1 Illustration of the increase in electronic circuit
density with time [91TUM]


Figu










[900HS], biological systems [89SER], neural networking [89SER],

superconductor-based logic and communications [89SER,89TUM3], etc.

Furthermore, electronic performance will be advanced via the

continued evolution of traditional technologies, in pursuit of

theoretical limitations. One goal is to reduce current packaging

hierarchies by at least one level, in order to reduce signal flight

distances. This change would result in a reduction in the number of

interconnects as well, thereby improving reliability and device

longevity, while reducing production costs. The first goal may be

achieved by successful implementation of another goal, which is to

economically obtain ultra large scale and/or wafer scale integration

(ULSI and WSI, respectively). Wafer scale integration results in a

dramatic increase in the scaling of microcircuitry, which, in theory,

leads to reduced signal flight times due to reduced signal transmission

distances. Ironically, however, WSI offsets some of the advantages of

removing a packaging level since production costs would definitely

increase. Furthermore, it would no longer be possible to replace one

individual chip since the smallest field replaceable unit (FRU) would

become the integrated wafer itself. As discussed below, there are other

drawbacks to WSI as well.

Another goal is to change to higher performance semiconductor

materials, having higher electron-hole mobilities, such as GaAs. It is

also preferred that the replacement semiconductor materials) be direct

band gap materials, thereby allowing more efficient usage of power as

well as less phonon-initiated heat generation.

Finally, a great deal of research effort is currently involved

with improving traditional microprocessor and packaging technologies.

The focus of such research is to increase the performance of

microelectronic systems beyond the state of the art and closer to

fundamental theoretic limitations, as discussed in section 1.2 below.

Increased clock frequencies; finer scales of microcircuitry; larger










scales of integration; larger, cheaper, and faster memories and

microprocessors; use of lower resistivity conductors as well as low

dielectric constant, cofirable packaging materials and implementation of

increased performance cooling designs and materials are all desired

goals of said research. Figure 1.2 illustrates the current and

projected trends in the performance of computers based upon traditional

silicon IC technology.

Furthermore, environmental concerns are becoming increasingly

important. Hazardous materials, involved in the production of

electronic appliances, must be properly disposed of or recycled. Also,

many of the cleaners and solvents used in IC production and electronic

packaging are being replaced by environmentally benign materials and

processes [89SER].

In summary, it is quite apparent that the microelectronics

industry has a great many opportunities for advancement. However, it is

also true that said industry is subject to unparalleled competition as

well as a great deal of regulation.



1.2 Fundamental Microelectronic Packaging Limitations

The fundamental limitations discussed in this section relate to

microelectronic packaging only. Surprisingly, the switching speed of a

microelectronic apparatus is as much a function of the packaging

configuration and materials as it is a function of the actual switching

devices. Figures 1.3 and 1.4 illustrate the theoretical limitations

that are involved in digital electronics, in a graphical sense, and are

a valuable summary as well as an illustration of the combination of each

fundamental limitation. The figures outline the perimeters that provide

the limits of maximum performance of a digital electronic system

(including switching devices, packaging, interconnection, etc.).









3




2 -- 5




.1 -- / 25 5
O -3








-1 2500




-2 I 'I II


Year










Figure 1.2 Current and projected trends in traditional, silicon-
based, computer performance [91TUM]
a-






-2














based, computer performance [9lTUM]

































-9 -7 -5 -3 -1 1 3


log {element spacing (m)}


Figure 1.3


Element spacing versus delay time plane of electronic
packaging space, illustrating the theoretical
limitations in electronic packaging performance with
respect to spacing of electronic lines and signal
elements [89SER]


-6



-8



-10


-12



-14
































-8 -6 -4 -2 0 2 4


log {element spacing (m)}


Figure 1.4


Depiction of the theoretical limitations encountered
in electronic packaging as defined by the electronic-
element-spacing versus signal-line-spacing plane of
electronic packaging space [89SER]


2


0


-2
C


S-


-6


-8


-101
-10










1.2.1 Electron Light Speed Limit

Electrons can not travel at speeds exceeding the fundamental speed

of light in a perfect vacuum (i.e. approximately 3 x 108 m/s or 186,000

miles/s), regardless of the medium that they travel through. Electrons

travel through perfect (lossless) conductors at the speed of light if

said conductor is surrounded by free space. However, if the perfect

conductor is surrounded by a dielectric medium other than free space,

the speed at which electronic signals will traverse the conductor is

expressed through the relation:








where K is the dielectric constant of the insulating material

surrounding said perfect conductor. From the above discussion, it is

evident that use of lossless, low dielectric constant insulating

materials, in combination with non-magnetic, nearly perfect conductors,

will increase electronic signal speed, and thus, overall performance.

Furthermore, it is important to minimize packaging scale (i.e.

miniaturization) in order to minimize the signal time of flight (TOF) at

the signal speed indicated by the above equation. Therefore, it is

important to carefully chose both the electronic packing material and

the packaging metallization, as well as to minimize the scale of

electronic packaging integration.



1.2.2 Conductor Spacing Limit

While the quantum electron tunneling limit is not currently in

danger of being approached, using traditional electronic packaging,

there are other limitations that do effect conductor spacing in

electronic packages. In any electronic package, there is a finite

amount of space available for signal transmission lines. It has been

shown [89SER,89TUM3,90SHI2,90SHII,91TUM] that as the number of switching










devices increases, the number of input-output signal lines (I/Os) must

also increase according to the relation:


I=bCP




where I is the number of I/Os, b is the average number of signal

connections per circuit, and p is a positive exponential (research has

found that p is always < 0.67 and is usually about 0.5). This relation

is commonly know as Rent's rule. In two-dimensional space (i.e. single

layer or double sided electronic packaging), this limit has already been

approached or exceeded using traditional thick film packaging

technology, and, in some cases, using thin film technology [89SER].

The conductor spacing limitation may be circumvented, to a certain

extent, by using three dimensional packaging. Multilayer packages,

having signal planes interconnected with vias, are an example of three

dimensional packaging. However, there are limitations even to

multilayer packaging systems. These limitations depend upon the size of

the interlayer vias used and the number of layers used [89SER].

The minimum size of signal traces is theoretically limited by

quantum effects. Realistically though, the actual size and separation

distance of signal traces is most often determined by the ability to

produce straight and smooth traces having a uniform cross section.

At high frequencies the skin effect limits electronic current to

the outside (skin) of a conductor. At said frequencies the skin depth

is on the order of the conductor diameter, thereby decreasing the

effective diameter of the conductor. This serves to increase resistive

losses. Furthermore, since the current traverses the outside (skin) of

the conductor, interruptions in surface smoothness have a much greater

effect upon signal integrity. At said frequencies, as the signal

changes from one medium to another, any change in conductor cross

section will further enhance attenuation and signal reflection.










Thus, it is important not only to match impedances, but also to match

signal cross section sizes and geometries in the frequency regime

characterized by significant skin effect. Other factors include,

switching energy (i.e. maximum current density) and switching frequency

as well as dielectric strength and hermeticity of separating insulators.

The homogeneity of the conductor material as well as the overall

conductor quality (i.e. its resistivity, magnetic susceptibility, and

characteristic skin depth as a function of frequency, etc.) is also an

important considerations when pursuing minimum conductor spacings.

Conductor spacing limitations are also affected by electronic

noise. There are four types of internal electronic noise possible in a

packaging system: inductive, capacitive, reflected and power

distribution or AI noise.

Reflected noise is a result of a mismatch in impedance between

signal traces and active devices. It is not significant until higher

frequencies are reached (i.e. above 10MHz). Reflections may be

eliminated by matching the impedance of all elements in the device. In

practice, however, this is quite difficult and design goals are toward

realistic minimization of reflections.

Power distribution (PDN) or AI noise results from the switching

process itself. As a device switches, it requires a certain amount of

power, (typically about 1--10 mW [91TUM]). In a microprocessor, it is

possible for many elements to switch simultaneously. Said switching

processes are fast, usually occurring in tens of nanoseconds.

Therefore, the current demand upon the power supply can be excessive and

may cause a drop in the supply voltage. This drop causes a voltage

pulse to be sent to the switching devices, due to the parasitic

inductance of each microcircuit. The voltage pulses, if significant,

cause spurious switching.

Power distribution noise may be reduced through use of high power,

self-regulating power supplies, reduction in parasitic inductances










through package design, increased power and ground availability,

reducing signal path lengths and placement of signal traces more closely

to power and ground traces, etc.

Perhaps the best way to reduce or eliminate AI noise is to place a

small capacitor, having very little parasitic inductance (i.e. a

decoupling capacitor), as closely as is feasible to the switching

elements themselves. Decoupling capacitors serve as a local current

source during periods of transience, reducing AI noise to acceptable

levels.

Both inductive noise and capacitive noise are types of coupling

noise. Both are resultant from current changes in adjacent signal

traces and may result in the phenomenon commonly known as crosstalk.

Inductive noise involves a single voltage pulse, travelling in the

opposite direction of the original signal, in signal traces neighboring

the element carrying the original pulse. Capacitive coupling noise

results in two pulses, travelling in opposite directions from each

other, in signal traces neighboring an active trace. The first pulse

travels in the direction of the parent pulse and the second in the

opposite direction. Both pulses are in phase with the parent. In the

reverse direction, capacitive and inductive elements interact. The

magnitudes of said pulses depend directly on the distance between the

conductive traces and in the dielectric permittivity of the material

separating the traces. The ability of these pulses to result in

crosstalk depends upon both the voltage and the width of the resultant

coupled noise pulses. Both types of pulses can cause erratic switching

if the pulse voltage exceeds either the forward or the reverse bias

(depending upon the pulse direction), of the switching elements in

question, for a duration long enough to switch the elements.

Furthermore, reflected coupled pulses may also interact with first order

coupled pulses. The entire process is quite complex to model and is

handled in several publications [89SER,89TUM3, etc.]. It is sufficient









here to note that reductions in dielectric permittivity of the

insulating material will reduce coupled noise in an electronic packaging

system. Furthermore, coupled noise may be reduced through utilization

of prudent design configurations and criteria [89SER].



1.2.3 Cooling Limitations

The issue of electronic device cooling is very involved. As chip

integration evolves, switching elements are placed with increasing

density. While per device power dissipation has steadily decreased, the

rate of decrease of microdevice separation has surpassed this effect

(see Figures 1.5, 1.6 and 1.7). As a result advanced ICs have cooling

demands that require cooling technology at or beyond the state of the

art. Figure 1.7 illustrates the increased trend in cooling requirements

for IBM microelectronic packages. The cooling limitation may well be

the theoretical limitation that is first reached.

One method to meet cooling needs is to use direct band gap

materials or superconducting Josephson logic configurations as switching

devices, since they do not dissipate as much switching energy in the

form of heat as do indirect bandgap solid state switching materials (see

Fig 1.8). However, these switching devices have many drawbacks which

limit their successful implementation.

Another method is to use high thermal conductivity packaging

materials. Both of the above methods are passive in nature and are

somewhat limited, however, because all switching materials dissipate

some energy as heat, and because efficient heat sinking as well as heat

transfer at interfaces are required, in conjunction with high thermal

conductivity materials. These requirements are due to the relatively

small difference between heat source and sink temperatures typical in

electronic packaging applications.

The most successful cooling methods utilized to date involve

active cooling, such as immersion technology [89SER]. A new method, not




















1000



0 15 1 1 1 100











Year
10 N







1970 1975 1980 1985 1990 1995

Year


Figure 1.5


Increase in chip signal connections (i.e. device
integration) and chip size with respect to time
[91TUM]


10000


1000



100


10


0
C
.2-0
.C
U
So>
0 0
Oc
L0

-ro


C)


1 L
1965
























































Figure 1.6


10 100 1000 10000


Heat Dissipation (W/cm2)
















Illustration of IC power density as a function of chip
integration [91TUM]






































1965 1970 1975 1980


1985 1990 1995


Year


Figure 1.7


Cooling ability (i.e. requirements) of IBM electronic
packages as they have evolved with time (i.e.
increased packaging integration) [91TUM]


C4'



C
Cu


0

a.
o
a,


0)
Q.,

()

,.


0L
196


Model 900 (390/9000)









Model 3090S (TCM)

Model
Model Model 3081 Model
Model 370 3033 (TCM) 3090
360 (TCM)
I I I I


.0















-8


0


E

u,

O
a,


-9


-10


-11


-12


Figure 1.8


-7 -6 -5 -4 -3 -2 -1

Power Per Gate (log{W})











Comparison of different switching device technologies
with respect to device power dissipation [91TUM]


Key:
Si-Silicon
GaAs-Gallium Arsenide
HEMT-High Electron Mobility Transistor










currently used in production, but showing great promise, is that of

microchannel cooling [89SER]. Microchannel cooling involves routing

coolant through the back of the IC chip itself. The chip is modified by

etching microchannels into its back, using traditional lithography

techniques. A plate is then affixed to the chip back, enclosing the

channels. Manifolds are then affixed to the chip ends, allowing flow of

coolant through the microchannels. This technique allows for a heat

dissipation of approximately 600 W/cm2 using water, flowing at the rate

of 10 cm3/s, and using a temperature differential of 600C and has

exhibited a heat exchange as high as 870 W/cm2 [89SER]. Using the

treatment outlined in [89SER], this cooling technology could allow for a

minimum nearest-to-next-nearest propagation delay time of 5 x 10-13 s

without overheating, using the logic restoration basis theoretical

minimum switching energy (E,,) of 7.7 x 1015 J. This could allow for a

theoretical maximum switching frequencies in the THz range (if only a

few switching elements are involved).



1.3 Electronic Packaging: Overview of the Field

1.3.1 History

Electronic packaging was first used, in significant amounts, in

Hollerith's card reader [89SER]. The mechanical relays utilized in the

machine had slate mounting plates as well as varnish covered solenoid

wires. Electronic packaging has advanced a great deal since then. Many

packaging changes have been implemented between Hollerith's

electromechanical relay-based technology and today's solid state

electronics. This section covers packaging methods used only since the

introduction of solid state logic.

Until very recently, emphasis for advancement in the field of

electronic packaging was limited to the scale of integration of solid

state devices. Contemporary chips incorporate up to several million










logic or storage elements, and thus, have eliminated the need for

several hierarchies of packaging that were formerly necessary.

Standard modular system (SMS) technology was the first concept

introduced for solid state device packaging [89SER]. This technology

interconnected singular electronic devices (i.e. transistors,

capacitors, etc.) on a printed circuit board. It was developed in 1959

and afforded a far superior alternative to tube technology in speed,

size, power consumption and reliability. The circuit boards were

connected to a panel and interconnected via wrapped wire and cable

connections. Apparatii utilizing this technology were still quite

limited, however, and a great deal of effort has since been expended

attempting further integration. With the invention of the IC a new

implement was provided for use toward this goal.

Solid logic technology (SLT) introduced many of the technological

advancements that are used, in modified form, today in ceramic packages.

The package was made from 96% A1203, 4% glass, and used swaged pin

technology. The chip was soldered in place, then encapsulated using a

metal cap held in place with epoxy. The method of chip attachment

utilized was called the controlled collapse chip technology (C4) which

involves depositing solder balls on either the IC or the package I/O

pads, flipping the chip face down upon the ceramic package carrier, then

heating the assembly to let the solder flow and attach the chip to the

package. This process is also known as flip-chip technology and is used

frequently today [89SER,88TUM,89TUM,91TUM].

Advanced solid logic technology (ASLT) improved upon SLT by

screening conductors onto both sides of the substrate. Furthermore, the

substrates were made stackable by soldering the pins from the bottom of

one package to the top of another. The wiring density was also

increased. All these advances yielded significant performance increases

[89SER,88TUM,89TUM). Monolithic systems technology (MST) further








20

expanded upon this technology. This system basically replicated SLT and

ASLT but provided further integration. The MST package provided 18

I/Os.

Vendor transistor logic (VTL) technology helped to introduce the

first universal industry standard for ICs [88TUM]. A variation upon

vendor transistor logic, card on board (COB) technology, allowed

manufacturers the ability to produce electronic appliances using

prepurchased ICs. Thus the precedent was established for second party

electronics, opening a huge industry and bringing the concept of

component interchangability to integrated logic-based components.

Initially ICs were available with up to fourteen leads. Later,

planar or dual in-line packages (DIPs) were developed having as many as

64 leads (88TUM,89TUM]. The DIPs were plugged into cards, which also

included other active and passive elements. The cards were plugged into

boards and the boards connected to a gate. The gates provided power as

well as interconnection [89SER].

Metallized ceramic (MC) technology was the first packaging genre

to utilize photolithographic techniques. As circuit integration

increased, I/O density requirements mandated that either thin film or

multilayer technology be utilized [88TUM,89TUM]. Metallized ceramic

technology used the former. The thin films were deposited by either

sputtering or thermal evaporation on both sides of an A1203 substrate.

The deposition process involved a three-layer deposition of chromium on

copper on chromium. The chromium layers were thin and were used to

improve adhesion on the inner layer [88TUM,89TUM].

Metallized ceramic polyimide (MCP) technology was the first

multilayer thin film technology. A polyimide layer was added to the top

of a ceramic substrate, and the polymer surface was deposited with

chromium then copper then chromium as above. This process was repeated

for several layers, then standard photolithographic techniques were










utilized to etch via spaces between layers. The vias were then back

filled with paste, thereby connecting the layers [89SER].

The discussion until now has been centered around the first level

of packaging hierarchy. Evolution of chip packages (the zeroeth level),

specifically LSI packaging, will now be discussed briefly in order to

introduce the next generation of first level packaging. Early large

scale integration (ELSI) involved packaging of 100 to 500 circuits, and

utilized pluggable module packaging, making it a field replaceable unit

(FRU) [89SER]. Large scale integration (LSI) technology was introduced

in 1979. The first LSI circuits contained 704 switching elements. The

chips had a switching speed as fast as 1 ns. Because the packages had

delicate I/O terminations, they were mounted to the first level module

utilizing wave soldered through holes. Up to nine LSI chip packages

were mounted to a single multilayer ceramic (MLC) module in this manner.

The MLC had been developed in order to accommodate ever increasing

chip integration levels. With up to 23 layers, the MLC presented a

technologically challenging processing hurdle. Multilayer ceramic

packaging technology was borrowed from the field of multilayer

capacitors, originated by RCA in the late 1950s [88TUM,89TUM]. Also

borrowed from the multilayer capacitor community was the concept of the

interlayer connection, or via, as well as tape casting and laminating

technologies [88TUM,89TUM]. Variations of MLC technology are still

utilized today. The basic process of MLC fabrication is outlined in

Figure 1.9 for both the old and new thermal conduction module (TCM)

production process. Said technology has been very successful in the

area of advanced performance ceramic packaging and is expected to

dominate that field, in varied form and in conjunction with thin film

multilayer polymer technology, in the future. There are excellent

literature sources which describe the process and related fields in

detail [82BLO,84BLO,84SCH2,88TUM,89SER,89TUM,91TUM].



















Raw Materials

Slurry Preparation
i
Casting and Blanking

Via Hole Punching

Metallization (Thick Film)

Stacking/Registering

Lamination

Organics Removal
and
Sintering
i
Final Ceramic
i
Electrical Tests

Attachment of Pins
and Flange

Substrate Machining
and Surface Treatment

Chip Attachment (C-4 Process)

Electrical Testing of Module

Final Module Assembly

Helium Gas Filling of Module


Alumina/Mo Based TCM Glass-Ceramic/Cu Based TCM


Alumina + Glass (4-10%)


Glass Powder


Acid-Base Acid-Acid

Continuous Casting Continuous Casting

Mechanical Mechanical

Mo Paste Cu Paste

Automated Automated

Automated Automated


Controlled Steam Atm.
Controlled Hydrogen Atm.
Crystallization Step

Alumina + Glass Glass Ceramic

Automated Automated

Automated
Automated
Ni and/or Au Plating

Seal Flange Top and Bottom Surface
Finishing and Seal Flange

Automated Automated

Automated Automated

Automated Automated


Automated


Automated


Figure 1.9


Flow chart of the MLC production process used in the
IBM TCM [82BLO,89TUM,91TUM]










Perhaps the best known example of MLC technology is the IBM TCM

series. When introduced in 1981 for the IBM 3081 computer system, the

IBM TCM used 96% alumina (4% glass) as the dielectric and either Mo or W

metallurgy [89SER,83BLO]. The multilayer module consisted of 33 layers

and could accommodate up to 118 IC chips. The layers were configured as

either signal (X or Y plane), redistribution, or voltage-reference

layers. Said module had up to 320 cm of wiring per cm3 of package.

Furthermore, an ingenious cooling device was utilized on the IBM TCM

which used chilled water forced through a hermetically sealed and He

backfilled chamber. Said technology was capable of accommodating chip

heat dissipations as high as 3 W/cm2. Much of the cooling ideologies

used in the original TCM (for the 3081) are used in the current TCM.

The state of the art TCM (introduced in 1991 for the IBM 390/9000)

seems only subtly different from the original TCM. However, it exhibits

markedly improved performance, by utilizing Cu metallurgy as well as low

sintering temperature (-1000C), low K (-5) crystallizable dielectric

materials cordieritee with minor clino-enstatite). Furthermore, the

390/9000 TCM can accommodate up to 121 LSI chips, and has 63 wiring

layers as well as 9 polyimide signal redistribution layers. All of this

was accomplished using special processing to avoid oxidation of the Cu

metallurgy during thermal treatment. The CTE of the dielectric used in

said package was matched carefully to Si over a broad range of

temperatures [91KUM2]. The packaging heat accommodation was increased

to -18 W/cm2 as well. This TCM represents the current state of the art

in high performance electronic packaging, although other corporations

have also marketed excellent examples [88BAB,89EMU,89SAW,89SER,89TUM3,

91SHE2,etc.].










1.3.2 Importance of the Electronic Package

1.3.2.1 Economic

Electronic packaging and interconnects account for a large portion

of the advanced ceramics market. The electronic ceramics market is the

largest niche within the field of advanced ceramics [91SHE2]. The

electronic packaging and interconnects market accounts for approximately

0.05% of the GNP of the United States [90WRI]. This industry involves

over $2.7 billion annually, accounting for approximately 1.5% of the

total sales of the entire US electronics industry [88SCH1,91SHE2].

Furthermore, the electronic packaging and interconnects industry

currently is experiencing a growth rate of approximately 8.5% per annum

[91SHE2], projecting a total market value of approximately $6.5 billion

by the year 2000 [91SHE2].



1.3.2.2 Functional

Upon first inspection, electronic packaging seems deceivingly

simple. The components of the package are passive and the final

packaged structure usually seems like an elementary monolith. Upon

further inspection, however, one learns that the electronic package is

quite complex. Perhaps no other type of passive device is subject to as

many material and environmental constraints.

Electronic packaging is typically divided into as many as six

levels. The zeroeth level of packaging involves the IC chip itself

(i.e. intra-chip integration), while first level packaging involves the

I/Os of the IC chip (i.e. chip level integration). In many instances,

the zeroeth order is not considered packaging, since it is inherent in

the chip integration itself. First level packaging brings power and

signal lines to the IC chip while providing mechanical and hermetic

protection.

The second level of the electronic packaging hierarchy involves

the interconnection between IC chips as well as other on-card devices











(i.e. card level integration). Second level electronic packaging is

task oriented, in that it involves the interconnection of electronic

devices that perform a specific task (i.e. video cards, etc.). The

second level allows for task diversity (i.e. different cards for

different tasks) as well as traditionally offering the smallest scale of

easy replacability (i.e. the field replaceable unit (FRU)). The third

level of packaging involves interconnection of cards (i.e. board level

integration) and the fourth level in the electronic packaging hierarchy

involves the interconnection of boards (i.e. gate level integration).

Finally, gates are interconnected to form a main frame in the fifth

level of the packaging hierarchy.

As digital systems have evolved, some of these packaging levels

have been eliminated. For instance, personal computers (usually denoted

card on board (COB) systems) do not have a fourth level of packaging.

Use of multichip modules (i.e. chip on board (also COB) systems) also

eliminates the second level in the electronic packaging hierarchy.

Eventually, the board level may be partially replaced as well if wafer

scale integration (WSI) comes to fore.

An electronic package basically provides a fixed structure for

active electronic devices. Said structure is subject to many, varied

constraints. The structure must be mechanically strong in order to

protect the delicate active devices from shock and external forces. The

package must also provide shelter from moisture and corrosive

environments. Furthermore, the thermal expansion of the electronic

packaging material must be similar to that of the active materials that

it packages, so that the packaging does not destroy its active occupants

when changes in overall temperature, or temperature gradients are

experienced.

The electronic package must also provide for one or more means of

dissipating heat generated by the active components. Heat dissipation

may be either passive or active. For either type of cooling, it is best










(although not mandatory) that the electronic packaging have a high

thermal conductivity. A high thermal conductivity is beneficial when it

is desirable to avoid thermal shock of the device. Furthermore, by

utilizing packaging materials having high thermal conductivities, heat

generated via the active devices is spread more quickly and more

homogeneously throughout the package, thereby avoiding detrimental hot

spots.

The packaging must also provide a satisfactory medium for

encapsulating power and signal transmission elements. As a result of

the current emphasis upon device miniaturization, this packaging

requirement has become quite important. Electrically conductive

elements have decreased greatly in height, width and pitch now that high

conductivity metals are being utilized, resulting in the need for

packaging materials having exceptional surface smoothness, interlayer

planarity [90REC] and either minimal or predictable shrinkage and

warpage during processing. In ceramic materials, these goals may be

attained only with proper processing. It is desirable that the starting

ceramic powders be very small in size and that said powders consolidate

to a very high green density. Furthermore, the consolidation must not

result in particle segregation.

The electronic package must also provide a medium that is suitable

for high quality electronic communication, since the electronic devices

housed in the package require "clean," constant power and high quality

signals. With the current emphasis upon increasing signal speed, this

requirement has mandated changes in both materials and design in order

to obtain satisfactory packages. As discussed below, this criterion

presents perhaps the greatest impediment to advancement in the field of

high speed computing.










1.3.3 Properties Desired of Packaging Materials

Table 1.1 summarizes both the requirements and the weight of said

requirements for electronic packages and packaging materials.

Surprisingly, the major barrier to the realization of the next

generation of high performance computing lies in limitations in

packaging materials and not in switching materials [83VEN,87MOH,87SHI,

87YAR]. The unavailability of satisfactory high speed electronic

packaging materials results from the fact that successful candidates

must satisfy several stringent criteria. First and foremost the

candidate must have satisfactory dielectric property requirements. The

dielectric constant and loss tangent must be low (3 to 5 or below, and

<0.005, respectively [86CRO,87KEL,87MOH,88GER3,89LEA]), and stable at

the frequencies used (MHz to tens of GHz [87YAR]). There are several

reasons for the dielectric properties criterion. The time delay (Td) of

signal propagation of an electronic pulse through a circuit element is

given by the relation:



Td c




where K is the material dielectric constant, L is the propagation

distance, and c is the speed of light [84SCH3,84SCH4]. Thus the signal

delay is proportional to the square root of the dielectric constant of

the surrounding packaging material. This effect is illustrated for

various ceramic materials in Figure 1.10.

The characteristic impedance (Z,) of package signal traces must

rest within a narrowly defined field of approximately 40 to 110 0

[89TUM3] (the most preferable value is 50 0 [88BAL]) due to noise,

signal delay and current draw considerations.










Table 1.1

Requirements and Importance of Said Requirements
for Electronic Packages and Packaging Materials [91TUM]


High Performance Applications

Property Importance Importance
Weighting

Dielectric Constant (minimize) Highest 5

Wiring Density (maximize) Highest 5

Metallization Conductivity Highest 5
(minimize)

Coefficient of Thermal Expansion High 4
(match to IC chip material)

Dimensional Control (maximize) High 4

Mechanical Strength (maximize) Medium-Low 2

Low Performance Applications

Property Importance Importance
Weighting

Cost (minimize) Highest 5

Thermal Conductivity (maximize) Highest 5

Coefficient of Thermal Expansion High 4
(match to IC chip material)

Wiring Density (maximize) Medium 3

Mechanical Strength (maximize) Medium-Low 2



















-. U


Key:


Ceramics in Production
Experimental Ceramics


+ Glass-Ceramics


Mullite


Alumina
Aluminum Nitride



te



Alumina + Glass Systems


-' IBM Cordierite/Clinoenstatite


J Cordierite + Glass
- Silica + Borosilicate Glass
Porous Silica


4 R 7 R 9 10


Dielectric Constant


Figure 1.10


Depiction of propagation delay time versus dielectric
constant for various ceramic materials [91TUM]


Mullil








30

Figure 1.11 graphically illustrates the design criteria for selection of

package characteristic impedance.

Furthermore, the minimal thickness of packaging layers between

circuit elements required for impedance matching is lowered when a lower

dielectric constant material is used, due to the following relation:



zo-





where Z0 is the characteristic impedance, L is the inductance associated

with the signal line, and C is the capacitance associated with the

signal line [84SCH3,84SCH4]. By lowering K, C is reduced per unit

thickness, thereby increasing Zo per unit thickness. Thus a thinner

packaging layer may be utilized while maintaining the characteristic

impedance, further enhancing miniaturization. Therefore, use of low K

packaging materials allows for increased digital performance in two

ways, by increasing signal speed and by helping to decrease signal

propagation distance.

The dielectric loss factor must also be low, as illustrated by the

relation:


P=C E'f Vj tan (6)




where P is the power loss due to dielectric loss, f is the signal

frequency, e' is the real portion of the material dielectric

permittivity, V. is the peak signal voltage and 6 is the dielectric loss

angle (e''/E') [76KIN]. From the above relation, it is evident that

power dissipation due to dielectric loss may become rampant at high

frequencies if insulating materials are not chosen carefully.

Utilization of materials having low K and tan(6) values also aids

(along with correct design of ground planes) in lessening problems of





















0.6

0
0.4 -
o


0.2 -
.0
o
Z
0.0
0























Figure 1.11


0.6

Noise Tolerance (volts)
Acceptable Design Area
Total Noise (volts) 0.4 CD
r .. n 0.4



0.2
S I --Total Delay Adder (ns)
S.'---hmpedance Limits
II I' 0.0
20 40 50 60 80 100 120

Board Characteristic Impedance (ohms)





















Depiction of design considerations for choosing a
package characteristic impedance [89TUM3]










crosstalk, signal pulse rounding and other phenomena leading to signal

infidelity [87MOH,87YAR,89SER,89TUM,89TUM3,91TUM].

A second goal in the design of electronic packaging is one of

expense reduction. In order to reduce production expenses, packaging

materials should be developed that are processable at low temperatures.

Lower processing temperatures also allow for use of nonrefractory metals

(such as silver and copper) as conductive elements. This is

advantageous from a performance point of view, since silver and copper

have relatively high electrical conductivities (6.31 x 107 and 5.96 x 107

(Ohm--m)" respectively [85CRC]). Therefore, both resistive heating and

signal loss would be reduced through the implementation of either

conductor material. Thus, cofirability with copper or silver is

advantageous from both cost and performance standpoints. Cofirable

systems must be totally processable at temperatures significantly below

the melting point of the metallic constituents (1083C and 9820C for

copper and silver respectively [85CRC]). Furthermore, cofirable

packaging materials must allow for processing treatments which ensure

the total pyrolysis of organic, as well as the complete sintering of

the metallization, while not adversely affecting the desired properties

of the conductor metallurgy.

The coefficient of thermal expansion (CTE) also should be matched

closely to that of the semiconductor material utilized. This ensures

that the chip bonds will not fail with repeated usage (i.e. when the

power is turned on and off). The induced plastic strain (ep)

experienced by the solder connections during thermal cycling of a chip

and package assembly is quantified by the relation:


A CTEx A TxD
p H


where ACTE is the difference in the coefficient of thermal expansion










between the IC chip and the packaging material, AT is the difference

between the temperature at which there is no stress and the temperature

of interest, D, is the distance from the neutral point of shear stress

on the chip (i.e. the horizontal middle), and H is the height of the

solder pad [84SCH2]. From this relation the number of cycles to failure

(Nf) may be estimated from the Coffin-Manson equation:

1

Ep




where A and m are constants whose values must be empirically determined

for the particular system [89TUM3].

From the above relations, it is evident that reducing the

difference in CTE between the chip and the package will reduce thermal

fatigue. Figure 1.12 illustrates this equation for several materials.

Also, plastic shear strain on the solder connections increases toward

the outside of the IC chip (i.e. as D, increases). Therefore thermal

cycling fatigue increases in magnitude with the use of larger IC chips

(i.e. VLSI). Not as obvious in this discussion is the effect of thermal

conductivity of the materials involved. Low thermal conductivities tend

to increase stresses within the packaging material but tend to decrease

ep by decreasing AT at the chip-solder-package interface. For this and

many other reasons, it is considered most prudent to use cooling methods

which extract heat from the back of the chip rather than through the

substrate.

Thus it is desirable to have a CTE which is adjustable for

different switching materials. Since Si is, by far, the predominant

switching material currently in use, the most utilitarian electronic

packaging materials will have a CTE that is customized to match that of

Si. Furthermore, it is important to match the CTE of Si over all

temperatures that the chip-package assembly will experience.













100000




10000




1000




100




10


- C
w,


Mullite + Silica + Alumina
Aluminum Nitride
Alumina + Borosilicate

Alumina

Epoxy-Kevlar



Polyimide-Glass

Epoxy-Glass



Coffin--Manson Equation


h.b


0 4.0


8.0 12.0 16.0 20.0 24.0


CTE (ppm/ 0C)


Figure 1.12


Illustration of the Coffin-Manson equation for several
materials [91TUM]


a)
U-



--

(D
3_
0)

LL.













Figure 1.13 exhibits the CTE of Si with respect to temperature.

Adjustability of CTE may be provided to varying extent by using ceramic

composite systems as packaging materials.

Furthermore, stress resultant from CTE mismatch is reduced between

packaging and metallization when lower firing temperatures are used (as

in low temperature, cofirable systems) by reducing AT. Differential

stress between metallization and packaging may be further reduced if

packaging materials that densify via a viscous sintering mechanism are

used, since localized stress may be alleviated if an annealing step is

used at temperatures slightly above the glass transition (T,) of the

packaging material. Stress on chip pads may be relieved similarly if

the chip bonding material requires heat treatment above T, of the matrix

glass.

The fourth desirable property of an electronic packaging material

system is that of high surface smoothness. Surface roughness may cause

disabling discontinuities within the package. Acceptable surface flaws

are usually no larger than about one tenth the metallization width

(typically >50 pm, [89SER,89TUM3]). As technological advances allow for

further miniaturization (i.e. substitution of photolithography for

screen printing as the application method for circuit metallizations

[90NEB]) this limit will surely decrease markedly.

Hermeticity is also desirable in a satisfactory packaging system.

If atmospheric moisture enters the package, dielectric properties will

change markedly [89SER,89TUM3,91WAL]. Moisture also contributes to

corrosion (and thus embrittlement, due to stress corrosion cracking),

exfoliation and delamination of both the packaging and the active

electronic elements. Hermeticity of the packaging material may be

achieved in several ways such as hermetic coatings, etc. However, it is

much simpler and more cost effective if the packaging material is

inherently hermetic subsequent to thermal processing.
















0.280
0.260 Alumina
0.240 Tungsten/Copper
0.220 --Kovar
0.200 -
0.180 -
0.160
0.140 -
<3 0.120 .--,Corning 9641
S Silicon -
0.100 -
0.080 -Corning 7070
[88COR]
0.060 [88COR1
0.040 -
0.020-
0 -
0 50 100 150 200 250 300 350 400 450 500

Temperature (C)




























Figure 1.13 Thermal expansion of Si and other selected materials
as a function of temperature [88COR,90GEI,91DIL]








37

This is accomplished in most ceramic and glass materials when sintered

to more than approximately 95% of theoretical density [76KIN].

Adequate mechanical properties and high thermal conductivity are

also desirable in electronic packaging materials. Since mechanical

failure is frequently due to CTE mismatch or improper thermal treatment,

this problem can be avoided by careful design and processing.

Frequently, it is becoming more important that the green package have

greater green strength, in order to avoid damage during processing.

Packaging design evolution also has moved away from using the

electronic package as a supporting or structural member for the

apparatus. Conventional wisdom more frequently dictates that it is

better if the package provides support and protection only for the

elements that it packages. This further reduces mechanical requirements

of the electronic packaging material. However, a minimal mechanical

strength is still desirable. The materials utilized in the IBM TCM

currently have a bending strength of about three quarters of that of

Al203 (i.e. -210 MPa) [91KUM1,91KUM2,91SHE2,91TUM], while other

institutions have decided that lower strengths are permissible

[89EMU,89SAW,90RIC,91ALE,etc.].

Indeed, if ceramic materials are to be continued in use as

dielectric insulating materials in high performance electronic packages,

K will have to decrease, necessitating that composites of ceramic and

either polymer materials or porosity be used in the future. This will

surely decrease the mechanical strength of said materials [91KUM]. In

the future, the consequences of using lower strength packaging materials

will be circumvented through proper package design and processing as

well as careful materials selection.

High thermal conductivity is no longer as important a material

attribute either, since ingenious designs now remove generated heat from

the back of the chip instead of through the substrate [82BLO,83BLO,

89SER,89TUM3,91TUM].










This method is advantageous in several ways. First, since heat removal

through the back of the IC chip is quite amenable to active cooling

technologies, a much greater amount of heat may be dispersed through its

use. Also, removal of heat through the substrate is generally regarded

as an inferior method since it requires that the heat flux traverse the

metallizations and chip bonding materials. This increases thermal

stresses while reducing electrical conductivity. Also, with continued

decreases in conductor scale (i.e. reduction in the size of chip-package

interconnections), thermal conductivity would be further retarded. This

effect can be offset only through the utilization of thermal vias, which

are very costly in terms of IC chip "real estate."

Removal of heat, through the substrate, to a thermal sink rather

than to a cold finger on top of the chip, also results in thermal

resistances which are significantly greater than in the cold finger

method unless ultra high thermal conductivity materials (i.e. diamond,

or cubic BN) are used. The Franz-Weiderman rule [83POB] indicates that

this technique is not useful in high performance packaging applications

where a low dielectric constant is also required (with a few notable

exceptions such as diamond, cubic BN, or BeO, etc.). The Franz-

Weiderman principle states that no material may have both an ultra high

thermal conductivity as well as a low dielectric constant. The

exceptions to this rule are either prohibitively expensive or toxic.

Furthermore, there are no exceptions to the Franz-Weiderman rule when it

is necessary to select materials having a K below 5.5. Since, in high

speed electronic applications, satisfactory dielectric properties are

most important, the material designer must prioritize on the side of low

dielectric constant, low dielectric loss materials.

High thermal conductivity is also important from a thermal shock

point of view since a high thermal conductivity promotes heat spreading

throughout the package, thus reducing thermal fluctuations within the

package. However, as stated in section 1.3.3, use of a high thermal









conductivity material in conjunction with a through-the-substrate

cooling mechanism will actually reduce the solder-package interface

temperature, thereby increasing the thermally induced shear stresses on

the solder pads (relative to use of a lower thermal conductivity

material in the same heat removal configuration).

It should be noted that the development of a successful packaging

candidate (i.e. one which satisfies the above packaging criteria)

requires a two-pronged, holistic approach. Both materials selection and

packaging design are extremely important in achieving the criteria

discussed above. Furthermore, there is no one package that satisfies

all the requirements in all systems. In some cases, mechanical

integrity or hermeticity is the most important characteristic, while in

others, signal processing is tantamount. Therefore, no one design or

material is universally satisfactory to all electronic packaging

applications. Furthermore, pursuing more than one of the above

packaging criteria, requires skillful design as well as use of

engineered (i.e. composite) materials. Therefore, it is of extreme

importance to decide what packaging criteria are most important when

developing packaging materials or designs for a specific application or

family of applications. Table 1.1 can help to serve as a guide in

packaging design and materials selection.

This study attempts to present a viable packaging material system

that satisfies the materials-based (not design-based) factors of the

packaging criteria outlined above. Furthermore, the greatest importance

is placed upon a materials solution which emphasizes signal processing

speed (i.e. low dielectric loss materials), adjustability for varying

application (i.e. composite materials), and cost reduction (i.e. low

materials cost, applicability to traditional processing, and thermal

processability at reduced temperatures (low temperature cofirability))

while exhibiting environmental stability (i.e. hermeticity and at least

a minimum mechanical strength). It is the author's opinion that these










are the most important packaging criteria for the advancement of high

speed electronic computing.



1.4 Materials Solutions to Electronic Packaging Problems

1.4.1 Ceramics versus Polymers

Nearly 85% of all electronic packages currently produced are

polymer based while ceramic packages comprise approximately two thirds

of the monetary value of the electronic packaging market [89TUM3]. So-

called plastic packaging systems are based on some type of insulating

polymer encapsulant such as epoxy, polyimide, silicone, or, of late,

thermoplastics [89TUM3]. They offer several advantages over ceramic

systems such as lower cost, lower dielectric constant, and greater ease

and adaptability of manufacture as well as greater relative throughput.

Seemingly these advantages would mandate that all electronic packages be

polymer-based. However, the use of plastic packaging systems has

several disadvantages. Table 1.2 shows the advantages and disadvantages

of ceramic versus plastic electronic packaging materials.

Currently, no plastic package is truly hermetic although materials

are being developed which are less hydrophilic than traditional

polymeric packaging materials (i.e. polyquinolines, teflons, and BCBs)

[90LEE,90REC,91HEN,91HOR,91ZUS]. Therefore, the packaging thickness

must be carefully controlled in order to allow some of the moisture,

present within the package, to be evaporatively removed using IC chip

heating (89TUM3]. If the electronic device is one that consumes very

little power (i.e. dissipates very little heat), such as CMOS

devices,special packaging design considerations are mandated.

Furthermore, plastic packaging materials have a much greater CTE than

the materials which they encapsulate (i.e. Si). Resultant thermal

stresses may damage delicate microcircuitry. This requires

implementation of careful package design and manufacturing principles.










Table 1.2

Advantages and Disadvantages in the Polymeric
versus Ceramic Electronic Packaging Materials Debate


Topic Ceramic Polymeric Advantage

Adaptability to Moderate Moderate Depends
Multilayer Packaging (Usually
Ceramic)

Cost High Low Polymer

Breakdown Voltage High High Depends

Dielectric Constant Moderate Low Polymer

Dielectric Loss Low Low Depends
(Usually
Polymer)

Ease of Process Low High Polymer
Automation

Hermeticity Hermetic Non-Hermetic Ceramic

Inherent a--Radiation Variable Variable Depends
(Usually
Ceramic)

Process Complexity High Low Polymer

Process Temperature High Low Polymer

Process Throughput Moderate High Polymer

Rigidity High Flexible Ceramic

Strength High Flexible Depends
(Usually
Ceramic)

Surface Smoothness Moderate High Depends
(Usually
Polymer)

Tolerance Control and High Low Ceramic
Reproducibility

Thermal Conductivity High Low Ceramic

Thermal Expansion Low (Highly High Ceramic
Variable)

Volume Resistivity High High Depends










Plastic packaging materials are characterized by poor thermal

conductivity as well. Due to the encapsulating nature of most plastic

packaging methods used, this factor, when combined with the unfavorably

large CTE of polymers, can be quite deleterious. However, the moisture

evaporation methods used to compensate for a lack of hermeticity help

counteract this problem somewhat (at least in the lower scales of

integration), since evaporation is highly endothermic.

Ceramic packages offer the advantages of hermeticity, CTEs

comparable to switching materials or metallizations, higher thermal

conductivity, and greater integrity. However, ceramics, as a group,

have higher dielectric constants and higher dielectric losses, and are

more susceptible to stress corrosion cracking [89TUM3]. Furthermore it

is difficult and expensive to produce ceramic substrates having

relatively high surface smoothness.

Also disadvantageous to both plastic and ceramic packaging is

inherent alpha radiation that is emitted from trace impurities within

the polymeric and ceramic raw materials. Inherent a--radiation has been

found to cause spurious semiconductor device switching which results in

soft errors. For example, concentrations of approximately 1.0 ppm U2

or 0.4 ppm Th32 within a plastic or ceramic package would emit a flux of

alpha radiation on the order of 0.1 a/cm2/h. That level of radiation is

one to two orders of magnitude above the acceptable limit established

for memory devices [89TUM3].

This radiation problem is currently remedied by adding anti-

radiation coatings, as well as through improved raw material processing

and careful packaging design. However, these corrections add a great

deal to the packaging cost, (which is the main advantage of using

plastic packages). Furthermore, as the scale and pitch of integration

increase and decrease respectively, a--radiation switching is expected

to become more problematic. Ceramic packaging materials tend to exhibit

this problem to a lesser extent than polymeric materials [89TUM3].







43

However, radiation is a bonafide problem in both, thereby mandating that

electronic packaging materials be very highly refined (at least on the

first packaging level).

Thus, ceramics are used for high performance applications that are

not as cost sensitive as typical consumer electronics while plastic

packages are utilized for lower cost electronics. The disadvantages of

ceramic-based packaging, in the area of dielectric properties, are

currently circumvented through package design (i.e. by using 3--

dimensional, multilayer packages, etc.). For the highest electronic

performance applications, however, plastic-on-ceramic hybrids are

currently used [91KUM1,91KUM2,91SHE2,91TUM]. Porous ceramics and

ceramic-plastic composites are also being developed for use in the

highest performance applications as well [86CRO,86DAS,87KEL,87MOH,

88GER3,88IBR,89JUN,89LEA,89YAM2,90KAT,90STE,91SAC1,91ZUS, etc.].



1.4.2 Methods and Materials

1.4.2.1 Traditional

The history of ceramic electronic packaging is covered in section

1.3.1 above. From the above, it is evident that the evolution of this

field has been mainly design (and not materials) oriented. Most ceramic

electronic packages and packaging systems were established using

alumina-based substrate materials.

However, materials selection has become increasingly important

with the advancement of the field. Materials performance limitations

are currently thought to be the limiting factor to advancement of the

field.

It is of value here to elaborate upon the electronic packaging

system that is described in section 1.3.1 above and is generally

perceived to be the state-of-the-art in ceramic electronic packaging.

This system is IBM's thermal conduction module (TCM). The TCM

originally was an alumina-based multilayer package for the IBM 3081










computer system. The original package provided power, cooling and

signal integration to more than 100 ICs. The original TCM was a

"vertical" design, having 33 ceramic layers interconnected by vias. Due

to the relatively high processing temperatures of the original TCM, the

conductor metallurgy was based upon "refractory" metal (i.e. tungsten or

molybdenum based).

The TCM introduced a very advanced cooling system based upon

water-chilled cold fingers, enclosed within a helium-filled chamber,

that connected directly to the back of the thermal conductive-paste-

covered Si chips. This design made excellent use of C4 or flip chip

technology.

The IBM TCM has evolved over its 10+ year life span. The current

TCM (produced for use in the IBM system 390/9000), is glass-ceramic-

based and has copper metallization. It has 63 dielectric layers and

exhibits vastly improved performance. Table 1.3 delineates the

differences between one of the alumina-based TCMs (used in the IBM

system 3090, ca. 1986) and the latest generation of its evolution.

The process for producing the TCM is outlined in Figure 1.9 above.

The basic process has not changed except that the thermal processing

treatment now includes a crystallization step.

The thermal conduction module is not the only advanced ceramic

electronic packaging system in use today. Some other systems are the

liquid-cooled-module (LCM) of NEC, Fujitsu's double-sided board (DSB)

system, and Hitachi's card on board (COB) system. These systems, and

others, are elaborated upon in various literature sources [89SER,89TUM3,

etc]. These systems all would benefit (or have benefitted) through the

use of low dielectric loss, cofirable ceramic packaging materials.



1.4.2.2 Advanced

The subject of advanced electronic packaging is very large and

there are several excellent publications which cover the subject










Table 1.3

The IBM Thermal Conduction Module
Then and Now [91TUM]


Substrate IBM System 3090 IBM System 390/ES9000
Characteristic Alumina/Molybdenum Glass-Ceramic/Copper
(ca. 1986) (ca. 1991)

Size (mm) 110.5 x 117.7 127.5 x 127.5
Number of Layers 45 63

Number of Vias 4.7 x 105 2 x 106
(Total)
Wiring Density 450 844
(cm/cm3)
Line Width (pm) 100 75

Via Diameter (pm) 125 90 and 100

Dielectric Constant 9.4 5.0

Resistivity (pn-cm) 11 3.5

CTE (RT to 200C) 60 30
(ppm)
Shrinkage Control +0.15 +0.1
(%)










[89SER,89TUM3]. Table 1.4 is a comprehensive condensation of recent

research performed in the field of advanced ceramic electronic

packaging. Data on polymers and metals are also included. Because of

the considerable length of Table 1.4, it is placed at the end of Chapter

One.

The subject of advanced ceramic packaging may be divided into

three general processing categories: thin film, thick film and tape

cast processing. Thin films (in this context) may be produced by

several means including thermal evaporation, and sputter deposition,

etc. Thick films (in this context) are deposited by screen printing and

may be used for both insulation and metallization. Tape casting is

currently the most used method for producing high performance electronic

packaging. Thin film technology offers the advantages of producing

comparatively smaller size structures (thinner layers and narrower

lines) and thus will become most important in the future. Thin films

characteristically have a smoother surface structure than thick films,

thereby allowing advanced metallization techniques (i.e.

photolithography, e-beam lithography, etc.) to be used. Currently the

minimum line width feasible using thin film and optical lithography is

approximately 0.5 pm [91CAL].

Thick film materials typically do not display the surface

smoothness required for lithography processes and thus minimum line

widths are currently limited to approximately 25 to 50 pm [90STE].

However, with the use of smaller particle sizes and improved processing

technology, ceramic photolithography has also become the subject of

investigation [90NEB]. The thickness (or thinness) of thick film layers

is similarly limited. In the future, both types of packages will

involve multilayered structures almost exclusively.

Furthermore, as mentioned in section 1.4.1 above, polymer-on-ceramic

hybrid multilayer structures (similar to those used in the most current

IBM TCM) will become very popular.










Metal coated ceramic substrate materials also fit into the

category of advanced electronic packaging due to their novelty,

toughness, tailorable thermal expansion, high thermal conductivity and

low dielectric constant, as a group [81HAN,86SAT,86TEA,870KA,87SHU].

However, multilayer structures have not yet been produced by this method

and, therefore, they are limited to special applications. Generally,

ceramic coatings are deposited over metal bases by either

electrophoretic or thick film deposition techniques. These composites

will see limited future use in such applications as automotive

electronics as well as other high temperature, high stress, corrosive

environment applications.

From a materials point of view, advanced electronic packaging

materials fall into one of two categories: polymer or ceramic. It

should be noted that, in this discussion, polymer materials, are carbon-

based, organic materials and not ceramic, sol-gel processed materials.

The advantages and disadvantages of both types of materials are defined

in section 1.4.1.1 above. Generally, polymers are utilized in advanced

thin or thick film multilayer structures while ceramics are used to

produce advanced thick film or tape cast multilayer packages.

Current polymer materials research for electronic packaging

applications is centered mainly in two areas: developing low moisture

absorbing polymers, and developing polymeric or polymeric-ceramic

materials having thermal expansions matching either Si or GaAs. Thus

far, teflons, polyquinolines, and bisbenzocyclobutenes (BCBs) have shown

promise as reduced water absorption materials [90REC,91HEN,91ZUS] while

composites of epoxy/Kevlar, epoxy/Nextel, polyimide/Kevlar, and

polyimide/glass have shown promise as matched thermal expansion

materials [88IBR,91ZUS].

Recently, research in the area of advanced ceramic electronic

packaging materials has investigated several, varied topics. Low

temperature cofirability (allowing the use of low p (resistivity)










metallization) has been a universal trend in almost all of this

research. Advanced ceramic electronic packaging materials research may

be further divided into the categories of diamond films [91LYN],

glass+ceramics, glass-ceramics, and porous ceramics. Table 1.4, placed

at the end of this chapter, provides a condensation of materials and

processing information for all of these areas, as well as a bibliography

for the convenience of the reader. Diamond thin films have not yet been

successfully implemented for use in high speed microelectronic

packaging, due mainly to the infancy of the field.

Glass+ceramic and glass-ceramic materials are currently the

mainstay of the high performance electronic packaging field. However,

no ceramic material that is a viable future high speed electronic

packaging candidate has a dielectric constant below 3.78 [76KIN]. It

has been stated that electronic materials used in future high

performance packaging applications will necessarily have dielectric

constants below this value [86CRO,87MOH,87YAR,88GIL etc.]. Therefore,

the only way to achieve dielectric constant values below 3.78 while

using ceramic materials, is to fabricate composites of ceramic materials

with non-ceramic, electronically insulating materials, that have lower

dielectric constants (i.e. polymers, or air). The decisive majority of

this research has been in the area of porous ceramics.

Cofirable, porous ceramic materials may be produced from glass,

glass+ceramics or glass-ceramics and are, thus, considered a subset of

each group. Porous ceramics may be produced in several ways. Porous

ceramic thin films may be produced by partial densification of SiO2 sol-

gel films [86CRO,87MOH,88MOH], thermal oxidation of sputtered columnar

Si (86DAS], and reactive sputtering of Si02 [86DAS], as well as by

suspension of latex in silica sol [87MOH]. These methods have not yet

been implemented in electronic packaging, however, due to poor film

hermeticity as well as inadequate mechanical properties and surface

smoothnesses, etc.










Porous thick films have been produced by addition of hollow silica

glass microspheres (HGMS) [87KEL,89LEA,89JUN,90KEL], partial sintering

of glass frit pastes [90WAH], and controlled gas generation within fully

dense glass thick films [90STE,90WAH]. These methods have found greater

success. However, problems with surface smoothness necessitate extra

thick film applications with sealing pastes. Furthermore, the

repetition inherent in thick film processing limits the applicability of

the thick film process in general, since only one layer may be produced

at one time. Finally, the controlled gas generation method involves a

large volume expansion, and thus, dimensional stability becomes a

problem in multilayer structures containing porosity produced via

controlled gas generation. However, this method has been utilized to

produce metallization lines as narrow as 25 to 50 pm in a single layer

configuration [90STE].

It is not sufficient simply to add porosity to the insulating

material. In order to maintain a hermetic structure, porosity must be

non-continuous. Furthermore, the porosity must be small in order to

maintain surface smoothness as well as mechanical properties. While

surface roughness improves interlayer and metallization adhesion, it is

detrimental when the scale of said roughness is within approximately one

tenth of the smallest signal line dimension. Roughness on this scale

not only increases the possibility of electrical discontinuity of signal

traces, but promotes inhomogeneity of the signal trace cross section.

This is highly detrimental at high frequencies since it causes

inhomogeneities in the characteristic impedance (Zo). Furthermore,

variances in cross section force high frequency electronic signals

through a relatively tortuous path. This not only increases signal

propagation distance, but increases spurious signal reflection [89TYL).

Finally, it is best if included porosity be limited to as small a volume

fraction as possible in order to preserve dielectric breakdown strength,










volume resistivity, surface smoothness, sinterability, mechanical

properties and thermal conductivity, etc.

Currently, tape casting is the only feasible method by which

porous ceramic materials have been produced for electronic packaging.

Porosity has been introduced into tape cast ceramics via hollow silica

glass microspheres (HGMs) [88LEA1] as well as through the controlled

burnout and subsequent differential sintering of organic latex

microspheres (89YAM2,90KAT].

The HGM method allows for a greater amount of included porosity to

be added to the packaging material than the latex method, since the

added porosity, resultant from HGM additions, is non-continuous.

Therefore, the HGM method is better in theory and is the only currently

viable method for producing tape cast packaging materials having greater

than -13V% non-continuous porosity. However, the only successfully

produced and tested ultra low dielectric permittivity, multilayer

electronic packages produced, to date, have utilized the latex method

[89YAM2,90KAT]. There are several reasons for this. First, HGMs are

comparatively quite large (-80 Mm) and thus promote surface roughness.

Also, HGMs have very low density (-0.25 g/cm3 [89LEA]) and thus tend to

segregate during suspension processing. Third, HGMs tend to break down

during processing (such as pressing, laminating, sonic dismembrating,

etc.). Finally, as HGMs become smaller, it will become necessary to add

them to the ceramic matrix in larger amounts (compared to latex) due to

the wall thickness of HGMs. For example, pores resulting from the

burnout of latex and subsequent sintering of the surrounding matrix tend

to comprise a volume similar to the volume of the latex spheres which

formed them. With HGMs, however, the amount of SiO2 added to the

ceramic matrix per microsphere addition may, in fact, be similar to, or

greater than the amount of porosity added. An HGM having a diameter of

5 pm and a wall thickness of 0.5 pm is only 51% porous itself. Said HGM

would have a K of -2.4 (as compared to -1 for air). In this scenario,










the HGM method would be much less efficient for reduction of K than the

latex method. Since it is desirable to add a minimum of either HGM

(mainly for sinterability and mechanical integrity reasons) or latex

(mainly for hermeticity and mechanical integrity reasons), the latex

method is preferable in this sense.

Hermetic ceramic materials having dielectric constants as low as

3.4 have been produced, via tape casting, and utilized in multilayer

packages in the laboratory (89YAM2,90KAT]. Commercial introduction of

such a product has not yet occurred, however.

Therefore, it is imperative that further research be performed in

the area of controlled porosity ceramics for utilization in ultra high

speed electronic packaging. Many materials and processing related

questions remain in this field. Research in this area should focus upon

methods to minimize (and the theories involving minimization of)

dielectric constant and dielectric loss while maintaining a hermetic

material of dimensional and mechanical adequacy.



1.5 Proposed Packaging Material System: Statement of Thesis

1.5.1 Choice of Electronic Packaging Material System

The choice of the electronic packaging material system to

investigate was based upon creating a relatively low cost, hermetic,

ceramic packaging material for use in very high speed electronic

packaging applications. From the above criteria, it becomes apparent

that no one material is satisfactory for this application. Therefore,

it was decided to chose a composite system having carefully selected

constituents. This methodology is useful in that the composite may be

optimized for different applications. Properties of the materials

utilized are outlined in Table 1.4 at the end of this chapter.

Cofireability is obtained by using a borosilicate glass as the composite

matrix. Surface smoothness is also enhanced when a viscous sintering

matrix is used. Low dielectric constant and tan(6) are achieved by










utilization of materials having low K and tan(6) values as well as

through the addition of controlled porosity. Furthermore, all materials

utilized have dielectric properties which are stable over a broad range

of frequencies.

In this study, controlled porosity is achieved via the addition,

and subsequent pyrolysis, of uniform polystyrene latex microspheres

(UPLMs). The UPLMs are producible in a size range between 3 and 9 pm

and are quite monodisperse, thereby allowing a study of the effects of

UPLM size and dispersity upon the hermeticity of the sintered material.

The composite system of focus should also be easily adaptable to

standard ceramic tape casting processes. Since the maximum diameter of

the latex is less than 10 pm, the surface smoothness criterion should

also be satisfied for most current thick film signal line widths (if

proper dispersion and homogenization are achieved).

There are some problems associated with adding porosity to a

brittle material. Porosity in a ceramic material has been shown to

reduce the mechanical strength of said material [76KIN]. Furthermore,

it is possible to create a non-hermetic material from a formerly

hermetic one. Therefore, processing must be optimized to provide

hermetic materials having acceptable mechanical properties.

In order to increase the mechanical integrity of the composite

system, a hard particulate ceramic is added. Since mechanical strength

and toughness must be increased with minimal increase in dielectric

properties, the choices for ceramic filler are limited to strong

particulate ceramic materials having low K and tan(6) (such as diamond,

cubic BN or Si3N4). In order to reduce material costs, particulate Si3N4

was used. Silicon nitride represents the best compromise between

desired properties and expense, thereby making this packaging system

practical for most electronic packaging applications. Also, since the

Si3N4 was used as a nonreactive addition, all information related to

sintering and processed microstructure, gained from this study, should







53

be generally applicable to similar composites with other, similar, inert

additions.

1.5.2 Topics of Investigation

This study investigates several factors crucial to the development

of the proposed borosilicate glass-particulate Si3N4-controlled porosity

composite system. This section outlines the topics of research

investigated in this study.

The following constituent variables are investigated:

the effects of ball milling on the properties of the
borosilicate glass powder

the effects of borosilicate glass size and size distribution
upon sintering behavior of said glass

the effects of UPLM volume fraction, size and size
distribution upon both green and selected sintered materials
properties (see below)

the effects of Si3N4 volume fraction and/or included porosity
volume fraction upon sintering behavior, and selected
sintered materials properties (see below).

The following processing factors are investigated:

the effects of suspension sonication and aging upon green
and non-sintered properties

the effects of pyrolysis/presintering upon borosilicate
glass surface area and surface pore size distribution

the effect of heat treating Si3N4 powder in air, at or above
composite sintering temperatures, upon the properties of
said Si3N4

the effect of sintering temperature upon sintering rate.

The following materials parameters are investigated:

the effect of porosity and Si3N4 volume fraction upon the
dielectric constant of the composite

the effect of frequency upon dielectric properties

the effect of atmospheric exposure upon hermetic and non-
hermetic materials

the effect of porosity and Si3N4 volume fraction upon the
hardness of the composites.









Models of composite materials properties, as well as models

concerning the effect of pore percolation upon hermeticity, the effect

of non-sintering particulate and/or included porosity volume fraction

upon sintering behavior and the effect of porosity upon assorted

mechanical properties (as described in Chapters Two and Four), are

utilized to characterize the composite system. A discussion of the

universal applicability of said experimental results to other analogous

systems is included as well.

The main emphasis of this study, however, is to investigate and

model the phenomena involved in the creation and maximization of closed

porosity, produced using the methods described within, in order to

reduce the dielectric constant of the composite and while providing a

candidate material for MLC applications.










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57

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CHAPTER TWO
THEORETICAL AND TECHNICAL REVIEW


2.1 Overview

This chapter outlines selected theoretical and technical issues

important to this project. The microstructure desired in the porous,

glass+ceramic composite system is illustrated in Figure 2.1. Figure 2.2

outlines the process by which said composites are produced. Figure 2.2

also delineates the important factors involved in each processing step.

The topics that are discussed in this chapter are depicted in bold faced

italic print. The other topics mentioned in Figure 2.2 are not

discussed since it is assumed that the reader has sufficient knowledge

in said areas. Further information may be obtained from the references

accompanying said topics if needed.



2.2 Synthesis and Processing of Uniform Polystyrene Latex
Microspheres (UPLMs)

Spherical particles are currently utilized in several applications

such as printer inks, and time-released drugs, etc. Hollow spherical

particles, as well as organic spherical powders, are also used as

composite components in applications requiring low density, rigid

materials. There are several review articles in the literature on the

subjects of solid spherical fillers [78RYA1] and hollow spherical

fillers [78RYA2,86SMI] as well as composites containing them [85VER].

Due to the reasons outlined in Chapter 1, only uniform polymeric

microspheres were deemed suitable for this project. Furthermore, other

research [89YAM2,90KAT] has revealed that the best uniform polymeric

microspheres for this application are those made of polystyrene.







Microstructure


Figure 2.1


Depiction of the glass+ceramic, controlled porosity
microstructure desired


Key:

SB-S Glass Particle


SLatex UPLM

I 0 Si3N, Particles


Green Microstructure dispersantt omitted)


C. B-S Glass/Si ,N,


A. Pure B-S Glass


D. B-S Glass/Si ,N,/Latex UPLM


B. B-S Glass/Latex UPLM










A. Constituent Powders

1. Glass 2. UPLM 3. Silicon Niti

t 0







D- B. Ball Mill C. Settle and
Batch


D. Suspension Processing
and Casting







E. Green Characterization



-n^-

F. Thermal Processing







G. Characterization


Topics of Research:
A. General:
Density, Size, Size Distribution,
Surface Area, Structure [76KIN,88FUN,
88REE,89DIN,90RIN,90WAR,92SHE]
Al:
Chemistry [88REE]
A2:
Synthesis and Processing
B:
Surface Area, Structure, Chemistry,
Density [76KIN,88REE,91SEA]
C:
Particle Packing


Dispersion Systems,Rheology,
Solids Loading [76KIN,81SCH,88FUN,
88REE,90GOO,90RUY,91HOF,91KUR,
91RUS]

Settling, Segregation
Structural [56FATi,56FAT2,56FAT3,
76KIN,88REE,91 MIK,91 SEA,91TSA]


Fl. Pyrolysis:
Thermogravimetric Analysis,
Differential Thermal Analysis
Pore Structure, Surface Area [76KIN,
88REE,89SER,89TUM3,91TUM]

Pore Percolation, Pore Clustering,
Pore Packing

F2. Viscous Sintering
Sintering Rates, Differential Sintering
Microstructural Evolution
F3. Oxidation
Oxidation of Si3N, Powder [89SOM]
G:
Microstructural [53FUL,68DEH,88REE]
Mechanical
Dielectric


Figure 2.2


Process flow diagram for production of controlled
porosity composites, and delineation of important
factors for each processing step; topics depicted in
boldface italic are discussed in this chapter







78

There are several methods for synthesizing uniform particles. The

literature contains several review articles on the subject

[68STO,80UGE,820VE]. More specifically, there are several methods by

which uniform polystyrene latex microspheres (UPLMs) may be produced

[85LOK,86TSE,88LU,89FER]. More information about the properties and

applications of uniform latex particles is contained within references

87BAN2 and 88MIC as well.

As will be shown in Chapter 4, preliminary research for this

project [90RAN] indicated that the UPLM particles should be

approximately 4 pm (minimally 2 pm) in diameter in order to avoid

producing obscured porosity. Furthermore, it was decided that the

maximum UPLM diameter, used for included porosity, should be less than

10 pm in order to maintain surface smoothness requirements. Therefore,

it was necessary to either find or invent a reliable and reproducible

method for the synthesis of UPLMs in the size range between 2 and 10 pm.

Fortunately, researchers have found synthesis methods which satisfy the

above criteria (85LOK,86TSE,88LU]. Said synthesis techniques involve

the dispersion polymerization of styrene in EtOH-based solvents.

Dispersion polymerization is the only currently known method which may

be used to produce UPLMs in the size range of interest via a single set

of processing steps [85LOK]. Table 2.1 depicts the differences between

dispersion, emulsion and suspension polymerization methods.

The synthesis methods of Lu et al. and Tseng et al. [86TSE,88LU]

involve dispersion polymerization via an addition polymerization

mechanism in various mixtures of pure EtOH and stabilizer and/or

costabilizer while the method of Lok and Ober [85LOK] involves

dispersion polymerization of UPLMs via an addition polymerization

mechanism in solvent solutions of ethanol and methyl cellosolve mixed

with hydroxypropylcellulose (100,000 mw) as a dispersant.

Preliminary research, investigating both of the aforementioned

dispersion polymerization methods for synthesis of UPLMS, resulted in










Table 2.1

Comparison of the Different Types
of Particle Polymerization [85LOK]


Emulsion Dispersion Suspension

Monomer Droplets Particles Droplets
Micelles/Particles Mostly in Little in Medium
Little in Medium Medium

Initiator Mostly in Medium Particles and Particle/Droplet
Medium

Stabilizer May Be Present Necessary Necessary

Surfactant Present None None

Initial Multiple Phase Single Phase Dual Phase
Homogeneity










the conclusion that the method of Lok and Ober [85LOK] was far superior

for production of UPLMs in the desired size range on the bases of

monodispersity, amount of agglomeration and reproducibility of UPLM size

and dispersity from batch to batch. Therefore, the method of Lok and

Ober was utilized to produce UPLMs of various size for the current

study. The synthesis method of Lok and Ober is described in further

detail in Chapter 3 as well as in 85LOK.

Figure 2.3 illustrates the dispersion polymerization process.

Basically, dispersion polymerization is an addition polymerization which

includes nucleation and growth steps. The dispersity of the process

depends upon the monomer and initiator concentrations as well as on the

dispersive abilities of the dispersant, which is necessarily a graft

copolymer. Dispersion polymerization involves the nucleation and growth

of polymeric spheres from a single phase solvent via addition reaction.

As with other nucleation and growth processes, the size of each polymer

nucleus must surpass a critical radius before said nucleus becomes

stable. The critical nucleus size depends heavily upon the total system

solubility index (including that of the monomer itself) [85LOK].

Furthermore, growth processes apparently occur without further

nucleation (85LOK].

The major difference between dispersion polymerization and other

polymerization methods is that dispersion polymerization starts as

single phase homogeneous system. With dispersion polymerization it is

necessary that the monomer be soluble in the solvent while the polymer

not be soluble in the solvent. Particle size control with the

dispersion polymerization method is dependent mainly upon four factors,

monomer versus polymer solubility, reactant composition, temperature,

and solvent medium [85LOK].

Said process offers the advantage that it does not require

oligomer swelling, etc., in order to obtain the relatively large

particles and, therefore, is denoted a single step process.


































































Figure 2.3


I-; ; 81


INITIATION

AT
Stabilizer


Initiator



I r HYDROGEN
ABSTRACTION


I I

2 ,



GRAFT
S 'I FORMATION

f -Monomer


3 /



I -
NUCLEATION

Monomer
I



\ Monomer
5 '











Schematic illustration depicting nucleation and growth
of a UPLM via dispersion polymerization LOK
4 !




SGROWH I


I -'






Schematic illustration depicting nucreation and growth
of a UPLM via dispersion polymerization [85LOK,










The method of Lok and Ober offers a further advantage in that the

dispersion mechanism used is steric in nature (ie. non-electrostatic)

and, thereby reduces ionic impurities in the resultant UPLMs. Ionic

impurities are deleterious because they could leave ionic residues

subsequent to pyrolysis. These residual ions would increase K as well

as decrease both p and the dielectric breakdown strength.

Lok and Ober were able to produce exceptionally monodisperse

polystyrene latex particles of sizes ranging from 3 to 9 pm by varying

the solution solubility parameter (6) from 11.5 to 11.9 [85LOK]. The

solubility parameter is resultant from an accumulation of dispersion

forces (6,), polar forces (6p), and hydrogen bonding forces (6,)

according to the relation:

82=68+2+6+2




Table 2.2 lists the solubility parameter as well as other pertinent data

of selected dispersant liquids that Lok and Ober used for dispersion

polymerization. Figure 2.4 depicts a ternary composition diagram,

between EtOH, styrene and MeCell (methyl cellosolve), which outlines

the compositions at which their latexes were monodisperse as well as the

sizes of the respective UPLMs.

It is evident, from the above and from Figure 2.4, that the

dispersion polymerization method of Lok and Ober [85LOK] fulfills the

criteria necessary for the UPLMs used in this project. Furthermore,

through judicious mixing of the UPLMs (as described in the next

section), a polydisperse latex could be produced for maximum packing

efficiency (PE), thereby allowing an investigation of the effect of

included pore size distribution, or possibly pore packing, upon included


porosity.













Solubility Parameters of


.e 2.2

Selected Solvents [85LOK]


Solvent Dielectric Dipole 6 6, 6, 6H
Constant Moment (cal/cm3)'l
(K) (D)

Dimethoxy- 8.6
ethane

Tetrahy- 7.32 1.63 9.1 8.2 2.8 3.9
drofuran

Styrene 9.3 9.1 0.5 2.0

Cellosolve 2.08 10.5 7.8 4.5 7.0

t-Butanol 10.9 1.66 10.6

Me Cell 16 2.2 11.4 7.9 4.5 8.0

Isopro- 18.3 1.66 11.5
panol

Ethanol 24.3 1.69 12.7 7.7 4.3 9.5

Methanol 32.6 1.70 14.5 7.4 6.0 10.9

Water 78.5 1.84 23.4 6.0 15.3 16.7

Poly- 2.5 8.9
styrene










Key:
0 Monodisperse


Me Cell


Concentrations (V%)


Sample Styrene EtOH Me Cell Size (pm) 6, (cal/cm)"2


51
71
60
42.5
30
14
40
44
74
67


39
14
25
42.5
55
71
40
30
0
0


Figure 2.4


Ternary illustration depicting the relative dispersity
of UPLMs synthesized via dispersion polymerization in
the EtOH-MeCell-styrene system (85LOK]


Particle


Solubility
Parameter


1-3
1-4
3
7
9
1-50
5-20
5-20
1-5
7-9


11.9
12.1
11.9
11.7
11.5
11.3
11.6
11.5
11.9
11.7











2.3 Particle Packing

2.3.1 Monosized Spheres

2.3.1.1 Ordered Packing

Ordered packing of hard, uniform spheres may occur in five

different configurations: cubic, orthorhombic, tetragonal, pyramidal,

and tetrahedral [88REE]. Figure 2.5 illustrates the various

configurations and properties of said ordered packing configurations.

Table 2.3 depicts some of the characteristics of two types of ordered

packing structures: cubic and tetrahedral.

However, hard spheres do not naturally pack in the long range,

ordered structures characteristic of crystalline materials. Several

researchers have tried to explain the random packing of monosized

spheres in terms of mixtures of the above ordered structures

[29SMI,61MCG,80PAT], but while three-dimensional, packed beds of

monosized spheres may exhibit short range order, or even order

throughout a dimension, (depending upon the packing method, or the

packing container configuration used, etc.) they are essentially

considered to pack in random order over the long range

[60BER,62EPS,65LEV].



2.3.1.2 Random Packing

There are two types of random packing for non-interacting, hard

spheres, random close packing (RCP) and random loose packing (RLP).

Random packing (RP) is defined as packing that has no characteristic

ordering. These two types of random packing are considered to be the

upper and lower limits to the packing efficiency of randomly packed

monosized spheres, and are quite sensitive to both the size and

configuration of the bed container as well as the methods used to place

the spheres, in said container, in their final state. The generally

accepted packing efficiencies for these two types of packing are 64V%

and 60V% for RCP and RLP respectively [60SCO,61MCG].





















2. Orthorhombic
(Single Staggered)


3. Tetragonal
(Double Staggered)


5. Tetrahedral
(Hexagonal Close Packing)


Figure 2.5


4. Pyramidal
(Cubic Close Packing)


Illustration of the five possible types of ordered
packing of monosized hard spheres [80PAT,88REE]


1. Cubic


Packing
I Packing Configuration CN Densit (V%)

1 Cubic 6 52.4

2 Orthorhombic 8 60.5
(Single Staggered)
3 Tetragonal 10 69.8
(Double Staggered)
4 Pyramidal (Cubic 12 74.0
Close Packing) 12
Tetrahedral (Hex-
Sagonal Close Packing) 12 74.0












Table 2.3


Some Parameters of Simple Cubic and Tetrahedral
Uniform Spheres [88REE]


Packings of


Parameter Cubic Tetrahedral

Entry Pore Area 0.21D2 0.04D2

0.26 0.05
En try-Pore-Area
7ED2
4



0.51 0.22
En try-Pore-Diameter
D



0.42 0.15
En try-Sphere-Diame ter 0.42 0.15
D



Void Fraction 0.48 0.26

0.92 0.34
Vol ume- Voids
Vol ume-Spheres



1.37 4.44
DP imary-Sphere
DIntersti tial -Sphere-Si te



D = Sphere Diameter










The upper limit of random packing (RCP) is never reached in reality, due

to packing friction and interaction with the container. The effect of

the container interaction may be significantly reduced by using a

container having a width dimension that is relatively large compared to

the sphere diameter (usually several hundred times larger) as well as

through utilization of containers having walls which are either modified

with indentations, or that have the ability to conform (i.e. balloons,

etc.) [30WES,60SCO,61MCG,69SCO]. Figure 2.6 illustrates the effect of

the relative container size on the packing density of RCP beds of

monosized spheres. The lower limit to random packing of uniform spheres

(RLP) designates the limit below which packed beds cannot support

themselves without either cohesion or adhesion [60SCO,80SHA].

In practice, all randomly packed uniform spherical particles will

exhibit packing efficiencies (PEs) somewhere between the RCP and RLP

limitations. Most research indicates RP packing efficiencies of

approximately 61 to 63 V% for beds formed by tamping [30WES,60SCO,61MCG,

88REE] and approximately 57 to 59 V% for beds formed by careful pouring

[60SCO,62EPS]. This will occur, in packed beds of monosized spheres,

regardless of sphere size, unless surface area to volume ratio sensitive

factors, such as electrostatic repulsion, etc. become significant (i.e.

as in many micron to sub micron particles). In most instances involving

packed beds of uniform spheres, the packing is RCP and the generally

accepted packing efficiency is 62.5 V% [61MCG,88REE].



2.3.2 Packing of Multimodal, Discrete Distributions of Spheres

Furnas is generally believed to have introduced the first packing

model (the Furnas model) which predicts the random close packing of

multimodal beds of spheres [28FUR,31FUR]. Westman and Hugill also

introduced an analogous packing model at about the same time [30WES],

and it is believed that the actual mathematical treatment of Westman and

Hugill actually proceeded that of Furnas by about one year [79FED].
































1 5 10 50 100

D/d ( Container Diameter )
Sphere Diameter )


Figure 2.6


Effect of relative container size upon the packing
efficiency of random close packed uniform spheres
[61MCG]


70


65



60



55



50


0
C
0
c
o(


w
r-
LU

C


0-


45


200




Full Text

PROCESSING, CHARACTERIZATION AND MODELLING OF
BOROSILICATE GLASS MATRIX-PARTICULATE SILICON NITRIDE COMPOSITES,
CONTAINING CONTROLLED ADDITIONS OF POROSITY, FOR USE IN
HIGH SPEED ELECTRONIC PACKAGING
By
MICHAEL S. RANDALL
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
1993
UNIVERSITY CF FLORIDA LIBRARIES

Copyright 1993
by
Michael S. Randall

ACKNOWLEDGEMENTS
This work would not have been possible without the skilled help of
many individuals. First and foremost, I would like to thank my wife,
Sara, for her unconditional love, understanding and support. None of
this would have been possible without her. I would also like to thank
my parents (Randalls and Elders) for their support, understanding and
encouragement. I would like to thank my brothers and sisters for their
moral support as well.
On the technical side, I would like to sincerely thank Mr. Gary
Scheiffele for his vast amounts of training and advice in the area of
materials processing. I would like to thank R. Raghunathan and A.
Bagwell for their advice and creative discussions as well. Other
training and advice, in the area of materials processing, by Dr. M.
Amini, Dr. C. Khadilkar, Dr. T.S. Yeh, Dr. S. Vora, Dr. H.W. Lee, Dr. P.
Bendale, and Mr. M. Springate, are also greatly appreciated.
Furthermore, I would like to gratefully acknowledge the advice of Dr.
H.K. Ober, of Cornell University, in the area of dispersion
polymerization.
Complex impedance measurements were made possible through the
equipment and advice of Dr. L.L. Hench, Dr. J.K. West, and Dr. S.
Wallace, at the Advanced Materials Research Center (AMRC). Solution
(ICP) and surface (FTIR) analysis was also most graciously provided by
Dr. L. Hench and Mr. G. LaTorre. Technical advice and support in the
area of electron microscopy (SEM and TEM) from Mr. W. Aeree, Mr. R.
Crockett, Dr. Y.J. Lin and Dr. S. Bates is also acknowledged gratefully.
In addition, I would like to thank Mr. A. Cozzi and Dr. D. Clark for
advice and support in doing thermal oxidation experiments. Processing
equipment and support was provided by Dr. M.D. Sacks.
iii

I would like to sincerely thank my advisor, Dr. J.H. Simmons, for
all of his input and support. I would also like to acknowledge the co-
chairman of my committee, Dr. M.D. Sacks for his advice and support. I
would like to thank the rest of my committee, Dr. P.H. Holloway, Dr.
L.L. Hench, and Dr. D.E. Burke for their assistance as well.
Finally, I would like to thank the Engineering Offices of Gould,
Lewis and Proctor, as well as AVX Corporation for providing me
employment so that I could pursue my degree during difficult financial
times.
iv

TABLE OF CONTENTS
Page
ACKNOWLEDGEMENTS iii
ABSTRACT x
CHAPTER ONE: INTRODUCTION 1
1.1 The Impact of Electronics on Modern
Civilization 1
1.1.1 Economic and Political Aspects 1
1.1.2 The Future of the Electronics Industry:
Impact and Limitations 2
1.1.2.1 The Fourth Generation 2
1.2 Fundamental Microelectronic Packaging
Limitations 5
1.2.1 Electron Light Speed Limit 9
1.2.2 Conductor Spacing Limit 9
1.2.3 Cooling Limitations 13
1.3 Electronic Packaging: Overview of the Field 18
1.3.1 History 18
1.3.2 Importance of the Electronic Package ... 24
1.3.2.1 Economic 24
1.3.2.2 Functional 24
1.3.3 Properties Desired of Packaging
Materials 27
1.4 Materials Solutions to Electronic Packaging
Problems 40
1.4.1 Ceramics versus Polymers 40
1.4.2 Methods and Materials 43
1.4.2.1 Traditional 43
1.4.2.2 Advanced 44
1.5 Proposed Packaging Material System:
Statement of Thesis 51
1.5.1 Choice of Electronic Packaging Material
System 51
1.5.2 Topics of Investigation 53
V

Page
CHAPTER TWO: THEORETICAL AND TECHNICAL REVIEW 75
2.1 Overview 75
2.2 Synthesis and Processing of Uniform Polystyrene
Latex Microspheres (UPLMs) 75
2.3 Particle Packing 85
2.3.1 Monosized Spheres 85
2.3.1.1 Ordered Packing 85
2.3.1.2 Random Packing 85
2.3.2 Packing of Multimodal, Discrete
Distributions of Spheres 88
2.3.3 Continuous Size Distribution Particles . 105
2.3.3.1 Ideal Packing 105
2.3.3.2 Hindered Packing 110
2.3.4 Effects of Settling and Segregation .... 110
2.4 Clustering and Percolation Theory 112
2.4.1 Clustering 115
2.4.2 Percolation 116
2.4.3 Application of Percolation to
Microstructure 123
2.5 Sintering 134
2.5.1 General 134
2.5.2 Viscous Sintering 140
2.5.2.1 Viscous Sintering of
Real Systems 149
2.5.2.1.1 Effects of
Microstructure 149
2.5.2.1.2 Viscous Sintering of
Glass Matrix
Composites Having
Nonsintering
Inclusions 153
2.6 Dielectric Theory 158
2.6.1 Dielectric Materials 158
2.6.2 Measurement of Dielectric Properties ... 163
2.6.3 Dielectric Properties of Composite
Materials 170
2.7 Mechanical Properties 179
CHAPTER THREE: EXPERIMENTAL PROCEDURE 184
3.1 Overview 184
3.2 Powder Synthesis and Treatment 184
3.2.1 Overview 184
3.2.2 Synthesis, Characterization and
Preparation of Polystyrene Microspheres 184
3.2.3 Milling and Preparation of Borosilicate
Glass Powder 199
VI

Page
3.3 Powder Characterization 202
3.3.1 Overview 202
3.3.2 Visual 203
3.3.3 Density 204
3.3.4 Size Characterization of Ceramic
Powders 206
3.3.5 Surface Area 209
3.3.6 Chemical 220
3.4 Suspension, Casting and Green Compact Studies 224
3.4.1 Overview 224
3.4.2 Wet Processing and Characterization .... 225
3.4.2.1 Selection of the Dispersion
System 225
3.4.2.2 Characterization and
Optimization of the
Suspension System 228
3.4.2.2.1 Overview 228
3.4.2.2.2 Rheology of Dispersed
Composite Components . 228
3.4.2.2.3 Optimization of the
Suspension System ... 230
3.4.2.2.4 Effects of Sonication
and Aging Upon
Suspension Properties 232
3.4.2.2.5 General Rheology
Studies 235
3.4.3 Slip Casting of Compact Samples 236
3.4.4 Suspension Solids Loading Determination 242
3.4.5 Characterization of Green Compacts 243
3.4.5.1 Visual 243
3.4.5.2 Hg Porosimetry 243
3.5 Thermal Analysis: Oxidation and Pyrolysis Studies . 249
3.5.1 Overview 249
3.5.2 Oxidation Studies 250
3.5.3 Pyrolysis Studies 251
3.6 Thermal Treatments 252
3.6.1 Furnace Calibration 252
3.6.2 Pyrolysis and Presintering 258
3.6.3 Sintering 259
3.7 Materials Characterization 261
3.7.1 Archimedes Density Characterization .... 261
3.7.2 Dielectric Properties Characterization . 267
3.7.3 Microscopic Investigation of Composites 277
3.7.3.1 Overview 277
3.7.3.2 Specimen Preparation 277
3.7.3.3 Investigation of Segregation
of Included Porosity 281
3.7.4 Mechanical Properties Data 281
Vll

Page
CHAPTER FOUR: RESULTS AND DISCUSSION 286
4.1 Precursor Powders 286
4.1.1 Visual 286
4.1.2 Powder Density 295
4.1.3 Particle Size/Size Distribution 298
4.1.3.1 Polystyrene Microspheres ... 298
4.1.3.2 Ceramic Powders 315
4.1.4 Powder Surface Area 323
4.1.5 Effect of Ball Milling On BS Glass 326
4.2 Suspension and Green/Pyrolyzed Structure
Characterization 337
4.2.1 Suspension Characterization 337
4.2.3 Green/Pyrolyzed Structure
Characterization 349
4.2.3.1 Overview 349
4.2.3.2 Structural Characteristics
of Polystyrene Latex
Compacts 349
4.2.3.3 Structural Characteristics
of Green and Pyrolyzed
Composites 360
4.2.3.4 Effects of Aging and
Sonication Upon Green
Properties 382
4.2.3.4.1 Sonication 382
4.2.3.4.2 Aging 386
4.3 Thermal Processing and Characterization 395
4.3.1 Removal of Organics 395
4.3.2 Evolution of BS Glass Surface Area 399
4.3.3 Oxidation of Si3N4 Powder 404
4.3.4 Sintering 408
4.4 Characterization and Modelling of Processed
Materials 450
4.4.1 Characterization of Microstructure 450
4.4.2 Modelling of Included Porosity 482
4.4.3 Characterization of Dielectric
Properties 499
4.4.4 Microhardness Characterization 534
CHAPTER FIVE: SUMMARY AND CONCLUSIONS 542
5.1 Overview 542
5.2 Powder Development and Characterization 542
5.3 Green Processing and Characterization 543
5.4 Thermal Processing and Characterization 544
5.5 Characterization and Modelling of Densified Compacts 546
viii

Page
CHAPTER SIX: SUGGESTIONS FOR FUTURE WORK 549
APPENDIX I: MANUFACTURER'S DATA FOR CERAMIC CONSTITUENT
POWDERS 553
APPENDIX II: PARTICLE SIZE AND SIZE DISTRIBUTION DATA
OF UNSETTLED 4.6 fjm REGIME (061990 SERIES)
UPLM SPHERES 564
APPENDIX III: LEAST SQUARES POLYNOMIAL REGRESSION DATA
CURVE FITTING PROGRAM (BASIC) 576
APPENDIX IV: LIST OF ACRONYMS 579
REFERENCES 581
BIOGRAPHICAL SKETCH 630
IX

Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy
PROCESSING, CHARACTERIZATION AND MODELLING OF
BOROSILICATE GLASS MATRIX-PARTICULATE SILICON NITRIDE COMPOSITES,
CONTAINING CONTROLLED ADDITIONS OF POROSITY, FOR USE IN
HIGH SPEED ELECTRONIC PACKAGING
By
Michael S. Randall
August 1993
Chairman: Dr. Joseph H. Simmons
Major Department: Materials Science and Engineering
Borosilicate glass matrix-particulate silicon nitride composites,
with controlled additions of porosity, are produced through suspension
processing and slip casting of nonaqueous, codispersed suspensions.
Controlled porosity is obtained via the addition and pyrolysis of
polystyrene latex microspheres. The effects of latex size and size
distribution upon controlled pore structure are investigated. The
largest (9.0 pm monosized) latex, at a concentration of 17.6 V%, is
found to give the largest amount of closed porosity (15.6 V%).
The borosilicate glass-silicon nitride binary is also investigated
in order to determine the effect of nonsintering inclusion concentration
upon processing factors as well as upon final composite properties.
Composites containing all three constituents (borosilicate glass, Si3N4,
and polystyrene latex) are also investigated.
Above the percolation threshold of latex addition (i.e. a filled
fraction of approximately 16 V% of total space), the pore structure is
observed to change rapidly, greatly affecting densification behavior as
well as the pore structure. Additions of latex below the percolation
X

threshold result in hermetic, densified structures subsequent to
processing. Silicon nitride additions are found to retard densification
kinetics at and above concentrations of 16 volume percent of total space
and to arrest sintering at and above Si3N4 concentrations of 36 volume
percent of total space, in accordance with viscous sintering theory.
Hermetic, porous borosilicate glass-particulate silicon nitride
composites are produced having maximum closed porosities of
approximately 15.6 volume percent (at approximately 16.0 V% total
porosity). The densified included pore structure is accurately modelled
using a modification of standard series clustering and percolation
models.
Corresponding minimum composite dielectric constants of
approximately 3.5 are observed. The dielectric constant of the
composites are found to be stable over the range of frequencies
measured. Dielectric loss values are found to agree well with analogous
literature values for the borosilicate matrix glass. Composite
dielectric constants are modelled using effective medium theory as well
as traditional dielectric mixing rules.
Microhardness evaluations of representative composites are also
discussed. The elastic moduli of the composite system are modelled
using Mackenzie, linear regression, Voigt and Reuss models. Stoke's
settling theory is also extrapolated to explain the lack of segregation
observed in this system.
XI

CHAPTER ONE
INTRODUCTION
1.1 The Impact of Electronics on Modern Civilization
1.1.1 Economic and Political Aspects
The electronics industry is a $460 billion industry world wide
[88SCH1]. The American electronics industry accounts for 38.1% of this
amount, while Japanese and European electronics industries account for
37.7% and 24.2% of the world electronics industry, respectively
[88SCH1]. Domestically, the electronics industry accounts for 3.6% of
the gross national product (GNP) which amounts to approximately 170
billion dollars [88SCH1, 90WRI]. The electronics industry is currently
growing at an annual rate of 13% for Japan, and 11% and 6% for the
United States and Europe, respectively [88SCH1J.
Demand for improved electronic devices (i.e. higher speed, smaller
size, and greater ability, etc.) has provided a driving force for
continuous improvements in microelectronic technology. Never have Ralph
Waldo Emerson's words, "If a man can write a better book, preach a
better sermon, or make a better mouse-trap than his neighbor, though he
builds his house in the woods, the world will make a beaten path to his
door," been more applicable to an industry [88CAR, p. 84.8].
The electronics industry has generally progressed from analog to
digital electronics. The workhorse of digital electronics is the
integrated circuit. The IC was simultaneously invented by Jack Kilby of
Texas Instruments and by Robert Noyce of Fairchild Industries in 1958
[88MAC]. The field of IC technology has grown through three generations
of successively increasing integration (i.e. MSI for medium scale
integration, LSI for large scale integration, and VLSI for very large
scale integration, respectively), with more generations to come (i.e.
1

2
ULSI and WSI, for ultra large scale integration and wafer scale
integration, respectively). Furthermore, IC devices are available in
many configurations, as required by the exhaustive number of electronic
appliance applications. The general trend in these electronic devices
is toward maximization of circuit elements per unit volume. Figure 1.1
illustrates the evolution of circuit density for both field effect (FET)
and bipolar junction (BJT) transistor IC devices. The relative scale of
integration is also indicated in Figure 1.1
1.1.2 The Future of the Electronics Industry: Impact and Limitations
1.1.2.1 The Fourth Generation
The major goals influencing the evolution of electronic technology
is to increase performance and universality of application. Digital
microprocessor-based devices dominate the electronics industry.
Therefore, improvements in electronic technology will focus upon
advancement of microprocessor technology as well as in advances in
microprocessor interlinking and increasing the availability and amount
of memory accessible by microprocessors. Other goals include reduction
in power consumption, reduction in device size and weight, increased
device capability as well as increased device dependability and
environmental/thermal stability. Other important requirements are the
maximization of device output and quality, at minimized cost.
The methods that will be used in order to achieve the above goals
will be quite varied [see 89SER,89TUM3, etc.]. In order to increase
computing speed (i.e. electronics performance), non-traditional
technologies, which are currently in their infancy, will be applied.
Examples of these technologies include optical switching and
communication (including holography) [89SER,88YAN,88SRI,87COR1,
87COR2,83BER], electro-optical interfacing [88HUT,87JIN], advanced
semiconductor materials, parallel processing [92SKE], artificial
intelligence (AI), integrated services digital networking (ISDN)

t
Year
Figure 1.1
Illustration of the increase in electronic circuit
density with time [91TUM]

4
[90OHS], biological systems [89SER], neural networking [89SER],
superconductor-based logic and communications [89SER,89TUM3], etc.
Furthermore, electronic performance will be advanced via the
continued evolution of traditional technologies, in pursuit of
theoretical limitations. One goal is to reduce current packaging
hierarchies by at least one level, in order to reduce signal flight
distances. This change would result in a reduction in the number of
interconnects as well, thereby improving reliability and device
longevity, while reducing production costs. The first goal may be
achieved by successful implementation of another goal, which is to
economically obtain ultra large scale and/or wafer scale integration
(ULSI and WSI, respectively). Wafer scale integration results in a
dramatic increase in the scaling of microcircuitry, which, in theory,
leads to reduced signal flight times due to reduced signal transmission
distances. Ironically, however, WSI offsets some of the advantages of
removing a packaging level since production costs would definitely
increase. Furthermore, it would no longer be possible to replace one
individual chip since the smallest field replaceable unit (FRU) would
become the integrated wafer itself. As discussed below, there are other
drawbacks to WSI as well.
Another goal is to change to higher performance semiconductor
materials, having higher electron-hole mobilities, such as GaAs. It is
also preferred that the replacement semiconductor material(s) be direct
band gap materials, thereby allowing more efficient usage of power as
well as less phonon-initiated heat generation.
Finally, a great deal of research effort is currently involved
with improving traditional microprocessor and packaging technologies.
The focus of such research is to increase the performance of
microelectronic systems beyond the state of the art and closer to
fundamental theoretic limitations, as discussed in section 1.2 below.
Increased clock frequencies; finer scales of microcircuitry; larger

5
scales of integration; larger, cheaper, and faster memories and
microprocessors; use of lower resistivity conductors as well as low
dielectric constant, cofirable packaging materials and implementation of
increased performance cooling designs and materials are all desired
goals of said research. Figure 1.2 illustrates the current and
projected trends in the performance of computers based upon traditional
silicon IC technology.
Furthermore, environmental concerns are becoming increasingly
important. Hazardous materials, involved in the production of
electronic appliances, must be properly disposed of or recycled. Also,
many of the cleaners and solvents used in IC production and electronic
packaging are being replaced by environmentally benign materials and
processes [89SER].
In summary, it is quite apparent that the microelectronics
industry has a great many opportunities for advancement. However, it is
also true that said industry is subject to unparalleled competition as
well as a great deal of regulation.
1.2 Fundamental Microelectronic Packaging Limitations
The fundamental limitations discussed in this section relate to
microelectronic packaging only. Surprisingly, the switching speed of a
microelectronic apparatus is as much a function of the packaging
configuration and materials as it is a function of the actual switching
devices. Figures 1.3 and 1.4 illustrate the theoretical limitations
that are involved in digital electronics, in a graphical sense, and are
a valuable summary as well as an illustration of the combination of each
fundamental limitation. The figures outline the perimeters that provide
the limits of maximum performance of a digital electronic system
(including switching devices, packaging, interconnection, etc.).

6
Year
Figure 1.2
Current and projected trends in traditional, silicon
based, computer performance [91TUM]
Cycle Time (ns)

log {delay (s)}
7
-2
-4
6 -£
-8 -
10-
12
14
CO
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C
CD
C
C CO
3
H
1 ms Rise Time
o
-Synaptic Cleft
1 fjs Rise Time
Intel 8085
////
Jr/f*
085 Series â–º //Stanford Cray \/
Allowed Region(s)
MOS DRAM
Bipolar TTLv^
Intel APXB6
MIPS RISC /
NMOS *
ns Rise Time
CMOS —>
CMOS SOS '
MESFET 1
M0DFET-— (y/
/ /•
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.x-v Motorola /—— //
Q 68000 -^(aK VHSJC I WvJ
306-4^ >^,0
>M0S . .a ¿'¿A®
//â– & Forbidden
Josephson
‘Current ^
Injection <0
/7
/A ps Rise Time
log {element spacing (m)}
Element spacing versus delay time plane of electronic
packaging space, illustrating the theoretical
limitations in electronic packaging performance with
respect to spacing of electronic lines and signal
elements [89SER]
Figure 1.3

8
-10 -8 -6 -4 -2 0 2 4
log {element spacing (m)}
Depiction of the theoretical limitations encountered
in electronic packaging as defined by the electronic-
element-spacing versus signal-line-spacing plane of
electronic packaging space [89SER]
Figure 1.4

9
1.2.1 Electron Light Speed Limit
Electrons can not travel at speeds exceeding the fundamental speed
of light in a perfect vacuum (i.e. approximately 3 x 108 m/s or 186,000
miles/s), regardless of the medium that they travel through. Electrons
travel through perfect (lossless) conductors at the speed of light if
said conductor is surrounded by free space. However, if the perfect
conductor is surrounded by a dielectric medium other than free space,
the speed at which electronic signals will traverse the conductor is
expressed through the relation:
V-
c
JK
where K is the dielectric constant of the insulating material
surrounding said perfect conductor. From the above discussion, it is
evident that use of lossless, low dielectric constant insulating
materials, in combination with non-magnetic, nearly perfect conductors,
will increase electronic signal speed, and thus, overall performance.
Furthermore, it is important to minimize packaging scale (i.e.
miniaturization) in order to minimize the signal time of flight (TOF) at
the signal speed indicated by the above equation. Therefore, it is
important to carefully chose both the electronic packing material and
the packaging metallization, as well as to minimize the scale of
electronic packaging integration.
1.2.2 Conductor Spacing Limit
While the quantum electron tunneling limit is not currently in
danger of being approached, using traditional electronic packaging,
there are other limitations that do effect conductor spacing in
electronic packages. In any electronic package, there is a finite
amount of space available for signal transmission lines. It has been
shown [89SER,89TUM3,90SHI2,90SHI1,91TUM] that as the number of switching

10
devices increases, the number of input-output signal lines (I/Os) must
also increase according to the relation:
I=bCp
where I is the number of I/Os, b is the average number of signal
connections per circuit, and p is a positive exponential (research has
found that p is always < 0.67 and is usually about 0.5). This relation
is commonly know as Rent's rule. In two-dimensional space (i.e. single
layer or double sided electronic packaging), this limit has already been
approached or exceeded using traditional thick film packaging
technology, and, in some cases, using thin film technology [89SER].
The conductor spacing limitation may be circumvented, to a certain
extent, by using three dimensional packaging. Multilayer packages,
having signal planes interconnected with vias, are an example of three
dimensional packaging. However, there are limitations even to
multilayer packaging systems. These limitations depend upon the size of
the interlayer vias used and the number of layers used [89SER].
The minimum size of signal traces is theoretically limited by
quantum effects. Realistically though, the actual size and separation
distance of signal traces is most often determined by the ability to
produce straight and smooth traces having a uniform cross section.
At high frequencies the skin effect limits electronic current to
the outside (skin) of a conductor. At said frequencies the skin depth
is on the order of the conductor diameter, thereby decreasing the
effective diameter of the conductor. This serves to increase resistive
losses. Furthermore, since the current traverses the outside (skin) of
the conductor, interruptions in surface smoothness have a much greater
effect upon signal integrity. At said frequencies, as the signal
changes from one medium to another, any change in conductor cross
section will further enhance attenuation and signal reflection.

11
Thus, it is important not only to match impedances, but also to match
signal cross section sizes and geometries in the frequency regime
characterized by significant skin effect. Other factors include,
switching energy (i.e. maximum current density) and switching frequency
as well as dielectric strength and hermeticity of separating insulators.
The homogeneity of the conductor material as well as the overall
conductor quality (i.e. its resistivity, magnetic susceptibility, and
characteristic skin depth as a function of frequency, etc.) is also an
important considerations when pursuing minimum conductor spacings.
Conductor spacing limitations are also affected by electronic
noise. There are four types of internal electronic noise possible in a
packaging system: inductive, capacitive, reflected and power
distribution or Al noise.
Reflected noise is a result of a mismatch in impedance between
signal traces and active devices. It is not significant until higher
frequencies are reached (i.e. above 10MHz). Reflections may be
eliminated by matching the impedance of all elements in the device. In
practice, however, this is quite difficult and design goals are toward
realistic minimization of reflections.
Power distribution (PDN) or Al noise results from the switching
process itself. As a device switches, it requires a certain amount of
power, (typically about 1—10 mW [91TUM]). In a microprocessor, it is
possible for many elements to switch simultaneously. Said switching
processes are fast, usually occurring in tens of nanoseconds.
Therefore, the current demand upon the power supply can be excessive and
may cause a drop in the supply voltage. This drop causes a voltage
pulse to be sent to the switching devices, due to the parasitic
inductance of each microcircuit. The voltage pulses, if significant,
cause spurious switching.
Power distribution noise may be reduced through use of high power,
self-regulating power supplies, reduction in parasitic inductances

12
through package design, increased power and ground availability,
reducing signal path lengths and placement of signal traces more closely
to power and ground traces, etc.
Perhaps the best way to reduce or eliminate Al noise is to place a
small capacitor, having very little parasitic inductance (i.e. a
decoupling capacitor), as closely as is feasible to the switching
elements themselves. Decoupling capacitors serve as a local current
source during periods of transience, reducing Al noise to acceptable
levels.
Both inductive noise and capacitive noise are types of coupling
noise. Both are resultant from current changes in adjacent signal
traces and may result in the phenomenon commonly known as crosstalk.
Inductive noise involves a single voltage pulse, travelling in the
opposite direction of the original signal, in signal traces neighboring
the element carrying the original pulse. Capacitive coupling noise
results in two pulses, travelling in opposite directions from each
other, in signal traces neighboring an active trace. The first pulse
travels in the direction of the parent pulse and the second in the
opposite direction. Both pulses are in phase with the parent. In the
reverse direction, capacitive and inductive elements interact. The
magnitudes of said pulses depend directly on the distance between the
conductive traces and in the dielectric permittivity of the material
separating the traces. The ability of these pulses to result in
crosstalk depends upon both the voltage and the width of the resultant
coupled noise pulses. Both types of pulses can cause erratic switching
if the pulse voltage exceeds either the forward or the reverse bias
(depending upon the pulse direction), of the switching elements in
question, for a duration long enough to switch the elements.
Furthermore, reflected coupled pulses may also interact with first order
coupled pulses. The entire process is quite complex to model and is
handled in several publications [89SER,89TUM3, etc.]. It is sufficient

13
here to note that reductions in dielectric permittivity of the
insulating material will reduce coupled noise in an electronic packaging
system. Furthermore, coupled noise may be reduced through utilization
of prudent design configurations and criteria [89SER].
1.2.3 Cooling Limitations
The issue of electronic device cooling is very involved. As chip
integration evolves, switching elements are placed with increasing
density. While per device power dissipation has steadily decreased, the
rate of decrease of microdevice separation has surpassed this effect
(see Figures 1.5, 1.6 and 1.7). As a result advanced ICs have cooling
demands that require cooling technology at or beyond the state of the
art. Figure 1.7 illustrates the increased trend in cooling requirements
for IBM microelectronic packages. The cooling limitation may well be
the theoretical limitation that is first reached.
One method to meet cooling needs is to use direct band gap
materials or superconducting Josephson logic configurations as switching
devices, since they do not dissipate as much switching energy in the
form of heat as do indirect bandgap solid state switching materials (see
Fig 1.8). However, these switching devices have many drawbacks which
limit their successful implementation.
Another method is to use high thermal conductivity packaging
materials. Both of the above methods are passive in nature and are
somewhat limited, however, because all switching materials dissipate
some energy as heat, and because efficient heat sinking as well as heat
transfer at interfaces are required, in conjunction with high thermal
conductivity materials. These requirements are due to the relatively
small difference between heat source and sink temperatures typical in
electronic packaging applications.
The most successful cooling methods utilized to date involve
active cooling, such as immersion technology [89SER]. A new method, not

Number of Chip
Signal Connections
14
Year
Figure 1.5 Increase in chip signal connections (i.e. device
integration) and chip size with respect to time
[91TUM]
Chip Size (mm

log {Number of circuits on a 10mm x 10mm chip}
15
Heat Dissipation (W/cm2)
Figure 1.6
Illustration of IC power density as a function of chip
integration [91TUM]

Package Power Dissipation (W/cm
16
Figure 1.7
Cooling ability (i.e. requirements) of IBM electronic
packages as they have evolved with time (i.e.
increased packaging integration) [91TUM]

Access Time (log{s}>
17
-8 -7 -6 -5 -4 -3 -2 -1
Power Per Gate (log{W})
Figure 1.8
Comparison of different switching device technologies
with respect to device power dissipation [91TUM]

18
currently used in production, but showing great promise, is that of
microchannel cooling [89SER]. MicroChannel cooling involves routing
coolant through the back of the IC chip itself. The chip is modified by
etching microchannels into its back, using traditional lithography
techniques. A plate is then affixed to the chip back, enclosing the
channels. Manifolds are then affixed to the chip ends, allowing flow of
coolant through the microchannels. This technique allows for a heat
dissipation of approximately 600 W/cm2 using water, flowing at the rate
of 10 cm3/s, and using a temperature differential of 60°C and has
exhibited a heat exchange as high as 870 W/cm2 [89SER]. Using the
treatment outlined in [89SER], this cooling technology could allow for a
minimum nearest-to-next-nearest propagation delay time of 5 x 10'13 s
without overheating, using the logic restoration basis theoretical
minimum switching energy (Es„) of 7.7 x 10'15 J. This could allow for a
theoretical maximum switching frequencies in the THz range (if only a
few switching elements are involved).
1.3 Electronic Packaging: Overview of the Field
1.3.1 History
Electronic packaging was first used, in significant amounts, in
Hollerith's card reader [89SER]. The mechanical relays utilized in the
machine had slate mounting plates as well as varnish covered solenoid
wires. Electronic packaging has advanced a great deal since then. Many
packaging changes have been implemented between Hollerith's
electromechanical relay-based technology and today's solid state
electronics. This section covers packaging methods used only since the
introduction of solid state logic.
Until very recently, emphasis for advancement in the field of
electronic packaging was limited to the scale of integration of solid
state devices. Contemporary chips incorporate up to several million

19
logic or storage elements, and thus, have eliminated the need for
several hierarchies of packaging that were formerly necessary.
Standard modular system (SMS) technology was the first concept
introduced for solid state device packaging [89SER]. This technology
interconnected singular electronic devices (i.e. transistors,
capacitors, etc.) on a printed circuit board. It was developed in 1959
and afforded a far superior alternative to tube technology in speed,
size, power consumption and reliability. The circuit boards were
connected to a panel and interconnected via wrapped wire and cable
connections. Apparatii utilizing this technology were still quite
limited, however, and a great deal of effort has since been expended
attempting further integration. With the invention of the IC a new
implement was provided for use toward this goal.
Solid logic technology (SLT) introduced many of the technological
advancements that are used, in modified form, today in ceramic packages.
The package was made from 96% A1203, 4% glass, and used swaged pin
technology. The chip was soldered in place, then encapsulated using a
metal cap held in place with epoxy. The method of chip attachment
utilized was called the controlled collapse chip technology (C4) which
involves depositing solder balls on either the IC or the package I/O
pads, flipping the chip face down upon the ceramic package carrier, then
heating the assembly to let the solder flow and attach the chip to the
package. This process is also known as flip-chip technology and is used
frequently today [89SER,88TUM,89TUM,91TUM].
Advanced solid logic technology (ASLT) improved upon SLT by
screening conductors onto both sides of the substrate. Furthermore, the
substrates were made stackable by soldering the pins from the bottom of
one package to the top of another. The wiring density was also
increased. All these advances yielded significant performance increases
[89SER,88TUM,89TUM]. Monolithic systems technology (MST) further

20
expanded upon this technology. This system basically replicated SLT and
ASLT but provided further integration. The MST package provided 18
I/Os.
Vendor transistor logic (VTL) technology helped to introduce the
first universal industry standard for ICs [88TUM]. A variation upon
vendor transistor logic, card on board (COB) technology, allowed
manufacturers the ability to produce electronic appliances using
prepurchased ICs. Thus the precedent was established for second party
electronics, opening a huge industry and bringing the concept of
component interchangability to integrated logic-based components.
Initially ICs were available with up to fourteen leads. Later,
planar or dual in-line packages (DIPs) were developed having as many as
64 leads [88TUM,89TUM]. The DIPs were plugged into cards, which also
included other active and passive elements. The cards were plugged into
boards and the boards connected to a gate. The gates provided power as
well as interconnection [89SER].
Metallized ceramic (MC) technology was the first packaging genre
to utilize photolithographic techniques. As circuit integration
increased, I/O density requirements mandated that either thin film or
multilayer technology be utilized [88TUM,89TUM]. Metallized ceramic
technology used the former. The thin films were deposited by either
sputtering or thermal evaporation on both sides of an Al-,03 substrate.
The deposition process involved a three-layer deposition of chromium on
copper on chromium. The chromium layers were thin and were used to
improve adhesion on the inner layer [88TUM,89TUM].
Metallized ceramic polyimide (MCP) technology was the first
multilayer thin film technology. A polyimide layer was added to the top
of a ceramic substrate, and the polymer surface was deposited with
chromium then copper then chromium as above. This process was repeated
for several layers, then standard photolithographic techniques were

21
utilized to etch via spaces between layers. The vias were then back
filled with paste, thereby connecting the layers [89SER].
The discussion until now has been centered around the first level
of packaging hierarchy. Evolution of chip packages (the zeroeth level),
specifically LSI packaging, will now be discussed briefly in order to
introduce the next generation of first level packaging. Early large
scale integration (ELSI) involved packaging of 100 to 500 circuits, and
utilized pluggable module packaging, making it a field replaceable unit
(FRU) [89SER]. Large scale integration (LSI) technology was introduced
in 1979. The first LSI circuits contained 704 switching elements. The
chips had a switching speed as fast as 1 ns. Because the packages had
delicate I/O terminations, they were mounted to the first level module
utilizing wave soldered through holes. Up to nine LSI chip packages
were mounted to a single multilayer ceramic (MLC) module in this manner.
The MLC had been developed in order to accommodate ever increasing
chip integration levels. With up to 23 layers, the MLC presented a
technologically challenging processing hurdle. Multilayer ceramic
packaging technology was borrowed from the field of multilayer
capacitors, originated by RCA in the late 1950s [88TUM,89TUM]. Also
borrowed from the multilayer capacitor community was the concept of the
interlayer connection, or via, as well as tape casting and laminating
technologies [88TUM,89TUM]. Variations of MLC technology are still
utilized today. The basic process of MLC fabrication is outlined in
Figure 1.9 for both the old and new thermal conduction module (TCM)
production process. Said technology has been very successful in the
area of advanced performance ceramic packaging and is expected to
dominate that field, in varied form and in conjunction with thin film
multilayer polymer technology, in the future. There are excellent
literature sources which describe the process and related fields in
detail [82BLO,84BLO,84SCH2,88TUM,89SER,89TUM,91TUM].

22
Alumina/Mo Based TCM
Glass-Ceramic/Cu Based TCM
Raw Materials
1
Alumina + Glass (4-10%)
Glass Powder
T
Slurry Preparation
Acid-Base
Acid-Acid
Casting and Blanking
1
Continuous Casting
Continuous Casting
1
Via Hole Punching
Mechanical
Mechanical
1
Metallization (Thick Film)
1
Stacking/Registering
Mo Paste
Cu Paste
Automated
Automated
T
Lamination
Automated
Automated
1
Organics Removal
and
Sintering
Controlled Hydrogen Atm.
Controlled Steam Atm.
Crystallization Step
1
Final Ceramic
Alumina + Glass
Glass Ceramic
T
Electrical Tests
Automated
Automated
T
Attachment of Pins
and Flange
1
Automated
Ni and/or Au Plating
Automated
T
Substrate Machining
and Surface Treatment
Seal Flange
Top and Bottom Surface
Finishing and Seal Flange
T
Chip Attachment (C-4 Process)
Automated
Automated
T
Electrical Testing of Module
Automated
Automated
Final Module Assembly
Automated
Automated
â–¼
Helium Gas Filling of Module
Automated
Automated
Figure 1.9
Flow chart of the MLC production process used
IBM TCM [82BLO,89TUM,91TUM]
in
the

23
Perhaps the best known example of MLC technology is the IBM TCM
series. When introduced in 1981 for the IBM 3081 computer system, the
IBM TCM used 96% alumina (4% glass) as the dielectric and either Mo or W
metallurgy [89SER,83BLO]. The multilayer module consisted of 33 layers
and could accommodate up to 118 IC chips. The layers were configured as
either signal (X or Y plane), redistribution, or voltage-reference
layers. Said module had up to 320 cm of wiring per cm3 of package.
Furthermore, an ingenious cooling device was utilized on the IBM TCM
which used chilled water forced through a hermetically sealed and He
backfilled chamber. Said technology was capable of accommodating chip
heat dissipations as high as 3 W/cnr. Much of the cooling ideologies
used in the original TCM (for the 3081) are used in the current TCM.
The state of the art TCM (introduced in 1991 for the IBM 390/9000)
seems only subtly different from the original TCM. However, it exhibits
markedly improved performance, by utilizing Cu metallurgy as well as low
sintering temperature (~1000°C), low K (-5) crystallizable dielectric
materials (cordierite with minor clino-enstatite). Furthermore, the
390/9000 TCM can accommodate up to 121 LSI chips, and has 63 wiring
layers as well as 9 polyimide signal redistribution layers. All of this
was accomplished using special processing to avoid oxidation of the Cu
metallurgy during thermal treatment. The CTE of the dielectric used in
said package was matched carefully to Si over a broad range of
temperatures [91KUM2]. The packaging heat accommodation was increased
to -18 W/cm2 as well. This TCM represents the current state of the art
in high performance electronic packaging, although other corporations
have also marketed excellent examples [88BAB,89EMU,89SAW,89SER,89TUM3,
91SHE2,etc.].

24
1.3.2 Importance of the Electronic Package
1.3.2.1 Economic
Electronic packaging and interconnects account for a large portion
of the advanced ceramics market. The electronic ceramics market is the
largest niche within the field of advanced ceramics [91SHE2]. The
electronic packaging and interconnects market accounts for approximately
0.05% of the GNP of the United States [90WRI]. This industry involves
over $2.7 billion annually, accounting for approximately 1.5% of the
total sales of the entire US electronics industry [88SCH1,91SHE2].
Furthermore, the electronic packaging and interconnects industry
currently is experiencing a growth rate of approximately 8.5% per annum
[91SHE2], projecting a total market value of approximately $6.5 billion
by the year 2000 [91SHE2].
1.3.2.2 Functional
Upon first inspection, electronic packaging seems deceivingly
simple. The components of the package are passive and the final
packaged structure usually seems like an elementary monolith. Upon
further inspection, however, one learns that the electronic package is
quite complex. Perhaps no other type of passive device is subject to as
many material and environmental constraints.
Electronic packaging is typically divided into as many as six
levels. The zeroeth level of packaging involves the IC chip itself
(i.e. intra-chip integration), while first level packaging involves the
I/Os of the IC chip (i.e. chip level integration). In many instances,
the zeroeth order is not considered packaging, since it is inherent in
the chip integration itself. First level packaging brings power and
signal lines to the IC chip while providing mechanical and hermetic
protection.
The second level of the electronic packaging hierarchy involves
the interconnection between IC chips as well as other on-card devices

25
(i.e. card level integration). Second level electronic packaging is
task oriented, in that it involves the interconnection of electronic
devices that perform a specific task (i.e. video cards, etc.). The
second level allows for task diversity (i.e. different cards for
different tasks) as well as traditionally offering the smallest scale of
easy replacability (i.e. the field replaceable unit (FRU)). The third
level of packaging involves interconnection of cards (i.e. board level
integration) and the fourth level in the electronic packaging hierarchy
involves the interconnection of boards (i.e. gate level integration).
Finally, gates are interconnected to form a main frame in the fifth
level of the packaging hierarchy.
As digital systems have evolved, some of these packaging levels
have been eliminated. For instance, personal computers (usually denoted
card on board (COB) systems) do not have a fourth level of packaging.
Use of multichip modules (i.e. chip on board (also COB) systems) also
eliminates the second level in the electronic packaging hierarchy.
Eventually, the board level may be partially replaced as well if wafer
scale integration (WSI) comes to fore.
An electronic package basically provides a fixed structure for
active electronic devices. Said structure is subject to many, varied
constraints. The structure must be mechanically strong in order to
protect the delicate active devices from shock and external forces. The
package must also provide shelter from moisture and corrosive
environments. Furthermore, the thermal expansion of the electronic
packaging material must be similar to that of the active materials that
it packages, so that the packaging does not destroy its active occupants
when changes in overall temperature, or temperature gradients are
experienced.
The electronic package must also provide for one or more means of
dissipating heat generated by the active components. Heat dissipation
may be either passive or active. For either type of cooling, it is best

26
(although not mandatory) that the electronic packaging have a high
thermal conductivity. A high thermal conductivity is beneficial when it
is desirable to avoid thermal shock of the device. Furthermore, by
utilizing packaging materials having high thermal conductivities, heat
generated via the active devices is spread more quickly and more
homogeneously throughout the package, thereby avoiding detrimental hot
spots.
The packaging must also provide a satisfactory medium for
encapsulating power and signal transmission elements. As a result of
the current emphasis upon device miniaturization, this packaging
requirement has become quite important. Electrically conductive
elements have decreased greatly in height, width and pitch now that high
conductivity metals are being utilized, resulting in the need for
packaging materials having exceptional surface smoothness, interlayer
planarity [90REC] and either minimal or predictable shrinkage and
warpage during processing. In ceramic materials, these goals may be
attained only with proper processing. It is desirable that the starting
ceramic powders be very small in size and that said powders consolidate
to a very high green density. Furthermore, the consolidation must not
result in particle segregation.
The electronic package must also provide a medium that is suitable
for high quality electronic communication, since the electronic devices
housed in the package require "clean," constant power and high quality
signals. With the current emphasis upon increasing signal speed, this
requirement has mandated changes in both materials and design in order
to obtain satisfactory packages. As discussed below, this criterion
presents perhaps the greatest impediment to advancement in the field of
high speed computing.

27
1.3.3 Properties Desired of Packaging Materials
Table 1.1 summarizes both the requirements and the weight of said
requirements for electronic packages and packaging materials.
Surprisingly, the major barrier to the realization of the next
generation of high performance computing lies in limitations in
packaging materials and not in switching materials [83VEN,87MOH,87SHI,
87YAR]. The unavailability of satisfactory high speed electronic
packaging materials results from the fact that successful candidates
must satisfy several stringent criteria. First and foremost the
candidate must have satisfactory dielectric property requirements. The
dielectric constant and loss tangent must be low (3 to 5 or below, and
<0.005, respectively [86CRO,87KEL,87MOH,88GER3,89LEA]), and stable at
the frequencies used (MHz to tens of GHz [87YAR]). There are several
reasons for the dielectric properties criterion. The time delay (Td) of
signal propagation of an electronic pulse through a circuit element is
given by the relation:
rn _ UK
d~
where K is the material dielectric constant, L is the propagation
distance, and c is the speed of light [84SCH3,84SCH4]. Thus the signal
delay is proportional to the square root of the dielectric constant of
the surrounding packaging material. This effect is illustrated for
various ceramic materials in Figure 1.10.
The characteristic impedance (Zc) of package signal traces must
rest within a narrowly defined field of approximately 40 to 110 n
[89TUM3] (the most preferable value is 50 0 [88BAL]) due to noise,
signal delay and current draw considerations.

28
Table 1.1
Requirements and Importance of Said Requirements
for Electronic Packages and Packaging Materials [91TUM]
High Performance Applications
Property
Importance
Importance
Weighting
Dielectric Constant (minimize)
Highest
5
Wiring Density (maximize)
Highest
5
Metallization Conductivity
(minimize)
Highest
5
Coefficient of Thermal Expansion
(match to IC chip material)
High
4
Dimensional Control (maximize)
High
4
Mechanical Strength (maximize)
Medium-Low
2
Low Performance Applications
Property
Importance
Importance
Weighting
Cost (minimize)
Highest
5
Thermal Conductivity (maximize)
Highest
5
Coefficient of Thermal Expansion
(match to IC chip material)
High
4
Wiring Density (maximize)
Medium
3
Mechanical Strength (maximize)
Medium-Low
2

Propagation Delay (ns/m)
29
Dielectric Constant
Figure 1.10
Depiction of propagation delay time versus dielectric
constant for various ceramic materials [91TUM]

30
Figure 1.11 graphically illustrates the design criteria for selection of
package characteristic impedance.
Furthermore, the minimal thickness of packaging layers between
circuit elements required for impedance matching is lowered when a lower
dielectric constant material is used, due to the following relation:
where Z„ is the characteristic impedance, L is the inductance associated
with the signal line, and C is the capacitance associated with the
signal line [84SCH3,84SCH4]. By lowering K, C is reduced per unit
thickness, thereby increasing ZG per unit thickness. Thus a thinner
packaging layer may be utilized while maintaining the characteristic
impedance, further enhancing miniaturization. Therefore, use of low K
packaging materials allows for increased digital performance in two
ways, by increasing signal speed and by helping to decrease signal
propagation distance.
The dielectric loss factor must also be low, as illustrated by the
relation:
P=Tce/fV'o tan (6)
where P is the power loss due to dielectric loss, f is the signal
frequency, e' is the real portion of the material dielectric
permittivity, Vc is the peak signal voltage and 6 is the dielectric loss
angle (e''/e') [76KIN]. From the above relation, it is evident that
power dissipation due to dielectric loss may become rampant at high
frequencies if insulating materials are not chosen carefully.
Utilization of materials having low K and tan(6) values also aids
(along with correct design of ground planes) in lessening problems of

Noise Tolerance (volts)
31
Figure 1.11
Depiction of design considerations for choosing a
package characteristic impedance [89TUM3]
Delay Adder (ns)

32
crosstalk, signal pulse rounding and other phenomena leading to signal
infidelity [87MOH,87YAR,89SER,89TUM,89TUM3,91TUM].
A second goal in the design of electronic packaging is one of
expense reduction. In order to reduce production expenses, packaging
materials should be developed that are processable at low temperatures.
Lower processing temperatures also allow for use of nonrefractory metals
(such as silver and copper) as conductive elements. This is
advantageous from a performance point of view, since silver and copper
have relatively high electrical conductivities (6.31 x 107 and 5.96 x 107
(Ohm—m)'1 respectively [85CRC]). Therefore, both resistive heating and
signal loss would be reduced through the implementation of either
conductor material. Thus, cofirability with copper or silver is
advantageous from both cost and performance standpoints. Cofirable
systems must be totally processable at temperatures significantly below
the melting point of the metallic constituents (1083°C and 982°C for
copper and silver respectively [85CRC]). Furthermore, cofirable
packaging materials must allow for processing treatments which ensure
the total pyrolysis of organics, as well as the complete sintering of
the metallization, while not adversely affecting the desired properties
of the conductor metallurgy.
The coefficient of thermal expansion (CTE) also should be matched
closely to that of the semiconductor material utilized. This ensures
that the chip bonds will not fail with repeated usage (i.e. when the
power is turned on and off). The induced plastic strain (ep)
experienced by the solder connections during thermal cycling of a chip
and package assembly is quantified by the relation:
A CTExA TxDnp
£p= H
where ACTE is the difference in the coefficient of thermal expansion

33
between the IC chip and the packaging material, AT is the difference
between the temperature at which there is no stress and the temperature
of interest, is the distance from the neutral point of shear stress
on the chip (i.e. the horizontal middle), and H is the height of the
solder pad [84SCH2]. From this relation the number of cycles to failure
(Nf) may be estimated from the Coffin-Manson equation:
ep
where A and m are constants whose values must be empirically determined
for the particular system [89TUM3].
From the above relations, it is evident that reducing the
difference in CTE between the chip and the package will reduce thermal
fatigue. Figure 1.12 illustrates this equation for several materials.
Also, plastic shear strain on the solder connections increases toward
the outside of the IC chip (i.e. as increases). Therefore thermal
cycling fatigue increases in magnitude with the use of larger IC chips
(i.e. VLSI). Not as obvious in this discussion is the effect of thermal
conductivity of the materials involved. Low thermal conductivities tend
to increase stresses within the packaging material but tend to decrease
ep by decreasing AT at the chip-solder-package interface. For this and
many other reasons, it is considered most prudent to use cooling methods
which extract heat from the back of the chip rather than through the
substrate.
Thus it is desirable to have a CTE which is adjustable for
different switching materials. Since Si is, by far, the predominant
switching material currently in use, the most utilitarian electronic
packaging materials will have a CTE that is customized to match that of
Si. Furthermore, it is important to match the CTE of Si over all
temperatures that the chip-package assembly will experience.

Fatigue Life (cycles)
34
Figure 1.12
Illustration of the Coffin-Manson equation for several
materials [91TUM]

35
Figure 1.13 exhibits the CTE of Si with respect to temperature.
Adjustability of CTE may be provided to varying extent by using ceramic
composite systems as packaging materials.
Furthermore, stress resultant from CTE mismatch is reduced between
packaging and metallization when lower firing temperatures are used (as
in low temperature, cofirable systems) by reducing AT. Differential
stress between metallization and packaging may be further reduced if
packaging materials that densify via a viscous sintering mechanism are
used, since localized stress may be alleviated if an annealing step is
used at temperatures slightly above the glass transition (Tg) of the
packaging material. Stress on chip pads may be relieved similarly if
the chip bonding material requires heat treatment above T6 of the matrix
glass.
The fourth desirable property of an electronic packaging material
system is that of high surface smoothness. Surface roughness may cause
disabling discontinuities within the package. Acceptable surface flaws
are usually no larger than about one tenth the metallization width
(typically >50 pm, [89SER,89TUM3]). As technological advances allow for
further miniaturization (i.e. substitution of photolithography for
screen printing as the application method for circuit metallizations
[90NEB]) this limit will surely decrease markedly.
Hermeticity is also desirable in a satisfactory packaging system.
If atmospheric moisture enters the package, dielectric properties will
change markedly [89SER,89TUM3,91WAL]. Moisture also contributes to
corrosion (and thus embrittlement, due to stress corrosion cracking),
exfoliation and delamination of both the packaging and the active
electronic elements. Hermeticity of the packaging material may be
achieved in several ways such as hermetic coatings, etc. However, it is
much simpler and more cost effective if the packaging material is
inherently hermetic subsequent to thermal processing.

36
[90GEI] [91DIL]
Figure 1.13
Thermal expansion of Si and other selected materials
as a function of temperature [88COR, 90GEI,91DIL]

37
This is accomplished in most ceramic and glass materials when sintered
to more than approximately 95% of theoretical density [76KIN].
Adequate mechanical properties and high thermal conductivity are
also desirable in electronic packaging materials. Since mechanical
failure is frequently due to CTE mismatch or improper thermal treatment,
this problem can be avoided by careful design and processing.
Frequently, it is becoming more important that the green package have
greater green strength, in order to avoid damage during processing.
Packaging design evolution also has moved away from using the
electronic package as a supporting or structural member for the
apparatus. Conventional wisdom more frequently dictates that it is
better if the package provides support and protection only for the
elements that it packages. This further reduces mechanical requirements
of the electronic packaging material. However, a minimal mechanical
strength is still desirable. The materials utilized in the IBM TCM
currently have a bending strength of about three quarters of that of
A1203 (i.e. -210 MPa) [91KUM1,91KUM2,91SHE2,91TUM], while other
institutions have decided that lower strengths are permissible
[89EMU,89SAW,90RIC,91ALE,etc.].
Indeed, if ceramic materials are to be continued in use as
dielectric insulating materials in high performance electronic packages,
K will have to decrease, necessitating that composites of ceramic and
either polymer materials or porosity be used in the future. This will
surely decrease the mechanical strength of said materials [91KUM]. In
the future, the consequences of using lower strength packaging materials
will be circumvented through proper package design and processing as
well as careful materials selection.
High thermal conductivity is no longer as important a material
attribute either, since ingenious designs now remove generated heat from
the back of the chip instead of through the substrate [82BLO,83BLO,
89SER,89TUM3,91TUM].

38
This method is advantageous in several ways. First, since heat removal
through the back of the IC chip is quite amenable to active cooling
technologies, a much greater amount of heat may be dispersed through its
use. Also, removal of heat through the substrate is generally regarded
as an inferior method since it requires that the heat flux traverse the
metallizations and chip bonding materials. This increases thermal
stresses while reducing electrical conductivity. Also, with continued
decreases in conductor scale (i.e. reduction in the size of chip-package
interconnections), thermal conductivity would be further retarded. This
effect can be offset only through the utilization of thermal vias, which
are very costly in terms of IC chip "real estate."
Removal of heat, through the substrate, to a thermal sink rather
than to a cold finger on top of the chip, also results in thermal
resistances which are significantly greater than in the cold finger
method unless ultra high thermal conductivity materials (i.e. diamond,
or cubic BN) are used. The Franz-Weiderman rule [83POB] indicates that
this technique is not useful in high performance packaging applications
where a low dielectric constant is also required (with a few notable
exceptions such as diamond, cubic BN, or BeO, etc.). The Franz-
Weiderman principle states that no material may have both an ultra high
thermal conductivity as well as a low dielectric constant. The
exceptions to this rule are either prohibitively expensive or toxic.
Furthermore, there are no exceptions to the Franz-Weiderman rule when it
is necessary to select materials having a K below 5.5. Since, in high
speed electronic applications, satisfactory dielectric properties are
most important, the material designer must prioritize on the side of low
dielectric constant, low dielectric loss materials.
High thermal conductivity is also important from a thermal shock
point of view since a high thermal conductivity promotes heat spreading
throughout the package, thus reducing thermal fluctuations within the
package. However, as stated in section 1.3.3, use of a high thermal

39
conductivity material in conjunction with a through-the-substrate
cooling mechanism will actually reduce the solder-package interface
temperature, thereby increasing the thermally induced shear stresses on
the solder pads (relative to use of a lower thermal conductivity
material in the same heat removal configuration).
It should be noted that the development of a successful packaging
candidate (i.e. one which satisfies the above packaging criteria)
requires a two-pronged, holistic approach. Both materials selection and
packaging design are extremely important in achieving the criteria
discussed above. Furthermore, there is no one package that satisfies
all the requirements in all systems. In some cases, mechanical
integrity or hermeticity is the most important characteristic, while in
others, signal processing is tantamount. Therefore, no one design or
material is universally satisfactory to all electronic packaging
applications. Furthermore, pursuing more than one of the above
packaging criteria, requires skillful design as well as use of
engineered (i.e. composite) materials. Therefore, it is of extreme
importance to decide what packaging criteria are most important when
developing packaging materials or designs for a specific application or
family of applications. Table 1.1 can help to serve as a guide in
packaging design and materials selection.
This study attempts to present a viable packaging material system
that satisfies the materials-based (not design-based) factors of the
packaging criteria outlined above. Furthermore, the greatest importance
is placed upon a materials solution which emphasizes signal processing
speed (i.e. low dielectric loss materials), adjustability for varying
application (i.e. composite materials), and cost reduction (i.e. low
materials cost, applicability to traditional processing, and thermal
processability at reduced temperatures (low temperature cofirability))
while exhibiting environmental stability (i.e. hermeticity and at least
a minimum mechanical strength). It is the author's opinion that these

40
are the most important packaging criteria for the advancement of high
speed electronic computing.
1.4 Materials Solutions to Electronic Packaging Problems
1.4.1 Ceramics versus Polymers
Nearly 85% of all electronic packages currently produced are
polymer based while ceramic packages comprise approximately two thirds
of the monetary value of the electronic packaging market [89TUM3]. So-
called plastic packaging systems are based on some type of insulating
polymer encapsulant such as epoxy, polyimide, silicone, or, of late,
thermoplastics [89TUM3]. They offer several advantages over ceramic
systems such as lower cost, lower dielectric constant, and greater ease
and adaptability of manufacture as well as greater relative throughput.
Seemingly these advantages would mandate that all electronic packages be
polymer-based. However, the use of plastic packaging systems has
several disadvantages. Table 1.2 shows the advantages and disadvantages
of ceramic versus plastic electronic packaging materials.
Currently, no plastic package is truly hermetic although materials
are being developed which are less hydrophilic than traditional
polymeric packaging materials (i.e. polyguinolines, teflons, and BCBs)
[90LEE,90REC,91HEN,91HOR,91ZUS]. Therefore, the packaging thickness
must be carefully controlled in order to allow some of the moisture,
present within the package, to be evaporatively removed using IC chip
heating (89TUM3]. If the electronic device is one that consumes very
little power (i.e. dissipates very little heat), such as CMOS
devices,special packaging design considerations are mandated.
Furthermore, plastic packaging materials have a much greater CTE than
the materials which they encapsulate (i.e. Si). Resultant thermal
stresses may damage delicate microcircuitry. This requires
implementation of careful package design and manufacturing principles.

41
Table 1.2
Advantages and Disadvantages in the Polymeric
versus Ceramic Electronic Packaging Materials Debate
Topic
Ceramic
Polymeric
Advantage
Adaptability to
Multilayer Packaging
Moderate
Moderate
Depends
(Usually
Ceramic)
Cost
High
Low
Polymer
Breakdown Voltage
High
High
Depends
Dielectric Constant
Moderate
Low
Polymer
Dielectric Loss
Low
Low
Depends
(Usually
Polymer)
Ease of Process
Automation
Low
High
Polymer
Hermeticity
Hermetic
Non-Hermetic
Ceramic
Inherent a—Radiation
Variable
Variable
Depends
(Usually
Ceramic)
Process Complexity
High
Low
Polymer
Process Temperature
High
Low
Polymer
Process Throughput
Moderate
High
Polymer
Rigidity
High
Flexible
Ceramic
Strength
High
Flexible
Depends
(Usually
Ceramic)
Surface Smoothness
Moderate
High
Depends
(Usually
Polymer)
Tolerance Control and
Reproducibility
High
Low
Ceramic
Thermal Conductivity
High
Low
Ceramic
Thermal Expansion
Low (Highly
Variable)
High
Ceramic
Volume Resistivity
High
High
Depends

42
Plastic packaging materials are characterized by poor thermal
conductivity as well. Due to the encapsulating nature of most plastic
packaging methods used, this factor, when combined with the unfavorably
large CTE of polymers, can be quite deleterious. However, the moisture
evaporation methods used to compensate for a lack of hermeticity help
counteract this problem somewhat (at least in the lower scales of
integration), since evaporation is highly endothermic.
Ceramic packages offer the advantages of hermeticity, CTEs
comparable to switching materials or metallizations, higher thermal
conductivity, and greater integrity. However, ceramics, as a group,
have higher dielectric constants and higher dielectric losses, and are
more susceptible to stress corrosion cracking [89TUM3]. Furthermore it
is difficult and expensive to produce ceramic substrates having
relatively high surface smoothness.
Also disadvantageous to both plastic and ceramic packaging is
inherent alpha radiation that is emitted from trace impurities within
the polymeric and ceramic raw materials. Inherent a—radiation has been
found to cause spurious semiconductor device switching which results in
soft errors. For example, concentrations of approximately 1.0 ppm U238
or 0.4 ppm Th232 within a plastic or ceramic package would emit a flux of
alpha radiation on the order of 0.1 a/cm2/h. That level of radiation is
one to two orders of magnitude above the acceptable limit established
for memory devices [89TUM3].
This radiation problem is currently remedied by adding anti¬
radiation coatings, as well as through improved raw material processing
and careful packaging design. However, these corrections add a great
deal to the packaging cost, (which is the main advantage of using
plastic packages). Furthermore, as the scale and pitch of integration
increase and decrease respectively, a—radiation switching is expected
to become more problematic. Ceramic packaging materials tend to exhibit
this problem to a lesser extent than polymeric materials [89TUM3].

43
However, radiation is a bonafide problem in both, thereby mandating that
electronic packaging materials be very highly refined (at least on the
first packaging level).
Thus, ceramics are used for high performance applications that are
not as cost sensitive as typical consumer electronics while plastic
packages are utilized for lower cost electronics. The disadvantages of
ceramic-based packaging, in the area of dielectric properties, are
currently circumvented through package design (i.e. by using 3—
dimensional, multilayer packages, etc.). For the highest electronic
performance applications, however, plastic-on-ceramic hybrids are
currently used [91KUM1,91KUM2,91SHE2,91TUM]. Porous ceramics and
ceramic-plastic composites are also being developed for use in the
highest performance applications as well [86CRO,86DAS,87KEL,87MOH,
88GER3,88IBR,89JUN,89LEA,89YAM2,90KAT,90STE,91SAC1,91ZUS, etc.].
1.4.2 Methods and Materials
1.4.2.1 Traditional
The history of ceramic electronic packaging is covered in section
1.3.1 above. From the above, it is evident that the evolution of this
field has been mainly design (and not materials) oriented. Most ceramic
electronic packages and packaging systems were established using
alumina-based substrate materials.
However, materials selection has become increasingly important
with the advancement of the field. Materials performance limitations
are currently thought to be the limiting factor to advancement of the
field.
It is of value here to elaborate upon the electronic packaging
system that is described in section 1.3.1 above and is generally
perceived to be the state-of-the-art in ceramic electronic packaging.
This system is IBM's thermal conduction module (TCM). The TCM
originally was an alumina-based multilayer package for the IBM 3081

44
computer system. The original package provided power, cooling and
signal integration to more than 100 ICs. The original TCM was a
"vertical" design, having 33 ceramic layers interconnected by vias. Due
to the relatively high processing temperatures of the original TCM, the
conductor metallurgy was based upon "refractory" metal (i.e. tungsten or
molybdenum based).
The TCM introduced a very advanced cooling system based upon
water-chilled cold fingers, enclosed within a helium-filled chamber,
that connected directly to the back of the thermal conductive-paste-
covered Si chips. This design made excellent use of C4 or flip chip
technology.
The IBM TCM has evolved over its 10+ year life span. The current
TCM (produced for use in the IBM system 390/9000), is glass-ceramic-
based and has copper metallization. It has 63 dielectric layers and
exhibits vastly improved performance. Table 1.3 delineates the
differences between one of the alumina-based TCMs (used in the IBM
system 3090, ca. 1986) and the latest generation of its evolution.
The process for producing the TCM is outlined in Figure 1.9 above.
The basic process has not changed except that the thermal processing
treatment now includes a crystallization step.
The thermal conduction module is not the only advanced ceramic
electronic packaging system in use today. Some other systems are the
liquid-cooled-module (LCM) of NEC, Fujitsu's double-sided board (DSB)
system, and Hitachi's card on board (COB) system. These systems, and
others, are elaborated upon in various literature sources [89SER,89TUM3,
etc]. These systems all would benefit (or have benefitted) through the
use of low dielectric loss, cofirable ceramic packaging materials.
1.4.2.2 Advanced
The subject of advanced electronic packaging is very large and
there are several excellent publications which cover the subject

45
Table 1.3
The IBM Thermal Conduction Module
Then and Now [91TUM]
Substrate
Characteristic
IBM System 3090
Alumina/Molybdenum
(ca. 1986)
IBM System 390/ES9000
Glass-Ceramic/Copper
(ca. 1991)
Size (mm)
110.5 x 117.7
127.5 x 127.5
Number of Layers
45
63
Number of Vias
(Total)
4.7 x 10s
2 x 10*
Wiring Density
(cm/cm3)
450
844
Line Width (pm)
100
75
Via Diameter (pm)
125
90 and 100
Dielectric Constant
9.4
5.0
Resistivity (pO-cm)
11
3.5
CTE (RT to 200°C)
(ppm)
60
30
Shrinkage Control
(%)
±0.15
+0.1

46
[89SER,89TUM3]. Table 1.4 is a comprehensive condensation of recent
research performed in the field of advanced ceramic electronic
packaging. Data on polymers and metals are also included. Because of
the considerable length of Table 1.4, it is placed at the end of Chapter
One.
The subject of advanced ceramic packaging may be divided into
three general processing categories: thin film, thick film and tape
cast processing. Thin films (in this context) may be produced by
several means including thermal evaporation, and sputter deposition,
etc. Thick films (in this context) are deposited by screen printing and
may be used for both insulation and metallization. Tape casting is
currently the most used method for producing high performance electronic
packaging. Thin film technology offers the advantages of producing
comparatively smaller size structures (thinner layers and narrower
lines) and thus will become most important in the future. Thin films
characteristically have a smoother surface structure than thick films,
thereby allowing advanced metallization techniques (i.e.
photolithography, e-beam lithography, etc.) to be used. Currently the
minimum line width feasible using thin film and optical lithography is
approximately 0.5 pm [91CAL].
Thick film materials typically do not display the surface
smoothness required for lithography processes and thus minimum line
widths are currently limited to approximately 25 to 50 pm [90STE].
However, with the use of smaller particle sizes and improved processing
technology, ceramic photolithography has also become the subject of
investigation [90NEB]. The thickness (or thinness) of thick film layers
is similarly limited. In the future, both types of packages will
involve multilayered structures almost exclusively.
Furthermore, as mentioned in section 1.4.1 above, polymer-on-ceramic
hybrid multilayer structures (similar to those used in the most current
IBM TCM) will become very popular.

47
Metal coated ceramic substrate materials also fit into the
category of advanced electronic packaging due to their novelty,
toughness, tailorable thermal expansion, high thermal conductivity and
low dielectric constant, as a group [81HAN,86SAT,86TEA,870KA,87SHU].
However, multilayer structures have not yet been produced by this method
and, therefore, they are limited to special applications. Generally,
ceramic coatings are deposited over metal bases by either
electrophoretic or thick film deposition techniques. These composites
will see limited future use in such applications as automotive
electronics as well as other high temperature, high stress, corrosive
environment applications.
From a materials point of view, advanced electronic packaging
materials fall into one of two categories: polymer or ceramic. It
should be noted that, in this discussion, polymer materials, are carbon-
based, organic materials and not ceramic, sol-gel processed materials.
The advantages and disadvantages of both types of materials are defined
in section 1.4.1.1 above. Generally, polymers are utilized in advanced
thin or thick film multilayer structures while ceramics are used to
produce advanced thick film or tape cast multilayer packages.
Current polymer materials research for electronic packaging
applications is centered mainly in two areas: developing low moisture
absorbing polymers, and developing polymeric or polymeric-ceramic
materials having thermal expansions matching either Si or GaAs. Thus
far, teflons, polyquinolines, and bisbenzocyclobutenes (BCBs) have shown
promise as reduced water absorption materials [90REC,91HEN,91ZUS] while
composites of epoxy/Kevlar, epoxy/Nextel, polyimide/Kevlar, and
polyimide/glass have shown promise as matched thermal expansion
materials [88IBR,91ZUS].
Recently, research in the area of advanced ceramic electronic
packaging materials has investigated several, varied topics. Low
temperature cofirability (allowing the use of low p (resistivity)

48
metallization) has been a universal trend in almost all of this
research. Advanced ceramic electronic packaging materials research may
be further divided into the categories of diamond films [91LYN],
glass+ceramics, glass-ceramics, and porous ceramics. Table 1.4, placed
at the end of this chapter, provides a condensation of materials and
processing information for all of these areas, as well as a bibliography
for the convenience of the reader. Diamond thin films have not yet been
successfully implemented for use in high speed microelectronic
packaging, due mainly to the infancy of the field.
Glass+ceramic and glass-ceramic materials are currently the
mainstay of the high performance electronic packaging field. However,
no ceramic material that is a viable future high speed electronic
packaging candidate has a dielectric constant below 3.78 [76KIN]. It
has been stated that electronic materials used in future high
performance packaging applications will necessarily have dielectric
constants below this value [86CRO,87MOH,87YAR,88GIL etc.]. Therefore,
the only way to achieve dielectric constant values below 3.78 while
using ceramic materials, is to fabricate composites of ceramic materials
with non-ceramic, electronically insulating materials, that have lower
dielectric constants (i.e. polymers, or air). The decisive majority of
this research has been in the area of porous ceramics.
Cofirable, porous ceramic materials may be produced from glass,
glass+ceramics or glass-ceramics and are, thus, considered a subset of
each group. Porous ceramics may be produced in several ways. Porous
ceramic thin films may be produced by partial densification of SiO: sol-
gel films [86CRO,87MOH,88MOH], thermal oxidation of sputtered columnar
Si [ 86DAS ] , and reactive sputtering of SiO-, [86DAS], as well as by
suspension of latex in silica sol [87MOH]. These methods have not yet
been implemented in electronic packaging, however, due to poor film
hermeticity as well as inadequate mechanical properties and surface
smoothnesses, etc.

49
Porous thick films have been produced by addition of hollow silica
glass microspheres (HGMS) [87KEL,89LEA,89JUN,90KEL], partial sintering
of glass frit pastes [90WAH], and controlled gas generation within fully
dense glass thick films [90STE,90WAH]. These methods have found greater
success. However, problems with surface smoothness necessitate extra
thick film applications with sealing pastes. Furthermore, the
repetition inherent in thick film processing limits the applicability of
the thick film process in general, since only one layer may be produced
at one time. Finally, the controlled gas generation method involves a
large volume expansion, and thus, dimensional stability becomes a
problem in multilayer structures containing porosity produced via
controlled gas generation. However, this method has been utilized to
produce metallization lines as narrow as 25 to 50 pm in a single layer
configuration [90STE].
It is not sufficient simply to add porosity to the insulating
material. In order to maintain a hermetic structure, porosity must be
non-continuous. Furthermore, the porosity must be small in order to
maintain surface smoothness as well as mechanical properties. While
surface roughness improves interlayer and metallization adhesion, it is
detrimental when the scale of said roughness is within approximately one
tenth of the smallest signal line dimension. Roughness on this scale
not only increases the possibility of electrical discontinuity of signal
traces, but promotes inhomogeneity of the signal trace cross section.
This is highly detrimental at high frequencies since it causes
inhomogeneities in the characteristic impedance (Z0). Furthermore,
variances in cross section force high frequency electronic signals
through a relatively tortuous path. This not only increases signal
propagation distance, but increases spurious signal reflection [89TYL].
Finally, it is best if included porosity be limited to as small a volume
fraction as possible in order to preserve dielectric breakdown strength,

50
volume resistivity, surface smoothness, sinterability, mechanical
properties and thermal conductivity, etc.
Currently, tape casting is the only feasible method by which
porous ceramic materials have been produced for electronic packaging.
Porosity has been introduced into tape cast ceramics via hollow silica
glass microspheres (HGMs) [88LEA1] as well as through the controlled
burnout and subsequent differential sintering of organic latex
microspheres [89YAM2,90KAT].
The HGM method allows for a greater amount of included porosity to
be added to the packaging material than the latex method, since the
added porosity, resultant from HGM additions, is non-continuous.
Therefore, the HGM method is better in theory and is the only currently
viable method for producing tape cast packaging materials having greater
than —13V% non-continuous porosity. However, the only successfully
produced and tested ultra low dielectric permittivity, multilayer
electronic packages produced, to date, have utilized the latex method
[89YAM2,90KAT]. There are several reasons for this. First, HGMs are
comparatively quite large (-80 pm) and thus promote surface roughness.
Also, HGMs have very low density (-0.25 g/cm3 [89LEA]) and thus tend to
segregate during suspension processing. Third, HGMs tend to break down
during processing (such as pressing, laminating, sonic dismembrating,
etc.). Finally, as HGMs become smaller, it will become necessary to add
them to the ceramic matrix in larger amounts (compared to latex) due to
the wall thickness of HGMs. For example, pores resulting from the
burnout of latex and subsequent sintering of the surrounding matrix tend
to comprise a volume similar to the volume of the latex spheres which
formed them. With HGMs, however, the amount of Si02 added to the
ceramic matrix per microsphere addition may, in fact, be similar to, or
greater than the amount of porosity added. An HGM having a diameter of
5 pm and a wall thickness of 0.5 pm is only 51% porous itself. Said HGM
would have a K of -2.4 (as compared to -1 for air). In this scenario,

51
the HGM method would be much less efficient for reduction of K than the
latex method. Since it is desirable to add a minimum of either HGM
(mainly for sinterability and mechanical integrity reasons) or latex
(mainly for hermeticity and mechanical integrity reasons), the latex
method is preferable in this sense.
Hermetic ceramic materials having dielectric constants as low as
3.4 have been produced, via tape casting, and utilized in multilayer
packages in the laboratory [89YAM2,90KAT]. Commercial introduction of
such a product has not yet occurred, however.
Therefore, it is imperative that further research be performed in
the area of controlled porosity ceramics for utilization in ultra high
speed electronic packaging. Many materials and processing related
questions remain in this field. Research in this area should focus upon
methods to minimize (and the theories involving minimization of)
dielectric constant and dielectric loss while maintaining a hermetic
material of dimensional and mechanical adequacy.
1.5 Proposed Packaging Material System: Statement of Thesis
1.5.1 Choice of Electronic Packaging Material System
The choice of the electronic packaging material system to
investigate was based upon creating a relatively low cost, hermetic,
ceramic packaging material for use in very high speed electronic
packaging applications. From the above criteria, it becomes apparent
that no one material is satisfactory for this application. Therefore,
it was decided to chose a composite system having carefully selected
constituents. This methodology is useful in that the composite may be
optimized for different applications. Properties of the materials
utilized are outlined in Table 1.4 at the end of this chapter.
Cofireability is obtained by using a borosilicate glass as the composite
matrix. Surface smoothness is also enhanced when a viscous sintering
matrix is used. Low dielectric constant and tan(5) are achieved by

52
utilization of materials having low K and tan(ó) values as well as
through the addition of controlled porosity. Furthermore, all materials
utilized have dielectric properties which are stable over a broad range
of frequencies.
In this study, controlled porosity is achieved via the addition,
and subsequent pyrolysis, of uniform polystyrene latex microspheres
(UPLMs). The UPLMs are producible in a size range between 3 and 9 pm
and are quite monodisperse, thereby allowing a study of the effects of
UPLM size and dispersity upon the hermeticity of the sintered material.
The composite system of focus should also be easily adaptable to
standard ceramic tape casting processes. Since the maximum diameter of
the latex is less than 10 pm, the surface smoothness criterion should
also be satisfied for most current thick film signal line widths (if
proper dispersion and homogenization are achieved).
There are some problems associated with adding porosity to a
brittle material. Porosity in a ceramic material has been shown to
reduce the mechanical strength of said material [76KIN]. Furthermore,
it is possible to create a non-hermetic material from a formerly
hermetic one. Therefore, processing must be optimized to provide
hermetic materials having acceptable mechanical properties.
In order to increase the mechanical integrity of the composite
system, a hard particulate ceramic is added. Since mechanical strength
and toughness must be increased with minimal increase in dielectric
properties, the choices for ceramic filler are limited to strong
particulate ceramic materials having low K and tan(6) (such as diamond,
cubic BN or Si3N4) . In order to reduce material costs, particulate Si3N4
was used. Silicon nitride represents the best compromise between
desired properties and expense, thereby making this packaging system
practical for most electronic packaging applications. Also, since the
Si3N4 was used as a nonreactive addition, all information related to
sintering and processed microstructure, gained from this study, should

53
be generally applicable to similar composites with other, similar, inert
additions.
1.5.2 Topics of Investigation
This study investigates several factors crucial to the development
of the proposed borosilicate glass-particulate Si3N4-controlled porosity
composite system. This section outlines the topics of research
investigated in this study.
The following constituent variables are investigated:
the effects of ball milling on the properties of the
borosilicate glass powder
the effects of borosilicate glass size and size distribution
upon sintering behavior of said glass
the effects of UPLM volume fraction, size and size
distribution upon both green and selected sintered materials
properties (see below)
the effects of Si3N4 volume fraction and/or included porosity
volume fraction upon sintering behavior, and selected
sintered materials properties (see below).
The following processing factors are investigated:
the effects of suspension sonication and aging upon green
and non-sintered properties
the effects of pyrolysis/presintering upon borosilicate
glass surface area and surface pore size distribution
the effect of heat treating Si3N4 powder in air, at or above
composite sintering temperatures, upon the properties of
said Si3N4
the effect of sintering temperature upon sintering rate.
The following materials parameters are investigated:
the effect of porosity and Si3N4 volume fraction upon the
dielectric constant of the composite
the effect of frequency upon dielectric properties
the effect of atmospheric exposure upon hermetic and non-
hermetic materials
the effect of porosity and Si3N4 volume fraction upon the
hardness of the composites.

54
Models of composite materials properties, as well as models
concerning the effect of pore percolation upon hermeticity, the effect
of non-sintering particulate and/or included porosity volume fraction
upon sintering behavior and the effect of porosity upon assorted
mechanical properties (as described in Chapters Two and Four), are
utilized to characterize the composite system. A discussion of the
universal applicability of said experimental results to other analogous
systems is included as well.
The main emphasis of this study, however, is to investigate and
model the phenomena involved in the creation and maximization of closed
porosity, produced using the methods described within, in order to
reduce the dielectric constant of the composite and while providing a
candidate material for MLC applications.

Table 1.4
Pertinant Materials Properties for Selected Electronic Packaging Materials
Electronic Properties
Thermal Properties
Physical
Properties
Material
t/i.
@lMHz
tan 6
@lMHz
Volume Res.
(fl-cm)
Breakdown
Voltage
(V/fim)
Thermal
Con.
(W/nTC)
CTE
(ppm/”C)
Process
Temp. CQ
P
(glee)
Flexural
Strength
(MPa)
Ref(s).
Ceramic Materials (Crystalline)
AIN
8.0-10.0
0.0001-0.0028
>10'*
8380
70-320
3.7-4.5
1800-1900
("CaO add.)
3.20-3.30
280490
85WEA.86HAM,
87CHO,87KUR,
88GER3.88SEI,
89HIM.89MAT,
89NIW.89TAK,
90REC.91LYN,
91KUM2.91TUM
.92RIC.92SHE2
AljOj
8.2-10.2
0.0002-0.002
10'M O'4
9650-15800
19-50
5.6-9.0
1500-1600
3.59-3.97
280-552
84MUS.85WEA,
86HAM.87CHO,
88CER.88GER3.
89KON.89NIW,
89TAK.89TAN,
90LEE.90REC,
91HAN,91KUM2
.91SHE2.91TUM
,91ZUS,92RIC
Anorthite
(CaO-A l20j-2Si02)
4.5
91TUM
BeO
5.8-6.9
0.0003-0.001
10”-1014
9500-13800
135.5-370
4.2-94
1600-2000
1.8-3.01
170490
85WEA.87CHO,
87KUR.88CER,
88GER3.89MAT,
89TAK.90LEE,
90REC.91LYN,
91KUM2,
91SHE2.91TUM,
92RIC
OI
OI

Table 1.4 Continued
Electronic Properties
Thermal Properties
Physical
Properties
Material
«/*„
@lMHz
tan 6
@lMHz
Volume Res.
(fl-cm)
Breakdown
Voltage
(V//i m)
Thermal
Con.
(W/m °Q
CTE
(ppm/'O
Process
Temp. (°Q
P
(glee)
Flexural
Strength
(MPa)
Ref(s).
UN (a-Hex)
4.0-4.4
0.001
10"
35000-55000
28-42
3.7-4.3
2.1-2.25
110
85WEA.87CHO,
88CER.880ER3,
89MAT.91CER
BN (cubic)
5.6-5.8
>10"
760-1300
4
1400 (@6.5
GPa
Pressure,
with AIN
add.)
3.48
87CH0.88GER3,
89HIR.89MAT,
91WES
Celsian
(Ba0-AI20,-2Si0j)
2.7
91TUM
Ceria (CeOj)
15.0
0.0007
l(f
12.1
10.0
7.0-7.13
110
85WEA.88CER
Clinoenstatite
(MgO-SiOj)
7.8
91TUM
Cordierite
(2Mg0-2Al20,-5Si02)
4.1-6
0.003-0.007
10'*
5500-9100
1-4
1-3
925-1050
(IBM,
Viscous
Sintering,
Subsequent
Crystallizatio
n)
2.0-2.9
70-300
84MUS.87CHO,
88CER.880ER3,
89MAT.89NIW,
89SAW.9IKUM2
.91TUM
Diamond (Q
55-5.7
0.001
10l#
650-2000
1.1-3.5
3.5
1400
87CH0.88GER3,
89MAT.91LYN,
91WES
Eucryptite
(LijO-AljOj^SiOj)
5.3
0.005
10"
I 67
-10 lo 0.5
2.67
62
66WEB.88CER,
91TUM
Forstcritc
(2MgO-SiOz)
5.8-6.7
0.0004-0.001
10„
7900-11900
1 674.18
9.4-10.6
2.8-2.9
140-170
66WEÍ1.88CER,
89MAT.89NIW,
91TUM
U1
a\

Table 1.4 Continued
Electronic Properties
Thermal Properties
Physical
Properties
Material
«/i0
@lMHz
tan 8
@lMHz
Volume Res.
(O-cm)
Breakdown
Voltage
(V/fim)
Thermal
Con.
(W/m°Q
CTE
(ppm/°C)
Process
Temp. CQ
P
(g/cc)
Flexural
Strength
(MPa)
Ref(s).
Gallium Arsenide
(GaAs)
12.8
43.0
5.9
90GAG.90REC
Hafnia (HfO*)
12.0
0.01
10*
1.67
6.5
9.0-9.68
110
85WEA.88CER
Magnesia (MgO)
8.2-10
0.001
>10'*
8500-11000
39.7-146
8.8-13.5
2.5-3.58
138
85WEA.87CHO,
88CER.90LEE
Micas
5.4-8.7
0.0002
10l#
39500-79100
0.33-0.83
7.6-27.0
2.6-3.8
88CER.90LEE
Mullite
(3Al20,-2Si02)
6.2-6.8
0.00095-0.005
> 10”-10”
7800
2.51-7.0
4.0-5.5
1400-1600
(CaO,
MgO,Si02
add.)
2.5-3.1
131-302
84MUS,'87CHO,
88CER.88GER3,
89MAT.89NIW,
89TAN.90KUR,
91KUM2,
91SHE2.91TUM
Silicon (Si)
11.7-12
100-200
2.64.0
2.32-2.34
85WEA.87CHO,
87KUR.90GAG,
90LEE.90REC,
90RIC.91LYN
Silicon Carbide
(SiC, BeO Doped)
4045
0.05
>10”
270490
3.74.3
2000-2100
3.2-3.22
420450
85WEA.86HAM.
87CHO,87KUR,
88GER3.89MAT,
89TAK.91KUM2
,91SHE2,91TUM
,92RIC
SijN4 (a-Hexagonal)
6.0-7.0
0.0001
10”
15800-19800
12.5-33.5
2.3-3.1
1600-2000
3.1-3.44
350-697
84SCH2.84SCH3
,85WEA,87CHO,
88CER.88GER3,
88REE.89SAN1,
89SAN2,
91KUM2,
91SHE2.91TUM

Table 1.4 Continued
Electronic Properties
Thermal Properties
Physical
Properties
Material
«/«„
@lMHz
tan 5
@lMHz
Volume Res.
(ii-cm)
Breakdown
Voltage
(Vl/x m)
Thermal
Con.
(W/m°Q
CTE
(ppm/“C)
Process
Temp (°C)
P
(glee)
Flexural
Strength
(MPa)
Ref(s).
Si02 (Quartz)
4.1-4.6
2-40
11.2 (Quartz)
12.5
(Cristoballite)
17.5
(Tridymite)
2 6-2.66
140
85WEA.87CHO,
88GER3.89MAT,
90LEE.91TUM.
Spinel (Mg0-Al205)
7.5
o.oow
10M
11900
7.53
6.6
2.8
103
88CER
Spodumene
(LiAlSi206)
6.0-6.4
0.004
lO"1
5.0-5.02
2.0
950
24-3.2
250
66WEB.88CER,
91KUM2
/9-Spodumene (IBM)
53-5.7
0 9-5.5
850-990
89SAW.91TUM
Steatite (MgO-SiO^)
5.7-6.1
0.0008-0 0035
10”
7900-13800
2.5-3.34
7.2-10.4
2.7-2.8
145-170
88CER.89MAT
Thoria (Th02)
13.5
0.0003
10'°
-5300
13.8
5.3-59
9.7-9.86
131
85WEA.88CER
Titania (TiO^
100
7
3.3
3.844.26
85WEA.87CHO
Zirconia (Zr02)
12.0-13.0
0.01
10"
-5000
25.7
3.0-10
5.6-5.89
186400
85WEA.88CER,
89NIW
Zircon (ZrSiOJ
8-10.5
0.001-0.0014
>10u
6300-11500
5.02-8.36
3.5-5.5
3.74.3
172
88CER
Ceramic Materials (Amorphous)
Glass (General)
4.3-8.5
0.0005-0.01
10”
7800-13200
0 83-1.67
0.8-1.3
2.0-8.0
110
87CH0.88CER
Aluminum Silicate
6.3
3.0-4.8
SP = 910
89NIW
U1
00

Table 1.4 Continued
Electronic Properties
Thermal Properties
Physical
Properties
Material
e/t„
@lMHz
tan 6
@lMHz
Volume Res.
(O-cm)
Breakdown
Voltage
(V/jrni)
Thermal
Con.
(W/m°Q
CTE
(ppm/“C)
Process
Temp. (°Q
P
(g/cc)
Flexural
Strength
(MPa)
Rcf(s).
Borosilicate Glass
3.74.9
1.2-4.0
3.04.3
SP=700850
2.1-2.2
5070
87CHO,89MAT,
89NIW.89SAN1.
89SAN2,
91KUM2,
91SHE2.91TUM
Barium Borosilicate
Glass
5.8
4.6
SP = 840
89NIW
Cordierite
Composition Glass
6.3
3.7-3.8
100
84MUS
Coming 7052
Borosilicate Glass
4.9
0.013
10”
2.09
4.6-53
SP=712
WP = 1128
2.27
79COR,84SCH2,
84SCH3.91 WIL1
Coming 7070
(Borosilicate Glass,
see Appendix I for
Composition)
4.1
0.0006-0.0025
>10”
3.2-3.9
Sir. Pi. =456
Ann. Pi. =
496
WP= 1068
2.13
79COR.88COR,
89MAT.91WIL1
Coming 7913
(96% Si02)
3.8
0.0004
>10”
0.75
Sir. Pt. = 890
Ann.
Pi. = 1020
2.18
79COR
E--Glass
6.4
0.0012
5.2
2.58
5.5
91ART
in
vo

Table 1.4 Continued
Electronic Properties
Thermal Properties
Physical
Properties
Material
@lMHz
tan 5
@lMHz
Volume Res.
(O-cm)
Breakdown
Voltage
(V/pm)
Thermal
Con.
(W/m°C)
CTE
(ppnv/°Q
Process
Temp. (°Q
P
(g/cc)
Flexural
Strength
(MPa)
Rcf(s).
Kyocera Matrix
Glasses
1) 74W% SiO„21W%
B,0„3W%
A1,0„2W% Other
2) 74W% SiO„17W%
B,0„3W%
A1,0„1W%
CaO,MgO,5W%
Other
3) 80W% SiO„12W%
B,0„2W%
A^Oj.lWt*
MgO,CaO,5W%
Other
1) 3.5
2) 3.8
3)4 6
89EMU
Lead Alumino Silicate
Glass
8.2-15
0.001
10"
8900-16000
88CER
SiOj (Amorphous)
3.78-5.4
0.0001-0.0005
10,!-10''
9652-25000
1.25-2.1
0.3-1.0
2.2
5.5-50
84SCH2.84SCH3
,88CER,88GER3
.89MAT.89SAN1
.89SAN2.91 ART
,91ZUS
Ceramic Matrix Composite Materials
96% Al,0„ 4% Glass
8.9-9.6
0.0001-0.0015
>10'J-10'6
13970
20-25.1
6.0-7.5
1550-1600
3.73-3.9
317455
84SCH2.84SCH3
,85KAW,87IWA,
871WA2.87KUR,
89SAN1.89SAN2
.90REC,
91DIL.91KUM2,
92RIC
o

Table 1.4 Continued
Electronic Properties
Thermal Properties
Physical
Properties
Material
OlMHz
tan b
@lMHz
Volume Res.
(fi-cm)
Breakdown
Voltage
(V//xm)
Thermal
Con.
(W/m°Q
CTE
(ppm/”C)
Process
Temp. (°C)
P
(g/cc)
Flexural
Strength
(MPa)
Ref(s).
92% A1,0„ 8% Glass
8.5
16.73
6.5
331
84SCH2.84SCH3
89SAN1.89SAN2
Aluminosilicate
(Derived from Ion
Exchanged Zeolite
Precursor)
5.2-6.5
0.0005-0.002
10'MO”
2.4-4.4
950-1050
89SUB
A12Os in CaO-Al20,-
I^Oj-SiOj Glass
Matrix (60W%
Glass/40W % A120„
Crystalllizes to Mainly
Anorthite, Narumi
LFC-I,LFC-II, and
LFC-III)
7.7
0.0003
>10”
> 6000 V/90
//m
2.51
5.5
880-900
2.9
196
86NIS.89NIS1,
89SAW
AI2Oj in Magnesia-
Calcio--A lumino—
Borosilicate Glass
Matrix (Proprietary
Composition,
Matsushita)
7.1
0.0025
1000
89SAW
A120, + CaZrO, in
Lead—Alumino—
Borosilicate Glass
Matrix (Proprietary
Composition, Hitachi)
9-12
0.001-0.003
850
89SAW

Table 1.4
Continued
Electronic
Properties
Thermal Properties
Physical
Properties
Material
tan 5
Volume Res.
Breakdown
Thermal
CTE
Process
P
Flexural
Ref(s).
(S’1 MHz
@lMHz
(ii-cm)
Voltage
Con.
(ppmTC)
Temp. ("O
(glee)
Strength
(V//*m)
(W/m°C)
(MPa)
AI20} + Forsterite in
Bario—Alumino¬
silicate Glass Matrix
5.0-6.5
0.0008-0.002
>10“
2.93
3.8-6.8
850-900
196
85KAW.89SAW
(Proprietary
Composition, Asahi
Glass)
Boron Doped Colloidal
2.664.53
0.0005-0.005
0 8-1.2
0.4-3.1
1050
2.19(@
642-663
89SAN1.89SAN2
Sol-Gel Silica
Full
kg/cm2
Density)
Borosilicate
49-5.7
2.5-6.0
4.04.5
850-1000
200-250
85NIW.89SAW,
Olass/AIjO,
9IKUM2.91VOK
Lead Borosilicate
7.5-7.8
0.002-0.003
>10“
>15000
3.6-6.0
4.2-6.1
900-950
3.1-3.15
295-300
84SHI.86UTS,
Glass/Al20,
90LEE.90SHI1,
(45W%/55W%, NEC)
90SHI2,91HAB,
91KUM2.91SH12
.91TUM
CERA COM 001
1) 4.0
1) 0.0066-
1) 2.2x10“-
1) 22 Kv/mm
1) 0.9
1) 3 8
Partially
1) 1.8
1) 177
86IWA.87IWA2
Epoxy Filled Porous
0.0068
3.5x10“
Sinter
Ceramics with glass
2) 4.2
2) 15.2
2) 7.0
Ceramics,
2) NA
2) 167
cloth outer layer
Impregnate
reinforcements
3) 4.0
3) 2.4
3) 10.0
w/Epoxy
3) 2.9
3) 206
(Machinable):
1) Cordicrite (30V %
Porous)/Epoxy
2) AIN (38V % Por-
4) NA
4) 2.8
4) 4.7
4) 2.4
4) 345
ous)/Epoxy
3) A1,0, (33V % Por-
ous)/Epoxy
4) SiC (30V % Por-
ous)/Epoxy
o\
to

Table 1.4 Continued
Electronic Properties
Thermal Properties
Physical
Properties
Material
e/e .
@lMHz
tan 6
@lMHz
Volume Res.
(17-cm)
Breakdown
Voltage
('V/fim)
Thermal
Con.
(W/m°Q
CTE
(ppm/“C)
Process
Temp. CQ
P
(g/cc)
Flexural
Strength
(MPa)
Ref(s).
Cordierite (92W%),
BijOj (8W%)
5.0
1000
(Reactive
Liquid
Sintering)
89DUP
Cordierite (a),
w/minor clino-
enslalite, (Crystallized
Glass-Glass Comp.,
50-55W% SiO„ 18-
23W% Al,Oj,18-
25 W% MgO, 0-3 W%
P,0,, 0-3W5S B,0,),
IBM
5.0
0.0025
5.0
3.0
950-1000
2.62
210
91KUM1,
91KUM2,
91SHE2.91TUM
Coming 7070 Glass
Matrix + Hex. BN
4.5-5.5
88CLA
DEC Glass Ceramic
(Proprietary
Composition) with
Hollow Glass
Microsphcres (Siü2
HGMs)
1) C8001-C8004
(with Si02 HGMs)
2) C8300 (without
Si02 HGMs)
1) 3.3-4.5
2) 6-8
1) 0.0006-
0.0016
2) <0.005
1) 101!-10,!
2) >101J
1) 238-657
V/mil
2) >700
V/mil
87KEL.89JUN
G\
U)

Table 1.4 Continued
Electronic Properties
Thermal Properties
Physical
Properties
Material
t/e,
@lMHz
tan 6
@lMHz
Volume Res.
(fí-cm)
Breakdown
Voltage
(V//*m)
Thermal
Con.
(\V/m00
CTE
(ppm/°C)
Process
Temp. (°Q
P
(g/cc)
Flexural
Strength
(MPa)
Ref(s).
DSP Cement +
Colloidal Silica
5.1 (Strongly
Humidity
and
Frequency
Dependent)
0.006
(Strongly
Humidity and
Frequency
Dependent)
89LEI
DuPont Green Tapeâ„¢
(Ceramic in Alumino—
Borosilicate Glass
Matrix, Proprietary
Composition)
7.8-8
0.002-0.003
2.20
7.9
850
3.02
127-206
85STE.86SAW,
87ROM.88BEN,
89SAW.89TYL,
90RIC
Electro—Science
REGAL (REinforced
Glass ALumina
Composite,
Proprietary
Composition)
-5 @ 1GHz
850
86BI.E
Electro-Science
(Proprietary Thick
Film Compositions)
1) D- 111
2) D 4911
3) TF 4000
(Porous)
1) 4.5
2) 4.3
3) 2.5-4 2
1) 0.0009
2) 0.0005
3) 0.0005-
0.0009
1) >10"
2) >10"
3) >10"
1) 1500
V/25pm
2) 1650
V/25¿im
2) 850
3) 930-985
90STE.90WAH
Ferro EMD
(Crystallizing Glass,
Proprietary
Composition(s))
4.5-5.8
0.002-0.003
> 10M-10"
>1000 V/mil
7.7
850
127
88SHA1.88SHA2
.91ALE
Glass Ceramics
(General)
4.0-8.0
0.002-0.004
14
4.5
<1000
100-200
91HAN.91SHI1,
91STE.92RIC
4*

Table 1.4
Continued
Electronic
Properties
Thermal Properties
Physical
Properties
Material
«/i.
tan 6
Volume Res.
Breakdown
Thermal
CTE
Process
P
Flexural
Ref(s).
@lMHz
@lMHz
(0-cm)
Voltage
Con.
(ppmTO
Temp. CQ
(g/cc)
Strength
(V//x m)
(W/rn'O
(MPa)
Kyocera Glass
1A) 4.7
1A) 9.2
1A) 900
1A) 98
89EMU
Ceramic Composites
(Utilizing Kyocera
Matrix Glasses Above,
IB) 4.8
IB) 11.5
IB) 925
IB) 118
50/50 Glass/Ceramic
1C) 5.3
lO 9.0
lO 950
lO 128
(by Weight))
2A) 4.9
2A) 2.2
2A) 950
2A) 128
1. A Si02/Glass 1
B Si02/Glass 2
2B) 5.1
2B) 2.4
2B) 950
2B) 137
C Si02/Glass 3
20 5.8
20 8.0
20 975
20 167
2. A Cordierite/
Glass 1
B Cordierite/
3A) 6.3
3A) 5.5
3A) 950
3A) 177
Glass 2
C Cordierite/
3B) 6.5
3B) 5.6
3B) 950
3B) 196
Glass 3
30 7.3
30 5.7
30 975
30 245
3. A A^O,/Glass 1
B AljOj/Glass 2
C AljOj/Glass 3
Kyocera LEC Glass
Ceramic (50/50
Mixture (by Weight)
5.2
0.003
>10"
> 15 kV/mm
3.0
950
2.4
177
89EMU
of Kyocera
Compositions IB and
3B Above)
Kyocera LTCC
(AljO, + Si02 in Lead
7.9
7.9
850
150
91SHE2
Borosilicate Glass,
Proprietary
Composition)

Table 1.4 Continued
Electronic Properties
Thermal Properties
Physical
Properties
Material
tit.
@lMHz
tan d
@lMHz
Volume Res.
(0-cm)
Breakdown
Voltage
(V//zm)
Thermal
Con.
(W/m°Q
CTE
(ppm/"C)
Process
Temp. (°Q
P
(g/cc)
Flexural
Strength
(MPa)
Ref(s).
LaFarge SECARâ„¢ 71
(Calcium Alumínate
Cement)
10.7-10.9
0.003-0.006
2.8x10”
1450
2.66
89SLI
Lead Borosilicatc
(45W%)/Alumina
(55 W%)
7.8
0.002-0.003
>10'*
>15000
3.6-6.0
4 2-6.1
900-950
3.1
300
91BAB.91KUM2
.91SHI2
Lead Glass + Hollow
Glass Microspheres
(Si02 HGMs, 80/xm
ave. size, 55-68 \%
Porosity)
3.28-3.93
0.004
530-550
1.18-1.70
89LEA
MDF (Macro Defect
Free Cements)
A. Without Hollow
Glass Microspheres
(Si02HGMs)
B With Si02 HGMs
A. 4-8
B. 4.7
A. 0.02-0.10
B. 0.02
86CRO
Matsushita Glass
Ceramic Crystallizes
to: Labradorite
(0.35NaAISi,O,-
0.65CaAl2Si2O,-
Major), Albite
(NaAlSi,Og--Minor),
and Anorthite
(CaA l2Si2Or-Minor)
(See Ref. for
Precursor
Compositions)
7.4
0.002
>10'*
> 15 KV/mni
2.93
6.12
900
3.07
245
88BAB

Table 1.4 Continued
Electronic Properties
Thermal Properties
Physical
Properties
Material
«/i.
@lMHz
tan 5
@lMHz
Volume Res.
(fl-cm)
Breakdown
Voltage
(V/jtm)
Thermal
Con.
(W/m°Q
CTE
(ppnt/°Q
Process
Temp. (°C)
P
(glee)
Flexural
Strength
(MPa)
Ref(s).
Mica (Glass Bonded)
6.4-92
0.0015-0.003
1014
10600-23700
0.50
10.0-14.5
2.6-3.8
117
88CER
Mullite/Cordierite/
Glass Composites (See
Ref. for Details)
5.1-7.5
0.002
2-4
1.5-4.5
1400-1550
2.5-32
150-190
84MUS.89AND
Mullite/Glass (72W%
Mullitc, 28W% Glass,
Glass Composition,
90W% SiO„ W%
Al^O,, 2W% MgO),
Hitachi
5.9
3.5
3.5
1600-1650
2.75
215
91FUJ
Murata Proprietary
Composition (contains
BaO, Si02, A^O,,
CaO, and B2Oj)
6.1
0.0007
8
950-1000
89SAW
NEC Proprietary
Compostions (Glass
Matrix with either
1)A12Oj, 2)Cordierite,
or 3)Si02(Quartz)
Ceramic Filler (see
87SHI)
1)7.8
2) 5.0
3) 3.9
1) 0.003
2) 0.005
3) 0.003
1) >1014
2) >10”
3) >10”
1) 4.2
2) 7.9
3) 1.9
1) 900
2) 900
3) 900
1) 3.10
2) 2.40
3) 2.15
1) 343
2) 147
3) 137
87SH1.88SHI,
89SAW
NGK C-01 or FC-01
Cordierite in Glass
Matrix (Crystallizes
From Proprietary
ZnO-MgO-AljOj-SiOj
Glass)
5.0-5.6
0.0013
5x10”
2.51
2.4-3.0
900-950
2.56
170-200
85KON.89KON
Porcelain
5-6.6
0.008-0.02
10'4
6100-13000
1.6-2.5
4.4-6.0
1250-1450
2.4
83-90
84SCH2,84SCH3
,88CER,89SAN1,
89SAN2

Table 1.4 Continued
Electronic Properties
Thermal Properties
Physical
Properties
Material
tit,
@lMHz
tan 6
@lMHz
Volume Res.
(O-cm)
Breakdown
Voltage
(V//xm)
Thermal
Con.
(W/m 0O
CTE
(ppm/°0
Process
Temp. (°Q
P
(glee)
Flexural
Strength
(MPa)
Rcf(s).
Porous Vycor
2.6-35
0.001-0.005
1.45-1.5
79S1M.86CRO,
87MOH,
89YAM2
Pyroceram
5.5-6.3
0.0017-0.013
10"
9900-11900
1.67-3.67
0.2-4.0
2.4-26
248
88CER
Quartz + Borosilicate
Glass + Cordierite
(NEC, Proprietary
Compositions):
A. With Porosity:
1) 15W% Si02
Glass, 20W%
Cordierite
Glass,65W%
Borosilicate
Glass
2) 35W% Si02Glass,
65W% Borosilicate
Glass, 0W%
Cordierite Glass
B. Without Porosity
A:
1) 2.9-4.20
2) 3.2-4.1
B. 4.4
A:
1) 0.002
2) 0.002
B. 0.002
A:
1) 10'°-10"
2) 10'"
A:
1) 65-150
KV/cm
A:
1) 3.2
2) 1.5
B. 3.2
A:
1) 950
2) 950
A:
1) 58.8-
127.5
2) 68.6-
110.8
B. 157.0
89YAM2,
90KAT.91TUM.
91SHI2
Silica, Air
(Porosity Range of
-5 V% to —85 V%)
1.54-4.3
0.008-0.056
87MOH.87YAR,
88GER3.89CAO,
89DAS
Silica (Sol—Gel,
Partial—to—full
Density)
1.6-7.05
0.0015-0.05
>10l!
376 V/^m
(Film)
500-1200
(Film)
2.20
86CHA.86CRO,
86DAS.87MOH,
88MOH.89CAO,
91SHO
03
00

Table 1.4 Continued
Electronic Properties
Thermal Properties
Physical
Properties
Material
«/«„
@lMHz
tan 5
@lMHz
Volume Res.
(ii-cm)
Breakdown
Voltage
(W/fim)
Thermal
Con.
(W/m°C)
CTE
(ppm/'Q
Process
Temp. (°Q
P
(g/cc)
Flexural
Strength
(MPa)
Ref(s).
Taiyo Yuden
Proprietary
Composition (Contains
A^Oj, CaO, Si02,
MgO, and B20„
6.7
0.001
4.8
900-1000
89SAW
Tektronix Proprietary
Glass Ceramic
5.8
0.0016
>10"
17780
2.10
4.8
850-900
2.60
214
91DIL
Toshiba Proprietary
Composition (Contains
BaO, Sn02, Ti02,
BjOj)
7-13
0.0005-0.0008
850-1050
89SAW
Wollaslonile (Derived
from 80W% Cement,
20W% Si02, Cement
Composition, 48.4W$
CaO, 5.8W% MgO,
12.4W% Al20„
30.6 W% SiO¡)
-5
9.4
800-900
1.85-2.70
89PER1,
89PER2.91TUM
ZnO/Cordierile
(Proprietary
Composition, NGK)
5.2-55
0.001
I.5-3.0
900-1000
89SAW
Ceramic Coated Metal Composites
CERCIC (Ceramic
Coated, Copper Clad
Invarâ„¢, Texas
Instruments)
7-9
0.0003-0.003
10"
500 V/mil
850
(Electro¬
phoretic
Deposition)
87SHU

Table 1.4 Continued
Electronic Properties
Thermal Properties
Physical
Properties
Material
ele.
@lMHz
tan 6
@lMHz
Volume Res.
(fl-cm)
Breakdown
Voltage
(V/fxm)
Thermal
Con.
(W/m °Q
CTE
(ppm/°C)
Process
Temp. (°C)
P
(g/cc)
Flexural
Strength
(MPa)
Ref(s).
MCS (Metal Core
Ceramic Coated
Substrate, Sun Wave
Industrial)
7.5-8.5
0.005-0.01
10"
4000V
@ 190/xm
10-120
12.0-14.0
900
(Electro¬
phoretic
Deposition)
86SAT.870KA
PCS (Porcelain Coated
Steel, RCA)
7.5-8.5
0.005-0.01
10"
4000V
@\90nm
1.4
(Porcelain)
70 (Steel)
10.0-14.0
800-900
(Electro¬
phoretic
Deposition)
81HAN
SCCMS (Selective
Ceramic Coated Metal
Substrate, Allied
Signal)
6.5
0.006
6.3x10”
400-600 V/mil
6-13
1000-1250
(Thick Film)
86TEA
Polymeric Materials
BCB
(Bisbenzocyclobutene,
Polycon)
2.7
90REC
Epoxy
3.4-36
0.024-0.032
10'MO”
91ZUS
FLAREâ„¢ (Fluorinated
poly(arylethers)
2.62-2.66
65
91HOR
General Polyimide
(‘ Low CTE
Polyimide, Hughes
Aircraft)
2.94.42
0.002
> 10,s
> 5000 V/mil
0.17-0.47
28-50
3.0'
Tg >400
89BAC.89HIM,
90GAG
Kaptonâ„¢ (Polyimide)
3-4
0.01
10”
177800
91ZUS
Lcxanâ„¢
0.19
67.5
1.30
90LEE
Mylar
0.14
16.9
1.38
90LEE

Table 1.4 Continued
Electronic Properties
Thermal Properties
Physical
Properties
Material
(/«.
@lMHz
tan 6
@lMHz
Volume Res.
(0-cm)
Breakdown
Voltage
(V//xm)
Thermal
Con.
(W/m°Q
CTE
(ppm/'O
Process
Temp. (°Q
P
(g/cc)
Flexural
Strength
(MPa)
Ref(s).
Nylon
0.23
90.0
1.13
90LEE
Polyethylene
2.2
0.0003
10'*
12700
91ZUS
PQ-100
(Polyquinoline)
2.57-3.0
91HEN
Silicone
2.9-3.7
0.003-0.005
101S-10"
7620-17780
91ZUS
Teflonâ„¢ AF2400
(Poly(tetrafluorethyl-
ene-co-per-
fluorodimethyl-
dioxole))
1.9
0.00008
80-100
91ZUS
Teflonâ„¢ ETFA
(Poly(ethylene-co-
telranuorocthy lene))
2.6
0.005
113
1.7
91ZUS
Tenonâ„¢ FEP
(Poly(tetranuoroethyl-
ene-co-
hexanuoropropylene))
2.1
0.0004
182
2.15
91ZUS
Tenonâ„¢ PFA
(Poly(tetranuorcthyl-
ene-co-
pernuoropropylene
vinyl ether))
2.05
0.0002
184
2.15
91ZUS
Tettonâ„¢ PTFE
(Polytetra-
nuoroc thy lene)
2.05-2.1
0.00009-
0.0001
10"
10922
0.2-0.21
90-156
2.13-2.2
87CH0.88GER3.
88WAN.90LEE,
91ART.91ZUS

Table 1.4 Continued
Electronic Properties
Thermal Properties
Physical
Properties
Material
tU0
@lMHz
tan 5
@lMHz
Volume Res.
(O-cm)
Breakdown
Voltage
(V/fim)
Thermal
Con.
(W/m °Q
CTE
(ppm/°C)
Process
Temp. (°C)
P
(g/cc)
Flexural
Strength
(MPa)
Ref(s).
Triazine
(Photodefinable
Polymer, ATT)
3.6
>3.7x10"
36
0.2
Tg = 150
(Thermal
Stability to
180)
88IAF
Polymeric Matrix Com
Dosites
Epoxy/Glass
4.0-5.8
0.02-0.045
>10"
10160
0.2-0.26
9.9-72
1.8-1.96
441
87IWA2.88IBR,
88WAN.90LEE,
91ZUS
Epoxy/Kevlar
6-7
88IBR
Epoxy/Nextcl
7.4
881BR
Polyimide/Glass
4.2-4.8
0.01
10"
17780
11-14
88IBR.91ZUS
Polyimide/Kevlar
3-7
88IBR
Miscellaneous Materials
Air
1.0
0
0.024-0.025
2000
~0
85WEA.87MOH,
88GER3.89MAT,
90GAG
Helium (He)
0.149
90GAG
Water (H,<))
-78
BP=100
1.0
90REC
Aluminum (Al)
138-250
22.0-23.4
2.71
90LEE.90REC,
91WIL1
Beryllium (Be)
163
12.2
1.82
90LEE
Beryllium/Copper
(Be/Cu)
106
39.6
8.21
90LEE
M

Table 1.4 Continued
Electronic Properties
Thermal Properties
Physical
Properties
Material
@lMHz
tan 5
@lMHz
Volume Res.
(fl-cm)
Breakdown
Voltage
(V/pm)
Thermal
Con.
(W/m°Q
CTE
(ppm/°C)
Process
Temp. (°Q
P
(glee)
Flexural
Strength
(MPa)
Ref(s).
Cadmium (Cd)
91
13.1
8.62
90LEE
Carbon Steel (1010)
58
11.5
8.02
90LEE
Copper (Cu)
1.72x10*
368-398
16.7-17.6
<100,
MP = 1084
(Reducing
Atmosphere
Required)
8.90-8.92
84SCH2.84SCH3
,85WEA,87CHO,
90GAG.90LEE,
90REC.91KUM2,
91WIL1
Chromium (Cr)
20x10s
66.9
6.3
MP = 1900
84SCH2.84SCH3
Gold (Au)
2.2-2.35x10s
297-306
14.0-14 2
< 1000,
MP= 1064
18.88-
19.29
84SCH2.84SCH3
.85WEA.90BUR.
90LEE.91KUM2
Gold/Tin (Au 80%/Sn
20%)
57
15.9
90LEE
Gold/Silicon (Au
97%/Si 3%)
27
12.3
90LEE
Kovarâ„¢
16.3-21
13.9-49
8.16-8.84
90LEE.91W1LI
Lead (Pb)
22x10s
MP = 327
11.34
85WEA.90BUR
Lead/Silicon
(Pb 95%/Si 5%)
63
29.0
90LEE
Magnesium (Mg)
86
26.5
1.80
90LEE

Table 1.4 Continued
Electronic Properties
Thermal Properties
Physical
Properties
Material
e/e.
@lMHz
tan 6
@lMHz
Volume Res.
(Q-cm)
Breakdown
Voltage
(V/n m)
Thermal
Con.
(W/m °Q
CTE
(ppm/°C)
Process
Temp. (°Q
P
(g/cc)
Flexural
Strength
(MPa)
Ref(s).
Molybdenum (Mo)
5.2x10®
146
5.0-6.0
>1500,
MP = 2610-
2625
(Reducing
Atmosphere
Required)
12.2
84SCH2.84SCH3
.85WEA.90BUR,
91KUM2
Nickle (Ni)
6.8-7.8xia6
(Magnetic, has
large skin
effect)
75-92
13.1-13.3
MP= 1452-
1455
8.84-8.90
84SCH2.84SCH3
.85WEA.90BUR
Palladium (Pd)
10.8x10®
71.1
11.0
MP= 1550-
1554
12.02
84SCH2.84SCH3
.85WEA.90BUR
Platinum (Pt)
10.6x10®
71.1
9.0
MP= 1772-
1774
21.45
84SCH2.84SCH3
.85WEA.90BUR
Silver (Ag)
1.59x10®
418-420
19.0-19.7
<1000,
MP = 962
10.5
84SCH2.84SCH3
.85WEA.90BUR,
90LEE.91KUM2
Silver/Palladium
(Ag/Pd)
>20x10®
>19.0
<1000
85WEA.91KUM2
Stainless Steel
16
16.0
8.02
90LEE
Tungsten (W)
5.5x10®
200.8
4.5
>1500,
MP = 3410-
3415
(Reducing
Atmosphere
Required)
19.35
84SCH2.84SCH3
.85WEA.90BUR,
91KUM2

CHAPTER TWO
THEORETICAL AND TECHNICAL REVIEW
2.1 Overview
This chapter outlines selected theoretical and technical issues
important to this project. The microstructure desired in the porous,
glass+ceramic composite system is illustrated in Figure 2.1. Figure 2.2
outlines the process by which said composites are produced. Figure 2.2
also delineates the important factors involved in each processing step.
The topics that are discussed in this chapter are depicted in bold faced
italic print. The other topics mentioned in Figure 2.2 are not
discussed since it is assumed that the reader has sufficient knowledge
in said areas. Further information may be obtained from the references
accompanying said topics if needed.
2.2 Synthesis and Processing of Uniform Polystyrene Latex
Microspheres (UPLMs)
Spherical particles are currently utilized in several applications
such as printer inks, and time-released drugs, etc. Hollow spherical
particles, as well as organic spherical powders, are also used as
composite components in applications requiring low density, rigid
materials. There are several review articles in the literature on the
subjects of solid spherical fillers [78RYA1] and hollow spherical
fillers [78RYA2,86SMI] as well as composites containing them [85VER],
Due to the reasons outlined in Chapter 1, only uniform polymeric
microspheres were deemed suitable for this project. Furthermore, other
research [89YAM2,90KAT] has revealed that the best uniform polymeric
microspheres for this application are those made of polystyrene.
75

Microstructure
Green Microstructure (dispersant omitted)
A. Pure B-S Glass
B-S Glass/Si 3N.
,N Cluster
J 4
B. B-S Glass/Latex UPLM
D. B-S Glass/Si 3N4/Latex UPLM
Figure 2.1
Depiction of the glass+ceramic, controlled porosity
microstructure desired

77
A. Constituent Powders
1. Glass 2. UPLM 3. Silicon Nitride
D. Suspension Processing
and Casting
E. Green Characterization
F. Thermal Processing
G. Characterization
Topics of Research:
A. General:
Density, Size, Size Distribution,
Surface Area, Structure [76KIN,88FUN,
88REE,89DIN,90RIN,90WAR,92SHE]
A1:
Chemistry [88REE]
A2:
Synthesis and Processing
B:
Surface Area, Structure, Chemistry,
Density [76KIN,88REE,91SEA]
C:
Particle Packing
D:
Dispersion Systems,Rheology,
Solids Loading [76KIN,81SCH,88FUN,
88REE,90GOO,90RUY,91 HOF,91KUR,
91 RUS]
E:
Settling, Segregation
Structural [56FAT1,56FAT2,56FAT3,
76KIN,88REE,91MIK,91SEA,91TSA]
F:
F1. Pyrolysis:
Thermogravimetric Analysis,
Differential Thermal Analysis
Pore Structure, Surface Area [76KIN,
88REE,89SER,89TUM3,91TUM]
Pore Percolation, Pore Clustering,
Pore Packing
F2. Viscous Sintering
Sintering Rates, Differential Sintering
Microstructura! Evolution
F3. Oxidation
Oxidation of S¡3N4 Powder [89SOM]
G:
Microstructural [53FUL,68DEH,88REE]
Mechanical
Dielectric
Process flow diagram for production of controlled
porosity composites, and delineation of important
factors for each processing step; topics depicted in
boldface italic are discussed in this chapter
Figure 2.2

78
There are several methods for synthesizing uniform particles. The
literature contains several review articles on the subject
[68STO,80UGE,82OVE]. More specifically, there are several methods by
which uniform polystyrene latex microspheres (UPLMs) may be produced
[85LOK,86TSE,88LU,89FER]. More information about the properties and
applications of uniform latex particles is contained within references
87BAN2 and 88MIC as well.
As will be shown in Chapter 4, preliminary research for this
project [90RAN] indicated that the UPLM particles should be
approximately 4 pm (minimally 2 pm) in diameter in order to avoid
producing obscured porosity. Furthermore, it was decided that the
maximum UPLM diameter, used for included porosity, should be less than
10 pm in order to maintain surface smoothness requirements. Therefore,
it was necessary to either find or invent a reliable and reproducible
method for the synthesis of UPLMs in the size range between 2 and 10 pm.
Fortunately, researchers have found synthesis methods which satisfy the
above criteria [85LOK,86TSE,88LU]. Said synthesis techniques involve
the dispersion polymerization of styrene in EtOH-based solvents.
Dispersion polymerization is the only currently known method which may
be used to produce UPLMs in the size range of interest via a single set
of processing steps [85LOK], Table 2.1 depicts the differences between
dispersion, emulsion and suspension polymerization methods.
The synthesis methods of Lu et al. and Tseng et al. [86TSE,88LU]
involve dispersion polymerization via an addition polymerization
mechanism in various mixtures of pure EtOH and stabilizer and/or
costabilizer while the method of Lok and Ober [85LOK] involves
dispersion polymerization of UPLMs via an addition polymerization
mechanism in solvent solutions of ethanol and methyl cellosolve mixed
with hydroxypropylcellulose (100,000 mw) as a dispersant.
Preliminary research, investigating both of the aforementioned
dispersion polymerization methods for synthesis of UPLMS, resulted in

79
Table 2.1
Comparison of the Different Types
of Particle Polymerization [85LOK]
Emulsion
Dispersion
Suspension
Monomer
Droplets
Micelies/Particles
Little in Medium
Particles
Mostly in
Medium
Droplets
Little in Medium
Initiator
Mostly in Medium
Particles and
Medium
Particle/Droplet
Stabilizer
May Be Present
Necessary
Necessary
Surfactant
Present
None
None
Initial
Homogeneity
Multiple Phase
Single Phase
Dual Phase

80
the conclusion that the method of Lok and Ober [85LOK] was far superior
for production of UPLMs in the desired size range on the bases of
monodispersity, amount of agglomeration and reproducibility of UPLM size
and dispersity from batch to batch. Therefore, the method of Lok and
Ober was utilized to produce UPLMs of various size for the current
study. The synthesis method of Lok and Ober is described in further
detail in Chapter 3 as well as in 85LOK.
Figure 2.3 illustrates the dispersion polymerization process.
Basically, dispersion polymerization is an addition polymerization which
includes nucleation and growth steps. The dispersity of the process
depends upon the monomer and initiator concentrations as well as on the
dispersive abilities of the dispersant, which is necessarily a graft
copolymer. Dispersion polymerization involves the nucleation and growth
of polymeric spheres from a single phase solvent via addition reaction.
As with other nucleation and growth processes, the size of each polymer
nucleus must surpass a critical radius before said nucleus becomes
stable. The critical nucleus size depends heavily upon the total system
solubility index (including that of the monomer itself) [85LOK].
Furthermore, growth processes apparently occur without further
nucleation [85LOK],
The major difference between dispersion polymerization and other
polymerization methods is that dispersion polymerization starts as
single phase homogeneous system. With dispersion polymerization it is
necessary that the monomer be soluble in the solvent while the polymer
not be soluble in the solvent. Particle size control with the
dispersion polymerization method is dependent mainly upon four factors,
monomer versus polymer solubility, reactant composition, temperature,
and solvent medium [85LOK].
Said process offers the advantage that it does not require
oligomer swelling, etc., in order to obtain the relatively large
particles and, therefore, is denoted a single step process.

81
2
'i HYDROGEN
\ ABSTRACTION i
3
GRAFT
FORMATION
Monomer
a-
i
\
)
4
/
t
I
I
NUCLEATION
Monomer
i
l /
I
I
PARTICLE
GROWTH
Monomer
Figure 2.3
Schematic illustration depicting nucleation and growth
of a UPLM via dispersion polymerization [85LOK]

82
The method of Lok and Ober offers a further advantage in that the
dispersion mechanism used is steric in nature (ie. non-electrostatic)
and, thereby reduces ionic impurities in the resultant UPLMs. Ionic
impurities are deleterious because they could leave ionic residues
subsequent to pyrolysis. These residual ions would increase K as well
as decrease both p and the dielectric breakdown strength.
Lok and Ober were able to produce exceptionally monodisperse
polystyrene latex particles of sizes ranging from 3 to 9 pm by varying
the solution solubility parameter (6) from 11.5 to 11.9 [85LOK]. The
solubility parameter is resultant from an accumulation of dispersion
forces (6d), polar forces (Sp), and hydrogen bonding forces (6H)
according to the relation:
62=6d+6p+6^
Table 2.2 lists the solubility parameter as well as other pertinent data
of selected dispersant liquids that Lok and Ober used for dispersion
polymerization. Figure 2.4 depicts a ternary composition diagram,
between EtOH, styrene and MeCell (methyl cellosolve), which outlines
the compositions at which their latexes were monodisperse as well as the
sizes of the respective UPLMs.
It is evident, from the above and from Figure 2.4, that the
dispersion polymerization method of Lok and Ober [85LOK] fulfills the
criteria necessary for the UPLMs used in this project. Furthermore,
through judicious mixing of the UPLMs (as described in the next
section), a polydisperse latex could be produced for maximum packing
efficiency (PE), thereby allowing an investigation of the effect of
included pore size distribution, or possibly pore packing, upon included
porosity.

83
Table 2.2
Solubility Parameters of Selected Solvents [85LOK]
Solvent
Dielectric
Constant
(K)
Dipole
Moment
(D)
6
(cal/cm3)1/2
6d
5P
6«
Dimethoxy-
ethane
8.6
Tetrahy-
drofuran
7.32
1.63
9.1
8.2
2.8
3.9
Styrene
9.3
9.1
0.5
2.0
Cellosolve
2.08
10.5
7.8
4.5
7.0
t-Butanol
10.9
1.66
10.6
Me Cell
16
2.2
11.4
7.9
4.5
8.0
Isopro¬
panol
18.3
1.66
11.5
Ethanol
24.3
1.69
12.7
7.7
4.3
9.5
Methanol
32.6
1.70
14.5
7.4
6.0
10.9
Water
78.5
1.84
23.4
6.0
15.3
16.7
Poly¬
styrene
2.5
8.9

84
Me Cell
Solubility
Concentrations (V%)
Particle
Parameter
Sample
Styrene
EtOH
Me Cell
Size (pm)
6, (cal/cm3)
1
10
51
39
1-3
11.9
2
15
71
14
1-4
12.1
3
15
60
25
3
11.9
4
15
42.5
42.5
7
11.7
5
15
30
55
9
11.5
6
15
14
71
1-50
11.3
7
20
40
40
5-20
11.6
8
26
44
30
5-20
11.5
9
26
74
0
1-5
11.9
10
33
67
0
7-9
11.7
Ternary illustration depicting the relative dispersity
of UPLMs synthesized via dispersion polymerization in
the EtOH-MeCell-styrene system [85LOK]
Figure 2.4

2.3 Particle Packing
85
2.3.1 Monosized Spheres
2.3.1.1 Ordered Packing
Ordered packing of hard, uniform spheres may occur in five
different configurations: cubic, orthorhombic, tetragonal, pyramidal,
and tetrahedral [88REE]. Figure 2.5 illustrates the various
configurations and properties of said ordered packing configurations.
Table 2.3 depicts some of the characteristics of two types of ordered
packing structures: cubic and tetrahedral.
However, hard spheres do not naturally pack in the long range,
ordered structures characteristic of crystalline materials. Several
researchers have tried to explain the random packing of monosized
spheres in terms of mixtures of the above ordered structures
[29SMI,61MCG,80PAT], but while three-dimensional, packed beds of
monosized spheres may exhibit short range order, or even order
throughout a dimension, (depending upon the packing method, or the
packing container configuration used, etc.) they are essentially
considered to pack in random order over the long range
(60BER,62EPS,65LEV].
2.3.1.2 Random Packing
There are two types of random packing for non-interacting, hard
spheres, random close packing (RCP) and random loose packing (RLP).
Random packing (RP) is defined as packing that has no characteristic
ordering. These two types of random packing are considered to be the
upper and lower limits to the packing efficiency of randomly packed
monosized spheres, and are quite sensitive to both the size and
configuration of the bed container as well as the methods used to place
the spheres, in said container, in their final state. The generally
accepted packing efficiencies for these two types of packing are 64V%
and 60V% for RCP and RLP respectively [60SCO,61MCG].

86
1. Cubic
2.Orthorhombic
(Single Staggered)
3.Tetragonal
(Double Staggered)
4.Pyramidal
(Cubic Close Packing)
5.Tetrahedral
(Hexagonal Close Packing)
«
Packing Configuration
CN
Packing
Density (V%)
1
Cubic
6
52.4
2
Orthorhombic
(Single Staggered)
8
60.5
3
Tetragonal
(Double Staggered)
10
69.8
4
Pyramidal (Cubic
Close Packing)
12
74.0
5
Tetrahedral (Hex¬
agonal Close Packing)
12
74.0
Figure 2.5
Illustration of the five possible types of ordered
packing of monosized hard spheres [80PAT,88REE]

87
Table 2.3
Some Parameters of Simple Cubic and Tetrahedral Packings of
Uniform Spheres [88REE]
Parameter
Cubic
Tetrahedral
Entry Pore Area
0.2 ID2
0.04D:
Entry-Pore-Area
71D2
4
0.26
0.05
Entry-Por e-Diame ter
D
0.51
0.22
En try-Sphere-Di ame ter
D
0.42
0.15
Void Fraction
0.48
0.26
Volume-Voids
Vol ume-Spheres
0.92
0.34
^Primary-Sphere
^' IntersCiCial-Sphere-SiCe
1.37
4.44
D = Sphere Diameter

88
The upper limit of random packing (RCP) is never reached in reality, due
to packing friction and interaction with the container. The effect of
the container interaction may be significantly reduced by using a
container having a width dimension that is relatively large compared to
the sphere diameter (usually several hundred times larger) as well as
through utilization of containers having walls which are either modified
with indentations, or that have the ability to conform (i.e. balloons,
etc.) [3OWES,60SCO,61MCG,69SCO]. Figure 2.6 illustrates the effect of
the relative container size on the packing density of RCP beds of
monosized spheres. The lower limit to random packing of uniform spheres
(RLP) designates the limit below which packed beds cannot support
themselves without either cohesion or adhesion [60SCO,80SHA].
In practice, all randomly packed uniform spherical particles will
exhibit packing efficiencies (PEs) somewhere between the RCP and RLP
limitations. Most research indicates RP packing efficiencies of
approximately 61 to 63 V% for beds formed by tamping [3OWES,60SCO,61MCG,
88REE] and approximately 57 to 59 V% for beds formed by careful pouring
[60SCO,62EPS). This will occur, in packed beds of monosized spheres,
regardless of sphere size, unless surface area to volume ratio sensitive
factors, such as electrostatic repulsion, etc. become significant (i.e.
as in many micron to sub micron particles). In most instances involving
packed beds of uniform spheres, the packing is RCP and the generally
accepted packing efficiency is 62.5 V% [61MCG,88REE].
2.3.2 Packing of Multimodal, Discrete Distributions of Spheres
Furnas is generally believed to have introduced the first packing
model (the Furnas model) which predicts the random close packing of
multimodal beds of spheres [28FUR,31FUR]. Westman and Hugill also
introduced an analogous packing model at about the same time [30WES],
and it is believed that the actual mathematical treatment of Westman and
Hugill actually preceeded that of Furnas by about one year [79FED].

89
70
>
o
c
0
‘o
â–  mmm
S—
H—
LU
O)
C
O
CD
Ü_
65
60
55
50
45
D/d
(Container Diameter \
Sphere Diameter /
Figure 2.6
Effect of relative container size upon the packing
efficiency of random close packed uniform spheres
[61MCG]

90
Both treatments are similar, however. Therefore, they both shall be
denoted as the Furnas model, henceforth, in order to follow the more
generally accepted convention. The Furnas model involves packing of
smaller spheres within interstices produced by larger spheres. A third,
smaller size of spheres may also be packed within the interstices
between either medium size spheres and large spheres, or between medium
size spheres. The common denominator for this type of packing is that
the next smallest size of spheres packs "tightly" within the interstices
created by larger size spheres. This type of packing shall be denoted
type 1 packing. Another type of packing (type 2 packing) occurs when
the interstices, created by the large particles, are much larger than
the next smallest size of spheres. Figure 2.7 illustrates these two
multimode packing relationships. The number of size modes applicable is
unlimited as long as the size ratio of each successively smaller size
sphere addition is significantly smaller than the next nearest larger
size.
The size ratio of the smaller sphere, to the interstice is
important in two senses. First, the smaller sphere must be able to fit
through the interstice opening, if the smaller sphere is not already
there before the interstitial structure formed. Interstitial placement
prior to stable bed formation is possible in the case of casting
processes, but not when using the methods (i.e. adding smaller particles
and vibrating after the large sphere packed bed is formed) used by most
researchers in this field [30WES,60BER,60SCO,61MCG,65AYE,66AYE,69SCO,
80PAN]. Secondly, packing of the smaller spheres within interstices
will be affected by the relative size of the containment volume (i.e.
the interstice), just as the PE of monosized spheres is affected by the
relative size of the packing container. Thus, PE increases as the
relative size of the interstices increase, in a packed bed of spheres.
Figure 2.8 illustrates this relationship in terms of relative size.
Interestingly, Figure 2.8 is similar to Figure 2.6, without the

Type 1 Packing Examples
Square Packing Triangular Packing
Type 1 Packing: d ¡ > 0.1 d ; i
Type 2 Packing Example
Type 2 Packing: d ¡ < 0.1 d
Figure 2.7
Illustration of the two types of multimode packing
[80PAT,88REE]

92
Diameter of Coarse Spheres
Diameter of Fine Spheres
Figure 2.8
Illustration of the effect of relative sphere size
upon the maximum packing efficiency of randomly packed
beds of bimodal spheres [61MCG]

93
discontinuities, and that both asymptotically approach a maximum near a
value of approximately ten.
Both Furnas [31FUR], and Fedors and Landel [79FED] have developed
equations that estimate the packing efficiency of random close packed
multimodal beds of spheres as a function relative sphere sizes. The
Furnas analog of this relationship, which assumes that all size modes
pack with the same efficiency in a monosized sense, and that the volume
fractions of each mode are chosen to maximize the packing efficiency, as
discussed below, is given by the equation:
(1 -PE) nlnPE(l-PE)
(1 ~PEn+1) [1- (1 -PEn) ]
1 2
(2.62iC n -3.2AK n) InK
_i 1
(1.0-2.6 2K n +1.62K n ) n2
where PE is the packing efficiency, n is one less than the number of
size modes and K is the ratio of the smallest to the largest sphere size
[79FED]. The numerical values of the above Furnas equation were
determined experimentally. The Fedors and Landel relationship,
describing the effect of relative sphere size upon the maximum packing
efficiency of a random close packed bed of multimodal spheres, is
described by the equation:
_i
PEmax=PE1+ (l-a1;2) U-PEjPEz+Ul-a^) (1 -a2#3) ] 2
1
x(l-pex) (l-PE2) PE3 + . . . + [ (l-al n) (l-a2 n) . . . (1 -an_1 x(l-PE±) (1 -PE2) . . . (l-PEn.1)PEn
where PE^ is the maximized packing efficiency, PE¡ is the packing

94
efficiency of sphere size i, and a^ is given by
where j is the respective term in the multiplication series for the
respective mode of size, i is the mode number of the particular series
set of interest (i.e. one series set per size mode), and r¡ is the
radius of sphere size mode i [79FED]. A comparison of both models is
illustrated in Figure 2.9 for a bimodal distribution of spheres, where
PE, and PE2 are set at a value of 0.60. It may be seen that, for a
radius ratio (r) of less than 0.01, both models agree well, giving a
maximum packing efficiency of approximately 82%. This is reinforced by
the fact that the model of Fedors and Landel has the same characteristic
shape as that exhibited by the relation in Figure 2.8.
The Furnas model, and its numerous variations, may also be
utilized to determine the maximum packing efficiency (PE) of random
close packed beds of multimodal discrete distributions of spheres, as
well as to determine the relative amounts of each mode of sphere
necessary to accomplish said goal. The Furnas model utilizes the
normalized volumes (the inverse of the respective packing efficiencies)
for RCP beds of each discrete mode of spheres. For bimodal mixture of
spheres, said normalized volumes are used as the ordinate values of a
binary relationship that is analogous to a binary phase diagram. A
bisection is placed between the ordinate value for the pure coarser size
and the zero value of the normalized volume of the pure finer size. A
similar bisection is placed between the unit value of normalized volume
of the coarser size of spheres and the ordinate value of normalized
volume of the pure finer spheres. The intersection of these bisectors
is the indicator of both the minimum normalized volume (i.e. the maximum
in packing efficiency (PE^)) and the relative volume fractions of each
mode necessary to achieve PE^.

m«x(d/D)
95
loníd/D) I Smaller Sphere Mode Diameter
y \ Larger Sphere Mode Diameter
Note: PE is the Maximum Packing Efficiency
at the Diameter Ratio (d/D)
Illustration of both the Furnas, and the Fedors and
Landel models of packing efficiency, as a function of
relative sphere size, of a bimodal distribution of RCP
spheres [79FED]
Figure 2.9

96
Figure 2.10 illustrates the Furnas relationship for a two component
mixture of uniform spheres.
From Figure 2.10, the first bisector, mentioned above (i.e. Vc-F),
follows the equation:
where VNM is the normalized volume of the mixture, Vc is the normalized
volume of the pure RCP coarse spheres, and x is the volume fraction of
coarse spheres. The second bisector (Vf-1) follows the equation:
Vm=Vf~VfX+x
where Vf is the normalized volume of a RCP bed of pure fine spheres.
The maximum packing efficiency (PE^, = VNMmin) is found by setting the
two equations equal to each other, and solving for x, which results in
the equation:
â– ^inax
Vf
vc+vt-
where x,^ is the volume fraction of coarse spheres resulting in the
minimization of VNM (or PE^) .
If the packing efficiencies of both components of the binary
system are 0.625 (the generally accepted value for RCP beds of uniform
spheres [61MCG,88REE]), the volume fraction of the coarse spheres needed
to achieve PE^ is 0.727, and the volume fraction of the fine component
of uniform spheres needed to achieve PE^ is 0.272.

Percent Theoretical Density
97
62.5
65
70
75
80
85
90
95
100
100 80 60 40 20 0
Volume Percent Coarse Spheres
0 20 40 60 80 100
Volume Percent Fine Spheres
Figure 2.10
Illustration of the Furnas model for bimodal mixtures
of uniform spheres [30WES]
Volume of Packing (cm

The actual value of PE^, may be found by solving the reciprocal of
either of the above bisector equations for said value of x (x^), or
98
P£maX ^Aax '
For the above situation (i.e. PE,, equal to PEf which equals 0.625, or Vc
equal to Vf which equals 1.60), the value of PE^ is equal to 0.859 (V^
equals 1.16). Thus, the highest packing efficiency (PE^) achievable in
a mixture of bimodally sized spheres is 0.859. This would occur under
conditions of perfect tamping and mixing, using an infinitely large,
relatively coarse sphere size. Figure 2.10 illustrates the validity of
the Furnas model, compared to the work of various researchers, when used
to estimate PE in bimodal mixtures of spheres.
The Furnas model may be applied to mixtures of trimodal and
higher-modal, discrete distributions of monosized sphere components as
well. For a trimodal mixture of discrete sizes of spheres, the three
possible binaries are combined to form a ternary diagram, analogous to a
three dimensional ternary phase diagram (Figure 2.11). The ternary
surface through each of the ordinates (i.e. Coarse (C) Medium (M) and
Fine (F)) is a plane determined by the equation:
V=Vcx+Vmy+Vfz
where V is the ordinate value of the plane, V¡ is the normalized volume
of RCP monosized spheres of size regime i (i.e. coarse (c), medium (m)
or fine (f)). There are also three planes of minimization, necessary to
consider in said trimodal system, in order to determine PE^.

99
Medium
Figure 2.11
Illustration of the Furnas model for trimodal mixtures
of random close packed spheres [3OWES]

100
Said planes are denoted by the equations:
Vc=VcX
VrX+V'y
VF=x+y+Vfz
for the coarse (Vc) , medium (VM) and fine (VF) planes of normalized
volume minimization, where x, y and z are the volume fractions of the
coarse, medium and fine components respectively. The three planes
intercept at the point of minimum normalized volume (or PE,,,^) . Said
point (VNMmin), where Vc equals VM equals VF, is determined by the
relation:
The compositional values leading to VNMmm (PE,,^) are determined by the
relations:
y=
c
2 =

101
for the coarse (x), medium (y) and fine (z) volume fractions
respectively. If Vc equals Vm equals Vf the equation for VNM^ reduces
to the equation:
where VRCP is the general normalized volume of RCP uniform spheres.
By utilizing the simplification used for the bimodal system above (i.e.
the assumption that VRCP is equal to 1.60) the value of VNM ^ becomes
1.06, which corresponds to a PE^ value of 0.947 for a ideal packing of
a trimodal, discrete distribution of uniform spheres. The respective
volume fractions of each component of said trimodal mixture of spheres
is then 0.660, 0.247 and 0.093 for the coarse medium and fine spheres.
This model may be extended to n-modal systems, where PE^ is
determined from the equation:
where n is the number of size modes of the mixture. The corresponding
volume fractions of each component may be determined by the relations:
PEi
(1 -PEJ PEZ
-P-^inax
(1 -PEX) (1 ~PE2) . . . (1 -PEn.1)PEn
PEmax

102
where VF¡ is the volume fraction of size mode i, and PE¡ is the RCP
packing efficiency of mode i. Table 2.4 delineates the PE,^ values and
respective compositions, as well as experimental data, for multimodal
random close packings of spheres. The data of McGeary [61MCG] seems to
agree well with the predictions of the Furnas model. Said data is
always slightly lower than the prediction (as would be expected) and
always within 6% of the calculated PE^ values (see Table 2.4). Thus,
the Furnas model works well for multimodal RCP beds of spheres formed by
the method of successive additions with tamping. Furthermore, it is also
evident that the Furnas model predicts that component systems, having
more than four to five components, result in very little, if any,
increase in packing efficiency.
The Furnas model always over-predicts the packing efficiency of a
particle system. This is especially true for particle beds which were
formed by mixing of the particles prior to bed formation and for systems
utilizing non-spherical (mainly angular) particles. Messing and Onoda
[78MES1,78MES2] proposed a model to estimate corrections to Furnas-type
models necessary to more successfully estimate PE for packed beds of
bimodal particles, formed by mixing prior to bed formation [78MES1].
Messing and Onoda hypothesized that the Furnas model was legitimate in
localized regions. They hypothesized that the differences between
predicted and experimental values are due to compositional fluctuations
(i.e. mixing imperfections) in the particle bed [78MES1,78MES2]. By
splitting the Furnas bimodal composition diagram (see Figure 2.10) into
two regions, one following the PE due to the establishment of a stable
coarse particle structure (i.e. x values below VNM^ or Region I) and
the other due to a PE determined by the establishment of a stable fine
particle structure (i.e. x values above VNMmm or Region II), Messing and
Onoda hypothesized that a sampling of any small and discrete volume
element of a packed bed of spheres would necessarily fall into one of
the above two regimes.

103
Table 2.4
Packing Efficiencies and Compositions of
Random Close Packed Beds of Multimodal
Mixtures of Spheres [61MCG,79FED,88REE]
# Modes
VF,
VF 2
vf3
VF,
vf5
(%)
Calc.
Exp.
1
1.00
60.5
to
63.0
58.0
2
0.726
to
0.730
0.270
to
0.274
84.8
to
86.0
80.0
3
0.647
to
0.670
0.244
to
0.250
0.090
to
0.109
95.0
to
95.2
89.8
4
0.607
to
0.640
0.230
to
0.240
0.090
to
0.102
0.040
to
0.061
97.5
to
98.0
95.1
5
0.640
0.230
0.080
0.030
0.010
99.0
Notes:
1. Experimental Data From [61MCG], Sphere Size Ratio
320/39/7/1
2.
Calculated Data was Provided by [61MCG] and [79FED]

104
Messing and Onoda used either experimental values for the compositional
fluctuation values, or mathematically determined mixture functions to
estimate PE as a function of the distribution of particle compositions.
Karlsson proposed a different model to estimate the disparities
between the Furnas model and experimental data from beds made from
premixed discrete distributions of particles [70KAR]. He hypothesized
that the stable structure (i.e. x values below VNMmm) dilates as a
result of adding finer particles. Said dilation reduces PE^.
He further hypothesized this effect is most pronounced in the region
immediately encompassing VNMmlI1. Karlsson provided a factor to correct
for the "lattice" dilation upon adding fine particles to RCP coarse
particles as well as one to correct for the addition of coarse particles
to packed beds of fine particles (i.e. the dominant correction factor
for Region II above).
Ayer and Soppet later introduced a further correction to the
Furnas model, which provided a more correct estimate of the maximum
packing efficiency when using angular (as opposed to spherical)
particles [66AYE]. The equation, proposed by Ayer and Soppet, for the
packing of a discrete bimodal distribution of spheres is
PE=1.27 0-0.216e~°'312Dcon/D-0.737 e-°-201D/d
where is the container diameter, D is the diameter of the coarse
spheres and d is the diameter of the fine spheres. The relation, which
estimates PE^ for bimodal packings of angular (tetragonal shaped)
particles, is
PE=0.812- °'017 -0.037e
-0.207 ^20
D -0.01 Oe~°-09BD/d.
D

105
Table 2.5 illustrates PE^, for the Ayer and Soppet models for spherical
as well as angular particles, which may be satisfactorily modelled by
tetragonal shapes.
2.3.3 Continuous Size Distribution Particles
2.3.3.1 Ideal Packing
While it may not be possible to achieve the packing efficiencies
detailed above, it is of interest to be able to predict which particle
size distributions will pack with the greatest efficiency. This is
desirable when it is important to produce near-net-size shapes in the
green state. In order to maximize PE in a packed particle system,
manipulation of the particle size range as well as the shape of the
particle size distribution is necessary [88REE]. Andreasen and Andersen
were among the first to introduce an equation to predict the
distribution necessary to maximize PE [30AND]. In the Andreasen model,
the portion at a particle size is a constant fraction of the proportion
of the distribution that is finer than the size of interest. The
Andreasen equation is
CVFF= ( —— ) n
Tnax
where CVFF is the cumulative volume fraction finer, d is the particle
diameter, d^ is the maximum particle diameter of the distribution, and
n"1 is the modulus of the particle size distribution [ 88REE ] . The
research of Andreasen and Andersen indicated that, for a particular d,,^,
PE increased as the distribution modulus increased (i.e. porosity
decreased as n decreased). Their research indicated that practical
values for n were between 0.33 and 0.50. Thus, Andreasen and Andersen
discovered that wide size distributions of particles packed to greater

106
Table 2.5
Values of Maximum Packing Efficiency as Estimated
by the Models of Ayer and Soppet [66AYE]
Number
of Components
Maximum Packing Efficiency
Spherical Shapes
Angular (Tetragonal)
Shapes
1
0.635
0.635
2
0.867
0.812
3
0.951
0.903

107
efficiency than narrower ones, if both distributions were otherwise
identical. Sohn and Moreland later confirmed this conclusion by stating
that PE is dependent only upon the size distribution shape and extent
within a given system [68SOH]. Their research investigated the effects
of log normal and Gaussian size distributions of particles upon PE.
Particle shape was also found to be a factor effecting PE of a given
particle system. It was found that continuous distributions of angular
particles pack less efficiently than analogous, spherical mixtures of
particles.
Later, Funk and Dinger proposed a modification to the Andreasen
equation. They realized that the Andreasen equation was flawed in the
sense that it assumes that all distributions contain infinitely small
particles [88FUN]. Said modification included the addition of a minimum
particle size term to the Andreasen equation. This equation, frequently
termed either the Alfred equation or the Funk and Dinger equation, has
the following form:
CVFF=—
C-Cn
where d^ is the minimum size of the particle size distribution. Funk
and Dinger were able to produce a coal slurry particle size distribution
(having a d,,^ of 1pm and a d^ of 200pm and an n of 0.37) which
exhibited a PE of 0.90 [90ZHE). Neither Andreasen and Andersen nor Funk
and Dinger, offered a physical explanation of the distribution modulus
(n1) or reasons as to why a certain n value would give a certain PE,
however [90ZHE].
Zheng, et. al offered an elegant solution to explain the physical
basis of the distribution modulus [90ZHE]. Their model takes particle
packing models "full circle" in that it uses the Furnas model to explain
the basis of the distribution modulus. Said model further confirms the

108
empirical conclusions of Funk and Dinger as well (i.e. n values of 0.37
to 0.40 give the highest PE values for continuous size distributions).
Zheng, et. al envisioned that the continuous particle size
distribution, giving the greatest PE, is simply a summation of many
discrete Furnas models. Figure 2.12 illustrates this concept. After an
exhaustive derivation, Zheng, et. al derived a relation, identical in
form to the Alfred equation, that explains the physical meaning of n, or
the distribution modulus.
The Zheng equation states that
logi?
iog
where 0 is the interstitial pore fraction (0 = 1- PE), and R is the
particle size ratio of the particular Furnas model used. This model
assumes that 0 is a constant, regardless of particle attributes. The
value of 0 is estimated from the interstice volume of the largest and
smallest particle groups by the relation:
-log =
log^coarse
2
where coarse or fine). In the case that R is approximately 10, the above
relation for n reduces to
17 = -log(J).
Zheng, et. al found that n values of approximately 0.40 give maximum
packing efficiencies. This is quite similar to the values given by both
Andreasen and Andersen, and Funk and Dinger.

109
Discrete Furnas Groups Fill the Whole Particle Size Range
Figure 2.12 Illustration of the concept of applying discrete
Furnas models to a continuous size distribution of
particles in order to maximize packing efficiency
[90ZHE]

110
Therefore, as the interstitial volume for the particle bed is
reduced, the overall packing efficiency is increased. The effectiveness
of n is regulated by the particle size ratio (R) of the Furnas model
used to model said system. Both these results are quite logical and
totally in agreement with the packing discussions above. Thus, the
model of Zheng, et. al provides an interfacing between the theories of
Andreasen and Andersen, Funk and Dinger, and Furnas. The model of
Zheng, et. al is indirect, however, in that it provides for the effect
of particle angularity by allowing modification of the

Thus, further research in the area of particle packing of continuous
size distributions of angular particles would be prudent.
2.3.3.2 Hindered Packing
Particle packing may be hindered by several mechanisms, including
particle bridging or flocculation, container wall interaction,
interparticle friction or adhesion, particle anisometry, binder
interaction, and particle segregation. All these factors can only be
reduced, and not eliminated, in most real systems. It is sufficient
here to state that each factor should be minimized. There are several
reviews which cover these factors as they apply to real world situations
[76KIN,88REE,89SER,89TUM3].
2.3.4 Effects of Settling and Segregation
Settling, as in slip casting, allows for particle rearrangement
prior to the formation of a stable particle structure. In this sense,
settling is advantageous. However, formation of particle beds via
settling allows segregation to occur in systems having particles of
varying size and or density. Settling rates of particles may be
estimated by the stokes equation

Ill
9d2{Ps-Pj)
18rii
where g is the gravitational constant, p¡ is the density of either solid
particles (s) or the suspending liquid (1), d is the particle diameter
ti, is the viscosity of the suspending liquid, and V is the terminal
velocity of said particle in said suspending liquid [88REE]. The
Stokes relation is valid only for cases of laminar flow at the particle-
suspension liquid interface. Laminar flow occurs when the Reynold's
number (Re), at the interface, is less than 0.2. The Reynold's number,
in this instance is, determined by the equation:
Re =
(Vdp2)
’ll
For ceramic particles, the Reynold's criterion indicates that the upper
size boundary is approximately 50 pm [88REE]. Furthermore, the Stokes
relation is invalid in instances where there is particle interaction.
In ceramic particulate systems, in situations where it is desirable to
have conformity to the Stoke's relation (i.e. for particle sizing), the
solids loading is kept below approximately 5 V% for this reason.
It is evident from the Stoke's equation that particles of
different sizes and or densities will settle at different rates thereby
creating a segregated particle bed. Thus, in the settling of wide size
distribution particle systems, segregation is an inherent problem.
There are various methods by which segregation may be minimized in
settled systems of wide size distribution particles, but as mentioned
above, it is impossible to completely eliminate segregation in said
systems.
Segregation may be reduced by increasing the viscosity of the
suspending liquid as well as by reducing the settling distance.
Furthermore, in systems having relatively high solids loadings,

112
segregation may be reduced through particle interaction. A "bridging
structure" may occur, trapping the smaller or less dense particles in
with the larger or more dense particles.
2.4 Clustering and Percolation Theory
Percolation theories constitute an entire field of scientific
literature. Percolation is a universally important concept throughout
many scientific fields including, composite design, sol to gel
transformations, alloy and microstructure modelling, and mass transport,
etc. [83ZAL2,91SAV]. Initial percolation theories were all based upon
some type of n-dimensional lattice. Furthermore, these discrete
percolation models were based upon the filling of either allowed sites
or bonds between allowed sites. Figure 2.13 illustrates each type of
discrete percolation. The bond model is a special case of the site
model, and any site model may be modified into a bond model with the
proper choice of covering lattice [64SYK].
Percolation theory has further evolved to include entities that
are not constrained to a defined or discrete lattice [88SEV,90BLE,
91SAV]. Said continuum or random percolation models involve the
interaction of entities which are randomly placed in n-dimensional
space. Continuum percolation may be subdivided as well, into theories
involving either randomly centered particles or particles placed
randomly within concentric shells [85CHI,89WU]. Finally, both continuum
percolation models may be further subdivided into mechanisms involving
totally hard particles (impenetrable), or penetrable particles, or any
variance in between [85CHI,85RIC,88LEE,89VJU]. Figure 2.14 illustrates
each of the continuum models of percolation theory.
All percolation theories have a common theme. A function is
utilized to determine the mean cluster size, as a function of entity
concentration. The percolation threshold (pc) is defined as the entity
concentration at which the mean cluster size becomes infinitely large.

113
Plumbing Analogy for the Distinction
Figure 2.13
Illustration of discrete site and bond mechanisms of
percolation [83ZAL2]

114
Continuum Percolation
1.
Randomly Centered
A. Impenetrable Spheres
a = 1
B. Penetrable Spheres
2. Concentric Shells
Note: Concentric Shell Models May Also Use Penetrable Spheres
Figure 2.14
Illustration of
[85BUG,88LEE,89WU]
continuum percolation models

115
This phenomenon is physically correlatable to a cluster structure which
spans the n-dimensional space, thereby percolating said space. The
various methods utilized, by each model, to produce the mean cluster
size function vary significantly with each model, and are not covered in
this paper. However, the literature is filled with excellent overviews
of each of the areas of percolation theory [59DOM,61FIS1,61FIS2,63FRI,
83ZAL2,85CHI,85STA,88LEE,88SAV,89CHI,89WU,9OBLE,91SAV).
Furthermore, the above percolation studies may be categorized as
either classical or mechanistic. Classical percolation models involve
theoretic ideologies combined with mathematical simplifications, in
order to solve the percolation problem. Mechanistic models involve
computer generation and monitoring of clusters of randomly placed
entities according to a set of specifically defined criteria.
Mechanistic models usually are Monte Carlo simulation based and are very
computationally intensive, while theoretic models are mathematically
complicated, but not as computationally intensive. The common goal of
each of these methods is to obtain results that agree with each other as
well as with available experimental data.
2.4.1 Clustering
Clustering theory involves the interaction of units, with one
another, in n-dimensional space, as the volume fraction of said units is
increased [83ZAL2]. As described above, there are two types of
clustering, site and bond. The site model involves the occupation of
either lattice or random sites, while the bond model involves the
interconnection of units placed previously at said sites.
While there are many ways to predict cluster size as a function of
either site or bond occupied volume fraction, the simplest and most
straight forward method is that involving exact series expansions
[61DOM,64SYK]. The series method is valuable in that it provides a
simple, physical-based, model which provides estimations for both the

116
average cluster size as a function of volume fraction of occupied sites
(or bonds) as well as a method of accurately estimating the percolation
threshold (pc) for a diverse range of site (or bond) lattices for any
dimensionality (as long as the number of combinations necessary to form
a cluster, for each incremental cluster size, is definable).
The method of exact series expansions for determining cluster size
as well as percolation statistics was introduced by Domb and Sykes
[61DOM], and was later refined by Sykes and Essam [64SYK]. The mean
cluster size, as a function of basic unit concentration (S(p)), is
described by the series expansion
S(p) =1+Hnanpn
where n is the number of unit members in the cluster, a„ is the number
of possible configurations for cluster size n, and p is the fraction of
lattice bonds or sites occupied. Table 2.6 depicts the an coefficients
for several, three dimensional site and bond configurations. In its
present state, this method is valid only for discrete percolation. As
shall be outlined in Chapter 4 below, this method may be extended to RCP
structures as well.
Until now, the discussion has covered the clustering of monosized
spherical entities only. Clustering and percolation of n-modal size
distributions of spheres, as well as nonspherical particles, is touched
upon in section 2.4.2, below.
2.4.2 Percolation
As mentioned above, all percolation models involve defining where
the mean cluster size (S(p)) becomes infinity. Figure 2.15 illustrates
the generic evolution of mean cluster size, and of a conductive-type
percolation property, as a function of filled site or bond fraction. At
pc the site or bond interconnection length as well as the mean cluster

117
Table 2.6
The Number of Possible Configurations (an)
for a Cluster Size of n+1 (Three Dimensional
Bond and Site Configurations) [64SYK]
a„ for Various Lattice Configurations
n
Site Mechanism
Face
Centered
Cubic
(PE=0.74)
Body
Centered
Cubic
(PE=0.68)
Simple
Cubic
(PE=0.52 )
Diamond
Cubic
(PE=0.34)
i
1
1
1
1
2
12
8
6
4
3
84
56
30
12
4
504
248
114
36
5
3012
1232
438
108
6
17142
5690
1542
264
7
26636
5754
708
8
113552
19574
1668
9
71958
4536
10
10926
11
28416
Bond Mechanism
1
1
1
1
1
2
22
14
10
6
3
234
98
50
18
4
2348
650
238
54
5
22726
4202
1114
162
6
214642
26162
4998
456
7
1993002
163154
22562
1302
8
984104
98174
3630
9
6015512
434894
10158
10
1855346
27648
11
77022
12
206508

Average Cluster Number or Length
118
1.0
0.8
0.6
0.4
0.2
0.0
Fraction of Bonds or Sites Filled
Evolution of mean cluster size and percolation
properties as a function of filled fraction of sites
or bonds [83ZAL2]
Figure 2.15
Percolation Probability or Property Value

119
size goes to infinity. At this point, the conductive-type material
property becomes finite, increasing gradually, then linearly to its
maximum at a site or bond fraction of unity. The percolation
probability initially increases rapidly, then gradually increases to one
at a filled bond or site fraction of unity.
It should be noted that the actual value of pc depends upon the
packing arrangement of either the entities or the bonds between said
entities. The percolation threshold also is heavily dependent upon the
dimensionality of the filled space. Various pertinent percolation data
for both discrete and continuum (i.e. RCP) percolation is shown in Table
2.7. It should be noted that there is debate as to whether random close
packing is truly a purely continuum case or if it is a combination of
separate discrete lattices, or a combination of discrete and continuum
models [29SMI,61MCG,83ZAL2,90ZHE]. There is also debate as to whether a
discrete system may be universally modified for use in continuum-type
systems [9OBLE ] .
Perhaps the most interesting result of discrete percolation theory
is that there is a dimensional universality of the volume fraction at
percolation (i.e. PEpcSlle) [ 83ZAL2 ] . Table 2.7 illustrates this effect for
two and three dimensional spaces. For the three dimensional case, said
universal volume fraction at percolation has been found to be
approximately 0.157. Analogously, there is a dimensional universality
of total bond fraction at percolation (i.e. ZpcBond) . Said value was
found to be approximately 1.45. Thus, the total volume fraction of
entities at pc is a universal constant, regardless of the lattice used.
Zallen also applied said universality to a random close packed structure
with success, thereby heavily implying that said dimensional
universality may be extrapolated to the appropriate continuum models
(i.e. randomly placed or bonded, hard, impenetrable particles) [83ZAL2].
Zallen termed this dimensional universality as the critical volume
fraction for the site percolation case and as the critical bond fraction

120
Table 2.7
Pertinant Factors for Site and Bond Percolation
on a Variety of Lattices [83ZAL2]
Dimen¬
sion¬
ality
(d)
Lattice
or
Struc¬
ture
Pc
Bond
Pc
Site
Coor¬
dinat¬
ion
Number
(Z)
Pack¬
ing
Effi¬
ciency
(PE)
rj ___ Bond
¿Pc
PEpcsiIC
1
Chain
1
1
2
1
2
1
2
Tri¬
angular
0.3473
0.5000
6
0.9069
2.08
0.45
2
Square
0.5000
0.593
4
0.7854
2.00
0.47
2
Kagum'e
0.45
0.6527
4
0.6802
1.80
0.44
2
Honey
comb
0.6527
0.698
3
0.6046
1.96
0.42
Dimensional Average
2.0+
0.2
0.45 +
0.03
3
FCC
0.119
0.198
12
0.7405
1.43
0.147
3
BCC
0.179
0.245
8
0.6802
1.43
0.167
3
SC
0.247
0.311
6
0.5236
1.48
0.163
3
Diamond
0.388
0.428
4
0.3401
1.55
0.146
3
RCP
0.27'
0.637
0.6'
0.16'
Dimensional Average
1.5+
0.1
0.16+
0.02
4
SC
0.160
0.197
8
0.3084
1.3
0.061
4
FCC
0.098
24
0.6169
0.060
5
SC
0.118
0.141
10
0.1645
1.2
0.023
5
FCC
0.054
40
0.4653
0.025
6
SC
0.094
0.107
12
0.0807
1.1
0.009
Notes
'Experimentally Derived Values

121
for the bond case [83ZAL2]. These phenomena are illustrated in Figure
2.16, where the inverse of the percolation threshold (pc') is plotted as
function of either the packing efficiency (PE) or the coordination
number (Z) for site and bond models respectively. This is perhaps the
most important revelation of percolation theory.
The material property resultant from percolation, and possibly the
percolation threshold, may have a dependence upon particle size. This
was experienced by Ruschau, et. al and by Newnham, et. al in their
investigations of volume resistivity as a function of conductor particle
size and volume fraction [78NEW,90RUS]. They experienced a shift in pc
to higher values with smaller particle size. They attributed this to
more contacts in systems using smaller particles, since the contact
resistance would be decisively larger for systems utilizing smaller
conductive particles. This would effectively increase the minimum
resistivity as well as possibly push pc to higher fractions. Thus, in
percolation experimentation, it is important to realize that the
physical size of the volume investigated must be several orders of
magnitude larger than the entity size as well as that other factors
(such as contact resistance, etc.) must be considered.
Percolation theories involving bimodal distributions of spherical
particles or monosized, nonspherical particles are still in a stage of
relative infancy. Chiew, et. al and Wu and Chiew modelled the effect of
bimodality of entity size on the percolation threshold for various
continuum systems (i.e. randomly centered impenetrable and penetrable
systems) [85CHI,89WU].
Using Ornstein-Zernike forms of cluster integral equations, in
combination with the Percus-Yevik approximation for pair connectedness
and, ultimately, for mean cluster size, Chiew, et. al found that a
multicomponent mixture of randomly centered, impenetrable spheres
percolates at a constant value, regardless of concentration and size
distribution [85CHI]. They extended this conclusion to multimodal and

122
'q.°
2 -
>^FCC
*
BCC
y
/' WRCP
^ Simple Cubic
4^
x Diamond
0.2
0.4
0.6
0.8
1.0
Packing Efficiency (PE)
A. Site Percolation
10
8
6
I
4
2
0
0 2 4 6 8 10 12
Coordination Number (Z)
B. Bond Percolation
.Afcc
„*BCC
Simple Cubic
i- -t/P* > Diamond
Figure 2.16
Illustration of the critical volume and bond fractions
at percolation in three dimensional space [83ZAL2]

123
continuous distributions as well. They calculated that said continuum
percolation occurs at an inclusion volume fraction of 0.393. This is a
somewhat different value than that cited in Table 2.7 above. The value
of Chiew, et. al has been the subject of correction, however, and the
accuracy of said value is still somewhat debatable [89CHI]. Thus, it
may be assumed that the philosophy of Chiew, et. al is correct while the
actual percolation value may not be.
2.4.3 Application of Percolation to Microstructure
Percolation theory may be utilized to describe many phenomena,
such as composite properties, catalytic reactions, ferroelectricity,
etc. The expansion of percolation theory in this section is limited to
porous structures and the characterization of porous structures using
penetration-extrusion and sorption techniques, however.
Percolation theory has been utilized to model both real and ideal,
pore structures. Modelling of real systems requires experimental data,
which are generally obtained by either microscopic, porosimetric, or
sorption techniques. Yanuka, et. al proposed a percolation model which
utilized intersecting ellipsoids to estimate pore structure as
determined via microscopic techniques [86YAN]. Said investigations are
tedious when many samples need to be investigated, however, and are
frequently subject to error due to the relatively traumatic sample
preparation techniques involved.
Porosimetry and nitrogen (N;) sorption techniques are more
convenient techniques of characterizing pore structure.
Both characterization methods also have associated problems. It is
difficult to discern pore shape of the material structure using either
technique. Indeed, the Washburn equation, which is the generic equation
utilized in the characterization of porosity via mercury (Hg)
porosimetry, assumes that all pores are cylindrical in geometry [86LAN].
Other problems with porosimetry techniques are the hysteresis exhibited

124
by intrusion-extrusion curves, which has been (until recently)
insufficiently attributed to contact angle hysteresis as well as to the
stranding of Hg as modelled by the classical "ink bottle" pore model
[86LAN,91ZGR]. Furthermore, there is a definite breakthrough intrusion
pressure, commonly observed when using Hg porosimetry, which is
frequently obscured by surface effects [86YAN,91SHI3].
Porosimetry and sorption techniques have other inherent errors as
well. Intrusion porosimetry overestimates the volume fraction of small
pores, since intrusion will only occur when the system pressure is
sufficient to overcome the surface tension that results from
constricting the Hg through the smallest area indigenous to the pore
channel [86LAN]. Due to mass balance, the volume fraction of large
pores indicated by intrusion porosimetry is underestimated as well.
Extrusion porosimetry has inherent errors as well. In order to extrude
to the surface of the sample, a continuous Hg path must be present. As
the system pressure is reduced, the Hg extrudes from throats in pore
channels due to surface tension. Thus, menisci are formed in the pore
channels. Said formation initially occurs only at the smallest
restrictions in each pore channel, effectively blocking extrusion from
other parts of the pore structure. Therefore, extrusion porosimetry
underestimates the volume fraction of small pores [86LAN]. A second
phenomenon associable to extrusion porosimetry is the underestimation of
the volume fraction of larger pores due to mercuric stranding. This
results from the same factor that causes shadowing. As Hg extrudes from
the pore structure, menisci form at pore channel constrictions (throats)
first, thereby creating a discontinuous (i.e. impossible) path for Hg
extrusion. As extrusion continues, this effect becomes increasingly
significant until the largest Hg-filled pores become stranded [86LAN].
Thus, extrusion porosimetry underestimates the volume fractions of both
the smallest and the largest members of a porous structure.
Furthermore, since some of the Hg is stranded within the pore structure,

125
mass balance is no longer satisfied. In the event that stranding is
relatively small, however, a mass balance is still an appropriate
approximation and, thus, the volume fraction of intermediate sized pores
is necessarily overestimated [86LAN].
Sorption techniques have analogous errors that are inherent in the
technique as well. In the case of N2 gas adsorption-desorption
analysis, hysteretic relations similar to those characteristic of
porosimetry, are exhibited. Said hysteretic behavior is not dependent
upon pore restriction properties in the same sense as in porosimetry,
however. In the sorption case, the displayed hysteresis is resultant
from pore channel blockage. Upon adsorption, the gas is free to adsorb
on any surface having the proper surface curvature [87ZHD]. The areas
of greatest curvature will adsorb first. As the relative pressure of N2
is increased, smoother surfaces (i.e. larger pores) will adsorb the gas
as well. As the nitrogen partial pressure (PN2) is further increased
capillary condensation occurs in pore channel throats, thereby blocking
access of nitrogen (or other adsorbate gas) to the larger pores.
Conversely, as PN: is decreased (i.e. gas evaporation and desorption),
evaporation and desorption can only occur from surface accessible pores.
Thus, gas adsorption in porous materials is not a cooperative
phenomenon, while gas desorption is. This is different from the
situation characteristic of Hg porosimetry, in that porosimetric
intrusion and extrusion are both cooperative. However, both hysteretic
phenomena are quite similar (i.e. adsorption "leads" desorption and
intrusion "leads" extrusion) [91ZGR].
There is a great deal of debate about which values (i.e.
adsorption versus desorption, or intrusion versus extrusion) should be
utilized to define the pore size distribution of a porous material
(91MAS2,91NEI,91ZGR]. It seems that an average of both curves, that is
weighted according to the various phenomena involved, should be utilized
in the case of porosimetry, while adsorption data (if and only if

126
condensation is prevented) should be used in the case of nitrogen gas
sorption characterization. This is usually not the case however.
Generally, intrusion data is quoted in porosimetry studies, while
desorption data is cited in studies involving gas sorption [88REE].
Fortunately, both curves of each type of hysteresis contain
valuable information. Many percolation models have recently been
developed which attempt to correlate hysteresis structure with pore
structure data [85RIC,86LAN,86YAN,87ZHD,91MAR,91MAS2,91NEI,91SHI3,
91ZGR]. This area of research is not mature as of yet, and more
research in this field is warranted. Percolation theory was first
applied to porous systems by Fatt [56FAT1,56FAT2,56FAT3]. The field has
developed greatly since then. The most successful percolation models of
this type involve site and bond percolation models which are utilized in
conjunction [86LAN,87ZHD,91ZGR]. In said models sites are used as pore
bodies (i.e. the physical pores) and bonds are used for pore channels or
channel restrictions. The coordination number (Z) is defined as the
number of bonds per site. Thus far, these models involve Z only as a
constant and not a distribution function. Furthermore, these models
typically do not correlate bond size with site size (i.e. they are
totally random), which is usually not the case in real systems [91ZGR].
However, as presented, these models are all highly intuitive, and thus,
are useful for investigating pore structure.
Zgrablich, et. al introduced a site-bond, continuum percolation
model which utilizes size distribution functions for both the sites and
the bonds of a porous material [91ZGR]. For materials having a large
difference between bond and site distributions (i.e. pores and throats
formed by RCP beds of monosized spheres), both size distributions are
discrete. For lamellar or platey structures, having similar pore and
pore channel structure sizes, the relative size distributions of bonds

127
and sites, overlap. Figure 2.17 illustrates both the bond-site
structure model as well as the bond and site distributions and overlaps
that are associable to selected microstructures.
Zgrablich, et. al then calculated bond and site percolation
probabilities (Ps and PB respectively) using the bond and site size
distributions for various microstructures. They used a correlated Bethe
lattice model (although other models may be used as well). The
percolation probabilities were then used to determine the sorption and
porosimetry hystereses for each of the selected microstructures. The
models used were solely bond sensitive in the sorption case, and bond
sensitive and site sensitive in the cases of intrusion and extrusion
porosimetry respectively, due to the reasons of relative cooperativity,
espoused above. The relationship utilized to determine the selected
adsorption-desorption hystereses is
l-Vdes(rk)=(l-Vads(rk))PB(rk)
where 1-Vdcs(rk) is the fraction of emptied pores as a result of
desorption, l-V^frJ is the total volume that could be desorbed,
independent of pore structure considerations, and PB(rk) is the bond
percolation probability (note that all are functions of the Kelvin
radius, rk) . The relationships used for the various porosimetry
hystereses are
$=PB(rL) [1 -B(rL) ] V'{rL)
and
l-$=Ps(rL) [S(rL) ] V-(rL)
for intrusion and extrusion porosimetry respectively. In these
equations, 4> is the fraction of available porous volume filled, Ps(rL)

Site-Bond Analogy to Porous Structure
128
/— Site
Throat^3to
LBond
Site and Bond Size Distributions for Selected Pore Structures
^Bond
1 = 0
/ '
/ »
i i
i i
i i
i i
i i
i \
i i
/ i
l ' Site 1
1 = 0.5
/Bond \ Site >
/ 1 \ 1
/ ' \ 1
/ ' \ *
/ ‘ \ X
J ' V x
1 = 1
Bond
Site
in
a coa
CD oo
CID CCD CCD
â–¡O
m
I = Size Distribution Overlap
Illustration of the bond-site model of continuum
percolation, and the bond and site size distributions
and overlap related to selected microstructures
[91ZGR]
Figure 2.17

129
and PB(rL) are the site and bond percolation probabilities respectively,
V+ is the fraction of volume corresponding to sites that are larger than
the Laplace radius (rL), V is the fraction of volume corresponding to
sites that are smaller than rL, and B(rL) and S(rL) are the bond and site
distribution functions respectively (note that they are both functions
of the Laplace radius, rL) , and rL is the Laplace radius.
Figures 2.18 and 2.19 illustrate the sorption and porosimetry
hystereses, calculated by the appropriate equations above, for
theoretically packed beds of spheres rods needles and plates. The site
and bond distributions for said model porous structures are included as
well.
Finally, the model was subjected empirically to available
experimental data [91ZGR]. Data were obtained from porosimetry
hystereses of real porous materials of the categories mentioned above.
The ratio of intrusion pressure to extrusion pressure (P¡/Pe) was plotted
as a function of volume fraction filled ($). The results are
illustrated in Figure 2.20. It is evident, from Figure 2.20, that both
sphere and rod structures should yield hystereses having relatively
constant P¡/Pe values. This would result in both the intrusion and
extrusion curves being very similarly shaped. Conversely, structures
having a site-bond size distribution overlap (i.e. changing P¡/Pe) would
be expected to have dissimilarities in shape between the respective
intrusion and extrusion curves. Furthermore, the negative slopes in
P;/Pe of the plate and needle pore structures would lead to relatively
narrow shoulders in the respective hystereses.
Lane, et. al also accounted for the expected correlation between
relative site and bond sizes (i.e. nonrandom, correlated bond
distributions). Figure 2.21 illustrates the general effect of
correlated bonds on a hypothetical intrusion curve. Other models are
valuable for determination of the relative amount of stranded Hg as a
function of pore structure (i.e. "ink bottles" having a near-infinite

Volume of Sorption
130
Figure 2.18 Generic sorption hystereses, calculated using a bond-
site continuum percolation model, and the
corresponding site and bond size distributions for
each respective pore structure [91ZGR]

Volume Filled
131
Size Distribution Overlap (I)
Generic porosimetry hystereses, calculated using a
site-bond continuum percolation model, and the site
and bond size distributions corresponding to the
respective pore structures [91ZGR]
Figure 2.19

Intrusion Pressure at Volume Fraction Filled
132
0.2 0.4 0.6 0.8 1.0
Fraction of Total Intrusion Volume Filled
Relationship of the ratio of the pressure of intrusion
to the pressure of extrusion, at a specific filled
volume fraction ($), as a function of filled volume
fraction ($) [91ZGR]
Figure 2.20

Volume Fraction of Accessable Pores Filled
133
Illustration of the difference between intrusion
porosimetry curves, calculated for totally random and
for correlated site-bond structures [86LAN]
Figure 2.21

134
relative diameter ratio, leave maximal amounts of stranded Hg) as well
as the dimensionality of the corresponding pore structure
[86LAN,91SHI3].
2.5 Sintering
2.5.1 General
Sintering may be defined as the consolidation and densification of
particulate materials below the melting point (or range) of said
materials. Other definitions have also been proposed. In fact the very
definition of the term sintering is the subject of a great deal of
debate, due to the complexity of the process [79HAU,85KUC]. Sintering
theory is generally delineated into two categories, solid state
sintering and viscous sintering. Solid state sintering occurs in
crystalline materials, while viscous sintering occurs in amorphous
solids. Solid state sintering is usually considered to occur via either
various diffusional mechanisms or by an evaporation-condensation
mechanism, while viscous sintering is generally agreed to be a flow
process. Table 2.8 outlines the various diffusion and flow mechanisms
involved in both types of sintering. Densification of a packed bed of
particles will normally start when the heat treatment temperature is
approximately 40 to 50% of the melting point (or range) of said
material, while consolidation, or interparticulate bonding may initiate
well below this temperature [79HAU].
Sintering of particles is an exothermic reaction [FRE45]. The
driving force for all types of sintering (as with all thermodynamic
reactions) is the ultimate reduction of the total free energy of the
system. Specifically, the factors involved, are delineated by the
following relation:
AGT=AGv+AGb+AGs

135
Table 2.8
Mass Transport Mechanisms Involved in Sintering [88REE]
Mechanism
Densification?
Surface Diffusion
No
Evaporation-Condensation
No
Boundary Diffusion
Yes
Lattice Diffusion
Yes
Viscous Flow
Yes
Plastic Flow
Yes

136
where AGt is the system total free energy, AGV is the change in volume
free energy, AGb is the change in boundary free energy, and AG, is the
change in surface free energy, with respect to the sintering reaction
[88REE].
Sintering is frequently modelled using spherical particles.
Figure 2.22 illustrates a sintering model that involves two spheres in
contact. The diameter of the contact area of the two spheres (X)
increases with time when appropriately heat treated. Table 2.9 denotes
the rate of change of contact area diameter (X), with respect to
sintering mechanism, for isothermally treated systems. Figure 2.22 also
shows that material transport depends upon the relative surface
curvature involved. Basically, material flows from convex surfaces to
concave ones, via one of the previously mentioned mass transport
mechanisms. As a result, the centers of the spheres gradually approach
each other, thereby resulting in densification.
It is generally agreed that sintering from green compact to fully
dense material involves three distinct stages. In the first stage of
sintering, particle rounding and interparticle bonding dominates. The
total volume change during the initial stage of sintering is usually
less than 12% [88REE]. The second stage of sintering involves the
movement of particle centers toward each other as the result of mass
transport. This intermediate stage results in the greatest amount of
densification. During the intermediate stage, the pores remain
connected. The final stage of sintering is the slowest, involving the
lowest driving force. Final stage sintering initiates at approximately
92% of theoretical density [88REE]. During this stage, all porosity
becomes discrete and will either shrink or expand depending upon the
size of the pore, and the amount and solubility of the gas entrapped by
the pore. The three stages of sintering are illustrated in Figure 2.23.
There have been other sintering models proposed as well. In fact,
the initial viscous sintering model was a two stage model [45FRE].

137
X = Sphere Contact Area Diameter
Y = Amount of Movement of Sphere Centers
Toward One Another (per Sphere)
R = D/2 = Sphere Radius
r = Radius of Curvature of Throat Interconnection
Illustration of a classical sintering model,
consisting of two spheres interacting at a contact
surface (the diameter of which is denoted as X)
[88REE)
Figure 2.22

138
Table 2.9
The Rate of Change of Contact Area Diameter
with Respect to Sintering Mechanism for Isothermally
Treated Monosized Spheres [49KUC]
Sintering Mechanism
Time Dependence of Contact Area
Viscous Flow
X2 « t
Evaporation-Condensation
X3 « t
Volume (Lattice) Diffusion
Xs « t
Surface Diffusion
X7 « t

Percent of Theoretical Density
139
Figure 2.23
Illustration of the three stages of sintering [88REE]

140
Others have added a fourth stage (or second part of the third or final
stage) in order to explain pore bloating and/or grain growth [88REE].
2.5.2 Viscous Sintering
Among the first sintering models, was that of Frenkel [45FRE).
Kuczynski was the first to confirm Frenkel's theory that glasses sinter
via a viscous flow mechanism [49KUC]. It is generally agreed upon that
the Frenkel model, while not adequate for solid state sintering, is a
satisfactory basis for viscous sintering theory [49KUC,55KIN,88REE,
90EWS]. Unlike the classical, three-stages-of-sintering model, the
Frenkel model divides the sintering process into two stages which are
governed by the following relations,
AL_( 1} , A V' X )2_ 3vst
L0 3 Vc 2 D0 2r\Da
(which was later corrected to reflect another factor of two in the
denominator of the last term [75EXN,84SCH1]) for the initial stage of
sintering and,
3 Y,
for the second and final stage. In the above equations, AL/L0 is the
initial rate of shrinkage, AV/V0 is the volume shrinkage, X is the
sphere contact area diameter, t is the time required to close off
discrete porosity, Dc is the initial particle diameter (assuming a
uniform spherical approximation), t is the isothermal sintering time, t)
is the viscosity of the sintering material, and y, is the surface
tension of the glass powder [45FRE,88REE]. In the Frenkel model the
first stage involves volume shrinkage of packed particles, as well as
increasing interparticle contact. The first stage ends with the

141
formation of enclosed, residual pores. The second stage begins with a
matrix of enclosed pores, and predicts sintering behavior until maximum
density is achieved [4SFRE]. The mathematical assumption, used by
Frenkel, in the first stage equation has since been shown to be
incorrect for volume shrinkages of greater than 10% [84SCH1]. However,
said relation has been found to model the viscous sintering process well
beyond 10V% densification. This is probably the result of unknown
factors which tend to offset Frenkel's error [84SCH1].
Later, Mackenzie and Shuttleworth contributed to viscous sintering
theory by modelling the final stage of sintering using a pressure
balance relation [49MAC]. The Mackenzie-Shuttleworth (MS) model
considers the effect of gas entrapment, in closed porosity, upon the
rate of densification in the final stage of viscous sintering. The MS
model predicts that the sintering rate of an amorphous bed of particles,
depends upon the net summation of pressure differences resultant from
the combination of the negative pressure, exerted by trapped gas, and
the hydrostatic sintering pressure, resultant from surface curvature.
According to the MS theory, the rate of densification of an amorphous
matrix of monosized, discrete pores may be determined by the relation,
dp =_3 , 4_n , 3 y sn 3
dt 2 3 r)
(1-p) 3P 3
where p is the density of the compact relative to the theoretical
density of the material, ys is the surface tension of the material, r| is
the viscosity of the material, and n is the number pore density [49MAC].
With manipulation of this relation (i.e. integration from green density
to theoretical density to determine isothermal sintering time, then
inversion to solve for p as a function of reduced time), the compact
relative density may be plotted as a function of reduced time, where

142
reduced time is given by the relation,
_1
K=Reduced-Time=—^— (t-ta) .
Figure 2.24 illustrates the rate of sintering predicted by the MS model.
The MS model is applicable to viscous sintering materials, having
microstructures which contain discrete, spherical pores, providing that
the fields of flow, surrounding each of the pores, do not interact
significantly with one another (i.e. usually at or above 90% of
theoretical density) [84SCH1].
The MS model was the first to introduce a theory which, when
modified, can account for pore expansion or bloating. Bloating of
closed pore materials may occur via either gas dissolution-evolution
processes or by Ostwald ripening.
The glass matrix will dissolve gases present in the sintering
atmosphere and may later evolve said gases, depending upon the gas
solubility equilibrium (which changes with temperature, etc.).
Gas dissolution-evolution is a kinetic phenomenon as well. Therefore,
the actual conditions that result in bloating, via this mechanism, are
complex. Kiparisov and Levinskij have modelled gas dissolution-
evolution bloating using a model which considers the dynamic balance
between the gas existing in a pore and that dissolved in the glass
matrix [79KIP]. Generally, less soluble sintering atmospheres (i.e. N2,
air, SO;, Cl2, etc.) will increase the amount of bloating observed, while
more soluble gases (i.e. H2, 02, etc.) will allow the elimination of
porosity, because the pore gases dissolve into the glass matrix.
Subsequently, bloating is reduced [88REE].
Ostwald ripening theory states that pores, below a critical size,
will shrink, while pores above a critical size will expand (i.e. the
larger pores grow at the expense of the smaller ones) [73KUC]. In the
case of closed pore expansion, this effect is further augmented, since

Relative Density
143
0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6
Reduced Time (K)
Densification of a viscous material, with respect to
reduced time, as predicted by the Mackenzie-
Shuttleworth sintering model [49MAC]
Figure 2.24

144
the sintering (or pore closure) potential is reduced as surface
curvature is reduced. A constant volume of entrapped gas will have a
constant outward pressure. Thus, pores having low surface area to
volume ratios (i.e. relatively low sintering potentials) will tend to
expand.
Scherer later proposed a more advanced model of viscous sintering
[77SCH1]. Realizing that the MS model was not accurate during the
initial stages (i.e. before pore closure) of sintering, Scherer devised
a model based upon a novel microstructure of intersecting cylinders, of
length L and diameter A, interconnected upon a cubic lattice (see Figure
2.25). Said structure is totally open, and thus, appropriate for the
initial stages of sintering, even though it bears little resemblance to
typical packed powder structures. If one imagines spheres placed at the
interconnections of the cylinders, the structure resembles that of
simple cubic packing, however. The model was found to be applicable for
continuous, interconnected pore structures (that are throatless), in
sintering situations prior to pore closure [77SCH2,85RAB].
Scherer determined that the limit of this structure (i.e. the onset of
pore closure) occurs at a value of A/L of 0.5. This was found to occur
at a corresponding relative density of 94.2% [77SCH1,85RAB]. Scherer
then combined the cubic array of cylinders model with the MS model (at
theoretical densities above 94.2%) using the assumption that
n= (
LoPo)
Pt
-1
where n is the pore number density, L0 is the unit cylinder cell length,
p„ is the initial (green) density, and pT is the theoretical density of
the material. Using mathematical manipulation similar to that involved
in the MS model, Scherer's model may be directly compared with the MS
model. However, the reduced time, as used in the Scherer model of
viscous sintering, is different from that used in the MS model, and is

145
Basic cell model, of cylinders of length L and
diameter D, and interconnected in a cubic arrangement,
used in the Scherer viscous sintering model [77SCH1]
(later, other cell configurations were introduced
[91SCH3])
Figure 2.25

146
described by the relation,
Y P 4
K=Reduced-Time= (——) ( —) 3 (t-ta)
P o
where p, is the theoretical density of the material, p0 is the initial
density, q is viscosity, ys is the surface tension, Lc is the initial
cell length of the cylinders, t is the time, and t0 is time at the
beginning of the experiment.
Figure 2.26 compares the MS and Scherer models. In order to
superimpose the two relations, it was necessary to derive a corrected
reduced time. The corrected reduced time is determined by the relation,
_l
y n 3
Corrected-Reduced-Time= (— ) (t- tf)
n
where t( is the time at which the material densifies to theoretical
density [84SCH1]. It is evident from Figure 2.26 that the Scherer model
has a low density "tail" that is not given by the MS model and is thus
more realistic. Both models are valuable to experimentalists in that
the actual sintering time may be compared to the reduced time at a
specified relative density. A plot of reduced time as a function of
relative density, as a function of isothermal sintering time as a
function of relative density, should yield a linear relation, having a
slope equal to the reduced time constant (K) [77SCH1,84SAC2,85RAB,
90VOR]. From the slope value, either the material surface tension, or
the material viscosity may be determined, if either is known. It is
also necessary to know one microstructural parameter of the green
material. In the case of the Scherer model, it is necessary to
determine L0, and in the MS model, n must be known. L0 may be determined
via Hg porosimetry, with the caveats mentioned in section 2.4.3 above.

Relative Density
147
Corrected Reduced Time (K)
Figure 2.26
Comparison of the MS and the Scherer viscous sintering
models (relative density is plotted as a function of
corrected reduced time, K) [77SCH1]

148
To a first approximation, L0 may be (and has been) equated with the
median pore channel diameter [77SCH2,84SAC2,90VOR]. In order to
determine the number density of porosity (n), which is necessary to
determine either y« or , from K, when the MS model is utilized.
The Scherer model (and in several cases, the MS model) has been
applied to silica, in the forms of flame-hydrolysis preforms, and gel
monoliths, as well as to a phase separated and differentially etched,
high silica glass (Corning Code 7930 Porous VycorR) [77SCH2].
Said model has also been somewhat successfully expanded to the
characterization of the sintering of packed spherical powders
[84SAC2,90VOR].
The Scherer model has also been modified for different situations,
including various pore structures and configurations [91SCH3,91SCH4],
various pore size distributions [77SCH3,84SCH2], uniaxial load [86SCH],
and sintering on a rigid substrate [85SCH2]. Bordia and Scherer have
also introduced models that attempt to predict sintering behavior in
materials that are constrained (either internally, or externally),
through the utilization of self consistent models, based upon the
constitutive equations [87SCH3,88BOR,88BOR2,88BOR3,88SCH2,91SCH2,
91SCH3,91SCH4], some of which will be discussed, where appropriate,
below.
Many other sintering models exist as well. Most are based upon
some variation of the above models however. In fact, Scherer proved
that the Frenkel, MS, and cylinder models predict viscous densification
kinetics that are similar to the extent of being experimentally
indistinguishable from one another [84SCH1]. Experimental research in
the area of sintering is usually quite difficult, due to the various
competing transport phenomena, etc., involved. Indeed, there is a great
deal of debate as to which experimental methodology(ies) is(are) best
for investigating sintering kinetics [73JOH]. Some researchers have
investigated near-ideal systems [ 84SAC1,84SAC2,87CL.A, 90VOR, etc . ] , while

149
others have proposed increasingly complex models or modifications of
basic models.
2.5.2.1 Viscous Sintering of Real Systems
Real systems of particles may deviate greatly from the above
viscous sintering models. Sintering may be expedited or retarded if the
viscosity of the glass changes during heat treatment. Water vapor in
the sintering atmosphere, will tend to enhance densification initially
due to a reduction in the viscosity of the glass [64HET,82BAR,85SCH,
88REE]. Inherent water in an amorphous material will also enhance
viscous sintering. Specifically, this has been observed in sol-gel
derived SiO: powders, where it has been found that the removal of
inherent hydroxyls increases viscosity during sintering, thus resulting
in an initial enhancement in sintering kinetics, that fades with heat
treatment time [90VOR]. When significant crystallization occurs during
viscous sintering, the sintering process may be severely retarded. This
is generally regarded as a hinderance, since it is usually desirable
that the fired material be fully dense. Residual hydroxyls, as well as
alkali and other impurities, may also enhance crystallization kinetics
during viscous sintering [59BRO,66WAG,85RAB]. When the sintering heat
treatment is nonisothermal, the effect of heating rate upon
crystallization is also of concern [89PAN]. In short, there are many
factors which effect viscous sintering and sintering kinetics. The
effects of initial microstructure are discussed below.
2.5.2.1.1 Effects of Microstructure
The ideal microstructure for sintered powder compacts is that of
uniform sized spheres, close packed in an ordered fashion (i.e. all pore
channels are identical, or simple cubic packing). There are several
reasons why most sintering models use this microstructure. In a uniform
packing having universally identical pore channels, all spheres (except

150
for those at the compact surface) have the same number of contacts per
sphere. Furthermore, in a close packed arrangement, no particle
rearrangement occurs during sintering, since the force distribution
around each sphere in the interior of the compact, is homogeneous.
Finally, the spherical shape of powders guarantees that the surface
energy distribution is homogeneous throughout the ideally packed powder.
In the above situation the pore size distribution is very sharp and
decreases continuously throughout the sintering process. This has been
experimentally confirmed in compacts of uniform spherical powders,
having random close packing [90VOR].
Most powder compacts are far from the above ideal, however. In
most situations, it is desirable to start with a green compact having
greater density than that typical of the above situation (i.e. a PE
greater than 0.524). In fact, it is usually not possible to arrange
monosized, microscopic, spherical particles in a simple cubic
arrangement, due to nesting, etc. The compaction method used also
introduces packing heterogeneities which significantly affect sintering
[88REE,88ROO]. Furthermore, most powders have constituent particles
which are neither spherical nor monosized. Frequently, said constituent
powders have a significant amount of agglomerates that further affect
sintering. Thus, it is important to be able to model and predict
sintering of nonideal powder compacts.
The particles in an amorphous powder, formed by traditional
techniques (i.e. crushing, grinding, and milling, etc.), are usually
conchoidal in nature and, thus, deviate from sphericity. The
nonuniformity of this structure produces heterogeneities in surface
curvature that cause differential sintering potentials. The nonuniform
shape of the powders also affects the number of interparticle contacts,
as well as the packing efficiency of the powder compact. Sintering of
conchoidal amorphous powders tends to be accelerated, in the initial
stages of sintering, due to interparticle contacts at sharp regions of

151
the particles, and to the greater net surface curvature (i.e. higher
surface area to volume ratio) of the nonspherical powders. Cutler and
Henrichsen investigated the effect of particle geometry upon the
sintering kinetics of amorphous powders [68CUT]. They found that the
sintering rate could be accelerated as much as five fold by using
crushed and sieved glass powders.
Using crushed glass powders is not a panacea, however. As
mentioned above, both packing efficiency (PE) and packing uniformity are
adversely affected when nonspherical particles are used. Therefore, the
later stages of sintering should be retarded when using traditional
powders. Powder agglomerates also retard later stage sintering.
Furthermore, in nonideal packing situations, particles will rearrange
during sintering in order to minimize localized stresses
[73EXN,75EXN,89SCH3]. The above factors may result in localized
sintering without overall densification [73EXN].
Traditional glass powders typically have a particle size
distribution as well. This increases packing efficiency, but produces
compacts having comparatively wide pore size distributions [85PAT].
Said pore size distributions affect the evolution of pore structure
during sintering. Small pores tend to shrink and disappear while large
pores either shrink more slowly or not at all. In the final stage of
sintering, larger pores may even grow, as discussed above.
Evolution of the mean pore size will reflect this relationship.
If the mean pore size constantly increases during sintering, the smaller
pores are reduced at a much greater rate than the larger pores. This
behavior is characteristic of a bimodal pore size distribution, and will
be discussed below. If the mean pore size constantly decreases, the
difference in pore reduction rate is relatively insignificant and the
sintering may be characterized by a single pore size, instead of a pore
size distribution [77SCH3]. In the sintering of traditional powders,

152
the mean pore size usually will either initially decrease, then
increase, or will constantly increase [79WHI,88REE].
Kingery and Francois introduced the concept of a critical pore
size in relation to sintering kinetics of crystalline materials
[76KIN2]. They stated that there is a critical pore size to mean
particle size ratio, above which, pore size reduction is retarded.
Zheng and Reed later expanded upon this work and postulated that pores
could be categorized into one of two classes, pores smaller than a
critical size and pores larger than a critical size [89ZHE]. This
quasi-bimodal model states that the subcritical sized pores affect the
ultimate sintering shrinkage while the supercritical porosity controls
the ultimate density of the sintered material.
Zheng and Reed further proposed that the critical pore size to mean
particle size ratio is approximately 0.5 [89ZHE].
Zhao and Harmer also expanded upon the theories of Kingery and
Francois [88ZHA]. In their experimentation they added large size,
included porosity to alumina compacts, through controlled pyrolysis of
monosized spherical latex. The latex was added to the compacts during
green processing in order to create packed beds of particles having a
bimodal pore size distribution. They produced sintering maps for this
situation and, using thermodynamic criteria, they concluded that
supercritical pores would be eliminated as a result of increasing grain
size. Therefore, the critical pore size will continuously increase as a
result of grain growth. However, they further concluded that it is not
beneficial to augment grain growth for kinetic reasons. It is
interesting to note that Zhao and Harmer observed no effect of sintering
atmosphere (either soluble H: or insoluble N;) upon the removal of
supercritical pores [88ZHA].
The above models were all proposed for solid state sintering, and,
although the concept of pore size to mean particle size ratio is
applicable to viscous sintering, that of grain growth is not.

153
Scherer expanded his model of cylinders to predict the sintering of
glass powders that have a bimodal pore size distribution [84SCH1]. He
used the phenomena of localized stresses, due to particle packing and
pore size heterogeneities [82EVA,86HSU2], to predict the effect of a
bimodal pore size distribution on the sintering behavior of amorphous
materials. Scherer stated that the small pores would be subjected to
tensile forces, while the large pores would be subjected to compressive
forces during sintering. The net result of these forces is to impede
sintering of the small pores while enhancing the shrinkage of large
porosity in the initial stages of sintering. Figure 2.27 shows the
local stresses on each the two size regimes throughout sintering. This
effect was determined to be substantial for a large to small pore size
ratio of 4. The effect was predicted to increase with increasing large
to small pore size ratio.
The sintering of amorphous powders, having bimodal pore size
distributions, was also found to be influenced by the relative volume
fractions of each of the porosity sizes. Furthermore, it was found that
the small pores controlled the sintering rate in the initial stages of
sintering, while the large pores dominated the final stages of
sintering. Figure 2.28 illustrates the predicted sintering curves for
various relative pore volume fractions.
2.5.2.1.2 Viscous Sintering of Glass Matrix Composites Having
Nonsinterinq Inclusions
The viscous sintering of amorphous particulate compacts, having
bimodal porosity distributions, is similar to the sintering of amorphous
powder compacts that contain nonsintering inclusions, in that both
examples are subtopics of the field of constrained sintering. The
densification rate of compacts, containing rigid inclusions, is retarded
in comparison to that of the pure glass. This is a result of the
hydrostatic tensile forces that the inclusions place upon the glass
matrix during the sintering process. Said forces are quite analogous to

Hydrostatic Local Stress
Capillary Sintering Stress
154
ffl
‘co
c
CD
£
CD
>
'co
CO
CD
l_
D.
E
O
o
â–¼
ó Jó
T
<5m - matrix density
óT= Theoretical Density
Stresses imposed upon large and small pores during
viscous sintering (oL and a, are imposed stresses, acL
and aa are capillary stresses) [84SCH1]
Figure 2.27

Relative Density
155
A.Initial Relative Volume
Fraction of Small Pores = 0.3
B.Initial Relative Volume
Fraction of Small Pores = 0.7
Reduced Time (K(t-t0))
C.Intitial Relative Large Pore
Volume Fraction Varied From 0 to 1
Illustration of sintering curves modelling viscous
sintering of bimodal pore size distribution compacts,
having various relative volume fractions of pore sizes
[84SCH1]
Figure 2.28

156
those in large pores in amorphous powder compacts, containing bimodally
sized pores, mentioned above. There are two exceptions, however.
First, the nonsintering inclusions are hard and, thus, are not
influenced by hydrostatic compressive forces. This is in contrast to
the behavior of pores subjected to hydrostatic stresses. Second, when
nonsintering inclusions interact, they can form rigid, contiguous
structures (at volume fractions above the percolation threshold) that
drastically hinder, or even halt, the sintering process. When pores
interact, they combine with one another, and no such rigid, contiguous
network can form at any pore volume fraction.
When nonsintering rigid inclusions (NSRIs) interact with one
another, they may stick to each other or slide over each other,
depending upon whether or not the glass matrix material wets the NSRI
surfaces. If the NSRI particles stick to each other (either because of
surface roughness, or due to interparticle reaction) local hydrostatic
stresses will be enhanced due to viscous drag, thereby, greatly
retarding the sintering process. If the volume fraction of NSRIs is
significantly above the percolation threshold, a rigid network will form
and sintering will cease.
Conversely, if the NSRI particles are wetted by the glass matrix,
interacting NSRIs will not form a rigid network until well above the
percolation threshold (i.e. 30 to 50 V%) [91SCH2]. This limit has been
approached or exceeded in the case of carefully prepared, glass coated
NSRIs. Sacks, et. al have produced fully dense glass-Si3N4 (NSRI)
composites, containing 40V% or greater ceramic filler [91SAC1].
Scherer has also extended his viscous sintering models (both the
cylinder and the self consistent models, as well as a spherical
composite model) for the situation of sintering of amorphous glass
powders, containing NSRIs [87RAH1,87SCH3,88BOR3,88SCH2,91SCH2,91SCH3,
91SCH4]. The extention of said models, however, has been limited to the
case of NSRIs that bond together when they contact. In real systems,

157
this is frequently not the case. Usually NSRIs are wetted (at least
somewhat) by the matrix glass. Therefore, said sintering models, are
accurate only below the percolation threshold [87RAH1,91SCH2,91SCH3,
91SCH4]. For comparison, the rule of mixtures also gives acceptable
results at volume fractions of NSRIs below approximately 10V%
[87RAH1,91SCH2,91SCH3,91SCH4]. Investigation of the situation of
sintering under conditions of NSRI wetting is currently underway,
however [91SCH3].
Ewsuk has recently proposed another model to predict the sintering
behavior of glass powders that contain NSRIs [90EWS,91EWS]. Ewsuk
investigated ceramic filled glass (CFG) composites that density via
nonreactive liquid phase sintering (NLPS). Ewsuk stated that NLPS is a
three stage process that describes the densification of CFG composites
by a combination of glass particle redistribution, NSRI grain
rearrangement, and viscous flow. He postulated that the NLPS rate is a
function of pore size, filler particle size, filler concentration, and a
combination of glass properties, including glass viscosity, wetting
angle, and surface tension. Ewsuk's model predicts densification rates
for the final stage of sintering, where densification is controlled by
the remnant pores, as well as the surface tension of the glass and the
viscosity of the CFG composite material. He utilized Eiler's relative
viscosity model for concentrated suspensions to estimate the CFG
composite viscosity. Ewsuk then constructed sintering maps that predict
critical filler concentrations, below which dense composites may be
produced (for a specific composite viscosity, and a predetermined
sintering time period).
Ewsuk successfully modelled final stage sintering of an alumina-
filled borosilicate glass composite system, using the above model. Said
model predicts that fully dense composites could be produced having NSRI
concentrations as high as 51 V% [90EWS,91EWS].

158
2.6 Dielectric Theory
Dielectric theory is the investigation of the polarization
characteristics of insulating materials. The field may be divided into
two regimes, linear and nonlinear dielectric materials. This section
discusses linear dielectrics. The different polarization mechanisms,
and their frequency dependence, are discussed. A description of
dielectric loss and loss tangent is included. Various models, used to
predict the dielectric constant of composite materials as a function of
porosity and/or composite composition are discussed. Methods of
measuring dielectric constant are also discussed.
2.6.1 Dielectrics Materials
Dielectric materials respond to an applied electric field by
exhibiting a short range motion of internal charge carriers (i.e.
internal polarization) [90HEN]. The absence of long range electrical
conduction necessitates that dielectric materials be electrical
insulators. Linear dielectric materials exhibit a linear polarization
response to applied electrical fields, while nonlinear dielectric
materials do not. Some materials may exhibit both linear and nonlinear
dielectric behavior, depending upon crystal structure, etc. [90HEN].
Dielectric materials may be characterized by several factors, such
as dielectric constant and dielectric loss (and the effect of electrical
field frequency upon both), as well as dielectric conductivity and
dielectric breakdown strength. The selection of dielectric material for
an application, is usually based upon the above materials values. As
mentioned in Chapter 1, favorable candidates for electronic packaging
materials should have a minimized dielectric constant and dielectric
loss (that are stable over all frequencies of use) as well as dielectric
conductivity, while exhibiting maximized dielectric breakdown strength.
There are four mechanisms which give rise to polarization (i.e.
short range motion or alignment of internal charge carriers), electronic
polarization, atomic or ionic polarization, dipole or orientational

159
polarization, and interfacial or space charge polarization. Figure 2.29
provides an illustration of each type of polarization mechanism. These
polarization mechanisms vary greatly in magnitude. Similarly, the
electrical field frequency ranges, in which each of the polarization
mechanisms is operational, also vary.
Interfacial polarization is a relatively low frequency phenomenon
(i.e. below 1000 Hz), which may have a relatively large magnitude. It
is the result of charge carriers amassing at either blocking electrodes
or grain boundaries, etc. Interfacial polarization has the longest
range of the polarization mechanisms, and is thus the slowest or lowest
frequency phenomenon involved in ceramic dielectric materials.
Dipole polarization results from the perturbation and subsequent
rearrangement of either ionic or molecular dipoles, in an electric
field, and against thermal randomization forces. This polarization
mechanism may be separated into two categories, Stevels deformation
polarization and spontaneous dipole polarization [90HEN].
Stevels deformation polarization involves the oscillation of
molecular bonds about an equilibrium position when subjected to an
oscillatory, or alternating current (AC), electric field. Stevels
deformation polarization is important in silicate glasses, since the Si-
-O—Si bond exhibits an asymmetry, which results in a molecular dipole
moment, when subject to AC fields [90HEN]. Oscillation of hydroxyls in
Si—OH bonds in silicate glasses may also result in a Stevels
deformation dipole polarization [90HENJ. Both mechanisms are operant to
relatively high frequencies (i.e. 10" to 10i: Hz).
Spontaneous polarization involves the spontaneous arrangement of
dipoles into one of two equilibrium positions. This polarization
mechanism is responsible for the nonlinear dielectric behavior exhibited
in ferroelectric materials, where the effect is coherent over large
domains and has a potentially large magnitude (i.e. leading to
dielectric constant values as great as 10'* or more [90HEN]).

160
No Field Applied Field
E
Electronic Polarization
Applied Field
No Field *• E
©-’VWsMAg
Atomic Polarization
Applied Field
No Field
E
No Field
Applied Field
/A
"ll//
- f ¡ x
A- S
- E
v
A. Dipole Orientational Polarization
A
A
No Field
A
Applied Field
E
nAn
Stevels Deformation Polarization
^Equivalent Energy Positions-^
B. Cation Dipole Polarization
Spontaneous Dipole Polarization
Dipole (Orientational) Polarization
Blocking Electrodes
Blocking at Heterogeneities
Applied Field
E
Space Charge Polarization
Figure 2.29
Illustration of polarization mechanisms operant in
dielectric materials [76KIN1,90HEN]

161
In linear dielectric materials spontaneous dipole polarization results
from the motion of ions between equivalent positions within the atomic
structure. Said ionic motion occurs continuously, as well as randomly,
in the material at appreciable temperatures (i.e. around room
temperature). When an electric field is applied, the random nature of
this process is statistically skewed in the direction of the electric
field, thereby causing a net polarization of the material. An
appreciable distance is involved in these ionic jumps. Thus,
spontaneous dipole polarization is a relatively low frequency
phenomenon, occurring at frequencies below 106 Hz at room temperature).
Atomic or ionic polarization involves the displacement of ions in
a molecule, with respect to one another, under an applied electric
field. This is a high frequency phenomenon, operating up to frequencies
of 1013 Hz [76KIN1,90HEN]. At the resonant frequency of the bonds, the
polarizability increases greatly, causing a dispersion in polarization
behavior. The frequency at which said polarization increase occurs
depends upon the masses of the ions involved, the bond strengths between
the ions and the configuration of the atomic or ionic molecule of
interest. Furthermore, the frequency broadness of the resonant
polarization will increase as the complexity and number of both the
atomic constituents and the interatomic bonds increases.
Electronic polarization is the highest frequency mechanism of
polarization. It involves the deformation of the electron clouds, that
surround each atom, in the atomic structure of a material. This
polarization mechanism is responsible for the index of refraction at
visible frequencies. Electronic polarization can operate up to
frequencies of 1015 Hz [ 7 6KIN1,90HEN ] .
Figure 2.30 illustrates the generic frequency dependence of each
polarization mechanism at room temperature. It should be noted that
each of the lower frequency polarization mechanisms will shift to higher
frequencies as the temperature of the materials is increased.

Log tan (6) Generic Dielectric Constant
162
-3 -1 1 3 5 7 9 11 13 15
Log Frequency
Illustration of the contribution of polarization
mechanisms to the generic dielectric constant and loss
tangent as a function of AC electric field frequency
[90HEN)
Figure 2.30

163
Temperature affects dielectric loss and conductivity of ceramic
materials (especially glasses) similarly. Excellent and exhaustive
discussions of dielectric properties of materials may be found in
available literature [76KIN1,90HEN].
2.6.2 Measurement of Dielectric Properties
The dielectric constant of a material (K or K") is a measure of
the electrical polarizability of said material. Dielectric constant is
related to polarizability through the Clausius-Mosotti relation:
JT-1_ 1
K' +2 3ec
'^aaa+Ndad+
Nitti]
where K* is the complex dielectric constant, ec is the dielectric
permittivity of free space (8.854 x 10'12 F/m) , N; is the number of
dipoles per unit volume of type i (i = e, a, d, and i, for electronic,
atomic, dipole, and interfacial polarization mechanisms respectively),
and a, is the polarizability of the ith polarization mechanism operant
in the material of interest (where i is explained above). Therefore,
the total polarizability of a material may be determined directly from
the dielectric constant, where the total polarizability is defined as
the summation of the numbers and polarizabilities of each polarization
mechanism, for the material of interest.
There are many ways to measure the dielectric constant of a
material. Exhaustive discussions of said methods may be found in the
literature [54VON,88ST01,88SAE,88SLI,89HEW1,89HEW2,89RIA,89TED,90ANG,
90CAN,91SU1,91SU2]. Relative capacitance techniques are most generally
used, but are limited to lower frequencies (i.e. <20 MHz) than other,
more recently investigated techniques, due to stray capacitances, signal
reflectance and device impedance matching problems. For higher
frequencies (i.e. into the GHz regime), resonant cavity or time domain

164
reflectoraetry (TDR) techniques are usually used [88SAE,89RIA,90ANG,
91SU1,91SU2]. For dielectric characterization in the far infra-red
(FIR) frequency regime, Kramers-Kronig analysis of reflectance
spectroscopy has been utilized [88SLI]. Indeed, at optical frequencies,
the dielectric constant is simply the square of the index of refraction,
since electronic polarization is the only polarization mechanism operant
[76KIN1].
For this study, dielectric properties investigations were limited
to relative capacitance techniques due to limited equipment
availability. However, since most K values are reported at 1 MHz, and
since K generally either remains constant or decreases between 1 MHz and
the highest frequencies that high performance electronic packaging is
subjected to, this is not considered a significant limitation.
Generally, relative capacitance techniques measure dielectric
constant by comparing the capacitance of a set electrode geometry, with
the dielectric material of interest in place (C) and comparing this
capacitance value to that obtained with the dielectric material removed
(C0). The dielectric constant is found by the relationship,
There are many variations of relative capacitance techniques and the
subject is covered in several publications [54VON,88ST01, etc.].
The best relative capacitance techniques are those that provide a
guard electrode to minimize fringing of electrical fields. Methods that
utilize fixed (and not applied) electrodes are also better, since they
eliminate errors associable with electrode application, electrode area
measurement, electrode geometry assumptions, and sample thickness
measurement, as well as being more reproducible and easier to use
[54VON,88STO!,89HEW1,89HEW2]. Therefore, fixed electrode testing

165
devices generally provide more data (that is more accurate and
reproducible) in less time.
The air gap or non-contacting electrode method fulfills the above
criteria [89HEW1,89HEW2]. Figure 2.31 illustrates the air gap method of
measuring dielectric constant. Using the air gap technique, the
dielectric constant of a material under test (MUT) is determined through
the relation,
K=
1-
where CD is the measured capacitance of the device under test (DUT) with
the sample removed, C is the measured capacitance of the DUT with the
sample inserted, tg is the distance between the fixed electrodes, and ta
is the average measured thickness of the sample. This techniques is
quite accurate if the distance of the air gap (i.e. tg - ta) is held
within 10% of the value of t, and if the electrodes, as well as circular
surfaces of the sample, are made parallel. In this method, the cross-
sectional shape of the sample is irrelevant (as long as it is larger
than the electrodes) since the electrodes are of fixed size. Using the
non-contacting electrode technique, dielectric constants may be measured
with accuracy as high as +1% while the dissipation factor (tan(S)) may
be measured with accuracies as high as +5% [89HEW1].
It is also desirable to use instrumentation that measures complex
impedance, of variable AC electric fields, when measuring dielectric
properties so that dielectric loss may also be determined from the shift
in phase angle, as described below. Use of said instrumentation also
makes it possible to measure dielectric properties as function of
applied voltage and frequency.

166
1. Measure Capacitance with Sample Inserted (C)
2. Measure Capacitance with Sample Removed (C„)
Electrode
Unguarded Electrode
^—Dielectric Test Fixture
Illustration of the air gap or non-contacting
electrode technique used to measure material
dielectric constant [89HEW1,89HEW2]
Figure 2.31

167
The dielectric loss tangent (tan(5)) may also be obtained from
complex impedance analysis. In a perfectly capacitive material,
subjected to an AC electrical field, the voltage-current characteristics
are such that the charging current leads the applied voltage by a phase
angle (0) of exactly 90° [76KIN1]. In a real capacitive dielectric
material, this is not exactly the case.
The charging current leads the applied AC voltage by an angle that is
less than 90°. The deviation of the voltage-current characteristics of
a real material from an ideal capacitive material is given by the loss
or phase defect angle (6), where
6+0=90°.
Figure 2.32 illustrates the concept of phase defect angle for a
real dielectric material when modelled as either a series or a parallel
resistance-capacitance (RC) circuit. The tangent of the loss angle is
termed the dissipation factor (D) or loss tangent. It can be shown that
v'H
13= tan (6) = —
K'
where K" is the imaginary portion of the dielectric constant and K' is
the real portion of the dielectric constant [88ST01]. The complex
dielectric constant (K or K*) may be found via the relation
K=K*=K'-iK"
where i is the square root of -1. In near perfect dielectric materials,
6 is very small, and thus, K is approximately equal to K'. Furthermore,
it may be shown that the dissipation factor may also determined from the

168
Cs
Rs
Series Circuit
R.l
Series Model
—VAV
Cp
Parallel Circuit
VG
Key:
G = Conductance
V = Voltage
E = Measured Electrical Field
I = Current
6 = Loss Angle
0 = Phase Angle
f = Hertzian Frequency
Cs = Series Capacitance
Cp = Parallel Capacitance
R s = Series Resistance
R = Parallel Resistance
Figure 2.32
Illustration of phase defect angle (6) in a real
dielectric material, using series and parallel RC
circuit vector modelling [88AST1]

169
following relation
Y
£>=tan (6) =cot (8) =-re = —%r =—— =o¿RsCs=-^-
Rp uCp oiCpRp Q
where X,, is the equivalent parallel reactance, is the equivalent
parallel resistance, G is the AC conductance, Cp is the equivalent
parallel capacitance, C, is the equivalent series capacitance, R, is the
equivalent series capacitance, Q is the quality or storage factor, and w
is the angular frequency of the AC field (u = 2nf, in a sinusoidal field
wave, where f is Hertzian frequency). As mentioned above, real
dielectric materials may be represented by equivalent parallel or series
RC circuits. Usually, it is preferable to use the parallel RC circuit
model, but the series model may be used in certain situations. The
relationships between equivalent series and parallel RC circuit models
are
C=-
CL
(1+D2)
for capacitance conversion, and
RP_ (1 +D2)
Rs~ D2
= 1+Q2
for the relationship between equivalent series and parallel resistances
[88ST01]. In come cases, more complex circuit models may be used.
However, in the situation of near perfect, high Q materials (i.e. 6 <7°
or 0.1 radians), dielectric properties may be satisfactorily
approximated by an ideal capacitor, and a small angle approximation
(i.e. 6 — tan(5)) is valid.

170
Once K' and tan(S) are measured, the loss index or loss factor
(K”) may be determined from the product of K' and tan(6). The power
dissipation factor (PF) may also be determined from the relation,
PF= D - .
sJl+D2
When the dissipation factor (D or tan(6)) is less than 0.1, the PF
differs from D by less than 0.5% [88ST01].
Thus, the dielectric material may be evaluated as an electronic
packaging material candidate using the above technique. Dielectric
properties should be evaluated either at the temperatures, atmospheres
and frequencies of usage, or over as broad a range of these factors as
is feasible.
2.6.3 Dielectric Properties of Composite Materials
The area of study of dielectric properties of composite materials
is very large. A comprehensive overview of the dielectric behavior of
heterogeneous systems has been provided by van Beek [67VAN]. Other
models (i.e. the Banno and percolation models) are covered elsewhere
[83ZAL2,85HSU,87BAN1]. Discussion in this section is limited to
composites having constituents that are near perfect insulators, as well
as having low K and D values. The majority of the available literature
involving the modelling of the dielectric constant of porous materials
mentions four basic models that may be used to predict K as a function
of pore concentration [86CRO,88GER3,89CAO,89LEA]. In all of these
models the size of the constituent components is irrelevant as long as
they are small with respect to the sample size.
Said models are the parallel slabs model, the perpendicular slabs
model, the Maxwell spherical inclusions model, and the Lichteneker
logarithmic model. Figure 2.33 shows the equations involved as well as
the microstructures that they model. In theory, these models predict K

171
Perpendicular Slabs (2-2 Binary Composite)
Phase 2
K'c = V, K’, + V2K‘2 + ...
Electrodes
Parallel Slabs (2-2 Binary Composite)
1 V, V2
— — + b ...
K’c K', K’2
Lichteneker's Logarithmic Mixing Model
(3-3 Binary Composite,
Each Phase Continuous)
iasa 1
lase 2
log K' = IV log(K')
Equations and microstructures associated with the
parallel slabs, perpendicular slabs, logarithmic and
Maxwell models for predicting the dielectric constant
of composite materials
Figure 2.33

172
for different pore structures (or composite microstructures), and thus
provide a means by which composite microstructure may be predicted.
The parallel slabs model predicts the dielectric behavior of
composites that have the slabs oriented parallel to the capacitor
electrodes (in a parallel plate capacitor configuration), while the
perpendicular slabs model predicts the behavior of composites having
slabs oriented parallel to the capacitor electrodes. Both models are
special cases of the general empirical relationship,
ViK'l
where K'c is the composite dielectric constant, Vj is the volume fraction
of the ith constituent, K'¡ is the dielectric constant of the ith
component, and n is a structural configuration parameter. The value of
n for the parallel and perpendicular slabs models is -1 and 1
respectively [76KIN1]. Figure 2.34 illustrates the additivity rule for
these models (as well as the Maxwell and Lichteneker models) for a
binary composite system, having one component with K = 1 and the other
with K = 10. The perpendicular slabs model gives linear (i.e. standard
rule of mixtures) results, while the parallel slabs model gives maximum
deviation from linearity.
Similarly, Lichteneker's logarithmic dielectric mixing rule is
another special case of said empirical relationship where n is set to 0
[76KIN1]. Logically, the logarithmic mixture rule gives values
intermediate between the parallel and perpendicular slabs models, which
are extrema of the, above mentioned, empirical relationship. The
logarithmic mixing model predicts values of K for composites in which
all constituents are continuous and interconnected.
The Maxwell model predicts K for binary composites having
spherical inclusions (i.e. 0-3 composites). From Figure 2.34 it is
evident that the Maxwell model predicts K values that are quite close to

173
Illustration of the parallel slabs, perpendicular
slabs, Lichteneker's logarithmic mixing and Maxwell
models for a binary composite having K, of 1 and K; of
10 [76KIN1]
Figure 2.34

174
(but are slightly less than) those predicted by the logarithmic mixing
model, when the dielectric constant of the dispersed phase is
significantly larger than the matrix phase. It is also evident that the
Maxwell model more closely resembles the perpendicular slabs model, when
the dielectric constant of the dispersed phase is significantly less
than that of the matrix phase.
An advantage of all of the empirically based models is that
composites having more than one component may be modelled relatively
easily. This is not the case for the Maxwell model. Dielectric values
of binary composites may be predicted accurately for structures, that
are different than those covered by either of the empirical-based
models, or the Maxwell model, by using general effective medium (GEM)
theory [83HSU,85HSU]. The GEM model is similar to the above mentioned
empirical models, with the exception that the structural parameter value
it gives (which is analogous to n used in empirical models), has
significance for non-integer values as well as for integer values.
Effective medium theories replace the composite matrix,
surrounding a discrete inclusion, with a homogeneous field value.
The effective medium model, of Hsu et. al, is generally applicable to
many materials properties, including elastic modulus, conductivity,
dielectric constant, etc., as long as the material property of interest,
of each of the components of the binary composite follow the relation,
x
icr2<; y^io2
X2
where X; is the material property of interest (i.e. dielectric constant)
of composite component i [83HSU,85HSU].
In this model, the composite contains spheroidal inclusions which
may be stretched into fibrils or lamellae. This is accomplished by
assigning an eccentricity value (e) to the spheroids characteristic of
the internal composite structure of interest.

175
The eccentricity is defined by the relation,
e=(l-(-f)2)
A
1
2
where C/A is the aspect ratio of the semi-principal axes of the
spheroids (in all cases, two of the three semi-principal axes are set
equal to each other). When the aspect ratio is 1, all the axis of the
spheroid are equal, and the eccentricity value is 0, relating to the
case of perfect spheres. Figure 2.35 illustrates the geometry of the
spheroids used in the model of Hsu, et. al.
In the case of prolate spheroids, the A axis is larger than the
two equal minor axes (i.e. A > B = C). When A is much greater than C,
the model predicts K values for fibrillar microstructures having the
fibers oriented perpendicular to the electrodes (parallel to the
electric field). This is analogous to the perpendicular slabs model
mentioned above. For oblate spheroids, the two major axes are set equal
to each other (i.e. A = B > C) which, in the extreme case, this
represents a lamellar structure having the planes of the lamellae
oriented parallel to the electrodes (perpendicular to the electrical
field). This is analogous to the parallel slabs model.
For a binary composite system, the effective medium equation
derived by Hsu et al. is
[l-F(e) ] (K\[F(e) -Vj +k'2 [F(e) -V2] ) K^-K^K^Fie) =0
where F(e) is a function of spheroid eccentricity and is
F(e) =1zé1 [ln(-ij^) -2e]
2e3 1-e
for prolate spheroids, and

Electric Field
176
E
Sphere (A = B = C)
Oblate Spheroid (A = B > C)
C/A = Aspect Ratio
In All Cases: 0 < C/A < 1
Figure 2.35
Geometry and orientation of prolate, oblate and
perfect spheroids, used in the effective medium model
of Hsu, et. al [85HSU]

177
F(e) = -±- [
ez
\/(l-e2)
tan'1 (
:)]
for the oblate spheroids, K'c is the composite dielectric constant, K'¡
is the dielectric constant of the ith component (either 1 or 2), and V*
is the volume fraction of component i. The F(e) values for both prolate
and oblate spheroids are plotted as a function of spheroid eccentricity
(e) in Figure 2.36.
The effective medium equation may be solved for K'c using the
quadratic equation,
„/ _ ~B±\JB2 -4AC
c 2 A
where,
71= [l-F(e) ] ,
B=K\ [F(e) -Vj +K'2 [Fie) -V2] ,
and
C=-K,1K,2Fie) .
It can be shown that for F(e) = 0 (i.e. maximum prolation), the
effective medium theory (EMT) model reduces to the perpendicular slabs
equation and that for F(e) = 1 (i.e. maximal oblation), the EMT model
reduces to the parallel slabs equation [83HSU,85HSU]. Similarly, the
EMT model has been shown to be nearly analogous to models predicting
properties of 0—3 composites when F(e) = 1/3 (i.e. perfect sphericity)
[83HSU,85HSU]. Thus, the EMT model may be used to predict K'c for
binary composites having structures intermediate of those discussed
above. The EMT model may be used to estimate K'c for composites having

Cavity Depolarization Factor (F(e))
178
Figure 2.36
Cavity depolarization factor (F(e) for dielectric EMT)
as a function of spheroid eccentricity, for prolate
and oblate spheroids [85HSU]

179
more than two constituents, if an iterative process (i.e. combining two
phases into one for each iteration) is used.
2.7 Mechanical Properties
Inclusions (either soft or hard), within glass matrix composites,
greatly affect the mechanical properties of the material. Porosity
(i.e. very soft inclusions) tends to decrease the mechanical strength
and elastic modulus of a material, while hard inclusions usually
increase the fracture toughness and strength of a material, if the
additions of said inclusions do not result in a large concentration of
flaws or stress concentrators [76KIN1]. Soft inclusions do not alter
the crack path, but do alter crack velocity, while hard inclusions alter
the crack path [81BIS]. Both these mechanisms may serve to increase
fracture toughness [81BIS].
Inclusions may act as flaws within a material, thereby decreasing
mechanical strength and fracture toughness [84RIC]. Both fracture
toughness and mechanical strength are inversely proportional to
inclusion, or flaw size [76KIN1,81BIS]. In amorphous materials the
stress field about inclusions may be modified to either increase or
decrease fracture toughness, by either deflecting or attracting cracks
[81KRS,89JES ] . This is a function of both differential thermal
expansion of the composite constituents and of heat treatment near the
glass transition temperature [81KRS,89JES].
In glasses, pores tend to act as blunt cracks, with pore clusters
increasing the effective flaw size [84RIC]. Smoother pores (i.e. pores
without sharp discontinuities) act as blunter cracks. The strength and
elastic modulus of porous materials are also predicted to decrease
rapidly at and above the porosity percolation threshold [85SIE].
This section discusses the elastic modulus as a function of
inclusion concentration. It is important to look at various models,
considering the maximum and minimum values predicted. Models covering

180
both types of inclusions (hard and soft) are discussed, since the
composite system studied involves both hard and soft inclusions.
The effect of porosity concentration upon elastic modulus (Ep) is
modelled by the MacKenzie equation,
Ep=E0( l-l.9VptO.9Vp2)
where E0 is the elastic modulus of the fully dense material, and Vp is
the volume fraction of porosity [76KIN1]. This is an empirical model,
that has been shown to fit experimental data well [76KIN1]. Dean and
Lopez fitted experimental elastic modulus data to four other empirical
models, including the linear model, the two-thirds power law model, an
exponential model, and the Hasselman or nonlinear model [83DEA]. Table
2.10 lists the empirical elastic modulus versus porosity relations they
studied. They found that, on the whole, the linear law gives a superior
fit to experimental data, using the criteria of fit to data,
extrapolation to E0, and the consistency of correctly predicting
Poisson's ratio and bulk modulus from said extrapolation to full
density.
Ramakrishnan and Arunachalam modelled the effect of porosity upon
elastic modulus using quantum mechanical principles [90RAM]. They found
this model fit experimental data well when a variable Poisson's ratio
factor was used. Said factor is not calculable from experimental data,
and it was necessary to use finite element analysis to model the
effective Poisson's ratio.
Elastic modulus, as a function of inclusion (hard or soft)
concentration, is found to be intermediate between the Voigt and Reuss
models, which predict the extrema for said relationship [76KIN1].
The Voigt model uses the assumption that strain is homogenous throughout
the composite. It predicts the upper limit of E as a function of

181
inclusion volume fraction. The Voigt equation is
Ecv^Ei + V2E2+. . .
where Ecll is the upper limit composite elastic modulus prediction, and E¡
and Vi are the elastic modulus and the volume fraction of the ith
component respectively. It is evident that the Voigt model is similar
to the perpendicular slab model, mentioned above, in that they both use
a simple rule of mixtures to predict composite properties. Thus, both
models predict the upper limit of the respective effects.
The Reuss model assumes that the stress is homogeneous throughout
the composite, and predicts the lower limit of elastic modulus as a
function of inclusion concentration. It is defined by the relation,
where EcL is the lower limit of the composite elastic modulus. The
Reuss model is similar to the parallel slab model, for predicting
composite dielectric constant, in that both predict lower limits to
composite properties.
Intermediate values of the Ec, as a function of inclusion
concentration, are predicted by the Hashin-Shtrickman relations
[76KIN1]. The Hashin-Shtrickman model predicts upper and lower bounds
that are considerably narrower than those set by the Voigt and Reuss
models. The model also does not include any assumptions about relative
phase geometries. The upper and lower bounds to the Hashin-Shtrickman
relation are simply the same equation, with the modulus values
interchanged (i.e. E, and E, are switched).
The Hashin-Shtrickman model is not easily applicable to
experimental data, however. Also, it is difficult to expand it to
composite systems having more than two components. Furthermore, the
Hashin-Shtrickman model requires both bulk modulus and shear modulus

182
Table 2.10
Empirical Elastic Modulus versus Porosity
Models Investigated by Dean and Lopez [83DEA]
Model Type
Model Equation
Linear
Ep=E0 (1 ~bVp)
Exponential
Ep=E0exp(~bVp]
Hasselman (Non-Linear)
Two-Thirds Power
2
EP=E0 (1 -bVp )
Note: b is an empirical constant that is sensitive
to pore structure, as well as to the particular
material, in each of the above models.

183
data of both components, as well as statistical details of the phase
distributions, and thus, has found limited application [76KIN1].
However, when it has been applied to experimental data, it has predicted
the elastic modulus, as a function of inclusion concentration, more
accurately than the Voigt-Reuss extrema [76KIN1].
The elastic modulus of a material (E) may be measured, using
microhardness indentation techniques (combined Knoop and Vickers), using
the following equation:
c<_ 0.45 (H)
<3 a'
where H is the measured Vicker's hardness, b/a is the dimension ratio of
the indenter (b/a = 1/7 for the Knoop anvil) and b' and a' are one half
the length values of the minor and major dimensions of the Knoop
indentation, respectively. The fracture toughness (K,c) of a material
may also be calculated using microhardness indentation, using the
equation:
p — r -2
Kic=Hy/A (-= ) 5 [0.057 (±) 2]
12
where A is one half the dimension of the Vicker's indentation, and C is
one half the imposed crack length. This is only valid if C is greater
than 2A, since the crack must exceed the field of complex localized
stress, caused by the indentation [81ANS,81CHA]. Furthermore, said
technique is valid only if radial cracks are formed, since
circumferential cracks might interact with the radial cracks, absorbing
energy [81ANS,81CHA]. Also, this technique is only valid when the
microstructure is significantly smaller than the indenter. Finally,
when investigating porous materials, or when circumferential cracking is
significant, crushing may occur. Thus, the microhardness indentation
technique is only valid under certain, limiting circumstances.

CHAPTER THREE
EXPERIMENTAL PROCEDURE
3.1Overview
This chapter describes the actual experimental procedures used.
The sequence of experimental investigation is outlined in Figure 3.1,
which is a flow diagram denoting both the succession of experiments and
the feedback optimization mechanisms utilized. Figure 3.1 also aids in
the clarification of where each experimental procedure is utilized and
the importance of each procedure to the overall research project.
3.2Powder Synthesis and Treatment
3.2.1 Overview
Of the materials chosen for the investigation, only one was used
as-received, the Si3N4. The polystyrene latex used for creating
controlled porosity was produced and classified as described in section
3.2.2. The borosilicate glass powder was milled and prepared as
described in section 3.2.3.
3.2.2 Synthesis, Characterization and Preparation of Polystyrene
Microspheres
Production of the uniform polystyrene latex microspheres (UPLMs or
latex) was based largely upon work performed by Lok and Ober [85LOK]
involving dispersion polymerization of polystyrene latex. A block
diagram outlining the procedure used to the produce UPLMs is illustrated
in Figure 3.2. A schematic representation of the apparatus utilized for
UPLM production is illustrated in Figure 3.3.
184

185
Figure 3.1
Block Diagram depicting the experimental flow of the
research project as well as the feedback
optimization mechanisms used

186
Figure 3.2
Block diagram outlining the procedure used for
production of dispersion polymerized latex

187
Key:
A. Stirrer/Hotplate, Modified to Accept Controllers
B. Digital Setpoint Controller
C. Type K Thermocouple Assembly
D. Variable Transformer Stirrer Controller
E. 120 V AC Single Phase Power Source
F. Controlled Temperature Oil Bath
G. Ringstand/Clamps Assembly
H.Thermometer
I. Ar Purge Assembly (septum vented
with hypodermic needle)
J. Reaction Bath Assembly
K. 500ml Round Bottom Flask
L. Clamped Glass Stopper (PTFE lined)
M. EtOH/MeCell/HPC/Styrene/BPO Solution
N. Magnetic Stirrers
O. Insulated Bath Cover
P. Ar Purge Rate Control Valve
Argon In
With Ar Purge
L—
Without Ar Purge
Á.
Figure 3.3
Schematic representation of the apparatus used to
produce UPLMs via dispersion polymerization

188
Into a 500 ml round bottom flask,1 in which a magnetic stir bar2
had been placed, predetermined amounts of EtOH,3 methylcellosolve
(MeCell, also known as ethylene glycol monomethyl ether),4 and
hydroxypropyl cellulose 100,000 molecular weight,5 (HPC 100,000 MW) were
mixed until the HPC had completely dissolved (approximately 12 h).
During the mixing process, the flask was sealed using a glass stopper6
sleeved in teflon7 and clamped with a plastic joint clamp.8 During said
mixing process, the flask was also isothermally maintained at 65°C.
This was accomplished by way of the hot oil bath/mixer depicted in
Figure 3.3. The hot oil bath/mixer temperature was controlled via a
digital setpoint controller9 which had been previously calibrated to
agree with the 0.1°C resolution thermometer10 also depicted in Figure
3.3. In order to achieve temperature homogeneity, a second magnetic
1 Catalog Number: 10-067G, Fisher Scientific, 1600 Parkway View
Drive, Pittsburgh, PA 15205
2 Catalog Number: 14-511-58B, Fisher Scientific, 1600 Parkway View
Drive, Pittsburgh, PA 15205
3 Reagent Grade Ethanol, Florida Distillers Company, Lake Alfred,
FL 33850.
4 Catalog Number: E-182, Fisher Scientific, 1600 Parkway View
Drive, Pittsburgh, PA 15205
5 Catalog Number: 19188-4, Aldrich Chemical Company, Inc.,
Milwaukee, WI, 53233.
6 Catalog Number: 14-640J, Fisher Scientific, 1600 Parkway View
Drive, Pittsburgh, PA 15205
7 Catalog Number: 6194, Nalge Company, Rochester, NY, 14602
8 Catalog Number: 05-880E, Fisher Scientific, 1600 Parkway View
Drive, Pittsburgh, PA 15205
9 Model Number: 49 (type K thermocouple), Love Controls Corp.,
1714 S. Wolf Rd., Wheeling, IL 60090
10 Model Number: 15168B, Fisher Scientific, 1600 Parkway View
Drive, Pittsburgh, PA 15205

189
stirrer11 was used in the controlled temperature oil bath. The mixing
rate used was controlled via a variable AC transformer12 and was
adjusted to the maximum rate achievable before the onset of stirrer
instability.
After the above mixing step, predetermined amounts of styrene13
and benzoyl peroxide (BPO),14 both previously refrigerated, were added
to a 50 ml graduated cylinder.15 Next the cylinder was double sealed
with laboratory film,16 then capped with a rubber septum.17 The styrene
and BPO were then vigorously mixed by inverting the sealed graduate for
approximately 50 repetitions.
During this time, the flask containing the EtOH-MeCell-HPC
solution was purged for 30 min. with Ar18 introduced via a metal lance19
puncturing a rubber sealing septum17 which covered the opening of the
flask. Exhaust of purging gases was provided via a hypodermic needle,20
also penetrating the sealing septum.
11 Catalog Number: 14-511-93, Fisher Scientific, 1600 Parkway View
Drive, Pittsburgh, PA 15205
12 Model Number: 3PN1510 Variac, Staco Energy Products Co., Dayton,
OH
13 Catalog Number: 04507, Fisher Scientific, 1600 Parkway View
Drive, Pittsburgh, PA 15205
14 Catalog Number: 17998, Aldrich Chemical Company, Inc.,
Milwaukee, WI 53233
15 Catalog Number: 08-552D, Fisher Scientific, 1600 Parkway View
Drive, Pittsburgh, PA, 15205
16 Parafilm M, American National Can, Greenwich CT, 06836
17 Catalog Number: Z10,145-1, Aldrich Chemical Company, Inc.,
Milwaukee, WI 53201
18 Catalog Number: UN1006, Jacksonville Compressed Gases Corp.,
Jacksonville, FL 32204
19 Catalog Number: 14-819-169, Fisher Scientific, 1600 Parkway View
Drive, Pittsburgh, PA 15205
20 Catalog Number: 14-826-5B, Fisher Scientific, 1600 Parkway View
Drive, Pittsburgh, PA 15205

190
The Ar flow rate was adjusted to a level high enough to visibly expand
the septum thus ensuring the purged system was under a slight positive
pressure. During the purging operation, the previously mentioned mixing
and temperature conditions were maintained.
After Ar purging for 30 min., the styrene-BPO solution was added
to the EtOH-MeCell-HPC solution in the flask, the flask opening
recovered, and the above-mentioned purging continued for another 30 min.
After this purging step was completed, the teflon sheathed7 glass
stopper6 was quickly clamped in the flask opening, thereby sealing the
system.
Two hours after the styrene-BPO addition, the oil bath temperature
was raised to 75°C. This treatment was maintained for 22 more hours.
After a total of 24 h, the sealed flask was removed from the stirred oil
bath and stirred at room temperature on a different stir plate21 while
cooling. When the flask reached a comfortably handleable temperature
(approximately 50°C) , it was washed on the outside with tap water in
order to cool the UPLM suspension more quickly. The resulting UPLM
suspension was quite viscous, having a consistency similar to glycerin
at room temperature. After cooling, the flask was opened and the UPLM
suspension decanted into a 1 pint (473 ml) clear glass bottle and
capped.
Later the suspension was centrifuged22 in 50 ml polyallomer
centrifuge tubes.23 An initial centrifugation time and speed of about
4,000 rpm for 30 min. worked well for all UPLM sizes produced. This
centrifuge treatment separated the latex from the relatively viscous
21 Catalog Number: 14-493-120M, Fisher Scientific, 1600 Parkway
View Drive, Pittsburgh, PA 15205
22 Model Number: J2-21, Beckman Corp., Palo Alto, Ca, 94303-0803
23 Catalog Number: 05-563-10G, Fisher Scientific, 1500 Parkway View
Drive, Pittsburgh, PA 15205

191
supernatant effectively, yet still allowed for easy redispersion of the
latex.
The supernatant was then replaced with denatured EtOH,24 and the
centrifugation process was repeated for 2 more repetitions, further
washing the UPLMs. For the second and third washing repetitions, the
centrifuge speed was adjusted for the UPLM size being washed. A speed
of 3,000 rpm for approximately 20 min. was sufficient to separate the
smallest spheres while 1,500 rpm for 20 min. was found satisfactory for
the largest spheres.
As will be discussed later, the target diameter for the UPLMs used
in most experiments was approximately 5 pm. Thus, the batch recipe was
modified to target this sphere diameter using an interpolation of data
reported by Lok and Ober [85LOK].
After the centrifugation/washing process, a sample was taken for
preliminary size/size distribution characterization via scanning
electron microscopy (SEM).25 Approximately one drop of the UPLM
suspension was decanted into a 20 ml polystyrene sample vial24 using a
5 ml capacity (24 to 26 drops per ml) PE disposable transfer pipette.27
Denatured EtOH was then added to the vial to dilute the UPLM suspension
until turbidity was barely apparent via visual inspection. The vial was
then capped and the diluted suspension was subjected to 15 min. of sonic
24 Catalog Number: A407, Fisher Scientific, vacuum filtered through
numbers 4 and 1 Whatman qualitative filter paper, Whatman International,
Ltd., Maidstone, England, using Catalog Number: 10-437-23A, Fisher
Scientific suction funnel
25 Model Number: JSM-35CF, JEOL Ltd., Tokyo, Japan
24 Catalog Number: 03-341-13, Fisher Scientific, 1600 Parkway View
Drive, Pittsburgh, PA 15205
27 Catalog Number: 13-711-5A, Fisher Scientific, 1600 Parkway View
Drive, Pittsburgh, PA 15205

192
exposure, in a sonic dismembrator,31 in order to break apart any
agglomerates in the suspension. After sonication, the suspension was
vigorously hand shaken for approximately one minute, the vial uncapped,
and approximately 3 drops decanted from another disposable transfer
pipette27 onto a precleaned glass substrate29 affixed to a 1" (2.54 cm)
diameter aluminum SEM specimen stub30 via double stick tape.31 The
specimen was then placed into a covered petri dish32 and allowed to dry.
The dried specimen was then examined with an optical microscope,33 in
reflection mode, in order to determine if it was satisfactory.
Satisfactory samples were then Au-Pd DC sputter coated34 and packaged
for future SEM analysis.
Preliminary SEM sphere size analysis involved imaging the spheres
at a magnification of 1000X, then measuring and recording the diameter
of 125 spheres. The diameter measurements were taken on the viewing CRT
using a pair of vernier calipers.35
28 Either Model Number: LW-375, Heat Systems Ultrasonics, Inc.,
Plainview, NY 11803, or Model Number: VC-600, Sonics and Materials,
Inc., Danbury, CT, the sample container was clamped over the sonic
transducer, immersed within a chilled circulating water bath
29 Catalog Number: 12-568-15, Fisher Scientific, 1600 Parkway View
Drive, Pittsburgh, PA 15205, the suspension was deposited upon
nonfrosted areas, the glass was made the appropriate size (approximately
20 x 20 mm) by scribing to size, wetting the scribe mark, then snapping
the glass to size using a Model Number: 08-675, Fisher Scientific
diamond scribe
30 Fabricated from 1" (2.54 cm) diameter aluminum rod stock at the
Department of Materials Science and Engineering Machine Shop, University
of Florida, Gainesville, FL 32611
31 Model Number: 665, Scotch Double-Coated Tape, Commercial Office
Supply Division of 3M, St. Paul, MN 55144-1000
32 Catalog Number: 08-757-100B, Fisher Scientific, 1600 Parkway
View Drive, Pittsburgh, PA 15205
33 Nikon Optiphot Model, Nikon Instruments, Japan
34 Model: Desk II Sputter Coater, Denton Vacuum, Inc., Cherry Hill,
NJ
35 Catalog Number: 12-122, Fisher Scientific, 1600 Parkway View
Drive Pittsburgh, PA 15205

193
The size reference bar was also measured and recorded periodically in
order to provide a conversion factor. The raw data were then encoded
into a computer spreadsheet program36 which converted the measured
diameters into actual diameters. From the spreadsheet, mean size,
largest size, smallest size, standard deviation and variance were
obtained. The spreadsheet was also used to sort the diameter data from
largest to smallest size. The sorted diameter data was then used to
create a size histogram. The histogram system utilized diameter
increments of 0.1 pm and the number of spheres at the diameter of
interest were encoded manually on a data sheet. These data were then
encoded into another computer spreadsheet program36 which converted the
data into number, volume and estimated surface area data. This
spreadsheet was also utilized in plotting various characteristics
dependent upon sphere diameter. Table 3.1 outlines the equations used
to perform all size, size distribution, surface area and geometric
standard deviation calculations to characterize all powders sized.
This method of measurement was used for preliminary (presettled)
diameter characterization. Subsequent to the settling process
(described below) diametric measurements were also provided by taking
micrographs of 1000 spheres at a magnification of 1000X. The UPLM
diameters were then measured directly from the micrographs utilizing a
6X optical comparator37. All other methods used in sphere diameter
measurement (i.e. specimen preparation and data manipulation, etc.) were
the same for both sets of UPLM diameter measurement.
The latter method was used to characterize the settled UPLMs
because it removes an element of possible data biasing since almost all
spheres photographed are measured.
36 A product of LOTUS Development Corporation, Cambridge, MA
37 Catalog Number: 12-056, Fisher Scientific, 1600 Parkway View
Drive, Pittsburgh, PA 15205

194
Table 3.1
Equations Used Determine UPLM Size, Size
Distribution, Geometric Standard Deviation
and Surface Area Data of the Latexes Produced
Sphere Diameter, X (pm):
X= — xlO
D
where: A is length of measured magnified diameter (mm)
D is length of measured magnified 10 pm
reference marker (mm)
Mean Sphere Diameter, Xav<. (pm):
„ n>Xi
Aave ^
where: n¡ is the number of measured spheres at size
increment i
X; is the diameter of the spheres at increment i
(pm)
Number Fraction at Size, Nf:
N,~
Volume Fraction at Size, Vf
y 3
(T>
Ei
Powder Surface Area, SA (m2/g):
where: p is the powder density (g/cm3)
Cumulative Number Percent Larger Than, CNPL (%):
CNPLuell
ni
—xl
Eini
00

195
Table 3.1 (continued)
7. Cumulative Number Percent Finer Than, CNPF (%)
CNPF*
Ei
â– xlOO
8.
Cumulative Volume Percent Larger Than, CVPL (%):
CVPL*
y 3
£i 4> -i
xlOO
9.
Cumulative Volume Percent Finer Than, CNPL (%)
CVPF*
£í“J” (-=*> «i
â– xlOO
where: CNPL + CNPF = 100
CVPL + CVPF = 100
10. Geometric Standard Deviation, GSD (for log normal distributions):
A. Traditional:
GSD =
CPF =84.13%
*
mediann
where:
B. Inverse:
CPF is cumulative percent finer than
m is mode (either number or volume basis)
GSD~
X.
»CPL=Sl.13%
*median_
where:
All types of geometric standard deviation
are 1 for a perfectly monodisperse system

196
It also is more accurate due to the measurement technique used.
However, this method is less precise since the comparator scale limit is
0.125 pm on 1000X micrographs.
From presettled diametric characterization, the initial batch was
deemed satisfactory, uniform in size and having a mean sphere diameter
of 4.6 pm. As a result, nine more batches of the same recipe were
produced. Ten batches, of approximately 50 g UPLM each, were produced
in order to provide an amount sufficient for planned experimentation, as
well as for settling losses and for exclusion of up to two batches, in
order to keep the size distribution as tight as possible. Appendix II
depicts sizing data of the batches before classification via settling
(obtained using the first measurement technique described). From
additive analysis of the initial sizing results for each batch, it was
deemed that batches 03199001-08 and 03199001-10 would widen the size
distribution the greatest amount. Therefore, these batches were not
used in the mixed batch. The remaining 8 batches were then mixed
together and settled. Subsequent to said characterization, the eight
batch amalgam was diluted to approximately 5 V% solids in denatured
EtOH, then settled in two 4,000 ml polymethylpentene (PMP) graduated
cylinders38 to eliminate the fines. The supernatant (which included the
fines) was then pumped off using a peristaltic pump39 with flexible
plastic tubing.40 The liquid pickup utilized was a glass tube having a
hooked end,41 which allowed a maximum pumping rate with minimal loss of
settled latex.
38 Catalog Number: 08-572-5J, Fisher Scientific, 1600 Parkway View
Drive, Pittsburgh, PA 15205
39 Model Number: 7520-25, Cole Parmer Instrument Company, Chicago,
IL, 60648
40 Model Number: R-1000, Tygon plastic tubing, Norton Performance
Products, Akron, OH, 44309-3660
41 Catalog Number: 11-365A, Fisher Scientific, 1600 Parkway View
Drive, Pittsburgh, PA 15205, the hook was made on one end using an oxy-
hydrogen torch

197
After supernatant removal, the settled material was then redispersed in
fresh denatured EtOH. This process was repeated until the supernatant
was visibly clear. At this point, the settled powder was redispersed in
a minimal amount of denatured EtOH and the resulting dispersion was
moved to a 2,500 ml clear glass jug. After settling within the jug,
more supernatant was pumped off, thereby maximizing the solids loading
of the UPLM dispersion. The solids loading of the batch was determined
after this point, as described below, and the packaged UPLMs were then
stored for future use.
In order to allow investigation of the effects of size of included
porosity upon properties of the materials containing included porosity,
single batches of UPLMs were made of 6 other sizes. The fabrication
method of these UPLMs was as described above.
Basically, the EtOH to MeCELL ratio (and thus, the solution
solubility parameter) was manipulated using interpolations of both the
data of Lok and Ober [85LOK] and from sizing data of the batches
produced for this study, as the data became available. Modifications
were made in said ratio as deemed necessary to pursue a specific uniform
sphere diameter. Table 3.2 outlines the batches produced as well as
other pertinent characteristics of said batches.
In order to investigate the effect of size distribution of
included porosity upon the composite microstructure, a suspension of
latex was produced by mixing controlled portions of the largest, median
and smallest latex batches (07249001, 06199001-07+09 and 07269001
respectively) together. The amount of each batch used was determined
following a maximization of packing factor criterion. Since the
smallest batch was found to be bimodal in size distribution, the
required portions of each batch were determined by interpolating between
3 and 4 component sphere models for packing maximization, introduced by
Westman and Hugill [30WES) and later elaborated further upon by McGeary
[61MCG].

198
Table 3.2
Batch Compositions and Target Sizes For Dispersion
Polymerized Uniform Polystyrene Latex Microspheres
Batch
ID
Number
Component Concentration'
Solu¬
bility
Para¬
meter
(cal/cm3)1/2
Target
Mean
Sphere
Diam.
(pm)
EtOH
(V%)
MeCell
HPC
(g)
Sty¬
rene
(V%)
BPO
(g)
07269001
70
15
5.00
15
2.00
12.1
3.0:
07309001
65
20
5.00
15
2.00
12.0
3.0:
07199001
60
25
5.00
15
2.00
11.9
3.0:
06199001
-10
51.25
33.75
5.00
15
2.00
11.8
5.0
07219001
42.5
42.5
5.00
15
2.00
11.7
7.03
08029001
36.25
48.75
5.00
15
2.00
11.6
7.03
07249001
30
55
5.00
15
2.00
11.5
10.0
Notes:
1 Volume fraction calculations assume no volume
additions from dissolved powders (i.e. HPC and BPO)
2
3
Each successively dated batch was calculated pursuing
a 3.0 pm target diameter from the most current data
available at the time (i.e. using feedback
optimization)
Each successively dated batch was calculated pursuing
a 7.0 pm target diameter from the most current data
available at the time (i.e. using feedback
optimization)

199
Table 3.3 indicates the amounts of each batch used to produce the
wide size distribution (quadramodal) latex batch with the goal of
achieving a maximized packing factor. Microscopic analysis was also
used to determine the size and surface area characteristics of the wide
size distribution latex batch through the use of the previously
mentioned spreadsheet programs.
3.2.3 Ball Milling and Preparation of Borosilicate Glass Powder
The as-received, borosilicate (BS) glass powder4: size was <325
mesh and was used, during experimentation, either as-received or after
ball milling, in methanol, for 20 hours. The ball milling procedure
follows.
To a large, precleaned, ceramic milling vessel,43 5000 g of A1203
milling media44 was added. Next, 780 g of the glass powder was added to
the milling vessel. Subsequent to the glass powder addition, 700 ml of
methanol45 was added. The container was then carefully sealed, and
placed upon a rolling mill44 for 20 h, after which the vessel was
removed. The milling jar was then unsealed and the milled glass/MeOH
slurry was decanted into an evaporation dish47 through a 14 mesh sieve48
42 Glass Number: 7070, Materials Business, Corning Glass Works,
Corning, NY 14831
43 Origin unknown: Similar to Catalog Number: 08-382D, Fisher
Scientific, 1600 Parkway View Drive, Pittsburgh, PA 15205
44 Origin unknown: Similar to Catalog Number: 08-412-15A, Fisher
Scientific, 1600 Parkway View Drive, Pittsburgh, PA 15205
43 Catalog Number: A411-20, Fisher Scientific, 1600 Parkway View
Drive, Pittsburgh, PA 15205
46 Model Number: CF-81106, Norton Chemical Process Products
Division, Akron OH, 44309
47 Catalog Number: 08-741H, Fisher Scientific, 1600 Parkway View
Drive, Pittsburgh, PA 15205
48 The W.S. Tyler Company, Cleveland, OH

200
Table 3.3
Composition of Polysized (Quadramodal) Latex Batch
1.Maximization of Packing Factor:
A. 3 Uniform Components [30WES]:
Component Size
Component Volume Fraction
A
66.0
B
25.0
C
9.0
B. 4 Uniform Components [61MCG]:
Component Size
Component Volume Fraction
A
60.7
B
23.0
C
10.2
D
6.1
C. Hybrid System Produced (interpolation of the above models):
Component Size
Volume Fraction
(4 Component Eq.)
Volume Fraction
(3 Component Eq.)
A
62.8
62.8
B
23.8
23.8
C
10.4
13.4
D
3.0
Notes:
1. A>B>C>D
2. Each Component is Perfectly Uniform
3. The Size Ratio Between Two Consecutive Components
is Recommended to Be (At Least) 7:1 [61MCG]

201
in order to separate the slurry from the milling media. A magnetic stir
bar40 was then placed in the decanted slurry. The container was then
placed on a stirrer/hot plate,50 and covered loosely with aluminum
foil.51 The heat was set to a low level (3) and the stirring to a
moderate speed (6). The latter was chosen to promote vigorous stirring
without causing splashing of the slurry. The entire apparatus was
enclosed within a fume hood5: to vent the MeOH fumes. The slurry was
heated and stirred in this manner until it became a solid cake. At this
point the evaporating dish was removed from the stirrer/hot plate and
the cake was broken up into small chunks using both a metal spatula53
and a pestle.54 The evaporating dish, containing the glass powder, was
then placed in a vacuum oven55 and heated to approximately 17 5°C in a
vacuum of >30" Hg (gauge) until dry (usually overnight).
The criterion for powder dryness was that the vacuum gauge
indicate a maximum vacuum reading (>30" Hg (gauge)), and remain stable
over a period of at least, 30 min. without vacuum pumping. Pumping was
limited to periods of no longer than 15 min. in order to prevent
contamination of the milled glass powder with backstreamed vacuum pump
oil. A total of 10 batches were milled in this manner. After drying,
each powder batch was mixed with the others in one of two 1 gallon (3.79
49 Catalog Number: 14-511-93, Fisher Scientific, 1600 Parkway View
Drive, Pittsburgh, PA 15205
50 Model Number: PC-520, Corning Inc., Corning, NY 14831
51 Heavy Duty Reynold's Wrap, Reynold Metals Company, Richmond, VA,
23261
52 8' laboratory fume hood, Kewaunee Scientific Corp., Statesville,
NC 28677
53 Catalog Number: 14-373-25A, Fisher Scientific, 1600 Parkway View
Drive, Pittsburgh, PA 15205
54 Catalog Number: 12-961-5D, Fisher Scientific, 1600 Parkway View
Drive, Pittsburgh, PA 15205
55
Model Number: 5831, National Appliance Company, Portland, OR

202
1) polyethylene (PE) jarsS6 by inverting the powder-filled container for
approximately 250 repetitions after each batch addition. After all the
batches were mixed together in this manner, portions of the powder in
each of the two PE jars were removed and mixed together in the opposite
jar, using the above method, in order to further pursue powder
homogeneity. This removal/mixing process was repeated 5 times. The
powder was then stored in the two PE jars and sealed for future
experimentation.
3.3 Powder Characterization
3.3.1 Overview
Powder characterization was performed in order to gain a knowledge
of the composite precursor powders and to investigate the effect that
ball milling, in MeOH, has upon the BS glass. It is necessary to know
the powder density when designing and batching composites. Furthermore,
a knowledge of the powder size and size distribution, as well as the
powder surface area and appearance is helpful in optimizing processing
parameters and material properties.
Composition data is necessary in order to ensure that the powder
precursors are what they are supposed to be. This is very valuable when
comparing experimental results to data reported in the literature. Since
the Si3N4 was used as-received (and came with a guaranteed analysis),
composition investigation was not necessary. Chemical composition
analysis of the latexes investigated was also deemed unnecessary, since
the UPLMs were produced from pure styrene, and since the latexes were
only used as a filler and were removed completely during pyrolysis and
sintering procedures (as indicated by dielectric data). However, it was
deemed necessary that a study be performed investigating the effects of
ball milling, in MeOH, on the composition of the BS glass powder since
56 Catalog Number: 11-815-11B, Fisher Scientific, 1600 Parkway View
Drive, Pittsburgh, PA 15205

203
milled powder compositions are frequently different from their
precursors, due to dissolution of either the powder or the milling
media.
Finally, a knowledge of how the powder surface evolves with heat
treatment is also helpful when optimizing thermal treatment schedules.
Since crystalline silicon nitride is stable with regard to sintering and
viscous flow at the temperatures investigated, no such study was
performed upon the Si3N4 powder used in this study. Since the
polystyrene latexes were removed via pyrolysis, no studies of surface
area, as a function of thermal treatment, were performed upon them
either. However, investigation of the evolution of powder surface area
with thermal treatment was performed upon the ball milled BS glass
powder since it was the sintering matrix in the materials investigated.
3.3.2 Visual
Visual inspection of the precursor powders was provided via SEM.25
The powder specimens were prepared as via a method similar to that
described in section 3.2.2 above, with the exception that the dispersion
system used was aqueous (pH -9.5). As will be discussed below, it was
desirable to investigate the surface smoothness of the borosilicate
glass powder both prior and subsequent to milling in order to
investigate dissolution effects of milling upon the glass. Since said
porosity was expected to be smaller than the minimum resolution of the
SEM, transmission electron microscopy (TEM)57 was used.
Specimens were prepared by dispersing approximately 20 mg of the
respective powder in denatured EtOH24 in a polystyrene sample vial,26
capping the vial, and subjecting the dispersion to approximately 15 min.
of sonic treatment in order to assure destruction of soft agglomerates.
57
Model Number: 200CX, JEOL Ltd, Tokyo, Japan

204
Approximately 1 drop of said suspension was then gently decanted onto a
holey-carbon-substrate-covered TEM specimen grid58 using a 20 pi
capillary pipette.59 The specimen grid was placed on top of 0.22 pm
pore size, nylon filter paper,® which had been previously placed upon
absorbent tissue,61 in order to provide a driving force for dispersion
flow through the holes in the carbon substrate. A glass specimen
cover62 was then placed over the specimen, during drying, in order to
prevent contamination. Specimens were viewed uncoated in a TEM57
utilizing 200 KeV electron accelerating potential at magnifications of
up to 300,000X.
3.3.3 Density
Powder density was determined using He gas pycnometry,63 as
recommended,64 using the large sample cell. A representative powder
sample was taken from the powder container and placed in a preweighed
large sample cup. The sample with cup weight was then measured and
recorded. The cup and powder were then dried in a vacuum oven55 at >30"
Hg (gauge). The drying temperature used was approximately 60 and 175°C
for polymeric and ceramic materials respectively. A vacuum was pulled
on the chamber periodically for durations not exceeding 15 min. in order
58 Prepared by C. E. Randall, NYSCC at Alfred University, Alfred,
NY
59 Catalog Number: 5878 Unopette pipette, Becton Dickinson
Vacutainer Systems, Rutherford, NJ 07070
“ Catalog Number: N02-SP142-25, Fisher Scientific, 1600 Parkway
View Drive, Pittsburgh, PA 15205
61 Catalog Number: 06-666-11, Fisher Scientific, 1600 Parkway View
Drive, Pittsburgh, PA 15205
62 Catalog Number: 08-749, Fisher Scientific, 1600 Parkway View
Drive, Pittsburgh, PA 15205
63 Model Number: MVP-1 Multipycnometer, Quantachrome Corporation,
Syosset, NY, 11791
64 See pages 7-14 of Operating Manual for footnote 66.

205
to reduce backstreaming of vacuum pump oil onto the powder samples. The
samples were dried in this manner for approximately 12 h. The sample
was allowed to cool, in the vacuum oven, to ambient temperature.
UPLM powder samples were obtained by filtering from suspension
using a vacuum filtering apparatus.65 The filter cake was then dried at
approximately 60°C at ambient pressure. The dry cake was then broken
up, placed in a clean 125 ml PE bottle.66 The bottle was then tightly
capped and shaken vigorously by hand for approximately 3 min. in order
to further break up agglomerates. The resulting powder was then
subjected to the drying treatment outlined above for polymers, and was
then ready for density characterization.
After powder sample drying, the cup was removed from the vacuum
oven and quickly placed inside the pycnometer sample chamber. The
sample was then subjected to a He67 gas flow for no less than 15
minutes. Subsequent to said gas purging the experiment was performed.
All external gas valves were closed and the chamber/reservoir
valve was closed. The external He valve was then opened allowing the
pycnometer reservoir to fill with gas. This valve was then closed as
the pressure gauge reading approached 15 psi (0.103 MPa) and said
reading was recorded. Next the chamber/reservoir valve was opened,
allowing the pycnometer sample chamber to fill with the He previously in
the pycnometer reservoir. After pressure equilibration of the two
chambers was achieved (as determined by a stable pressure gauge reading)
the pressure was again recorded. The He external exhaust valve was then
opened and the reservoir and sample chamber allowed to come to ambient
65 Filtered through number 1 Whatman qualitative filter paper,
Whatman International, Ltd., Maidstone, England, using Catalog Number:
10-437-23A, Fisher Scientific suction funnel
66 Catalog Number: 02-893-5C, Fisher Scientific, 1600 Parkway View
Drive, Pittsburgh, PA 15205
67
Catalog Number: UN1046, Liquid Air Corp., Walnut Creek, CA 94596

206
pressure as indicated by a null reading of the pycnometer pressure
gauge. The gauge was then rezeroed and the process repeated.
After no less than 4 repetitions of this procedure, the sample
container and sample were removed for the sample chamber and reweighed.
The powder density was then determined. The equations used to calculate
powder density by way of gas pycnometry are outlined in Table 3.4. The
powders were then returned to their original container for further use.
No less than two independent runs were performed upon each powder
in order to provide a measurement of precision for said experimentation.
The pycnometer was also calibrated prior to testing following the
recommended procedure.64
3.3.4 Size Characterization of Ceramic Powders
The particle sizes and size distributions of the ceramic powders
were determined using both gravitational and centrifugal sedimentation
techniques. Latex powder sizes and size distributions were determined
as described above in section 3.2.2. Gravitational sedimentation
characterization utilized an x-ray attenuation technique.68 A variety
of dispersion mediums were used on each ceramic powder, including
aqueous (approximately pH 9.5 via concentrated NH^OH69 addition), MeOH45
and denatured EtOH.24 The powder volume fraction used in all cases was
between 2 and 3 V%.
Centrifugal sedimentation characterization was provided via a
horizontal platen centrifuge, light attenuation technique.70 The
dispersion medium utilized for this technique was approximately pH 9.5
68 Model Number: 5000 Sedigraph, Micromeritics, Corp., One
Micromeritics Drive, Norcross, GA 30093
69 Catalog Number: A669-500, Fisher Scientific, 1600 Parkway View
Drive, Pittsburgh, PA 15205
70
Model Number: CAPA 700, Horiba Ltd., Kyoto, Japan

207
Table 3.4
Equations Used to Determine Powder Density
Using He Gas Pycnometry
1. Powder Density, p (g/cm3):
P
where: Wp is powder weight (g)
Vp is powder volume (cm3)
2. Powder Volume, Vp (cm3):
Vp=Vc-Vr[(^)-l]
where: Vc is sample cell volume (cm3)
V, is reference volume (cm3)
P, is pressure reading after pressurizing
the reference cell (psi)
P; is pressure reading after including the
sample cell in the pressurized circuit
(psi)
Notes: 1. Powder weights obtained to nearest tenth of milligram
using a model number: XD 100A, Fisher Scientific
precision scale
2. Vc used for the large cell was 149.064 cm3
V, used for the large cell was 66.820 cm3
3.

208
aqueous (pH adjusted using concentrated NH4OHw). A much lower
(approximately 0.1 V%) powder volume fraction was used in making
suspensions for this technique. The suspension solids loading was
adjusted until a maximum light attenuation of greater than 90% of full
scale was achieved. For both particle sizing techniques, the
suspensions were sonicated for approximately 15 min., prior to testing,
in order to break up agglomerates.
The x-ray sedimentation-derived ceramic particle sizing data for
each ceramic powder characterized was obtained by averaging the data of
no less than three separate settling repetitions at cumulative volume
percent less than (CVPF) intervals of 5 V%. It was necessary to average
the data in this manner since the instrument68 provided output in a log-
linear fashion. This methodology was used in order to avoid errors of
estimation associated with reading constant intervals on a log axis.
The averaged data was then fitted utilizing the least squares
polynomial regression computer program illustrated in Appendix III. The
order of the polynomials used for curve fittings was determined from the
same program and was chosen to minimize the standard error of estimate.
The averaged data was then manually encoded into a computer spreadsheet36
program, and the experimental data and the corresponding polynomial fit
were compared.
Typically, polynomial regression becomes inaccurate at range
extrema. In cases where this occurred, linear and linear spline fits
were utilized to make the least squares regression polynomials fit the
data better at the range extrema. The spreadsheet utilized converts the
input CVPF data to cumulative volume percent larger than (CVPL),
cumulative number percent finer than (CNPF), cumulative number percent
larger than (CNPL) and estimated powder surface area (SA) data. All
particle sizing calculations are based upon spherical particle
geometries. The spreadsheet also provides output in histogram form, as
well as a medium for calculating geometric standard deviation (GSD).

209
The equations used by the spreadsheet to perform said calculations are
outlined in Table 3.5 (part A). Centrifugal particle sizing data was
taken from an average of at least three experimental repetitions as
well. In this case however, the averaging involved the volume fraction
between two contiguous sizes on a linear axis, and thus, no polynomial
fitting was required. The averaged data were then encoded manually into
a computer spreadsheet, as above, to obtain similar outputs. The
equations utilized for centrifugal particle size analysis are outlined
in Table 3.5 (part B) as well.
3.3.5 Surface Area
Surface areas of the respective powders were measured using gas
adsorption/desorption methods. Surface area and, when deemed necessary,
the powder surface pore size distribution was determined for each powder
used in the investigation. Data were obtained utilizing either a
manual71 or an automated77 surface area analysis unit.
When performing manual surface area analysis, the sample holder
tube was precleaned, dried and weighed. An amount of powder (previously
dried as described in section 3.3.3 above) was added to the sample
holder and any powder sticking to the inside of the vertical extensions
of the sample holder was brushed into the bottom using a pipe cleaner.73
A sealing apparatus was then connected to the sample holder and the
assembly was affixed to the outgas section of the manual surface area
analysis unit where it was purged with N; gas74 for not less than 2 h at
approximately 150°C.
71 Model Number: OS-7 BET unit with Model Number: LMFC-4 gas mixing
unit, Quantachrome Corp., 69 Glen Cove Rd, Greenvale, NY 11548
72 Model Number ASAP 2000, Micromeritics Corp., One Micromeritics
Drive, Norcross, GA 30093
73 Catalog Number: 03-642B, Fisher Scientific, 1600 Parkway View
Drive, Pittsburgh, PA 15205
74 Catalog Number: 1066, Liquid Air Corp., Walnut Creek, CA 94596

210
Table 3.5.
Equations Used to Calculate Size, Size Distribution,
Estimated Surface Area and Geometric Standard Deviation
of Sizing Data (Based on Spherical Powders) Obtained for the
Ceramic Powders Investigated Using X-Ray Sedimentation and
Centrifugal Particle Size Analysis Techniques
Size is determined by averaging the cumulative percent finer than
size data at 5 V% intervals for no less than three experimental
repetitions. The size distribution data is plotted as equivalent
spherical diameter (abscissa) versus cumulative volume percent
finer than (ordinate). The median particle size is determined by
said average at 50 V% CVPF. After polynomial fitting, cumulative
surface area and cumulative number percents are calculated.
2. Spherical Surface Area at Size, SSAAS, (Sedigraph Only,
Automatically Calculated with CPSA) m:/g:
6 x
SSAAS=
Aftf%
100
^Larger ^ smaller^
where: is the largest equivalent spherical
diameter of the size region of interest
(pm)
Amalle, i-s the smallest equivalent spherical
diameter of the size region of interest
(pm)
AM% is the change in mass percent between
^Larger and Dsmslkt
p is the theoretical density of the powder
g/cm3
3. Cumulative Spherical Surface Area, CSSA, m2/g:
CSSA=yi:eize2 SSAAS,
*1 -sizel
isi2<., and isi2c2 are set to the maximum and
minimum particle sizes of the powder for
Total Specific Surface Area
where:

211
Table 3.5 (continued)
4. Polynomial Curve Fit for Mass Percent at Size,
CtXD1
where: D is the equivalent spherical diameter
(pm)
C; is the i* polynomial coefficient
n is the order of the polynomial
Relevant Data and Coefficients Utilized
A. Sedigraph:
Corning 7070 As-Received Borosilicate Glass Powder
Coefficient
Value
0
2.562431
Order
5th
1
13.333852
Correlation
0.9979
2
-0.9415702
Standard Error
of Estimate
2.309 M%@size
3
0.03502355
Linear
Extrapolation
4
-6.219517 x 10-4
High End
Yes, Above
57.0 pm
5
4.107572 x 10'6
Low End
No
Corning 7070 Ball Milled Borosilicate Glass Powder
Coefficient
Value
0
0.191787
Order
6*
1
12.78353
Correlation
0.9999
2
18.60418
Standard Error
of Estimate
0.2795 M%^
3
-7.567243
Linear
Extrapolation
4
1.184119
High End
Yes, Above
7.5 pm
5
-0.08355908
Low End
No
6
2.169674 x 10'3

212
Table 3.5 (continued)
Ube SNE03 As-Received Silicon Nitride Powder
Coefficient
Value
0
131.1378
Order
11*
1
-497.6126
Correlation
0.9991
2
547.9822
Standard Error
of Estimate
2.014
3
-136.0857
Linear
Extrapolation
4
-31.98561
High End
Yes, Above
4.8 pm
5
7.148575
Low End
No
6
2.59008
7
-0.3918017
8
0.4788766
9
0.01901949
â– V:
10
5.456677 x 10-4
11
-1.595376 x 10’3
B. Centrifugal Particle Size Analysis:
Corning 7070 As-Received Borosilicate Glass Powder
Coefficient
Value
0
-1.825504
Order
gth
1
13.59646
Correlation
0.9995
2
-0.9358228
Standard Error
of Estimate
1.2 52 M%@s12j.
3
0.0254202
Linear
Extrapolation
4
-5.821581 x lO5
High End
Yes Above
28.0 pm
5
-2.938714 x 10'6
Low End
Yes, Below
0.7 pm
6
-9.496944 x 10‘9
7
-7.946381 x 10'9
8
2.832732 x lO’10
9
-2.477481 x 10'13

213
Table 3.5 (continued)
Corning 7070 Ball Milled Borosilicate Glass
Coefficient
Value
. i':,:-. '
0
0.110559
Order
8th
1
-2.9455459
Correlation
0.9997
2
25.04777
Standard Error
of Estimate
0.3146 M%@si2£
3
-5.796151
Linear
Extrapolation
4
-0.3954611
High End
Yes, Above
6.3 pm
5
0.2121908
Low End
Yes, Below
0.2 pm
6
3.228821 x 10‘4
7
-4.345972 x 10'3
8
3.132128 x lO"4
Ube SNE03 As-Received Silicon Nitride Powder
Coefficient
Value
0
8.467468
Order
8 th
1
-167.6861
Correlation
0.9995
2
331.6824
Standard Error
of Estimate
1.240 M%@sltt
3
-127.6637
Linear
Extrapolation
4
-4.449819
High End
Yes, Above
1.5 pm
5
1.441593
Low End
Yes, Below
0.7 pm
6
2.07041
7
0.3125768
8
-0.1546427
Note: For the specifics of the polynomial regression algorithm
used, see APPENDIX III
5. Polynomial Derived Values:
a. Mass Percent at Size, M%e>>iK: (see 4 above)
b. Equivalent Spherical Surface Area at Size, SSAAS, (see 2
above)

214
c.
d.
e.
f.
g-
h.
Note:
Table 3.5 (continued)
Cumulative Spherical Surface Area, CSSA: (see 3 above)
Relative Number of Equivalent Spherical Particles at Size,
RNSPAS:
M%.
RNSPAS= -
100
41 ^Lar ger+^smaller '
where: D^, is the largest equivalent spherical
diameter of the size region of interest
(pm)
^smaller i-s the smallest equivalent spherical
diameter of the size region of interest
(pm)
Total Relative Number of Spherical Equivalent Particles,
TRNP:
trnp=Yj
Largest
sma 1 lest
RNSPAS
Number Percent at Size, N%asiJe:
m
9size
RNSPAS
TRNS
xlOO
Cumulative Number Percent Finer, CNPF:
cnpf=Yj
sizeofinterest
smallest
N^asize
Cumulative Number Percent Larger, CNPL:
CNPL=YLazgest
¿—¿sizeofinterest
N%
9s i ze
g and h have exact analogs for Cumulative Mass Percent Finer
(CMPF), and Cumulative Mass Percent Larger (CMPL).

215
After outgassing was completed, the sample fixture was removed
from the outgassing unit and mounted to the adsorption unit of the
manual surface area analysis unit. The N;/He ratio was then set to
6.0/14.0 and the apparatus was switched to absorption mode. The mixed
gas signal meter as well as the digital gas counter was then zeroed. At
this point the sample was immersed in a liquid N275 (LN2) bath. After
the digital counter ceased counting, the mode switch was changed to
desorption and the previously mentioned zeroing procedure was performed
again. The LN2 immersion bath was then removed and the sample was
allowed to warm-up to ambient temperature. After a short period, this
procedure was aided by immersing the sample in an ambient temperature
water bath. After the digital gas counter stopped increasing, its
reading was recorded.
Next, a gas volume standardization was performed. The meters were
zeroed as previously mentioned and a known amount of gas was extracted
from the gas outlet port using a calibrated syringe,76 then reinjected
into the gas inlet port. After the digital counter ceased counting, the
reading was again noted. This was repeated until a reading was achieved
that was within 5% of the desorption reading. At this point, both the
volume of gas injected and the counter reading were recorded. The
N2/He ratio was then changed to the next lowest of the N2 concentration
investigated.
This process was performed at N2/He ratios of 6.0/14.0, 4.0/16.0,
3.0/17.0 and 2.0/18.0. The sample cell was then removed, the outside
thoroughly wiped off and quickly weighed. A computer spreadsheet36 was
then utilized to determine the specific surface area, the correlation of
data point linearity with N2 concentration coefficient and the mean
particle size using a spherical approximation.
75 Burmac Enterprises, Orlando, FL 32808
76 Model Number: 1010, Hamilton Corporation, Reno, Nevada

216
Table 3.6 illustrates the equations utilized to perform the manual
surface area analysis calculations. The entire process was repeated for
each sample tested in order to ensure data reproducibility.
Automated surface area analysis was performed when multipoint
surface area analysis was desired. Into a precleaned, dried and weighed
sample holder, an amount of powder was placed. Any powder sticking to
the cell walls was removed with a bottle brush.77 The sample cell was
then sealed and outgassed at 200°C (60°C for latex) in a vacuum for no
less than three h. The sample cell was then removed, allowed to cool
and reweighed. The sample cell was then placed in the BET unit, the
pressure gauges zeroed and the run initialized. The rest of the run was
automatically performed by the microprocessor controlled apparatus. At
the end of the run, the sample was removed and again weighed in order to
monitor any weight change during the analysis.
The data output of said instrument covers a myriad of various
factors. Most important to this study are the adsorption and the
desorption surface areas as a function of calculated pore size. Also
important were the specific surface area and the mean pore size during
desorption.
Surface area analysis was also utilized to investigate the effect
of MeOH exposure on the as-received BS glass powder. This investigation
was necessary in order to help determine the effects of ball milling, in
MeOH, on the BS glass powder. Two different routes were pursued.
The first involved mechanical stirring of a 10 V% solids BS glass
in MeOH45 suspension in an aluminum foil51 covered 250 ml beaker78 at
ambient temperature.
71 Catalog Number: 03-637, Fisher Scientific, 1600 Parkway View,
Pittsburgh, PA 15205
78 Catalog Number: 02-540K, Fisher Scientific, 1600 Parkway View
Drive, Pittsburgh, PA 15205

217
Table 3.6
Calculations Utilized to Perform Manual
Surface Area Analysis
1. Adsorption Calibration, Xa] is performed for each P/P0 (point)
characterized:
'cal'
62350 xT,
Abs
where: P^, is ambient pressure in mm Hg
MWn; is the molecular weight of N: in g/mol
is calibration volume of N; in ml
TAhs is temperature (°K)
P is the N; partial pressure of the
adsorption gas mixture
Pc is the total pressure of the
adsorption gas mixture
2. The Adsorption Value, X is the determined for each point:
X~Xcal* D
D
cal
3.
where: D is the desorption count number
D^, is the calibration count
The Normalized Adsorption Values (Y) are then plotted as a
function of P/P0:
and a linear least squares regression performed.

218
Table 3.6 (continued)
4. The Total Surface Area, SATa (nr) , is then calculated:
SAr
m+b
144,
5 .
where:
X,^ is the adsorption crossection of an N2
molecule (1.62 x 10'19 m:)
NAv is Avogadro' s number (6.023 x 1023
molecules/mol)
m is the slope of the linear regression
b is the intercept of the linear
regression
The Specific Surface Area, SA (m:/g), is then calculated:
SA =
SAr
W
where: W is the sample weight (g)
6. Also, the Equivalent Spherical Diameter, (pm), is calculated:
D =—-—
eq SAx p
where:
p is the powder density (g/cm3)

219
Stirring was achieved through the use of a 1" (2.54 cm)
polytetrafluoroethylene (PTFE) covered magnetic stir bar75 powered by a
magnetic stirplate.21 Stirring durations of 1, 3, 5 and 10 days were
investigated. After stirring, the suspensions were uncovered and
allowed to dry without stirring, at ambient temperature. The resulting
powder was then dried as described in section 3.3.3 above. After
drying, manual surface area analysis was performed upon the respective
powders as outlined above. It was realized, however, that this
methodology may be flawed since mechanical stirring might result in
powder milling, which would also increase powder surface area.
Thus, a second experiment was performed in which no milling was
involved. The as-received BS glass powder was dispersed in MeOH45 at the
same concentration as that prepared during ball milling. Approximately
50 ml of said suspension was mixed in a 125 ml PE bottle.80 The bottle
was sealed and placed within a heated shaker81 bath for 20 h (the
duration used for ball milling). The temperature was set at 40°C (an
estimate of the temperature achieved during milling processes). The
bottle was then removed, uncapped and dried in a vacuum of >30" Hg
(gauge) at ambient temperature. The dry powder was then further dried
at approximately 180°C overnight in a similar vacuum. Automated surface
area and pore size analysis was then performed on said powder as
described above.
Automated surface area analysis was also utilized in order to
investigate changes in both surface area and surface pore size
distribution of both ball milled BS glass powder and slip cast compacts
of ball milled BS glass powder (produced by the method described below)
79 Catalog Number: 14-511-60B, Fisher Scientific, 1600 Parkway View
Drive, Pittsburgh, PA 15205
80 Catalog Number: 02-923-C, Fisher Scientific, 1600 Parkway View
Drive, Pittsburgh, PA 15205
81 Model Number: 129 Shaking Heated Water Bath, Fisher Scientific,
1600 Parkway View Drive, Pittsburgh, PA 15205

220
as a result of thermal treatment. The thermal treatments emulated the
time-temperature schedule used for both organics pyrolysis and sintering
with the exception of ultimate temperature. Samples were heat treated
to ultimate temperatures of 250, 350, 450, 500, 550, and 600°C then
furnace cooled.
Figure 3.4 illustrates the heat treatments used for said
experiments. The procedure used for the heat treatments is described
below in the pyrolysis/presintering section.
3.3.6 Chemical
In order to further investigate changes in the BS glass powders,
both prior and subsequent to ball milling and dissolution, inductively
coupled plasma (ICP)8: solution analysis was performed on the glass
powder. Table 3.7 outlines the various BS glass powders analyzed via
ICP spectroscopy.
From 0.05 to 0.15 g of finely ground BS glass powder was weighed
into a pre-tared teflon digestion bomb.83 The digestion bomb was then
placed within a fume hood and 15 ml of concentrated (49%) HF84 was added
dropwise to the powder, using a class B polypropylene pipette,85 taking
care to avoid possible violent reaction(s). The digestion bomb was then
carefully and securely assembled.
82 Model Number: PLASMA 200 Inductively Coupled Plasma
Spectrometer, Instrumentation Laboratory Inc., Lexington, MA 02173
83 Catalog Number: 01-023, Fisher Scientific, 1600 Parkway View
Drive, Pittsburgh, PA 15205
84 Catalog Number: A147-1LB, Fisher Scientific, 1600 Parkway View
Drive, Pittsburgh, PA 15205
85 Catalog Number: 13-662-10, Fisher Scientific, 1600 Parkway View
Drive, Pittsburgh, PA 15205

Temperature (C)
221
Curve
Set Point (°C)
Rate to Set Point (°C/h)
Time at Set Point (h)
All
20
0
0.0167 (1 minute)
All
120
100
0.5
All
240
50
0.25
A
250
20
3.0
B
350
20
3.0
C
450
20
3.0
D
500
20
3.0
E
550
20
3.0
F
600
20
3.0
All
RT
Furnace Cool
End
Note: RT designates Room Temperature (usually 20 to 25 °C)
Atmosphere: Compressed Air
Flow Rate: Approximately 240 cm3/m
Figure 3.4 Thermal treatment schedules used in the
investigation of the effect of thermal treatment
upon the surface areas of ball milled BS glass
powder and of slip cast BS glass compacts

222
Table 3.7
Description of BS Glass Powders
Investigated Chemically Using ICP and FTIR
I.D. #
Designation
Description
1
7070 INGOT
Ground BS Glass Ingot Received From
Corning Glass
2
7070 AR
<325 Mesh BS Glass Powder As
Received From Corning Glass
3
7070 MEOH
7070 AR Powder Stirred in MeOH
at 40°C for 20 h (see section 3.3.5)
4
7070 BM
7070 AR Powder, Ball Milled in MeOH
For 20 h (see section 3.3.3)

223
The bomb was then removed from within the fume hood and placed inside an
oven86 for 12 h at a temperature of 80°C. During this time, a 100 ml
capacity polypropylene volumetric flask87 was filled with approximately
75 ml of deionized (DI)H20.88 After said heat treatment, the digestion
bomb was removed from the oven, placed again in the fume hood and
allowed to cool to ~60°C. The digestion bomb was then opened, being
careful not to spill the contents (the acid bomb must be opened while
still fairly hot in order to avoid vacuum sealing of the digestion
bomb). The dissolved BS glass-HF solution was then transferred to the
volumetric flask. Any remaining solution was carefully rinsed from the
digestion bomb with approximately 5 ml of DI H-,0.8* The polypropylene
volumetric flask was then filled to its calibration mark with DI H;0,
then allowed to cool to room temperature (RT).
Reference standards for ICP analysis were produced by dilution of
commercially available reference standards,89 in the above volumetric
flask, using the same HF/H:0 concentration as the samples had.
Standards were made for Si, B, Al, Na and Li in the above manner (K was
not analyzed, due to the lack of a proper PM (photomultiplier)
detector). The quantitative chemical analysis data were then examined
for variance both from the literature data90 and between each type of
treatment the powders received.
86 Catalog Number: 13-258-10B, Fisher Scientific, 1600 Parkway View
Drive, Pittsburgh, PA 15205
87 Catalog Number: 10-198-50B, Fisher Scientific, 1600 Parkway View
Drive, Pittsburgh, PA 15205
88 Continental Deionized Water Service, 2300 N.W. 7151 PI.,
Gainesville, FL 32606
89 Catalog Numbers: SS465-500, SB155-500, SA442-500, SS139-500,
and SL45-500 for Si, B, Al, Na and Li Reference Standards respectively,
Fisher Scientific, 1600 Parkway View Drive, Pittsburgh, PA 15205
90
Corning Glass Product Data Literature

224
Fourier transform infrared (FTIR) spectroscopy” was also
performed, upon the BS glass powders in Table 3.7 in order to
characterize possible differences in surface chemistry between the
different powders. The powders were first dried at 120°C for
approximately 48 h. A representative sample of the dried powder was
then placed in a DRIFT,: cell and the apparatus placed within the
spectrometer. Analysis was then performed in the diffuse reflection
mode (which measures both the diffuse and specular components of the
reflected infrared radiation) over wave numbers ranging from 4000 to 400
cm'1. A nitrogen74 purge was used during the analysis. All spectra
recorded were normalized to a background standard in order to provide a
background correction.
3.4 Suspension, Casting and Green Compact Studies
3.4.1 Overview
This section discusses the batching, wet processing and
characterization, and green characterization of the BS glass, Si3N4,
latex composites produced for this study. Details of processing and
characterization methods used to investigate suspensions of each pure
component are also described. These studies were necessary in order to
pursue ideal green microstructures, so that the controlled
microstructures could be characterized and manipulated most predictably
and reproducibly over a wide range of composite compositions.
51 Model Number: 20FXB, Nicolet Instrument Corporation, 5225 Verona
Rd, Madison, WI 53711
92 Spectratech Corporation, 200 Harry S. Truman Parkway, Annapolis,
MD 21401

225
3.4.2 Wet Processing and Characterization
3.4.2.1 Selection of the Dispersion System
In the system studied, all materials seemed to disperse well in
aqueous suspensions at high pH (approximately pH 9.5). However, in
order to avoid powder dissolution and/or powder surface modification
during dispersion of the BS glass powder, a satisfactory non aqueous
suspension system was pursued. The BS glass used (Corning 7070) is a
Class I glass in regard to corrosion resistance in aqueous media (see
Figure 3.5). Although the dissolution rates at the pHs of interest are
not yet devastating, they could be somewhat significant for a fine
powder of comparatively high surface area.
Also, an aqueous system at pH 9.5 would have a significant
concentration of hydroxyls that could adversely effect dielectric
properties if not totally removed during the pyrolysis/presintering,
sintering or dielectric specimen preparation processes. Therefore it
was decided to investigate nonaqueous dispersion systems. Initially,
methyl isobutyl ketone (MIBK)93 and either MeOH45 or EtOH,24 in the volume
ratio of 3 to 1, were used as the dispersion solvent. The dispersant
utilized for this system was polyvinyl butyral (PVB).94 This system was
found satisfactory for making quality dispersions of BS glass and Si3N4.
However, it was soon found that MIBK dissolves the polystyrene latex
used. Furthermore, both MIBK and MeOH are toxic. Therefore a different
dispersion system was investigated. Since the latex is synthesized via
dispersion polymerization in MeCell and EtOH, the next dispersion
systems investigated used EtOH24 as the dispersion solvent. The
dispersants investigated for the EtOH based dispersion system were SMA
93 Catalog Number: M-213, Fisher Scientific, 1600 Parkway View
Drive, Pittsburgh, PA 15205
94
Butvar B-98, Monsanto Company, St. Louis, MO 63166

Attack Rate (relative)
226
PH
General Effect of pH in Aqueous Solutions
Source: Corning Glass Works, Properties of Coming's Glass and Class Ceramic
Families: Materials for the Design Engineer, p. 5, (1979).
Figure 3.5
Dissolution characteristics of Corning Glasses in
aqueous media (source: [COR79])

227
1440A,95 Klucel E,96 and PVP K-30.97 Preliminary investigation
indicated that Klucel was not a satisfactory candidate due to its
limited solubility in EtOH. Further investigation indicated that both
PVP K-30 and SMA 1440 performed quite similarly as dispersants in this
system, with PVP K-30 giving a slightly increased casting density.
Therefore, PVP K-30 was used, as received, in making all suspensions.
Since the main impetus of this study was to produce a cofirable
material, having controlled porosity (i.e decreased dielectric loss), no
other materials were used in the dispersion system that could make the
microstructure less ideal. Therefore, no plasticizers, defoaming
agents, etcetera, were used in this study. Only powders, dispersion
solvent and dispersant (in a minimal amount) were used.
Preliminary investigations indicated that green density increased
about 1 to 2% of theoretical density as the PVP K-30 concentration was
increased from 0.5 to 1.0 wt% of the total solids in the suspension in
pure, ball milled BS glass suspensions. Said characterization indicated
that the green density increased less than 0.5% of theoretical density
as the PVP K-30 concentration was further increased from 1.0 to 2.0 wt%
of the total solids in similar suspensions. Therefore, in order to
pursue maximization of green density while using a minimal amount of
dispersant, the concentration of the PVP K-30 dispersant used was 1.0
wt% of the total solids in the suspension for all suspensions produced
for this study.
95ARCO Chemical Company, 1500-T Market Street, Philadelphia, PA
19101
96 Hercules Incorporated, Wilmington, DE 19894
97 Polyvinyl Pyrrolidone, Catalog Number: PVP K-30 (molecular
weight - 30,000), GAF Chemicals Corporation, 1361 Alps Road, Wayne, NJ
07470

228
3.4.2.2 Characterization and Optimization of Suspension System
3.4.2.2.1 Overview
When investigating composite systems, it is necessary to maximize
component homogenization. Component mixing is augmented in suspensions
having relatively low viscosities, while segregation during casting
processes is minimized in suspensions having relatively high
viscosities. Thus, a compromise must be reached in suspension viscosity
that allows for adequate mixing, in reasonable time frames, while
minimizing segregation during casting. Furthermore, it is necessary to
choose a suspension viscosity that is low enough to allow one to handle,
dispense and cast the suspension.
Finally, in order to compare different composite compositions,
processing factors should remain reasonably constant.
Therefore, where possible, constant solids loadings were pursued when
preparing all composite suspensions investigated. This methodology was
utilized so that changes in suspension parameters and green
characteristics, as a function of composite composition, could be
investigated.
3.4.2.2.2 Rheology of Dispersed Composite Components
In order to investigate how well each of the composite components
disperses in the EtOH/PVP system described above, suspensions of 20, 30
and near maximum solids loading (as described in section 3.4.2.2.3
below) were produced using the standard dispersion method described in
section 3.4.3 below. Table 3.8 describes the suspensions produced for
this study. A precision viscometer,98 maintained isothermally at 25°C,
was utilized to perform viscometry measurements.
98 Model Number: CV100 Precision Viscometer, utilizing Model
Numbers: RV20 and RC20 Control Units; the sensor system used was
Number: ZA-15 Cup and Spindle, Haake, Mess-Technik GmbHa. Co.,
Dieselstr. 4, 7500 Karlsruhe 41, West Germany

229
Table 3.8
Specifications for Single Composite Component
Batches Used for Rheological Characterization
Designation
Composite Component
Vol. % Solids Loading
7070-01
Ball Milled BS Glass
Powder
20
7070-02
Ball Milled BS Glass
Powder
30
03209001
Ball Milled BS Glass
Powder
52
SNE03-01
As-Received Si3N4
Powder
20
SNE03-02
As-Received Si3N4
Powder
30
01319101
As-Received Si3N4
Powder
46
LATEX-01
Monodisperse Polystyrene
Latex Powder
20
LATEX-02
Monodisperse Polystyrene
Latex Powder
30
02159103
Monodisperse Polystyrene
Latex Powder
52
Notes: 1. All suspensions dispersed in denatured EtOH54 using the
methods described in section 3.4.3 below
2. All suspensions had PVP K-30 concentrations of 1 wt%
of the total solids in said suspension

230
The system was first set to recommended calibration presettings as
outlined." The system was then allowed to equilibrate for
approximately 30 min. before the measurements were taken. During this
warm-up period, several blank runs were performed with tap water. After
this period, the sample cup and spindle were thoroughly cleaned and
dried.
The dry spindle was carefully replaced and the sample cup was
filled with approximately 1.5 ml of suspension, decanted from a
disposable pipette.100 The sample cup was then quickly placed within
its holder, and an evaporation shield was placed over the sample cup
holder assembly. The measurement was then initiated. The shear rate
was increased from 0 to 300 s’1 in a period of 2 min., then decreased to
a shear rate of 0 s'1 in a period of another 2 min. The sample was then
removed and the sample cup and spindle thoroughly cleaned and dried.
This process was repeated until two runs, having excellent agreement,
were obtained.
3.4.2.2.3 Optimization of Suspension System
As mentioned above, it was necessary to find a solids loading that
would give a corresponding viscosity that would allow for a balance
between maximization of mixing and minimization of composite component
segregation during casting. Therefore, studies were performed to
determine both the maximum possible solids loading (i.e. the point at
which the suspension appears "doughy" or non-liquid), and the maximum
process solids loading (i.e. the solids loading giving the maximum
viscosity allowable for the processing methods utilized, henceforth
denoted as the optimum solids loading).
" See the Operations Manual of Footnote 96
100 Catalog Number: 13-711-5A, Fisher Scientific, 1600 Parkway View
Drive, Pittsburgh, PA 15205, modified by cutting approximately 0.5
inches (1.77 cm) from the bottom of the pipette to allow transfer in the
case of relatively viscous suspensions

231
A suspension of pure ball milled BS glass was prepared, having an
initial solids loading of 45 V%, using the standard method outlined
below in section 3.4.3. In this case however, a slight excess of PVP K-
30 was added to allow for additional powder charging of the suspension.
Powder additions of a few grams were made and recorded, and the
suspension was again shaken and sonicated as in the standard dispersion
method. This process was repeated until the suspension became
overloaded. Suspension overloading was evident when the suspension
would no longer flow and obtained a "doughy" rather than a liquid
appearance.
The suspension solids loading was then calculated by summing the
total powder additions, converting this value to a volume using the
powder density, and dividing the obtained value by the summation of the
solvent volume plus itself. The entire process was then repeated in
order to insure a measure of reproducibility. The maximum solids
loading obtainable by this method was approximately 54 V% solids
loading.
The optimum solids loading was then determined by diluting the
overloaded suspension with a relatively small amount of denatured EtOH,24
to the suspension, then reshaking. This process was repeated until the
suspension became liquid-like again. The amount of EtOH used for each
dilution was 1 g per each dilution, to an approximately 80 cm3
suspension. The optimum solids loading was determined by adding the
number of additional grams of EtOH necessary for dilution to the amount
in the original suspension, converting it to a volume of EtOH, then
performing the solids loading calculation described above using the
total amount of BS glass powder used. This process was also repeated to
determine reproducibility and yielded an optimum solids loading of
approximately 52 V%. This number was utilized in all the batches
produced for this study.

232
While both these investigations were crude and by no means
exacting, they did provide valuable insight that allowed for the
production of homogeneous composite samples.
3.4.2.2.4 Effects of Sonication and Aging Upon Suspension Properties
It was decided that a sonication experiment should be carried out
in order to determine the amount of sonication necessary to insure a
homogeneous suspension. This experiment involved making an 80 ml
suspension (initially calculated to have 52V% total solids loading) of a
60/40 mixture of ball milled BS glass and Si3N4 powders, in EtOH with 1
wt% PVP K-30 as a dispersant. This particular mixture was used since it
had the highest viscosity and lowest green density and therefore was
most difficult of the composite compositions to disperse via sonication.
The batch was made in the normal manner (outlined in section 3.4.3
below), with the exception that no sonication was used during batching.
It should be noted that 52V% solids loading could not be achieved,
in this manner, without overloading the suspension. Therefore, the
entire batching materials were added, then a small amount of EtOH was
added in order convert the overloaded paste back into a liquid-like
slurry.
After significant mixing, via shaking on a paint shaker,101 the
slurry was Theologically characterized using the method described in
section 3.4.2.2.2 above, with the exception that the M-Head102 sensing
system, with sensor SVII, was utilized instead of the CV100 sensing
unit. This was necessary because, at this point, the suspension was too
viscous to characterize via the standard sensor system.
101 Model Number: 5400-02 Paint Conditioner, Red Devil Co., Union
NJ 07083
102 Part Number: M-HEAD, utilizing sensor SVII, Haake, Mess-Technik
GmbHa. Co., Dieselstr. 4, 7500 Karlsruhe 41, West Germany

233
Even using the above sensor system, the shear stress overloaded the
system at approximately 400 s'1. Therefore, no decreasing shear rate
data was obtained for the totally unsonicated suspension.
At this point, percent solids loading analysis (as outlined in
section 3.4.4 below) was performed, in order to determine the solids
loading of the suspension. Also, a sample was slip cast (as outlined in
section 3.4.3 below) for characterization by Hg porosimetry (as
described in section 3.4.5.2 below) and by SEM (as described in section
3.4.5.1 below).
The remainder of the suspension was again paint shaken for 5 more
minutes and sonicated for 15 min. After sonication, the suspension was
shaken by hand for about 2 min., and another sample was taken for
viscosity measurement. This time the ZA—15 sensor system was utilized
in the RV—100 system (the standard protocol).
Again the upper limit of shear stress was reached before the
decreasing shear rate portion of the cycle was reached, and thus, no
decreasing shear rate data is available for this particular sample set
either. At this point, samples were again cast for characterization via
Hg porosimetry and SEM.
This procedure was repeated for sonication times of 30, 45, 60,
90, 120, and 180 min. of total sonication time. Solids loading of the
suspension was measured again after 120 and 180 min. of sonication in
order to monitor solvent evaporation.
After drying, the cast specimens were removed and Hg porosimetry
was performed upon them. Since it was assumed that some of the samples
might contain large voids, low pressure porosimetry was also performed
upon the 0, 15 and 30 min. sonicated samples. Since no intrusion
(within the sensitivity limits of the porosimeter) was observed, only
high pressure porosimetry was deemed necessary for the characterization
of the green microstructures. Mercury porosimetry experimentation was
performed by the standard method, outlined below in section 3.4.5.2.

234
There are two problems observable from this study. First, since
additional EtOH had to be added to the suspension in order to convert
the overloaded suspension to a liquid-like suspension, the solids
loading of the suspension (ranging from 50.0 to 50.9) is less than that
of the standard suspensions used. Secondly, since samples were
continuously removed from the suspension, the total amount of the
suspension was constantly reduced. The final amount of suspension was
approximately 35 cm3. Thus total sonication times used were greater
than those deemed necessary by this study. Therefore, it was decided
that total sonication times should be no less than 120 min. for a
standard batch. This sonication duration proved satisfactory and was
used as a minimum total sonication time when producing batches for this
study.
A final flaw in this study is that suspension aged approximately 5
h from the initial sonication treatment to the final sonication
treatment. Since aging also has an effect upon rheological properties,
this factor can not be discounted. However, there is no way to perform
said experimentation without limited aging due to the time required for
shaking and sonication.
In order to determine the effect of aging upon rheological
properties, an aging study was also performed. A 180 ml suspension of
64 V% ball milled BS glass, 16 V% Si,N4 powder and 20 V% 4.6 pm UPLM
powder was produced by the standard method outlined in section 3.4.3
below, with the exception that the suspension was not aged prior to the
investigation (other than the time required for batching and
sonication). This composition was chosen since it also should be
relatively viscous compared to the rest of the batches produced.
Suspension solids loading was determined as outlined in section 3.4.4
below after 38 and 70 h of aging. Rheometry characterization was
performed, as described in section 3.4.2.2.2 above, at aging durations
of 0, 12, 24, 48 and 72 h. Samples were also cast at the above aging

235
times for green characterization via Hg porosimetry, as outlined in
section 3.4.5.2 below as well as compact top surface visual inspection
via SEM as outlined in section 3.4.5.1 below.
This experimentation provided valuable insight into the effect of
aging on the suspension and green properties of codispersed composites
within this system. From the results of the study, it was decided that
the standard batch aging time should be 48 h.
3.4.2.2.5 General Rheology Studies
A description of the method used for rheological characterization
of the slurries produced is outlined in section 3.4.2.2.2 above. The
general rheology studies were performed to investigate various
rheological trends of the slip systems used in this study.
Each batch was characterized after an aging time of approximately 48 h.
The ZA—15 sensor was utilized for all viscosity characterization of
suspensions in this section. All characterization was performed for
shear rates ranging form 0 to 300 s'1. The shear rate was increased from
0 to 300 s'1 in 2 min., then decreased to 0 s'1 in another 2 min. time.
All the suspensions characterized in this study had a total solids
loading of approximately 52 V% with the exception of the samples having
a Si3N4 concentration greater than 50 V% (total solids basis) which were
characterized at a total solids loading of 46 V%. This was necessary
because suspensions containing Si3N4 concentrations greater than 50 V%
became overloaded as solids loadings neared 52 V%. The single value of
46 V% was chosen for these three suspensions in order to afford a
comparison between the rheological properties of the three. Generally,
the viscosity of these batches was greater than all of the others.

236
3.4.3 Slip Casting of Compact Samples
The samples were produced via slip casting of codispersed slurries
as described below. Figure 3.6 illustrates a flow diagram of the
procedure utilized for the convenience of the reader.
In a clean polyethylene (PE) bottle,103 to which a (2.54 cm)
polytetrafluoroethylene (PTFE) stir bar79 had been added in order to
facilitate mixing, the appropriate amount of latex/EtOH dispersion was
added. This amount was determined from both the solids loading of the
latex/EtOH mixture (determined twice, as outlined in section 3.4.4
below) and the required amount of latex and EtOH determined from batch
calculations. The additional EtOH,24 required to round out the batch
calculations, was then added. After this addition, 1 wt% (of the total
solids weight) PVP K-30 was added to the suspension. The suspension was
then shaken for approximately 5 min., while the PVP K-30 dissolved.
Next the total required batch amount of Si3N4 was added to the
suspension. The suspension was then shaken for another 5 min. and
sonicated for 15 min. The shaking and sonication was again repeated,
without further addition, for another repetition. At this point,
approximately one half of the total batch amount of the BS glass powder
was added. The resultant slurry was shaken again for 5 min. and
sonicated for 15 more min. Approximately one half of the remaining
glass was then added and the shaking and sonication step repeated. The
final amount of glass powder was then added and further shaking and
sonication were performed upon the slurry (again 5 and 15 min.
respectively). After these treatments, the slurry was subjected
immediately to two more repetitions of shaking/sonication (5 and 15 min.
again).
103 Catalog Number: 02-893-5C, Fisher Scientific, 1600 Parkway
View Drive, Pittsburgh, PA 15205

237
Figure 3.6
Flow diagram illustrating the procedure utilized to
produce, via slip casting of codispersed
suspensions, the samples used in this study

238
The suspension was then subjected to rotary mixing (aging), upon a
rotary conditioner,104 for approximately 48 h. Some time during the
aging process, the suspension was subjected to the shaking/sonication
process, mentioned above, for two repetitions of 5 min. of shaking and
30 min. of sonication. After these treatments, the suspension was
replaced on the rotary mixing apparatus for the remainder of the aging
time.
Just before the casting process, rheology measurements were
performed, upon the suspension, as described in sections 3.4.2.2.2 and
3.4.2.2.5 above. Suspension solids loading measurements were performed,
as outlined in section 3.4.4 below at this point as well.
The suspension was then slip cast onto 0.22 pm nylon filter
paper,105 setting on plaster106 ingots, that had been presaturated with
EtOH24 prior to casting. Phenolic casting rings107 (29 mm diameter),
which had been polished on one end to a 600 grit surface finish, and to
which a very light coating of vacuum grease108 had been applied as a
mold release agent, were used as the suspension container during the
casting process.
104 Bodine Electric Company, Chicago, IL
105 Catalog Number: N02-Spl42-25, Fisher Scientific, 1600 Parkway
View Drive, Pittsburgh, Pa 15205
106 Item Number: 53005, Bondex International Inc., 3616 Scarlet
Oak BLVD, St. Louis, MO 63122
107 Item Number: 20-8152-010, Buehler Ltd., 41 Waukegan Rd. , Lake
Bluff, IL 60044
108 High Vacuum Grease, Dow Corning Corp. , Midland, MI 48640

239
Approximately 6 ml of suspension was then quickly dispensed into the
casting rings, using a disposable glass pipette109 attached to a pipette
pump."0 After approximately three samples were cast, the remaining
uncast suspension was recapped and reshaken, and the pipette was
replaced with a fresh one. The suspension-filled casting rings were
then covered with glass slip covers'" in order to prevent solvent
evaporation form the top of the compact, which would cause surface
drying and cracking. Said drying and cracking not only increases the
size of the meniscus on the cast sample, but also causes casting flaws
in the compact which make the compacts very fragile.
Before the compacts were completely dry, they were gently removed
from the filter paper and then very carefully removed from the casting
rings. The first and last cast samples were then stored separately for
Hg porosimetry characterization, as outlined in section 3.4.5.2 below.
The remaining samples were then stored for further processing and
characterization, as outlined in Figure 3.1. Table 3.9 depicts each
batch produced and the pertinent characteristics of each. It should be
noted that the pure latex batches were not aged and were sonicated for
only approximately 30 min. Also, the solids loadings were not adjusted
to 52 V% prior to casting.
109 Catalog Number: 13-668-80, Fisher Scientific, 1600 Parkway
View Drive, Pittsburgh, PA 15205
110 Catalog Number: 13-683D, Fisher Scientific, 1600 Parkway View
Drive, Pittsburgh, PA 15205
'" Catalog Number: 12-550C, Fisher Scientific, Glass Microscope
Slides, cut to size by scribing and snapping. The scribes were produced
using a Catalog Number: 08-675, Fisher Scientific Diamond Marking
Pencil

240
Table 3.9
Specifications of Each Codispersed and Slip Cast
Sample Batch Produced for This Study
Desig¬
nation
Glass
Type
Borosi
licate
Glass-
Si3N4
Ratio
Composition
BS Glass/
Si,N4/Latex
Ratio
Volume
Percent
Latex
Latex
Mean
Dia¬
meter
(pm)
Latex
Dis-
persity
12119001
As
Rec.
100/0
100/0/0
0
NA
NA
03209001
Ball
Milled
100/0
100/0/0
0
NA
NA
05109102
Ball
Milled
100/0
95/0/5
5
4.6
Uniform
01039101
Ball
Milled
100/0
90/0/10
10
4.6
Uniform
05179101
Ball
Milled
100/0
85/0/15
15
4.0
Quadra
modal
05179102
Ball
Milled
100/0
85/0/15
15
2.4
Bimodal
05069101
Ball
Milled
100/0
85/0/15
15
4.6
Uniform
05099101
Ball
Milled
100/0
85/0/15
15
9.0
Uniform
05069102
Ball
Milled
100/0
82.4/0/17.6
17.6
9.0
Uniform
12109001
Ball
Milled
100/0
80/0/20
20
4.6
Uniform
02069101
Ball
Milled
100/0
80/0/20
20
4.6
Uniform
05109101
Ball
Milled
100/0
75/0/25
25
4.6
Uniform
06019101
Ball
Milled
100/0
72.5/0/27.5
27.5
4.6
Uniform
05079101
Ball
Milled
100/0
70/0/30
30
4.6
Uniform
05079102
Ball
Milled
100/0
60/0/40
40
4.6
Uniform
01049101
Ball
Milled
90/10
81/9/10
10
4.6
Uniform
05119101
Ball
Milled
85/15
72.25/12.75
/15
15
4.6
Uniform

241
Table 3.9 (continued)
Desig¬
nation
Glass
Type
Borosi
licate
Glass-
Si3N4
Ratio
Composition
BS Glass/
Si3N4/Latex
Ratio
Volume
Percent
Latex
Latex
Mean
Dia¬
meter
(urn)
Latex
Dis-
persity
03219001
Ball
Milled
80/20
80/20/0
0
NA
NA
01249101
Ball
Milled
80/20
72/18/10
10
4.6
Uniform
01069101
Ball
Milled
80/20
64/16/20
20
4.6
Uniform
03199001
Ball
Milled
60/40
60/40/0
0
NA
NA
01279101
Ball
Milled
60/40
54/36/10
10
4.6
Uniform
10109001
Ball
Milled
60/40
48/32/20
20
4.6
Uniform
08159001
Ball
Milled
50/50
40/40/20
20
4.6
Uniform
02149101
Ball
Milled
40/60
40/60/0
0
NA
NA
02149102
Ball
Milled
20/80
20/80/0
0
NA
NA
01319101
NA
0/100
0/100/0
0
NA
NA
05169101
NA
NA
0/0/100
100
4.0
Quadra
modal
07269001
NA
NA
0/0/100
100
2.4
Bimodal
07309001
NA
NA
0/0/100
100
3.1
Bimodal
07199001
NA
NA
0/0/100
100
3.6
Bimodal
06199001-
07+09
NA
NA
0/0/100
100
4.6
Uniform
07219001
NA
NA
0/0/100
100
6.1
Uniform
08029001
NA
NA
0/0/100
100
6.8
Uniform
07249001
NA
NA
0/0/100
100
9.0
Uniform

242
3.4.4 Suspension Solids Loading Determination
Knowledge of suspension solids loading is valuable in several
ways. In order to determine the correct amount of latex suspension to
use in sample production, it was necessary to know the solids loading of
said dispersion. This was also true when making the wide size
distribution latex dispersion. Knowledge of the suspension solids
loading is also valuable when comparing viscosity data of different
batch compositions. Finally, by monitoring the total solids loading of
each dispersion produced, as described in section 3.4.3 above, a measure
of quality control is assured. If the solids loading varies
significantly from that calculated, the researcher is informed
immediately that there maybe a batching problem. The procedure used to
determine solids loading follows.
An aluminum sample pan"2 was weighed and recorded. Next, a well
shaken and dispersed sample was quickly removed from the suspension and
decanted into the sample pan, which was already placed on the
balance,"3 utilizing a disposable dropper.27 The combined weight of the
sample pan and wet suspension was then measured and recorded. The
suspension-filled sample pan was then transferred to a drying oven55
using nylon-reinforced, fiberglass tweezers"4 to prevent adding
additional weight to the pan by touching. The pan was placed upon a
precleaned setter inside the oven.
The sample was then dried at approximately 60°C for no less than 3 h.
After drying, the sample pan was removed from the drying oven and
reweighed. This amount was recorded as the dry weight.
1,2 Catalog Number: 08-732, Fisher Scientific, 1600 Parkway View
Drive, Pittsburgh, PA 15205
113 Model Number: XD 100A, Fisher Scientific, 1600 Parkway View
Drive, Pittsburgh, PA 15205
114 Catalog Number: 02-354, Fisher Scientific, 1600 Parkway View
Drive, Pittsburgh, PA 15205

243
These values were then utilized to calculate the total volume percent
solids loading utilizing the methods and equations outlined in Table
3.10. Two repetitions of the above procedure were performed upon each
batch in order to insure reproducibility. The solids loadings values
from each repetition were then averaged. All solids loadings values
were found to agree within approximately 0.5 V% between the two
repetitions.
3.4.5 Characterization of Green Compacts
3.4.5.1 Visual
Visual analysis of representative green compacts was provided via
SEM.25 A compact was gently broken into smaller pieces in order to allow
the sample to fit upon the sample stub.30 Care was taken not to damage
or disrupt the sample surface. The green compact piece was then affixed
to the sample holder with double stick tape.31 The compacts were then
Au/Pd DC sputter coated.34 A conductive path was then put between the
sample and the sample holder with carbon paint.115 The samples were
then viewed using the SEM. During viewing, an accelerating potential of
20 KV was used and the working distance was approximately 30 mm. The
samples were generally not tilted, unless necessary, and the condenser
lens setting used was between 2 and 4.
3.4.5.2 Ha Porosimetrv
Mercury porosimetry was utilized to investigate the green
microstructures of the samples made for this study. Porosimetry data
was obtained from at least four samples, for each batch produced. The
first and last cast sample from each batch was further divided into as
cast and presintered categories.
115 Conductive Carbon Paint, SPI Supplies, a Division of Structure
Probe Inc., P.O. Box 656, West Chester, PA 19381
• /

244
Table 3.10
Method and Equations Used to Calculate
Suspension Total Solids Loading
1.Determine the Dry Solids Weight, D (g):
D=Dp-p
where: Dp is the dried sample pan with suspension
weight (g)
p is the pan weight (g)
2.Determine the Liquids Weight, L (g):
L=Wp-Dp
where: L is the sample pan with wert suspension
weight (g)
3.Determine the Density of Composite Solids, ps (g/cm3):
f2
where: Vf,dr> is the dry basis volume fraction of
the iu' component
Pi is the density of solid component i
(g/cm3)
Calculate the Volume of Solids in the Suspension, V( (cm3):
Vs
D
Ps
4.

245
Table 3.10 (continued)
5. Calculate the Volume of the Liquids in the Suspension, V, (cm3):
vl =
L
Pi
where:
p, is the density of the liquid in the
suspension (g/cm3)
6. Calculate Volume Percent Solids Loading, V% (%):
V% =
vs
xlOO
Notes: 1. In systems using non reactive
multicomponent liquids, the liquid density
may be calculated using a weighted average
similar to step 3 above.
2. The effect of dispersant volume (PVP K-30)
is not included.

246
The as-cast samples were characterized without further treatment, while
the presintered samples were subjected to pyrolysis and presintering
treatments, as described in section 3.5.2 below. This experimental
methodology allowed for differentiation of green properties between as
cast and presintered samples of the same batch. The methodology also
was useful as a quality control measure, since the first and last cast
samples were both characterized. Differences in microstructural
properties between the first and last cast samples would indicate
segregation, flocculation or mixing problems.
The Hg porosimetry unit"6 and sample cells used were calibrated
using the recommended procedure,117 prior to experimentation. All
experimental calculations were performed using the constants outlined in
Table 3.11.
In order to determine whether relatively large (i.e. greater than
approximately 5 pm pore channel radius) porous microstructures exist
within the green and presintered samples, low pressure porosimetry was
performed, as outlined,117 upon selected samples. The samples chosen for
low pressure porosimetry were from batches suspected to have the largest
pore structures of the materials studied (i.e. presintered samples of
batches containing relatively high amounts of latex, large latex, etc.).
None of the samples tested (including an as cast sample of pure
latex, from the largest size of latex) intruded a detectable amount in
the low pressure regime. Therefore, only high pressure porosimetry was
used to investigate the porous green and presintered structures of the
materials made for this study.
116 Model Numbers: FA-1 and SP-20LV Computer Interfaced Autoscan
Mercury Porosimeter Apparatus using 2 cm3 sample volume sample cells,
each separately calibrated, Quantachrome Corporation, Syossett, NY 11791
117
See the Operations Manuals for Footnote 116

247
Table 3.11
Experimental Values and Parameters Utilized During
Experimentation and/or in the Computation of Hg Porosimetry Data
Experimental Parameter
Value
Mercury Density
13.534 g/cm3
Mercury Contact Angle (0)
140°
Mercury Surface Tension (yLV)
480 ergs/cm3
Scan Rate
5.5
Moving Point Average
9
Cell Sample Chamber Volume
2 cm3
Cell Stem Volume
0.5 cm3
Evacuation Pressure
< 50 pm Hg
Modes for Taking Data
Intrusion/Extrusion
Mode for Calculations
Intrusion
High Pressure Range (PH)
Ambient to 60 Kpsi
Pressurizing Fluid
Hydraulic Oil
Low Pressure Range (PL)
< 50 pm Hg to 25 psi
Pressurizing Fluid
N2 gas74
Notes: 1. Data is obtained by monitoring the volume intruded
(calculated from changes in capacitance measured) as a
function of pressure. The pressure is then converted
to a pore channel radius using the equation in Note 2.
This gives a plot of V (volume intruded) versus R.
2. The equation used to convert pressure to a pore
channel radius (the Washburn Equation [88REE]), R
(pm) :
g_-2yLvcos6>in6
yLV is Hg liquid-vapor surface tension
(N/m)
0 is the Hg-sample contact angle (°)
P is the intrusion pressure (Pa)
1 erg/cm: = 10'3 N/m
1 Pa = 1.451 x 10': psi
where:

Table 3.11 (continued)
The fractional pore size distribution is given
by:
f (R) = —
dR
The median pore channel radius occurs at the
maximum of the relationship depicted in Note 3.

249
High pressure porosimetry was performed upon four samples from
each batch as described above. The general parameters used for this
study are outlined in Table 3.11 as well as a brief explanation of how
porosimetry calculations are preformed.
High pressure Hg porosimetry was also used to investigate the
packing efficiency of slip cast pure latex compacts with respect to size
and size dispersity.
3.5 Thermal Analysis: Oxidation and Pyrolysis Studies
3.5.1 Overview
Thermal analysis studies were performed upon the components of
this system and upon a slipcast compact in order to characterize the
materials in the system with respect to several factors. Oxidation
studies were performed upon the Si,N4 powder in order to determine if the
Si3N4 utilized in this study was truly inert with respect to oxidation
when subjected to the thermal processing conditions of this study. Any
oxidation of the Si3N4 could provide experimental error since the
composite density would change. Also the event of a substantially large
siliceous layer, forming on the Si3N4 could change the sintering
characteristics of the composites in the system.
The second part of the thermal analysis studies were used in two
ways. Preliminary thermal analysis studies were used in conjunction
with empirical experimentation to determine the best pyrolysis and
presintering schedule to use for the green compacts in this study. After
a pyrolysis/presintering schedule was established, a second set of
thermal analysis experiments were performed in order to confirm that
said pyrolysis/presintering schedule was satisfactory. Preliminary
dielectric properties data were also examined in order to determine
whether or not significant carbon remained subsequent to
pyrolysis/presintering heat treatment.

250
3.5.2 Oxidation Studies
Thermal analysis studies were performed upon the Si3N4 powder using
a computerized TGA/DTA apparatus."8 The first set of experiments
involved heating approximately 0.2 g of powder at a rate of 10°C/min
from 100 to 1500°C, in air"9 flowing at a rate of approximately 2 ft3/h
(47 cm3/min.). This experimentation was performed in order to determine
the onset temperature regime of oxidation of the Si3N4 powder. The
reference powder used in each instance was alumina120 (which is inert
over the conditions experienced during the thermal analysis
experimentation). Two repetitions of this experiment were performed,
one with the Si3N4 powder as the sample powder and one with Al-,03120 powder
as the sample powder. The A1;03 sample powder run was performed in order
to provide a baseline standardization. The data for each run were
stored and developed via a computer spreadsheet program36 which also
provided graphical output.
The above-mentioned TGA data provided the non-isothermal onset
temperature of oxidation of the Si3N4 powder. In order to simulate
conditions similar to those of the sintering treatments, a second set of
oxidation studies were performed. In the second oxidation study, the
temperature was held isothermally at 820°C (the highest sintering
temperature used in this study), under the air flow conditions of the
above thermal analysis experiment. The sample was heated to a
temperature of 820°C at a rate of 45°C/min. The sample was then
isothermally treated for 12 h. Since the computer software did not
allow for said characterization, the sample weight was manually recorded
118 Model Number: ST-736, Harrop Industries, Inc., 3470 E. 5th
Ave., Columbus, OH 43219-1797
119 Grade E Compressed Air, Liquid Air Corp. , 2121 North California
BLVD, Walnut Creek, CA 94596
120 Catalog Number: A-591, Fisher Scientific, 1600 Parkway View
Drive, Pittsburgh, PA 15205

251
periodically over the 12 h period. Due to the above-mentioned software
limitations, however, differential thermal analysis was not possible.
Again, two repetitions of the above experiment were performed, one
with Si3N4 powder and one with A1,03 powder to provide a baseline
standardization. The sample weight used was approximately 0.2 g in each
case also. Alumina powder was also used as the reference powder.
3.5.3 Pyrolysis Studies
A second TGA/DTA apparatus121 was utilized for pyrolysis studies.
The materials analyzed had been stored and not predried in order to
determine the amount of adsorbed moisture within the materials. This
was relatable to the actual materials used in this study. Experimental
runs were performed upon latex powder, PVP K-30 powder (the dispersant)
in both air117 and N;,74 and upon a green slip cast sample of a compact
representative of this study (i.e. 80 V% BS glass powder, 20 V% latex,
prepared as outlined in section 3.4.3 above) in air.
Preliminary experiments were performed upon the latex only. The
latex powdered samples were heated at a rate of 10°C/min from ambient to
1000°C in air only. From this data and from preliminary pyrolysis
experiments, within the pyrolyzation furnace, the pyrolysis/presintering
schedule was established (see section 3.4.2 below).
Later, thermal analysis characterization was performed upon both
the polymer powders utilized in this study (i.e. the latex and the
dispersant). Sample weights of approximately 50 and 100 mg were used
for air117 and N;74 atmosphere experiments respectively. The gas flow rate
used was approximately 60 ml/min.
121 Model Number: SAT409, Netzsch, Inc., Exton, PA, data
acquisition through Model Numbers: HP 3421A data acquisition/control
unit and Model Number: HP86B computer, Hewlett Packard Co., P.O. Box
3640, Sunnyvale, CA 94088

252
The reference powder used in all experiments was 100 mg of A1:03,'~ and
buoyancy correction was utilized in each experimental repetition.
During organic powder thermal analysis, the measuring head utilized was
one designed for TGA/DTA measurements.
In the case of the green slip cast compact, a different
measurement head, designed for TGA, was utilized. Therefore, no DTA
data was obtained for this experimentation. The sample weight used in
this case was approximately 525 mg. The thermal schedule utilized in
this instance mimicked that depicted in Figure 3.10. The gas flow rate
used in this experiment was also approximately 60 ml/min. Only air"7
was used as the atmosphere in this experimentation. Due to the
relatively high sample weight, no buoyancy correction was used in this
case.
3.6 Thermal Treatments
3.6.1 Furnace Calibration
Figure 3.7 illustrates the apparatus used for
pyrolysis/presintering operations as well as for sintering studies
discussed below. The digital controller123 utilizes a PLII type control
thermocouple placed centrally within in the furnace124 and slightly
outside the pyrolysis tube apparatus.125 Prior to experimentation, the
controller was calibrated following a standard calibration procedure.126
122 Powder Number: C75RG, Alcan Aluminum Corp. , 100 Erieview
Plaza, Cleveland, OH 44114, previously calcined to 1000 °C
123 Model Number: 58114-P programmable control console, Lindberg
Corp., A Unit of General Signal, 304 Hart Street, Watertown, WI 53094
124 Model Number: 58114-P Lindberg Corp., A Unit of General Signal,
304 Hart Street, Watertown, WI 53094
125 2" O.D. fused quartz tube modified for use at the Department of
Chemistry Glass Shop, University of Florida, Gainesville, FL 32611
126 As outlined in Chapter 7 of DOC. 818/EN-l, Eurotherm
Corporation, 11485 Sunset Hills Road, Reston, VA 22090-5286

253
Key:
A. 1200 C Clamshell Type Tube Furnace
B. Digital Furnace Controller
C. 0.001 mV Resolution Voltmeter
D. Type PLII Control Thermocouple
E. Type PLII Reference Thermocouple
F. Controllable Flow Meter
G. Exhaust Gas Bubbler
H. 220 V AC Power Source
I. 120 V AC Power Source
K
N
M
To Controller/
/ Voltmeter
D
J. Furnace Tube Assembly
K. Furnace Tube
L. Sample Setter
M. Sample
N. Tube End Sealing Elements
O. Controlled Atmosphere Inlet
P. Tube Gas Exhaust
Q. 0.1 t Resolution Cold Junction
Compensation Thermometer
Q
N
To Voltmeter
O
View of Sample/Tube Assembly
Schematic
apparatus
representation of the tube furnace
used in this study
Figure 3.7

254
The microvoltage source used for calibration was provided via a standard
1.5 V alkaline battery127 connected to the furnace controller in series
with a 500 ohm, 5% tolerance resistor128 and a 10,000 part adjustable
resistance apparatus.129 Also connected in parallel at the controller
input nodes were two high impedance (>1 G-ohm), 100 nV resolution
digital multimeters130 which where utilized to monitor the input signal
to the controller. Two meters were used in order to insure both
accuracy and reproducibility of the input signal. Each had been
recently calibrated by two independent sources.131
Temperature monitoring was provided during pyrolysis/presintering
treatments via a second type PLII thermocouple132 located centrally
inside the pyrolysis tube (next to the sample compacts). Said reference
thermocouple output was direct to a 100 nV resolution digital
multimeter.123 At this point, a cold junction compensation was manually
added to the voltage reading and the temperature found from a reference
table.133 A 0.1°C resolution thermometer, manually fixed to the
reference thermocouple cold junction housing, was utilized to obtain
said cold junction compensation values.
127 Model MN1500, 1.5 V AA Duracell Battery, Duracell, Inc.,
Bethel, CT 06801
128 Two 5% tolerance, 1000 ohm resistors connected in parallel,
Model Number: 271-023, Radio Shack, A Division of Tandy Corp., Fort
Worth, TX 76102
129 Kelvin-Varley Type 10,000 part voltage divider, Manufactured by
C.E. Randall, Arkport, NV 14807
130 Model Number 195 Digital Multimeter, Keithley Instruments,
Inc., 28775 Aurora Road, Cleveland, OH, 44139
131 A. Digital Design Facility, University of Florida, Gainesville,
FI 32611 B. Keithley Instruments, Inc. 28775 Aurora Road, Cleveland, OH
44139
132 Model P/N PII-E-B/28-0-TP/96 thermocouple modified with P2X-20-
TEF extension wire, Engelhard Corporation, Engineered Materials
Division, Industrial Products, 70 Wood Ave. South, CN770, Iselin, NJ
08830
133
Source: Lindberg Corp., 304 Hart Street, Watertown, WI 53094

255
An experiment was performed in order to characterize the
relationship between setpoint and actual reference temperature. With
the reference thermocouple centered within the furnace tube, the
controller setpoint was established and allowed to equilibrate for a
duration not less than 30 min. The reference thermocouple output was
then obtained, cold junction compensated, then transformed to a
temperature. A new, higher setpoint was then established and the
process repeated. Said experiment was performed on 16 different
setpoints, ranging from 100°C to 1000°C. The resulting furnace
temperature as a function of set point relationships are illustrated in
Figure 3.8. These data indicate that the reference temperature is never
more than 14°C different from the setpoint and that the actual
temperature is generally slightly greater than the indicated setpoint
for the temperatures of interest in this study.
Similarly, an experiment was performed in order to determine the
fluctuation of actual temperature within the pyrolysis tube with respect
to the longitudinal distance from the point of maximum temperature of
the furnace since the furnace utilized for pyrolysis/presintering was a
single heating zone type. The reference thermocouple was centered
radially within the furnace tube at a longitudinal distance of 10 cm
from the physical center of the furnace toward the exhaust end of the
furnace tube. The furnace controller setpoint was then adjusted to
750°C and allowed to equilibrate for no less than 1 h. After
equilibration, the temperature was corrected, as described above, and
recorded. The reference thermocouple was then repositioned 0.5 cm
displaced toward the physical center of the furnace, equilibrated again
and a temperature again measured. The above process was repeated until
a range of 17.0 cm, equally distributed about the physical center of the
furnace, had been characterized. The data are illustrated in Figure
3.9. Figure 3.9 shows that the point of maximum temperature is
displaced slightly from the physical center of the furnace. The point

256
Furnace Controller Setpoint ( C)
A. Actual Temperature Versus Furnace Controller Setpoint
Furnace Controller Setpoint ( C)
B. Actual Minus Furnace Contoller Setpoint Versus
Furnace Controller Setpoint
Figure 3.8 Actual centerpoint temperature versus setpoint for
the furnace used in pyrolysis/presintering and in
sintering; A. Actual Temperature, B. Temperature
Variance

257
Distance From Temperature Maximum (cm)
Distance From Physical Center of Furnace (cm)
A. Temperature versus Distance
Distance From Temperature Maximum (cm)
Distance From Physical Center of Furnace (cm)
B. Percent Temperature Variance From Setpoint versus Distance
Figure 3.9
Measured temperature versus lateral placement in the
furnace tube center

258
of maximum temperature was then marked on the furnace and the reference
thermocouple was always adjusted to said mark using a plastic drafting
triangle'54 prior to either pyrolysis/presintering or sintering
treatments.
It was assumed that temperature variation radially within the tube
is minor, due to excellent insulation as well as the radial symmetry of
the tube furnace. Also, due to the tube configuration, only a small
radial displacement of either the thermocouple or the sample is
possible. Therefore, no experimentation, attempting to characterize
radial temperature variation within the furnace tube assembly, was
performed.
3.6.2 Pyrolysis and Presinterinq
The dry, slip cast disks were pyrolyzed and presintered.
Typically from 3 to 7 compacts were arranged upon an A1203135 setter then
placed within a tube apparatus115 inside the furnace.124 An end cap136 was
then clamped137 in place on the tube and compressed air,"7 at the rate
of approximately 240 cm3/min, was flowed through the pyrolysis tube. A
slight positive pressure of air in the pyrolysis tube was assured by
flowing the tube exhaust through a bubbler unit.138
134 Model Number: 12014-12, Dietzgen Corp. , 250 Willie Rd., Des
Plaines, IL 60018
135 Ceramics Process Systems, 840 Memorial Dr., Cambridge, MA 02139
136 Catalog Number: 7655-72 pyrex socket member enclosed at the end
via Catalog Number: 8847-04 pyrex end plug, Ace Glass Inc., 639 South
Hanock St., Louisville, KY 40201. Glasswork performed by Department of
Chemistry Glass Shop, University of Florida, Gainesville, FL 32611
137 Catalog Number: 7670, Ace Glass Inc., 639 South Hanock St.,
Louisville, KY 40201
138 Catalog Number: 11-184-1C, Fisher Scientific, 1600 Parkway
View Drive, Pittsburgh, PA 15205

259
The exhaust gas was then vented to a fume hood139 via plastic tubing.140
The pyrolysis run was then initialized. The time-temperature schedule
was controlled and monitored through the digital furnace programmer.116
At the end of each pyrolysis/presintering run, the specimens were
removed and packaged for future treatment or characterization.
The appropriate pyrolysis/presintering schedule was determined
with the aid of TGA/DTA data, obtained as described in section 3.5.2
above, as well as with empirical experimentation. It was necessary to
pyrolyze both the polystyrene latex and the dispersant as much as
possible before the onset of sintering of the BS glass matrix phase.
Since the BS glass sinters at relatively low temperatures, the pyrolysis
time-temperature schedule had to be chosen carefully. The standard
pyrolysis/presintering treatment chosen is illustrated in Fig. 3.10.
The presintered samples appeared very white (for pure BS glass and BS
glass-UPLM samples; however, the Si3N4 powder used has a greyish
appearance, and thus, imparts that hue to compacts containing the Si,N4),
indicating a successful pyrolysis of included organics.
The pyrolysis condensate at the exhaust end of the pyrolysis tube
was a brownish-black substance with the consistency of a thick tar. It
dissolves completely in EtOH.24 Thus, EtOH was utilized to thoroughly
clean the tube apparatus prior to sintering treatments.
3.6.3 Sintering
As previously mentioned, sintering treatments were performed in
the same apparatus a the pyrolysis/presintering treatments, after
thorough cleaning. The furnace was allowed to equilibrate at the
predetermined setpoint (618 and 644°C for sintering temperatures of 625
and 650°C respectively).
139 Kemmetal 4' model, Kewaunee MFG. Co. Adrian, MI
140 Catalog Number: 14-169-1M, Fisher Scientific, 1600 Parkway View
Drive, Pittsburgh, PA 15205

Temperature (C)
260
Point
Set Point (°C)
Rate to Set Point (°C/h)
Time at Set Point (h)
A
20
0
0.0167 (1 minute)
B
120
100
0.5
C
240
50
0.25
D
550
20
3.0
All
RT
Furnace Cool
End
Note: RT designates Room Temperature (usually 20 to 25 °C)
Atmosphere: Compressed Air
Flow Rate: Approximately 240 cm3/m
Figure 3.10
The pyrolysis-presintering thermal treatment
schedule utilized in this study

261
The specimen to be sintered was placed upon an A1;03 setter,128 then
placed in the uncapped end of the furnace tube. A hooked rod141 was
then used to move the specimen/setter to directly beneath the reference
thermocouple join. At this point, the furnace end was recapped and the
setpoint increased 3°C until the actual temperature reached the desired
value. The setpoint was then reduced gradually to the appropriate
setpoint. This temperature equilibration was observed to take
approximately 5 min., and thus, said amount was added to each isothermal
sintering duration. A count down timer142 was utilized to ensure
accuracy and the actual temperature monitored periodically throughout
the process. Compressed air at a rate of 240 cm3/niin. was flowed
through the tube during the entire process. When the sintering duration
had expired, the sample/setter was gradually removed from the tube using
the hooked rod and a pair of forceps.143 Removal time was approximately
3 to 5 min. in order to avoid thermally shocking the sintered specimen.
The specimen was then packaged, labelled and stored for future
archimedes density characterization.
3.7 Materials Characterization
3.7.1 Archimedes Density Characterization
Material bulk properties were determined using ASTM standard C
373-72 [88ST01] as a guideline. The general method and apparatus
utilized is illustrated in Figure 3.11.
141 Catalog Number: 11-365B, Fisher Scientific, 1600 Parkway View
Drive, Pittsburgh, PA 15205. The hook (a 90° bend) was made on one end
using an oxy-hydrogen torch.
142 Catalog Number: 06-662-7, Fisher Scientific, 1600 Parkway View
Drive, Pittsburgh, PA 15205
143 Catalog Number: 15-200, Fisher Scientific, 1600 Parkway View
Drive, Pittsburgh, PA 15205

262
A. Vacuum Impregnation
Key:
A. Vacuum Dessicator
B. D.l. Water Valve
C. Vacuum Valve
D. Sample Holder/
Beaker Assembly
E. Vacuum Swivel
Stopper
F. Archimedes Bath
Apparatus
G. 0.1 mg Sensitivity
Digital Balance
H.Immersion Bath
I.Immersed Sample/
Holder
J. Saturated Specimen
on Weighing Paper
K. Vacuum Oven
L. Drying Sample
M. Dry Specimen
N. 120 VAC Power
Source
O. Thermometer
B. Immersed Weight
C. Saturated Weight
Figure 3.11
Schematic representation of the methods and
apparatii used in the Archimedes Method density
characterizations performed for this study

263
The samples were placed in a supported basket inside a beaker.144 The
beaker was then placed within a vacuum desiccator145 which had been
modified as shown in Figure 3.11. A vacuum of >32" Hg (gauge) was then
pulled on the desiccator for no less than 15 min. in order to remove
residual gases within the pores of each specimen. At this point,
deionized (DI) water88 was introduced to the samples (see Figure 3.11)
and a similar vacuum was pulled on the desiccator for no less than 2 h
more. The side of the desiccator was periodically tapped during this
stage in order to help remove bubbles sticking to specimens. When few
or no bubbles were released during the tapping process (after the
prestated 2 h period), the samples were subjected to atmospheric
pressure. This further aided in total impregnation of the specimens
with water.
The beaker of impregnated specimens was then removed from the sample
desiccator and placed next to the archimedes water bath overnight in
order to allow temperature equilibration.
The immersed weight of each specimen was obtained by first zeroing
the 0.1 mg sensitivity balance,"1 then placing the specimen into the
nylon mesh basket and recording the balance reading. This procedure was
repeated until two recorded balance readings agreed to within 0.0002 g.
The two values were then averaged and used as the specimen immersed
weight.
The specimen saturated weight was obtained by first patting the
specimen off on a tissue61 to remove water from the surface, placing the
saturated specimen on a pretared balance pan, then recording the balance
readout. The saturated specimen was then placed in its open packaging
144 Catalog Number: 02-540P, Fisher Scientific, 1600 Parkway View
Drive, Pittsburgh, PA 15205
145 Catalog Number: 08-594-15C, Fisher Scientific, 1600 Parkway
View Drive, Pittsburgh, PA 15205

264
container which was then placed within a vacuum oven55 at approximately
100°C for no less than 4 h.
Next a >30" Hg (gauge) vacuum was pulled on the vacuum oven and the
vacuum pump14* then shutoff. The gauge of the vacuum oven was then
monitored over a period of approximately 10 min. in order to determine
if the drying process was complete. The dry specimen weight was then
obtained from the previously zeroed balance. This measurement was
performed quickly in order to minimize readsorption of atmospheric water
by the specimen.
The bulk density, percent of theoretical density, apparent
density, open porosity, total porosity and closed porosity were then
calculated via a computer spreadsheet program.36 The calculated bulk
density data were stored in said spreadsheet for future use. Table 3.12
denotes the various equations used for bulk density characterization.
The above archimedes density characterization process was repeated
until the following two criteria were satisfied:
1. values of bulk and apparent density,
from two separate repetitions,
agreed within 0.01 g/cm3
2. values of % of theoretical density,
% total, % open, and % closed
porosity respectively, from the same
two runs, agreed within 0.5 %
The respective values from the two archimedes method characterization
repetitions were then averaged. Said average was used for all sintering
characterizations.
It should be noted at this point that, generally, samples that
were sintered to approximately 5 % closed porosity required several
repetitions to complete this process. The general behavior of said
specimens was to increase in apparent density and open porosity until an
equilibrium was achieved.
146 Model Number: 1405-6 Duo Seal vacuum pump, W.M. Welch
Manufacturing Co., Chicago, IL

265
1.
Equations
Bulk Density,
Table 3.12
Utilized in Bulk Density
P Bulk (g/cm3):
Characterization
P bulk
MpryPUq
WSaC-MImm)
where: is sample dry mass (g)
Mj,, is sample saturated weight (g)
is sample immersed weight (g)
pLjq is immersion liquid density (g/cm3)
2.Percent Theoretical Density, %ThD (%):
%rh£)=_PsüLLx 100
P Theo.
where: p-,^ is the theoretical density of the
material (g/cm3)
3.Apparent Specific Gravity, ASG (g/cm3):
ASG=
MpryP L
iq_
Mp
4.Percent Total Porosity, %TP (%):
%TP=100-%rAD
Percent Open Porosity, %OP (%):
%OP= SaC .-glixlOO
r Mrmm
5.

266
Table 3.12 (continued)
6. Percent Closed Porosity, %CP (%):
% CP- % TP- % OP
7. Composite Theoretical Density, Piwon.po.itc (g/cm3):
P
Theo. Compos ite
=E, viP
Theo.i
where: V¡ is the volume fraction of component i
Ptwi i-s the theoretical density of
component i (g/cm3)

267
This behavior was most pronounced in specimens containing controlled
porosity and will be discussed further in Chapter 4 below.
Archimedes density measurements were repeated, on each specimen,
after dielectric properties characterization (described in section 3.7.2
below). This was done in order to determine if any of the density-
related values changed as a result of preparation for dielectric
properties measurements. If the above values agreed within the
prestated criteria, the values used for sintering characterizations were
also used in dielectric properties characterizations. If the new data
did not satisfy the above criteria, the process was repeated until the
above criteria were satisfied and these new data were used in all
dielectric properties characterizations.
3.7.2 Dielectric Properties Characterization
Sintered/presintered specimens that were large enough were then
prepared for dielectric properties measurement. This involved grinding
the disks to a thickness of approximately 1 to 5 mm to a surface
smoothness of 600 grit. The thickness criterion above was chosen with
consideration of the dielectric standards data depicted below. It was
also paramount that both surfaces of circular cross section be parallel.
The following procedure helped achieve these goals.
A specimen for grinding was mounted to the grinding fixture
illustrated in Figure 3.12 using Canadian balsam.147 The removable
inner portion of the grinding fixture was placed in boiling water to
heat it to the melting temperature of the balsam. It was then removed
and dried. The balsam was applied at this point and the flattest
portion of the sample (the bottom) was affixed to the grinding fixture.
The affixed pair were then placed in water at ambient temperature to
cool the balsam below its hardening point. After cooling, the affixed
147 Catalog Number: 40-8110-004 BALSAM, Buehler Ltd. , 41 Waukegan
Rd., Lake Bluff, IL 60044

268
TOP VIEW
Plunger Stop Nut
Screw Driver Slot
Sample Thickness Adjustment Plunger
(Tool Steel)
Skid Disk Retention Allen Screws (4)
Skid Disk (Machine Steel)
Sample
Support Collet
(Machine Steel)
Dimensions:
A. 42.5 mm
B. 50.8 mm
C. C, 13.0 mm, C2 29.5 mm
D. 4.6 mm
E. 9.5 mm, Threaded 0.945 turns/mm
F. 60.0 mm
G. 50.6 mm
H.4.5 mm
I. 2.3 mm
J. 9.5 mm, Threaded 0.945 turns/mm
K. Number 4/40 Allen Screws (4)
L. 32.0mm of Threaded Length
M. 6.2 mm
N. 9.5 mm, Threaded 0.945 turns/mm
Figure 3.12
Schematic illustration of the plane-parallel,
dielectric specimen grinding fixture utilized

269
pair were reinstalled within the rest of the grinding fixture, and the
decking height was adjusted using vernier calipers.148 A locking nut
was then tightened to ensure that the decking height did not change.
The specimen was then ground to the decking height using Sic
powders'49 dispersed in DI water on glass plates.150 A circular
grinding motion was used and the entire apparatus was thoroughly rinsed
with tap water between each grinding or polishing stage. The
grinding/polishing stages were 120, 240, 320, 400 and 600 grit.
After the last polishing stage, the apparatus was disassembled and
washed. The removable portion (with the specimen) was again immersed in
boiling water and the specimen was removed after heating. The empty
grinding fixture was then reimmersed in ambient temperature water to
again cool the remaining balsam. The remaining hard balsam was then
removed by scraping the flat surface with a flat spatula.151 The clean
grinding fixture was then reheated in the boiling water and the opposite
side (i.e. the side that had just been ground and polished) was affixed
to the grinding fixture. The entire process was then repeated in order
to insure that the previously mentioned conditions for satisfactory
specimens were met.
The collet of the grinding fixture was cleaned between grinding
and polishing each side and the inner surface was coated with a thin
layer of silicone grease.106 The fixture was stored greased and dry in
order to prevent corrosion.
148 Catalog Number: 12-122, Fisher Scientific, 1600 Parkway View
Drive, Pittsburgh, PA 15205
149 Catalog Number: 40-6905-XXX-080, where XXX denotes SiC powder
grit size, Buehler Ltd., 41 Waukegan Rd., Lake Bluff, IL 60044
150 E Float Glass, Ace Hardware
151 Catalog Number: 14-373, Fisher Scientific, 1600 Parkway View
Drive, Pittsburgh, PA 15205

270
The parallel ground and polished specimens were washed in 3
separate acetone152 baths. The first was used to remove bulk balsam
remaining on the specimens. The second two washes in acetone were
performed in a sonication bath in order to remove all soluble
impurities.
The washed specimens were then placed within their respective,
open packaging containers and dried within a vacuum oven at
approximately 70°C overnight at ambient pressure. After drying the
specimens were repackaged and stored for future dielectric properties
measurements.
Immediately prior to dielectric characterization the samples were
placed in their respective open containers and dried at 180°C for no
less than 2 h in a microprocessor controlled153 drying oven154 in order
to remove any bound water which would result in erroneous dielectric
data. Dielectric measurements were performed using the air gap
method155 in a guarded electrode dielectric test fixture,156 using
electrode B (5 mm solid electrode) connected to a low frequency
impedance analyzer.157
The test fixture was connected to the impedance analyzer which was
allowed to warm up for approximately 30 min. At this point the proper
frequency and circuit mode were set and the device subjected to a zero-
15: Catalog Number: A18-20 ,Fisher Scientific, 1600 Parkway View
Drive, Pittsburgh, PA 15205
153 Model Number: 828D Micristar, Research Inc., Box 24064,
Minneapolis, MN 55424
154 Model Number: LEB-1-27, Despatch Corp. , 619 SE 8th St., P.0.
Box 1320, Minneapolis, MN 55440
155 See Operations Manual for Footnote 156
156 Model Number: HP 16451B, Yokogawa-Hewlett-Packard, LTD., 9-1,
Takakura-cho, Hachioji-shi, Tokyo, Japan
157 Model Number: 4912A, Hewlett Packard, Yokogawa-Hewlett-Packard,
Ltd., 9-1, Takakura-cho, Hachioji-shi, Tokyo, Japan

271
short/open calibration correction.158 The test fixture electrodes were
then adjusted as recommended.155 After electrode adjustment, a second
zero-short/open correction was performed. Since no load feature is
available on the dielectric test apparatus, a tan(6) compensation
correction factor was determined for each frequency of interest.
After the previously mentioned calibrations and adjustments were
performed, the electrodes were moved together with no sample between
them until a tan(6) value was indicated by the impedance analyzer. This
value was monitored over time and is indicated in Table 3.13 for the
various frequencies. These values were observed to oscillate
approximately +0.0005 with time and thus should be considered accurate
only within that range. In order to check the accuracy of said tan(5)
compensation, several standards of known tan(5) were tested at 1 MHuz.
These data are also in Table 3.13 in order to provide a basis for the
accuracy of tan(6) data.
In order to investigate the relative accuracy of the dielectric
measurement apparatus, discoidal quartz159 and pyrex160 standards of
various diameters and thicknesses were obtained and measured via the
method above (without the 180°C heat treatment) at 1 MHz. Table 3.13
depicts this data as well as pertinent literature data, thereby allowing
the reader an estimate of the relative accuracy of said apparatus. From
this data, it was decided that it would be best to try to keep sample
thickness between approximately 2 and 4 mm. Also from these data, it
was decided to keep the sample diameter between 0.75 (1.91 cm) and 1.5"
(3.81 cm).
158 See Operations Manual for Footnote 157 above
159 GM Associates, 9803 Kitty Lane, Oakland, CA 94603
,eo Ace Glass Inc., 639 S. Hancock St., Louisville, KY 40201

272
Table 3.13
Measured Dielectric and Physical Data
of the Dielectric Standards Used
Description
Bulk Properties
Dielectric
Properties
Dia¬
meter
(mm)
Thick¬
ness
(mm)
Bulk
Density
(g/cm3)
%Th D
e
tan(6)
7070 INGOT
(SQUARE
AS RECEIVED)
NA
3.37
2.13
100
4.06
0.0006
FUSED SiO-,
1.5" (A)'
37.90
9.56
2.20
100
4.14
<0.0001
FUSED SiO,
1.5" (B) ~
38.40
6.22
2.20
100
3.95
<0.0001
FUSED SiO;
1.5" (C)
38.05
3.20
2.16
98.0
3.80
<0.0001
FUSED SiO-,
1-5" (D)‘
38.15
1.60
2.10
95.6
3.71
<0.0001
FUSED Si02
1.0" (E)
25.45
9.50
2.19
99.5
3.95
<0.0001
FUSED SiO:
1.0" (F)
25.41
6.63
2.20
100
3.92
<0.0001
FUSED SiO;
1.0" (G)
25.05
3.26
2.20
100
3.82
<0.0001
FUSED SiOj
1.0" (H)
25.32
1.65
2.20
100
3.73
<0.0001
FUSED SiO-,
0.5" (I)'
12.75
9.56
2.20
100
3.68
<0.0001
FUSED SiO;
0.5" (J)‘
12.50
6.41
2.22
101
3.69
<0.0001
FUSED SiOj
0.5" (K)
12.60
3.17
2.19
99.5
3.64
<0.0001
FUSED SiO;
0.5" (L)
12.85
1.54
2.21
100
3.66
<0.0001

273
Table 3.13 (continued)
Description
Bulk Properties
Dielectric
Properties
Dia¬
meter
(mm)
Thick¬
ness
(mm)
Bulk
Density
(g/cm3)
%Th D
e
tan(6)
7740 PYREX
0.75" (M)
18.85
10.00
2.23
100
4.66
0.0048
7740 PYREX
0.75" (N)
18.80
6.49
2.23
100
4.63
0.0044
7740 PYREX
0.75” (O)
19.05
3.29
2.23
100
4.61
0.0043
7740 PYREX
0.75" (P)
19.05
1.74
2.23
100
4.56
0.0045
Notes:
1. The bulk density of all samples other than the 7070
sample was determined by measuring the sample
diameter, calculating the volume using a discoidal
approximation, and dividing the measured sample weight
by said volume. The bulk density of the 7070 sample
was measured using the Archimedes method.
2. The literature value theoretical densities used were,
2.20 g/cm3 for fused SiO, [79COR], 2.13 g/cm3 for 7070
[79COR, 88COR] and 2.23 g/cm3 for 7740 Pyrex [79COR,
88COR].
3. Literature value dielectric constants (e) are 3.78 for
fused SiO, [76KIN], 4.1 for 7070 [79COR, 88COR] and
4.6 for 7740 Pyrex [79COR,88COR].
4. Literature value loss tangents (tan(6)) are 0.0001 for
fused Si02 [76KIN], 0.0006 for 7070 [79COR, 88COR] and
either 0.0057 [79COR] or 0.004 [88COR] for 7740 Pyrex.

274
Therefore, the casting tubes used during slip casting (as described in
section 3.4.3 above) were chosen to have an inner diameter of
approximately 1.125" (2.86 cm). Thus, the sample diameters remained
between the diameter limits, established using the data in Table 3.13,
after densification.
The specimen to be measured was quickly removed from the drying
oven using tweezers112 and placed between the electrodes of the
dielectric test fixture. The electrode distance was then quickly
reduced (using the clutch drive to avoid damage) until the electrode
touched the sample. The sample thickness was then measured using the 10
pm resolution micrometer on the dielectric test fixture. The electrode
distance was then increased to an amount between 100 and 110% of the
measured sample thickness. This reading was also recorded with said
micrometer. After equilibration of values (i.e. the capacitance and
tan(6) of the specimen decreases until cooling to near ambient
temperatures), the capacitance and tan(6) were recorded. The specimen
was then removed and the process repeated for other specimens. Once
dielectric characterization was completed on the specimen, the sample
thickness was remeasured, using a precision micrometer.161 This
thickness measurement was recorded and used in all calculations
requiring the sample thickness. The specimen was then repackaged and
stored for the second set of archimedes density characterizations.
Table 3.14 depicts the calculations used for dielectric properties
calculations.
The effect of atmospheric moisture adsorption was also
investigated. Seven samples, representative of the composite matrix
produced, were heated in the previously mentioned drying oven at 180°C
for no less than 2 h.
161 Catalog Number: 12-125, Fisher Scientific, 1600 Parkway View
Drive, Pittsburgh, PA 15205

275
Table 3.14
Equations Used in Calculating Dielectric Properties
1. Dielectric Constant, e:
e =
where: tg is the air gap width (i.e. the distance
between the sample top and the electrode
surface (mm))
t, is the thickness of the specimen under
test (mm)
CSg is the series analog capacitance
measured with the material under test
(MUT) removed (pF)
Csi is the series analog capacitance
measured with the MUT inserted (pF)
2. Dissipation Factor, tan(6):
tan 6=D*CF
where: D is the measured dissipation factor of
the MUT
CF is the estimated correction factor for
the DUT
Notes: 1. Standard measurements taken at a frequency of 1 MHz
2. CF is frequency dependent:
Correction Factor (CF) as a Function of Frequency
Frequency (Hz)
Correction Factor
106
0.0012
107
0.0040
1.3 x 107
0.0083

276
These specimens were also of two different groups, one having less than
1% open porosity, one having almost totally open porosity. Furthermore,
the highly sintered samples would have very low specific surface areas,
whereas the specific surface areas of the open porosity samples where
greater as outlined above and further explained below. Each specimen
was then removed and the dielectric properties were quickly measured.
The sample weight was also recorded using a 0.1 mg resolution balance at
that time.162 This was established as a zero point of time and a
timer142 was started. This procedure was performed at 0, 1, 2, 5, 10,
30, 60, 120, 180, 240 and 1440 min. for each sample. In order to avoid
time discrepancies, the procedure was performed up to the 10 min.
repetition on each consecutive sample before starting the next.
Specimens were characterized in sets of three samples in this manner
(since the timer had three separate timing circuits).
Finally, the effect of frequency upon dielectric properties was
investigated. Dielectric properties measurements were performed on 4
representative hermetic samples at frequencies of 1 kHz, 10 kHz, 100
kHz, 1 MHz, 10 MHz and 13 MHz. At each frequency, an zero-short/open
calibration158 was performed prior to measurement. It should be noted
that at lower frequencies, the dielectric test apparatus loses accuracy
in capacitance measurements and therefore, relationships concerning
capacitance related dielectric properties with respect to frequency are
plotted with dashed lines below frequencies of 10 kHz. It is assumed
however, that changes in capacitance related dielectric properties with
decreasing frequency are directly a result of this inaccuracy, since the
data of others indicates that the dielectric constant of these materials
is very stable with respect to frequency (as will be discussed in
Chapter 4 below), at low frequencies.
i6:
Model Number: AE 100, Mettler Instrument Corp., Hightstown, NJ

277
Furthermore, tan(5) was not measurable below 1 MHz due to the previously
mentioned limitations of the test apparatus.
3.7.3 Microscopic Investigation of Composites
3.7.3.1 Overview
This section describes the experimental procedures utilized to
microscopically investigate sintered composites. The experimental
details of microscopic investigations of the latex powders used in this
study are described in section 3.2.2 above. The procedures used to
microscopically characterize the ceramic powders are outlined in section
3.3.2 above. Microscopic investigation of green compacts is detailed in
section 3.4.5 as well.
Microscopic investigation of sintered compacts was used mainly to
investigate the appearance of included porosity (i.e pore size,
smoothness, cluster size, dispersedness, and possible segregation).
Microscopy was also utilized to examine Si3N4-BS glass interfaces in
order to determine if the Si3N4 powder reacted noticeably with the BS
glass matrix. A rough, qualitative measure of surface smoothness was
also obtained by examining the top surface of representative sintered
compacts.
Where possible, polished specimens were examined. However, as is
common in porous composite systems, it was not always possible to do so.
In these situations, fracture surfaces were examined.
3.7.3.2 Specimen Preparation
Polished specimens were produced by mounting the specimen in
polymethyl methacrylate (PMMA) prior to polishing. The specimen of
interest was placed inside a glass vial.163 The specimen was held
163 Catalog Number: 03-337-5, Fisher Scientific, 1600 Parkway View
Drive, Pittsburgh, PA 15205

278
vertically within the vial with a mounting clip164 and approximately 3
ml of 2,2'-Azobis [ 2-methyl-propionitrile ] (AIBN) l65/MMA (methyl
methacrylate)166 solution was decanted inside the glass vial using a
disposable pipette.167 The AIBN/MMA concentration used was 9 mg to 5 ml
(AIBN to MMA). The AIBN acted as the initiator of the addition
polymerization reaction that forms PMMA. This process was carried out
beneath a fume hood52 in order to avoid exposure to hazardous MMA fumes.
The glass vial was then sealed tightly and placed within an oven168 to
promote polymerization of the MMA. The oven was isothermally maintained
at approximately 63°C as indicated by an 0.1°C resolution thermometer.10
The thermometer bulb was placed next to the MMA in the glass vial in
order to assure accurate temperature measurement.
After the MMA polymerized, the vial was removed from the oven and
allowed to cool to ambient temperature. The vial was then decapped and
wrapped in a tissue.61 A hard object was then used to break the vial and
the PMMA mounted sample was removed.
The sample was then ground flat on a polishing wheel169 using a
120 grit SiC abrasive paper.170 Each sample was similarly ground and
polished to 600 grit using successively smaller SiC papers (i.e. 120,
164 Catalog Number: MK-C-101, Fisher Scientific, 1600 Parkway View
Drive, Pittsburgh, PA 15205
165 Catalog Number: 118-4746, Eastman Kodak Company, Rochester, NY
14650
166 Catalog Number: 03629-4, Fisher Scientific, 1600 Parkway View
Drive, Pittsburgh, PA 15205
167 Catalog Number: 13-711-5A, Fisher Scientific, 1600 Parkway
View Drive, Pittsburgh, PA 15205
168 Model Number: 126G ISOTEMP OVEN, 100 Series, Fisher
Scientific, 1600 Parkway View Drive, Pittsburgh, PA 15205
169 Model Number: ECOMET III, Buehler Ltd., 41 Waukegan Rd, Lake
Bluff, IL 60044
170 Catalog Number: 30-5108-XXX-100, where XXX is grit size,
Buehler Ltd., 41 Waukegan Rd., Lake Bluff, IL 60044

279
180, 240, 320, 400 and 600 grits). Tap water was used as the lubricant
during these polishing and grinding steps. The sample was rinsed
thoroughly in tap water after each step.
Each sample was then polished using 1000 grit SiC powder171 on a
glass plate.150 The grinding lubricant used in this instance was DI H^.88
Each sample was then rinsed and sonically cleaned for several minutes
then rinsed again in DI H;0. Each sample was then dried with a tissue.61
The dry samples were then polished with diamond177 either by hand
or on a vibrating polisher.173 Lapping oil174 was utilized for the
lubricant during diamond polishing. Hand polishing was performed on a
raised nap cloth,175 while cloths having no nap176 were used for
vibratory polishing. The samples were polished using 6, 1 and 0.25 pm
size diamond paste. The samples were sonically cleaned between each
diamond size, then dried with a tissue.
After polishing, the PMMA was removed from each specimen by a two
step process. Each mounted specimen was first put in an oven177 at
approximately 300°C for about 10 min. in order to soften the PMMA.
After removal from the oven each polished specimen was quickly removed
171 Catalog Number: 40-8418-000-016, 1000 grit SiC Powder, Buehler
Ltd., 41 Waukegan Rd, Lake Bluff, IL 60044
172 Designation Series: METADI II, Buehler Ltd., 41 Waukegan Rd,
Lake Bluff, IL 60044
173 Model Numbers: VIBRAMET I and VIBRAMET 2, Buehler, Ltd., 41
Waukegan Rd, Lake Bluff, IL 60044
174 Catalog Number: 60-3250-128, Buehler Ltd., 41 Waukegan Rd,
Lake Bluff, IL 60044
175 Catalog Number: 40-7218 MICROCLOTH, Buehler Ltd., 41 Waukegan
Rd, Lake Bluff, IL 60044
176 Catalog Number: 40-7070 NYLON, Buehler, Ltd. , 41 Waukegan Rd,
Lake Bluff, IL 60044
177Catalog Number: 10-553, Fisher Scientific, 1600 Parkway View
Drive, Pittsburgh, PA 15205

280
from the PMMA using two pairs of tweezers.178 The polished specimen was
then heat treated in an oven at approximately 600°C for approximately 4
h in order to remove any remnant PMMA.
After cooling, the each Si3N4-containing specimen was etched in HF.
Preliminary studies indicated that an HF etch of approximately 60
seconds, in 2% HF, was the best and samples produced subsequent to said
studies were etched at that exposure. Each etched sample was next
thoroughly rinsed in tap water, then sonically cleaned.
Each polished specimen was mounted on a 1" (2.54 cm) aluminum SEM
specimen stub30 with silicone sealant.179 After the silicone dried, a
conductive path was painted from the specimen to the specimen stub with
carbon paint.115 The sample was then sputter coated with a film of Au/Pd
and was ready for viewing via SEM.
The above method worked well for samples containing mainly open
porosity. In the later stages of sintering however, this is not the
case. Polished specimens of samples containing mainly closed porosity
were characterized by pullout around said porosity. Furthermore,
samples containing Si3N4 also exhibited substantial pullout when
polished. Also it was possible to view only relatively small areas of
each etched surface of Si3N4-containing specimens. Therefore, no
segregation studies of Si,N4 in this system were possible.
Thus, samples containing an appreciable amount of closed porosity and/or
Si3N4 were prepared from fracture surfaces.
Specimen fracture surfaces were obtained by fracturing sintered
samples with a hard object. Contaminants were blown off from fracture
178 Catalog Numbers: 08-953D and 08-887, Fisher Scientific, 1600
Parkway View Drive, Pittsburgh, PA 15205
179 Catalog Number: 04-769-5, Fisher Scientific, 1600 Parkway View
Drive, Pittsburgh, PA 15205

281
surfaces using compressed gas.180 The specimens were then mounted and
coated utilizing the procedures described above for polished specimens.
Specimens of sintered compact surfaces were prepared in a manner
identical to the method used to prepare specimens of fracture surfaces.
3.7.3.3 Investigation of Segregation of Included Porosity
In order to determine if segregation of included porosity occurred
within the composite system, several micrographs of the top, middle and
bottom of a sintered specimen containing approximately 14 V% closed
porosity were obtained. The volume fractions of included porosity at
the top middle and bottom of the specimen were determined by a manual
point count method [68DEH]. The manual count was continued in each of
the above-mentioned areas until one hundred pore points had been
obtained. The volume fraction of included porosity was then obtained by
dividing the number of pore points observed by the total number of
points observed.
3.7.4 Mechanical Properties Data
Limited mechanical properties data were obtained using
microhardness indentation techniques. Figure 3.13 illustrates the
pertinent relationships utilized in said characterization.
Representative samples were mounted in epoxy181 and were then ground to
a 1000 grit surface finish with SiC as described in section 3.6.3 above.
A final polish was obtained, manually, with CeO: dispersed in H;0 on a
napped cloth.175 The polished specimens were then cleaned sonically,
swabbed with a clean tissue,61 and dried at ambient temperature
overnight. Samples to be characterized were chosen on the basis of
180 Catalog Number: 15-232-20, Fisher Scientific, 1600 Parkway
View Drive, Pittsburgh, PA 15205
181 Catalog Number: 12-253-50A, Fisher Scientific, 1600 Parkway
View Drive, Pittsburgh, PA 15205

282
1. Vickers Hardness, (H):
t
A
|
Average of A and B
(calculated by the microhardness tester)
T
— B —
2. Knoop Hardness, (K):
b’
Í
(hardness calculated by
microhardness tester)
>
— a ■
Knoop Indenter Ratio: b/a =1/7
Knoop Indentation Dimensions (a’, b’)
3. Elastic Modulus, (E):
0.45(H)
(*- - tL)
a a’
Figure 3.13
Microhardness indentation techniques and
relationships used in this study

283
maximum variability in both closed porosity and silicon nitride content.
Table 3.15 illustrates the samples chosen for characterization via
microhardness indentation. A specimen from an as-received Corning 7070
BS glass ingot was also produced for this study. Since it is an
optically clear sample having no visible seeds, it was assumed that
porosity of the sample is near zero. Said assumption was used when
performing data characterization.
The samples were then characterized using microhardness
indentation. Each sample was evaluated using both Vickers and Knoop
indenters. First, each specimen was subjected to successively
increasing loads (25, 50, 100, 200, 500, 1000, 2000 g) until cracking
(either lateral or radial) was observed. This load was noted. After
determining the lowest values at which cracking occurs, for all samples,
the indent loads to be used on all samples were determined. These loads
were determined to be 25 and 50 g for Vickers indentation and 100, 200
and 300 g for Knoop indentation. On two samples, said Vickers loads
were determined to be too low and higher loads were used (100 and 200 g
respectively).
Vickers microhardness determination consisted of measuring and
averaging both the indentation dimensions. The microhardness was then
calculated by the microhardness tester182 and the output was recorded in
units of kg/mm2. Similarly, both Knoop indentation dimensions were
measured and the Knoop hardness was recorded in the same units as above.
Both dimensions of the Knoop indentation were documented, since both are
required in order to determine the elastic modulus of a material. A
total of 25 data points were taken for each sample. The raw data was
then encoded into a computer spreadsheet36 which gave output for elastic
modulus as well as standard deviation data of the above values.
182 Model Number: MICROMET 3, Buehler Ltd., 41 Waukegan Rd, Lake
Bluff, IL 60044

284
Table 3.15
Samples Investigated by Microhardness Indentation
Designation
Composition
Lat.
Dia.
(pm)
Thermal
Treatment
Bulk
P
%ThD
BS
Glass
Si3N4
Latex
(°C)
(h)
7070 INGOT
100
0
0
NA
NA
NA
100
03209001E
100
0
0
NA
650
6
97.0
05109102F
95
0
5
4.6
625
12
92.2
01039101B
90
0
10
4.6
625
18
90.2
05069101A
85
0
15
4.6
625
18
86.2
05179102A
85
0
15
2.4
625
24
89.7
05099101G
85
0
15
9.0
625
15
85.9
05179101B
85
0
15
POLY
625
18
86.7
03219001F
80
20
0
NA
650
24
96.9
01249101G
72
18
10
4.6
650
24
91.4
01069101F
64
16
20
4.6
625
144
89.0
03199001F
60
40
0
NA
650
72
89.6
01049101B
81
9
10
4.6
625
18
88.7
05119101C
72.25
12.75
15
4.6
625
48
87.7
Notes: 1. Lat. Dia. is the number basis mean UPLM diameter (POLY
means polydisperse latex).
2
NA means Not Applicable.

285
It was not possible to determine the fracture toughness of samples
within the composite system of this study because the type of cracking
that occurred within the pure BS glass samples (both with and without
added porosity) was always lateral. No radial cracks were evident in
these samples at any loadings. In samples containing Si3N4 however, some
radial cracking was vaguely evident. Therefore, samples containing Si3N4
were Au/Pd sputter coated for 40 s at 45 mA and at a pressure of 50
mTorr, in order to increase the reflectivity of the samples so that
microcracking would be more evident.
Vickers indentation was again performed on the samples in order to
attempt to determine the fracture toughness of the material. In order
for this method to be valid, however, the radial crack length initiated
via the indentation must be at least twice that of the dimension of the
indentation itself. All radial cracks were smaller than this value at
all loads at which radial cracking was observed. Therefore, this method
is not a viable technique for determining fracture toughness of
compositions in this composite system.

CHAPTER FOUR
RESULTS AND DISCUSSION
4.1 Precursor Powders
4.1.1 Visual
Figures 4.1 and 4.2 illustrates the BS glass powders used in this
study. Figure 4.1 depicts the as-received powder while Figure 4.2
illustrates the powder after ball milling, as described in Chapter
Three. Both glasses appear to have a conchoidal nature and a wide
distribution in particle size. It is evident from these that figures
the ball milled BS glass powder also has a smaller mean size.
Figure 4.3 depicts the Si3N4 powder used. The Si3N4 powder was used
as-received. The Si3N4 powder has a characteristic shape of either cubes
or hexagonal cross-section cylinders. The powder appears to have a
narrower size distribution than the BS glass powder as well. It should
be noted that the as-received Si3N4 powder has a significant amount of
agglomerates, which remained even after aggressive sonic dismembration.
Figures 4.4 through 4.6 illustrate the range of polystyrene latex
powders (largest, medium and smallest sizes respectively) utilized in
this study. Figure 4.7 portrays the guadramodal ("wide") size
distribution latex powder used. Figure 4.8 depicts a representative
latex powder (medium sized), before settling, to provide a comparison
between settled (i.e. compare Figs. 4.5 and 4.8) and non-settled uniform
polystyrene latex microspheres (UPLMs). It can be seen that the latex
particles are quite spherical and that the UPLMs are predominantly
monomodal. It may also be observed that UPLM powders may be produced
with different sizes and size distributions.
286
UNIVERSITY OF FLORIDA LIBRARIES

287
Scanning electron micrograph of the, as-received,
borosilicate glass powder used in this study (Bar = 10
pm)
Figure 4.1

288
Scanning electron micrograph of ball
borosilicate glass powder (Bar = 10 pm)
Figure 4.2
milled

289
Scanning electron micrograph of the Si3N4
(Bar = 1 pm)
Figure 4.3
powder used

290
Scanning electron micrograph of settled,
UPLM powder (Bar = 10 pm)
Figure 4.4
large size

291
Scanning electron micrograph depicting the settled,
medium sized, UPLM powder utilized in the study (Bar
= 10 pm)
Figure 4.5

292
Figure 4.6
Scanning electron micrograph depicting the settled,
smallest size, latex powder used (Bar = 10 pm)

293
Figure 4.7
Scanning electron micrograph of the wide (guadramodal)
size distribution latex powder used in this study (Bar
= 10 pm)

294
Scanning electron micrograph depicting a
representative sample of the medium size latex powder
before classification via settling (Bar = 10 pm)
Figure 4.8

295
4.1.2 Powder Density
Powder densities were determined using helium gas pycnometry, as
described in Chapter 3. Table 4.1 indicates the results of said
analyses for the BS glass powder (as-received as well as ball milled),
the Si3N4 powder, and the polystyrene latex UPLMs. Table 4.1 also
provides manufacturers or literature data in order to provide a basis
for comparison to the measured powder density values.
Table 4.1 indicates that the density values for both the Si3N4
powder and the polystyrene latex powders agree very well with either the
manufacturer's values or available literature values. Table 4.1 also
indicates that the density values of both the BS glass powders is higher
than the manufacturer's value for the bulk glass. It may be further
noted that the ball milled BS glass powder has a greater density than
the as-received glass powder.
Since smaller powder particles have a greater surface area to
volume ratio, the relative concentration of surface-connected porosity
is increased as well. The result of this effect is to increase the
measured powder density through the decrease of the relative amount of
closed porosity [88REE]. Thus, it is logical that the as-received (i.e.
<325 mesh) BS glass powder would have a greater density than the
manufacturer's value for the bulk glass. Furthermore, it is logical
that the ball milled BS glass powder would have the highest measured
density of the three, since the size of the ball milled powder is
smaller than that of the as-received BS glass powder (as will be
discussed in section 4.1.4 below).
The effect of aggregate and particle size upon density has been
documented, and Figure 4.9 illustrates this relationship for tabular
A1;03 particles [88REE]. From Figure 4.9 it may be ascertained that
apparent density may increase more than 8% from a reduction in particle
size from the bulk value. Thus, it is reasonable that the increase in
measured density be due solely to a reduction in particle size.

296
Table 4.1
Measured Powder Densities and Relevant Data
Powder
Experimental Values
Liter¬
ature
Value
(g/cm3)
%A
Den¬
sity
(g/cm3)
Standard
Deviation
(± g/cm3)
# of
Inde-
pend-
ant
Samples
Total #
of
Repet¬
itions
Pop.
Sample
BS
Glass,
(As-
Rec¬
eived )
2.176
0.0104
0.0112
2
8
2.13
2.2
BS
Glass
(Ball
Milled)
2.197
0.0040
0.0041
4
17
2.13
3.1
Si3N4
Powder
3.175
0.0113
0.0116
3
20
3.10-
3.44
(3.18)
0.2
Poly¬
styrene
Latex
1.055
0.0030
0.0031
3
12
1.05
0.5
Notes: 1. Literature values cited for the BS glass are
manufacturer's data (for Corning 7070 bulk
borosilicate glass) [79COR,88COR]. The Si3N4 values
were obtained from Table l.IV.B.2.1, and the
manufacturer's data, in parentheses, for UBE SN—W
(Si3N4 whiskers [89SOM]). The density value for UBE
SNE03, Si3N4 powder was not available. The %A, for the
Si3N4 powder, is calculated using the manufacturer's
data as described. The literature value for the
polystyrene latex is that cited for polystyrene
[87BAN2,88MIC).
2. The relationship utilized to calculate %A is
%A = lPexP7PjA?/Pa"j xlOO
P lit/man
where: pcxp is the experimentally measured mean
density value
pUiym4n is either the literature or
manufacturer's density value

Apparent Density (g/cm
297
Figure 4.9 Relationship between particle size and apparent density for
tabular alumina particles [88REE]

298
However, there are other phenomena that occur during ball milling
that may also influence the measured density of a powder. Said
phenomena shall be discussed in section 4.1.5 below.
4.1.3 Particle Size/Size Distribution
4.1.3.1 Polystyrene Microspheres
Particle size and size distribution data for the polystyrene
microspheres produced for this study are illustrated in Figures 4.10
through 4.16. Said data are presented using a number basis, and the
tabulated data gives two significant digits plus an extra digit, in
order to give significance to the geometric standard deviation (GSD)
values. In these figures, the GSD values were calculated using the
diameter at 84.13% finer than values divided by the respective 50.00%
finer than values. It should be noted that, since these distributions
are not log normal, the meaning of the GSD values is somewhat negated.
However, these values still have meaning among similar particle size
distribution sets. The median value corresponds to the diameter at
which the cumulative number percent finer (CNPF) value is 50.00%, while
the standard deviation values correlate to the arithmetic mean values.
It should be noted that the smallest three batches actually
exhibited bimodal size distributions, even though they had been
classified by settling numerous times. The GSD values only reflect this
bimodality in the smallest size batch of spheres, however. Again, this
is a flaw inherent in using GSD values to characterize the width of non¬
log-normal size distributions.
The polystyrene microsphere batches having a mean diameter of
greater than 4 pm were highly monodisperse however. They are designated
uniform polystyrene latex microspheres (UPLMs). The advantage of
classification via settling may be noted by comparing Figure 4.13 to
Figure All.11. Settling effectively removed the small particle portion
(the tail) from the size distribution. It is interesting to note that,

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90
80
70
60
50
40
30
20
10
0
35
30
25
20
15
10
5
0
299
Batch 07269001, Settled 12 times
Size Data (Number Based):
Arithmetic
Mean:
2.42 (fjm)
Median:
2.46 U/m)
Geometric
Standard
Deviation:
1.27 (Bimodal)
Standard
Deviation:
± 0.60 li/m)
Number of Points: 1000
&
pip
I I I I I I I I I h I'
•0 14.0 13.0 12.0 11.0 10.0 9.0 8.0 7.0 6.0 5.0 4.0 3.0 2.0 1.0 0
Particle Diameter (//m)
.10 Number basis particle size and size distribution data
for polystyrene microsphere batch 07269001, classified
by settling

Number Percent at Size CNPF
300
Batch 07309001, Settled 16 times
no
100
90
80
70
60
50
40
30
20 -
10
0
Size Data (Number Based):
Arithmetic
Mean:
3.06 (^m)
Median:
3.38 (^m)
Geometric
Standard
Deviation:
1.05 (Bimodal)
Standard
Deviation:
± 0.51 (^m)
Number of Points: 1000
\
35 H
30
25 H
20
15 H
10
5
0
TT
15.0 14.0 13.0 12.0 11.0 10.0 9.0 8.0 7.0 6.0 5.0 4.0 3.0 2.0 1.0 0
Particle Diameter (/;m)
Figure 4.11 Number basis particle size and size distribution data
for polystyrene microsphere batch 07309001, classified
by settling

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00
90
80
70
60
50
40
30
20
10
0
35
30
25
20
15
10
5
0
301
Batch 07199001, Settled 17 times
\
Size Data (Number Based):
Arithmetic
Mean:
3.63 (//m)
Median:
3.91 (//m)
Geometric
Standard
Deviation:
1.06 (Bimodal)
Standard
Deviation:
± 0.62 (//m)
Number of Points: 1000
.0 14.0 13.0 12.0 11.0 10.0 9.0 8.0 7.0 6.0 5.0 4.0 3.0 2.0 1.0 0
Particle Diameter (pm)
12 Number basis particle size and size distribution data
for polystyrene microsphere batch 07199001, classified
by settling

10
00
90
80
70
60
50
40
30
20
10
0
35
30
25
20
15
10
5
0
302
Batches 06199001-07 + 09, Settled 6 times
Size Data (Number Based):
Arithmetic
Mean:
4.59 (//m)
Median:
4.61 (pm)
Geometric
Standard
Deviation:
1.06
Standard
Deviation:
± 0.27 (^m)
Number of Points: 1000
.0 14.0 13.0 12.0 11.0 10.0 9.0 8.0 7.0 6.0 5.0 4.0 3.0 2.0 1.0 0
Particle Diameter (//m)
.13 Number basis particle size and size distribution data
for polystyrene microsphere batch 06199001-07+09,
classified by settling

Number Percent at Size CNPF
303
110 -i
100
90 -
80
70 -
60 -
50
40 -
30 -
20 -
10 -
0 -
Batch 07219001, Settled 7 times
Size Data (Number Based):
Arithmetic
Mean:
6.11 (//m)
Median:
6.22 (^m)
Geometric
Standard
Deviation:
1.03
Standard
Deviation:
± 0.26 (//m)
Number of Points: 1000
I
V
35 -
30 -
25 -
20 -
15 -
15.0 14.0 13.0 12.0 11.0 10.0 9.0 8.0 7.0 6.0 5.0 4.0 3.0 2.0 1.0 0
Particle Diameter (//m)
Fiaure 4.14 Number basis particle size and size distribution data
for polystyrene microsphere batch 07219001, classified
by settling

10
00
90
80
70
60
50
40
30
20
10
0
35
30
25
20
15
10
5
0
304
Batch 08029001, Settled 7 times
Size Data (Number Based):
Arithmetic
Mean:
6.77 (//m)
Median:
6.83 (pm)
Geometric
Standard
Deviation:
1.03
Standard
Deviation:
± 0.29 (//m)
Number of Points: 1000
.o 14.0 13.0 12.0 11.0 10.0 9.0 8.0 7.0 6.0 5.0 4.0 3.0 2.0 1.0 0
Particle Diameter (//m)
15 Number basis particle size and size distribution data
for polystyrene microsphere batch 08029001, classified
by settling

10
00
90
80
70
60
50
40
30
20
10
0
35
30
25
20
15
10
5
0
305
Batch 07249001, Settled 11 times
Size Data (Number Based):
Arithmetic
Mean:
8.95 (y/m)
Median:
8.96 U^m)
Geometric
Standard
Deviation:
1.06
Standard
Deviation:
± 0.46 (//m)
Number of Points: 1000
*
.o 14.0 13.0 12.0 11.0 10.0 9.0 8.0 7.0 6.0 5.0 4.0 3.0 2.0 1.0
Particle Diameter (/ym)
0
16 Number basis particle size and size distribution data
for polystyrene microsphere batch 07249001, classified
by settling

306
even though the settled spheres (i.e. settled batch 06199001-07+09)
clearly are closer to a monodisperse distribution than the unsettled
spheres (i.e. unsettled batch 06199001-07+09), the GSD values for both
size distributions are the same. Thus, it may be concluded that GSD
values should not be used alone to compare particle size distributions.
This is logical, since GSD values only involve 34.13% of the total size
distribution.
Figure 4.17 illustrates the experimental data of this study,
compared to the data of Lok and Ober [85LOK]. The data of the current
study agrees quite well with that of Lok and Ober, with the possible
exception that the range of monodispersity is slightly narrower (i.e. it
was not possible to produce 3 pm UPLMs in this study, although it was
attempted three times). Furthermore, the size distribution of the
largest size UPLM batch was the broadest of the monodisperse batches
produced for this study, possibly indicating the beginning of an upper
limit to the monodisperse region of the phase composition relationship.
Generally, the mean size data matched that of Lok and Ober quite well.
Figure 4.18 illustrates the particle size and size distribution
data for the polysized batch of polystyrene microspheres produced for
maximum packing efficiency (PE) using the methods of Westman and Hugill
[30WES] and McGeary [61MCG], as described in Chapter 3. It should be
noted that the size distribution data for the middle two nodes of the
quadramodal size distribution are based at slightly greater particle
diameter values than the same nodes illustrated in Figures 4.10 and
4.13. This effect may be due to the smaller spheres being hidden among
the largest spheres, although the particle size measurements were
carefully taken in order to minimize this effect. This explanation also
does not explain the near exact match of the smallest node to that
illustrated in Figure 4.10. It is also possible that the measurements
taken to minimize the effects of small sphere hiding, slightly biased
the measured distribution or that this is an effect of sampling

307
Key:
B
Concentrations (V%)
Particle
Solubility
Parameter
Sample
Styrene
EtOH
Me Cell
Size iium)
6¡ (cal/cm3)
1
10
51
39
1-3
11.9
2
15
71
14
1-4
12.1
07269001
15
70
15
2.4
12.1
07309001
15
65
20
3.1
12.0
3
15
60
25
3
11.9
07199001
15
60
25
3.6
11.9
06199001
15
51.25
33.75
4.6
11.8
07219001
15
42.5
42.5
6.1
11.7
4
15
42.5
42.5
7
11.7
08029001
15
36.25
48.75
6.8
11.6
07249001
15
30
55
9.0
11.5
5
15
30
55
9
11.5
6
15
14
71
1-50
11.3
7
20
40
40
5-20
11.6
8
26
44
30
5-20
11.5
9
26
74
0
1-5
11.9
10
33
67
0
7-9
11.7
Comparison of the size and composition data for
polystyrene microspheres produced for this study
versus that of Lok and Ober
Figure 4.17

10
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80
70
60
50
40
30
20
10
0
35
30
25
20
15
10
5
0
e 4
308
Batch 05169101, Polysized
A
Size Data (Number Based):
Arithmetic
Mean:
4.01 (pm)
Median:
3.31 (pm)
Geometric
Standard
Deviation:
1.60 (Tetramodal)
Standard
Deviation:
± 2.12 U/m)
Number of Points: 1000
\
Particle Diameter (//m)
Number basis particle size and size distribution data
for the guadramodal polystyrene microsphere batch,
prepared as outlined in Chapter 3

309
statistics. In any event, the measured size distribution data for the
quadramodal assemblage of polystyrene microspheres is acceptably close
to that expected in comparison with Figures 4.10, 4.13 and 4.16, for the
purposes of this study.
It is also important to note that a particle size distribution may
change a great deal, depending upon the basis of the particle sizing
data. For example when a mass or volume basis is used the particle size
distribution will be shifted toward larger sizes with respect to the
same particle sizing data presented using a number basis (assuming that
the distribution is not perfectly monosized). This effect is largest in
wide particle size distribution powders, decreasing as the size
distribution tightens. For a perfectly monomodal size distribution
powder, there is no difference between mass or volume, and number-based
particle size data.
For this study, mass and volume bases are used interchangeably.
This is true only for powders that do not change density with particle
size [88REE]. In most cases, this is not strictly true (i.e. see Figure
4.9), but the error of said approximation is usually relatively small.
Consequently, mass and volume basis are generally used interchangeably
when discussing particle sizing data [88REE].
Since particle sizing data depends upon the basis used, it is
important to present said data using the same basis for all the powders
investigated. The polystyrene latex particle size data were presented
using a number basis, while the techniques utilized to characterize the
ceramic powders use a mass basis. In order to provide a legitimate
comparison between the two classes of powders, the particle sizing data
of the latexes used to produce controlled porosity in this study are
illustrated in Figures 4.19 to 4.22 below. The top portion of each of
these graphs illustrates the effect of mass versus number basis, and,
for increased clarity, the bottom portion of each figure represents the
mass basis particle size distribution of each of the respective latexes.

10
00
90
80
70
60
50
40
30
20
10
0
00
90
80
70
60
50
40
30
20
10
0
310
Batch 07249001, Settled 11 times
Basis:
Number — — — — — — —
Mass
Number
Median
Size (//m):
9.00
8.96
Geometric
Standard
Deviation:
1.06
1.06
.0 14.0 13.0 12.0 11.0 10.0 9.0 8.0 7.0 6.0 5.0 4.0 3.0 2.0 1.0 0
Particle Diameter (//m)
.19 Illustration of the contrast and similarity between
mass and number-based particle size distributions for
the largest monosized latex (07249001) used in this
study

10
00
90
80
70
60
50
40
30
20
10
0
00
90
80
70
60
50
40
30
20
10
0
11
â– e 4
311
Batch 06199001-07 + 09, Settled 6 times
Basis:
Number — — — — — -
Mass
Number
Median
Size Omri):
4.64
4.61
Geometric
Standard
Deviation:
1.07
1.06
3.0
2.0 1.0 0
Particle Diameter (jym)
20 Illustration of the similarity and contrast of mass
versus number-based particle size distribution data
for the medium sized latex spheres (06199001-07+09)
used in this study

10
00
90
80
70
60
50
40
30
20
10
0
00
90
80
70
60
50
40
30
20
10
0
1
re 4
312
Batch 07269001, Settled 12 times
Particle Diameter (/ym)
21 Illustration of the similarity and contrast between
mass and number-based particle size distributions of
the smallest sized latex powder (07269001) used in
this study

10 -
00
90
80 •
70
60 â– 
50
40 â– 
30
20
10
0
00
90
80
70
60
50
40
30
20
10
0
1
:e 4
Batch 05169101, Polysized
313
62.8% @ 9.0 //m
L
Basis:
Number
Mass
Number
Median
Size (//m):
8.93
3.31
Geometric
Standard
Deviation:
1.06
1.60
.0 9.0 8.0 7.0 6.0 5.0 4.0 3.0 2.0 1.0 0
Particle Diameter (//m)
The contrast between mass and number-based particle
size data for the quadramodal latex (05169101) used,
vertical bars illustrate target composition for
maximization of PE (as outlined in Chapter 3)

314
Figure 4.19 illustrates this affect for the largest monosized batch,
while Figure 4.20 shows this affect for the midsized latex powder.
Figure 4.21 illustrates the number versus mass-based size distributions
for the smallest (bimodal) sized latex powder, and Figure 4.22 shows
this effect for the guadramodal latex powder. Figure 4.22 also shows
the target amounts of each size mode of the quadramodal latex powder, as
calculated to maximize packing efficiency (PE), as outlined in Table
3.3, (shown as vertical lines, in the bottom portion of the figure).
It is interesting to note that the shift in particle size depends
upon the size distribution. In the extreme case (i.e. the quadramodal
latex distribution), the median size increases almost three-fold when
the sizing basis is changed from number-based to mass-based.
Conversely, the two distributions most closely modelling true
monodispersity (Figures 4.19 to 4.20) change very little with a change
in sizing basis.
The vertical bars in Figure 4.22 may be used to compare the
measured particle size distribution with the target size distribution
predicted for maximal PE. The mass (or volume) percentage of each mode
quite closely matches the target amounts calculated in Chapter 3.
However, as mentioned above, the median sizes of the two intermediate
modes do not closely match the measured median size of the latexes that
were used to make the quadramodal mixture. Thus, the technique used to
measure the particle size distribution of the quadramodal powder was not
biased as far as the relative portions of each size mode, but was biased
with respect to measured size. This is quite enigmatic, and the above
explanation for the difference between the measured versus predicted
size distribution (i.e. hidden spheres) does not sufficiently explain
this occurrence. Thus, there must have been biasing in the sizing
technique that did not affect relative fractions of each size, but did
affect the median size of each of the intermediate modes.

315
4.1,3.2 Ceramic Powders
The particle size distributions of the three ceramic powders used
in this study (i.e. the as-received BS glass, the BS glass, ball milled
in MeOH, and the as-received Si3N4 powder) were measured using two
separate techniques, x-ray sedigraph and centrifugal particle size
analysis (CPSA), as described in section 3.3.4. The sedigraph technique
gives data on a mass-basis, while the data obtained using the CPSA
technique are area-based.
Figure 4.23 illustrates the particle sizing data for the as-
received BS glass, while Figure 4.24 illustrates the sizing data for the
ball milled BS glass powder. Similarly, Figure 4.25 illustrates the
particle sizing data for the as-received Si3N4 powder.
As shown in Figures 4.23 to 4.25, the sedigraph and CPSA data are
in good agreement. However, it is interesting to note that, in both of
the BS glasses, the CPSA data are skewed toward slightly larger sizes,
while the CPSA data for the as-received Si3N4 powder are skewed (after a
crossover) to slightly smaller particle sizes. It is not known whether
this is an effect traceable to the difference in the methods used, or
the actual apparatus used, or to the relative dispersedness of the
powders in the dispersion medium. It is also possible that this is due
to the slight increase in density with respect to reduction in particle
size discussed in section 4.1.2 above.
However, it is also possible that Si3N4 agglomeration, or poor
dispersion of the Si3N4 powder, or both are influential in this effect as
well, since the dispersions used in CPSA were more dilute than those
used in sedigraph, thus improving the dispersion condition (all other
things being equal). Furthermore, both the BS glass powders behaved
similarly. Finally, it may be that this effect is just a result of the
different bases used to measure the particle size distribution.
However, the latter hypothesis does not explain why the BS glass powders
did not exhibit this effect while the Si3N4 powders did.

10
00
90
80
70
60
50
40
30
20
10
0
18
16
14
12
10
8
6
4
2
0
(
are
316
Equivalent Spherical Diameter (^m)
•23 Illustration of the particle sizing data (both
sedigraph and CPSA) for the as-received BS glass
powder

Mass Percent at Size
317
Equivalent Spherical Diameter (//m)
Figure 4.24
Illustration of the particle sizing data (both
sedigraph and CPSA) for the ball milled BS glass
powder used in this study

10
00 •
90 •
80
70
60
50
40
30
20
10
0-
18
16
14
12
10
8
6
4
2
0
1
318
CPSA
Sedigraph
Designation
Median Size
1.05 pm
1.23 pm
Geometric
Standard
Deviation
1.47
1.36
CPSA
Sedigraph
Designation
■i ’"'"i’
r—-Jrti ImOTV
.0 9.0 8.0 7.0 6.0 5.0 4.0 3.0 2.0
Equivalent Spherical Diameter (pm)
1.0 0.0
•25 Illustration of the particle sizing data (both
sedigraph and CPSA) for the as-received Si3N4 powder
used in this study

319
A measure of maximal packing efficiency for a continuous size
distribution powder may be made through an extension of discrete sphere
packing, as outlined in section 2.3. The Andreasen model was the first
to predict powder size distributions that would result in maximal PE
[30AND,88REE]. Later, Funk and Dinger extended the Andreasen model
[88FUN], and recently Zheng, et al. proposed the most evolved
extrapolation of the model [90ZHE], which showed that the Andreasen and
Funk and Dinger models are simplified extrapolations of the Furnas model
to continuous particle size distributions.
A conclusion, common to all of these models is that a log normal,
or nearly log normal (in the Funk and Dinger and Zheng, et al. models)
particle size distribution, having a slope between 0.33 and 0.5, gives
the greatest packing efficiency [30AND,88REE,90ZHE]. The Andreasen
equation indicates that optimal particle size distributions (from a
particle packing viewpoint) will be linear, having a slope between 0.33
and 0.5, when plotted in a log-log manner. Consequently, it is
important to determine the slope of the log-log particle size
distribution in order to compare it to the ideals set by the above-
mentioned models (i.e. slopes between 0.33 and 0.5).
Figures 4.26 to 4.28 illustrate the log-log distributions of the
as-received BS glass, the ball milled BS glass, and the as-received Si3N4
powder respectively. Each figure also illustrates the Andreasen
distributions (with slopes of 0.33 and 0.5), based upon the maximum and
minimum measured particle sizes of the respective powders.
While none of the powders are linear when plotted in a log-log
manner, there is a definite trend in their respective log-log particle
size distributions. The as-received BS glass powder is the most linear,
while the ball milled BS glass is the next closest to linear. The as-
received Si3N4 powder is the least linear of the powders characterized in
this manner. Furthermore, the as-received BS glass most closely fits
the Andreasen targets (i.e. log normal, with a slope of between 0.33 and

CMPF
320
Corning 7070 As-Received Borosilicate Glass Powder
Equivalent Spherical Diameter (//m)
Figure 4.26 Log-log plot of the as-received BS glass particle
sizing data, also showing respective Andreasen
distributions, having slopes of 0.33 and 0.50

CMPF
321
Corning 7070 Ball Milled Borosilicate Glass Powder
Figure 4.27
Log-log illustration of the ball milled BS glass
powder sizing data, including the respective Andreasen
plots having slopes of 0.33 and 0.50

CMPF
322
UBE SNE03 As-Received Silicon Nitride Powder
Figure 4.28
Log-log illustration of the as-received Si3N4 powder
size distribution, including respective Andreasen
distributions of slope 0.33 and 0.50

323
0.5), while the ball milled BS glass is second closest, and the Si3N4 is
third. Thus, the as-received BS glass powder should exhibit the highest
PE, while the ball milled BS glass should give an intermediate PE, and
the lowest PE should be exhibited by the as-received Si3N4 powder (all
other things being equal).
It should be noted that all of these powders should pack more
efficiently than perfectly monodisperse, irregularly shaped powders, if
they are well dispersed during packing.
4.1.4 Powder Surface Area
Specific surface area of both the BS glass powders, the Si3N4
powder and the 4.6 pm UPLM powder was measured, as outlined in section
3.3.5, using either an automated or a manual technique (or both). The
results of said measurements are illustrated in Table 4.2. Table 4.2
also includes estimated surface areas calculated from the various
particle size measurement techniques (i.e. CPSA, Sedigraph and manual
SEM) utilized in this study. Where applicable (i.e. for the two BS
glass powders), the automated and manual surface area analysis
techniques agree with each other within experimental variation.
The calculated value for the specific surface area of the 4.6 pm
UPLM powder is in reasonable agreement with its respective measured
surface area. It is logical that the calculated surface area of the 4.6
pm UPLM powder is closest to the respective measured value, of the
powders investigated, since the UPLM powder is almost perfectly
monosized and spherical. Also, the SEM pictures showed the UPLM
surfaces to be smooth. Therefore, the surface area of said powder
should be estimated most accurately (and most simply) of the powders
studied. Furthermore, the agreement of the measured and calculated
surface areas further proves that the latex powders are high surface
smoothness materials.

324
Table 4.2
Measured and Calculated Specific Surface Areas
of the Powders Used in This Study
Powder
Specific Surface Area (m:/g)
Measured
Calculated
Manual
#
Reps
Automated
#
Reps
CPSA
Sedi-
graph
SEM
BS
Glass
(As-
Rec. )
3.39+0.04
2
3.36+0.04
2
0.97
1.55
BS
Glass
(Ball
Milled)
13.05+0.41
3
12.69+0.52
2
1.87
3.44
SijN4
Powder
(As-
Rec. )
2.82+0.06
3
1.96
1.58
4.6 pm
UPLM
1.05+0.04
3
1.23
Note: # Reps is the number of experimental repetitions used to
obtain the measured specific surface area value

325
The estimated surface areas of the three ceramic powders,
calculated by both CPSA and Sedigraph, do not agree well with the
measured surface areas of said powders. Furthermore, the two calculated
surface areas of each respective ceramic powder do not agree well with
each other. The specific surface areas estimated by CPSA show an
increase in calculated surface area with decreasing median particle
size. The Sedigraph estimates also predict that the surface area will
increase with decreasing median particle size, for the BS glass powders.
However, the Sedigraph calculated specific surface area estimate of the
Si3N4 powder is less than that estimated for the larger median particle
size ball milled BS glass. In fact, the specific surface areas of the
as-received BS glass powder and the as-received Si3N4 powder, as
calculated by Sedigraph, are quite similar. The only possible
explanation for this phenomenon is that the as-received BS glass powder
has a much broader particle size distribution than the Si3N4 powder.
Since small particles contribute to surface area to a much greater
degree than large particles, it is logical that a broad size
distribution powder could have a surface area comparable to, or larger
than, a relatively narrow size distribution powder having a smaller
median size. It is interesting to note that this phenomenon is evident
when comparing the measured surface areas of the two as-received ceramic
powders. The respective measured surface areas of the two powders are
quite similar. Thus, the trend in the Sedigraph calculated values is
not unrealistic. However, the Sedigraph estimated surface area values
for the two as-received ceramic powders are off by approximately a
factor of two.
The calculated surface areas for the ball milled BS glass powder
disagree with the respective measured values by a factor of between 4
and 7, depending upon the surface area estimation technique of
comparison. A possible reason for the relatively large difference
between estimated and measured specific surface area is that the BS

326
glass may experience significant surface dissolution or reaction during
ball milling in MeOH (e.g. micropore formation at the powder surface),
or that some glass may dissolve during milling, and later may reattach
to the powder surface, as high surface area precipitates, during the
drying step subsequent to ball milling. The effect of ball milling on
the BS glass is discussed in the next section.
4.1.5 The Effect of Ball Milling on BS Glass
As mentioned in section 4.1.4, the measured surface area of the BS
glass powder increased by a factor of approximately 3.8 as a result of
ball milling in MeOH, while the increase in calculated surface area was
only approximately a factor of 2.1. It was also noted that this
difference may be a result of an increasing portion of ultrafine powder
resulting form milling. This is not obvious when comparing Figures 4.1
and 4.2, however. Furthermore, there are other possibilities that can
explain the unexpectedly large increase in surface area subsequent to
ball milling, such as surface corrosion (MeOH has a strong tendency to
dissolve B,03), differential dissolution, or dissolution and
precipitation, etc. Therefore, further investigation of the ball
milling process was warranted.
Selected area diffraction (SAD), during transmission electron
microscopy (TEM) investigation, indicated that there were no
precipitated crystallites on any of the powder particles viewed (i.e.
all SAD patterns were diffuse, indicating the powders to have an
amorphous atomic structure). Thus, dissolution and precipitation of
high surface area crystalline compounds as a source for the extra
increase in surface area is not likely. Furthermore, the powder
surfaces, as viewed during TEM investigation, appeared to be free of
precipitates.
However, the surfaces of the ball milled BS glass powder particles
appeared to be somewhat rougher than the those of the as-received BS

327
glass powder particles. Representative TEM micrographs of the particle
surfaces of an as-received BS glass powder and of a ball milled BS glass
powder are illustrated in Figure 4.29 and 4.30 respectively. The
surface of the ball milled glass powders appears to have a structure on
the order of about 4 to 14 nm (i.e. 2.5 to 10 mm on Figure 4.30), that
is not as apparent when viewing the as-received powder. This "pitting"
may be resultant from B;03 corrosion.
Inductively coupled plasma photospectroscopy (ICP) analysis
indicated that the relative concentration of SiO: increases with milling
(and/or MeOH exposure), as compared to the B,03 concentration of the BS
glass. This effect is shown in Table 4.3. The table also indicates
that there is a gradual decrease in both [Li] and [Na] during milling
and/or MeOH exposure. As discussed in chapter 3, it was not possible to
measure [K].
Table 4.3 also indicates that there is little difference between
the composition of the MeOH treated and the ball milled BS glass, with
the exception that the ball milled BS glass is significantly increased
in A1 concentration. Said increase in Al is a result of using alumina-
rich milling media. Thus, it may be concluded that most of the change
in concentration of the BS glass, during milling (except for the
increase in [Al]), is due to MeOH interaction, and that mechanical
milling does not significantly increase this effect, other than to
create new surfaces for MeOH interaction (assuming that the temperature
during milling was the same as during the MeOH treatment (i.e. 40°C) ) .
It is also interesting to note that the composition of the BS
glass changed from the bulk glass to the as-received <325 mesh powder.
It is not known how the manufacturer milled the BS glass from the bulk
to the powdered form. Furthermore, it is interesting that the measured
composition of the bulk glass was not necessarily any closer to the
manufacturer's data than the measured compositions of the powdered
glasses. The as-received glass powder was closest to the Air Force

328
Figure 4.29 TEM micrograph illustrating a representative surface
of a particle of as-received BS glass (Scale: 1 mm =
1.4 nm)

329
Figure 4.30 TEM micrograph illustrating the surface of a
representative particle of ball milled BS glass
(Scale: 1 mm = 1.4 nm)

330
Table 4.3
ICP Measured Composition of BS Glasses Investigated
1. Bulk Borosilicate Glass
Constituent
Measured ICP
Composition
Composition (Oxide)
Element
Oxide
PPM
(pg/ml)
St. Dev.1
(±pg/mi)
Measured2
(Wt%)
Literature3
(Wt%)
Si
SiO:
414.70
3.78
68.5 + 0.6
72.0
(70.0)
B
B;03
116.70
0.82
29.0 + 0.2
25.0
(28.0)
Al
ai2o3
2.42
0.04
0.4 + 0.0
1.0
(1.1)
Li
Li:0
6.03
0.22
1.0 + 0.0
0.5
(1.2)
Na
Na.O
1.42
0.12
0.2 + 0.0
0.5
(0.0)
K
K:0
N/A
N/A
N/A
1.0
(0.5)
2. As-Received Borosilicate Glass Powder
Constituent
Measured ICP
Composition
Composition (Oxide)
Element
Oxide
PPM
(pg/ml)
St. Dev.1
(+pg/ml)
Measured2
(Wt%)
Literature3
(Wt%)
Si
SiO:
467.20
8.50
70.6 ± 1.3
72.0
(70.0)
B
B;Oj
119.00
1.55
27.1 + 0.4
25.0
(28.0)
Al
Al;°3
2.90
0.00
0.4 + 0.0
1.0
(1.1)
Li
Li20
5.10
0.30
o
CD
1 +
O
h-*
0.5
(1.2)
Na
Na;0
1.93
0.18
0.2 + 0.0
0.5
(0.0)
K
K:0
N/A
N/A
N/A
1.0
(0.5)

331
Table 4.3 (continued)
3. MeOH Treated Borosilicate Glass
Constituent
Measured ICP
Composition
Composition (Oxide)
Element
Oxide
PPM
(/jg/ml)
St. Dev.1
(+^g/ml)
Measured1
(Wt%)
Literature3
(Wt% )
Si
SiO;
575.20
9.75
73.8 + 1.2
72.0
(70.0)
B
BA
125.30
1.37
24.2 + 0.3
25.0
(28.0)
A1
ai,o3
2.77
0.05
0.3 + 0.0
1.0
(1.1)
Li
Li.O
4.95
0.21
0.6 + 0.0
0.5
(1.2)
Na
Na;0
1.28
0.38
0.1 + 0.0
0.5
(0.0)
K
K:0
N/A
N/A
N/A
1.0
(0.5)
4. MeOH Ball Milled Borosilicate Glass
Constituent
Measured ICP
Composition
Composition (Oxide)
Element
Oxide
PPM
(pg/ml)
St. Dev.1
(±pg/mi)
Measured3
(Wt%)
Literature3
(Wt%)
Si
SiO;
611.80
7.31
73.7 + 0.9
72.0 (70.0)
B
b:°3
129.70
1.37
23.5 + 0.3
25.0 (28.0)
A1
ai2o3
10.47
0.05
1.1 + 0.0
1.0 (1.1)
Li
Li20
5.28
0.26
0.7 + 0.0
0.5 (1.2)
Na
Na;0
1.32
0.57
0.1 + 0.1
0.5 (0.0)
K
K20
N/A
N/A
N/A
1.0 (0.5)
Notes: 1. The standard deviation of each ICP PPM value is
based upon 6 measurements.
2. Measured oxide composition includes a correction
for K:0, + values indicate plus or minus one
standard deviation.
3. Literature values outside of parentheses are
those from Corning Incorporated [79COR,88COR],
while those in parentheses are those provided by
the Air Force Materials Laboratories (prepared
by the Electronic Properties Information Center,
Hughes Aircraft Company, Culver City, CA) . Note
that the parenthetical values sum to 100.8 wt%.

332
Materials Laboratory compositional data, while the two MeOH exposed
glasses were closest to the manufacturer's data.
Reflection mode Fourier transform infrared spectroscopy (FTIR) was
also used to investigate the powder surface of the various BS glasses,
as outlined in section 3.3.6. The respective FTIR reflection spectra of
each of the BS glasses are illustrated in Figure 4.31. The spectral
peaks at 1150 and 1096 cm"1 are resultant from Si-O-B and Si-O-Si
stretching peaks (they are actually one peak, but due to the Restrahlen
effect, they are recorded as a doublet) on the surface or near-surface
of the glass powder. The shoulders centered about 1004 cm'1 are a result
of silicon-non-bridging oxygens. The spectral peaks at 859 cm"1 are a
due to the Si—0--Si bending mode, the peaks at 767 cm"1 are resultant
from an Si—O—Si tetrahedron response, the peaks at 650 cm"1 are also
due to a vibration of SiO:, and the spectral peaks at 453 cm'1 result
from rocking of Si—O—Si bonds [85LEE1).
Normally (in bulk material analysis) the stretching peak shifts to
lower wavenumber [79HEN]. However, since the IR radiation penetrates
approximately 0.5 ijm into the sample [79HEN], it is expected that the IR
radiation would penetrate into the "bulk” of the powder particles.
Thus, in the BS glass powder, it would be expected that the stretching
peak would remain stationary (possibly shrinking in intensity somewhat)
while the non-bridging oxygen peak would develop. Therefore, the
relative ratio of the non-bridging to the stretching peak should be a
measure of corrosion on the powder particle surfaces. Figure 4.31
illustrates the ratio of the 1004 peak height divided by the 1160/1096
peak height for each of the respective BS glasses. It is evident from
Figure 4.31 that, while there is little difference between the spectra
of any of the glasses, there is a definite increase in the
number of non-bridging oxygens as a result of MeOH interaction and/or
mechanical milling. The peaks occurring at 1004 cm'1 increase steadily
from bulk to as-received powder, to the MeOH interacted powders.

Reflectance (%)
Powder
Peak Height Ratio
MeOH Treated
0.631
Ball Milled
0.670
As-Received
0.554
Bulk
0.468
Note: Ordinate values do not reflect spectra offsets.
Peak height ratio = B/A (corrected for offset).
Figure 4.31
FTIR reflection spectra of the BS glasses investigated
in the ball milling study

334
Furthermore, the difference between the non-bridging oxygen peaks
of the two MeOH interacted powders is substantial, (i.e. the B/A ratio
of the ball milled glass is significantly greater than that of the MeOH
treated glass) indicating that non-bridging oxygens occur as a result of
both mechanical milling and of MeOH interaction.
This hypothesis is also supported by BET surface area analysis
data. Figure 4.32 shows the relatively dramatic increase in surface
area during milling. Figure 4.32 also indicates that the surface area
approximately doubles after 10 days of stirring in MeOH at room
temperature (as outlined in section 3.3.6). Furthermore, the figure
also illustrates the effect of shaking in MeOH for 20 h, at 40°C. The
surface area of the BS glass, treated in this manner, also approximately
doubles, in spite of the significantly shorter stirring time, as well as
using a non-interactive shaking mechanism. Thus, it may be concluded
that the temperature at which the MeOH exposure occurs is quite a
significant factor.
Figure 4.33 illustrates the multipoint isothermal gas desorption
relationships for the as-received BS glass powder, the MeOH-treated
powder and the ball milled BS glass powder. From Figure 4.33 it is
evident that both the MeOH-treated and the MeOH ball milled BS glasses
exhibit a significant desorption peak at a pore diameter of
approximately 4 nm, while the as-received BS glass powder did not. This
behavior was exhibited only during desorption and not during adsorption.
Furthermore, the peak is significantly larger in the ball milled BS
glass powder, indicating that the exposure of fresh surfaces augments
the MeOH-BS glass interaction. It is interesting to note that the pore
size of the desorption peaks is on the order of the surface roughness of
the ball milled BS glass, as viewed by TEM (see Figure 4.30).
Thus, it may concluded that milling in MeOH did affect both the
surface area and the composition of the BS glass used. However, this
effect did not significantly alter the properties of the BS glass (i.e.

335
Figure 4.32
Illustration of the effect of MeOH exposure on BS
glass surface area

336
35
S
e
-if
o
o
30
25
S 20
j3
O
>
J-h
O
0.
o
IS
O
Oh
m
15
10
0
1 10 100
Pore Diameter (nm)
Í i i i i 11
1000
Figure 4.33
Multipoint desorption isotherm of the as-received BS
glass powder, the MeOH treated BS glass powder, and
the ball milled BS glass powder

337
dielectric constant and loss, etc.) for the purposes of this study, as
will be seen in subsequent sections. It is assumed, however, that the
exposure to MeOH during ball milling effectively increased the surface
area of the BS glass powder by a factor of approximately 2. It is not
known whether the change in measured density subsequent to ball milling
is a result of compositional change during MeOH exposure, or to the
effect of decreased particle size as indicated in section 4.1.2, since
this increase in density is quite small and could be accounted for by
either or both effects. It should be noted that centrifugal particle
size analysis (CPSA) indicated no discernable change in particle size
between the as-received BS glass powder and the powder shaken in MeOH
for 20 h at 40°C. Therefore, the size of the powder is not
significantly effected by the above-described corrosion process.
However, the surfaces of the powder particles are affected measurably.
4.2 Suspension and Green/Pvrolvzed Structure Characterization
4.2.1 Suspension Characterization
Rheometry was utilized to characterize the shear stress versus
shear flow rate behavior as well as the viscosity of suspensions
utilized in this study, as described in section 3.4.2.2.2. All data
illustrated in the following figures were taken during increasing shear
rate. Rheometry was utilized to investigate the effect of solids
loading upon the rheological properties of said suspensions.
Unfortunately, it was not possible to obtain shear stress data at
shear rates near zero, due to the noise of the data. Therefore, it is
not possible to comment of the yield behavior of these suspensions.
The effects of increased solids loading upon the viscosity and the
shear stress of pure suspensions of ball milled BS glass powder, Si3N4
powder, and UPLM powder in EtOH are illustrated in Figures 4.34 through
4.36 respectively.
As shown in Figure 4.34 the ball milled BS glass is nearly
Newtonian at solids loadings of 20 and 30 V%, while it is slightly shear

Shear Stress (Pa) Viscosity (mPa-s)
338
Figure 4.34
Viscosity and shear stress as functions of shear rate
and solids loading of suspensions of pure ball milled
BS glass powder in EtOH

Shear Stress (Pa) Viscosity (mPa-s)
339
Figure 4.35
Viscosity and shear stress as functions of shear rate
and solids loading of suspensions of pure Si3N4 powder
in EtOH

Shear Stress (Pa) Viscosity (mPa-s)
340
Viscosity and shear stress as functions of shear rate
and solids loading of suspensions of pure UPLM powder
in EtOH
Figure 4.36

341
thickening (dilatant) at a solids loading of 52 V%. Figure 4.35
indicates that the 20 and 30 V% solids loading, pure Si3N4 suspensions in
EtOH, are also nearly perfectly Newtonian. However, the 46 V% solids
loading suspension of Si3N4 powder in EtOH is slightly shear thinning
(pseudoplastic). It should be noted that it was not possible to load
the Si3N4 suspension significantly beyond 46 V% solids loading and, thus,
the Si3N4 powder did not flow as efficiently in EtOH suspension as the
other constituent powders did.
Figure 4.36 indicates that the suspensions of UPLM in EtOH are
nearly perfectly Newtonian at all solids concentrations investigated.
This is contradictory to other studies performed upon latex suspensions
(both aqueous and nonaqueous) [70PAP,70WOO,72KRI]. This discrepancy may
be due to the limited range of shear rates investigated in this study.
For example, the data of Woods and Krieger indicate a near Newtonian,
behavior in the shear rate range of approximately 10 to 300 s'1 [70WOO].
Furthermore, none of the previously mentioned studies investigated latex
suspensions in EtOH. Thus, the character of the dispersions studied
could be somewhat different than those investigated by others. There
are other differences between the above-mentioned studies and this one
as well, such as synthesis techniques, etc. Also, these data are not
normalized to the rheological character of the solvent-dispersant
solution. Therefore, there may be effects of unadsorbed dispersant,
etc. Finally, as mentioned above, the scale of viscosity used in this
study is approximately two orders of magnitude coarser than the scales
used in the studies [70WOO,70PAP].
Upon decreasing shear rate, a shear stress hysteresis was
indicated in almost all of the high solids loading (i.e. >46 V% solids)
suspensions investigated. Initially, this may appear to be an indicator
of rheopexy (i.e. a hysteretic dilation of a suspension upon dynamic
shear rate cycling [81SCH]). However, upon further cycling, the shear
stress continued to increase, indicating that the increase in resistance

342
to shear is a result of solvent evaporation and not of the highly rare
condition of rheopexy [81SCH].
Figure 4.37 illustrates the viscosity and shear stress of
suspensions of as-received and ball milled BS glasses in EtOH. It is
evident from Figure 4.37 that the BS glass does not flow as efficiently
(i.e. exhibits greater shear stress and is dilatant) as the as-received
BS glass in suspension. The as-received BS glass suspension is more
nearly Newtonian than the ball milled BS glass suspension. This is most
likely a result of the narrower particle size distribution of the ball
milled BS glass.
Figure 4.38 illustrates the effect of volume percent latex
addition upon the viscosity of co-dispersions of ball milled BS glass
and Si3N4 powders at shear rates of 100 and 300 s'1. The figure indicates
that the viscosity decreases slightly as the volume percent UPLM is
increased up to approximately 10 V% UPLM, then increases with increasing
V% UPLM up to 20 V% UPLM. Furthermore, in suspensions of pure ball
milled BS glass with UPLM, the suspension viscosity traverses another
minimum from 15 to 30 V% UPLM, and decreases again as UPLM concentration
increases toward 40 V%. These changes in viscosity do not correlate
well with the minor fluctuations in measured solids loading (also shown
in Figure 4.38). Thus, it may be concluded that said viscosity
fluctuations, with changing UPLM concentration, are real.
Figure 4.39 illustrates the effect of latex powder mean size and
size dispersity upon the viscosity of pure ball milled BS glass
suspensions having 15 V% latex additions. It is illustrated that,
within the confines of this study, the viscosity does not change greatly
with the different latexes used (the dotted lines are shown as an
indicator of relative relationships only). However, there apparently is
a gradual decrease in viscosity as latex size is increased (with both
monosized and polysized latexes). This relationship also does not
correlate with fluctuations in total solids loading.

Shear Stress (Pa) Viscosity (mPa-s)
343
Shear Rate (s’1)
Figure 4.37
Viscosity and shear stress of suspensions of as
received versus ball milled BS glass powders in EtOH

Viscosity (mPa-s)
344
350
100 s'1
300 s'1
—■ - 100-X/0/X
—♦— 100-X/0/X
—♦ - 80-0.8X/20-0.2X/X
—*- 80-0.8X/20-0.2X/X
—60-0.6X/40-0.4X/X
- 60-0.6X/40-0.4X/X
250
50 -
0 -Í 1 1 1 1 1 1 1
0 10 20 30 40
Volume Percent UPLM (X)
Note: First value denotes BS glass concentration, and
Second value denotes Silicon Nitride concentration
• • ■XtfewXvXvAV.;.;. •
Measured Solids Loading (%)
X
100-X/0/X
80-0.8X/20-0.2X/X
60-0.6X/40-0.4X/X
0
52.3
52.4
52.6
5
52.8
10
52.7
52.8
52.3
15
52.6
20
52.5
52.6
52.6
25
52.6
27.5
52.7
30
53.0
40
52.8
Figure 4.38
Viscosity as a function of volume percent UPLM
concentration of the various suspensions used in this
study

Viscosity (mPa-s)
345
•S' -v .•• •'
â– :-:-:>wKvXyXs>>:-XvXv::-XwX+:
• " ¡5 . .. - -v
Bimodal
Quadramodal
Monosized
4.6 fim
9.0 /j.m
Measured
Vol % SL
52.8
52.7
52.6
52.7
Figure 4.39
Viscosity of 85 V% ball milled BS glass, 15V% latex
suspensions as a function of latex size and size
dispersity

346
Figure 4.40 illustrates the effect of normalized V% Si3N4 upon the
viscosity of ball milled BS glass and UPLM suspensions, where normalized
V% (VnSN) follows the relation:
where:
V%
SN.
n
V%SN
y^BSglass
xlOO
V% bs glass t^e actual V% of BS glass (total
solids basis)
V%SN is the actual V% Si3N4 (total solids basis)
similar to the relations in Figure 4.38, the viscosity traverses a
minimum around 20 normalized V%. It is not known why this effect is
greatest for suspensions containing 10 V% UPLM, while the 0 and 20 V%
UPLM suspensions mirror each other closely (disregarding the actual
difference in viscosity). The minimum is not as apparent at shear rates
of 100 s'1 as it is at 300 s'1.
Again, the above relation does not correlate with the measured
variations in solids loadings and, thus, is also a real effect. It is
not known why these minima in viscosity occur. It may be that they may
truly exhibit more efficient flow behavior, or it may be a an effect of
comparing raw viscosities as opposed to relative viscosities, as
discussed above.
Furthermore, the viscosity of ball milled BS glass-Si3N4
suspensions increases greatly from 60 to 100 V% Si3N4 concentration, and
the BS glass-Si3N4 suspensions become pseudoplastic above a Si3N4
concentration of approximately 80 V%. Again, this real effect does not
correlate with the minor variations in measured solids loadings.
It should be noted that the above suspensions were formulated for
this study, upon the basis of minimization of segregation, while
attempting to maximize homogenization. These suspensions were not
formulated for use in tape casting, or to be utilized as thick film
dielectric inks. This was done in order to minimize the complexity of

Viscosity (mPa-s)
347
Measured Solids Loading (%)
X
0 Vol % UPLM
10 Vol % UPLM
20 Vol % UPLM
0
52.3
52.7
52.5
10
52.8
52.6
20
52.4
52.8
52.6
40
52.6
52.3
60
46.2
80
46.1
100
45.7
Figure 4.40
Effect of normalized volume percent concentration of
Si3N4 upon the viscosity of suspensions characterized
in this study

348
this system with respect to the number of organic suspension components,
as well as to minimize the volume fraction of non-volatile organics.
In tape casting slurries, it is desirable that the suspension be
pseudoplastic in the shear rate range of approximately 15 to 80 s'1, and
have a viscosity between 1000 and 5000 mPa-s throughout said shear rate
range [88REE,90MIS]. It is evident, from the above rheology data, that
all of the suspensions produced for this study exhibit viscosity values
well below 1000 mPa-s in the shear rate range of 15-80 S'1. Furthermore,
all the suspensions used in this study were either nearly Newtonian or
slightly shear thickening (i.e. dilatant) within the above-mentioned
range of shear rates. Therefore, the suspension systems investigated in
this study would require modification before they could be
satisfactorily utilized in either tape casting or thick film processing.
However, it is very encouraging that the viscosities of the suspensions,
prepared for this study, were below the 1000 to 5000 mPa-s range, and
that the rheological properties, by and large, were nearly Newtonian in
the shear rate range of 15 to 80 s'1, since the viscosity properties of
tape suspensions are largely determined by the binder/plasticizer system
used [88REE,90MIS]. It is further encouraging that said suspension
system could be loaded to (and somewhat in excess of) 52 V% non-volatile
solids. The ability to pack a suspension at this great a solids loading
indicates that the suspension is relatively well dispersed.
Furthermore, highly loaded suspensions create dried tapes
that experience relatively low drying shrinkages, thereby minimizing the
stresses and defects that occur during drying.
Preliminary investigations also indicated that all of the powder
precursors disperse quite well in basic (i.e. pH > 9) aqueous media,
thereby promoting the possibility of creating satisfactory tapes from
aqueous suspensions. This is very important since aqueous systems are
currently favored (and will be even more so in the future) due to
environmental concerns and regulations [90NAH].

349
4.2.3 Green/Pvrolvzed Structure Characterization
4.2.3.1 Overview
Green and pyrolized compact structures were characterized using
both SEM and Hg porosimetry as discussed in sections 3.4.5.1 and
3.4.5.2. The first subsequent subsection (4.2.2.2) covers the green
structure of pure latex compacts, in order to investigate the packing
characteristics of said powders. The second subsequent sub-section
(4.2.2.3) discusses the general characteristics of green and post
pyrolized composite compacts, in order to investigate pore percolation,
as well as the general packing characteristics and pore structures
exhibited by the various compositions in the composite system as a
whole. The third and final subsequent sub-section (4.2.2.4) discusses
the effects of two processing parameters (i.e. sonication dispersion and
suspension aging) upon the rheological and compact characteristics of
representative composites investigated in this study. It is important
to note that, with the exception of pure BS glass compacts, all
composites investigated contained ball milled BS glass.
4.2.3.2 Structural Characteristics of Polystyrene Latex Compacts
Figures 4.41 to 4.44 illustrate the representative surfaces of as-
cast compacts of the smallest (2.4 pm, bimodal, 07269001), medium sized
(4.6 pm, monomodal, 06199001-07+09), largest (9.0 pm, monomodal,
07249001) and polysized (4.0 pm, quadramodal, 05169101) latexes used in
this study. It is interesting to note that none of the compact surfaces
appear to have ordered packing. This is expected in this type of
system. Furthermore, no ordered packing defects are evident in any of
the micrographs. Similar behavior has been exhibited in slip cast
compacts of monospherical silica [90VOR].
The packing efficiencies (green densities), as determined using Hg
porosimetry (as outlined in section 3.4.5.2), of each of the slip cast

350
Figure 4.41
SEM micrograph of a representative
cast compact of the smallest latex
07269001) used in this study
surface of a slip
(2.4 pm, bimodal,

351
SEM micrograph illustrating a representative surface
of a slip cast compact of the medium sized latex (4.6
pm, monosized, 06199001-07+09) used in this study
Figure 4.42

352
SEM micrograph illustrating a representative surface
of a slip cast compact of the largest latex (9.0 pm,
monosized, 07249001) used in this study
Figure 4.43

353
SEM micrograph illustrating a representative surface
of a slip cast compact of the polysized latex (4.0 ^m
(arithmetic mean), quadramodal, 05169101) used in this
study
Figure 4.44

354
latexes are illustrated in Figure 4.45. It is evident that all of the
monosized spheres packed to green densities between 61 and 63 % of
theoretical density. This is in agreement with other investigations
involving random close packing (RCP) of monosized spheres [3OWES,60SCO,
61MCG,88REE]. From these density data, it may be concluded that the
containers (i.e. the slip casting mold rings) did not affect the
measured PEs significantly. This is logical since the slip casting
rings were over 3000 times larger in diameter that the largest size
latex investigated. According to Figure 2.6, this container diameter to
sphere diameter ratio should have little or no impact upon PE.
Figure 4.45 also indicates that the green density of slip cast
UPLM compacts deviates slightly with changing latex sphere diameter.
This is most likely an effect of deviations from monomodality rather
than an effect of container-to-sphere-size ratio, since the size
distributions of the 4.6, 6.1, 6.8 and 9.0 pm diameter UPLMs get
progressive narrower (with the exception of the 9.0 pm UPLM, see Figures
4.13 to 4.16) should result in higher green densities, all other factors
remaining equal). This effect is also responsible for the increase in
green density with respect to increasing particle size modality. The
bimodal compacts exhibited increased PEs as compared to the monomodal
compacts, while the quadramodal compacts exhibited the greatest PE of
all. Furthermore, Figure 4.45 indicates that the green density of the
bimodal slip cast latex compacts increases with decreasing particle
size. This is also resultant from increasing deviation from
monomodality (see Figures 4.10 to 4.12).
It should be noted that the green densities of the slip cast
bimodal and quadramodal latexes are less than 7 % greater than the green
density of the monomodal latexes. This nominal increase in green
density is due to the fact that the different modes of the respective
size distributions do not differ enough in size. As indicated in Figure
2.8, in order to obtain the maximum PE in a multimodal packing of

355
Slip Cast Latex Particles
Polystyrene Latex Mean (Arithmetic) Diameter (/ym)
Latex
Mean Diameter (pim)
Green Density
(% of Theoretical)
07269001
Bimodal
2.4
64.7
07309001
Bimodal
3.1
63.7
07199001
Bimodal
3.6
63.5
05169101
Quadramodal
4.0
67.9
06199001-07 +09
Monomodal
4.6
62.2
07219001
Monomodal
6.1
61.3
08029001
Monomodal
6.8
61.5
07249001
Monomodal
9.0
61.4
Figure 4.45
Green density (depicted as a percentage of theoretical
density) as a function of mean sphere diameter of slip
cast latex compacts

356
spheres, it is necessary that the diameter ratio of successively smaller
size modes (i.e. DUree over D,^) be at least 7 and preferably greater
than 10 [61MCG,80PAT]. In this study, said size ratio is less than 2 in
all cases. Again, referring to Figure 2.8, said diameter ratio is
expected to increase green density only a few percent, at most (to a
maximum of approximately 65 % of theoretical density for a bimodal
mixture). As indicated in Figure 4.45 the increase in PE for the
quadramodal distribution latex is higher than for the bimodal sphere
distributions. This is expected as indicated by Table 2.4).
As shall be discussed below, this is a limitation to the
investigation of the effect of latex size distribution upon maximization
of closed porosity, in this study. However, this effect could not be
avoided, due to the maximum size limitation of included porosity, as
dictated by the maximum allowable surface flaw size as well as the
minimum size limitation of included porosity, as determined by the BS
glass powder size (as also shall be discussed below).
Figure 4.46 illustrates the relationship between latex mean
(arithmetic) particle diameter and median pore channel radius (using Hg
intrusion porosimetry). It is evident from Figure 4.46 that the median
pore channel radius increases linearly with increasing particle size.
Linear regression produced a fit with correlation of 0.9975, with an
intercept of 0.012 pm. This intercept value is quite close to 0.
It is interesting to note that the ratio of sphere diameter to
median pore channel diameter (D/MPCD), in the monomodal UPLM slip cast
compacts, was a quite reproducible 3.0 to 3.1. This is a smaller ratio
than would be expected in either square planar or triangular planar
packing. Furthermore, this ratio is about one half that offered by
McGeary [61MCG] and by Patankar and Mandal [80PAT], as the minimum ratio
to allow smaller size spheres to pack within a bed of larger sized
spheres (both used the model of triangular planar packing which gives a
size ratio of 6.5, see Figure 2.7). However, when the third dimension

Median Pore Channel Radius (Hg Intrusion (pm))
357
Slip Cast Latex Particles
Latex
Mean Diameter (pm)
Pore Channel Size
(Hg Intrusion, pm)
Mean Diameter
Radius
Diameter
Pore Channel Diameter
07269001
Bimodal
2.4
0.39
0.78
3.1
07309001
Bimodal
3.1
0.48
0.96
3.2
07199001
Bimodal
3.6
0.59
1.18
3.1
05169101
Quadramodal
4.0
0.74
1.48
2.7
06199001-07 +09
Monomodal
4.6
0.75
1.50
3.1
07219001
Monomodal
6.1
1.01
2.02
3.0
08029001
Monomodal
6.8
1.08
2.16
3.1
07249001
Monomodal
9.0
1.43
2.86
3.1
Volume basis median pore channel radius (using Hg
intrusion porosimetry) as a function of arithmetic
mean latex sphere diameter of slip cast polystyrene
latex compacts
Figure 4.46

358
of packing is considered, this value changes significantly. For
example, the ratio of sphere diameter to pore entry diameter (D/P) in
cubic and tetrahedral packing of monosized spheres is 1.96 and 4.55
respectively, while the ratio of sphere diameter to entry sphere
diameter (D/S) is 2.38 and 6.67 respectively for cubic and tetrahedral
packing [88REE]. These values are more realistic, since they involve
three dimensional packing. The D/P value should represent a lower limit
of validity for comparison with the ratio of sphere diameter to measured
pore channel diameter (D/MPCD), while the D/S value should provide upper
limits for comparison. Whether the D/P versus PE or the D/S versus PE
criterion is a better gauge of D/MPCD versus PE depends upon how the Hg
intrudes the pore channels. If the Hg deforms to fit the pore channel,
the D/P versus PE criterion is best. If the Hg remains circular in
cross-section, upon infiltrating the pore, the D/S versus PE criterion
is most correct.
The ratio of sphere diameter to pore channel diameter measured in
the slip cast UPLM compacts with respect to PE is within both of these
ranges. Figure 4.47 illustrates the relationship of pore channel size
versus PE for cubic and tetrahedral packing, using the two criteria
above. Figure 4.47 also shows the relationship of D/MPCD versus PE for
the slip cast UPLM compacts. From the figure, it is obvious that the
D/P versus PE criterion is most appropriate for comparison with D/MPCD
versus PE. The UPLM data lie almost perfectly upon the theoretical
interpolation between simple cubic and tetrahedral packing. This
indicates that the Hg does conform to fit the pore channel.
Furthermore, this relationship indicates that, even though the slip cast
UPLMs are arranged in a random (i.e. RCP) fashion, the pore channel size
may be accurately and reproducibly estimated using ordered packing
theory. This is an extremely beneficial conclusion, since ordered
systems may be characterized by exact mathematical models.

359
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8 -
7
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5 -
4 -
3 -
2 -
1 -
0
Key:
1
D/S
â– 
D/P
♦
Slip Cast UPLM Compact Data
Tetrahedral
â– I
Tetrahedral
Simple Cubic
Simple Cubic
i i
50 52 54 56 58 60 62 64 66 68 70 72 74 76
Packing Efficiency (%)
Figure 4.47
The relationship of D/S and D/P to PE for simple cubic
and tetrahedral packing, the ratio of sphere diameter
to pore channel diameter is also illustrated

360
It is also interesting to note that the bimodal compacts also fit
the linear regression fit depicted in Figure 4.46. Finally, the
quadramodal slip cast latex compact also fit the relationship
illustrated in Figure 4.46, although not as well as either the UPLM
compacts or the Bimodal latex compacts. It should be noted that the Hg
intrusion curve was smooth for each of the latexes, regardless of
modality, and the derivative curves showed only one peak. Therefore, it
may be concluded that all of the slip cast latexes had only one
distribution of pore channel sizes.
Unfortunately, it was not possible to investigate Hg intrusion-
extrusion hysteresis, since ambient pressure was reached before the
extrusion curve reached a median point (i.e. a change in concavity
during the extrusion process) in all of the latex compacts investigated.
4.2.3.3 Structural Characteristics of Green and Pvrolvzed Composites
An SEM micrograph of a representative green composite compact
surface is illustrated in Figure 4.38. All three of the particulate
constituents are apparent in this figure. The spherical particles are
latex, the cubic or hexagonal particles are Si3N4, and the angular or
non-symmetric particles are BS glass particles.
As predicted by both particle size/size distribution data and by
rheometry data, the as-received BS glass packed to higher green density
than the ball milled BS glass. The green/pyrolyzed density (as a
percentage of theoretical density and determined using Hg intrusion
porosimetry) of slip cast as-received BS glass compacts averaged 72.0 +
0.1 %, while the green/pyrolized density of the ball milled BS glass
compacts averaged 68.1 + 0.3 %. The median pore channel radius (MPCR,
volume basis, Hg intrusion) of the smaller particle size ball milled BS
glass compacts was less than half that of the MPCR of the larger
particle size as-received BS glass. Thus, it would be expected that the
ball milled BS glass compacts sinter at a greater rate than the as-

361
Micrograph of a representative surface of a green,
Si3N4 and UPLM filled, BS glass matrix composite
Figure 4.48

362
received BS glass powder compacts (all other factors remaining
constant), despite the initially greater green density of the slip cast,
as-received BS glass compacts.
In both categories of BS glass, there was a small (i.e. less than
0.5 %), but reproducible decrease in green density, as well as a
correspondingly small (i.e. less than 0.01 pm) increase in median pore
channel size, resulting from the process of organics pyrolyzation.
It was not possible to satisfactorily evaluate the Hg
intrusion/extrusion hysteresis of the slip cast as-received BS glass
compacts since the extrusion curves did not plateau to a stranded volume
at ambient pressure. The slip cast ball milled BS glass compacts
exhibited hysteresis behaviors that were not consistently reproducible
as a result of inconsistencies in both the shapes and the final stranded
volumes exhibited by the extrusion curves. However, the intrusion
curves were quite reproducible.
Both slip cast BS glasses exhibited skewed pore channel size
distributions. The distribution for the ball milled BS glass was much
sharper as well as skewed toward smaller pore channel radii, as compared
to the as-received BS glass. Figure 4.49 illustrates this effect.
In agreement with rheology data, the green density of slip cast
composites in this system decreases with increasing Si3N4 concentration.
Figure 4.50 indicates that green density decreases monotonously from
68.1 % of theoretical density (pure ball milled BS glass compacts) to
51.5 % (pure Si3N4 compacts). Figure 4.50 shows that this behavior is
common in composites containing 10, 15 and 20 V% Si,N4 as well. It is
interesting to note that the green densities of composites in this
system increase to approximately 71.5 % of theoretical with additions of
10, 15 and 20 V% of 4.6 pm UPLM, and remain consistently greater than
the green densities exhibited by the 0 V% UPLM system, throughout the
entire range of normalized Si3N4 concentrations investigated.

dV/dlogR (cc/g)
363
Pore Channel Radius (/xra)
Volume Basis, Hg-Intrusion Porosimetry
Figure 4.49 Pore channel radius distribution of slip cast as-
received and ball milled BS glass samples

364
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03
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20 40 60 80
Normalized Volume Percent Silicon Nitride
100
Figure 4.50
Green density (as a percent of theoretical density) of
green (organics present) compacts with respect to
normalized Si3N4 concentration

365
This indicates that the particle size distribution is made progressively
more favorable, from a packing standpoint, by the addition of 4.6 pm
UPLMs.
Figure 4.51 illustrates the effect of increasing Si3N4
concentration upon pore channel radius, as measured via Hg intrusion
analysis. It is evident from the figure that, in general, median pore
channel size increases with increasing Si3N4 concentration. The median
pore channel radii do decrease slightly, with increasing Si3N4
concentration in the 0 to 20 normalized V% Si3N4 range, for most of the
UPLM containing samples, however. It is interesting to note that, with
one minor exception, the 0 V% UPLM samples consistently had the lowest
median pore channel radii despite the fact that the 0 V% UPLM samples
had the lowest green densities. This is due to the smaller average
particle size of the 0 V% UPLM addition BS glass compacts. It is also
interesting to note that the 0 V% UPLM compacts, exhibited very little
difference in median pore channel radius between samples investigated
before and after organics removal, via pyrolysis. This indicates that
as the polymer latex is removed via pyrolysis, the pore channel
structure enlarges. This effect is universally applicable to all the
composite compositions studied.
Figure 4.52 illustrates the effect of increasing 4.6 pm UPLM
concentration upon green density for BS glass/UPLM composites in this
system. The green density of the pure BS glass compacts in this system
increases to a plateau at approximately 10 V% UPLM. The plateau
continues to approximately 20 V% UPLM for 0, 20 and 40 normalized V%
Si3N4. The green density values of the pure BS glass compositions
continuously increase (with the exception of a dip at 27.5 V% UPLM) up
to 40 V% UPLM, probably due to widening of the particle size
distribution.
It is important to note that the PE value of the pure 4.6 pm UPLM
was approximately 62 %. Thus, the increase in PE with increasing UPLM

Pore Channel Radius (/ym)
366
Normalized Volume Percent Silicon Nitride
Figure 4.51 Median pore channel radius (volume basis, Hg-
intrusion) with respect to normalized Si3N„
concentration

Green Density (% of Theoretical)
367
Organics Present
Volume Percent Latex Addition
Green density (as a percent of theoretical density)
with respect to V% UPLM for 0, 20, and 40 normalized
V% Si3N4 families
Figure 4.52

368
addition may be qualitatively explained by the Furnas model described in
Chapter 2.
The dip in green density from 25 to 30 V% UPLM concentration
corresponds somewhat to the dip in viscosity exhibited in the same
system (see Figure 4.38). The minimum in viscosity with increasing V%
UPLM concentration occurs over a larger range (i.e. 15 to 30 V% UPLM)
however, and thus, does not exactly correlate with the dip in green
density. It also should be noted that said dip is not apparent in the
post pyrolysis Hg intrusion data (as shown below), and thus, may be an
anomaly.
Figure 4.53 illustrates the increase in median pore channel
radius (MPCR) with increasing UPLM concentration for the 0, 20 and 40
normalized V% Si3N4 families of composites. Said increase is continuous,
with one exception, throughout the range of samples studied.
Figure 4.54 illustrates the effect of both normalized V% Si3N4
addition as well as V% UPLM addition upon green density and MPCR. As
discussed above, green density (GD) increases to 10 V% (both UPLM and
normalized V% Si3N4) , then plateaus to 15 V%. In this case, however, GD
decreases slightly in the abscissa range from 15 to 20 V%. Again, MPCR
increases with increasing concentration as well, with larger values
being reported for samples having organics removed prior to testing.
Figure 4.55 illustrates the effect of latex size and size
distribution upon GD and MPCR of compacts of BS glass containing 15 V%
latex additions. The figure indicates that GD remains relatively
constant with increasing latex size. Furthermore, dispersity seems to
have little effect upon GD. However, MPCR does appear to be affected by
the size and dispersity of the latex added. Pore channel radius
continuously decreases with increasing size. This is important, since
it is desirable that the ratio of MPCR to included pore size be as small
as possible (as discussed below). This effect is most apparent in post-
pyrolized samples, further amplifying the importance of this effect.

Median Pore Channel Radius (//m)
Hg-Intrusion, Organics Present
369
0.15
0.14
0.13
0.12
0.11
0.10
0.09
0.08
0.07
0 10 20 30 40
Volume Percent Latex Addition
Figure 4.53
Illustration of the effect of V% UPLM addition upon
median pore channel radius of green samples in 0, 20
and 40 normalized V% families of composites

370
and Volume Percent UPLM
Figure 4.54 Illustration of the effect of both V% UPLM and
normalized V% Si3N4 additions on both GD and MPCR of
composite compacts

82
80
78
76
74
72
70
68
66
64
62
0.15
0.14
0.13
0.12
0.11
0.1
0.09
0.08
0.07
Hg-Intrusion
371
Key:
# Bimodal Latex
â–  Quadramodal Latex
â–² UPLM
Organics Removed
Organics Present
1 i i i i i i i
2 4 6 8 10
Latex Mean (Arithmetic) Diameter (//m)
.55 Illustration of the effect of size and size dispersity
of added latex upon GD and MPCR for samples of ball
milled BS glass containing 15 V% latex additions

372
Through the methodologies utilized in this study, it was possible
to accurately predict the amount of porosity (for additions of up to
40 V% latex) added to the green structure via addition and subsequent
pyrolysis of polystyrene latex microspheres. This was accomplished
through the relation:
PPD=GDx(l-VFLatex)
where PPD is the predicted pyrolyzed density value, GD is the compact
green density (pre-pyrolysis) and VFUleI is the volume fraction of latex
(solids basis).
Figure 4.56 illustrates these predictions. Figures 4.57 and 4.58
further confirm the ability to produce controlled amounts of porosity
using the latex pyrolysis method outlined in this study. This is a very
important factor in producing controlled porosity. In fact, after this
step, it is necessary only to "sinter in" the porosity, to the final,
desired porosity and pore structure.
Figure 4.59 illustrates that controlled amounts of porosity may be
added to BS glass/latex composites regardless of latex size and size
dispersity (within the size and size dispersity confines investigated in
this study) via the methods used in this study.
A very interesting phenomenon is illustrated in Figure 4.60. The
figure illustrates the difference between pre and post pyrolyzed MPCR as
a function of UPLM (4.6 )jm) concentration. It is evident that the
difference between pre and post pyrolyzed MPCR increases monotonously
with increasing UPLM concentration until a discontinuity, resultant from
a dramatic increase in post pyrolysis MPCR, is encountered. This
discontinuity results from the creation of a continuous pore structure.
One that is a remnant of the pyrolyzed UPLMs. This is, in effect, a
percolation onset, similar to that depicted in Figure 2.15.
Figure 4.60 shows that the extrapolated onset of the percolation
occurs at approximately 23.5 V% UPLM. When multiplied by the

Median Pore Channel Radius (//m) Green Density (% of Theoretical)
373
85
Hg-Intrusion: 0 V% Silicon Nitride
Measured Density
•
Pre-pyrolysis
Post Pyrolysis
â–  â–  â–  â– 
Predicted Density
Post Pyrolysis
á • 4<
Organics Present
10 20 30
Volume Percent Latex Addition
40
Figure 4.56 Illustration of the ability to produce controlled
amounts of porosity in BS glass/UPLM composites via
organics removal

Median Pore Channel Radius (//m) Green Density (% of Theoretical)
374
Figure 4.57
Illustration of the ability to create controlled
amounts of porosity in BS glass/Si3N4 (20 normalized
V%)/UPLM composites via pyrolysis of latex

Median Pore Channel Radius (//m) Green Density (% of Theoretical)
375
85
80
75
70
65
60
55
50
45
40
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0 10 20 30 40
Volume Percent Latex Addition
Figure 4.58 Illustration of the ability to produce controlled
amounts of porosity in BS glass/Si3N4 (40 normalized
V%)/UPLM composites using organics removal methods
Hg-Intrusion: 40 V % Silicon Nitride
Measured Density
•
Pre-pyrolysis
Post Pyrolysis
Predicted Density
Post Pyrolysis

85
80
i
i
i 75
; w
' 65
’ 60
i
I
i 55
I
¡ 50
i
i
45
40
0.18
0.16
0.14
0.12
0.10
0.08
0.06
0.04
0.02
0
376
Hg-Intrusion: 15 V% Latex Addition
Measured: Organics Present
Predicted: Organics Removed
*
Measured Values:
•
Bimodal Latex
â– 
Quadramodal Latex
â–²
UPLM
Predicted: Organics Removed
2 4 6 8 10
Mean (Arithmetic) Diameter of Latex (//m)
Illustration of the ability to produce controlled
amounts of porosity over a range of latex sizes and
size distributions, via the latex pyrolysis methods
utilized in this study
.59

Median Pore Channel Radius (¿/m)
377
Figure 4.60 Illustration of the difference between pre and post
pyrolysis MPCR as a function of V% UPLM concentration,
the onset of discontinuity in post pyrolysis MPCR
(-23.5 V% UPLM) is also depicted

378
interpolated green density of BS glass/UPLM composites at 23.5 V% UPLM
(i.e. 0.732 or 73.2 % of space filled, see Figure 4.56), this value
becomes approximately 17.2 % of the bulk space occupied by the compact.
This value (17.2%) is very close to the value of 16 that has been
experimentally measured for RCP structures (see Table 2.7 [83ZAL2]). It
is also interesting to note, as mentioned in section 2.4.2, that all
types of three dimensional packing (both repetitious and random)
converge to a value of approximately 0.16 when PE is multiplied by the
corresponding percolation onset (see Figure 2.16). Figure 4.60 adds
further validity to the body of evidence that indicates that there is a
universality of the value of PE multiplied by the percolation threshold.
These data further prove the existence of a percolation onset in
this system, as well as the validity of applying percolation and related
theories to the investigation of microstructure evolution in this
system.
Representative pore channel radius distributions (Hg intrusion,
post-pyrolysis) of BS glass/UPLM composites are depicted in Figure 4.61.
The figure shows a change in the general shape of the pore channel size
distribution with changing amounts of porosity additions via the latex
addition/pyrolysis method used in this study. Relatively large amounts
of included porosity (i.e. 25 V% or greater) tended to create a
bimodality in the pore channel size distribution (PCSD), while smaller
amounts of included porosity (i.e. below 25 V%) resulted in a skewed,
monomodal PCSD. The transition concentration of included porosity
occurred at approximately 25 V%, where it is evident that the PCSD is on
the verge of becoming bimodal in nature.
It is interesting to note that the maximum of the larger mode of
the 40 V% included porosity BS glass/UPLM composites occurs at
approximately 0.8 pm, a value that is surprisingly close to the MPCR of
pure 4.6 pm UPLM (the same UPLM used to make the above composite
samples, compare Figures 4.46 and 4.61). This coincidence is surprising

dV/dlogR (cc/g)
379
5.0
4.5
4.0
3.5
3.0
2.5
2.0
1.5
1.0
0.5
0
Figure 4.61 Hg intrusion (post-pyrolysis) pore channel size
distributions (PCSDs) of BS glass/UPLM composites
showing the changing nature of PCSD with changing
amounts of included porosity
Hg-Intrusion, Post Pyrolysis
Key:
â– â– â–  0 V% UPLM
5 V% UPLM
— 10 V% UPLM
■•■15 V% UPLM
20 V% UPLM
- â–  25 V% UPLM
â„¢ 27.5 V% UPLM
-â–  30 V% UPLM
40 V% UPLM
H
!! 5
ü
ji
Ü
0.5
0.2
0.1
0.05
Pore Channel Radius (um)

380
since the MPCR of the pure UPLM composites is a measure of the size of
pore channels between UPLM spheres, while the PCSD of the BS glass/UPLM
composites is a measure pore channels between ceramic particles, after
pyrolysis (i.e. after thermal removal of UPLM additions). Thus, no
physical relationship between the two analyses is apparent, and the
phenomenon shall be considered only a coincidence.
It was not possible to directly compare the shapes and hystereses
of the Hg intrusion/extrusion curves to the generic porosimetry
hystereses of different microstructure categories, as illustrated in
Figure 2.19, due to software and equipment limitations. However,
several observations about the effect of this type of included porosity
upon porosimetry hysteresis may be made. Table 4.4 depicts the
pertinent available relationships between the porosimetry curves of the
BS glass/UPLM composites produced. The stranded volume increases with
an increasing amount of included porosity. It is not known whether this
is a result of the larger MPCRs of the composite containing a larger
amount of included porosity, or a result of the changing microstructure
(i.e. from a spinodal-like structure to a ink-bottle type structure).
Second, the generic shape of all of the porosimetry hystereses
differed somewhat from those depicted in Figure 2.19. The general shape
of the porosimetry curves seemed to be that of a hybrid of a sphere
microstructure (extrusion) and needle-like or a platey microstructure
(intrusion).
The hysteresis was, by far, the smallest for the 0 V% UPLM
composite. Said hysteresis increased with increasing V% UPLM up to about
20V% UPLM, then began to decrease above UPLM additions of 20 V%. Above
20V% UPLM addition, the porosimetry curves also changed shape somewhat.
The generic hystereses are what is generally expected from an ink
bottle-type structure [88REE]. The small channels between ceramic
particles impede Hg intrusion, while the spherical, included pores act
as Hg reservoirs. Upon extrusion, these reservoirs must be emptied

381
Table 4.4
Pertinent Available Data for Porosimetry Curves
of BS glass/UPLM Composites (Post-Pyrolysis)
I.D.
Number
V% UPLM
Stranded
Volume
(%)
Relative
Magnitude of
Hysteresis
Hysteresis Shape
03209001
0
26.3
9
Needle/Platey (I/E)
05109102
5
32.3
5
Needle/Platey (I/E)
01039101
10
45.6
2
Needle/Platey (I)
Rod/Sphere (E)
05069101
15
50.0
1
Needle/Platey (I)
Rod/Sphere (E)
02069101
20
49.6
8
Needle/Platey (I)
Rod/Sphere (E)
05109101
25
54.2
7
Needle/Rod (I)
Sphere (E)
06019101
27.5
60.0
6
Needle/Rod (I)
Sphere (E)
05079101
30
61.2
4
Needle/Rod (I)
Sphere (E)
05079102
40
73.0
3
Needle/Rod (I)
Sphere (E)
Notes:
1. Stranded volume is displayed as a percent of
total volume intruded.
2. Relative magnitude of hysteresis is 1 for
largest, 9 for smallest, there is little
difference from 4 to 7.
3. Hysteresis shape denotes a comparison with
generic curves (see Figure 2.19), I denotes
intrusion, E denotes extrusion.

382
through the relatively fine pore structure between ceramic particles.
Thus a highly hysteretic porosimetry curve would be expected. This
hysteretic structure changes depending upon the relative amounts of
included porosity (reservoirs) and upon the relative size of the pore
structure of the ceramic (which increases with increasingly large
additions of UPLM, see Figure 4.61).
Table 4.5 shows a comparison between the densities of
representative, non-latex-containing, green and pyrolyzed samples,
measured using both Hg porosimetry and the Archimedes method. This
table provides a measure of comparison between the Hg porosimetry values
and the archimedes density values, as well as a measure of the
difference between green versus pyrolyzed samples.
4.2.3.4 Effects of Aging and Sonication Upon Green Properties
4.2.3.4.1 Sonication
Sonic dismembration was utilized in this study to aid in proper
dispersion. In order to determine the proper sonic dismembration
treatment, a sonication experiment was performed as outlined in section
3.4.2.2.4.
Figure 4.62 illustrates the change in viscosity of the suspension
tested, with increasing sonication duration. Figure 4.63 depicts the
analogous relationship for properties measurable by Hg intrusion
porosimetry (i.e. MPCR and GD). It is readily apparent that a minimal
amount of sonication results in a significant reduction in viscosity as
well as in an increase in both green density and median pore channel
radius. From Figure 4.63, it is evident that the maximum green density
increases monotonously up to approximately 90 m of sonication, then
appears to plateau, hitting a relative maximum at approximately 120 m.
It is also apparent that MPCR increases and GD decreases slightly after
120 m of sonication. This is most likely resultant from solvent
evaporation, and not from an optimum value of sonication time, as the

383
Table 4.5
Comparison of Green and Pyrolyzed Densities
and Measurement Method
Batch
Number
Composition
(BS Glass/SN)
Green Density
(% Th, Hg
Intrusion)
Pyrolyzed Density (% Th)
Hg Intrusion
Archimedes
Method
03209001
100/0
67.8
68.3
68.2
12119001
100/0
72.0
71.9
71.8
03219001
80/20
66.8
66.7
66.8
03199001
60/40
63.3
62.7
62.5
02149101
40/60
58.2
57.3
★
02149102
20/80
54.5
53.5
★
01319101
0/100
51.9
51.0
*
Note: * Indicates that sample was too delicate for archimedes
method density analysis

Viscosity (mPa-s)
384
BS Glass/SN/UPLM (60/40/0)
Figure 4.62
Effect of sonication duration upon suspension
viscosity

MPCR (/vm) Green Density (%)
385
Hg-Intrusion, Pre-pyrolysis (60/40/0)
Figure 4.63
Effect of sonication duration upon GD and MPCR of the
composite suspension tested

386
container was opened several times during the experiment. This effect
is depicted in Figure 4.64.
Figures 4.65 to 4.68 depict micrographs of representative surfaces
of green compacts treated to 0, 30, 60 and 120 m of sonication
respectively. It is apparent from the figure that sonication enhances
packing efficiency.
From these data (primarily green density data) it was decided to
expose each ceramic loaded suspension, in this study, to no less than
120 m of sonic dismembration prior to casting compacts. This practice
was adopted for all of the ceramic loaded suspensions investigated.
4.2.3.4.2 Aging
Frequently it is desirable to age a suspension, in order to
provide better homogenization of the dispersants, powders, solvent, etc.
In this study, aging was performed on a rotisserie-type mixer. The
optimum time for aging the suspensions was determined experimentally.
The details of this experiment are outlined in section 3.4.2.2.4.
Figure 4.69 illustrates the effect of aging on suspension
viscosity, while Figure 4.70 depicts the effect of suspension aging upon
GD and MPCR. Both figures indicate that aging is immediately
beneficial. The benefit from aging appears to plateau at about 24 h of
aging. As in the sonication experiment, longer times appear to lead to
slightly higher viscosity suspensions that make slightly less dense
compacts having slightly larger MPCRs. Again, this is probably
attributable to solvent evaporation rather than an optimum aging time.
From these data, it was decided that all composite suspensions
containing ceramic would be aged for no less than 48 h.
Figure 4.71 depicts solids loading with aging. The solids loading
was measured only twice during this experiment. However the solids
loading increased similar to the increase during the sonication
experiment. Again, the suspension container was opened frequently

Solids Loading (V%, Total Basis)
387
BS Glass/SN/UPLM (60/40/0)
Figure 4.64
Measured change in percent solids loading occurring
throughout the sonication study

388
Figure 4.65
SEM micrograph of the surface
to 0 m of sonic dismembration
of a compact subjected
(sonication study)

389
SEM micrograph of the surface of a compact, the
anomalous suspension was subjected to 30 m of sonic
dismembration
Figure 4.66

390
SEM micrograph illustrating the surface of a compact,
the corresponding suspension was subjected to 60 m of
sonic dismembration
Figure 4.67

391
SEM micrograph depicting the surface of a compact, the
analogous suspension was subjected to 120 m of sonic
dismembration
Figure 4.68

Viscosity (mPa-s)
392
BS Glass/SN/UPLM (64/16/20)
Figure 4.69
Illustration of the effect of aging upon suspension
viscosity

Green Density (Percent of Theoretical)
393
Hg-Intrusion, Pre-pyrolysis (64/16/20)
Figure 4.70
Illustration of the effect of suspension aging upon GD
and MPCR of resulting compacts

Solids Loading (V%, Total Basis)
394
BS Glass/SN/UPLM (64/16/20)
Figure 4.71
The increase in solids loading measured during the
aging experiment

395
during the experiment, allowing evaporation. This study had the further
disadvantage that, because this is a relatively low energy process, soft
agglomerates that were created as suspension dried on the container
walls would not necessarily be dismembrated (as in the sonication
experiment).
4.3 Thermal Processing and Characterization
4.3.1 Removal of Organics
In low dielectric loss insulator applications it is important that
all organic materials and elemental carbon be removed to levels below
100 ppm (and ideally to below 30 ppm), prior to sintering, in order to
insure that materials having favorable dielectric properties (i.e.
insulation resistance and dielectric loss) were produced [91KUM2].
Unfortunately, residual carbon analysis (RCA) was not performed during
this study. However, residual carbon levels above 100 ppm usually
result in a slight discoloring of samples subsequent to the pyrolysis
treatment [91KUM2].
For the experimental purposes of this study, it was most desired
that all of the composite compositions experience the same pyrolysis
heat treatment. Thus, the heat treatment schedule for organics removal
was formulated to remove all amounts of latex used (i.e. up to 40 V%),
and the same heat treatment schedule was used for all of the composite
compositions. Therefore, it is important to note that the pyrolysis
heat treatment schedule was longer than necessary in most cases.
The methodology utilized to determine the pyrolysis schedule, as
well as the actual pyrolysis schedule used, is described in sections 3.5
and 3.6. While not optimized, the heat treatment schedule proved
adequate, providing samples having tan(6) values comparable to
literature values (as discussed below). This section presents thermal
analysis data in order to better understand the organics removal process
in this system.

396
Figure 4.72 illustrates time and temperature based TGA analyses of
a sample (BS glass/SN/UPLM, 80/0/20) heat treated with the pyrolysis
schedule used in this study (see Figure 3.10). This sample is
representative of the entire composite system in that it contains an
appreciable amount of latex UPLM as well as the proper amount of the
dispersant (PVP K30). For the composition illustrated in Figure 4.72 a
total weight loss of approximately 21 wt% is expected. It is
interesting to note, from Figure 4.72, that approximately 8 weight % of
the composite was lost at temperatures below 125 °C. This is probably
due to evaporation of residual EtOH within the UPLM. This is logical
since the precursor powders were carefully dried and kept in well-sealed
storage containers prior to the batching process, while the compacts
were formed from a wet (EtOH) process and were dried, at ambient
temperature only, prior to the thermolysis treatment.
Figure 4.72 also illustrates a plateau toward the end of the
pyrolysis treatment. This indicates that polymer removal is as complete
as possible at the maximum temperature of heat treatment.
Figure 4.73 illustrates TGA and DTA analyses of the latex used in
this study. Thermogravimetric analysis indicates that the UPLM powders
pyrolyze over a sharp temperature range near 400 °C, leaving very little
ash. It should be noted that the weight loss resultant from latex
thermolysis, as indicated in Figure 4.72, occurred over a broader, lower
temperature range (i.e. near 300 °C) . Thus, it is important to note
that the effects of both heating rate (i.e. 10 °C/min. versus 0.33
°C/min.) and (i.e. pyrolysis acceleration due to the presence of ceramic
powder) can influence the pyrolysis process [88REE].
Differential thermal analysis of the latex powder indicates that
the pyrolysis process is complex. The reaction corresponding to the
major TGA weight loss is endothermic, indicating that the reaction
mechanism is probably a type of polymer scission. At higher

Weight Loss (%) Weight Loss (%)
397
Temperature ( C)
B. Temperature Based
Figure 4.72 Thermogravimetric data of a representative sample
(80/0/20 BS Glass/SN/UPLM) heat treated using the
pyrolysis schedule used in this study, A. time based,
B. temperature based

398
Figure 4.73
Illustration of TGA and DTA curves (10 °C/min) for
pure latex in air and in N: gas atmosphere
ó T( C)

399
temperatures the resulting organic residue burns off via an exothermic
mechanism.
Figure 4.74 illustrates the TGA and DTA analyses of the dispersant
polymer used. The dispersant has a significant amount of water (or
solvent) adsorption, as indicated by the weight loss near 100 °C. This
is reasonable since the powder was used as-received, and was not dried
prior to the batching process. Thermogravimetric analysis indicates
that the polymer is not completely removed until above 700 °C, and that
a slight amount of residue may remain even at 1000 °C. Differential
thermal analyses indicate that the reactions involved in the process of
PVP pyrolysis are complex and continue to relatively high temperatures.
These factors did not prove detrimental in this study however, since
very little of the dispersant was used (i.e. 1 wt % of solids).
Regardless, it would probably be beneficial to replace this dispersant
with a less refractory system when developing thick film or tape cast
systems.
Figures 4.73 and 4.74 also exhibit corresponding DTA and TGA data
for pure latex and dispersant treated in N2. These analyses were
included since it would be advantageous to change to nitrogen organics
pyrolysis when using these materials in a cofirable system that uses
non-noble metals such as Cu or Pd [91KUM1,91KUM2,91SHE2,91TUM]. It is
interesting that the latex pyrolysis process in N-, is quite similar to
that in air. Nitrogen pyrolysis of the PVP dispersant is also somewhat
similar to air pyrolysis. However, N2 pyrolysis of the dispersant
resulted in a significantly greater portion of residue than did the
analogous air pyrolysis. This would add further impetus to change
dispersant systems if developing these materials for N: thermolysis.
4.3.2 Evolution of BS Glass Surface Area
It is important to know how surface area (SA) of a powder, or of
powder compacts, is affected by thermal treatments. For example, as

PVP-k30 (as-received)
400
100
90
80
70
60
50
JS
W>
» 40
30
20
10
0
3
2
U
5
H
<]
1
0
-1
-2
Figure 4.74
Illustration of both air and N2 atmosphere TGA and DTA
curves (10 °C/min) for the PVP dispersant used in this
study
A T ( C)

401
powder surface porosity is reduced, there is a possibility of entrapment
of carbonaceous materials. It may also be important to know how SA
evolves from a sintering standpoint. In the initial stages of sintering
powder SA is reduced.
The SA evolution experiment was performed as outlined in section
3.3.5. The heat treatments used are depicted in Figure 3.4. Figure
4.75 illustrates the relationship of SA reduction with increasing heat
treatment temperature maximum. It is evident, from the figure, that the
SA of the ball milled BS glass powder decreases gradually up to the heat
treatment maximum of 450 °C, then decreases at a greater rate, past the
450 °C heat treatment.
The SA of BS powder compacts is initially about one third that of
the corresponding powder. It is not evident why this is the case, it
may be an effect of dispersant coverage of the powder surface. This
effect was not confirmed experimentally, however.
It is interesting to note that the general trend of the evolution
of SA of the BS glass compacts with temperature is similar to that of
the BS glass powder. In both cases, the SA reduction is greatest at
heat treatment máximums exceeding 550 °C. It is interesting that the
slip cast BS glass compacts did not exhibit significant densification
when heat treated to these temperatures (see section 4.3.4), even though
the SA of these compacts had decreased almost tenfold, using the 600 °C
heat treatment. This reduction in surface area may be attributed to the
elimination of the surface porosity, via a viscous flow mechanism,
during these heat treatments. As mentioned earlier, the surface
porosity resulted from corrosion during ball milling in MeOH.
Figure 4.76 illustrates the evolution of the ball milled BS glass
powder pore structure (both 4 and 45 nm pore diameters) with successive
thermal treatment, using gas desorption (similar to Figure 4.33). The
figure shows a successive reduction in the height of the 4 nm pore
diameter peak with increasing heat treatment temperature. The analogous

Surface Area (m /g)
402
Maximum Temperature Duration of 3 h, Air Atmosphere
Maximum Heat Treatment Temperature ( °C)
Figure 4.75 Illustration of the effect of heat treatment maximum
temperature (for 3 h, in air) upon the measured
surface areas of the ball milled BS glass powder and
compacts investigated

403
Multipoint Gas Desorption, BS Glass Powders
Figure 4.76
Illustration of the evolution of BS glass powder SA (4
and 45 nm pore diameter peak heights) with respect to
heat treatment, using multipoint BET desorption

404
data for the as-received BS glass powder is included as well, for
comparison. The desorption peaks (primarily the 4 nm peak), which
resulted, or grew, from ball milling the BS glass powder in MeOH (see
Figure 4.33), were reduced significantly with these heat treatments.
Both peak heights values became more similar to those of the as-received
BS glass powder with maximum heat treatment. The 45 nm peak height
changed less with heat treatment than the 4 nm peak. This is logical
since higher SA structures are more sensitive to temperature. It is
interesting that the SA of the ball milled powder reverted to a value
similar to that of the as-received powder (i.e. SA changes to 3.8 rrr/g,
which is comparable to the 3.4 m:/g value of the as-received glass).
This analysis was not performed upon the BS glass compacts, since
the desorption peak at approximately 4 nm was never present. This fact
gives further credence to the hypothesis that the polymer dispersant
covered the powder particle surfaces during wet processing and casting.
Unfortunately, it is not possible to discuss the effects of these
heat treatments upon measured particle size, because particle size
analyses of the heat treated powders were not performed. This would be
beneficial in order to compare the post heat treatment particle size to
both the as-received and the ball milled BS glass powders. However,
after the 600 °C heat treatment was performed, a minor amount of
agglomeration was observed. Thus, measurement of the particle size of
this sample would have been sensitive to any regrinding process used.
4.3.3 Oxidation of Si,N, Powder
In this study it is important that the Si3N4 powder used not
oxidize appreciably. This is true because oxidation would alter the
density of the Si3N4 powder, thereby altering the density of the
composite. This could become a significant source of error in
determining percent of theoretical density when investigating sintered

405
composites containing Si3N4. Thus, oxidation experiments were performed
on the Si3N4 powder used in this study as outlined in section 3.5.2.
Figure 4.77 illustrates the TGA curve for Si3N4 powder heated in
air at a rate of 10 °C/min. The weight loss from RT to approximately
1300 °C was due mainly to baseline variance in the TGA instrument. This
fact was determined from reference runs using reference alumina.
However, the weight gain after approximately 1300 °C was real and is
attributed to oxidation of the Si3N4 powder.
The highest temperature used to sinter composites in this study
was 820 °C. The relationship in Figure 4.77 seems to indicate that this
temperature is well below the onset of oxidation of the Si3N4 powder.
However, as mentioned above, reactions tend to be shifted to lower
temperatures when heating rates are decreased. In the case of sintering
the 820 °C heat treatment was isothermal and lasted for relatively long
periods.
Figure 4.78 illustrates isothermal TGA at 820 °C for the Si3N4
powder. The reference curve (tabular alumina) is provided as a
rudimentary means of baseline correction. It is evident from the
figure, that little or no weight gain occurs over long periods of time
at said temperature. The reference (baseline) curve has the same
general shape and magnitude as the Si3N4 curve. It is not known whether
the relatively small difference between the curves is real or is a
variable of the TGA apparatus, since the runs were not performed
simultaneously (i.e. non-identical conditions). Thus, it may be
hypothesized that Si3N4 oxidation should not have significantly affected
the various measurements (i.e. density, dielectric properties, etc.)
taken during this study.
It should be noted that this experiment was performed upon pure
Si3N4 powder and, thus, is not indicative of any reactions between the BS

Weight
406
Silicon Nitride Powder (As-Received, Air)
Figure 4.77
TGA curve of Si3N4 powder heated to approximately
1500 °C, at a rate of 10 °C/min, in air

407
Figure 4.78
Isothermal TGA of Si3N4 and reference powder (alumina)
at 820 °C in air

408
glass and the Si3N4 powder. As discussed below, microscopy studies
indicate that there is little if any BS glass-Si3N4 interaction, however.
4.3.4 Sintering
In studies of the densification of glass matrix composite
materials it is important that sintering of the viscous matrix material
is first understood. After this understanding is obtained, the effects
of additions of porosity and of nonsintering particulates upon
densification may be characterized.
Figure 4.79 illustrates isothermal densification curves of slip
cast compacts made of pure, as-received and ball milled BS glass powders
at 625 °C. Even though the as-received glass started with approximately
4% greater green density (~72 versus -68 % of theoretical density), the
ball milled BS glass sintered at a much greater rate, surpassing the
density of the as-received compact in the initial stage of
densification. This may be explained by the higher surface area and
smaller MPCR of the ball milled BS glass compacts as compared to the as-
received BS glass compacts.
Thus, the increased surface area of the ball milled glass powder
greatly increased the rate of sintering of the BS glass. It should be
noted that after the organics removal process the surface area of the
ball milled BS glass was significantly reduced (see Figure 4.75). No
analogous data is available upon the as-received BS glass, however, so
it is difficult to gauge this effect. Regardless of the operant
mechanism, the rate of sintering is significantly increased (i.e. 0.77
versus 3.05 % per hour for as-received and ball milled BS glass, in the
initial stages, respectively) when the BS glass powder is ball milled.
The effect of Si3N4 concentration upon the rate of densification is
illustrated in Figures 4.80 and 4.81. Figure 4.80 depicts isothermal
densification of BS glass/Si3N4 compacts at 625 °C, while Figure 4.81
depicts isothermal sintering of BS glass/Si3N4 composites at 650 °C.

409
Figure 4.79
Isothermal densification of as-received and ball
milled BS glass compacts at 625 °C

% Theoretical Density
410
100
95
90
85
80
75
70
65
60
55
0 1 0 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170
Isothermal Sintering Time (h)
0, 20, 40, 60 V% Silicon Nitride, 625 C
V % Silicon Nitride
--É- —
0 V%
â–  | â–  a a â–  a
20 V%
— -*
40 V%
*
60 W%
*
â– i ' "i 'i i
i r
Figure 4.80
The effect of Si3N4 concentration upon isothermal
densification of BS glass/SN composites at 625 °C

% Theoretical Density
411
0, 20, 40 V% Silicon Nitride, 650 °C
100
95
90
85
80
75
70
65
60
0 10 20 30 40 50 60 70 80 90 100 110 120 130140 150
Isothermal Sintering Time (h)
Effect of Si3N4 concentration upon isothermal
densification of BS glass/SN composites at
650 °C
Figure 4.81

412
From the figure, it is evident that densification is significantly
retarded with Si3N4 additions at and above 40 V%. In fact, with a Si3N4
concentration of 60 V%, very little densification occurred. This is in
agreement with theories presented in the literature [91SCH2].
It is interesting to note that, in both the 40 and 60 V% Si3N4
addition samples, the maximum volume occupied by Si3N4 is approximately
36 V% (i.e. 40 V% at a maximum observed density of approximately 90 % of
theoretical density, and 60 V% at a maximum observed density of
approximately 60 % of theoretical density). Thus, it may be
hypothesized that the maximum Si3N4 addition of approximately 36 V% may
be used in order to produce compacts that may be sintered to near-full-
density using pressureless sintering techniques. This is in general
agreement with the available literature [87RAH1,87SCH3,88BOR3,90EWS,
91EWS,91SCH2,91SCH3,91SCH4].
Conversely, concentrations of Si3N4 at and below 20 V% affected
densification of these composites relatively little. These Si3N4
concentrations are below the percolation threshold (i.e. - 26 V% for 60
% dense compacts) and thus, are not expected to affect densification
greatly [91SCH2]. In fact, both the 0 and 20 V% Si3N4 composites
exhibited bloating (i.e. a reduction in density with increased sintering
duration), which indicates that sintering proceeded relatively
uninhibited.
The small amount of retardation in the rate of densification in
the 20 V% Si3N4 composites probably results from the fact that at
approximately 80 % of theoretical density, the percolation threshold is
reached and thus, sintering is inhibited. This is in agreement with
Figures 4.80 and 4.81, where densification of the 20 V% Si3N4 composites
begins to differ from that of the pure BS glass at approximately 80 % of
theoretical density.
It should be noted that investigation of compositions containing
20 to 36 or 40 V% Si3N4 would be beneficial in order to further delineate

413
the composition at which severe retardation of sintering occurs. This
would help to determine if significant sliding or sticking occurs
between the Si3N4 particles [91SCH2].
The effect of sintering temperature upon isothermal rate of
densification is illustrated in Figures 4.82 through 4.85. Figure 4.82
illustrates this effect for pure ball milled BS glass, while Figures
4.83 and 4.84 depict these relationships for 80/20/0 and 60/40/0 BS
Glass/SN/UPLM composites respectively. The figures indicate that an
increase in temperature of 25 °C increases the initial rate of
densification rate (i.e. in the first linear region) by factors of
approximately 3.8, 3.2 and 2.8 (i.e. 9.15 versus 2.41 % per hour for
pure, ball milled BS glass, 7.89 versus 2.44 % per hour for 80/20 BS
glass/SN composites, and 1.78 versus 0.63 % per hour for 60/40 BS
glass/SN composites) for 0, 20 and 40 V% Si3N4 concentration composites,
respectively.
Using interpolated viscosity values, depicted in Figure 4.85, it
is evident that the viscosity of the bulk samples of the BS glass used
in this study is reduced by a factor of approximately 4 when temperature
is changed from 625 to 650 °C. This similarity to the above values is
logical since viscous sintering is the operant densification mechanism
in this system. Thus, the densification rate of the composites is
expected to increase in direct proportion to the decrease in viscosity
with temperature (all other factors remaining equal).
From Figure 4.84 it is evident that the 40 V% Si3N4 concentration
composites will not densify significantly in excess of 90 % of
theoretical density using pressureless sintering. Furthermore, it is
interesting to note that the compacts that were sintered at 820 °C did
not achieve 90 % of theoretical density. Blistering was observed in
these samples. Thus, it is assumed that 820 °C is too high a sintering
temperature for effective sintering of these samples.

% Theoretical Density
414
Pure, Ball Milled BS Glass
Isothermal Sintering Time (h)
Illustration of the effect of isothermal sintering
temperature upon densification rate of pure, ball
milled BS glass compacts
Figure 4.82

% Theoretical Density
415
BS Glass/SN/UPLM (80/20/0) Composites
Illustration of the effect of isothermal sintering
temperature upon the rate of densification of 80/20/0
BS glass/SN/UPLM composite compacts
Figure 4.83

% Theoretical Density
416
BS Glass/SN/UPLM (60/40/0) Composites
Isothermal Sintering Time (h)
Figure 4.84
Illustration of the effect of isothermal sintering
temperature upon the densification rate of 60/40/0 BS
glass/SN/UPLM composite compacts

Viscosity (Log(Pa-s))
417
Figure 4.85
Illustration of the reduction in viscosity from 625 to
650 °C in the BS glass used in this study

418
The effect of porosity addition upon densification rate is
illustrated in Figures 4.86 to 4.89. Figure 4.86 illustrates this
effect for pure BS glass systems, while Figure 4.87 depicts this
relationship for composites containing 20 normalized V% Si,N4.
Similarly, Figures 4.88 and 4.89 depict the effect of added porosity
concentration upon the densification behavior for composites containing
40 normalized V% Si3N4.
The effect of included porosity upon the densification behavior of
the pure BS glass compacts is quite interesting. Sintering is not
significantly impeded in samples containing 5 V% UPLM until densities in
excess of 90 % of theoretical density are achieved. This behavior is
imitated in samples containing 10 V% UPLM below approximately 80 % of
theoretical density as well. Nearer the percolation threshold,
densification is impeded almost from the onset of the sintering process.
Beyond the percolation threshold (i.e 30 V% UPLM), densification occurs
at a decreased rate. However, the densification behavior of the 30 V%
UPLM addition compacts proceeds to higher densities than the BS glass
compacts containing UPLM additions below the percolation threshold. In
this sense, the general shape of the 30 V% UPLM addition curve is
similar to the 0 V% UPLM addition curves (both as-received and ball
milled BS.
The reason for this behavior is related to pore structure. The
pore structure of the 30 V% UPLM addition material has considerably
larger pore channels than the pore structures of the materials having
latex additions below the percolation threshold (see Figures 4.60 and
4.61). The pore structures of the materials having UPLM additions below
the percolation threshold have much smaller pore channels, and are
similar to ink bottle-type pores. During densification the smaller pore
channels close off first in ink bottle-type structures. If there is a
large difference in size between the pores and the channels
interconnecting the pores, the relatively large pores will become

% Theoretical Density
419
0, 5, 10, 15, 20, 30 V% UPLM (4.6 fim), 625° C
Isothermal Sintering Time (h)
Illustration of the effect of added porosity
concentration upon the densification behavior pure BS
glass compacts at 625 °C
Figure 4.86

% Theoretical Density
420
Isothermal Sintering Time (h)
Illustration of the effect of added porosity
concentration upon the densification behavior of
normalized 80/20 BS glass/SN composite compacts at 625
°C
Figure 4.87

% Theoretical Density
421
BS Glass/SN (Normalized (80/20)), Varying UPLM, 650°C
Illustration of the effect of added porosity
concentration upon the densification behavior of
normalized 80/20 BS glass/SN composite compacts at 650
°C
Figure 4.88

% Theoretical Density
422
BS Glass/SN (Normalized (60/40)), Varying UPLM, 650 C
Isothermal Sintering Time (h)
Illustration of the effect of added porosity
concentration upon the densification behavior of
normalized 60/40 BS glass/SN composite compacts at 650
°C
Figure 4.89

423
isolated during sintering. These isolated pores are tenacious and
difficult to remove during sintering because transport to and from them
is greatly impeded. In the case of large pores and large channels of
pore interconnection, pore isolation does not occur until relatively
high densities (i.e. > 94 % of theoretical density), because the pore
channels do not sinter out of the structure prematurely as in ink
bottle-type pores. Therefore, while the densification process is slowed
in the 30 V% UPLM addition BS glass powder materials, it progresses to
ultimate densities similar to those exhibited by the 0 V% latex addition
curve (see Figure 4.86). This is not the case in materials having UPLM
additions below the percolation threshold, where it appears that an
asymptotic density level is approached (see 10 and 20 V% UPLM addition
curves in Figure 4.86). Unfortunately data was not collected at longer
sintering durations to further define these asymptotic values.
Figure 4.90 compares the densification curves for as-received and
ball milled BS glass compacts as well as for 30 V% UPLM ball milled BS
glass compacts. It is interesting that the as-received and the 30 V%
UPLM curves match each other fairly closely at longer times, while the
general shape of the 30 V% UPLM curve is similar to the densification
curve for the ball milled BS glass. The common denominator among these
materials (i.e. the 0 V% UPLM, as-received and ball milled BS glass
compacts, as well as the 30 V%, 4.6 pm addition, ball milled BS glass
compacts) is the presence of a continuous pore structure.
It is not known whether or not the asymptotic limits approached by
the compacts having UPLM additions below the percolation threshold are
real. Time did not permit such investigations. These compacts may
sinter to greater densities. However, the closed-off porosity may
become stable and may actually bloat in a manner similar to the behavior
exhibited by the 0 V% latex addition ball milled BS glass compacts.
Bloating occurs as a result of pore ripening. Small, sealed pores
have a higher surface curvature than larger, sealed pores.

% Theoretical Density
424
Isothermal Sintering Time (h)
Figure 4.90 Illustration depicting the isothermal densification
behaviors of pure as-received and ball milled BS glass
compacts, as well as ball milled BS glass compacts
with 30 V% UPLM additions at 625 °C

425
Therefore the sintering pressure (which is directly relatable to surface
curvature) on smaller pores is greater than on larger pores, and a
greater amount of gas pressure is required to stabilize a small pore
against sintering. Thus, the same molar amount of gas trapped within a
material, upon elimination of open porosity during the densification
process, would create a greater volume of large porosity than smaller
porosity, due to the pressure balance mentioned above. From Ostwald
ripening theory [76KIN1], gases are expected to diffuse from small pores
to local large pores. Thus, bloating would be expected in this system,
if the amount of trapped gases remains constant. Conversely, if the
trapped gases can diffuse to the material surface, bloating may be
retarded or eliminated, depending upon the rate of trapped gas removal.
The densification behavior of the normalized 80/20 (BS glass/SN)
composites containing UPLM additions do not seem to asymptotically
approach a density limit as the above materials did (see Figures 4.87
and 4.88). It may be speculated that this is a result of the larger
pore channels characteristic of the 20 normalized V% Si3N4 composites
(see Figure 4.51) as well as sintering for deficient sintering
durations. Said larger pore channel structure would allow sintering
behavior more similar to the continuous pore structure materials
described above.
These densification behaviors introduce an important concept. The
level of achievable closed porosity is affected not only by the amount
of porosity addition, but by the pore structure itself. Specifically it
is important that the ratio of the included pore size to the measured
pore channel size be maximized, in order to achieve closed porosities
similar to the porosity addition. This effect is called differential
sintering, in that it allows densification of one aspect of an internal
pore structure, with little or no densification of other aspects of the
pore structure.

426
It is also important to note that, above the percolation
threshold, this ratio is reduced significantly when using this method of
porosity addition. Therefore, it is not possible to achieve fractions
of closed porosity that exceed the percolation threshold (i.e. 16 V%) of
the included porosity. This shall be discussed in further detail below.
Figure 4.89 illustrates that all normalized 40 V% Si3N4 composites
investigated achieve an asymptote. This results from the establishment
of a continuous Si3N4 structure. It is interesting that the asymptote
achieved by the 20 V% UPLM addition composite is close to 0.8 of the
asymptote achieved by the 60/40 composite with 0 V% UPLM addition. This
further indicates that the asymptotes realized in the densification of
the 40 normalized V% Si3N4 samples are due to establishment of a stable,
percolated Si3N4 structure.
Figure 4.91 illustrates the effect of included porosity size and
size distribution upon densification behavior. While there is not a
great deal of difference between the curves, a couple of subtle
observations may be made. All of the curves appear to approach an
asymptote except for the smallest size of included porosity. The
asymptote approached by the largest size of included porosity
investigated is lowest in density of the groups. Unfortunately data
were not taken at longer sintering durations. This would have helped to
better establish the asymptotic relationships discussed above.
Figure 4.92 illustrates the densification behavior of composite
compositions on the diagonal of the 4.6 pm UPLM plane of the matrix of
compositions investigated. It is evident from the figure that there is
a large range in densification rate of these compositions.
It should also be noted that it was common, in those samples
having nearly closed pore structures, for the relative amount of closed
and opened porosity to change with the number of repetitions of density
measurement used. In all cases, the amount of open porosity was
observed to increase at the expense of closed porosity (without

% Theoretical Density
427
BS Glass/Sn/Latex (85/0/15 (Various Types)), 625 °C
Isothermal Sintering Time (h)
Figure 4.91 Illustration of the effect of included porosity size
and size distribution upon the isothermal
densification behavior of BS glass/SN/Latex (85/0/15)
compacts at 625 °C

% Theoretical Density
428
BS Glass/SN/UPLM Matrix Diagonal, 625 C
Isothermal Sintering Time (h)
Illustration of the densification behavior of
composite concentrations on the diagonal of the 4.6 pm
plane of the composition matrix investigated at 625 °C
Figure 4.92

429
noticeable change in total porosity). In extreme cases, this behavior
necessitated up to 8 repetitions of density measurement before the
criteria for reproducibility (see section 3.7.1) were met. Therefore,
the open porosity stated for these samples represent the maximum amounts
measured.
Possible reasons for this behavior include aqueous corrosion of
the relatively thin and delicate regions of material between included
pores, and/or erosion, of these interpore materials, due to the traumas
experienced during Archimedes density measurements (i.e. aqueous
infiltration and drying stresses, etc.). Using the these explanations,
it is reasonable to expect this type of behavior in samples in the
initial stages of pore closure. This behavior decreased with further
heat treatment (i.e. as the regions between included pores became more
robust, and porosity became more closed off). Thus, investigation
focusing upon maximization of closed porosity, concentrated upon samples
having measured closed porosities at, or slightly after the curve
maximum.
Another type of graph, that provides valuable representation of
pore structure, is indicated in Figure 4.93. Figure 4.93 illustrates
the total, open and closed porosities of as-received BS glass
composites, as a function of sintered density, at 625 °C. The total
porosity values were obtained by subtracting the percent density from
100 % (or full density). The open porosity was determined as outlined
in section 3.7.1, and the closed porosity was obtained from the
difference between the calculated total porosity and the measured open
porosity. From this description, it is evident that two different
techniques (as well as a couple of assumptions) are utilized to obtain
these data. Therefore, possible errors are amplified. However, the
amount of error may be determined by the graph itself using sintering
criteria. First, it is assumed that negative porosities are impossible
in reality. Also, in general, closed porosity does not occur until the

430
As--Received BS Glass, 625 °C
Illustration of the total, open and closed porosities
of as-received BS glass compacts as a function of
sintered density at 625 °C
Figure 4.93

431
matrix phase is densified in excess of 90 to 94 % of theoretical
density. Using these criteria, it is evident that these values are
accurate to within approximately 2 to 3 % at the initial stages of
sintering, and improve significantly as densification progresses. This
change in accuracy is also typically observed in buoyancy density
measurements due to the delicateness of the low density samples as well
as the hygroscopicity of the sample surfaces, etc.
Figure 4.93 illustrates behavior typical of the pure BS glass (no
included porosity) samples investigated in this study. It is observed
that the maximum closed porosity occurs at approximately 4 to 5 V%.
Figure 4.94 indicates a similar relationship for the pure, ball milled
BS glass (without porosity additions) compacts.
The effect of added porosity upon the total, open and closed
porosities of ball milled BS glass compacts is illustrated in several,
figures that follow. Figure 4.95 illustrates these relationships for
ball milled BS glass compacts containing 5 and 10 V% UPLM additions, and
sintered isothermally at 625 °C. It is evident from the figure that the
total amount of closed porosity measured increases with increasing UPLM
addition. It is also evident that the maximum measured amounts of
closed porosity, exhibited by these curves, are not simply an addition
of the included porosity (i.e. due to the addition of latex) plus the
inherent porosity (i.e. the porosity native to the BS glass matrix).
The maximum amounts of closed porosity measured for the 5 and 10 V% UPLM
addition compacts were - 7.7 and - 10.3 respectively. Thus, it may be
concluded that, as the amounts of porosity addition increase, the
inherent porosity is eliminated. Eventually (i.e. around 10 V%
addition), most or all of the inherent porosity is eliminated, and only
included porosity remains to create the closed porosity observed.
This trend is observed with increased additions of porosity as
well. Figures 4.96 and 4.97 illustrate the total, open and closed
porosities of BS glass compacts containing 15 V% additions of the

35
30
25
20
15
10
5
0
35
30
25
20
15
10
5
0
Ball Milled BS Glass
432
Density (Percent of Theoretical)
Illustration of the total, open and closed porosities,
as a function of sintered density, for pure BS glass
compacts sintered at 625 °C and 650 °C
94

35
30
25
20
15
10
5
0
30
25
20
15
10
5
0
BS Glass Compacts with Added Porosity
433
Illustration of the total, open and closed porosities
versus sintered density of BS glass compacts
containing 5 and 10 V% additions of 4.6 pm UPLM
isothermally sintered at 625 °C
.95

35 -
30
25 -
20 â– 
15
10 â– 
5 â– 
0
30
25
20
15
10
5
0
(
re 4
434
70 75 80 85 90 95 100
Density (Percent of Theoretical)
96 Illustration of the total, open and closed porosities
of BS glass compacts containing 15 V% of 2.4 pm
bimodal and 4.0 pm quadramodal respectively as a
function of sintered density

35
30
25
20
15
10
5
0
30
25
20
15
10
5
0
435
70 75 80 85 90 95 100
Density (Percent of Theoretical)
.97 Illustration of total, open and closed porosities of
BS glass compacts containing 15 V% additions of 4.6 pm
and 9.0 pm UPLMs respectively, as a function of
sintered density

436
various types of latex developed for this study. Figure 4.96
illustrates this behavior for the 2.4 pm bimodal and the 4.0 pm
quadramodal additions, while Figure 4.97 illustrates these relations for
the 15 V% additions of 4.6 pm and 9.0 pm UPLMs respectively. In fact,
this figure indicates that even some of the added porosity is either
eliminated or remains open, since 15 V% closed porosity is not achieved
in any of these compacts.
There are two reasons to explain this. First, added porosity that
is either at, or connected to, the sample surface through large pore
channels, will always remain as open porosity. Second, the large pores
may also decrease in size to some extent, as sintering proceeds. Thus,
the actual volume of added porosity would be reduced due to size
reduction in the added porosity. Both of these mechanisms will be shown
to have an influence upon the maximum amount of porosity achievable, and
will be discussed in further detail below.
It is also evident from Figures 4.96 and 4.97 that the maximum
amount of closed porosity obtainable is also a function of the size of
the latex added to create included porosity. The maximum amount of
closed porosity achieved with 15 V% additions of 2.4 pm latex was barely
greater than the analogous amount for 10 V% additions of 4.6 pm UPLM.
Furthermore, the greatest amount of closed porosity of the 15 V% latex
addition materials, was achieved using the additions of 9.0 pm UPLM.
Since the 9.0 pm UPLM additions gave the highest performance, and since
said additions resulted in nearly a 1 to 1 ratio in added to closed
porosity, the following recommendation is made. The recommended added
pore size to inherent, post-pyrolysis pore channel ratio should equal or
exceed 40. This is the approximate value of the 9.0 pm UPLM diameter
divided by the 0.230 pm post-pyrolysis pore channel diameter observed in
the 15 V% 9.0 pm UPLM addition compacts. It should be noted that the
4.6 pm addition UPLM gave only slightly decreased performance, and had a

437
similar ratio of approximately 20. Thus, this value may vary somewhat,
but should exceed at least 20.
This ratio is very valuable if it is desirable to design a system
of known closed porosity (up to - 15 V%) with minimal surface roughness.
For example, if it is desirable to limit surface roughness to a maximum
of 5 pm, one would use a target included porosity diameter near to, or
slightly less than, 5 pm (assuming that no pore clustering occurs, less
if it does). Thus, the glass matrix powder should pack to have a post-
pyrolyzed pore channel diameter of less than 0.25 pm (ideally less than
0.125 pm). If a monosized glass powder is utilized, and said powder
packs according to RCP theory, the maximum powder size used should not
exceed 1.75 pm (ideally, it would not exceed 0.875 pm), using the pore
channel size criteria outlined in section 2.3.
Figure 4.98 illustrates the total, open and closed porosity
relationships, as a function of sintered density, of BS glass compacts
having 4.6 pm UPLM additions of 20 and 30 V%. It is evident from
Figures 4.97 and 4.98 that there is little benefit from increasing the
additions of UPLM from 15 V% to 20 V%. This is probably a result of
included porosity exceeding the percolation threshold at the final
stages of sintering. This also explains the longer times to achieve the
maximum amount of closed porosity of the 20 V% UPLM addition compacts as
compared to those containing 15 V% additions.
Furthermore, it is evident from Figure 4.98 that additions of
latex, that surpass the percolation threshold in the green state, result
in maximum closed porosities that are no greater than those observed in
the pure glass compacts (i.e. without porosity additions). This is a
result of the onset of a continuous included pore structure, as
described above.
Therefore, it may be assumed that in order to maximize closed
porosity (which will not exceed the percolation threshold of - 16 V%) ,
the UPLM addition should be between 15 and 20 V%, and should be of 9.0

50
40 â– 
30 â– 
20
10
0
40
30
20
10
0
c
re 4
438
55 60 65 70 75 80 85 90 95 100
Density (Percent of Theoretical)
98 Illustration of the total, open and closed porosities,
as a function of sintered density, of BS glass
compacts containing 20 and 30 V% additions of 4.6 pm
UPLM

439
pm UPLM (for this study). Using the feedback data obtained from this
study, a batch of compacts of ball milled BS glass, containing 17.6 V%
additions of 9.0 pm UPLM were produced, processed and characterized.
Figure 4.99 illustrates the analogous relationship for the 82.4/0/17.6
BS glass/Si3N4/9.0 pm UPLM composition composite.
From Figure 4.99 it is evident that the maximum in closed porosity
in this configuration is greater than in all other systems measured
(i.e. approximately 15.6 V%) in this study. Thus, the feedback
optimization used was successful, indicating that enough knowledge has
been gained about this system to make precise and reasonably accurate
predictions of pore structure. This is very important when designing
materials for the properties desired. This is also very important in
the sense of defining limitations of a technique or system, as has now
been achieved for this system, in the sense of the maximization of
closed porosity (for the techniques utilized in this study).
Figures 4.100 to 4.104 illustrate the total, open and closed
porosity relationships, as a function of sintered density, for BS
glass/Si3N4/4.6 pm UPLM composites. Figures 4.100 and 4.101 depict these
relationships for 80/20 normalized concentrations of BS glass/Si3N4.
Figure 4.100 is for 80/20 BS glass/Si3N4 composites without added
porosity at isothermal sintering temperatures of 625 °C and 650 °C
respectively, and Figure 4.100 is for the same, except with 10 and 20 V%
additions of 4.6 pm UPLM (sintered at 625 °C).
It is evident that these relationships are quite similar to the
relationships in pure BS glass described above. The 10 V% UPLM addition
has a slightly greater maximum closed porosity (i.e. - 10.3 versus -
10.5 V% respectively) however.
Figure 4.102 illustrates this relationship for the two remaining
composite compositions on the diagonal of the 4.6 pm UPLM plane of the
composite composition volume (i.e. the 81/9/10 and the 72.25/12.75/15
compositions). From the figure, it is evident that the 10 V% UPLM

Porosity (Percent of Theoretical Density
440
65 70 75 80 85 90 95 100
Density (Percent of Theoretical)
Illustration of the total, open and closed porosities,
versus sintered density, of ball milled BS glass
compacts containing 17.6 V% additions of 9.0 pm UPLM,
isothermally sintered at 625 °C
Figure 4.99

35
30
25
20
15
10
5
0
35
30
25
20
15
10
5
0
441
BS Glass/SN (80/20) Composites
625 C
650 C
70 75 80 85 90
Density (Percent of Theoretical)
100
100
Illustration of total, open and closed
porosities of 80/20 BS glass/SN composites, as
a function of sintered density, isothermally
sintered at 625 °C and 650 °C respectively

35
30
25
20
15
10
5
0
35
30
25
20
15
10
5
0
442
BS Glass/SN (Normalized 80/20 V%) with UPLM Additions at 625 C
Density (Percent of Theoretical)
.101 Illustration of total, open and closed
porosities of normalized 80/20 (BS glass/SN)
composites containing 10 and 20 V% 4.6 pm UPLM,
respectively, as a function of sintered density

45
40
35
30
25
20
15
10
5
0
40
35
30
25
20
15
10
5
0
443
BS Glass/SNAJPLM (4.6 pm) Composites 625 °C
Density (Percent of Theoretical)
.102 Illustration of the total, open and closed
porosities of 81/9/10 and 72.25/12.75/15 (BS
glass/SN/4.6 pm UPLM) composite compositions,
as a function of sintered density

444
addition gives a maximum in closed porosity that is comparable to both
of the other 10 V% UPLM addition concentrations (i.e. -10.5 versus -10.5
versus - 10.3 V% closed porosity maximum). However, the 72.25/12.75/15
(BS glass/Si3N4/4.6 pm UPLM) composition curve does not exhibit as high a
maximum in closed porosity as is expected (i.e. - 11.3 versus - 13.4).
It is not known why this particular composition yielded a significantly
lower maximum closed porosity.
Figures 4.103 and 4.104 illustrate the above relationship for the
normalized 60/40 (BS glass/SN) family of composites produced for this
study. Figure 4.103 depicts the total, open and closed porosities of
60/40 composites, without added porosities, at 625, 650 and 730 °C
respectively. It is evident from the figure that a maximum in density
is not achieved at 625 °C for these composites (at isothermal sintering
times of up to 144 h) due to the lack of development of the pore
structure to the final stages of sintering. It also is evident from the
figure that the pore characteristics, of these samples, change when the
isothermal sintering temperature is changed from 650 °C to 730 °C. This
perceived effect may also be a result of the relatively limited data set
obtained at 730 °C. However, this effect is also somewhat logical,
since significant bloating was observed at 820 °C. Thus, gas evolution
may be significant enough at 730 °C to keep porosity open to the more
advanced stages of sintering.
It is also important to note that the 60/40 composites, sintered
at 650 °C, exhibited a relatively high (i.e. - 7.5 %) maximum in closed
porosity. This may be a result of sealing-off of the relatively porous
BS glass/Si3N4 through viscous flow of the BS glass composite structure
in the final stages of sintering.
Figure 4.104 indicates that the pore structure of the 48/32/20 (BS
glass/SN/4.6 pm UPLM) composites also remains relatively undeveloped
after isothermal sintering times of 144 h. This is logical since
60/40/0 composition also exhibited this behavior. However, these

35
30
25
20
15
10
5
0
35
30
25
20
15
10
5
0
35
30
25
20
15
10
5
0
445
BS Glass/SN (60/40) Compacts
Density (Percent of Theoretical)
.103 The total, open and closed porosity of 60/40/0
(BS glass/SN/UPLM) composites as a function of
sintered density, at isothermal sintering
temperatures of 625, 650 and 730 °C respectively

Porosity (Percent of Theoretical Density)
446
BS Glass/SN/UPLM 4.6 pm (48/32/20), 625 C
65 70 75 80 85 90
Density (Percent of Theoretical)
100
Figure 4.104 Illustration of the total, open and closed
porosities of 48/32/20 (BS glass/SN/4.6 pm
UPLM) composites as a function of sintered
density

447
compacts did sinter to a maximum observed density of approximately 76 %
of theoretical density, indicating that some pore rearrangement must
have occurred.
Table 4.6 depicts a summary of the data portrayed in the figures
above. As mentioned above, the maximum closed porosity observed in this
study is - 15.6 V%. The corresponding open porosity, at said maximum in
closed porosity, was - 0.4 V%. Thus, the total porosity at the maximum
in observed closed porosity is - 16 V%. This is in excellent agreement
with literature values for the three-dimensional percolation threshold
for monosized, randomly placed spheres in three dimensions (i.e. - 16 V%
[83ZAL1]), and indicates that the percolation onset probably cannot be
exceeded using these techniques for additions of controlled porosity.
A comparison with pertinent literature indicates that the above
values are reasonable. In a similar study, Kata, et al. noted that it
was difficult to produce borosilicate glass-matrix composites (filled
with either cordierite or quartz) with closed porosities in excess of 13
V% [90KAT]. Kata, et al. used 18 pm average polystyrene microspheres
having a relatively wide size distribution, as visually observed (exact
data is not available as to the sizing basis used or the size
distribution measured) in tape cast and laminated compacts. Polystyrene
latex was used because the investigators found that it is a superior
candidate from the standpoint of non-solubility in tape vehicles, as
well as from the standpoint of thermolysis (in both N2 and in air).
The ceramic powders used had average diameters from 2.5 to 3.8 pm
in diameter. Thus, the average sphere diameter to pore channel diameter
ratio ranged from approximately 33 to 50 (assuming that the packing of
the ceramic powders can be reasonably modelled as monosized, spherical
RCP structure). Due to the lamination process, the porosity additions
were oval, or egg-shaped instead of spherical. Furthermore, the tape
cast system had a relatively large amount of organic concentration,

448
Table 4.6
Maximum Closed Porosity Relationships for All
Composite Compositions Investigated
Composition
(V%)
Porosity (V%)
Sintering
I.D. #
UPLM
Max.
Temp
Time
BS1
SN
V%
S2
D2
Clos
ed
Open*
Tot3
(°C)
(h)
12119001
100
AR
0
0
NA
NA
4.9
2.9
7.8
625
48
03209001
100
0
0
NA
NA
5.64
0.0
5.6
650
96
03209001
100
0
0
NA
NA
4.8“
1.1
5.9
625
12
05109102
95
0
5
4.6
M
8.1
1.1
9.2
625
9
01039101
90
0
10
4.6
M
10.3
0.6
10.9
625
12
05179102
85
0
15
2.4
B
10.9
1.2
12.1
625
18
05179101
85
0
15
4.0
Q
13.3
0.8
14.1
625
15
05069101
85
0
15
4.6
M
13.4
0.5
13.9
625
18
05099101
85
0
15
9.0
M
13.9
0.7
14.6
625
12
05069102
82.4
0
17.6
9.0
M
15.6
0.4
16.0
625
18
12109001
80
0
20
4.6
M
14.3
0.7
15.0
625
24
05079101
70
0
30
4.6
M
5.9
1.0
6.9
625
72
01049101
81
9
10
4.6
M
10.5
0.8
11.3
625
18
05119101
72.25
12.75
15
4.6
M
11.3
0.9
12.2
625
48
03219001
80
20
0
NA
NA
4.7
1.2
5.9
650
6
03219001
80
20
0
NA
NA
4.2
1.4
5.6
625
24
01249101
72
18
10
4.6
M
10.4
0.8
11.2
625
72
01069101
64
16
20
4.6
M
10.5
0.3
10.8
650
27
01069101
64
16
20
4.6
M
14.6
1.1
15.7
625
96
03199001
60
40
0
NA
NA
1.7
9.7
11.4s
820
1
03199001
60
40
0
NA
NA
3.6
5.1
8.7
730
36
03199001
60
40
0
NA
NA
7.5
1.2
8.7
650
102
03199001
60
40
0
NA
NA
1.3
18.0
19.3s
625
144
10109001
48
32
20
4.6
M
1.5
20.9
22.4s
625
72

449
Notes:
Table 4.6 (continued)
1. Borosilicate glass powder (AR denotes as-
received, all others are ball milled
2. S is latex diameter, D is dispersity, B is
bimodal, Q is quadramodal, M is monodisperse
3. Open and Total porosities (in V%) are at the
maximum observed in closed porosity
4. Indicates value was influenced by bloating
5. Indicates that the porosity in this system did
not mature to the final stages of sintering

450
other than the latex (i.e. binder, plasticizer etc.), as compared to the
current study. Other than these factors, the two studies are similar.
The maximum in closed porosity observed by Kata, et al. is
remarkably close to that observed in this study. Percolation theory was
not utilized to describe this phenomenon, however.
In a related study Yamamoto, et al. also investigated the effects
of latex addition up on the amount of included porosity (and, ultimately
dielectric properties) achievable [89YAM]. In this study, three
different microsphere chemistries were utilized, polymethyl methacrylate
(PMMA), polystyrene (PS), and polyethylene (PE). The PS spheres were
found to function most satisfactorily of the three in this application
as well. Two sizes of PS latex were investigated, one having an average
size of 7 pm, the other having an average size of 18 pm (it is not known
what the dispersity of these spheres were, or the basis used to
determine the particle size). The samples were prepared similarly to
those in the study of Kata, et al. Also, some samples were formed using
dry pressing of intimately mixed powders.
The 7 pm spheres were found unsatisfactory (they attribute this to
agglomeration and segregation to the tape surface). The researchers in
this study were able to produce samples having porosities as high as
approximately 11 V%. Said additions were found to reduce dielectric
constant by approximately 13%, and to slightly increase dielectric loss,
due to residual Ca from the pyrolyzed latex (the manufacturer used CaP04
in the fabrication of the latex).
4.4 Characterization and Modelling of Processed Materials
4.4.1 Characterization of Microstructure
Figures 4.105 and 4.106 illustrate representative microstructures
of ball milled BS glass compacts. From the figure, it is evident that
the microstructure of the 81 % dense sample includes porosity in the
size regime of 1 pm, while the porosity apparent in the 97 % dense

451
Micrograph illustrating the microstructure
representative of a pure ball milled BS glass
sintered to approximately 81 % density
Figure 4.105

Figure 4.106
Micrograph illustrating the microstructure
representative of a pure, ball milled BS glass
compact sintered to approximately 97 % of
theoretical density

453
sample is much more sporadic, but is not significantly smaller in size.
A major difference between these two samples is that the porosity in the
81 % dense sample is almost totally open (i.e. approximately 17.5 V% of
the porosity is continuous, and connected to the sample surface), while
almost all of the remaining 3 % of porosity in the 97 % dense sample is
closed (i.e. the open porosity is less than 0.05 %).
Figure 4.107 depicts the relationship between the inherent
porosity and the included porosity. The sample has a 10 V% addition of
4.6 pm UPLM, and was sintered to approximately 72 % of theoretical
density (approximately 27 and 1 V% open and closed porosities
respectively). It is evident from the figure that the porosity created
via the UPLM addition is significantly larger than the inherent
porosity.
Figures 4.108 through 4.112 illustrate the representative
microstructures of samples of sintered, ball milled, BS glass compacts
containing 5, 10, 15, 20 and 30 V% of 4.6 pm UPLM. These pictures are
of fracture surfaces and represent various densities ranging from 86.2
to 92.2 % of theoretical density.
It is clearly evident from these pictures that the cluster size
(i.e. the average of the number of interacting included pores in the
plane of each, representative micrograph) increases as the amount of
included porosity increases. As indicated above, the included porosity
in the composition containing a 30 V% addition of 4.6 pm UPLM is clearly
interconnected. Relatively large clusters are apparent in the 20 V%
UPLM addition samples as well. The cluster size decreases with
decreasing UPLM addition, until no clusters larger than two included
pores are evident in the sample containing 5 V% UPLM addition. A model
that estimates the effect of volume fraction included porosity
(monosized and randomly placed) upon pore cluster size, using pre¬
percolation, series cluster theory, is introduced in section 4.4.2
below.

454
Figure 4.107
Micrograph illustrating the contrast between
inherent and included porosity in a
representative, ball milled BS glass compact,
containing 10 V% of 4.6 pm UPLM and sintered to
approximately 72 % of theoretical density

'::x:
455
Illustration of the microstructure
representative of a BS glass compact containing
5 V% of 4.6 pm UPLM and sintered to 92.2 % of
theoretical density (7.7 and 0.1 V% closed and
open porosities respectively)
Figure 4.108

456
Figure 4.109
Illustration of the
representative of a ball
microstructure
milled BS glass
compact containing 10 V% of 4.6 pm UPLM and
sintered to 90.2 % density (9.7 and 0.1 V%
closed and open porosities respectively)

457
Figure 4.110
Illustration of the
representative of a ball
compact containing 15 V% of
sintered to 86.2 % density (13.4 and 0.4
closed and open porosities respectively)
microstructure
milled BS glass
4.6 pm UPLM and
V%

458
microstructure
milled BS glass
Illustration of the
representative of a ball
compact containing 20 V% of 4.6 pm UPLM and
sintered to 87.5 % density (12.1 and 0.4 V%
closed and open porosities respectively)
Figure 4.111

459
Figure 4.112
Illustration of
representative of
compact containing
sintered to 87.0 %
the microstructure
a ball milled BS glass
30 V% of 4.6 pm UPLM,
density (3.0 and 10.0 V%
closed and open porosities respectively)

460
Figures 4.113 through 4.116 illustrate representative
microstructures of ball milled BS glass samples containing 15 V%
additions of the four different size and size distributions of latex
investigated, as included porosity, in this study. Figures 4.117 and
4.118 depict the difference between the smallest and largest included
porosities of these same samples. It is quite evident, from these
figures, that the shape and outline of the smaller included porosity is
much less spherical than for the larger included porosity. This
illustrates the concept of obscured porosity. In this context, obscured
porosity is added porosity that is inefficient, from the standpoint of
maximization of closed porosity, since the size of the added porosity is
not large enough (i.e. the ratio of included porosity diameter to
inherent pore channel size is not large enough to make satisfactory
differential sintering occur). This phenomenon is described in section
4.3.4 above, in more detail.
Figure 4.119 illustrates the intersection of a polished surface
with a top surface of a representative sample (80/0/15 BS glass/Si3N4/4.6
pm UPLM) , in order to provide a basis for comparison of surface
roughness, included porosity size, and glass particle size. This figure
also gives qualitative insight toward the connectivity of surface-
connected pores with internal included porosity in the 15 V% 4.6 pm UPLM
compacts.
Figures 4.120 through 4.123 illustrate representative composites
containing Si3N4 as well as included porosity. Due to difficulties with
particulate pullout during polishing and in sample etching, it was not
possible to obtain satisfactory quantitative microscopy data pertaining
to the included Si3N4. However, these investigations were important in
that they indicated that there is little, if any, chemical reaction
between the BS glass and the Si3N4 (due to the relative ease of pullout
of the Si3N4 particulates, as well as to the sharp patterns that the
pullouts left).

461
Figure 4.113
Illustration
representative
of the microstructure
of a ball milled BS glass
compact containing 15 V% of 2.4 pm bimodal
latex, sintered to 87.3 % density (12.3 and 0.4
V% closed and open porosities respectively)

462
Figure 4.114
Illustration
representative
microstructure
milled BS glass
of the
of a ball
compact containing 15 V% of 4.0 pm quadramodal
latex, sintered to 86.0 % density (13.3 and 0.7
V% closed and open porosities respectively)

463
Figure 4.115
Illustration of the
representative of a ball
compact containing 15 V%
sintered to 86.2 % density
microstructure
milled BS glass
of 4.6 pm UPLM
(13.4 and 0.4 V%
closed and open porosities respectively)

464
Figure 4.116
Illustration
representative
of the microstructure
of a ball milled BS glass
compact containing 15 V% of 9.0 pm UPLM
sintered to 85.4 % density (13.9 and 0.7 V%
closed and open porosities respectively)

465
Figure 4.117 Close-up illustration of the included porosity
resultant from additions of 2.4 pm bimodal
latex (the smallest size latex used)

466
Figure 4.118 Close-up illustration of included porosity
created using additions of 9.0 pm UPLM (the
largest size latex used in this study)

467
Illustration of the intersection of a polished
surface with a top surface in a representative
sample (BS glass/4.6 pm UPLM 80/15)
Figure 4.119

468
Figure 4.120 Illustration of the microstructure
representative of the top surface of a
composite containing ball milled BS glass,
particulate silicon nitride and 4.6 pm UPLM
(72/18/10)

469
Illustration of the microstructure
representative of an etched fracture surface of
a composite containing ball milled BS glass
compact, Si3N4 and 4.6 pm UPLM (81/9/10)
Figure 4.121

470
The microstructure of a polished and etched
surface of a composite containing 80 V% BS
glass and 20 V% Si3N4 (small porosity is due to
differential etching of the glass matrix)
Figure 4.122

471
The microstructure of a polished and etched
surface of a composite containing 60 V% BS
glass and 40 V% Si3N4 (showing pullout of the
particulate Si5N4)
Figure 4.123

472
Thus, it was not possible to quantitatively monitor the various
aspects associable with the particulate Si3N4 additions investigated in
this study. However, it was possible to monitor segregation of latex
used in this study. It is also possible, using an extrapolation of
Stoke's settling theory, to predict if appreciable segregation could be
expected, of either of the other components in the composite system
studied.
Segregation measurements for the 4.6 pm UPLM used in this study,
were performed by measuring the volume fraction of included porosity
(using the grid technique) at the top, middle and bottom of an 80/0/20
BS glass/Si3N4/4.6 pm UPLM compact. The sample surface was polished.
This analysis also provided a basis for the comparison of porosities
measured using Archimedes and quantitative microscopy techniques.
The results are indicated in Table 4.7. Table 4.7 shows that the
included porosities measured at the top, middle and bottom of the
compact are within 0.8 V%. Since the standard deviation of the
measurements varied from 2.4 to 3.4 Vi, it may be concluded that no
measurable segregation of the 4.6 pm UPLM occurs within the samples
investigated in this study. The amount of porosity measured in this
compact using the Archimedes method was 14.1 + 0.1 V% (12.8 + 0.1 V%
closed porosity and 1.3 + 0.1 V% open porosity). Thus, the total
porosity, measured by Archimedes density, agrees with the porosity
measured using quantitative microscopy to within a standard deviation of
the analyses, in all instances of measurement. Assuming that all of the
porosity in the sample is attributable to included porosity (a
reasonably valid assumption, see Figure 4.119), this indicates that the
two techniques give comparable results. It is interesting to note that
the measured porosity values were greater when quantitative microscopy
(QM), in all instances. This may be a result of pore enlargement, due
to polishing. It may also be due to both the grid line thickness as
well as to the subjectivity of the experimenter.

473
Table 4.7
Segregation Test Data
Area of Sample
Total Number of
Grids Examined
Measured
Porosity (V%)
Standard
Deviation (+ V%)
Top
2100
14.9
2.7
Middle
2100
15.7
3.4
Bottom
2100
15.3
2.4
Notes: Sample Statistics:
85/0/15 (ball milled BS glass/Si3N4/4.6 pm UPLM)
Measured Porosities (Archimedes method):
Total Porosity: 14.1 + 0.1 V%
Closed Porosity: 12.8 + 0.1 V%
Open Porosity: 1.3 + 0.1 V%

474
A representative fracture surface was also investigated using QM.
The sample (90/0/10 BS glass/Si3N4/4.6 pm UPLM) had a measured total
porosity (using the Archimedes method) of 9.8 V% (9.7 and 0.1 V% closed
and open porosities). The QM data (taken using 2000 grid points total)
gave a total porosity of 9.0 + 2.6 V%. This indicates that the
relatively large variation of measurement (and not necessarily pore
enlargement) may be responsible for the higher porosities measured
(combined with the effects of grid width and experimenter subjectivity
mentioned above). It should be noted that the fracture surface may not
be random due to the influence that inclusions may have upon the
fracture path in a material [89JES]. Consequently, it is possible to
hypothesize that the data obtained using the Archimedes technique is
more accurate (from the basis of standard deviation).
In order to determine if either of the other composite
constituents (i.e. either the BS glass powder or the Si3N4 powder) would
be expected to segregate, an extrapolation of Stoke's settling theory
was used to provide an indication of relative settling rates within this
composite system. It should be noted that Stoke's theory is
quantitatively valid only for systems containing less than approximately
5 V% solids. For this application, Stoke's theory is extrapolated to
the solids loadings used in this study (i.e. - 52 %). Another
modification of the Stoke's theory for this application is that the
suspension viscosity (rather than the suspension liquid viscosity) is
used in the denominator of the Stoke's equation. Because these
extrapolations are not legitimate, the data should be used in a
qualitative sense only. These data are valuable only from the
standpoint of relative settling velocity. However, since the particles
within a highly loaded dispersion typically form an interconnected
network that would trap other particles that would have settled at
different rates, these data should represent a maximum in segregation
potential. Thus, this application of modified Stoke's theory should be

475
legitimate for prediction of the degree of segregation, during slip
casting, within this composite system. The modified Stoke's equation
used for this exercise is
r_ d2g(pp-pL)
18r|s
where v is the particle settling velocity, d is the respective particle
diameter, p¡ is the density of the respective particle (P) or suspension
liquid (L), g is the acceleration due to gravity and r\s is the viscosity
of the suspension.
Table 4.8 depicts the relative velocities of the maximum, median
and minimum particle sizes of each of the constituent powders used to
make composites in this study. Said velocities were determined using
the Stoke's equation depicted above, then normalizing the respective
particle settling velocities to that of the median-sized 4.6 pm UPLM.
It is evident from the table that the wide size distribution powders
(i.e. both BS glasses) have a very wide range of relative settling
velocities (i.e up to six orders of magnitude variation in settling
velocity). Thus, it is reasonable to expect segregation of the BS glass
particles within the composites produced for this study. Similarly, the
velocities predicted for the Si3N4 powder used in this study vary up to
three orders of magnitude. Conversely, the latexes used exhibit a
maximum variation in relative settling velocity of approximately two
orders of magnitude. However, using the calculated velocities for the
median particle sizes of each of the composite constituents (e.g. 0.775,
0.620 and 1.000 for the ball milled BS glass powder, the Si3N4 powder and
the 4.6 pm UPLM powder, respectively), only minor differences in
settling velocity are to be expected for the major portions of each of
the powder constituents. Thus, it is reasonable to assume that the
segregation occurring within this composite system is less than or, at

476
Table 4.8
Relative Settling Velocities of the Powders Used
in this Study
Powder
Size (pm)
Relative Velocity
As-Received BS Glass
Maximum
58.00
802.06
Median
5.03
6.032
Minimum
0.18
0.007
Ball Milled BS Glass
Maximum
7.60
13.968
Median
1.79
0.775
Minimum
0.10
0.002
As-Received Si3N4
Maximum
4.73
9.168
Median
1.23
0.620
Minimum
0.48
0.094
2.4 pm (Mean Size)
Bimodal Latex
Maximum
4.88
1.104
Median
3.05
0.432
Minimum
1.13
0.059
4.0 pm (Mean Size)
Quadramodal Latex
Maximum
10.00
4.644
Median
8.93
3.704
Minimum
1.63
0.122
4.6 pm (Mean Size)
UPLM
Maximum
5.38
1.342
Median
4.64
1.000
Minimum
3.63
0.610
9.0 pm (Mean Size)
UPLM
Maximum
12.13
6.829
Median
9.00
3.762
Minimum
6.13
1.743
Notes: Maximum and minimum sizes are the largest and smallest
sizes measured respectively
Median is the mass based median size
All relative velocities are normalized to the median
velocity of the 4.6 pm (mean size) UPLM powder

477
most, equal to the amount that would be observed within each of the
ceramic powders (i.e. the ball milled BS glass powder and the Si3N4
powder), under similar dispersion conditions.
In order to determine the relative amounts of included pore
shrinkage in each of the compositions representative of this system, the
average area of the included porosity in each of the representative
compositions was measured in a manner similar to that used to measure
latex sphere diameters (the optical comparator method), as described in
section 3.2.2. The measured pore diameters were then converted to plane
intersection areas (assuming a perfectly circular plane-pore
intersection). These converted areas of intersection were then averaged
(Save) and converted to the equivalent pore diameter (D) using the
methods and assumptions of Fullman [53FUL,]. These assumptions include
monosized, perfectly spherical pores, intersected by a perfect plane,
totally at random. The relationship involved is
(l)5ave.
ft
Table 4.9 depicts the calculated equivalent pore diameters for the
compositions tested. In all but two cases, monosized latex was used to
create included porosity. Since the methods used to determine D are
number based, they should be directly comparable to the number basis
average size of each of the latexes used to create the included
porosity.
The results indicated in Table 4.9 are enigmatic. In general, the
standard deviations of these measurements are quite large, having a
great affect upon the analysis of this data. The difference between the
measured and calculated pore size and the included latex size apparently
increases with increasing size. This is contrary to differential
sintering theory (i.e. it is expected that the smallest included

478
porosity shrink the most during densification). This may be due to the
fact that the two smallest latexes, used for added porosity (i.e. the
2.4 pm bimodal distribution, and the 4.0 pm guadramodal distribution
latexes) are not monosized. Therefore, it is expected that the smallest
included pores would densify first, thereby skewing the pore size
distribution to larger sizes. One mode of the bimodal distribution of
the 2.4 pm latex is centered around 3.1 pm, while the other was centered
around approximately 1.8 pm. If the 1.8 pm mode pores were removed, the
resulting measured included pore size (i.e. 2.2 pm) would make sense,
indicating an approximate 30 % reduction in the diameter of the larger
size mode of included porosity. This is enforced by the fact that the
other 2.4 pm included porosity sample investigated was not significantly
densified, and had an average pore diameter of 2.4 pm (which is in
agreement with the average latex size).
This hypothesis is further reinforced through the examination of
the standard deviations of the two 2.4 pm bimodal samples investigated.
The variance of the later sample was larger than for the former,
indicating the tightening of the pore size distribution (as would be
expected as a bimodal system evolves toward a more monomodal system).
A pore size increase was also observed in the 4.0 pm quadramodal
latex included porosity samples (05179101 group) as well. In this case,
however, the standard deviation did not decrease with increasing density
between the two samples. This may be due to the large statistical
variance, since the amount of densification was small (i.e. 0.8 V%), and
since both standard deviations are quite large.
Perhaps the most surprising result depicted in Table 4.9 is that
of the measured pore diameter for the 9.0 pm UPLM sample (05099101).
The 6.9 pm value represents a 23.3 % reduction in diameter from the 9.0
pm UPLM addition used to create the included porosity. For comparison,
an analogous 4.6 pm UPLM sample experienced a reduction in diameter of
only 13 %. This is definitely not expected. In order to determine if

479
Table 4.9
Calculated Equivalent Included Porosity Diameters
of Representative Compositions
I.D. #
V%
Lat
Latex
Size
Porosity
(V%>
Microscopic
Measured/Calculated Data
(pm)
Ds
Closed
Open
s
u
r
f
a
c
e
Savc (pm2)
D
(pm)
n
S*"
05109102
5
4.6
M
7.6
0.1
F
6.0
3.3
3.4
48
01039101
10
4.6
M
0.8
26.7
P
9.8
3.6
4.3
76
01039101
10
4.6
M
1.2
17.6
P
10.1
3.4
4.4
69
01039101
10
4.6
M
9.7
0.1
F
7.5
2.9
3.8
100
01049101
10
4.6
M
1.8
10.7
P
10.6
2.9
4.5
79
01049101
10
4.6
M
10.5
0.8
P
9.0
3.6
4.1
71
01049101
10
4.6
M
10.5
0.8
F
9.1
3.4
4.2
100
05179102
15
2.4
B
1.7
19.9
P
3.1
1.5
2.4
100
05179102
15
2.4
B
9.9
0.4
F
2.6
1.1
2.2
100
05179101
15
4.0
Q
13.3
0.8
F
11.5
11.2
4.7
100
05179101
15
4.0
Q
12.9
0.4
F
12.8
12.1
4.9
99
05069101
15
4.6
M
13.4
0.5
F
8.5
3.4
4.0
100
05119101
15
4.6
M
1.6
15.3
P
8.0
3.1
3.9
100
05099101
15
9.0
M
13.9
0.7
F
25.0
10.1
6.9
79
12109001
20
4.6
M
12.1
0.4
F
6.6
2.5
3.5
100
12109001
20
4.6
M
12.1
0.4
F
7.1
2.4
3.7
100
05079101
30
4.6
M
3.2
9.8
P
3.5
1.8
2.6
100
Notes: V% Lat is V% latex
o„ is standard deviation
Ds is distributions type (M = monosize, B = bimodal, Q
= quadramodal
Surface is viewed surface type (F = fracture, P =
polished)
n is the number of pores measured
I.D. #'s 01049101 and 05119101 contain 9 and 12.75 V%
Si,N4 respectively

480
the sample investigated was representative, quantitative microscopy
(standard point count method) was used to determine the volume fraction
of included porosity. The measured volume fraction included porosity
was 15.5 V% + 1.78 V% (1000 point count). This agrees, to within a
standard deviation, with the closed porosity measured using Archimedes
techniques. Therefore, it was a representative sample from the
standpoint of volume fraction porosity. However, this reduction in pore
size correlates to a reduction of 45 V% of the pore volume. This would
result in a maximum included porosity of only 6.8 V%. Since the
measured porosities were in excess of 13 V%, this is impossible.
It should be noted that the standard deviation of S“vc in this
sample is very large (as would be expected). The included sphere
diameter would be 8.2 pm considering the maximum Save allowed within one
standard deviation. This would result in a sphere shrinkage of only 9%
(volume shrinkage of 24 %, and included porosity reduction of 3.6 %),
which is still too large, but more reasonable.
A possible explanation for this enigmatic behavior is that the
path of the fracture surface is influenced by the included porosity, or
that the standard deviations typical of this type of analysis are too
large for accurate analyses. Thus, the analysis was probably skewed in
some way.
Included pore clustering was determined by recording the average
number of interacting included pores, per included pore cluster, in the
plane of the micrograph. Table 4.10 depicts the clustering data of the
included porosity of the samples investigated. Again, it is readily
evident that the standard deviations of these measurements are
relatively large. As above, this is also due to the method of the
measurements (i.e. the measurement of a distribution of cluster sizes).
However, the cluster size was observed to increase with increasing V%
latex addition when comparing correlatable samples.

481
Table 4.10
Cluster Data of Representative Samples
I.D. #
V%
Lat
Latex
Size
Porosity
(V%)
Microscopic
Measured/Calculated Data
(pm)
Ds
Closed
Open
s
u
r
f
a
c
e
Cluster Statistics
#
Cl
#
ISP
ACN
05109102
5
4.6
M
7.6
0.1
F
52
61
1.17
0.47
01039101
10
4.6
M
0.8
26.7
P
44
52
1.18
0.66
01039101
10
4.6
M
1.2
17.6
P
48
58
1.21
0.41
01039101
10
4.6
M
9.7
0.1
F
189
267
1.41
0.69
01049101
10
4.6
M
1.8
10.7
P
61
71
1.16
0.37
01049101
10
4.6
M
10.5
0.8
P
113
149
1.32
0.62
01049101
10
4.6
M
10.5
0.8
F
138
193
1.40
0.71
05179102
15
2.4
B
1.7
19.9
P
90
140
1.56
0.79
05179102
15
2.4
B
9.9
0.4
F
235
404
1.71
1.16
05179101
15
4.0
Q
13.3
0.8
F
115
159
1.38
0.73
05179101
15
4.0
Q
12.9
0.4
F
99
157
1.59
0.93
05069101
15
4.6
M
13.4
0.5
F
120
172
1.43
1.01
05119101
15
4.6
M
1.6
15.3
P
94
122
1.33
0.59
05099101
15
9.0
M
13.9
0.7
F
58
80
1.38
0.76
12109001
20
4.6
M
12.1
0.4
F
272
491
1.81
1.22
12109001
20
4.6
M
12.1
0.4
F
226
391
1.73
1.16
05079101
30
4.6
M
3.2
9.8
P
208
522
2.51
1.95
Notes: V% Lat is V% latex
Ds is distributions type (M = monosize, B = bimodal, Q
= quadramodal
Surface is viewed surface type (F = fracture, P =
polished)
# Cl is the total number of clusters measured
# ISP is the number of included spherical pore units
measured
ACN is the average cluster number calculated
oD is standard deviation of the ACN
I.D. #'s 01049101 and 05119101 contain 9 and 12.75 V%
Si3N4 respectively

482
Furthermore, it is evident that there is little if any dependence
of average cluster number (ACN) upon included sphere size or size
distribution (it is possible that the smaller, wider size distribution
latexes had a slightly larger ACN, but this is not conclusive, since all
are within one standard deviation of each other).
4.4.2 Modelling of Included Porosity
Series cluster theory, as outlined in section 2.4.1 may be used to
predict the average cluster number of randomly placed spheres upon a
three dimensional lattice structure [64SYK]. The mean cluster size, as
a function of sphere concentration (Sp), may be determined by the
relationship
where n is the number of spheres in the cluster of interest, an is the
number of possible configurations for a cluster of size n and p is the
fraction of the lattice or space occupied by the spheres. The number of
configurations of each cluster size for both bond and site clustering of
diamond, simple cubic (SC), body centered cubic (BCC) and face centered
cubic (FCC) lattices are depicted in Table 2.6. It is now proposed that
this model may be utilized to predict the average cluster number for
random close packed (RCP) systems as well. This is an extension of the
theories covered in section 2.4.2.
Zallen showed that, even though RCP structures do not exhibit a
characteristic lattice structure (as do the ordered structures mentioned
above), they may be modelled as an interpolation between SC and BCC
structures (see Figure 2.15) [83ZAL2]. Figure 4.124 illustrates the
Napierian logarithm of the number of possible configurations of cluster
size n as a function of cluster size n for bond and site cluster models,
for the packing types mentioned above. The interpolated estimate for

12
11
10
9
8
7
6
5
4
3
2
1
0
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
0
e 4
483
Key:
FCC
--—
BCC
■ •. .X ■ ■■
RCP
— 0—
SC
â– i I â–  >
Diamond
i I
10 11 12
3 4 5 6 7 8 9
Cluster Number
124
Natural logarithm of the number of cluster
configurations (ln(an)) possible versus cluster
size (n) for site and bond clustering of
diamond, SC, RCP, BCC and FCC "structures"

484
RCP packing structures is also included. The interpolation was obtained
by standard weighted averaging between SC and BCC values (based upon
relative packing efficiencies (PEs)). It is evident from the figure
that this relationship is well defined, becoming linear, for each type
of packing, at cluster sizes larger than 2 for FCC site and bond, and
BCC bond, 3 for BCC site and RCP and SC bond, 4 for RCP site and diamond
bond, and 5 for SC and diamond site. The corresponding interpolated
RCP values (an's) for bond and site clustering are depicted in Table
4.11. This table indicates the equivalent next-nearest-neighbor
coordination number for RCP packed structures may be estimated by - 7.5
for site clustering and - 13 for bond clustering. The values for an for
the other types of packing are located in Table 2.6.
Table 4.12 depicts the linear regression modelling data for each
type of packing. It is evident from the table that the linear
correlations of these relationships are excellent. These data may be
utilized, in a novel manner, to estimate the onset of percolation.
Due to the linear relationship described above
In(an) ~mn+b
where n is the cluster number, m is slope and b is the intercept at the
ordinate. This may be modified to
ai2=Cexpmn
where
C-cons tant=exp¿.
Thus, the relation for mean cluster size (Sp) becomes
Sp“l+2£:“Cexpmnpn
where p is the fraction of the lattice filled. The relation of p° may
also be modified to

485
Table 4.11
Interpolated Cluster Number Values for RCP Packing
Cluster Number (n)
a„
Site
Bond
1
1
1
2
7.5
12.9
3
48.8
84.8
4
211.0
536.3
5
1013.0
3350.1
6
4545.7
20323.7
7
20875.4
124370.0
8
87676.7
739709.5
9
4476031.2

486
Table 4.12
Linear Regression Data of an
Site Clustering
Packing
Type
Regression Range
Regression Data
Minimum
n
Maximum n
Slope
(ln(a„)/n)
Intercept
(ln(aj )
Correlation
Coefficient
(R)
FCC
2
6
1.810830
-1.06373
0.99978
BCC
3
8
1.532376
-0.57278
0.99992
RCP
4
8
1.508447
-0.64621
0.99989
SC
5
9
1.275351
-0.29632
0.99996
Diamond
5
10
0.929321
0.024476
0.99990
Bond Clustering
Packing
Type
Regression Range
Regression Data
Minimum
n
Maximum n
Slope
(ln(aj/n)
Intercept
(ln(a„) )
Correlation
Coefficient
(R)
FCC
2
7
2.280134
-1.40713
0.99994
BCC
2
9
1.848492
-0.96318
0.99992
RCP
3
9
1.810573
-0.96055
0.99999
SC
3
10
1.501755
-0.52993
0.99994
Diamond
4
12
1.029219
-0.06587
0.99993
a„ is the possible number of cluster configurations of
size n
Notes

487
pn=expnin*p'
thus allowing manipulation of Sp to the desired form of
Sp=l+E£:“Cexp [n(j”+ln(p)n .
The percolation onset (pc) is defined as the lattice fraction at which Sp
becomes infinite, or undefined. Therefore, pc for each lattice type (as
well as for the interpolated RCP packing structure) occurs at the value
of p that delineates where the series for Sp changes from a convergent
series approximation to a divergent one. Said change from convergence
to divergence may be found using the integral test [81GIL], which states
that if a series converges, so will its corresponding integral. Since
the 1 in front of the series is irrelevant, with regard to convergence
or divergence of the series, it is sufficient to solve the following
integral
Sp“|“cex p [n(m+ln(p)]dn
then to determine the divergence boundary from the solution of,
m+ln (p)
exp
[n (m*In (p)
| n—n
ln=2 â– 
The above solution shall be convergent (with respect to p) when
m+ln(p)^0
Table 4.13 shows the results of the above solution, as well as a
comparison of the results of the above method with those in the
literature [83ZAL2]. From the table, it is evident that the solutions
agree closely, but not exactly with published values. These variances
range from - 8 % to - 18 %. It is interesting to note that the general
trends in these values mirror each other closely. This gives further
credence to the general accuracy of the above, series divergence model.

488
Table 4.13
Estimated Percolation Onsets
Site Mechanism
Packing
Type
pc Site
PE
PEpcsi“
Calcu¬
lated
Liter¬
ature
Calculated
Literature
FCC
0.164
0.198
0.7405
0.121
0.147
BCC
0.216
0.245
0.6802
0.147
0.167
RCP
0.221
0.27“
0.637'
0.141
0.16“
SC
0.279
0.311
0.5236
0.146
0.163
Diamond
0.395
0.428
0.3401
0.134
0.146
Bond Mechanism
Packing
Type
pc Bond
Z
i7 _ Bond
¿Pc
Calcu¬
lated
Liter¬
ature
Calculated
Literature
FCC
0.102
0.119
12
1.23
1.43
BCC
0.158
0.179
8
1.26
1.43
RCP
0.164
N/A
7.5
1.22
N/A
SC
0.223
0.247
6
1.34
1.48
Diamond
0.357
0.388
4
1.43
1.55
Notes
Indicates experimental (not calculated) literature
values

489
It is interesting that the literature values represent an upper limit of
the measured porosity values in Table 4.6, while the values calculated,
using the above methods, indicate a lower limit (of the group of samples
giving the greatest closed porosities (i.e. the 15 V% 4.6 pm, 9.0 pm
UPLM and 4.0 pm quadramodal latex additions, the 17.6 V% 9.0 pm UPLM
addition and the 20 V% 4.6 pm UPLM addition samples) to the measured
porosity values.
The source of the differences between the solution values and the
published values is not known, since the linear approximations were
extremely accurate. However, there is also some discrepancy in the
literature regarding the exact values of percolation onsets.
Regardless, the above method represents a novel and greatly simplified
method of determining percolation onsets. This method also is (to the
knowledge of the author) the only non-experimental method, currently
available, through which the onset of percolation may be estimated for
RCP structures.
The above model may also be modified to approximate cluster
numbers in RCP structures of pores. The expected value of Sp may be
calculated using the interpolated values indicated in Table 4.11. In
order to accurately estimate the average cluster number (Sp) for this
approximation, it is necessary to use a nominal number of terms in the
series. It also is evident, from the series equation for Sp, that the
necessary number of terms in the series increases with increasing p,
requiring infinitely many terms at the percolation threshold.
The necessary number of the terms in the series may be determined using
a modification of the integral test utilized in the
convergence/divergence test discussed above [81GIL]. The integral test,
when used in this context, states that the error of a convergent series,
computed to the N111 term, is no greater than the corresponding integral
computed from N + 1 to infinity. For purpose of this discussion, it

490
will be assumed that it is sufficient to model Sp using the interpolated
terms in Table 4.11 (an estimate of error is included).
From Table 4.13, it is evident that both the 20 and 30 V% UPLM
addition materials are in excess of the calculated bond percolation
threshold (pc bond), and that the 30 V% UPLM addition exceeds pc site as
well. It is interesting to note, however, that in the green state, the
actual p of the 30 and 20 V% UPLM addition samples is approximately 22.5
and 14.4 V% respectively. Therefore, percolation of the pore structure,
in the 20 V% UPLM samples, does not necessarily occur until significant
densification (i.e. to - 80 % of theoretical density) of the structure
occurs. In the 30 V% UPLM samples percolation is probably (but not
necessarily, see Table 4.13, pc site literature value) present from the
green stage of processing.
It is evident, from the above discussion, that the type of
clustering occurring in this system (i.e. site versus bond clustering)
may be postulated by using the cluster number model discussed above,
then comparing these predictions with the measured Sps (from the ACN
column of Table 4.10). Figure 4.125 illustrates the relationship of Sp
as a function of p, using the series method for RCP (both site and bond
clustering mechanisms). Figure 4.125 shows that Sp bond increases at a
greater rate than does Sp site. This also accounts for the lower pc
characteristic of the bond mechanism. Also apparent in the figure is
the two dimensional approximation of Sp (i.e.the three SpM) as well as
the estimate of error of both the two and three dimensional Sp
approximations. The estimate of error is defined (in this case) as the
value of the last term calculated. This value increases greatly as pc
is approached, and thus, is an indicator of the inaccuracy of the
approximation. The accuracies of these approximations are adequate for
the purpose of this comparison, however.
Figure 4.126 shows the above-mentioned two dimensional
approximations of Sp (site and bond, for RCP structures) as well as

491
Sp as a function of p (predicted using the
series approximation method) for both two and
three dimensional site and bond clustering
mechanisms in RCP structures, with associated
estimates of error
Figure 4.125

9
8
7
6
5
4
3
2
1
O
9
8
7
6
5
4
3
2
1
O
492
Site Clustering
Key:
■ ■«— Measured
- - Calculated
■■■+■■■ • Estimated Error of Calculation
Bond Clustering
• ■
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
Volume % of RCP Structure Filled (p x 100)
Measured versus calculated cluster size as a
function of percent of RCP "structure" filled
for representative BS glass/4.6 pm UPLM
composites, below the onset of percolation
. 126

493
representative values measured from microscopic samples (4.6 pm UPLM at
5, 10 and 15 V% additions, see Table 4.10). The approximation is
limited to V% values near the onset of percolation for the bond
clustering mechanism. Furthermore, the measured values are corrected
for the p values through the relation
UPLMaddi tion* P gieencompact
percp
where p is the volume fraction of the RCP "structure" filled, VFUPLM
is the volume fraction UPLM addition, PErcp is the packing efficiency of
RCP structures (0.637 was used), and pgreCTOTnp.„ is the fraction of
theoretical density of the green compact of the particular composite
composition of interest (see Figure 4.52). This model assumes that the
clustering configuration does not change between the green and densified
states. This potential source of error was minimized by using data from
samples having volume fraction additions of UPLM below the percolation
onset for either clustering mechanism. From the figure, it is apparent
that the site clustering mechanism models the measured cluster number
much better than does the two dimensional, bond clustering
approximation. Thus, it may be surmised that the site mechanism of
clustering was measured in this study. This is logical, since it is
expected that site filling (and not necessarily bonding between
previously filled sites) of the RCP "structure” is responsible for the
percolation phenomena observed. The source of the difference between
measured and approximated, two dimensional Sp values at higher p values
is not known, but is probably relatable to the microstructural changes
that occur during thermal processing.
The above model may also be used to predict maxima in closed
porosity. In materials that are isomorphous in three dimensions, the
volume fraction of an included phase is equivalent to the area fraction

494
of a plane randomly placed through the sample [68DEH]. This fact is
commonly used in the field of quantitative microscopy to correlate
measured area fractions of phases to actual volume fractions (and was
used above to determine included porosity concentrations). This
phenomenon, coupled with the relationship between uniform sphere
diameter and measured crossectional area of planes, randomly placed
through said spheres (discussed above) may be used to determine the
number of spheres intersecting the surface (Nsls) of a unit volume (in
cm3) of a compact of known surface area to volume ratio (S/V in cm'1)
through the equation
Usis-
(VFporex|)
((-£) (—£—)2)
6 10000
where VF^ is the volume fraction of included porosity, and D is the
UPLM diameter in pm. The value of NS1S is equivalent to the number of
clusters intersecting (Nsic) the surface (assuming no interaction between
surface connected clusters). Cluster theory is then utilized to
determine the number of surface connected spheres (NSOJ) per unit volume
(cm3) through the relation
Xscs-Xsisx(-f) •
The corresponding volume (in cm3) of the surface connected spheres (Vscs)
per unit volume is determined through the relation
., , 4 IT * i
scs“ T X 20000
D )3x(|+^cs)-
These equations are based upon the assumption that the average volume of
a surface intersected sphere is equal to one half of the volume of the
corresponding sphere. Another assumption is that the average number of
spheres connected to the surface is equal to one half the average

495
cluster number (Sp).
The volume percent total porosity (V%lol) of the compact
is
V%tot=100xVFpore
and the volume percent open porosity (V%op) is
V%op = 100xVscs.
Finally, the volume percent closed porosity is equal to
^cp=V%tot-
v%
op’
Figure 4.127 depicts these relationships as a function of volume percent
total porosity, and as a function of RCP (site) spaces filled (p) for a
representative hypothetical series of samples (i.e. 4.6 UPLM included
porosity in a disk-shaped compact of 25.4 x 2 mm) containing only
included porosity. Since a greater accuracy is required with these
approximations than with the cluster measurement investigations
discussed above, the number of terms used to determine Sp was increased
to 30, from 8 (the linear regression outlined in Table 4.12 (RCP site)
was extrapolated to an n value of 30). This afforded acceptable
accuracy slightly below pc. However, at pc an infinite number of terms
is required to determine Sp (which is also infinity). Again, it should
be noted that this model assumes no interaction between clusters. This
assumption is not valid as p approaches pc. However, from Figure 4.127,
it is evident that the error resultant from said simplification is not
detrimental for p slightly below pc.
Table 4.14 depicts the maxima in V% closed porosities and other
relevant data for compacts of discoidal shape and constant diameter, but
of varying thicknesses. Data for monospherical included pore sizes of

V% Open/Closed/Total Porosity Volume Percent Open/Closed Porosity
496
161
15 -
14 -
13 -
12 -
A \ :
11 -
X \
10 -
w
9 -
A L-
8 -
s s
7 -
Closed Porosity :i
6 -
\
5 -
A : i
4 -
y - »
3 -
/ '
2 -
^ Open Porosity —♦v
1 -
S
0 -J
i i 1 i 1 i i 1 1 1111111—
0 2 4 6 8 10 12 14 16
Volume Percent Total Porosity
Fraction of RCP (Site) Spaces Filled (p)
Illustration of closed and open porosities
versus V% total porosity and of total, closed
and open porosities versus p calculated using
pre-percolation cluster theory
Figure 4.127

497
Table 4.14
Effects of Disk Thickness and Included Sphere Size
Upon Maximum Closed Porosity
Disk
Thickness
(mm)
Included
Sphere
Diameter
(pm)
Maximum
Calculated
V% CP
Calculated Percent
Porosities at
Maximum Closed
Porosity
p at
Maximum
Closed
Porosity
Total
Porosity
Open
Porosity
0.1
4.6
11.51
13.00
1.49
0.204
1.0
4.6
13.57
14.00
0.43
0.220
2.0
4.6
14.21
15.00
0.79
0.235
5.0
2.0
15.31
16.00
0.69
0.251
5.0
4.6
14.62
15.00
0.38
0.235
5.0
9.0
14.25
15.00
0.75
0.235
10.0
4.6
14.99
16.00
1.01
0.251
100.0
4.6
15.49
16.00
0.51
0.251

498
2.0, 4.6 and 9.0 m is also included. From Table 4.14 it is evident
that the maximum amount of closed porosity (as well as p at said
maximum) decreases with decreasing disk thickness. The maximum amount
of closed porosity also decreases with increasing included pore
diameter. The former effect is reasonable, since the surface area to
volume ratio increases as disk thickness is decreased. Furthermore, it
is expected that clusters of spheres would interact more with the
surfaces of a thinner compact. This should be a caveat when designing
included pore systems for thin substrate applications (which is common
in high speed electronic packaging). The later effect was not observed
experimentally, however. This is because the model does not take the
effects of differential sintering into consideration. Therefore,
increasing the included porosity size serves only to reduce the
thickness to diameter ratio where this model is concerned. This is
important in that it provides further impetus to use included sphere
sizes that are small compared to the sample thickness. Thus, when
designing included porosity multilayer packages, with the goal of
maximization of closed porosity, it is important to maximize the ratio
of layer thickness to included pore diameter. It is interesting to note
that, with the exception of the first two entries, the value of p at
maximum calculated closed porosity in Table 4.14 is always between the
calculated and the literature values of pc (site) for the RCP structure
(see Table 4.13). This gives further credence to the accuracy of the
series approximation model.
Again, it should be noted that all of the above quantitative
analyses were not possible for the Si,N4 additions, due to problems
related to sample preparation and quantitative microscopic analysis of
composites containing Si3N4. This should be an area of focus for future
research.

499
4.4.3 Characterization of Dielectric Properties
Both dielectric constant (K) and dielectric dissipation factor
(tan(6)) were measured as explained in section 3.7.2. Figure 4.128
illustrates the dielectric constant of several representative (hermetic)
samples, investigated in this study, as a function of frequency. Figure
4.129 illustrates the loss tangent for the above representative samples
as a function of frequency. For comparative purposes literature values
for the pure, bulk BS glass are also included. The dotted portions of
the data in Figure 4.128 indicate that the accuracy of the impedance
analyzer-test fixture was questionable, therefore, the lines are
extrapolated at frequencies below 100 kHz, and none of the data measured
below 100 kHz are included. From Figure 4.128, it is evident that the
dielectric constants of the specimens prepared for this study do not
change appreciably with changing frequency. It is also evident that the
dielectric property characteristics of these materials closely follow
the general character of the corresponding literature data. It is
interesting to note the effects of included porosity, and of Si,N4
inclusions upon dielectric constant.
The dissipation factor data (Figure 4.129) agrees well with the
available literature data. The sporadic nature of the data (see closeup
of test data, Figure 4.129) is probably due somewhat to errors
associable with measurement. However, a general trend of increasing
tan(6) with increasing frequency is also indicated in the literature
data. This should be considered when designing for high frequency, low
loss packaging applications. However, the excellent agreement with the
tan(6) literature data, in general, indicates that the specimens were
not contaminated during processing. This is important in that it
indicates that the organics were removed sufficiently during thermal
processing. It also indicates that ball milling and subsequent
processing did not introduce significant contamination to the system.

Dielectric Constant
500
4.8
4.7
4.6
4.5
4.4
4.3
4.2
4.1
4.0
3.9
3.8
3.7
3.6
3.5
1 23456789 10 11
Log Frequency (Hz)
Source for Literature Values:
Air Force Materials Laboratory (prepared by the
Electronic Properties Information Center,
Hughes Aircraft Company, Culver City, CA)
-
Key:
-
—80/20/0, 95.8 % Dense
-•-o- 85/0/15, 4.6 pm UPLM, 87.7 % Dense
—
-■«- 85/0/15, 4.6 pm UPLM, 86.2 % Dense
85/0/15, 9.0 pm UPLM, 86.8 % Dense
-
«...
...» «, «, m m m •
#
Literature Data (Coming 7070 Glass)
\ â– 
-
■ ■•■■■■■■•■••■a ■ mmm ■ mam •(&
1 1 1 1 1 1 1 1 1 1 1 1 1 1 llm i'V'I V 1 1 iff
Dielectric constant (K) as a function of
frequency for representative samples
investigated in this study as well as pertinent
literature data
Figure 4.128

tan(ó)
501
0.0050
0.0040
0.0030
0.0020
0.0010
0.0000
1
Key: Test Data
•— . 85/0/1 5, 4.6 firn UPLM,
87.7 % Danse
— ■■*•■ ■ 85/0/15, 4.6 fim UPLM,
86.2 % Danse
-■■*•■-85/0/15, 9.0 fim UPLM,
86.8 % Dense
— — * — ■ 80/20/0, 95.8 % Dense
0.0012
0.0010
0.0008
0.0006
0.0004
0.0002
0.0000
Closeup of Test Data
â–²
i
23456789 10 11
Log Frequency (Hz)
Source for Literature Values:
Air Force Materials Laboratory (prepared by the
Electronic Properties Information Center,
Hughes Aircraft Company, Culver City, CA)
Dielectric dissipation factor (tan(S)) as a
function of frequency for representative
hermetic samples investigated in this study,
pertinent literature values are also included
Figure 4.129

502
Figures 4.130 and 4.131 illustrate measured dielectric constant
data of the pure BS glass system (both with and without 4.6 pm included
porosity). Figure 4.130 depicts this data with corresponding
traditional modelling (parallel and perpendicular slabs, logarithmic and
Maxwell models), while Figure 4.131 models the data using effective
medium theory (EMT). The dielectric constant values of 4.1 and 1 were
used for the BS glass and porosity phases respectively. From the
figures it is evident that, with few exceptions, the dielectric constant
data follow the same relation, regardless of the type of porosity. Said
relation is quite linear and generally falls between the Maxwell and
logarithmic models (see Figure 4.130). This linear relation is also
well modelled by the EMT approximation for perfectly spherical pores
within a matrix (i.e. c/a =1). It is interesting to note that there is
a slight difference between the Maxwell and EMT (c/a = 1) models.
The dielectric constant data fall between the Maxwell and
logarithmic models at lower densities, and are well modelled by the
Maxwell equation at higher densities, as is expected from the evolution
in pore structure during sintering. During the densification process
the pore structure changes from a continuous structure to a discrete
dispersion of spheres. The logarithmic model approximates a continuous
structure, while the Maxwell model approximates a discrete distribution
of spheres within a matrix. Therefore, "switching" of these data, from
logarithmic to Maxwell models, is expected.
Data from other studies have indicated similar relationships
between percent density and K. The K data, in a study by Cross and
Gururaja on microballoon-filled cement composites, fit well between
relations modelled by logarithmic and Maxwell models [86CRO]. The K
data of Cao, et. al, found during a study of porous colloidal silica,
had greater scatter, but still fit mostly between the Maxwell and log
model relations [89CAO]. Other data on porous silica shows a deviation
of K from the Maxwell model at very low densities (- 20 % dense), but a

503
4 -
I-
Z
< 3
I- J
in
z
o
cj
o
Í— 2
u
LU
_l
UJ
Q
Key:
— Parallel Slabs
Logarithmic
â–  Perpendicular
Slabs
0 100/0/0 AR
â–¡ 100/0/0 BM, 625
â–  100/0/0 BM, 650
4 95/0/5
â–² 90/0/10
• 85/0/15
â–¼ 80/0/20, Batch 1
V 80/0/20, Batch 2
ó 70/0/30
T&S /
/
' /
20
40
60
80
100
Percent Theoretical Density
Measured dielectric constant data as a function
of percent density for all pure BS glass
compositions (with and without 4.6 pm included
porosity), with associable traditional models
Figure 4.130

504
4 -
C
TO
+->
Ü)
C
o
U
o
o
_03
0)
b
Key:
Oblate
c/a
Prolate
0 100/0/0 AR
â–¡ 100/0/0 BM, 625
| 100/0/0 BM, 650
A 95/0/5
A 90/0/10
• 85/0/15
â–¼ 80/0/20, Batch 1
V 80/0/20, Batch 2
() 70/0/30
—
1.0
0.8
0.6
0.4
0.2
0
—
o
20
T“
40
T“
60
“T-
80
100
Percent Theoretical Density
Measured dielectric constant data as a function
of percent density for all pure BS glass
compositions (with and without 4.6 pm included
porosity) modelled using EMT theory
Figure 4.131

505
general agreement with the Maxwell model at densities higher than - 20 %
[88GER3]. The data of Leap, et. al, extracted from a study of
composites with a silica matrix with embedded Pb glass microspheres, fit
between Maxwell and parallel slabs models and thus, was slightly higher
[89LEA]. Sacks, et. al, found a linear relation between K and percent
density [91SAC1]. No further modelling was performed, however.
Unfortunately, EMT modelling was not performed in any of the above
studies.
Since the EMT model accounts for sphere overlapping at higher
fractions of spherical phase, it models both situations well. Thus, it
may be concluded that the EMT model (c/a = 1) is best for modelling K,
in this system, at all stages of densification. Furthermore, it is
logical that the compositions bereft of included porosity also follow
this relation, since the final stages of sintering of this type of
microstructure also involves changing from a continuous pore structure
to a discrete spheroidal pore structure. In order to better understand
the dielectric properties of this (and similar) composite system, it
would be interesting to model, using EMT, controlled porosity materials
such as those studied by Yamamoto, et al., and Kata, et al.
[89YAM,90KAT]. The pore shape within the materials investigated in
these studies was ellipsoidal, due to a unidirectional (Z-axis)
lamination step. Thus, the c/a value would be < 1 (prolate or oblate
depending upon sample orientation). This would be valuable for
determination of the validity of EMT theory for values of c/a near (but
not equal to) one. Modelling of the K values of tubular fiber
composites would also be beneficial in order to determine the validity
of EMT theory for ellipsoids having c/a values close to 0.
Figures 4.132 and 4.133 illustrate K data for 15 and 17.6 V%
included porosity compositions (2.4 pm bimodal, 4.0 pm quadramodal and
4.6 pm and 9.0 pm monomodal included porosity). It is evident from
these figures that included porosity size and size distribution have no

506
4 -
Z
<
h-
CO
z
o
o
o
o:
I—
o
Key:
1 Parallel Slabs
A 85/0/15, 2.4 pm Bimodal
â–¡ 85/0/15, 4.0 pm Quad.
— ••• Logarithmic
â–  85/0/15, 4.6 pm UPLM
— • Perpendicular
Slabs
• 85/0/15, 9.0 pm UPLM
O 82.4/0/17.6, 9.0 pm UPLM
20 40 60
Percent Theoretical Density
80
100
Figure 4.132 Measured K values as a function of percent
density for 15 or 17.6 V% (2.4 pm bimodal, 4.0
pm quadramodal and 4.6 pm and 9.0 pm monomodal
included porosity) compositions, with
associable traditional models

507
Percent Theoretical Density
Figure 4.133 Measured K values with respect to density for
15 or 17.6 V% (2.4 pm bimodal, 4.0 pm
quadramodal and 4.6 pm and 9.0 pm monomodal)
compositions, modelled with EMT

508
significant effect upon K. Again, the K values of these compositions
falls between the logarithmic and Maxwell predictions, coming closer to
the logarithmic model at lower densities and being more closely-
approximated by the Maxwell model at higher densities. Again, EMT (c/a
= 1) most closely models the K values for these compositions over all
densities investigated.
Figures 4.134 and 4.135 depict the K data as well as the
traditional and EMT predictions for the 10 V% (final) Si3N4 concentration
samples studied. Again, both figures indicate that the data fits
between the logarithmic and Maxwell models (favoring the log model at
lower densities and the Maxwell model at higher densities, as above),
and is well modelled over all densities (except the lowest ones
investigated) by EMT predictions. Figures 4.136 and 4.137, 4.138 and
4.139, and 4.140 and 4.141 illustrate analogous relationships for the
composites containing 15, 20 and 40 V% (final) Si3N4 concentrations.
Again, the above observations hold true, with the exception that the K
data for the 40 V% (final) Si3N4 concentration samples is more scattered
and generally more over-estimated by the models than the other
compositions. This is because the regression data for said compositions
also had a relatively large amount of scatter. The K values used for
the fully dense glass-Si3N4 composites were obtained from linear
regression analysis and subsequent extrapolation to full density. This
extrapolation represents a potential (albeit small) source of error in K
modelling of these compositions. The K values used for the fully dense
BS glass-Si3N4 particulates were 4.53, 4.65, 4.85 and 5.68 for the 10,
15, 20 and 40 V% (final) Si3N4 concentration composites respectively.
It should be noted that the corresponding extrapolated linear
regression value for pure BS glass compositions was 4.19. This value is
approximately 2 % greater than the literature value used for said glass
(i.e. 4.1). The standard deviation of the average of the extrapolated
linear regression values is 0.04 (13 data sets). This increase in K is

509
Percent Theoretical Density
Measured dielectric constant as a function of
percent density, with traditional modelling,
for the 10 V% (final) concentration silicon
nitride composition
Figure 4.134

510
Percent Theoretical Density
Figure 4.135 Measured dielectric constant as a function of
percent density, with EMT modelling, for the 10
V% (final) concentration silicon nitride
composition

511
Percent Theoretical Density
Measured dielectric constant as a function of
percent density, with traditional modelling,
for the 15 V% (final) concentration silicon
nitride compositions
Figure 4.136

512
Percent Theoretical Density
Measured dielectric constant as a function of
percent density, with EMT modelling, for the 15
V% (final) concentration silicon nitride
composition
Figure 4.137

513
Percent Theoretical Density
Measured dielectric constant as a function of
percent density, with traditional modelling,
for the 20 V% (final) concentration silicon
nitride composition
Figure 4.138

514
C
CD
â– *-'
tn
c
o
O
o
4 -
Key:
Oblate
c/a
Prolate
■ 80/20/0, 625 °C
□ 80/20/0, 650 °C
• 72/18/10, 4.6 tan UPLM, 625°C
O 72/18/10, 4.6 tan UPLM, 650 °C
A 64/16/20, 4.6 fan UPLM, 625 °C
A 64/16/20, 4.6 tan UPLM, 650°C
—
1.0
0.8
0.6
0.4
0.2
0
III I : i
20 40 60 80
Percent Theoretical Density
100
Measured dielectric constant as a function of
percent density, with EMT modelling, for the 20
V% (final) concentration silicon nitride
composition
Figure 4.139

515
C
03
+->
V)
c
o
O
o
5 -
4 -
3 -
Key:
■ 60/40/0, 625°C
□ 60/40/0, 650 °C
• 60/40/0, 730 °C
O 60/40/0, 820 °C
A 54/36/10, 4.6 tan
UPLM
4 48/32/20, 4.6 tan
UPLM, 650 °C
— ■— Maxwell
““““ Perpendicular
Slabs
20 40 60 80
Percent Theoretical Density
100
Measured dielectric constant as a function of
percent density, with traditional modelling,
for the 40 V% (final) concentration silicon
nitride composition
Figure 4.140

516
c
CD
â– M
CO
c
o
CJ
o
o
©
©
b
5 -
4 -
3 -
Key:
Oblate
c/a
Prolate
■ 60/40/0, 625°C
□ 60/40/0, 650 °C
• 60/40/0, 730 °C
O 60/40/0, 820 °C
4 54/36/10, 4.6 ¿un
UPLM
4 48/32/20, 4.6 tan
UPLM, 650 °C
—
1.0
0.8
0.6
0.4
0.2
0
II I l : i
20 40 60 80
Percent Theoretical Density
100
Measured dielectric constant as a function of
percent density, with EMT modelling, for the 40
V% (final) concentration silicon nitride
composition
Figure 4.141

517
not a result of changes experienced during ball milling, since the
extrapolated value for the as-received BS glass is well within a
standard deviation of the average (i.e. 4.17). It is possible that the
impedance analyzer and test fixture consistently indicated high.
However, it is more likely that the values are genuine, since the
density value used to determine percent of theoretical density was that
of the ball milled BS glass powder (i.e. 2.20 g/cm3) and not the
literature value of (2.13 g/cm3). The manufacturer's value (2.13 g/cm3)
was confirmed to be valid via the Archimedes method. Also, none of the
sintered densities of the pure BS glass powder compacts exceeded 2.13
g/cm3 during this investigation. However, none of the samples became
optically transparent after densification. Bloating was observed as
well. Thus, it is not likely that the samples reverted to the
manufacturer's value of bulk density (i.e. 2.13 g/cm3).
Using the extrapolated 100 % density value for K of the pure BS
glass, the data depicted in Figures 4.130 and 4.131, and 4.132 and 4.133
was replotted using the maximum K value of 4.19 (instead of 4.1).
Figures 4.142 and 4.143 and 4.144 and 4.145 depict these relations.
From the figures, it is evident that the above discussions, correlating
these data to values between the Maxwell and logarithmic models as well
as to the EMT model (c/a = 1), still apply, having even better fits to
the data to than originally discussed.
It is interesting that the above-mentioned extrapolated data for
each group of increasing Si3N4 concentration, do not fit the prediction
of any of the composite dielectric constant models well, if literature
values for pure Si3N4 are used. Figures 4.146 through 4.151 delineate
this relationship. From the figures, it is evident that 8.6 is the best
value for modelling the K of Si3N4 (assuming that the EMT model is best
for this application).
All available literature values for the K value of Si3N4 are
between 6 and 7 (see Table 1.4). Most of these references cited a K

518
C
CD
+-'
CO
c
o
o
o
_0)
O
Q
4 -
3 -
0
Key:
â– â–  1 Parallel Slabs
— ■■■ Logarithmic
“ • Perpendicular
Slabs
0 100/0/0 AR
â–¡ 100/0/0 BM, 625
â–  100/0/0 BM, 650
A 95/0/5
â–² 90/0/10
• 85/0/15
â–¼ 80/0/20, Batch 1
V 80/0/20, Batch 2
ó 70/0/30
0
BS Glass K = 4.19
20 40 60 80
Percent Theoretical Density
100
Figure 4.142 Measured K data as a function of percent
density for all pure BS glass compositions
(with and without 4.6 pm included porosity)
with traditional models, BS glass K = 4.19

519
4 -
c
TO
+->
W
c
o
(J
o
o
JU
CD
Q
3 -
0
Key:
Oblate
c/a
Prolate
0 100/0/0 AR
â–¡ 100/0/0 BM, 625
B 100/0/0 BM, 650
A 95/0/5
â–² 90/0/10
• 85/0/15
â–¼ 80/0/20, Batch 1
V 80/0/20, Batch 2
() 70/0/30
1.0
0.8
0.6
0.4
0.2
0
BS Glass K = 4.19
T
0
20 40 60 80
Percent Theoretical Density
100
Measured K values as a function of percent
density for all pure BS glass compositions
(with and without 4.6 pm included porosity)
with EMT models, BS glass K = 4.19
Figure 4.143

520
4 -
c
03
+->
C/3
C
o
(J
o
o
o
0)
b
0
Key:
—“ Parallel Slabs
1 85/0/15, 2.4 pm Bimodal
â–¡ 85/0/15, 4.0 pm Quad.
Logarithmic
â–  85/0/15, 4.6 pm UPLM
— • Perpendicular
Slabs
• 85/0/15, 9.0 pm UPLM
O 82.4/0/17.6, 9.0 pm UPLM
BS Glass K = 4.19
T
20 40 60 80
Percent Theoretical Density
100
Measured K values as a function of percent
density for (2.4 pm bimodal, 4.0 pm quadramodal
and 4.6 pm and 9.0 pm monosized included
porosity) compositions with traditional models,
BS glass K = 4.19
Figure 4.144

521
C
TO
+-1
C
o
O
o
o
_Q3
CD
Q
4 -
3 -
0 -
Key:
Oblate
c/a
Prolate
1 85/0/15, 2.4 fun Bimodal
O 85/0/15, 4.0 tun Quad.
â–  85/0/15, 4.6 tun UPLM
• 85/0/15, 9.0 tun UPLM
0 82.4/0/17.6, 9.0 tun UPLM
—
1.0
0.8
0.6
0.4
0.2
0
—
BS Glass K = 4.19
0
20 40 60 80
Percent Theoretical Density
100
Measured K values as a function of percent
density for (2.4 pm bimodal, 4.0 pm quadramodal
and 4.6 pm an 9.0 pm monosized included
porosity) compositions with EMT modelling, BS
glass K = 4.19
Figure 4.145

Dielectric Constant (K)
522
1° -T
9 -
8 -
7 -
Key:
— Parallel Slabs
---- EMT (c/a = 1)
Logarithmic
— ■ Perpendicular
Slabs
# Linear Regression
Extrapolated Data
Extrapolated K values for 0 V%, 10 V%, 15 V%,
20 V% and 40 V% (final) silicon nitride
concentration samples, modelled using a K value
of 6 for silicon nitride
Figure 4.146

Dielectric Constant (K)
523
10
Key:
â– â– â– " Parallel Slabs
—— EMT (c/a = 1)
— Logarithmic
— ■ Perpendicular
Slabs
Linear Regression
Extrapolated Data
l I I I I I I I I I
0 20 40 60 80 100
Volume Percent Silicon Nitride
Extrapolated K values for 0 V%, 10 V%, 15 V%,
20 V% and 40 V% (final) silicon nitride
concentration samples, modelled using a K value
of 7 for silicon nitride
Figure 4.147

Dielectric Constant (K)
524
Volume Percent Silicon Nitride
Extrapolated K values for 0 V%, 10 V%, 15 V%,
20 V% and 40 V% (final) silicon nitride
concentration samples, modelled using a K value
of 8 for silicon nitride
Figure 4.148

Dielectric Constant (K)
525
Volume Percent Silicon Nitride
Extrapolated K values for 0 V%, 10 V%, 15 V%,
20 V% and 40 V% (final) silicon nitride
concentration samples, modelled using a K value
of 8.6 for silicon nitride
Figure 4.149

Dielectric Constant (K)
526
Volume Percent Silicon Nitride
Extrapolated K values for 0 V%, 10 V%, 15 V%,
20 V% and 40 V% (final) silicon nitride
concentration samples, modelled using a K value
of 9 for silicon nitride
Figure 4.150

Dielectric Constant (K)
527
Volume Percent Silicon Nitride
Extrapolated K values for 0 V%, 10 V%, 15 V%,
20 V% and 40 V% (final) silicon nitride
concentration samples, modelled using a K value
of 10 for silicon nitride
Figure 4.151

528
value of 6 for Si3N4. However, the references did not specify the
purity, density or phase purity of the Si3N4 investigated. To the
knowledge of the author, bulk samples of fully dense, ultra pure and
phase correct a-Si3N4 have not yet been synthesized. This could help
explain the difference between predicted and literature K values for
Si3N4.
Another explanation is that the particulate Si3N4 used in this
study may have reacted with the BS glass matrix, creating a high K phase
at the BS glass Si3N4 interfaces. However, this is not likely due to the
relatively poor adherence of the Si,N4 particles to the glass matrix. It
is also unlikely that internal boundary layers were formed since the K
values remained constant with frequency over the range measured.
Therefore, further investigation which focuses upon measurement of the
actual dielectric constant of pure fully dense a-Si3N4, is warranted.
The goal of this study was to produce hermetic materials having
minimized K values. Table 4.15 depicts the lowest K value measured for
a hermetic sample of each of the composite compositions investigated.
As mentioned above, the interpretation of hermeticity, for this study,
is a material having an open porosity value of < 1. The table indicates
that, using the methods and materials of this study, hermetic materials
having K values as low as 3.5 may be produced. Similarly, hermetic, or
nearly hermetic, samples containing 10 V%, 15 V% 20 V% and 40 V% final
concentration of Si3N4 were produced having K values of 3.89, 4.05, 3.99
and 4.87 respectively. The relatively low value for the 20 V% Si3N4
concentration composite results from a greater amount of total porosity,
resultant from a greater controlled porosity addition. Thus, it should
be possible to consistently produce controlled porosity BS glass-Si3N4
composites having K values of - 4.0 with final Si3N4 concentrations as
high as 20 V%. It was not possible to produce hermetic samples in the
40 V% Si3N4 composition series. However, it is interesting to note that

529
Table 4.15
Dielectric Constant Data of Hermetic Samples
Composition (V%)
Porosity (V%)
Dielectric
Data (1 MHz)
BS1
SN
UPLM
Max.
Closed
Open3
Tot3
K
tan(5)
(%>
V%
S2
D2
100
AR
0
0
NA
NA
4.9
2.96
7.8
3.79
0.11
100
0
0
NA
NA
5.64
0.0
5.6
3.93
0.11
95
0
5
4.6
M
8.1
l.l6
9.2
3.74
0.07
90
0
10
4.6
M
10.3
0.6
10.9
3.71
0.08
85
0
15
2.4
B
10.9
1.2*
12.1
3.67
0.37
85
0
15
4.0
Q
13.3
0.8
14.1
3.56
0.07
85
0
15
4.6
M
13.4
0.5
13.9
3.62
0.07
85
0
15
9.0
M
13.9
0.7
14.6
3.52
0.06
82.4
0
17.6
9.0
M
15.6
0.4
16.0
3.51
0.07
80
0
20
4.6
M
14.3
0.7
15.0
3.56
0.07
70
0
30
4.6
M
5.9
1.0
6.9
3.87
0.08
81
9
10
4.6
M
10.5
0.8
11.3
3.89
0.06
72.25
12.75
15
4.6
M
11.3
0.9
12.2
4.05
0.06
80
20
0
NA
NA
4.7
1.26
5.9
4.53
0.16
80
20
0
NA
NA
4.2
1.46
5.6
4.59
0.06
72
18
10
4.6
M
10.4
0.8
11.2
4.27
0.06
64
16
20
4.6
M
10.5
0.3
10.8
4.31
0.10
64
16
20
4.6
M
14.6
l.l6
15.7
3.99
0.05
60
40
0
NA
NA
1.7
9.76
11.4s
4.64
0.14
60
40
0
NA
NA
7.5
1.2*
8.7
4.87
0.12
48
32
20
4.6
M
1.5
20.96
22.4s
4.22
0.21
Notes: 1. BS glass (AR is as-received, all others are ball milled
2.S is latex diameter, D is dispersity, B is bimodal, Q is
quadramodal, M is monodisperse
3. Open and Total porosity, at maximum observed closed porosity
4. Value was influenced by bloating
5. The porosity did not reach the final stages of sintering
Does not meet the hermeticity criterion (i.e. % OP < 1)
6

530
it was possible to form 7.5 V% closed porosity in the 60/40/0 (BS
glass/Si3N4/Latex). This is probably due to the porous, bridging
structure of the Si3N4 at 40 V% concentration.
The effect of atmospheric exposure upon the dielectric properties
and sample weights of both hermetic and non-hermetic materials
representative of this system was investigated as outlined in section
3.7.2. The relative humidity (RH) varied from approximately 70 to 74 %
over the duration of this study. Figure 4.152 depicts the effects of
atmospheric exposure duration upon the dielectric constant of hermetic
and non-hermetic samples. Figure 4.153 depicts the effects of
atmospheric exposure duration upon tan(6), and Figure 4.154
illustratesthe evolution of the normalized weight of the respective
samples over the time period of the investigation.
The above figures indicate that the dielectric properties (both K
and tan(S)) as well as normalized weight of the non-hermetic samples
increase with increasing atmospheric exposure time, while the analogous
values for the hermetic samples remain constant throughout the time
period of the investigation. This indicates that, when using the
materials investigated in this study, for low loss dielectric
applications, said materials must be hermetic in order to meet
dielectric stability requirements.
It is interesting to note that the dielectric data of the non-
hermetic samples experience maxima between approximately 15 and 150 min.
During this period, the normalized weights of the non-hermetic samples
also go through similar (albeit smaller) maxima. After this period, the
dielectric properties and the normalized weight of the non-hermetic
samples increases monotonously. The reason for this behavior is not
known. It may be relatable to changes in RH during the experiment, or
it may be due to the mechanism of moisture sorption operant in these
samples. This topic has been addressed for pure silica glasses [91WAL],
and would be an interesting topic for future investigation.

531
C
03
â– M
V)
c
o
O
o
o
o
03
Q
5.0
4.8
4.6
4.4
4.2
4.0
3.8
3.6
3.4
3.2
3.0
2.8
2.6
2.4
2.2
2.0
4.8
4.6
4.4
4.2
4.0
3.8
3.6
3.4
3.2
3.0
2.8
2.6
2.4
2.2
2.0
Hermetic
—T
f
=r. zr.Qf. rrgr. :
Key:
-H
85/0/15 (BS Glass/SN/4.6 //m UPLM), 86.1 % Dense
X
85/0/15 (BS Glass/SN/4.6 /mi UPLM), 87.7 % Dense
85/0/15 (BS Glass/SN/9.0/mi UPLM), 86.8 % Dense
v
80/20/0 (BS Glass/SN/Latex), 95.8 % Dense
Key:
Bill Al • • ■
82.4/0/17.6 (BS Glass/SN/9.0//m UPLM), 59.3 % Dense
60/0/40 (BS Glass/SN/4.6//m UPLM), 45.4 % Dense
72.25/12.75/15 (BS Glass/SN/4.6/mi UPLM), 59.3 % Dense
0.4 0.8 1.2 1.6 2.0 2.4 2.8
Log(Atmospheric Exposure Time (min.))
Figure 4.152 Dielectric constant as a function of
atmospheric exposure time for representative
hermetic and non-hermetic samples

Jan(ó)
532
Log(Atmospheric Exposure Time (min.))
Loss tangent as a function of atmospheric
exposure duration for representative hermetic
and non-hermetic samples
Figure 4.153

Normalized Weight
533
1.008
1.007 -
1.006 -
1.005 -
1.004 -
1.003 -
1.002 -
1.001 -
1.000
0.999
Key:
M 85/0/15 (BS Glass/SN/4.6 /mi UPLM), 86.1 % Dense
x 85/0/15 (BS Glass/SN/4.6 /mi UPLM), 87.7 % Dense
— ©■ — 85/0/15 (BS Glass/SN/9.0/mn UPLM), 86.8 % Dense
— 80/20/0 (BS Glass/SN/Latex), 95.8 % Dense
— ■ -B- — • 82.4/0/17.6 (BS Glass/SN/9.0/mi UPLM)
59.3% Dense
Jk 60/0/40 (BS Glass/SN/4.6/mi UPLM), 45.4 % Dense
— ♦ — 72.25/12.75/15 (BS Glass/SN/4.6/mi UPLM)
59.3% Dense
]
/
•
//-
// A
// /
/ / /
// /
/ /•’ v
// /
*/ /
i jf /
//
i i i i i i i i i i i i r
0.4 0.8 1.2 1.6 2.0 2.4 2.8
Log(Atmospheric Exposure Time (min.))
3.2
Figure 4.154 Normalized weight as a function of atmospheric
exposure time for the representative hermetic
and non-hermetic samples studied

534
4.4.4 Microhardness Characterization
Microhardness and elastic modulus data were obtained from
representative samples as outlined in section 3.7.4. As noted in said
section, it was not possible to determine fracture toughness using
microhardness indentation techniques. Table 4.16 shows the compiled
data from the microhardness investigation. The statistical variance of
the data is relatively high. This is expected, since the
microstructures of the materials tested was of a size regime similar to
that of the indentations characterized. This factor could affect the
variation in indentation size considerably, and thus, the statistical
variation of the material properties measured. The lowest porosity, BS
glass samples exhibited somewhat lower statistical variance, as
expected. The hardness and elastic modulus of the sintered, BS glass
sample is quite close to the values measured for the manufacturer's BS
glass ingot. This is logical, since they had almost identical bulk
density values (i.e. both bulk densities were 2.13 g/cm3 as measured
using the Archimedes method). Although the measured bulk densities were
identical, the calculated % densities were not, due to the different
bases used to calculate % density values (i.e. 2.13 g/cm3 for the bulk
BS glass versus 2.20 g/cm3 for the ball milled BS glass powder). This
relationship was discussed in section 4.4.3 above.
No literature hardness data was available for this particular
composition of BS glass. However, the Knoop hardness values obtained
are similar to literature values of similar BS glasses (i.e. -360 + 10
kg/mm: for both the BS glass samples versus 375, 418 and 442 kg/mm2 for
Corning 7052, 7740 and 7760 BS glasses respectively [79COR]).
The elastic modulus literature value for the BS glass used [79COR]
is 5200 kg/mirr versus 6071 and 6083 kg/mrrr (+ 1825 and 1436 kg/mrrr) for
the manufacturer's and sintered samples respectively. The literature
value is within one standard deviation of each of the measured values,
and thus, is comparable. The measured values agree even more closely

535
Table 4.16
Microhardness Data Culmination
Composition
Lat.
Dia.
Bulk
P
Vicker's
Hardness
(GPa)
Knoop
Hardness
(GPa)
Elastic
Modulus
(GPa)
BSG
SN
LTX
(pm)
%ThD
Ave
On
Ave
On
Ave
1003
0
0
NA
100
4.0
0.2
3.5
0.1
59.5
17.9
100
0
0
NA
97.0
4.1
0.1
3.5
0.1
59.6
14.1
95
0
5
4.6
92.2
3.8
0.4
3.2
0.2
66.1
34.2
90
0
10
4.6
90.2
4.1
0.8
3.2
0.3
39.1
8.0
85
0
15
4.6
86.2
3.8
0.5
2.7
0.3
34.0
7.9
85
0
15
2.4
89.7
3.8
0.5
3.0
0.2
34.2
7.2
85
0
15
9.0
85.9
3.8
0.7
3.0
0.5
34.2
6.3
85
0
15
POLY
86.7
3.6
0.8
2.7
0.3
32.8
6.8
80
20
0
NA
96.9
6.0
0.6
4.7
0.4
121.1
6.3
72
18
10
4.6
91.4
5.3
0.5
4.5
0.4
74.0
25.0
64
16
20
4.6
89.0
5.3
1.1
4.1
0.5
60.2
8.4
60
40
0
NA
89.6
5.1
0.7
3.8
0.4
120.1
8.2
81
9
10
4.6
88.7
4.7
0.6
3.3
0.4
46.9
1.2
72.25
12.75
15
4.6
87.7
4.5
0.5
3.4
0.6
61.3
24.7
Notes: 1. Lat. Dia. is the number basis mean UPLM diameter (POLY
means polydisperse latex).
2. NA means Not Applicable
3. Manufacturer's Sample
BSG is ball milled borosilicate glass powder, SN is
as-received Si3N4 powder, LTX is polystyrene latex.
4

536
with literature values for the elastic modulus of generic borosilicate
glasses [74MEC] (i.e. 63.7 GPa for the literature value versus 59.5 +
17.9 and 59.7 + 14.1 GPa for the manufacturer's and sintered samples
respectively). As expected, the hardness and elastic modulus values
increase with increasing Si3N4 concentration. Similarly, these values
decrease with increasing porosity concentration. The standard
deviations of these values are large, indicating that perhaps, other
methods of mechanical properties evaluation should be investigated in
future study.
Figure 4.155A demonstrates the Vicker's hardness of the samples
with respect to percent total porosity, while Figure 4.155B illustrates
the Vicker's hardness as a function of Si3N4 concentration. Figure 4.156
shows the above relationships using Knoop hardness data. It should be
noted that the Knoop data is probably more accurate, due to the larger
size of the Knoop indentations measured (i.e. the Knoop indentations
were larger with respect to the Si3N4 inclusions as well as the included
porosity). Furthermore, the Vicker's indentations tended to be
difficult to read if they interacted with the included porosity.
Figure 4.157 illustrates the decrease in elastic modulus (E) with
increasing porosity, as well as the increase in elastic modulus with
increasing silicon nitride content. The figures also illustrate the
Mackenzie, Voigt and Reuss models [76KIN1] for comparison of said models
with the experimental data. The Voigt model characterizes the increase
in E with increasing additions of Si3N„ better than the Reuss model.
With one exception however, the Reuss model is within one standard
deviation of the measured data as well. The data for the -10 V%
porosity set seem to mostly fit between the Voigt and Reuss bounds (i.e
they follow an intermediate path between the extrema of the Voigt and
Reuss models). This is expected in a real composite system [76KIN1],
and may indicate that said system has neither a constant stress nor a
constant strain between components (or that the effects of each state

VICKER'S HARDNESS (GPa) VICKER’S HARDNESS (GPa)
537
A. Vicker's Hardness as a Function of Porosity
VOLUME PERCENT SILICON NITRIDE (solids basis)
B. Effect of Silicon Nitride Concentration Upon Vicker's Hardness
Figure 4.155
The effects of included porosity (A) and Si3N4 (B)
additions upon the Vicker's hardness values of BS
glass-silicon nitride composites

KNOOP HARDNESS (GPa) KNOOP HARDNESS (GPa)
538
PERCENT TOTAL POROSITY
A. Knoop Hardness as a Function of Porosity
VOLUME PERCENT SILICON NITRIDE (solids basis)
B. Effect of Silicon Nitride Content Upon Knoop Hardness
The effects of included porosity (A) and Si3N4 (B)
additions upon the Knoop hardness values of BS glass-
silicon nitride composites
Figure 4.156

ELASTIC MODULUS (GPa) ELASTIC MODULUS (GPa)
539
PERCENT TOTAL POROSITY
A. Effect of Porosity Upon Elastic Modulus
10 15 20 25 30 35 40
VOLUME PERCENT SILICON NITRIDE (solids basis)
B. Effect of Silicon Nitride Concentration Upon Elastic Modulus
Figure 4.157
The effects of included porosity (A) and Si,N„ (B)
additions upon the elastic modulus of BS glass-silicon
nitride composites

540
are balanced in the system). The -3 V% porosity data do not fit between
the Voigt and Reuss limits, however. This may be due to the limited
data set.
Linear regression analysis proved better than the Mackenzie model
at predicting E with respect to porosity concentration. The MacKenzie
model assumes that the material of interest has a Poisson's ratio (a) of
approximately 0.3 and that the porosity is closed and isolated within a
continuous matrix. The porosity is closed and reasonably well isolated
within the composites investigated. However, the Poisson's ratio of the
BS glass is 0.22 [79COR], representing a greater than 25 % deviance from
this value. Also, the Poisson's ratio of a-Si3N4 is 0.27 [81ANS]. The
greatest deviation from the MacKenzie model was in the system containing
20 V% Si3N4. These differences in a may be a source of deviation of the
experimental values from those predicted via the MacKenzie model.
The size and/or dispersity of included porosity had no effect upon
the mechanical properties measured (within the regime of sensitivity of
the measurement technique used) as indicated in Figure 4.158. The data
in the figure are fitted using least squares linear regression. These
fits are almost perfectly horizontal. Therefore, it is concluded that,
within this size regime of porosity at least, pore size and/or size
dispersity has very little, if any, effect upon the elastic modulus,
Vicker's hardness or Knoop hardness. It seems to be simply a matter of
constituent concentration.

100
90 -
_ 80 -
TO
CL
52 70-
oo
=5
=>
Q
O
CJ
W
5
60 -
50 -
40 -
30 -
Key:
A Wide Size Distribution Included Porosity (app. 1-10 pm)
â–  Narrow Size Distribution Included Porosity
— Least Squares Linear Regression Fit
of Data
u
20 -
10 -
A.
'I 'I' i i i i i t """I "â–  â– '!
2 4 6 8 10
NUMBER BASIS MEAN LATEX DIAMETER (//m)
Elastic Modulus as a Function of Included Porosity Size/Dispersity
re 6 *
CO
Q_
CD
CO
CO
LLI
z
Q
CE
<
X
o
I-
<
LU
Q
5 -
2 -
1 -
Key:
A Wide Size Distribution Included Porosity (app. 1-10 //m)
â–  Narrow Size Distribution Included Porosity
â„¢ Least Squares Linear Regression Fit
of Data
4 -
I
Vickers Indentation Hardness
I 3
k
3 -
Í
7
k T Knoop Indentation Hardness --
2 4 6 8
NUMBER BASIS MEAN LATEX DIAMETER (pm)
B. Hardness as a Function of Included Porosity Size/Dispersity
10
The effects of included pore size and/or pore size
distribution upon the mechanical properties (A.
Elastic Modulus, B. Indentation Hardness) of pure BS
glasses containing included porosity
Figure 4.158

543
decreased then began to increase again as sphere diameter increased from
4.6 to 9.0 pm.
Along with the particle size and particle size distribution, the
composition, surface structure and density of the borosilicate glass
changed with ball milling, in MeOH (methanol). These changes were found
to affect green density slightly as well as measured powder density
(compared to the as-received glass). However, no other noticeable
changes in materials properties were evident.
The Si3N4 powder was used as-received, and was observed to contain
a small amount (not observed via sedigraph or CPSA (centrifugal particle
size analysis), but observed microscopically) of agglomeration. It was
observed that the Si3N4 powder did not oxidize measurably at the
temperatures, and in the atmospheres, used to process the composites.
Visual inspection, as well as mechanical polishing investigation,
indicated that the Si3N4 powder did not react appreciably with the BS
glass matrix material.
5.3 Green Processing and Characterization
Both sonication and rotisserie aging were found to significantly
improve both the suspension and green properties of these composites.
It can be safely assumed that these two treatments also improve the
final properties of the final composites.
All measured rheological properties were found to increase with
increased solids loading in all suspensions investigated. It was
possible to load both latex and BS glass suspensions in excess of 52 V%
solids. However, it was not possible to load the Si3N4 suspensions
significantly in excess of 46 V% solids. Poor behavior of the Si3N4
powder was also exhibited during green structure characterization as
well, leading to the conclusion that the Si3N4 powders are not well
dispersed using the EtOH-PVP (ethanol-polyvinyl pyrrolidone) dispersion
system used in this study. The latex microspheres exhibited near-

544
Newtonian, rheological behavior as opposed to the characteristically
dilatant behavior of the ceramic powders investigated.
The BS glass was found to pack very well using the dispersion
medium and dispersants investigated in this study. The as-received BS
glass packed more efficiently than the ball milled BS glass, as
predicted from pertinent literature [30AND,88REE,90ZHE]. The packing
behavior of the latexes investigated in this study was modelled both
accurately and predictably using random close packing theory
[30WES,60SCO,61MCG,88REE].
In general, increased latex concentration was found to increase
green density as well as to slightly decrease suspension viscosity.
Overall, the opposite behavior was found with increasing Si3N4
concentration.
It was demonstrated that the removal of latex additions (via
pyrolysis) produces accurately predictable, as well as consistently
reproducible amounts of included porosity in all of the composite
compositions studied, up to 40 V%, at the post-pyrolysis stage of
processing. The onset of a percolated pore structure was observed to
occur in the regime of 25 V% UPLM addition. This is in close agreement
with the, universally accepted, 16 V% for random placement on all types
of lattices (periodic or random) for structures of three dimensions,
when corrected for non-filled space. Above the percolation value, the
pore channel size was observed to increase at an accelerated rate with
increasing latex addition. The pore structure was also observed to
become bimodal after the percolation threshold of latex was exceeded.
5.4 Thermal Processing and Characterization
The polystyrene latex used in this study was observed to pyrolyze
adequately in both air and N2 atmospheres at temperatures below those
used for sintering. However, the dispersant (PVP k-30) was observed to
leave a small amount of residual ash in both N: and air atmospheres.

545
The ash was only removable in air at temperatures above the onset of
sintering for this glass system, and thus, could be problematic.
The onset temperature of sintering, within reasonable timespans, was
found to be 625 °C. The ball milled BS glass was observed to densify at
a greater rate than the as-received BS glass, despite the higher packing
efficiency of the latter.
Increasing temperature was observed to increase the rate of
densification of the glass composites studied. The magnitude of
densification acceleration was found to be in agreement with reduction
in viscosity, indicating that the sintering mechanism is purely viscous.
Silicon nitride additions at and above the percolation threshold
(i.e. - 16 V% of total space) was found to retard sintering. At and
above Si3N4 additions of - 36 V% of total space, the sintering process
was arrested. For example, in the case of 40 V% Si3N4 additions, it was
not possible to densify the composite significantly in excess of 90 % of
theoretical density using pressureless sintering techniques.
Furthermore, in the case of 60 V% Si3N4 addition, sintering was limited
to only a few percent increase in density, as predicted by Scherer
[91SCH2].
It was possible to create materials having closed porosities of -
15.6 V% (at - 16.0 V% total porosity) via the techniques utilized during
this study. This value is in excellent agreement with the percolation
threshold (- 16 V% of total space) for three dimensional percolation
[83ZAL2]. It was found that increasing the ratio of included pore size
to native pore size (i.e. to approximately 20 or 40 to 1) increased the
maximum amount of closed porosity attainable. It was also found that
quadramodal sphere additions did not noticeably change the amount of
maximum attainable closed porosity. However, it was denoted that this
experiment should be repeated using a different size distribution of

546
spheres (i.e. larger overall, with at least a 7 to 1 ratio in successive
sphere size) in order to be conclusive.
The greatest amount of closed porosity achieved in this study was
15.6 V% (16.0 V% total porosity) using additions of 17.6 V% 9.0 pm UPLM.
This is in excellent agreement with the onset of percolation in randomly
filled, three-dimensional space. Smaller amounts of closed porosity
(i.e. up to 14.6 V%) were observed in the systems using additions of 4.6
pm UPLM in both pure BS glass and in composites containing Si3N4
additions of 20 normalized V% or below. It is assumed that the maximum-
observed value of 15.6 V% could also be attained in these systems if the
9.0 pm UPLM was utilized for the porosity additions.
It was found that the densification behavior of BS glass compacts
containing additions of UPLM beyond the percolation onset (i.e. 30 V%)
was quite different than for UPLM additions below the percolation
threshold. The shape of the rate of densification curve was found to be
somewhat similar to the compacts that did not contain latex additions.
This behavior was attributed to the previously-mentioned percolated
(continuous) structure of the added porosity.
5.5 Characterization and Modelling of Densified Compacts
Quantitative microscopy results indicated that there is no
measurable segregation of the 4.6 pm UPLMs in this systems. Modified
Stokes' settling theory indicates that this should be the case. It also
indicates that there should be minimal segregation of all of the
composite components, with the possible exceptions of the large versus
small BS glass particles. Porosities measured using quantitative
microscopy techniques (QMTs) were slightly greater (but within the
variance) of data obtained via the Archimedes density technique. The
calculated diameters using QMTs were also smaller than expected. Pore
size measurements of both polished and fractured surfaces agreed within

547
the variance of the measurements. It was not possible to model pore
shrinkage during densification accurately using these techniques.
Series modelling was used to predict the 3 and 2 dimensional
average cluster numbers of included porosities, and to compare the
predicted 2-D values with those obtained using QMTs. It was found that,
before percolation, the data was modelled much more accurately via the
site clustering series model. The series clustering model was also
found to accurately predict the maximum amount of closed porosity (and
the associable open and total porosities at said maximum) obtainable in
the type of system studied.
An extrapolation of the series model proved accurate at predicting
the onset of percolation in this system. These predictions were found
to represent the lower limit to said onset. To the knowledge of the
author, this is the first successful application of percolation
modelling to random packed systems. The model used was accurate, as
well as relatively simple to use.
Measured dielectric properties (K and tan(6)) agreed well with
literature values over the frequency range investigated. Effective
medium theory (EMT), applied to perfectly spherical pore geometries, was
found to model the composite K values the most accurately. Using
traditional models, the data was best modelled as an intermediate fit
between the logarithmic and Maxwell models. Using these modelling
techniques, the literature K (dielectric constant) value (i.e. 4.1) for
the BS glass was found to be quite accurate. However, the literature K
values for Si3N4 (i.e. 6 to 7) were disputed using composite dielectric
modelling. Using EMT modelling, the K value of phase pure, fully dense
a-Si,N4 was predicted to be approximately 8.6.
Using the methods of this study, it was possible to produce
hermetic materials with K values as low as 3.51. It was also possible
to produce hermetic composites, containing 20 V% Si3N4 inclusions, with K
values of approximately 4.0. During these investigations, the K and

548
tan(ó) values of hermetic samples were found to be stable with
atmospheric exposure, while the K and tan(6) values of non-hermetic
samples were observed to increase significantly with atmospheric
exposure time.
Microhardness indentation techniques were used to quantify the
hardness and elastic modulus (E) values of representative materials
within this composite system. It was not possible to monitor fracture
toughness via these techniques, however. The variances of the data were
quite large, increasing with increasing included porosity and/or Si3N4
additions.
The knoop hardness values were found to agree with literature
values within the oD values of the experimental data. The E data were
also found to agree well with the literature values of similar BS
glasses. The size and size distribution of included porosity was found
to have no appreciable effect upon any of the mechanical properties
measured.
As expected, the hardness and E values decreased with increasing
porosity concentrations, and increased with increasing Si3N4
concentrations. However, the Mackenzie model did not predict the
decrease in E with increasing porosity well. The relationship of E with
respect to increasing Si3N4 concentration was found to generally fit
between the extrema predictions of the Voigt (upper limit) and Reuss
(lower limit) predictions.

CHAPTER SIX
SUGGESTIONS FOR FUTURE WORK
As in all studies, a complete knowledge is never truly achieved.
Many questions remain unanswered. This chapter, discusses some
recommended suggestions and experiments that, if employed, should help
to answer many of these questions. This discussion is intended to be an
addition to those suggestions contained within previous chapters.
The BS (borosilicate) glass used in this study should be either
modified or replaced to obtain more suitable properties. The glass
particle size should be reduced. This would promote surface smoothness
as well as allow the use of smaller latexes. The use of smaller latexes
would reduce the maximum surface flaw size of the resulting packaging
material. The modified or replacement glass should also sinter at a
higher temperature, in order to further augment removal of organic
materials from the ceramic body. A possible candidate for this
replacement would be boron-doped Stober's silica, which has been fully
densified below the melting point of Cu [89SAN1,89SAN2], thereby
allowing cofiring with Cu. Other candidates exist as well. Also, the
BS glass used could be modified chemically (i.e. lower [B], higher [Si],
reduce or eliminate Al, K, Na and Li) and classified/milled to smaller
particle size.
The investigation of wide size distribution latex additions should
be repeated using latex size modes having a consecutive mode size ratio
greater than 7 to 1. For example, a binary (or ternary), discrete size
distribution having size modes of approximately 35 and 5 pm (or 245, 35
and 5 pm) should be investigated to determine, conclusively, whether or
not the size distribution of the added porosity has an effect upon
maximization of closed porosity. This study probably would not give
549

550
insight into decreasing the size of surface flaws, but the resulting
knowledge could be invaluable from the standpoint of maximization of
closed porosity.
Alternative methods of porosity addition should also be
investigated. Theoretically, additions of hollow spherical shells of a
low loss, higher sintering temperature material (i.e SiO.) would allow
hermetic composites of higher porosity to be produced. Potentially,
this would also reduce the amounts of organic in the green system,
thereby simplifying the thermolysis process.
Further characterization of the composite system with respect to
Si3N4 fillers should also be performed. The BS glass-Si3N4 binary of this
composite system should be further investigated in order to determine
the maximum Si3N4 concentration that would allow full densification using
pressureless sintering techniques. It would also be interesting to
determine, more closely, the Si3N4 concentration at which no
densification occurs via pressureless sintering.
Studies should be performed characterizing the effects of Si3N4
powder size as well as agglomeration index upon green and mechanical
properties as well as densification characteristics. Additions of
microcomposite glass-Si3N4 powders, currently under development [91SAC1]
should also be investigated. The potential benefit of using said
microcomposites would be the ability to obtain fully dense composites,
having higher concentrations of Si3N4, without resorting to pressurized
sintering techniques.
Different ceramic filler candidates should be investigated in this
system. Diamond and cubic BN (boron nitride) should be usable in this
system with little processing modification. Other materials, such as
cordierite, quartz, etc., may also be of interest. Other shapes of
ceramic filler (i.e. whiskers or fibers, etc.) should also be
investigated in order to further advance the state of knowledge of
ceramic-filled, glass matrix composites containing controlled porosity.

551
An investigation of the effect of atmosphere on sintering should
also be performed. A potential benefit, from this experimentation,
would be the ability to enhance added porosity volume through the
evolution of previously dissolved gases, in the final stage of
sintering. The ability to sinter in an inert atmosphere is also
necessary if the ceramic is to be cofired with Cu metallization.
This composite system should be developed for tape and thick film
application. These tape and film systems should be formulated with
EPA/OSHA approved dispersant and solvent systems. The composite system
should be developed for use with metallization systems commonly used in
low loss electronic packaging. This development would include
characterization of thermolysis in low [0;] atmospheres (i.e. steam-
hydrogen systems, etc. [91KUM2,91TUM]) as well as studies attempting to
investigate the chemical compatibility of metallizations with the
ceramic composite system, etc.
The methods of testing and evaluation, used in this study, should
also be enhanced. Porosimetry characterization should be extended
beyond green and post pyrolysis samples. Mercury porosimetry would be a
valuable diagnostic tool for characterization of pore structures during
densification. This would give further insight into the evolution of
the pore structure during processing.
Dielectric data should be obtained at higher frequencies (i.e. to
> 10 GHz) using resonant cavity or low frequency Kramer's-Kronig
techniques [88EWS2,89YAM1,9OSAD,91GIP,91SU1]. Further mechanical
testing should be performed. Analysis of fracture strength and fracture
toughness should be performed using pure tension or other techniques
having sound fundamental bases (i.e. diametral compression, etc.
[67KIR,72WAC,8IANS,81CHA,83SHE,84SIM,89BER]). Theoretical strengths
could also be investigated using controlled flaw techniques [74MEC].
Also, polishing and etching techniques of these composites should
be improved in order to improve upon the ability to perform various

552
types of microstructure evaluation (i.e. determination of volume
fractions of Si3N4, more accurate pore diameter measurements and volume
fraction determinations, etc.).
Finally, other material properties should be evaluated (including
the above-mentioned properties), such as thermal conductivity, thermal
expansion, thermal shock resistance, insulation resistance, residual
carbon content, etc. This would help to provide a data-base, for this
system, that would prove to be a valuable resource when engineering
composites for specific applications. It would also be valuable in
identifying properties that need improvement for specific or general
applications.
All of these recommended experiments/studies would help to promote
a better understanding of BS glass matrix composites having non¬
sintering ceramic inclusions, and/or controlled porosity.

APPENDIX I
MANUFACTURER'S DATA FOR CERAMIC CONSTITUENT POWDERS
I. Corning 7070 Borosilicate Glass r79COR,88COR1
1.Composition:
Composition: Constituent Based
Constituent
Weight Percent
Mole Percent
Silica (SiO;)
72.0 (70.0)
74.8
Boria (B:03)
25.0 (28.0)
22.4
Alumina (A1203)
1.0 (1.1)
0.61
Potassia (K;0)
1.0 (0.5)
0.66
Soda (Na;0)
0.5 (0)
0.5
Lithia (Li;0)
0.5 (1.2)
1
Note: The values in parentheses are those provided by Air Force
Materials Laboratories (prepared by the Electronic
Properties Information Center, Hughes Aircraft Company,
Culver City, CA). Note that the parenthetical values sum to
100.8 wt%.
Composition: Element Based
Element
Weight Percent
Mole Percent
Silicon (Si)
33.7
31.8
Boron (B)
7.8
19
Aluminum (Al)
0.53
0.52
Potassium (K)
0.83
0.56
Sodium (Na)
0.4
0.4
Lithium (Li)
0.2
0.9
Oxygen (0;)
56.6
46.9
Note: Calculated values are based on the assumption that all the
constituent oxides are stoichiometric.
553

554
2. Description:
Glass Type: Borosilicate
Class: I
Corrosion Resistance:
Weathering: Class 2, (will occasionally show problem with
atmospheric liquids and gases if corrosion
products may not be used)
Water:
Class 2, (see above)
Acid:
Color: Clear
Forms Available:
Principal Uses:
Class 2, (10'6-10'5 inches lost when subjected to
5% HC1 @ 95°C, for 24h)
Blown, Multiform, Powder, Pressed, Tubing
Low Loss Electrical, Seals to Tungsten, used
with 3320, 7740, 7574
Materials Properties
Property
Metric Value
English Value
Mechanical
Density
2.13 g/cm3
132.9 lb/ft3
Young's Modulus
5.2 x 103 kg/mm2
7.4 x 10 6 psi
Poisson's Ratio
0.22
0.22
Viscosity
Working Point
(104 Poises)
1068°C
1954°F
Annealing Point
(1013 Poises)
496°C
92 5°F
Set Point
461°C
862°F
Strain Point
(1014 Poises)
456°C
853°F
Thermal
Coefficient of
Expansion (0-300°C)
32.0 x 10'7°C
17.7 x 10'7/°F
Coefficient of
Expansion (25°C to Set
Point, 461°C)
3 9.0 x 10-7/°C
21.7 x 10‘7/°F
Upper Working
Temperature
(Annealed, Normal
Service)
230°C
446°F
Upper Working
Temperature
(Annealed, Extreme
Service)
430°C
806°F

555
Materials Properties
Property
Metric Value
English Value
Upper Working
Temperature
(Tempered, Normal
Service)
230°C
446°F
Upper Working
Temperature
(Tempered, Extreme
Service)
230°C
446°F
Thermal Stress
Resistance
66°C
151°F
Optical
Refractive Index
(at 1=589.3 nm)
1.469-1.47
1.469-1.47
Electrical
Log,,, Volume
Resistivity @ 25°C
17+ ohm-cm
Log10 Volume
Resistivity @ 250°C
11.2 ohm-cm
Logl0 Volume
Resistivity @ 350°C
9.1 ohm-cm
Dielectric Constant
@ 20°C, 1MHz
4.1
4.1
Power Factor or
Loss Tangent
@ 20°C, 1MHz
0.06%
0.06%
Loss Factor
@ 20°C, 1MHz
0.25%
0.25%
The following figures further outline the materials properties of
Corning 7070 borosilicate glass (note: some of this information is not
manufacturer's data)

Viscosity (Poises)
556
Figure AI.1
Viscosity of Corning 7070 as a function of temperature
[88COR]

557
Figure AI.2
Resistivity of Corning 7070
reciprocal temperature [88COR]
as a function of

558
7200
6800
6400
6000
5600
_____ 5200
£ 4800
d 4400
— 4000
^ 3600
—j 3200
2800
2400
2000
1600
1200
800
400
0
Temperature (°C)
Figure AI.3
Thermal expansion of Corning 7070 borosilicate glass
[88COR]

Dielectric Constant
559
Figure AI.4
Dielectric Constant of Corning 7070 as a function of
temperature [88COR]

tan(c5)
560
Figure AI.5
Loss tangent of Corning 7070 borosilicate glass as a
function on temperature [88COR]

Dielectric Constant
561
Log Frequency (Hz)
Source: Air Force Materials Laboratory
(prepared by the Electronic Properties Information Center,
Hughes Aircraft Company, Culver City, CA)
Figure AI.6
Dielectric constant of Corning 7070 borosilicate glass
as a function of frequency

(f>)ue*
562
0.0050
0.0040
0.0030
0.0020
0.0010
0.0000
1
23456789 10 11
Log Frequency (Hz)
Source: Air Force Materials Laboratory
(prepared by the Electronic Properties Information Center,
Hughes Aircraft Company, Culver City, CA)
Figure AI.7
Loss tangent of Corning 7070 borosilicate glass as a
function of frequency

563
II. UBE SNE03 Silicon Nitride Powder
(Data obtained from UBE Industries Limited Quality Certificate for UBE
SN-series Si3N4 Powders and From Reference [89SOM])
Product Characteristics
Identification
Grade
SNE03
Lot Number
B 910062
Chemical
Nitrogen (N, Weight Percent)
>38.0
Oxygen (O, Weight Percent)
0.83
Chlorine (Cl, PPM)
<100
Iron (Fe, PPM)
<100
Calcium (Ca, PPM)
<50
Aluminum (Al, PPM)
<50
Crystal
Crystallinity (Weight Percent)
>99.5
Major Phase
a
P
(a + P)
<5
Physical
Specific Surface Area (m:/g)
3.5
Specific Gravity (g/cm3)
3.18

APPENDIX II
PARTICLE SIZE AND SIZE DISTRIBUTION DATA OF
UNSETTLED 4.6 REGIME (061990 SERIES) UPLM SPHERES

10
00
90
80
70
60
50
40
30
20
10
0
35
30
25
20
15
10
5
0
Batch 06199001, Unsettled
Size Data (Number Based):
Arithmetic
Mean:
4.53 (pm)
Median:
4.79 (pm)
Geometric
Standard
Deviation:
1.03
Standard
Deviation:
± 0.59 (pm)
Number of Points: 125
I
if'.
m
Ml
9.0 8.0 7.0 6.0 5.0 4.0 3.0 2.0
Particle Diameter (jjm)
1.0
0.0
Number basis particle size data for batch
number one of 061990 series UPLMs (4.6 pm size
regime, unclassified)
565

10
00
90
80
70
60
50
40
30
20
10
0
35
30
25
20
15
10
5
0
566
Batch 06199002, Unsettled
Size Data (Number Based):
Arithmetic
Mean:
4.45 U/m)
Median:
4.67 U/m)
Geometric
Standard
Deviation:
1.04
Standard
Deviation:
± 0.53 (^m)
Number of Points: 125
.0 9.0 8.0
7.0 6.0 5.0 4.0 3.0 2.0 1.0 0.0
Particle Diameter (jjm)
•2 Number basis particle size data for batch
number two of 061990 series UPLMs (4.6 fjm size
regime, unclassified)

10
00
90
80
70
60
50
40
30
20
10
0
35
30
25
20
15
10
5
0
567
Batch 06199003, Unsettled
Size Data (Number Based):
Arithmetic
Mean:
4.50 (^m)
Median:
4.77 (/rm)
Geometric
Standard
Deviation:
1.03
Standard
Deviation:
± 0.83 (//m)
Number of Points: 125
Particle Diameter Oum)
1.3 Number basis particle size data for batch
number 3 of 061990 series UPLMs (4.6 yjm size
regime, unclassified)

Number Percent at Size CNPF
568
110
100
90
80
70
60
50
40
30
20
10
0
35
30
25
20
15
10
5
0
10.0 9.0 8.0 7.0 6.0 5.0 4.0 3.0 2.0 1.0 0.0
Particle Diameter (^m)
Figure All.4 Number basis particle size data for batch
number four of 061990 series UPLMs (4.6 pm size
regime, unclassified)
Batch 06199004, Unsettled
Size Data (Number Based):
Arithmetic
Mean:
4.61 (pm)
Median:
4.81 (pm)
Geometric
Standard
Deviation:
1.06
Standard
Deviation:
± 0.65 (pm)
Number of Points: 125

10
00
90
80
70
60
50
40
30
20
10
0
35
30
25
20
15
10
5
0
569
Batch 06199005, Unsettled
!
Size Data (Number Based):
Arithmetic
Mean:
4.41 (y/m)
Median:
4.59 (y/m)
Geometric
Standard
Deviation:
1.02
Standard
Deviation:
± 0.37 (y/m)
Number of Points: 125
¡jb ,
i J i
V 1 1 1 1 " 1111 1 111'1 1 111 I n i II i1 " I " I mu " I
.0 9.0 8.0 7.0 6.0 5.0 4.0 3.0
Particle Diameter (yym)
2.0 1.0
0.0
1.5 Number basis particle size data for batch
number five of 061990 series UPLMs (4.6 pm size
regime, unclassified)

10 â– 
00 •
90 -
80 -
70 â– 
60 â– 
50 â– 
40 â– 
30 â– 
20 â– 
10 â– 
0 â– 
35 â– 
30
25 â– 
20
15
10
5
0
1
570
Batch 06199006, Unsettled
Size Data (Number Based):
Arithmetic
Mean:
4.35 Cum)
Median:
4.60 (pm)
Geometric
Standard
Deviation:
1.03
Standard
Deviation:
± 0.53 (pm)
Number of Points: 1 25
.0 9.0 8.0
T"
7.0
6.0 5.0 4.0 3.0 2.0 1.0 0.0
Particle Diameter (fjm)
X.6 Number basis particle size data for batch
number six of 061990 series UPLMs (4.6 pm size
regime, unclassified)

10
00
90
80
70
60
50
40
30
20
10
0
35
30
25
20
15
10
5
0
571
Batch 06199007, Unsettled
Size Data (Number Based):
Arithmetic
Mean:
4.25 (pm)
Median:
4.45 (pm)
Geometric
Standard
Deviation:
1.03
Standard
Deviation:
± 0.57 (pm)
Number of Points: 125
.0 9.0 8.0 7.0 6.0 5.0 4.0 3.0 2.0 1.0 0.0
Particle Diameter (jjm)
1.7 Number basis particle size data for batch
number seven of 061990 series UPLMs (4.6 pm
size regime, unclassified)

Number Percent at Size
572
Batch 06199008, Unsettled
Particle Diameter (//m)
Figure All.8 Number basis particle size data for batch
number eight of 061990 series UPLMs (4.6 pm
size regime, unclassified)

Number Percent at Size
573
110
100
90
80
70
60
50
40
30
20
10
0
35
30
25
20
15
10
5
0
10.0 9.0 8.0 7.0 6.0 5.0 4.0 3.0 2.0 1.0 0.0
Particle Diameter (jtfm)
Figure All.9 Number basis particle size data for batch
number nine of 061990 series UPLMs (4.6 pm size
regime, unclassified)
Batch 06199009, Unsettled
Size Data (Number Based):
Arithmetic
Mean:
4.91 (pm)
Median:
5.14 (pm)
Geometric
Standard
Deviation:
1.04
Standard
Deviation:
± 0.65 (pm)
Number of Points: 125
f I!

Number Percent at Size
574
Batch 06199010, Unsettled
Particle Diameter (pm)
Figure All.10 Number basis particle size data for batch
number ten of 061990 series UPLMs (4.6 pm size
regime, unclassified)

10
00
90
80
70
60
50
40
30
20
10
0
35
30
25
20
15
10
5
0
575
Batches 06199001-07+09, Unsettled
.0
1.0
0.0
Particle Diameter (pm)
1.11 Number basis particle size data for combined
batches 1-7+9 of 061990 series UPLMs (4.6 pm
size regime, unclassified)

10
20
30
40
50
60
70
80
90
100
110
120
130
140
150
160
170
180
190
200
210
220
230
240
250
260
270
280
290
300
310
320
330
340
350
360
370
380
390
400
410
420
430
440
450
460
470
480
490
500
APPENDIX III
LEAST SQUARES POLYNOMIAL REGRESSION
DATA CURVE FITTING PROGRAM (BASIC)
CLS
COLOR 13,1
PRINT " LEAST SQUARES APPROXIMATION"
PRINT
PRINT " Nth-ORDER REGRESSION (N < = 12)”
PRINT
DIM A(25), R(13,14), T(14)
PRINT "DEGREE OF EQUATION";
INPUT D
PRINT "NUMBER OF KNOWN POINTS”;
PRINT " (MUST BE >= N+2)"
INPUT N
A (1) = N
INPUT "TYPE 1 TO USE OLD FILE OR 2 TO START NEW FILE" ; L
IF L=1 GOTO 350
INPUT "WHAT IS THE FILE NAME FOR X";X$
INPUT "WHAT IS THE FILE NAME FOR Y”;Y$
OPEN X$ FOR OUTPUT AS #1
OPEN Y$ FOR OUTPUT AS #2
FOR 1=1 TO N
PRINT "X,Y OF POINT";I;
INPUT X,Y
WRITE #1,X
WRITE #2,Y
FOR J=2 TO 2*D+1
A(J) = A(J) + X-(J-l)
NEXT J
FOR K=1 TO D+l
R(K,D+2) = T(K) + Y *X"(K-l)
T(K) = T(K) + Y*K~(K-l)
NEXT K
T(D+2) = T(D+2) +Y'2
NEXT I
GOTO 510
INPUT "WHAT IS THE FILE NAME FOR X";X$
INPUT "WHAT IS THE FILE NAME FOR Y";Y$
OPEN X$ FOR INPUT AS #1
OPEN Y $ FOR INPUT AS #2
FOR 1=1 TO N
INPUT #1,X
INPUT #2,Y
FOR J=2 TO 2*D+1
A(J) = A(J) + X-(J-l)
NEXT J
FOR K=1 TO D+l
R(K,D+2) = T(K) +Y*X*(K-l)
T(K) = T(K) + Y*X~(K-1)
NEXT K
T(D+2) = T(D+2) + Y'2
NEXT I
576

510
520
530
540
550
560
570
580
590
600
610
620
630
640
650
660
670
680
690
700
710
720
730
740
750
760
770
780
790
800
810
820
830
840
850
860
870
880
890
900
910
920
930
940
950
960
970
980
990
577
CLOSE
FOR J=1 TO D+l
FOR K=1 TO D+l
R(J,K) = A(J+K-l)
NEXT K
NEXT J
FOR J=1 TO D+l
K=J
IF R(K,J) <> 0 THEN 640
K=K+1
IF K <= D+l THEN 590
PRINT "NO UNIQUE SOLUTION"
GOTO 1220
FOR 1=1 TO D+2
S = R (J, I)
R(J,I) = R(K,I)
R(K,I) = S
NEXT I
Z = 1/R(J,J)
FOR 1=1 TO D+2
R(J,I) = X*R(J,I)
NEXT I
FOR K=1 TO D+l
IF K=J THEN 790
Z = -R(K,J)
1=1 TO D+2
R(K,I) = R(K,I) + Z*R(J,I)
NEXT I
NEXT K
NEXT J
INPUT "1 FOR PRINTOUT OF X AND Y OR 2 FOR PRINTOUT OF STATISTICS
ONLY";M
IF M=2 GOTO 920
OPEN X$ FOR INPUT AS #1
OPEN Y$ FOR INPUT AS #2
LPRINT "X Y ”
NEXT I
INPUT #1,X
INPUT #2,Y
LPRINT X,Y
NEXT I
CLOSE
LPRINT
LPRINT " CONSTANT =";R(l,D+2)
FOR J=1 TO D
LPRINT J; "DEGREE COEFFICIENT ="; R(J+l,D+2)
NEXT J
LPRINT
p=o
FOR J=2 TO D+l
P = P + R(J,D+2)*(T(J) - A(J)*T(1)/N)
NEXT J
Q = T(D+2) - T(l)"2/N
Z = Q - P
I = N - D -1
LPRINT
J = P/Q
LPRINT "COEFFICIENT OF DETERMINATION (R/'2) = ";J
LPRINT "COEFFICIENT OF CORRELATION ="; SQR (J)
LPRINT "STANDARD ERROR OF ESTIMATE ="; SQR (ABS(Z/I))
LPRINT

1110
1120
1130
1140
1150
1160
1170
1180
1190
1200
1210
1220
578
PRINT "INTERPOLATION: (ENTER 0 TO END PROGRAM)”
P = R(1,D+2)
PRINT "X =";
INPUT X
IF X = 0 THEN 1220
FOR J=1 TO D
P = P + R(J+1,D+2)*X*J
NEXT J
PRINT "Y ="; P
PRINT
GOTO 1120
RUN "POLYREGR”

APPENDIX IV
LIST OF ACRONYMS
Acronym:
AC
ACN
AI
AIBN
ASG
ASLT
BCB
BCC
BPO
BS
C4
CFG
CMOS
CMPF
CMPL
CNPF
CNPL
COB
CP
CPSA
CSSA
CTE
CVFF
CVPF
CVPL
DIP
DTA
ELSI
EMT
EtOH
FCC
FRU
FTIR
GD
GEM
GNP
GSD
HGM
ICP
ISDN
LCM
LSI
MC
Definition:
Alternating Current
Average Cluster Number
Artificial Intelligence
Azobis (2-methyl-propionitrile)
Apparent Specific Gravity
Advanced Solid Logic Technology
Bisbenzocyclobutene
Body-Centered Cubic
Benzoyl Peroxide
Borosilicate glass
Controlled Collapse Chip Connection
Ceramic-Filled Glass
Complimentary Metal Oxide Semiconductor
Cumulative Mass Percent Finer than
Cumulative Mass Percent Larger than
Cumulative Number Percent Finer than
Cumulative Number Percent Larger than
Card On Board
Closed Porosity
Centrifugal Particle Size Analysis
Cumulative Spherical equivalent Surface Area
Coefficient of Thermal Expansion
Cumulative Volume Fraction Finer than
Cumulative Volume Percent Finer than
Cumulative Volume Percent Larger than
Dual In-line Package
Differential Thermal Analysis
Early Large Scale Integration
Effective Medium Theory
Ethanol
Face-Centered Cubic
Field Replaceable Unit
Fourier Transform Infrared spectroscopy
Green Density
General Effective Medium theory
Gross National Product
Geometric Standard Deviation
Hollow Glass Microspheres
Inductively Coupled Plasma spectroscopy
Integrated Services Digital Network
Liquid Cooled Module
Large Scale Integration
Metallized Ceramic
579

580
Acronym:
MCP
MeOH
MIBK
MLC
MMA
MPCD
MPCR
MS
MUT
NLPS
NSRI
OP
PCSD
PDN
PE
PE
PF
PLII
PM
PMMA
PMP
PS
PTFE
PVB
PVP
QM
QMT
RC
RCP
RH
RNSPAS
RP
SA
SC
SEM
SLT
SMS
SSA
SSAAS
TCM
TDR
TEM
TGA
ThD
TOF
TP
TRNP
ULSI
UPLM
VF
VLSI
VTL
WSI
Definition:
Metallized Ceramic-Polyimide
Methanol
Methyl Isobutyl Ketone
Multilayer Ceramic
Methyl Methacrylate
Median Pore Channel Diameter
Median Pore Channel Radius
Mackenzie-Shuttleworth
Material Under Test
Nonreactive Liquid Phase Sintering
Nonsintering Rigid Inclusions
Open Porosity
Pore Channel Size Distribution
Power Distribution Network
Packing Efficiency
Polyethylene
Power dissipation Factor
Platinel Two thermocouple
Photomultiplier tube
Polymethyl Methacrylate
Polymethylpentene
Polystyrene
Polytetrafluoroethylene
Polyvinyl Butyral
Polyvinyl Pyrrolidone
Qualitative Microscopy
Qualitative Microscopy Techniques
Resistive Capacitance
Random Close Packing
Relative Humidity
Relative Number of Spherical Particles at Size
Random Packing
Surface Area
Simple Cubic
Scanning Electron Microscopy
Solid Logic Technology
Standard Modular System
Specific Surface Area
Specific Surface Area At Size
Thermal Conduction Module
Time Domain Reflectometry
Transmission Electron Microscopy
Thermogravimetric Analysis
Theoretical Density
Time Of Flight spectroscopy
Total Porosity
Total Relative Number of spherical Particles
Ulta-Large Scale Integration
Uniform Polystyrene Latex Microspheres
Volume Fraction
Very-Large Scale Integration
Vendor Transistor Logic
Wafer Scale Integration

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[29SMI]
W.O. Smith, P.D. Foote, P.F. Busang, "Packing of Homogeneous
Spheres," Phys. Rev., 24, pp. 1271-74, (November, 1929).
[30AND]
A.H.M. Andreasen, J. Andersen, "Relation Between Grain Size
and Intersitial Space in Products of Unconsolidated
Granules,” Kolloid-Z., ¿0, pp. 217-28, (1930, German).
[30WES]
A.E.R. Westman, H.R. Hugill, "The Packing of Particles," J.
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[31FUR]
C.C. Furnas, "Grading Aggregates, I-Mathematical Relations
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[37WHI]
H.E. White, S.F. Walton, "Particle Packing and Particle
Shape," J. Am. Cer. Soc., 20, pp. 155-66, (1937).
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J. Frenkel, "Viscous Flow of Crystalline Bodies Under the
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385-91, (1945).
[49KUC]
G.C. Kuczynski, "Study of the Sintering of Glass,” Journal
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[49MAC]
J.K. Mackenzie, R.L. Shuttleworth, "A Phenomenological
Theory of Sintering," The Proceedings of the Physical
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[50HER]
C. Herring, "Effect of Change of Scale on Sintering
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(1950) .
[53FUL]
R.L. Fullman, "Measurement of Particle Sizes in Opaque
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A.R. Von HioDel, editor. Dielectric Materials and
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W.D. Kingery, M. Berg, "Study of the Initial Stages of
Sintering Solids by Viscous Flow, Evaporation-Condensation,
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pp. 1205-12, (1955).
[56FAT1]
I. Fatt, "The Network Model of Porous Media: I. Capillary
Pressure Characteristics," Petroleum Transactions of the
AIME, 207, pp. 144-59, (1956).
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582
[56FAT2]
I. Fatt, "The Network Model of Porous Media: II. Dynamic
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[56FAT3]
I. Fatt, "The Network Model of Porous Media: III. Dynamic
Properties of Networks with Tube Radius Distribution,”
Petroleum Transactions of the AIME, 207, dd. 164-81, (19561.
[56TEM]
C.C Templeton, S.S. Rushing, Jr., "Oil-Water Displacements
in Microscopic Capillaries," Petroleum Transactions of the
AIME, 202, PP- 211-14, (1956).
[57WAC]
J.B. Wachtman, Jr., L.H. Maxwell, "Plastic Deformation of
Ceramic-Oxide Single Crystals, II," J. Am. Cer. Soc., 40,
[11], PP- 377-85, (1957).
[59BRO]
S.D. Brown, S.S. Kistler, "Devitrification of High-Si02
Glasses of the System Al203-Si02, " J. Am. Cer. Soc., 42, [6],
pp. 263-70, (1959).
[59DOM]
C. Domb, On the Theory of Cooperative Phenomena in Crystals,
Advances in Phvsics, VIII., r 29 — 32 1 , Tavlor and Frances
Ltd., London, England, pp. 149-361, (1959).
[59FIS]
M.E. Fisher, M.F. Sykes, Excluded-Volume Problem and the
Ising Model of Ferromagnetism," Phys. Rev., 114, [1], pp.
45-58, (1959).
[60BER]
J.D. Bernal, J. Mason, "Co-ordination of Randomly Packed
Spheres," Nature, 188, pp. 910-11, (1960).
[60SCO]
G.D. Scott, "Packing of Equal Spheres," Nature, 188, pp.
908-909, (1960).
[61DOM]
C. Domb, M.F. Sykes, "Cluster Size in Random Mixtures and
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M. E. Fisher, J.W. Essam, "Some Cluster Size and Percolation
Problems," Journal of Mathematical Physics, 2, [4], pp. 609-
19, (1961).
[61FIS2]
M.E. Fisher, "Critical Probabilities for Cluster Size and
Percolation Problems," Journal of Mathematical Physics, 2,
[4], pp. 620-27, (1961).
[61FRI]
H.L. Frisch, E. Sonnenblick, V.A. Vyssotsky, "Critical
Percolation Probabilities (Site Problem)," Phys. Rev., 124,
[4], pp. 1021-22, (1961).
[61MCG]
R.K. McGeary, "Mechanical Packing of Spherical Particles,"
J. Am. Cer. Soc., 44, [10], pp. 513-22, (1961).
[61SEL]
J. Seising, "Internal Stress in Ceramics," J. Am. Cer. Soc.-
Discussions and Notes, 4_4, [8], p. 419, (1961).
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N. Epstein, M.J. Young, "Random Loose Packing of Binary
Mixtures of Spheres," Nature 196, pp. 885-86, (1962).

583
[62HET]
[62KIN]
[63DOM]
[63FRI]
[64HET]
[64SYK]
[65AYE]
[65LEV]
[65ROS]
[66AYE]
[66WAG]
[66WEB]
[67KIR]
[67VAN]
[68CUT]
G. Hetherington, K.H. Jack, "Water in Vitreous Silica: Part
I. Influence of 'Water' Content on the Properties of
Vitreous Silica,” Physics and Chemistry of Glasses, 3, [4],
pp. 129-33, (1962).
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Equipment: An Overview," Thermal Management Concepts in
Microelectronic Packaging, Edited by S.S. Furkay, R.F.
Kilburn, G. Monti, Jr., The International Society for Hybrid
Microelectronics, Silver Spring, MD, pp. 153-71, (1984).
B.H. Mussler, M.W. Shafer, "Preparation and Properties of
Mullite-Cordierite Composites," Ceramic Bulletin, 6_3, [5],
pp. 705-10, (1984).
W.P. Noble, A.R. Ellenberger, "Temperature Effects on Device
Functionality," Thermal Management Concepts in
Microelectronic Packaging, Edited by S.S. Furkay, R.F.
Kilburn, G. Monti, Jr., The International Society for Hybrid
Microelectronics, Silver Spring, MD, pp. 45-65, (1984).
B.R. Patterson, L.A. Benson, "The Effect of Powder Size
Distribution on Sintering," Progress in Powder Metallurgy,
39, pp. 215-30, (1984).
R. Raj, R.K. Bordia, "Sintering Behavior of Bi-Modal Powder
Compacts," Acta. Metall., 32, [7], pp. 1003-19, (1984).
R.W. Rice, "Pores as Fracture Origins in Ceramics," Journal
of Materials Science, .19, pp. 895-915, (1984).
M.D. Sacks, T.Y. Tseng, "Preparation of SiO, Glass from
Model Powder Compacts: I, Formation and Characterization of
Powders, Suspensions, and Green Compacts," J. Am. Cer. Soc.,
67, [8], pp. 526-31, (1984).
M.D. Sacks, T.Y. Tseng, "Preparation of SiO; Glass from
Model Powder Compacts: II, Sintering," J. Am. Cer. Soc., 67,
[8], pp. 532-37, (1984).
G.W. Scherer, J.C. Luong, "Glasses from Colloids," Journal
of Non-Crystalline Solids," 6r3, pp. 163-72, (1984).

592
[84SCH2]
[84SCH3]
[84SCH4)
[84SIM]
[84SMI]
[84TAY]
[84WAG1]
[84WAG2]
[84WEB]
[85BAR]
[85BLA]
[85BOR]
[85BUG]
[85CAN]
G.W. Scherer, "Viscous Sintering of a Bimodal Pore-Size
Distribution," J. Am. Cer. Soc., 6_7, [11], pp. 709-15,
(1984) .
B. Schwartz, "Microelectronics Packaging: II," Ceramic
Bulletin, 63^, [4], pp. 577-81, (1984).
B. Schwartz, "Review of Multilayer Ceramics for
Microelectronic Packaging," J. Phys. Chem. Solids, 45^, [10],
1051-68, (1984).
E. Simiu, D.A. Reed, C.W.C. Yancey, J.W. Martin, E.M.
Hendrickson, A.C. Gonzalez, M. Koike, J.A. Lechner, M.E.
Batts, Rinq-on-Rinq Tests and Load Capacity of Cladding
Glass, National Bureau of Standards Building Science Series
162, (August, 1984).
J.P. Smith, G.L. Messing "Sintering of Bimodally Distributed
Alumina Powders," J. Am. Cer. Soc., 61_, [4], pp. 238-42,
(1984).
B.E. Taylor, R.R. Getty, J. Henderson, C.R.S. Needes, "Air
and Nitrogen-Fireable Multilayer Systems: Materials and
Performance Characteristics, Part II," Solid State
Technology, pp. 291-95 (April, 1984).
A.J. Wagner, H.C. Cook, "Modeling the Temperature Dependence
of Integrated Circuit Failures," Thermal Management Concepts
in Microelectronic Packaging. Edited by S.S. Furkay, R.F.
Kilburn, G. Monti, Jr., The International Society for Hybrid
Microelectronics, Silver Spring, MD, pp. 1-43, (1984).
G.R. Wagner, "Circuit Board Material/Construction and its
Effect on Thermal Management," Thermal Management Concepts
in Microelectronic Packaging, Edited by S.S. Furkay, R.F.
Kilburn, G. Monti, Jr., The International Society for Hybrid
Microelectronics, Silver Spring, MD, pp. 173-84, (1984).
Webster's Illustrated Dictionary Encyclopedia, Crescent
Books, New York, NY, (1984).
D.R. Barbour, "Multichip Module Technology," Advances in
Ceramics, 19. The American Ceramic Society, Inc.,
Westerville, OH, pp. 15-30, (1985).
J.R.H. Black, "Technology and Market Trends in Multilayer
Ceramic Devices," Advances in Ceramics, 19, The American
Ceramic Society, Inc., Westerville, OH, pp. 3-11, (1985).
R.K. Bordia, R. Raj, "Sintering Behavior of Ceramic Films
Constrained by Rigid Substrate," J. Am. Cer. Soc., 68, [6],
pp. 287-92, (1985).
A.L.R. Bug, S.A. Safran, G.S. Grest, I. Webman, "Do
Interactions Raise or Lower a Percolation Threshold?"
Physical Review Letters, 5J5, [18], pp. 1896-99, (1985).
W.R. Cannon, J.R. Morris, K.R. Mikeska, "Dispersants for
Nonaqueous Tape Casting," Advances in Ceramics, 19, The
American Ceramic Society, Inc., Westerville, OH, pp. 161-74,
(1985) .

593
[85CHI]
Y.C. Chiew, G. Stell, E.D. Glandt, "Clustering and
Percolation in Multicomponent Systems of Randomly Centered
and Permeable Spheres," J. Chem. Phys., 83., [2], pp. 761-67,
(1985).
[85FRE]
S.W. Freiman, A.C. Gonzalez, "Electrical Failures Due to
Cracks in Multilayer Ceramic Capacitors," Advances in
Ceramics, 19, The American Ceramic Society, Inc..
Westerville, OH, pp. 191-201, (1985).
[85HOD]
J.D. Hodge, "Densification and Microstructural Aspects of
Mullite-Cordierite Ceramics," Advances in Ceramics, 19, The
American Ceramic Society, Inc., Westerville, OH, pp. 117-29,
(1985).
[85HSU]
W.Y. Hsu, T. Berzins, "Percolation and Effective-Medium
Theories for Perfluorinated Ionomers and Polymer
Composites," Journal of Polymer Science: Polymer Physics
Edition, 2_3, pp. 933-53, (1985).
[85KAH]
M. Kahn, "Effects of Partial Oxygen Pressure During Burnout
of Multilaver Structures," Advances in Ceramics, 19, The
American Ceramic Society, Inc., Westerville, OH, pp. 185-88,
(1985).
[85KAW]
K. Kawakami, M. Takabatake, T. Minowa, J. Chiba, M. Sisaki,
"A Low-Temperature Cofired Multilayer Ceramic Substrate,"
Advances in Ceramics, 19, The American Ceramic Society,
Inc., Westerville, OH, pp. 95-102, (1985).
[ 85KON ]
K. Kondo, M. Okuyama, Y. Shibata, "Low Firing Temperature
Ceramic Material for Multilayer Ceramic Substrates,"
Advances in Ceramics, 19, The American Ceramic Society,
Inc., Westerville, OH, pp. 77-87, (1985).
[85KUC]
G.C. Kuczynski, "Towards the Understanding of the Process of
Sinterina," Sinterina '85, Edited bv G.C. Kuczvnski, D.P.
Uskokovic, H. Palmour III, M.M. Ristic, Plenum Press, New
York, NY, pp. 3-16, (1985).
[85LEE1]
C.T. Lee, D.E. Clark, "Characterization of Glass Surfaces,"
Applications of Surface Science, pp. 397-412, (1985).
[85LEE2]
H.Y. Lee, L.C. Button, "Influence of Electrode-Ceramic
Interface on MLC Leakaae Current," Advances in Ceramics, 19,
The American Ceramic Society, Inc., Westerville, OH, pp.
219-27, (1985).
[ 85LOK ]
K.P. Lok, C.K. Ober, "Particle Size Control in Dispersion
Polymerization of Polystyrene," Can. J. Chem., &_3, pp. 209-
16, (1985).
[850GI]
S. Ogihara, T. Yasuda, K. Otsuka, F. Kobayashi, "Application
to LSI Packages of SiC Ceramics with High Thermal
Conductivity," The International Journal for Hybrid
Microelectronics, 8, [2], pp. 16-20, (1985).
[85NEE]
C.R.S. Needes, D.P. Button, "Reliability Testing of Thick
Film Multilayer Materials," Proceedings of the 35th
Electronic Components Conference, Washington, DC, IEEE, New
York, NY, pp. 505-11, (1985).

594
[85NIW]
K. Niwa, N. Kamehara, H. Yokoyama, K. Yokouchi, K. Kurihara,
"Multilayer Ceramic Circuit Board with Copper Conductor,"
Advances in Ceramics, 19, The American Ceramic Society,
Inc., Westerville, OH, pp. 41-47, (1985).
[85PAT]
B.R. Patterson, V.D. Parkhe, J.A. Griffin, "Effect of
Particle Size Distribution on Sinterinq," Sinterina '85,
Edited by G.C. Kuczynski, D.P. Uskokovic, H. Palmour III,
M.M. Ristic, Plenum Press, New York, NY, pp. 43-51, (1985).
[85RAB]
E.M. Rabinovich, "Review: Preparation of Glass by
Sintering," Journal of Materials Science, 20, pp. 4259-97,
(1985).
[85RIK]
P.A. Rikvoid, G. Stell, "Porosity and Specific Surface for
Inpenetrable-Sphere Models of Two-Phase Random Media," J.
Chem. Phys., 82, [2], pp. 1014-20, (1985).
[85SAC]
M.D. Sacks, G.W. Scheiffele, "Polymer Adsorption and
Particulate Dispersion in Nonaqueous A1:03 Suspensions
Containing Poly(vinvl butyral) Resins," Advances in
Ceramics, 19, The American Ceramic Society, Inc.,
Westerville, OH, pp. 175-84, (1985).
[85SCH1]
G.W. Scherer, "Sol-Gel-Glass: III. Viscous Sintering,"
Journal of Non-Crystalline Solids, 72., pp. 369-89, (1985).
[85SCH2]
G.W. Scherer, Relaxation in Glass and Composites, J. Wilev &
Sons, New York, NY, (1985).
[85SCH3]
G.W. Scherer, T. Garino, "Viscous Sintering on a Rigid
Substrate," J. Am. Cer. Soc., 68, [4], pp. 216-20 (1985).
[85SCH4]
B. Schwartz, "Multilayer Ceramics," Advances in Ceramics,
19, The American Ceramic Society, Inc., Westerville, OH, p.
13, (1985).
[85SHA]
D.J. Shanefield, "Competing Adsorptions in Tape Casting,"
Advances in Ceramics, 19, The American Ceramic Societv,
Inc., Westerville, OH, pp. 155-60, (1985).
[85SIE]
K. Sieradzki, "The Fracture Strength of Solids Near the
Percolation Threshold," J. Phys. C: Solid State Phys., 18,
pp. L855-56, (1985).
[85STA]
D. Stauffer, Introduction to Percolation Theorv, Tavlor and
Francis, Inc., Philadelphia, PA, (1985).
[85STE]
J.I. Steinberg, S.J. Horowitz, R.J. Bacher, "Low-Temperature
Cofired Tape Dielectric Material Systems for Multilayer
Interconnections." Advances in Ceramics, 19, The American
Ceramic Society, Inc., Westerville, OH, pp. 31-39, (1985).
[85VER]
H. Verweij, G. De, D. Veeneman, "Hollow Glass Microsphere
Composites: Preparation and Properties,” Journal of
Materials Science, 20, pp. 1069-78, (1985).
[85WEA]
[85WEB]
R.C. Weast, editor, CRC Handbook of Chemistry and Physics,
66, CRC Press, Boca Raton, FL, (1985-86).
J. Weber, Tomorrow's World: Computers, The Next Generation,
ARCO Publishing, Inc., New York, NY, (1985).
[85WEB]

595
[86BLE]
P. Bless, L. Ugol, C. Huang, S.J. Stein, "Reliable
Multilayer Thick Films Made with Low Impedance Ag-Based
Conductors," Proceedings of the 19th International Symposium
on Microelectronics, Atlanta, GA, ISHM, Reston, VA, pp. 450-
60, (1986).
[86BUC]
R.C. Buchanan, C.V. Beck, "Glass Films and Interfaces in
Microelectronic Applications," Mat. Res. Soc. Symp. Proc.,
72, pp. 41-45, (1986).
[86CHA]
G.V. Chandrashekhar, M.W. Shafer, "Dielectric Properties of
Sol-Gel Silica Glasses," Mat. Res. Soc. Symp., pp. 705-10,
(1986).
[86CRO]
L.E. Cross, T.R. Gururaja, "Ultra-Low Dielectric
Permittivity Ceramics and Composites for Packaging
Applications," Mat. Res. Soc. Symp. Proc., 72, pp. 53-65,
(1986).
[86DAS]
A. Das, R. Messier, T.R. Gururaja, L.E. Cross, "Low
Permittivity, SiO;/Void Nanocomposite Films," Mat. Res. Soc.
Proc., 7_2, pp. 27-33, (1986).
[86DEJ]
L.C. DeJonge, M.N. Rahaman, C.H. Hsueh, "Transient Stresses
in Bimodal Compacts During Sintering," Acta. Metall., 34,
[7), pp 1467-71, (1986).
[86GEN]
G. Gensse, U. Chowdry, "Non-Conventional Route to Glass-
Ceramics for Electronic Packaging," Mat. Res. Soc. Symp.,
73. pp. 693-703, (1986).
[86HAM]
Y. Hamano, M. Terasawa, "Advanced Packaging for High
Integration and High Speed Applications," Mat. Res. Soc.
Symp. Proc., 1_2, PP* 3-13, (1986).
[86HSU1]
C.H. Hsueh, A.G. Evans, R.M. Cannon, R.J. Brook,
"Viscoelastic Stresses and Sintering Damage in Heterogeneous
Powder Compacts," Acta. Metall., 34, [5], pp. 927-36,
(1986).
[86HSU2]
C.H. Hsueh, A.G. Evans, R.M. McMeeking, "Influence of
Multiple Heterogeneities on Sintering Rates," J. Am. Cer.
Soc., 69, [4], pp. C-64-C-66, (1986).
[86IWA]
Y. Iwata, S. Saito, Y. Satoh, F. Okamura, "Development of
Ceramic-Composite (Porous-Ceramic & Resin Composite with
Copper Foil)," IMC 1986 Proceedings, Kobe, Japan, pp. 65-70,
(1986).
[86KAH]
M. Kahn, B. Kriese, "Patterned Macrovoids for Dielectric
Constant Control of High Frequency Circuit Substrates," Mat.
Res. Soc. Symp. Proc., 12, pp. 35-40, (1986).
[86KHA]
A.K. Khaund, C.L. Cutts, "Defect Free Al:03 Substrates for
Thin Film Applications," Proceedings of the 19th
International Symposium on Microelectronics, Atlanta, GA,
ISHM, Reston, VA, pp. 209-16, (1986).
[86LAN]
A. Lane, N. Shah, W.C. Conner, Jr., "Measurement of the
Morphology of High-Surface-Area Solids: Porosimetry as a
Percolation Process," Journal of Colloid and Interface
Science, 109, [1], pp. 235-42, (1986).

596
[86LEV]
[86MAC]
[86NIS]
[86PON)
[86RAH1]
[86RAH2]
[86RAO]
[86SAT]
[86SAW]
[86SCH1]
[86SCH2]
[86SMI]
[86TEA]
R.A. Levy, K. Nassau, "Viscous Behavior of Phosphosilicate
and Borophosphosilicate Glasses in VLSI Processing," Solid
State Technology, pp. 123-30, (October, 1986).
R.B. Maciolek, "Packaging Very High I/O Chips with
Tab/Solder Reflow Technology, Electronic Packaging:
Materials and Processes, Edited by J.A. Sartell, ASM
International, Metals Park, OH, pp. 15-18, (1986).
S. Nishigaki, J. Fukuta, S. Yano, H. Kawabe, K. Noda, M.
Fukaya, "A New Low Temperature Fireable Ag Multilayer
Ceramic Substrate Having Post-Fired Cu Conductor (LFC-2),
Proceedings of the 19th International Symposium on
Microelectronics, Atlanta, GA, ISHM, Reston, VA, pp. 429-49,
(1986) .
R. G. Pond, C.J. Sabo, W.A. Vitriol, R.L. Brown, "Processing
and Reliability of Resistors Incorporated within Low
Temperature Cofired Ceramic Structures," Proceedings of the
19th International Symposium on Microelectronics, Atlanta,
GA, ISHM, Reston, VA, pp. 461-72, (1986).
M.N. Rahaman, L.C. DeJonghe, R.J. Brooke, "Effect of Shear
Stress on Sintering," J. Am. Cer. Soc., 6£, [1], pp. 53-58,
(1986).
M.N. Rahaman, L.C. DeJonghe, C.H. Hsueh, "Creep During
Sintering of Porous Compacts," J. Am. Cer. Soc., 6j3, [1],
pp. 58-60, (1986) .
M.K. Rao, K.Y. Chua, S.L. Lim, "Effects of Infra-Red Firing
on the Properties of Low-K Thick Film Dielectric
Compositions," Proceedings of the 19th International
Symposium on Microelectronics, Atlanta, GA, ISHM, Reston,
VA, pp. 119-23, (1986).
T. Satoh, K. Akiyama, Y. Fujita, N Ebina, Y. Fukuda,
"Properties of Copper Plated Metal Core Ceramic Substrates,"
Proceedings of the 19th International Symposium on
Microelectronics," Atlanta, GA, ISHM, Reston, VA, pp. 203-
07, (1987).
H.T. Sawhill, A.L. Eustice, S.J. Horowitz, J. Gar-El, A.R.
Travis, "Low Temperature Co-Fireable Ceramics with Co-Fired
Resistors," Proceedings of the 19th International Symposium
on Microelectronics, Atlanta, GA, ISHM, Reston, VA, pp. 473-
80, (1986).
G.W. Scherer, "Viscous Sintering Under a Uniaxial Load,” J.
Am. Cer. Soc., 69, [9], pp. C-206-C-207, (1986).
G.W. Scherer, Relaxation in Glass and Composites, Wiley &
Sons, New York, NY, (1986).
L.H. Smith, "Hollow Microspheres: More Than Just Fillers,”
Materials Engineering, 103, pp. 27-30, (February, 1986).
W.H. Teat, B.L. Marten, D.C. Blazej, R. Oboodi, "Properties
of a New Selective Ceramic-Coated Metal Substrate,"
Proceedings of the 19th International Symposium on
Microelectronics, Atlanta, GA, ISHM, Reston, VA, pp. 196-
202, (1986).

597
[86THO]
S.C. Thorstenson, "Compatible Substrates for Surface
Mountina Technoloav-A PWB Industry Review," Electronic
Packaaina: Materials and Processes, ASM International.
Metals Park, OH, pp. 1-7, (1986).
[86TSE1]
C.M. Tseng, Y.Y. Lu, M.S. El-Aasser, J.W. Vanderhoff,
"Uniform Polymer Particles by Dispersion Polymerization in
Alcohol," Journal of Polymer Science: Part A: Polymer
Chemistry Edition, 2j4, pp. 2995-3007, (1986).
[86TSE2]
T.Y. Tseng, J.J. Yu, "Various Atmospheric Effects on
Sintering of Compacts of SiO; Microspheres," Journal of
Materials Science, 2_1, pp. 3615-3624, (1986).
[86UTS]
K. Utsumi, Y. Shimada, H. Takamizawa, "Monolithic
Multicomponents Ceramic (MMC) Substrate," Mat. Res. Soc.
Symp. Proc. , 7_2, pp. 15-26, (1986).
[86VEN]
K. R. Venkatachari, R. Raj, "Shear Deformation and
Densification of Powder Compacts," J. Am. Cer. Soc., 69,
[6], pp. 499-506, (1986).
[86VES]
G.M. Vest, V.P. Cone, C.J. Herzfeld, A.K. Bansali, "Metallo-
Organic Decomposition (MOD) Films for Electronic Packaging,"
Mat. Res. Soc. Symp. Proc., 72., pp. 47-52, (1986).
[86YAN]
M. Yanuka, F.A.L. Dullien, D.E. Elrick, "Percolation
Processes and Porous Media, I: Geometrical and Topological
Model of Porous Media Using a Three-Dimensional Joint Pore
Size Distribution," Journal of Colloid and Interface
Science, 112, [1], pp. 24-41, (1986).
[87ALF]
N.M. Alford, J.D. Birchall, K. Kendall, "High-Strength
Ceramics through Colloidal Control to Remove Defects,"
Nature, 330, [5], 51-53, (1987).
[87BAN1]
H. Banno, "Effects of Shape and Volume Fraction of Closed
Pores on Dielectric, Elastic, and Electromechanical
Properties of Dielectric and Piezoelectric Ceramics-A
Theoretical Approach," Ceramic Bulletin, 66, [9], pp. 1332-
37, (1987).
[87BAN2]
L.B. Bañas, Uniform Latex Particles, Seraaen Diaanostics,
Inc., Indianapolis, IN, (1987).
[87BEL]
F.J. Belcourt, "Electrical Issues Associated with High
Density Packaaina," Electronic Packaaina and Corrosion in
Microelectronics, Edited bv M.E. Nicholson, ASM
International, Metals Park OH, pp. 71-77, (1987).
[87BEN]
[87BER]
L. Benguigui, J. Yacubowicz, M. Narkis, "On the Percolative
Behavior of Carbon Black Cross-Linked Polyethylene Systems,"
Journal of Polymer Science: Part B: Polymer Physics, 25, pp.
127-35, (1987).
K.A. Berry, "Corrosion Resistance of Military
Microelectronic Packages at the Lead-Glass Interface,"
Electronic Packaaina and Corrosion in Microelectronics,
Edited by M.E. Nicholson, ASM International, Metals Park,
OH, pp. 55-61, (1987).
[87BER]

598
[ 8 7 CAH]
D.G. Cahill, R.O. Pohl, "Thermal Conductivity of Amorphous
Solids above the Plateau," Physical Review B, 3J5, [8], pp.
4067-73, (1987).
[87CHO]
U. Chowdry, A.W. Sleight, "Ceramic Substrates for
Microelectronic Packaging," Ann. Rev. Mater. Sci., 17, pp.
323-40, (1987).
[87CLA]
R. Ciasen, "Preparation and Sintering of High-Density Green
Bodies to High-Purity Silica Glasses," Journal of Non-
Crystalline Solids, 89, pp. 335-44, (1987).
[87COR1]
M. Corke, K. Sweeney, R. Prater, J. Muhs, K. Schmidt, "Fiber
Optic Components for Communications Applications,"
Proceedings of the 37th Electronic Components Conference,
Boston, MA, IEEE, New York, NY, pp. 243-53, (1987).
[87COR2]
M. Corke, P. Akhavan-Leilabady, "Fiber Optic Components For
Sensor Applications," Proceedings of the 37th Electronic
Components Conference, Boston, MA, IEEE, New York, NY, pp.
254-64, (1987).
[87DET]
E.S. Dettmer, H.K. Charles, Jr., "Fundamental
Characterization of Aluminum Nitride and Silicon Carbide for
Hybrid Substrate Applications," The International Journal
for Hybrid Microelectronics, ¿0, [2], pp. 9-17, (1987).
[87FOS]
E.M. Foster, "The Electrical Effect of Single-Chip CMOS
Packages," Proceedings of the 37th Electronic Components
Conference, Boston, MA, IEEE, New York, NY, pp. 342-53,
(1987).
[87FRA]
R.P. Frankenthal, "Corrosion in Microelectronics Current
Status and Future Directions,” Electronic Packaaina and
Corrosion in Microelectronics, Edited bv M.E. Nicholson, ASM
International, Metals Park, OH, pp. 295-96, (1987).
[87GEH]
R.W. Gehman, "Materials Selection for Failure Prevention in
Hybrids," Electronic Packaqinq and Corrosion in
Microelectronics, Edited bv M.E. Nicholson, ASM
International, Metals Park, OH, pp. 103-10, (1987).
[87IWA1]
N. Iwase, T. Yanazawa, M. Nakahashi, K. Shinozaki, A. Tsuge,
K. Anzai, "Aluminum Nitride Multilayer Pin Grid Array
Packages," Proceedings of the 37th Electronic Components
Conference, Boston, MA, IEEE, New York, NY, pp. 384-91,
(1987) .
[87IWA2]
Y. Iwata, S. Saito, "New Ceramic and Plastic Composite
Substrate for Face Down Bonding & Large Silicon Chip
Mounting," Proceedings of the 37th Electronic Components
Conference, Boston, MA, IEEE, New York, NY, pp. 392-97,
(1987) .
[87JIN]
S. Jinsheng, C. Shanxiang, "A New Type of Optical and
Electric Hybrid Switch,” Proceedings of the 37th Electronic
Components Conference, Boston, MA, IEEE, New York, NY, pp.
265-68, (1987).

599
[87KEL]
D.W. Kellerman, "The Development and Characterization of a
Low Dielectric Constant Thick Film Material," Proceedings of
the 37th Electronic Components Conference, Boston, MA, IEEE,
New York, NY, pp. 316-27, (1987).
[87KIN]
K.R. Kinsman, "Integrated Circuit Packaging-A Materials
Microcosm," Electronic Packaaina and Corrosion in
Microelectronics, Edited bv M.E. Nicholson, ASM
International, Metals Park OH, pp. 1-10, (1987).
[87KUR]
Y. Kurokawa, H. Hamaguchi, Y. Shimada, K. Utsumi, H.
Takamizawa, "Highly Thermal Conductive Aluminum Nitride
Substrates," Proceedings of the 20th International Symposium
on Microelectronics, Minneapolis, MN, ISHM, Reston, VA, pp.
654-61, (1987).
[87LIN]
E. Liniger, R. Raj, "Packing and Sintering of Two-
Dimensional Structures Made from Bimodal Particle Size
Distributions," J. Am. Cer. Soc., 70, [11], pp. 843-49,
(1987) .
[87MOH]
U. Mohideen, T.R. Gururaja, L.E. Cross, W. Yarbrough, A.
Das, J. Yamamoto, R. Roy, "Ultra-Low Dielectric Permittivity
Ceramics and Composites for High Speed IC Packaging
Applications,” Proceedings of the 37th Electronic Components
Conference, Boston, MA, IEEE, New York, NY, pp. 406-12,
(1987).
[87NIS]
S. Nishigaki, S. Yano, H. Kawabe, J. Fukuta, T. Nonomura, S.
Hebishima, "LFC-III: A New Low Temperature Multilayered
Ceramic Substrate with Au(top)-Ag(internal)-Ti/Mo/Cu(bottom)
Conductor System," Proceedings of the 20th International
Symposium on Microelectronics, Minneapolis, MN, ISHM,
Reston, VA, pp. 400-07 (1987).
[87OKA]
H. Okamura, T. Fukuba, Y. Fujita, "The High Thermal
Conductive Ceramic Coated Substrate," Proceedings of the
20th International Symposium on Microelectronics,
Minneapolis, Minn., ISHM, Reston, VA, p. 386-99, (1987).
[87POR]
G. Poreux, P.C., "Transport in Heterogeneous Porous Media,"
Physica Scripta, T19, pp. 524-30, (1987).
[87RAH1]
M.N. Rahaman, L.C. DeJonghe, "Effect of Rigid Inclusions on
the Sintering of Glass Powder Compacts," J. Am. Cer. Soc.,
70, [12], pp. C-348-C-3 51, (1987).
[87RAH2]
M.H. Rahaman, L.C. DeJonghe, G.W. Scherer, R.J. Brook,
"Creep and Densification During Sintering of Glass Powder
Compacts," J. Am. Cer. Soc., J_0_, [10], pp. 766-74, (1987).
[87RAJ]
R. Raj, "Analysis of the Sintering Pressure,” J. Am. Cer.
Soc., 70, [9], pp. C-210-C-211, (1987).
[87RIC]
E.L. Rich, III, S.K. Suko, A.J. Martin, B.H. Smith, D.G.
Onn, A.J. Whittaker, R.E. Giedd, "Thermal Management
Considerations for a Low-Temperature, Co-Fireable Ceramic
System," Proceedings of the 20th International Symposium on
Microelectronics, Minneapolis, MN, ISHM, Reston, VA, pp.
408-18, (1987).

600
[87ROM]
B.M. Romensko, G.V Clatterbaugh, H.K. Charles, Jr., "Design,
Fabrication and Performance Testing of Large Area Multilevel
Thick Film Surface Mount Assemblies," Proceedings of the
37th Electronic Components Conference, Boston, MA, IEEE, New
York, NY, pp. 269-81, (1987).
[87RUS]
L.M. Russell, L.F. Johnson, D.P.H. Hasselman, "Thermal
Conductivity/Diffusivity of Silicon Carbide Whisker
Reinforced Mullite," J. Am. Cer. Soc., 70, [10], pp. C-226-
C-229, (1987).
[87SCH1]
M. Scheinfein, J. Prince, "Electrical Performance of
Integrated Circuit Packages: Three Dimensional Structures,"
Proceedings of the 37th Electronic Components Conference,
Boston, MA, IEEE, New York, NY, pp. 377-83, (1987).
[87SCH2]
M.A. Schmitt, B.K. Bhattacharyya, "Electrical
Characterization of a Multilayer Ceramic Pin Grid Array
Package," Proceedings of the 37th Electronic Components
Conference, Boston, MA, IEEE, New York, NY, pp. 370-76,
(1987).
[87SCH3]
G. W. Scherer, "Sintering With Rigid Inclusions," J. Am.
Cer. Soc., 70, [10], pp. 719-25, (1987).
[87SEN]
R. Senthinathan, J. Prince, M. Scheinfein, "Characteristics
of Coupled, Buried Microstrip Lines by Modelling and
Simulation," Proceedings of the 37th Electronic Components
Conference, Boston, MA, IEEE, New York, NY, pp. 362-69,
(1987).
[87SHI]
Y. Shimada, Y. Yamashita, Y. Shiozawa, M. Suzuki, H.
Takamizawa, "Low Dielectric Constant Multilayer Glass-
Ceramic Substrate with Ag-Pd Wiring for VLSI Package,"
Proceedings of the 37th Electronics Component Conference,
Boston, MA, IEEE, New York, NY, pp. 398-405, (1987).
[87SHU]
V.N. Shukla, P. Hingorany, A. Amin, "CERCIC-A Hybrid
Substrate," Proceedings of the 20th International Symposium
on Microelectronics, Minneapolis, MN, ISHM, Reston, VA, pp.
392-99, (1987).
[87THO]
R.G. Thompson, D.L. Shealy, H.T. Tohver, "Compatibility
Studies in Metal-Cordierite Systems For Electronic
Packaging," Proceedings of the 37th Electronic Components
Conference, Boston, MA, IEEE, New York, NY, pp. 420-26,
(1987).
[87YAR]
W.A. Yarbrough, T.R. Gururaja, L.E. Cross, "Materials for IC
Packaging with Very Low Permittivity via Colloidal
Processing," Ceramic Bulletin, 66, [4], pp. 692-98, (1987).
[87WHI]
H.S. White, "Corrosion Principles in Microelectronics,"
Electronic Packaaina and Corrosion in Microelectronics,
Edited by M.E. Nicholson, ASM International, Metals Park,
OH, pp. 33-34, (1987).
[87ZHD]
V.P. Zhdanov, V.B. Fenelonov, D.K. Efremov, "Determination
of Pore-Size Distribution from Sorption Isotherms:
Application of Percolation Theory," Journal of Colloid and
Interface Science, 120. [1], pp. 218-23, (1987).

601
[88ANG]
G. Angenieux, J. Chillo, "Dynamic Behavior of
Interconnection Lines in Wafer Scale Integration Circuits,”
Proceedings of the 21st International Symposium on
Microelectronics, Seattle, WA, ISHM, Reston, VA, pp. 498-
504, (1988).
[88ARI]
H. Arikawa, S. Hanada, T. Yokoi, T. Sekino, "Low Thermal
Resistance Hybrid IC Package,” Proceedings of the 21st
International Symposium on Microelectronics, Seattle, WA,
ISHM, Reston, VA, pp. 160-63, (1987).
[88ANZ]
K. Anzai, T. Takahashi, T. Yasumoto and N. Iwase, "Thin Film
Metallization on AIN Substrate," Paper No. 31-E-88, Annual
National Convention of The American Ceramic Society,
Cincinnati, OH, (1988).
[88BAB1]
K. Baba, N. Shohata and M. Yonezawa, "Preparation and
Properties of Ultrafine AIN Powder by RF Plasma," Paper No.
27-E-88, Annual National Convention of The American Ceramic
Society, Cincinnati, OH, (1988).
[88BAB2]
Y. Baba, K. Higashiyama, S. Segawa, "Co-Fireable Copper
Multilayer Ceramic Substrates,” Proceedings of the 21st
International Symposium on Microelectronics, Seattle, WA,
ISHM, Reston, VA, pp. 405-13, (1988).
[88BAL]
J.W. Balde, "Small Dimensions or Low Dielectric Constant:
The Competing Approaches to High Density Interconnect," Mat.
Res. Soc. Symp. Proc., 108, pp. 61-71, (1988).
[88BEN]
M.F. Bender, F.K. Patterson, E.A. Kemp, J.E. Gantzhorn, Jr.,
"Low Temperature Cofired Ceramic Tape System: A Cost
Effective Solution for Multilayer Packaging," Proceedings of
the 21st International Symposium on Microelectronics,
Seattle, WA, ISHM, Reston, VA, pp. 12-24, (1988).
[88BIR]
D.P. Birnie, III, "The Effect of an Intergranular Liquid
Phase on Thermal Conduction in Aluminum Nitride," Paper No.
30-E-88, Annual National Convention of The American Ceramic
Society, Cincinnati, OH, (1988).
[88BOR1]
R.K. Bordia, G.W. Scherer, "On Constrained Sintering-I.
Constitutive Model for a Sintering Body," Acta. Metall., 36,
[9], pp. 2393-97, (1988).
[88BOR2]
R.K. Bordia, G.W. Scherer, "On Constrained Sintering-II.
Comparison of Constitutive Models," Act. Metall., 36, [9],
pp. 2399-409, (1988).
[88BOR3]
R.K. Bordia, G.W. Scherer, "On Constrained Sintering-III.
Rigid Inclusions," Acta. Metall., 36, [9], pp. 2411-16,
(1988).
[88BOR4]
R.K. Bordia, R. Raj, "Sintering of Ti0,-Al;03 Composites: A
Model Experimental Investigation," J. Am. Cer. Soc., 71,
[4], pp. 302-10, (1988).
[88BOR5]
W. Borland, V.P. Suita, "Materials Interactions in the
Firing of Copper Thick Film Multilayer Ceramics," Mat. Res.
Soc. Symp. Proc., 108, pp. 287-300, (1988).

602
[88CAO]
W. Cao, R. Gerhardt and J.B. Wachtman, Jr., "Effects of
Alkali Ions and Water Adsorption on the Dielectric
Properties of Bulk Porous Silica by a Colloidal Processing
Method," Paper No. 21-E-88, Annual National Convention of
The American Ceramic Society, Cincinnati, OH, (1988).
(88CAR)
G. Carruth, E. Ehrlich, editors. The Harper Book of American
Quotations, Harper & Row, New York, NY, 84.8, Í1988Í.
[88CER]
E.W. Smothers, editor. Ceramic Source '88, The American
Ceramic Society, Inc., Westerville, OH, p. 198, (1988).
[88CLA]
S. Clark and R. Gerhardt, "Glass: Boron Nitride Composites
for Electronic Substrate Applications," Paper No. 94-E-88,
Annual National Convention of The American Ceramic Society,
Cincinnati, OH, (1988).
[88COR]
Cornina Glass Works, Inc., Materials Information, MI-7070-
88, Materials Business, Corning, NY, (1988).
[88COW]
C. Cowen, M.Y. Xu, H. Jain and M.R. Notis, "Structure and
Dielectric Behavior of Composite Oxide Ceramics," Paper No.
37-E-88, Annual National Convention of The American Ceramic
Society, Cincinnati, OH, (1988).
[88DET]
E.S. Dettmer, H.K. Charles, Jr., S.J. Mobley, B.M.
Romenesko, "Hybrid Design and Processing Using Aluminum
Nitride Substrates," Proceedings of the 21st International
Symposium on Microelectronics, Seattle, WA, ISHM, Reston,
VA, pp. 545-53, (1988).
[88DIN]
R.K. Dinsmore, "MIL-H-38534: Military Specifications for
Hybrid Microcircuits," Proceedings of the 21st International
Symposium on Microelectronics, Seattle, WA, ISHM, Reston,
VA, pp. 475-79, (1988).
[88ECK]
C. Eckert, K. Chan and D. Bausback, "Business Assessment of
Electronic Ceramics," Paper No. 34-E-88 , Annual National
Convention of The American Ceramic Society, Cincinnati, OH,
(1988) .
[88EWS1]
K.G. Ewsuk, L.W. Harrison and F.J. Walczak, "Thermal
Conductivity of Glass-Filled Ceramic Composites," Paper No.
39-E-88, Annual National Convention of The American Ceramic
Society, Cincinnati, OH, (1988).
[88EWS2)
K. Ewsuk, "High Frequency Dielectric Properties of Pure and
Magnesia-Doped, Polycrystalline Alumina," Paper No. 118-E-
88, Annual National Convention of The American Ceramic
Society, Cincinnati, OH, (1988).
[88FAR]
W.E. Farneth, R.H. Staley, T. Budzichowski, "Reaction
Mechanisms in Organic Binder Removal During Ceramic
Processing: PMMA/Cordierite as a Prototype System," Mat.
Res. Soc. Symp. Proc., 108, pp. 95-99, (1988).
[88FRE]
R.H. French, D.J Jones, W.Y. Hsu, B.A. Yost and M.A.
Subramanian, "Percolation Effects in the Dielectric
Properties of Polymer Ceramic Composite Systems," Paper No.
88-E-88, Annual National Convention of The American Ceramic
Society, Cincinnati, OH, (1988).

603
[ 88FUN ]
J.E. Funk, D.R. Dinger, "Slip Control Using Particle-Size
Analysis and Specific Surface Area,” Ceramic Bulletin, 67,
[5], pp. 890-94, (1988).
[88GER1]
R. Gerhardt, "Influence of Geometric Factors on Dielectric
Constant," Paper No. 69-E-88, Annual National Convention of
The American Ceramic Society, Cincinnati, OH, (1988).
[88GER2)
R. Gerhardt, "Composites for Electronic Substrate
Applications," Mat. Res. Soc. Svmp. Proc., 108, pp. 101-06,
(1988).
[88GER3]
F.J. German, B. Dillard, L. S. Riggs, R.W. Johnson,
"Transmission Line Matrix Method for Modelling the
Electrical Performance of Interconnections," Proceedings of
the 21st International Symposium on Microelectronics,
Seattle, WA, ISHM, Reston, VA, pp. 492-97, (1988).
[88GIL]
B.K. Gilbert, G.W. Pan, "The Application of Gallium Arsenide
Integrated Circuit Technology to the Design and Fabrication
of Future Generation Digital Signal Processors, Promises and
Problems," Proceedings of the IEEE, 76, [7], pp. 816-34,
(1988) .
[ 88GJE ]
P. Gjerde, W.D. Scott, "Binder Burnout in Multilayer
Capacitors," Proceedings of the 21st International Symposium
on Microelectronics, Seattle, WA, ISHM, Reston, VA, pp. 79-
83, (1988).
[88GLA]
W.R. Glave, L.J. Hagerty, J.D. Grier, Sr., R.E. Park, Jr.,
"Characterization of Nitrogen Furnace Atmospheres in Copper
Thick Film Multilayer Ceramic Board Manufacturinq," Advances
in Ceramics, 26, The American Ceramic Society, Inc.,
Westerville, OH, pp. 414-20, (1989).
[88HAE]
C. Haertling, S. Yoshikawa and R. Newnham, "Patterned
Ceramics Through Ultraviolet Curable Pastes," Paper No. 48-
EP-88, Annual National Convention of The American Ceramic
Society, Cincinnati, OH, (1988).
[88HAM]
M. Hama, W.Y. Shih, R. Kikuchi and I.A. Aksay, "Low
Temperature (1250°C) Sintering of High Purity a-Al201f" Paper
No. 18-E-88, Annual National Convention of The American
Ceramic Society, Cincinnati, OH, (1988).
[88HAY]
K. Hayashi, M. Sugie, and T. Hirao, "CVD-Silicon Nitride
with High Thermal Conductivity," Paper No. 33-E-88, Annual
National Convention of The American Ceramic Society,
Cincinnati, OH, (1988).
[88HIR]
S. Hirano, K. Ibata, T. Toyosawa, K. Togawa, "Three-
Dimensional Thermal Conduction Analysis on Thick Film
Thermal Head Using Finite Element Method," Proceedings of
the 21st International Symposium on Microelectronics,
Seattle, WA, ISHM, Reston, VA, pp. 480-84, (1988).
[88HOF]
L. Hoffman, "Crystallizable Dielectrics in Multilayer
Structures for Hybrid Circuits," Paper No. 36-E-88, Annual
National Convention of The American Ceramic Society,
Cincinnati, OH, (1988).

604
[88HON]
S. Hong, J.C. Bravman, T.P. Weihs, O.K. Kwon, "Materials and
Structures for High Density I/O Interconnection Systems,”
Mat. Res. Soc. Symp. Proc. , 108, pp. 309-17, (1988).
[88HUT]
L.D. Hutcheson, "Integrated Optoelectronic Materials and
Circuits for Optical Interconnects," Mat. Res. Soc. Symp.
Proc., 108, pp. 407-18, (1988).
[88IBR]
A.M. Ibrahim, "Surface Mount Technology (SMT) Substrate
Material Requirements- A Brief Review," Mat. Res. Soc. Symp.
Proc., 108. pp. 159-68, (1988).
[ 88ISH ]
J. Ishigama, T. Kubota, S. Sekihara, K. Fujimara,
"Technological Advances of Thick Film Resistors for Aluminum
Nitride Substrates with New Conductive Compositions,"
Proceedings of the 21st International Symposium on
Microelectronics, Seattle, WA, ISHM, Reston, VA, pp. 149-57,
(1988).
[88IYE]
L. Iyengar, Y. Berta and V.R.W. Amarakoon, "Dense-
Homogeneous Ceramics at Low Temperature via Sol-Gel Coating
of Powders," Paper No. 22-E-88, Annual National Convention
of The American Ceramic Society, Cincinnati, OH, (1988).
[88JAF]
D. Jaffe, "Materials and Processes for High Functionality
Hybrid Circuit Packages," Mat. Res. Soc. Symp. Proc., 108,
pp. 301-08, (1988).
[88JEN]
R.J. Jensen, "Recent Advances in Thin Film Multilayer
Interconnect Technology for IC Packaging," Mat. Res. Soc.
Symp. Proc., 108, pp 73-79, (1988).
[88KAC]
K.K. Kachelries, J.A. Olenick, S.G. Konsowski, "Evaluation
of Thick Film Multilayers on AIN," Proceedings of the 21st
International Symposium on Microelectronics, Seattle, WA,
ISHM, Reston, VA, pp. 170-82, (1988).
[88KEY]
R.W Keyes, "Device Limitations," Mat. Res. Soc. Symp. Proc.,
108, pp. 3-13, (1988).
[88KIN]
J.A. Kina, Materials Handbook for Hvbrid Microelectronics,
Artech House, Boston, MA, (1988).
[88KUN]
A. Kunioka, "Current Situation of Japanese Hybrid
Microelectronics,” Proceedings of the 21st International
Symposium on Microelectronics, Seattle, WA, ISHM, Reston,
VA, pp. 203-05, (1988).
[88KUS]
A.G. Kusmierczyk, A.D. Snicer, "Calculation of Extremely
High Temperature Effects in Conductors Suffering
Electromigration," Proceedings of the 21st International
Symposium on Microelectronics, Seattle, WA, ISHM, Reston,
VA, pp. 377-80, (1988).
[88LEA1]
M. Leap and W. Huebner, "Electrical Properties of Tape Cast
Hollow Glass Microsphere 0-3 Composites," Paper No. 38-E-
88, Annual National Convention of The American Ceramic
Society, Cincinnati, OH, (1988).

605
[88LEA2]
[88LEE]
[88LIC]
[88LU]
[88MAC]
[88MAD]
[88MIC]
[88MIE]
[88MOH]
[88MRO]
[88NEU]
[88NEW]
[880HU]
M. Leap, A. Das, L. Cross and W. Huebner, "Thin and Thick
Film Technology for Novel Approaches in Microelectronic
Packaging," Paper No. 46-EP-88, Annual National Convention
of The American Ceramic Society, Cincinnati, OH, (1988).
S.B. Lee, S. Torquato, "Pair Connectedness and Mean Cluster
Size for Continuum-Percolation Models: Computer-Simulation
Results," J. Chem. Phys., 89_, [10], pp. 6427-33, (1988).
J.J. Licari, L.R. Enlow, Hybrid Microcircuit Technology
Handbook: Materials, Processes, Design, Testing and
Production, Noyes Publications, Park Ridge, NJ, (1988).
Y.Y. Lu, M.S. El-Aasser, J.W. Vanderhoff, "Dispersion
Polymerization of Styrene in Ethanol: Monomer Partitioning
Behavior and Locus of Polymerization," Journal of Polymer
Science: Part B: Polymer Physics, 26, pp. 1187-1203, (1988).
D. MaCaulay, The Way Things Work, Houghton Mifflin Company,
Boston, MA, (1988).
C. Madhavan, T. Srinivasan, Q. Xu and R. Newnham, "Fired 0-3
Piezoelectric Composite Materials for Biomedical Ultrasonic
Imaging Applications,” Paper No. 49-EP-88, Annual National
Convention of The American Ceramic Society, Cincinnati, OH,
(1988).
Seradyn, Inc., Microparticle Immunoassay Techniques,
Particle Technology Division, Seradyn, Inc., Indianapolis,
IN, (1988).
K.M. Miessen and D.J. Shanefield, "Sintering Aids and Grain
Boundary Compositions in Aluminum Nitride," Paper No. 29-E-
88, Annual National Convention of The American Ceramic
Society, Cincinnati, OH, (1988).
U. Mohideen, T.R. Gururaja, L.E. Cross, R. Roy, "Ultra-Low
Dielectric Constant Porous Silica Thick Films for High-Speed
IC Packaging," IEEE Transactions on Components, Hybrids, and
Manufacturing Technology, 11. [1], pp. 159-162, (1988).
C.M. Mroz and J.A.T Taylor, "Characterization of Aluminum
Nitride-Metal Interface in Electronic Aluminum Nitride
Ceramics," Paper No. 6-EP-88, Annual National Convention of
The American Ceramic Society, Cincinnati, OH, (1988).
C.A. Neugebauer, "Materials Limitations in the Higher
Electronic Packaging Levels," Mat. Res. Soc. Symp. Proc.,
108. pp, 13-25, (1988).
C.E. Newberg and S.H. Risbud, "Interfacial Reactions of
Thick Film Metallizations and Aluminum Nitride Substrates,"
Paper No. 32-E-88, Annual National Convention of The
American Ceramic Society, Cincinnati, OH, (1988).
F. Ohuchi, M. Bortz, "Synthesis and Characterization of
Cordierite-Based Ceramic Thin Films," Paper No. 97-E-88,
Annual National Convention of The American Ceramic Society,
Cincinnati, OH, (1988).

606
[880NN]
D.G. Onn, H.M. Zhang, R.E Giedd and O. Guerrero,
"Percolation Effects in the Thermal Diffusivity of
Polymer/Ceramic Composites," Paper No. 89-E-88, Annual
National Convention of The American Ceramic Society,
Cincinnati, OH, (1988).
[88PAG]
R.A. Page, S. Spooner, W.B. Sanderson, D.L. Johnson, "Pore
Evolution During Glow Discharge Sintering of Alumina," J.
Am. Cer. Soc., 71, [12], pp. 1125-29, (1988).
[88PAR]
N.A. Park, T.F. Irvine, Jr., "Measurements of Rheological
Fluid Properties with the Falling Needle Viscometer," Re.
Sci. Instrum., 59^ [9], pp. 2051-58, (1988).
[88PHU]
P.P. Phule and S.H. Risbud, "Chemically Derived
Electroceramic Powders," Paper No. 19-E-88, Annual National
Convention of The American Ceramic Society, Cincinnati, OH,
(1988) .
[88PIL]
V. Pilletteri and E. Case, "Laser Surface Melting and
Cutting of Cordierite Substrates,” Paper No. 7-EP-88, Annual
National Convention of The American Ceramic Society,
Cincinnati, OH, (1988).
[88REE]
J.S. Reed, Introduction to the Principles of Ceramic
Processinq, J. Wilev & Sons, New York, NY, (1988).
[88ROB]
M.J. Robinson, C. Tsay, M. Buynoski, R. Pendse, "Measurement
of Die Stress From Packaging and Effects of Thermal
Cycling,” Mat. Res. Soc. Symp. Proc., 108, pp, 43-46,
(1988).
[88ROO]
A. Roosen, H.K. Bowen, "Influence of Various Consolidation
Techniques on the Green Microstructure and Sintering
Behavior of Alumina Powders," J. Am. Cer. Soc., 71, [11],
pp. 970-77, (1988).
[88SAC]
M.D. Sacks, S.D. Vora, "Preparation of SiO: Glass from Model
Powder Compacts: III, Enhanced Densification by Sol
Infiltration," J. Am. Cer. Soc., 71, [4], pp. 245-49,
(1988).
[ 88SAE ]
M.A. Saed, A.Y. Almazroo, A. Elshabini-Riad, S.M. Riad,
"Wideband (DC-10) GHz Characterization of Thick Film
Dielectric and Ferrite Materials," Proceedings of the 21st
International Symposium on Microelectronics, Seattle, WA,
ISHM, Reston, VA, pp. 340-44, (1988).
[88SAW]
H.T. Sawhill, Materials Compatibility and Sintering in Low
Temperature Co-Fired Ceramic Packages," Paper No. 129-E-88,
Annual National Convention of The American Ceramic Society,
Cincinnati, OH, (1988).
[88SCH1]
G. Scherer, K. Mikeska and R Bordia, "Warping During
Cofiring," Paper No. 130-E-88 , Annual National Convention
of The American Ceramic Society, Cincinnati, OH, (1988).
[88SCH2]
G.W. Scherer, "Viscous Sintering with a Pore-Size
Distribution and Rigid Inclusions," J. Am. Cer. Soc., 71,
[10], pp. C-447-C-448, (1988).

607
[88SCH3]
[88SEI ]
[87SEV]
[88SHA1]
[88SHA2]
[88SHA3]
[88SHE]
[88SHI]
[88SHU]
[88SIM]
[88SLI]
[88SOR]
[88SPE]
[88SRI]
M. Schober, "Electronics Market Strives for Higher Marks,"
Ceramic Bulletin, 67, [4], pp. 722-23, (1988).
R.W. Seibold, R.T. Lamoureux, S.H. Goodman, "Materials for
High Speed Circuit Boards," Mat. Res. Soc. Symp. Proc., 108,
pp. 141-52, (1988).
E.M. Sevick, P.A. Monson, J.M. Ottino, "Monte Carlo
Calculations of Cluster Statistics in Continuum Models of
Composite Morphology," J. Chem. Phys., 88, [2], pp. 1198-
1206, (1988).
P.T.B Shafer and S. Majorowski, "High Thermal Conductivity
AIN," Paper No. 28-E-88, Annual National Convention of The
American Ceramic Society, Cincinnati, OH, (1988).
M. Shah and J. Rigsbee, "Microstructural Characterization of
Vapor Deposited Ni/Al;03 Composites," Paper No. 108-E-88,
Annual National Convention of The American Ceramic Society,
Cincinnati, OH, (1988).
A. Shaikh, D. Hankey, D. Leandri, G. Roberts, "A Hermetic
Low K Dielectric for Alumina Substrates,” Proceedings of the
21st International Symposium on Microelectronics, Seattle,
WA, ISHM, Reston, VA, pp. 189-95, (1988).
L.M. Sheppard, "Automation of Particle Size Analysis,"<