• TABLE OF CONTENTS
HIDE
 Title Page
 Acknowledgement
 Table of Contents
 Abstract
 Introduction
 Literature review
 Experimental procedure
 Results and discussion
 Summary
 Suggestions for future work
 Histograms
 Procedure for gravity sedimentation...
 Densification data
 Microstructural properties
 Deflection versus time plots
 Reference
 Biographical sketch
 Copyright














Title: Effect of green microstructure on the sintering of model silica compacts
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Table of Contents
    Title Page
        Page i
    Acknowledgement
        Page ii
    Table of Contents
        Page iii
        Page iv
    Abstract
        Page v
        Page vi
    Introduction
        Page 1
        Page 2
        Page 3
    Literature review
        Page 4
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    Experimental procedure
        Page 36
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    Results and discussion
        Page 63
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    Summary
        Page 226
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    Suggestions for future work
        Page 232
    Histograms
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    Procedure for gravity sedimentation process
        Page 295
    Densification data
        Page 296
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    Microstructural properties
        Page 304
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    Deflection versus time plots
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    Reference
        Page 316
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    Biographical sketch
        Page 325
        Page 326
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    Copyright
        Copyright
Full Text










EFFECT OF GREEN MICROSTRUCTURE ON THE SINTERING OF
MODEL SILICA COMPACTS














By

SHAILESH D. VORA


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


1990













ACKNOWLEDGEMENTS


I am grateful to Dr. M. D. Sacks for his invaluable guidance and

support. His dedicated and conscientious approach to research was a

constant source of inspiration. I am thankful to Drs. R. T. DeHoff, D. O.

Shah, J. H. Simmons and E. D. Whitney for their helpful suggestions. I
would like to thank Dr. F. Ebrahimi for the use of the MTS machine for
viscosity measurements.

I would also like to thank Chandra Khadilkar, T.S. Yeh, H. W. Lee,

Oswaldo Rojas, Gary Scheiffele, Joan Dow, Arindam D6, Jesus Castillo,

Mohammad Saleem, Ramesh Raghunathan, Roger Bagwell, Nazim

Bozkurt and Greg Johnson for their assistance in carrying out various

experiments in this study.
Finally, I would like to thank my wife Kalpana for her patience and

encouragement throughout the course of this work.













TABLE OF CONTENTS
Page

ACKNOWLEDGEMENTS................................................................... ii

ABSTRACT................................................................................................ v

1. INTRODUCTION............................................................................... 1

2. LITERATURE REVIEW........................................................................ 4

Introduction...................................................................................... 4
V iscous Sintering................................................................................ 4
Influence of Water Content on the Properties of Silica.............. 9
Sintering of Silica Glass................................................................... 13
Effect of Particle Packing............................. ............................. 18
Effect of Particle Size Distribution...................... ............ 24
Suspension Processing...................... ........................ 29
Significance of This Study............................................................ 33

3. EXPERIMENTAL PROCEDURE........................................... 36

Powder preparation and Characterization....................... .......... 36
Suspension Preparation and Characterization............................. 42
Preparation and Characterization of Green Compacts................. 45
Pre-Sintering ...................................................... 48
Sintering................................................. .................. 49
Sample Preparation for Quantitative Microscopy............................. 51
Quantitative Microscopy....................... ................................... 53
Sample Preparation for Beam-Bending.......................................... 55
Viscosity Measurements by Beam-Bending.............................. 61

4. RESULTS AND DISCUSSION.............................. ....................... 63

Effect of Particle Packing......................................... ..... ................. 63
Effect of Particle size Distribution....................................................... 144
Determination of Viscosity by the Beam-Bending Method.......... 201

5. SUM M ARY...... ............................... ...................................... 226









L/6. SUGGESTIONS FOR FUTURE WORK.............................................. 232

APPENDIX A HISTOGRAM PLOTS....................................................... 233

APPENDIX B PROCEDURE FOR GRAVITY SEDIMENTATION
PRO CESS............................................................................................. ..... 295

APPENDIX C DENSIFICATION DATA.......................... ....... 296

APPENDIX D MICROSTRUCTURAL PROPERTIES.............................. 304

APPENDIX E DEFLECTION VERSUS TIME PLOTS.......... ...... 310

R EFER EN C ES................................................................................................... 316

BIOGRAPHICAL SKETCH....................................................................... 325














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

EFFECT OF GREEN MICROSTRUCTURE ON THE SINTERING OF
MODEL SILICA COMPACTS

By

Shailesh D. Vora

December 1990

Chairman: Dr. Michael D. Sacks
Major Department: Materials Science and Engineering

The effect of particle packing and particle size distribution on the

densification behavior and microstructural evolution during sintering of

spherical, sub-micron, amorphous silica powders was investigated. In

order to isolate the effects of particle packing on sintering behavior, a
powder with extremely narrow particle size distribution was used.

Compacts with varying particle packing characteristics were prepared

using suspension processing and dry pressing. Particle packing

arrangements had significant effects on the densification kinetics and the

path of microstructural evolution. To determine the effects of particle size
distribution on sintering behavior, powders were prepared with tailored

particle size distributions. Powders with constant average size but varying

widths of the distribution were produced. Green compacts with

homogeneous microstructures were prepared by slip casting dispersed

suspensions. Suspension rheology, green compact characteristics,








densification and microstructural evolution were highly dependent on

the width of the particle size distribution. An attempt was made to fit the

densification data to various sintering models available in the literature.

Experimental measurements of viscosity at the sintering temperature
were carried out by the beam bending method. This made it possible to

test the sintering models more rigorously by allowing a direct comparison
of viscosities calculated from the models to those obtained experimentally.













CHAPTER 1
INTRODUCTION


At the present time there is a rising demand for new ceramic

components for applications in electronics, communication, energy and

other fields of technology. These components must meet stringent

requirements of composition, purity, microstructural control and

processing in order to produce the desired properties. The consequence

will be a new generation of high performance ceramics with predictable

properties and reliability. To achieve this goal, a major emphasis is

placed on microstructural control, since the performance and reliability of

ceramics depend on the final microstructure attained after sintering. This

has led to studies on understanding the effects of green (i.e., unfired)

microstructure on densification kinetics and microstructural evolution

during sintering.

The nature of the green microstructure is determined by the

following factors: (1) particle characteristics (e.g., average size, size

distribution, state of agglomeration, particle shape, specific surface area),

(2) pore characteristics (e.g., average pore size, pore size distribution, pore
shape) and (3) particle packing characteristics (e.g., green density,

uniformity in packing density). The problem in understanding the effects

of the green microstructure on sintering behavior and microstructural

evolution is that it is difficult to isolate the effects of each factor. This is

primarily due to the fact that most of the factors listed above are often








inter-related. Difficulties are also encountered due to the non-ideal nature
of a majority of powders used in sintering studies. For example,
commercial powders invariably contain agglomerates which tend to have
a dominating effect on the sintering behavior and microstructural
evolution, thereby masking the effects of other characteristics under

investigation. Furthermore, during the sintering of crystalline powders,

several mechanisms of material transport (eg., surface diffusion, grain
boundary diffusion, evaporation and condensation etc.) can occur
simultaneously. Also, densification is accompanied by grain growth
which can give rise to additional complexities since grain growth is

detrimental to densification (for amorphous materials on the other hand,
the transport mechanism is less ambiguous because sintering occurs via
viscous flow and densification can be achieved without grain growth).
Based on above considerations, it follows that in order to
unambiguously determine the effects of green microstructure on
sintering, it is vital to prepare powders and powder compacts devoid of
such complexities. Thus ideal powders for sintering studies should
essentially be agglomerate free, consisting of particles with uniform shape

and controlled size distribution. These powders could then be used to

prepare the ideal compacts that have high green densities and
homogeneous green microstructures. In the present investigation,
powder compacts which approach ideal characteristics were used. Hence,
the effects of particle packing and particle size distribution on sintering
and microstructural evolution could be properly investigated.

The study was carried out using spherical, non-agglomerated, sub-

micron, amorphous silica powders. In order to isolate the effects of
particle packing on sintering behavior, a powder with extremely narrow








particle size distribution was used. Compacts with varying particle
packing characteristics were then formed using different consolidation
techniques (e.g., colloidal processing, dry pressing). To determine the

effects of particle size distribution on sintering behavior, powders were
prepared with tailored particle size distributions. Powders with constant

average size but varying widths of the distribution were produced. Green

compacts with homogeneous microstructures were prepared from these
powders by slip casting well-dispersed suspensions.
The objective of this study was to obtain a comprehensive and

detailed characterization of microstructural evolution during sintering.

Quantitative stereology was used to follow the path of the microstructure

(i.e., changes in pore structure) traversed during sintering. An attempt
was made to fit the densification data to viscous sintering models

available in the literature. Experimental measurements of viscosity at the

sintering temperature were carried out by the beam bending method. This
made it possible to test the sintering models more rigorously by allowing a

direct comparison of viscosities calculated from the models to those
obtained experimentally.

In chapter 2, a general review of the literature relevant to this

investigation is presented. In chapter 3 detailed procedures for powder
preparation and characterization, sintering, microstructural evolution,

sample preparation for beam bending and beam bending experiments for

viscosity measurements are described. The results and discussion are
detailed in chapter 4. The results are summarized in chapter 5 and

suggestions for future work are given in chapter 6.














CHAPTER 2
LITERATURE REVIEW


Introduction

A review on the theory of viscous sintering and viscous sintering

models will be described in this chapter. The influence of water (i.e.,

hydroxyl) content on the properties of silica glasses will also be discussed.

Previous research on sintering of glass closely related to this study will be

reviewed. This will be followed by a discussion on the effects of particle
packing and particle size distribution on sintering. Fundamental

principles of suspension processing will also be described in brief. Finally,

the significance and uniqueness of this investigation will be presented.


Viscous Sintering

The mechanism of sintering for amorphous materials is viscous

flow. Frenkel [Fre45] laid the foundation for all subsequent analyses of

viscous sintering. He pointed out that energy is dissipated as heat during

viscous flow, and suggested that the reduction of surface area (i.e.,

reduction of solid-vapor interfacial area due to neck growth and pore

elimination) provides the source of this energy during viscous sintering.

By equating these quantities, he derived the following expression for the

rate of neck growth (i.e. shrinkage rate) between two spherical particles of
equal size,

(X/R)2 = 3yt/2 2R (2.1)








where R is the particle radius, X is the neck radius, y is the specific surface
energy, 71 is the viscosity at the sintering temperature and t is the sintering
time. Experimental studies by Kuczynski [Kuc49] and Kingery and Berg
[Kin55] have verified Frenkel's prediction of the time dependence of
sintering as well as the underlying physical principles. Based on Eq. (2.1),
expressions have also been derived to describe the rate of approach of
centers of two spheres during the early stages of sintering [Exn75]. These
equations have been generalized to describe the linear rate of shrinkage of
an array of spherical particles by assuming that each pair of particles in the
array behaves in an identical manner. The expression for the rate of
linear shrinkage, AL/Lo is,
AL/Lo = 3yt/8TIR (2.2)
Since y, iT and R are generally assumed to remain constant, Eq. (2.2)
establishes a linear relationship between AL/Lo and t. This result,
however, is limited to the early stages of sintering (i.e., up to = 4% linear
shrinkage) because of the simplifying assumptions made on the shape of

the neck between two particles. Also, departures from the assumed
particle shape (i.e., spherical) can produce deviations from the expected
behavior. In general, the relationship (Eq. 2.2) can only be rigorously
applied to a regular array of monosized spherical particles [Exn75]. In

previous experimental studies, Eq. (2.2) was found to fit data over large

range of shrinkages in certain cases [Cut69, Nog80], but not at all in others
[Jon83, Sac84a].
Cutler and Henrichsen [Cutl68] have pointed out the effects of
particle shape on the sintering of glass. They found that compacts prepared
from crushed, jagged particles sintered as much as five times faster than
compacts prepared from spherical particles of the same size. They








attributed the faster sintering rates of crushed particles to the sharper radii
at points of contacts between the particles.
Mackenzie and Shuttleworth [Mack49] developed a model in
which densification results from the shrinkage of uniform spherical pores
in a viscous matrix. The simplicity of the geometry enabled them to write
exact expressions for the energy dissipation and change in surface area
during sintering. Their result is shown in figure 2.1 (solid curve) as a plot
of relative density p/pt, versus reduced time, K (t -tf) /TI where K is given

by
K= ynl/3/1n (2.3)

where n is the number of pores per unit volume of solid phase, p the bulk
density, pt the theoretical density and tf the time when p(t) equals pt. This

model can apply to bodies with a large volume fraction of pores, as long as
the flow fields surrounding neighboring pores do not interact
significantly. However, it is strictly applicable to the last stages of
densification (relative density > 90%), when the body contains only
isolated closed pores.

Scherer developed another model [Sch77a] that applies to the
entire densification process. He assumed a geometry consisting of a cubic
array of intersecting cylinders. Again, the analysis is based on an energy
balance. The microstructure in this model clearly does not resemble that
of a typical powder compact, but it is believed to provide a reasonable
representation of the structures of such materials as flame oxidation
reforms [Sche77] and alkoxide gels [Scherer84]. As in the Mackenzie-
Shuttleworth model, Scherer obtained a theoretical relationship between

the relative density and the reduced time (shown by the dashed curve in
Fig. 2.1). In this case






































OL
-3















Figure 2.1


I
(Yj/ l)(t- tf


Relative density versus reduced time for the Mackenzie-
Shuttleworth model [Mac49] (- ) and Scherer model
[Sch77a] (-).


I

I








K = y/ 11 lo (p / Po)1/3 (2.4)


where lo is the initial length of the cubic unit cell, ps the theoretical
density and po the initial compact density prior to sintering. The cylinder

radius is expected to represent the average particle size and the pore
diameter can be related to length of the unit cell (i.e., lo). Despite the
unique geometry of this model, the predicted sintering kinetics agree very
well with Mackenzie and Shuttleworth's analysis [Mack49] for the
sintering of closed isolated pores. Scherer's model, therefore, is widely
used since it is applicable over a large range of relative densities. Also,
unlike the Mackenzie Shuttleworth model, the geometrical parameters in
the Scherer model are readily related to the measured pore size (e.g.,
median pore radius obtained from mercury porosimetry) and bulk
density. Scherer model has also been extended to a Gaussian distribution
of pore sizes [Sch77b], to a bimodal pore size distribution [Sch84], to the
sintering of a porous glass layer on a rigid substrate [Scher85] and to the
sintering of glass subjected to applied stress [Sch86].
To compare experimental sintering data to theoretical models,
sintering times corresponding to experimentally measured densities are
plotted against the reduced times (obtained from the theoretical curves in
Fig. 2.1) corresponding to the density of the sample. The result should be a
straight line with a slope equal to K. Using the expressions for K (for
Mackenzie-Shuttleworth or Scherer models) values for the viscosity can
be calculated for each sintering temperature. However, it is important to
identify and determine an appropriate microstructural size parameter to
be used in the expressions for K. In the case of Mackenzie-Shuttleworth
model, the value of n (i.e., number of pores per unit volume) can only be








unambiguously determined through serial sectioning analysis [Deh72].

This procedure is effort intensive and may not be practical for fine
microstructures. On the other hand, for the Scherer model, the size
parameter is obtained from mercury porosimetry measurements. This

technique measures the size of the openings in a porous body rather than

"true" pore sizes. Therefore, if a large pore is accessible only via smaller

pores, then the larger pore will not be detected and the results could be
misleading.

The applicability of the models can then be evaluated by making a

direct comparison of the viscosities extracted from the models to those

determined experimentally (for example, by the beam bending method).

Scherer and Bachman [Sche77] have reported a good agreement between
the calculated and experimentally determined viscosities for SiO2

reforms, but the viscosity values (i.e., experimental and calculated) for

silica gel and porous glass differed by a factor of = 3. It should also be

pointed out that there were significant disparities in their methods of

sample preparation for sintering kinetics and beam bending
measurements. This could easily introduce the observed discrepancies

between the two viscosity values.


Influence of Water Content on the Properties of Vitreous Silica

Different methods for the manufacture of transparent vitreous

silica give products with different 'water' or hydroxyl contents which are

correlated with differences in physical and structural properties. For

example, the viscosity and density decrease with increasing hydroxyl

concentration, whereas the coefficient of thermal expansion increases

[Het62]. The role of 'water' is important, not only because the applications








for which vitreous silica is used depend on these properties, but also
because 'water' is involved in some of the stages of production and
fabrication (e.g., sintering) of silica components.

The influence of hydroxyl content on the properties of vitreous
silica was studied by Hethrington et al. [Het62, Het64]. They determined

the density and viscosity of three types of silica glasses produced by
different methods. The hydroxyl concentrations in these glasses ranged
from negligible (0.0003 wt.%) to a maximum of 0.12 wt.%. A comparison
of properties of these three types of glasses allowed the evaluation of the

effect of varying hydroxyl concentrations. They found that the measured
densities increased with decreasing hydroxyl content. A similar
observation was reported by Sacks and Tseng [Sac84b] in their study on the
sintering of sub-micron silica particles. True densities of their powders
increased with increasing calcination temperatures (from 2.08 g/cc for
uncalcined powders to 2.30 g/cc for powders calcined at 10500C for 24
hours). They attributed the increase in densities to the removal of

molecular water and hydroxyl groups with increasing calcination

temperatures. Oguri and Hattori [Ogu87] prepared sub-micron silica

powders by a method similar to that employed by Sacks and Tseng. True
density of their powder calcined at 1000C for 24 hours was 1.85 g/cc. A
possible explanation for these observations is the differences in water

content of these powders.

The influence of hydroxyl content on the viscosity of vitreous
silica was also investigated by Hethrington et al [Het64]. Viscosity
measurements were made using the fiber elongation technique [Mac62].
Comparison of the viscosities of glasses with varying amounts of hydroxyl

showed that the activation energy for viscous flow decreased with








increasing hydroxyl concentration. The decrease in activation energy was
attributed to the breaking of strong [Si-O-Si] bonds in the presence of water

to form weak [Si-OH HO-Si] bonds. The role of hydroxyl content in

reducing the viscosity of glass has been confirmed in a number of other

investigations [Bar82, Sche85].
The crystallization (also called devitrification) behavior of silica
glasses is also affected by hydroxyl content. Crystallization is a highly
undesirable phenomenon because it impedes sintering [Rab85]. In the
optimum process, the glass should sinter to full density before the onset of

crystallization.

Wagstaff et al. [Wag64, Wag66] have carried out extensive studies

on the effects of water on the crystallization of vitreous silica. They
suggested that hydroxyl ions rupture the strong silicon-oxygen-silicon
bonds and weaken the glass structure, thereby making it simpler for the
glass to rearrange into a crystalline lattice. They concluded, based on their

studies, that water acts as a catalyst in the crystallization process.

Several impurities can also aid in crystallization. For example,
even traces of alkali and alkali earth ions drastically increase the rate of

crystallization [Rab85]. Flemming [Fle61] prepared fused silica by slip
casting a slurry prepared from glass powders and subsequent sintering. He

observed enhancement in crystallization when a sodium bearing

compound was used as a mold release agent. Small amounts of Al+3
ions also enhance crystallization [Bro59].

Johnson et al. [Joh83] carried out sintering of glass in a chlorine

atmosphere to inhibit crystallization. Chlorine combined with the alkali

vapor released into the furnace atmosphere. This was confirmed by the
presence of KC1 deposits condensed near the exit of the muffle.








The effect of heating rate on the crystallization in glass was

studied by Panda et al [Pan89a, Pan89b]. They suggested that sinter-forging

experiments [Ven86] can be used to detect the onset of crystallization.
These (sinter-forging) experiments give continuous measurements of the
shear rate and the densification rate as a function of temperature. They

obtained information on the onset of crystallization of the glass from the

plots of shear strain versus temperature. Because the shear rate depends

only on the viscosity, the shear rate should continue to increase as the

temperature is increased. However, they observed a transition to a
plateau at high temperatures. They attributed this observation to

crystallization. Their interpretation was confirmed by x-ray diffraction

measurements.

They used two heating rates, one at 20C/min and the other at

0.20C/min to sinter an aluminosilicate glass. The crystallization was

delayed to a higher temperature in the sample heated at a faster heating
rate (9500 versus 8850C). They inferred that it was possible to delay

crystallization because the faster heating rate delayed nucleation. This was

explained on the basis that crystallization is dependent upon two kinectic

steps, nucleation and growth, whereas densification depends only upon

viscosity. Nucleation in turn, is proportional to undercooling, and hence

a slower heating rate gives an advantage to the crystallization process,

relative to the sintering process. In other words, by using a faster heating

rate, undercooling can be minimized and therefore, crystallization can be

delayed or avoided altogether until the glass is fully densified. These

results are somewhat ambiguous because the samples heated at the faster

heating rate reach the crystallization temperature in a much shorter time

compared to the samples heated at the slower heating rate. Hence, it is








possible that delayed crystallization in the samples heated at the faster
heating rate could be due to the shorter heat treatment.


Sintering of Silica Glass

Fused silica exhibits a low dielectric constant, excellent optical
properties, good chemical inertness, low thermal expansion, and good
thermal shock resistance. The major process for manufacturing fused
silica is by melting. The starting material may be natural quartz or

amorphous silica made by oxidizing a silicon compound, typically silicon
tetrachloride, in the vapor phase [Raw67]. The viscous fused glass is then
drawn into fibers, rolled into sheets or cast into shapes. However, due to

the very high viscosity of silica, high temperatures (= 20000C) are required.
To overcome the difficulties of melt processing, techniques have been

used to produce porous structures from fine sized (i.e., high surface area)
amorphous silica. These bodies can then be fully densified by sintering at
relatively low temperatures (in the range 7000 to 12000C).

Shimohira et al. [Shi78] were among the earliest to prepare
powder compacts from colloidal silica particles. They prepared spherical
monodispersed (average particle size 0.2 0.6 gm), amorphous silica
particles by hydrolysis of ethylsilicate and subsequent

condensation/precipitation in the presence of ester, ammonia and

alcohol. The particles suspended in the liquid media were allowed to settle
gradually over a period of several weeks. The settled powder cakes were
then dried in air. They observed that these cakes contained close-packed

face centered cubic arrays of spherical particles. Several pieces were cut
from the powder cakes for sintering experiments. The remaining powder

cakes were ground (each batch separately) in an agate mortar. Compacts








were prepared from a narrow size distribution powder (average particle
size 0.3 um) by dry pressing. In addition, a continuous particle size
distribution was produced by mixing several narrow size distribution
powders. Compacts were also prepared form this powder by dry pressing.
They observed that the packing in dry pressed samples was random as
opposed to ordered, in case of the samples prepared by gravity settling.
They sintered these three (i.e., narrow size prepared by settling,
and narrow and broad size prepared by dry pressing) series of samples at
temperatures in the range 8000 11000C for 24 hours. The changes in pore
size distribution after sintering were determined by mercury porosimetry.
They found that on sintering, the average pore size in samples (dry
pressed as well as settled) prepared from narrow size distribution powders
decreased. On the other hand, the average pore size in the samples
prepared from the broad size distribution powder increased. Based on
these observations, they concluded that an uniformity in particle size (i.e.,
narrow size distribution powder) is more desirable for sintering.

However, their conclusions are rather ambiguous because the dry pressed
powders may have contained agglomerates which have a dominating
effect on the sintering process. Also, since their interpretation was
entirely based on mercury porosimetry measurements, the results need
further evaluation.
A more systematic and controlled study on the sintering of silica
powder compacts was carried out by Sacks and Tseng [Sac84a, Sac84b].
They prepared powders with spherical, nearly monosized particles by the
hydrolysis/condensation of tetraethylorthosilicate in the presence of
ammonia and ethyl alcohol -- a method similar to the one used by
Shimohira et al [Shi78]. By controlling the reactant concentrations, they








produced a narrow size distribution powder with average particle size =
0.5 gm and specific surface area = 7.0 m2/gram. Powder compacts with
highly ordered packing were prepared by gravity sedimentation of well-
dispersed suspensions.
The samples were sintered at temperatures in the range 900-
10500C. Highly translucent samples (= 0.8 cm diameter and = 0.8 mm
thick) were obtained under sintering conditions of 24 hours at 10000C.
The use of higher sintering temperatures resulted in devitrification. They
also observed devitrification for long sintering times (i.e., 48 hours) at
10000C.

They analyzed the densification data in terms of Mackenzie-
Shuttleworth and Scherer models. The data showed very good fit for both
models. However, at short sintering times, the plots of experimental time
versus reduced time, K(t to), were non-linear (Scherer et. al. [Sche85]

have also reported a similar observation). This was attributed to the loss
of hydroxyl groups from the silica particles during the initial heating
period. This increases the viscosity, which in turn decreases the value of
K (refer Eq. 2.4). Hence the slope in the plot of K(t to) versus t decreases.

Experimental observation supports this interpretation. They used the
linear regions in these plots to calculate the "equilibrium viscosities."

Viscosity and activation energy values calculated from both
models, despite widely different geometric assumptions, were nearly
identical. They concluded that pore-particle shape considerations are
relatively unimportant in viscous sintering as long as an appropriate
microstructural size parameter can be defined.
The effect of sintering atmosphere on the sintering of highly
ordered silica powder compacts (prepared by the procedure similar to








Sacks and Tseng) was studied by Tseng and Yu [Tse86]. The samples were
sintered at 10000C. The different atmospheres that were used were a
mixture of water vapor and nitrogen, static air, nitrogen and a mixture of
5% HCI and nitrogen. The densification rate was found to be strongly
affected by the sintering atmosphere. This is illustrated in figure 2.2. The
compacts sintered in water vapor-nitrogen mixture attained full density in
less than 2 hours, whereas densification was impeded in the compacts
sintered in HCl-nitrogen mixture atmosphere. The compacts sintered in
static air required = 11 hours and the samples sintered in nitrogen
required = 110 hours to reach full densities. It was shown that the
viscosity of silica depended on the sintering atmosphere. This would
explain the observed differences in densification kinetics. Viscosities were
calculated using Mackenzie-Shuttleworth and Scherer models. The

viscosity value of 1.07 x 1011 poise in static air was very similar to that
obtained by Sacks and Tseng [Sac84b] (i.e., 9 x 1010 poise).
Several other investigations have been carried out using silica
powder compacts to form dense transparent.glass [Ogu87, Cla87, San89,
Cle89]. Both aqueous [Cla87] and non-aqueous [Cle89] suspensions with
silica powders were used. In the case of non-aqueous suspensions Clegg
et al. [Cle89] used poly (vinyl butyral) as a dispersing agent. These

suspensions were then consolidated by various techniques like slip-
casting, tape casting and extrusion. Sintering was carried out at
temperatures near 1000C to obtain transparent silica glasses.
The data of Clegg et al. [Cle89] had an excellent fit with the
Mackenzie-Shuttleworth model. They suggested a modification to the

Mackenzie-Shuttleworth model to account for the differences in packing
of powder compacts prepared in various investigations. These packing














z.9- SO

IAJ
,so'
1 so
S70

0 0







Figure 2.2


TIME (mini


Plots of relative density versus sintering time in
various atmospheres [Tse86].








differences could arise as a consequence of the presence of agglomerates in

powders or by the use of different forming methods. They proposed the
inclusion of a structure factor S, to be multiplied by K in Eq. 2.3. When the
structure factor S is unity, the compact behaves as a perfect geometrical
structure. However, when the structure factor < 1, the compact is
imperfect due to inhomogeneities in packing.

Based on these considerations, they assigned values of structure
factors for data obtained in various studies. Highly ordered compacts
prepared by Sacks and Tseng [Sac84a] were assigned a structure factor of 1.

The structure factors of compacts used in other investigations were

determined by taking the ratio of the relative viscosities (vis-a-vis Sacks
and Tseng) at 10000C. Very low structure factors (i.e., 1.3 x 10 -3) were
obtained for compacts prepared from powders agglomerated by drying
before redispersion and casting [Scherer84]. These compacts must be

sintered at higher temperatures and/or longer times to reach full density.


Effect of Particle Packing
It is widely known that the packing of particles in a powder

compact greatly influences the properties of the green body, the path of
microstructural change during densification and the properties of the
sintered product. Several important factors that affect particle packing are
particle size, particle size distribution, particle shape, agglomeration,

segregation (due to differences in size or density) and consolidation

methods. Particle packing determines the green density, pore size and

pore size distribution of a powder compact. Green density has been widely
used as an indicator of the status of particle packing. It should be pointed
out that green density is a measure of the overall packing characteristics,








and more details are usually needed (e.g. pore size and size distribution,
pore shape, surface area, etc.) to unambiguously describe the packing
structure.

There are two very different types of packing structures, random

and ordered. A random packing is formed by a sequence of events that are
not correlated with one another. This results in a structure without long-
range repetition. An ordered packing, on the other hand, is constructed

when the particles occupy specific sites with respect to each other such that

long-range order exists, as in a crystal structure.

Relatively few studies have been reported in which powder

compacts having ordered packing were prepared [Shi78, Bar82, Sac84b].
These compacts were prepared from spherical, monosized particles.
However, measured green densities in bulk compacts were significantly

lower than those calculated from geometric considerations (= 60-65%

compared to = 74% for three-dimensional close-packed structures). This is
probably due to the presence of packing defects. Thus, powder compacts

used in a majority of sintering studies exhibit random packing structures.

It is necessary to develop strategies in order to obtain high packing
densities with minimum defects.

For a given powder, the packing characteristics of the green
compact are determined by the method of consolidation. For example, it

is well established that dry pressing produces green bodies with

inhomogeneous microstructures (i.e., non uniform particle packing with

density gradients and presence of large voids). Homogeneous

microstructures and narrow pore size distributions can be produced by

colloidal processing techniques [Aks84].








Sacks and Tseng [Sac84a] showed that green compacts with
different packing characteristics can be obtained by controlling the

dispersing condition of silica powder in water. Green compacts prepared

from well-dispersed suspensions (at pH = 10) by gravity settling had high
green density (relative density = 60%) and ordered packing structure. The
pore size was small (= 39 nm). On the other hand, samples prepared from

flocculated suspensions (at pH = 3) had low green density (relative density

= 45%) and the packing structure was random. Pore size distribution was
highly bimodal containing small intrafloc pores (mode size = 50 nm) and
large interfloc pores (mode size = 120 nm). The differences in packing
structures between these compacts prepared from dispersed and

flocculated suspensions resulted in different sintering behaviors. Samples

prepared from well-dispersed suspensions (i.e., high green density, finer

pore size) sintered to high density and translucency at low temperatures
(10000C, 24 hours), whereas samples prepared from flocculated
suspensions remained highly porous after sintering at 10000C. The

enhanced densification in ordered compacts was attributed to the large

number of nearest-neighbor contacts per particle and the uniform pore

size.

Clegg et al. [Cle89] also examined the effect of particle packing on

the sintering behavior of silica powders. They prepared compacts by (1)
colloidal processing in which agglomerates in the starting powder were
broken down by shear deformation [Alf87], and (2) dry pressing at 100

MPa. They observed that the sintering kinetics were greatly enhanced in

the compacts prepared by the colloidal processing route. They concluded

that due to the presence of inhomogeneities in the pore structure of dry
pressed samples, the sintering rates were lowered.








Various investigations on the effect of particle packing on
sintering and microstructural evolution have been carried out using
crystalline powders (primarily alumina) [Kim87, Roo88, Cam90, Zhe89,
Yeh89]. Kimura et al. prepared alumina compacts by slip casting dispersed
(pH = 2) and flocculated (pH = 9) suspensions. Both porosity and average
pore sizes were higher in case of samples prepared from flocculated
suspensions. They studied the densification kinetics and microstructural
evolution during sintering in these samples. It was shown that due to the
higher green density and finer pore size, densification rates in the pH = 2
samples were higher.
Roosen and Bowen [Roo88] examined the influence of starting

powder characteristics and consolidation methods (both of which resulted
in different packing structures) on the sintering behavior of alumina
powders. The types of powders used were (1) as-received and (2) a powder
obtained by classifying the as-received powder through a semi-continuous
centrifugal classification process [Bar84]. These powders were then

consolidated at pH = 3 and pH = 9 (dispersed and flocculated states
respectively) by three different consolidation methods: viz, colloidal
pressing [Mof87], vacuum filter casting and centrifugal casting. In addition
to the above samples, they prepared compacts by dry pressing the as-
received powder at pressures of 50 MPa and 280 MPa. Thus, the different
consolidation techniques used with the two powders as well as the
different pH values of the suspensions used for the colloidal forming
techniques resulted in 14 different packing conditions.

The samples were then sintered in air at 15000C. Their results on

the effect of particle packing on sintering behavior can be summarized as
follows. Homogeneous green compacts with small average pore size and








narrow pore size distribution were obtained from well-dispersed classified

powder consolidated by colloidal forming techniques. Densification
kinetics in the initial and intermediate stages of sintering were strongly
influenced by the average pore size and the density in the green state.

Structures with finer average pore sizes and higher green densities

showed enhancement in densification. For the final stage of sintering, the
number of large voids in the green compacts were important.
Zheng and Reed [Zhe89] also studied the sintering behavior of
alumina compacts prepared by dry pressing and colloidal processing. Dry

pressing was done at two pressures (6.9 and 115 MPa) to obtain compacts
with different green densities. Samples dry pressed at low pressure
showed a significant increase in mean pore channel size (determined by
mercury porosimetry) as the samples densified. For the samples dry-

pressed at high pressure, a slight increase in the mean pore channel size

was observed. In contrast to the dry pressed samples, for compacts

prepared from well-dispersed suspension, the mean pore channel size

decreased with increasing densification. They suggested that essentially all
of the pores in the samples prepared from well-dispersed suspension were
smaller than the critical size proposed by Kingery and Francois [Kin67].

Hence, the mean pore channel size decreased due to shrinkage of all the
pores. On the other hand, two classes of pores (one larger than critical size

and another smaller than critical size) existed in the dry pressed samples.
During sintering, the smaller pores were eliminated which led to an

increase in the mean pore channel size for the dry pressed samples.

It should be noted, however, that as-received powders were used
in all of the above investigations on alumina. No attempts were made to

remove the agglomerates which are invariably present in commercial








powders. Also, these powders were made up of particles with broad size
distributions. Consequently, it is difficult to isolate the effects of particle
packing due to these factors. The observed differences in the sintering
behavior could have been due to the presence of agglomerates, particle
size distribution, particle packing or a combination of all these factors.
In a recent study by Yeh [Yeh89], a narrow size distribution
alumina powder (geometric standard deviation = 1.23 and average particle
size = 0.9 gm) was prepared and agglomerates were removed by the

sedimentation classification process. Compacts with varying particle
packing characteristics were formed by slip casting well-dispersed (pH = 4)
and flocculated (pH = 9) suspensions, as well as by dry pressing. The
samples prepared from well-dispersed suspensions had very
homogeneous green microstructures with high (= 64%) packing densities
and fine (95 nm) average pore sizes. The samples prepared from

flocculated suspensions also showed homogeneous green microstructures,

but coarser pore structures were obtained. The green densities were lower
(= 51%) and the average pore sizes were higher (172 nm). On the other
hand, heterogeneous green microstructures with bimodal pore size
distributions were obtained in the samples prepared by dry pressing.
Significant differences in the sintering behavior and microstructural
evolution were observed as a consequence of the disparities in particle
packing. High sintering rates and uniform, fine-grained, post-sintered
microstructures were obtained in the samples prepared from the well-
dispersed suspensions. A very significant observation was that there was
no evidence of grain growth in these samples up to 90% relative density.
In the case of samples prepared from flocculated suspensions,
densification rates were significantly reduced and the final microstructure








had coarser grains. Dry pressed samples showed very low overall
densification rates. Exaggerated grain growth was observed in these
samples, and even after prolonged sintering times at high temperatures
(48 hours at 16000C) the samples did not sinter to full density. He
concluded that green compacts with homogeneous microstructures and
higher packing densities show enhanced densification rates and less
microstructure coarsening (i.e., grain growth) during sintering.


Effect of Particle Size Distribution

The effect of particle size distribution on sintering is an area of
surprisingly little research and understanding. Coble [Cob73] developed a
model for the initial stage of sintering considering one and two-
dimensional arrays of particles with various sizes. Onoda [Ono76]
analyzed the sintering behavior of binary powders in which the coarse
particles were much larger than the fine particles.
A majority of experimental studies concerning the effect of
particle size distribution on sintering have been done using bimodal
mixtures of powders [Dehof66, Oha69, Smi84, Lin87]. This is perhaps due
to the difficulty in producing powder blends with controlled particle size
distributions. In recent years, due to the development of methods for
producing monodispersed powders [Sto68, Mat77], it has been frequently
proposed that narrow size distribution powders are desirable for
producing dense, uniform, fine-grained microstructures at low sintering
temperatures [Bar84, Yan83]. This is debatable, since controlled studies to
support this hypothesis has not been carried out. Recently, a few studies
[Pat86, Yeh88] have been carried out using powders with constant average
size, but varying widths of the size distribution which can lay this








controversy to rest. Previous work on the effect of particle size
distribution on sintering will be reviewed in this section.
O'Hara and Cutler [Oha69] studied the sintering behavior of
bimodal alumina powders. They observed that the linear shrinkage of
these compacts continuously decreased as the proportion of coarse

powders increased. Smith and Messing [Smi84] have also reported
similar results. O'Hara and Cutler pointed out that for a dense large
particle embedded in a fine particle matrix, the fine particles surrounding
the large particle will experience tensile hoop stresses during sintering.

These stresses can cause retardation in densification rate of the fine
particle matrix.
Sacks and Vora [Sac88] carried out sintering studies on

monodispersed silica powder compacts that were infiltrated with a 'silica'
sol. They reported significant enhancement in densification rate of the

sol-infiltrated samples over the samples without sol-infiltration. This
was explained by visualizing the sol-infiltrated samples as binary
mixtures of 'coarse' silica particles and 'fine' sol particles. Thus, Coble's
[Cob73] analysis for two-dimensional arrays in which densification rate
can be enhanced due to the presence of fine particles in a coarse matrix

was applicable to these samples. They also suggested the possibility of the
viscosity of 'sol' particles being lower than the viscosity of silica particles

due to differences in hydroxyl concentration.

Liniger and Raj [Lin87] investigated the packing and sintering of

two-dimensional structures made from bimodal polystyrene spheres.
They reported that monosized spherical particles formed hexagonal close-
packed domains with lower packing density regions between these
domains. During sintering, faster sintering rates were obtained within the








domains, resulting in the opening-up of domain boundaries (i.e., large
pores or cracks were generated). They also showed that instead of
monosized spherical particles, binary mixtures of spherical particles can be
used to produce random structures. The absence of domain boundaries in
the random packing arrangement reduced the probability of flaw
generation, resulting in a homogeneous sintered product without the
formation of large pores.
Gattuso and Bowen [Gat84] and Roosen and Bowen [Roo88]
compared the sintering behavior of a classified narrow size distribution
alumina powder with an as-received broad size distribution powder and
observed that higher densification kinetics, finer sintered microstructures
and higher final sintered densities were obtained for the classified powder.
They concluded that narrow size distribution powder produced better
sintering results. However, their conclusions are rather ambiguous

because: (1) the narrow size distribution powder was obtained by collecting
the fine fractions of the as-received powder, therefore, the classified
powder had a finer average particle size (i.e., 0.38 am relative to 0.61 arm
for the as-received powder) and higher surface area (i.e., 11.4 m2/g relative
to 7.9 m2/g for the as-received powder) (2) the as-received powder
contained large hard agglomerates but the classified powder was
agglomerate-free. Hence, it is not surprising to obtain higher densification
kinetics and finer microstructures for their narrow size distribution

powder.
Sordelet and Akinc [Sor88] compared the sintering behavior of
monosized, spherical Y203 with an as-received broad size distribution

powder. The samples were consolidated by dry pressing. They observed
that the sintering behavior of the monosized powder was superior to that








of the as-received broad size distribution powder. Hence, they were led to
believe that narrow size distribution powders are desirable for improved
sintering behavior.
A re-examination of their data reveals that certain basic scientific
details were overlooked. The average particle size of the broad size
distribution powder was an order of magnitude larger than the average
particle size of the narrow size distribution powder (i.e., 4.2 pgm for the
broad compared with 0.4 gpm for the narrow). Thus, based on Herring's

[Her50] prediction, the fine sized powder (in this case, narrow) should
exhibit enhanced sintering kinetics. Furthermore, the green compacts (in
both cases) contained large packing defects commonly observed in dry
pressed samples. Even in compacts prepared from the narrow size
distribution powder, they observed exaggerated grain growth and the
samples did not sinter to full density. Thus, their interpretation cannot
be said to be a logical consequence of their results.
Patterson and Benson [Pat84] studied the effect of width of the
particle size distribution on the densification behavior of spherical copper

powders. In one case, powders were prepared with constant average size

(54 gpm) based on weight but varying widths (geometric standard
deviations, Ino = 0, 0.24 and 0.54) of the distribution, and in another case
powders with constant average size (41 pm) based on number but varying
widths (geometric standard deviations Ino = 0, 0.24 and 0.54) of the
distribution were prepared. These powders were loosely packed in a

cylindrical graphite block and pre-sintered. After pre-sintering, the
samples were sintered in a furnace at 10250C using a stainless steel boat.
For the constant average particle size of the powder based on
weight, they observed that the sintering rate increased with increasing








distribution width. The plots of pore-solid interfacial area (determined by
quantitative stereology on polished cross-sections) versus density showed
that there was a gradual decrease in fineness of the pore structure from the
wide to the narrow distributions, and that, the widest distribution (Ino =
0.54) had the greatest slope. This was consistent with the observation of
enhanced sintering rates in the Ina = 0.54 sample. For the constant
average size based on number, the sintering rate increased with increasing
width of the distribution (from Ino = 0 to Ino = 0.24), but then showed a
decrease in densification rates upon further broadening of the distribution
(for Ino = 0.54). The pore-solid interfacial area versus density plots
showed that Ino = 0 and Ino = 0.24 distributions had similar pore
structures but the Ino = 0.54 distribution had a much coarser pore
structure indicated by low surface area. Hence, they concluded that the
rate of sintering was primarily dependent on the scale of the pore
structure (finer pore structures resulting in enhanced densification rates).
Patterson and co-workers [Pat85, Pat86] also studied the effect of
particle size distribution on the sintering of spherical copper powders
(these powders were different from those used in their earlier work) and
spherical as well as irregularly shaped tungsten powders. All the powders
were dry pressed to a constant green density (65% relative density).
They found that in the case of spherical powders (copper and
tungsten), broadening of the size distribution resulted in enhanced
sintering rates. In contrast to spherical powders, no consistent trend was

observed for the irregularly shaped tungsten powders. The narrowest and
widest distributions showed higher densification rates, whereas the
intermediate widths showed relatively lower densification rates. The








apparent inconsistency in their results could be attributed to the
inhomogeneous green compacts produced by dry pressing.
Yeh and Sacks [Yehs88b] investigated the effect of particle size
distribution on the sintering of high purity alumina powders.
Agglomerates in the as-received powders were removed by gravity
sedimentation. Powders with same median size (based on weight) but
varying widths of the distribution were prepared. Homogeneous, high
density green compacts were formed by slip casting well-dispersed
suspensions. A slight enhancement in the initial densification rate was
observed in case of samples prepared from the broad size distribution
powders. However, compacts prepared from both powders (narrow and
broad) reached 'final' density at the same time/temperature schedule.
The 'final' microstructures for both samples were virtually
indistinguishable.
They showed that the powder with the narrow particle size
distribution did not offer any advantage in obtaining a dense, uniform,
fine-grained microstructure. They also pointed out that by using powders
with a broad particle size distribution, it is usually possible to achieve
higher green densities and, therefore, reduced shrinkage during sintering.


Suspension Processing

A suspension is a two-phase mixture consisting of particles (solid)

suspended in a liquid (e.g. water, alcohol) medium. Suspensions prepared
with particles in the size range 1 nm to 1gm are often described as
colloidal suspensions. Detailed descriptions of suspension processing are
available in the literature [Hie77, Hun81, Hun87]. Recently, Khadilkar

[Kha88] has compiled an excellent review on suspension processing of








silica powders which were used in this study. Hence, only the basic
principles will be described in this section.
In a colloidal suspension, particles are randomly moving due to
Brownian motion. Particle encounters due to Brownian motion would

lead to flocculation. However, if strong repulsive forces between particles
are established, particles remain well-separated, and hence flocculation
can be avoided. A suspension in which particles remain essentially as
distinct single particles over a long time (e.g., days) is termed a well-

dispersed suspension. It has been established that homogeneous and high
density green compacts can be prepared from well-dispersed suspensions.
Thus, in ceramic processing, well-dispersed suspensions serve to improve
the green microstructures. This in turn, enhances the kinetics of sintering.
One of the ways to induce repulsion between particles is by
developing an electric charge (positive or negative) on the surface of the
particle and if all particles have the same charge, they will repel each other
during approach. For oxide systems (e.g., alumina, silica), the major
mechanism for charge development is the adsorption/dissociation of
hydroxyl and hydrogen ions. For example, the surface of a silica particle in
an aqueous medium can develop positive or negative charge by the
following reactions:


-SiOH(surface) + H (liquid) SiOH2+(surface) (2.5)


-SiOH(surface) + OH"(liquid) -4 SiO -(surface) + H20 (liquid)


(2.6)








The H+ and OH- ions are called the potential determining ions. By
changing the pH (i.e., H+ or OH- ion concentrations) of the suspension,
the sign and magnitude of the surface charge can be changed.
In order to maintain electroneutrality, the net charge developed
on the surface of the particles in a suspension must be balanced by an
equal charge of opposite sign produced by counter ions in the solution.
Some counter ions may physically adsorb on the particle surface due to the
electrostatic attractive force (Stem layer). The other counter ions form a
diffuse layer outside the Stern layer. The combination of the charged
particle surface and the surrounding counter ions in the solution is called
an electrical double layer.
When two particles approach each other (due to Brownian
motion or an applied shear field), the electrical double layers start to
overlap. This will produce a repulsive force because of (1) the increase in
the osmotic pressure due to increase in the concentration of ions between
two particles, or (2) the increase of free energy due to the electrostatic force
[Lyk68]. For two flat plates separated by a distance d, the repulsion energy
per unit area, VR, can be approximated by the following equation:


r -2
641n KT exp(ZeV0/2KT) -1e
R(plate) exp(ZeVo/2KT) + 1 (2.7)


where iTo is the bulk ion concentration (number of ions/volume), K is the

Boltzman constant, T is the absolute temperature, Z is the valence of ions
in a symmetrical electrolyte, e is the elementary charge, O~ is the potential

at the stern layer which is used to represent the surface potential, K is the








Debye-Huckel parameter (i.e., the reciprocal of the "thickness" of the
diffuse layer in the electrical double layer) which is given by:


2 2Y(nioZi)

e oKT (2.8)


where nio is the bulk concentration of ions of type i, Zi is the valence of

the ion i, er is the relative dielectric constant, and Eo is the permittivity of

vacuum.
In case of interaction between two spherical particles with large
values of Ka (i.e., particle radius a, is relatively large compared to the
thickness of the diffuse layer), the total repulsive energy can be

approximated by the following equation:

2
64xanoKT exp(Ze o0/2KT) 1
VR(sphere) 2 exp(Ze V0/2KT) +1 exp (-(
(2.9)


From the above expressions, it is clear that the major parameters

which determine the repulsive force as a function of inter-particle
separation distance are the ionic strength (i.e., valence of ions and ion
concentration), surface potential (0W), and the size of the particle.

In a suspension with constant ionic strength, the repulsive force
is mainly determined by the surface potential of the particles. However,
the surface potential is not readily available. Therefore, in practical

applications, a near surface potential (called the zeta potential) is used to

determine the magnitude of electrostatic charge.








The surface charge, and therefore, the zeta potential of oxide
powders in a suspension, can be adjusted by changing the pH of the
suspension. Figure 2.3 shows a plot of zeta potential versus pH for silica
powder [Kha88]. The zeta potential is zero at pH = 4. Thus pH = 4 is called
the isoelectric point (IEP) for silica powders. At pH values higher than the
IEP, the silica surface is negatively charged and the zeta potential is
negative whereas at pH values lower than the IEP, the silica surface is
positively charged and the zeta potential is positive. The magnitude of

the zeta potential increases as the pH deviates from the IEP.
Figure 2.3 shows that beyond pH = 8 there is no substantial
increase in zeta potential with increasing pH. This is because in order to
reach a high pH, a base (e.g., NH40H) is added. Since the base is an

electrolyte which contributes ions to the suspension, the ionic strength is
increased and the electrical double layer is compressed. Hence the
magnitude of the zeta potential is decreased. Thus, pH = 8 is an optimum
pH for developing high surface charge and hence obtaining well-dispersed

state for silica suspensions. On the other hand, at pH = 4, the suspension
is flocculated since there is no charge on the particles.


Significance of This Study
Quantitative descriptions of sintering are based on model systems

comprising two equally sized particles of circular or spherical geometry, or

regular arrangements of such particles [Fre45, Kuc49, Cob73]. However,
the powders used in experimental sintering studies usually have a wide
range of particle sizes, the particles are rarely spherical, and the particle
packing arrangements in powder compacts are not regular. Even with

spherical particles of uniform size, rearrangement processes can occur due

























20














a
fZ -2o









0 *

-00
-l *
P 4


2 4 10


SUSPENSION pH


Figure 23 Zeta potential versus pH for silica [Kha88l.








to inhomogeneities in packing, resulting in a sintering behavior that
deviates from that predicted by the models [Exne73]. Thus, the extension
of theoretical predictions to real systems is often difficult, if not
impossible.
In order to rigorously test the sintering theories, powders and
powder compacts that have the attributes of a model system should be
used. The present study was carried out using such powders and powder
compacts. By carefully selecting the structure (i.e., amorphous) and
morphology (i.e., spherical) of the powder as well as consolidation
methods, complexities stemming from non-ideal powder characteristics,
inhomogeneities in packing and grain growth were avoided.
The salient features of this study also include a detailed
characterization of the path of microstructural evolution during sintering
and experimental determination of viscosities at sintering temperatures.
Models for viscous sintering consider simple systems and provide
relationships between viscosity, densification rate and microstructural
parameters. Since all these variables were independently determined, this
investigation provided an ideal experimental set-up to test these models.












CHAPTER 3
EXPERIMENTAL PROCEDURE

Powder Preparation and Characterization

The silica powders used in this investigation were prepared by

the Stober method [Sto68]. It has been shown that by controlling the

concentrations of the reactants (tetraethylorthosilicate, ethanol and
concentrated ammonium hydroxide solution), the average particle
diameter could be varied [Sac84a].

In the present study, various batches of narrow size distribution

powders (= 70 grams each) were produced with average particle diameters

in the range = 0.15 to 1.2 gpm. Reagent grades of tetraethylorthosilicate
(TEOS)*, ethanol** and concentrated ammonium hydroxide (= 28 wt%
NH3) solution*** were used. In order to remove impurities, TEOS and

ethanol were distilled before use. The distillation of ethyl alcohol was
carried out at 800C in a round-bottomed flask connected to one end of a

glass condenser tube. A heating mantle was used to heat the flask. The

distilled alcohol was collected in another flask connected to the other end

of the condenser. At atmospheric pressure, TEOS decomposes at

temperatures below its boiling point (880C). By reducing the pressure, the

boiling point can be reduced considerably. Hence, TEOS was distilled at



*Fisher Scientific Co., Fair Lawn, NJ.

** Fisher Scientific Co.
*Fisher Scientific Co.








550C under a vacuum of 25 mm of mercury. Ammonium hydroxide was
used as-received. 4.5 liters of ethanol and 0.25 mole of TEOS/liter of

ethanol were used per batch of silica. The average particle size was varied

by varying the amounts of ammonium hydroxide solution (consequently,
the amount of water was also varied). Table 3.1 lists the amounts of

ammonia and water used to produce the various sizes of silica powders

prepared in this study.
Measuring cylinders and flasks used in powder preparation were
first cleaned with soap solution, rinsed with water and then cleaned with

2% HF solution*. Subsequently, they were rinsed with deionized water

and dried. Finally, the mixing flask was rinsed with ethanol and the

measuring cylinders were rinsed with the corresponding chemicals, viz,

ethanol, TEOS and ammonium hydroxide solution.

The chemicals were mixed in the mixing flask by the following
procedure. In a 6 liter mixing flask, 4.5 liters of ethanol was poured and

under conditions of constant stirring, concentrated ammonium hydroxide

solution was added to the ethanol. After 5 minutes, TEOS was added to

the alcohol-ammonia mixture. Within minutes, silica particles were

precipitated. The onset of precipitation was determined by the change in

color (from clear liquid to translucent) of the solution. To ensure that the

reaction was complete, the mixture was stirred for 30 minutes after the

observation of precipitation of silica particles.


* Fisher Scientific Co.














Concentrations of ammonia and
various sizes of silica powders.


water used to prepare


Average Particle size Ammonia Water (Moles/Liter)
based on Mass (im)* (Moles/Liter)


0.15 1.3 3.2

0.35 1.9 4.7

0.65 2.5 6.0

0.95 2.6 6.3

1.2 2.8 6.8



Determined by X-ray sedimentation method (Model Sedigraph,
Micromeritics Instrument Corp., Norcross, GA.)


Table 3.1








The precipitated silica powder was separated from the alcohol
solution by filtration using a pressure filtration apparatus*. A 0.22 p.m

poly (vinylidine difluoride) filter paper** was used. Pressure (1.8 MPa, i.e.,
80 psi) was applied using commercial grade compressed nitrogen gas. The
powder cake obtained was dried at 900C for 6 hours. In order to remove
ammonia and other soluble impurities, powders (each batch separately)

were washed with deionized water using the following procedure. Dried
powder cake was ground to a very fine size using high purity alumina
mortar and pestle. A dilute suspension of silica (= 2 vol% solids) with
deionized water was prepared. This suspension was then filtered using the
pressure filtration apparatus. A 0.22 pm mixed esters of cellulose filter

paper was used. The electrical conductivity of the filtrate was
measured using a conductivity meter"*** (the measured conductivity
gives an estimate of the concentration of the soluble impurities in water;
higher conductivity corresponds to higher concentration of soluble
impurities). The filtration procedure was continued by repeatedly adding
fresh deionized water until the conductivity of the filtrate was less than
twice the conductivity of deionized water (measured conductivity values
for deionized water were 0.5 x10-6 1.0 x 10-6 ohm-cm-1. Filtration was

discontinued when the filtrate conductivity was < 1.5 x 10-6 ohm-cm-1).
The filtered cake was dried at 900C for 6 hours and finely ground using
mortar and pestle. All powders (each batch separately) were subsequently


*Millipore Corp., Bedford, MA.

** GVHP Filter Paper, Millipore Corp.
GSWP Filter Paper, Millipore Corp.
Model 70 CB, The Barnstead Co., Boston, MA.








calcined at 2000C for 24 hours. To avoid aggregate formation during the
calcination treatment, the powders were loosely packed in a pure alumina
crucible*.

Powders with constant average size, but varying width of the size
distribution were prepared from these powder batches. Several batches of
powders with average particle size = 0.65 pgm were mixed together to form
a narrow size distribution powder (NSD). The coarsest and the finest
particles in the mixed powder were removed by gravity-sedimentation
process. This procedure is described in Appendix B. In addition to the
NSD powder, two powders with controlled particle size distributions
(broad and broad-CSA) were prepared by blending batches of narrow size
distribution powders with varying average particle sizes (0.15 p.m to 1.2
gim). In the broad size distribution powder (BSD), the median size based
on mass was maintained the same as the one in NSD powder (i.e., 0.65
jim), but the width of the distribution was varied. In the broad-CSA
powder, the specific surface area and the median size based on number
were maintained the same as NSD powder, but the width of the
distribution was varied. The BSD powder was prepared by mixing the
following powders ; 20 wt.% of 0.15 jim, 30 wt.% of 0.35 jim, 10 wt.% of
0.65 jim, 25 wt.% of 0.95 p.m and 15 wt.% of 1.2 jim, and the broad-CSA
powder was prepared by mixing the following powders ; 5 wt.% of 0.15 jim,
65 wt.% of 0.65 jim, 10 wt.% of 0.95 jim and 15 wt.% of 1.2 gm.

The average particle size and size distributions for these powders
(NSD, broad-CSA and BSD) were determined using the following
techniques: (i) X-ray sedimentation (mass based) and (ii) Scanning


* Coors Ceramic Co., Golden, CO.








electron microscopy* (number based). For measurements by the X-ray
sedimentation method, dilute silica suspensions (= 2 vol% solids) were
prepared. The suspension pH was adjusted to = 8.0 (to ensure electrostatic

stabilization) and extensive (two hours) ultrasonication** was used to

break down agglomerates.
Micrographs obtained by scanning electron microscopy (SEM)
were used to determine the number based average particle size and size
distribution. Powder samples for microscopy were prepared by the
following procedure. A 500 ppm poly (acrylamide), PAAt, solution in
deionized water was prepared in a 1 liter volumetric flask. A dean glass
slide was dipped in the polymer solution for about an hour. It was then
rinsed with running deionized water to remove excess polymer solution
and dried in air. The slide was then dipped in a dilute (< lvol% solids)

silica suspension and again rinsed with running deionized water. The

above procedure was effective in preventing the particles from
agglomerating during drying. The glass slide was attached to an
aluminum sample holder for loading into the SEM. A thin layer of gold-
palladium coating was deposited on all the samples prior to observation in

the microscope. A minimum of 20 micrographs (chosen at random) at a
magnification of 10000 were taken for NSD powder. For broad-CSA and

BSD powders a lower magnification was selected in order to include more
particles in a single field. For these two powders a minimum of 50
micrographs were taken at a magnification of 7000. Negatives of each


* Model JSM-35CF, Japan Electron Optics Co. Ltd., Tokyo, Japan.
** Model W-375, Heat Systems-Ultrasonics, Inc., Farmingdale, NY.

t Average M.W. 6,000,000, Cat. # 2806, Polysciences, Inc., Warrington, PA.








micrograph (for broad-CSA and BSD only) were then used to obtain
enlarged (8.5 in. x 11 in.) prints. Particle size was measured on these

micrographs (enlarged prints in the case of broad-CSA and BSD) using a

digitizing tablet* and a specially developed computer program.

Measurements were done on a minimum of 250 particles for NSD and a

minimum of 1200 particles for broad-CSA and BSD. Particle size

histograms were generated from these measurements using the computer

software.

Specific surface areas of the powders were measured by nitrogen

gas adsorption using the multipoint B.E.T. method**. Samples were
outgassed under flowing nitrogen at 1500C for 6 to 8 hours. True densities

of the powders as a function of calcination temperature were determined

by helium gas pycnometry**


Suspension Preparation and Characterization

The electrokinetic behavior of silica suspensions has been

described previously [Kha88]. It has been shown that aqueous silica

suspensions exhibit high zeta potentials at pH = 8.0 and very low (almost

zero) zeta potentials at pH = 3.6. In other words, at pH = 8.0, the

suspensions are well-dispersed and at pH = 3.6, the suspensions are

flocculated. For particle packing study, suspensions were prepared at pH =

8.0 and pH = 3.6. For particle size distribution study, suspensions were

prepared at pH = 8.0.


* Model 9111A, Hewlett-Packard, Cupertino, CA.

** Model QS 7, Quantachrome Corp., Syosett, NY.
*** Model PY 5, Quantachrome Corp.








Preliminary experiments were carried out to determine the
optimum suspension solids loading for casting high density green
compacts. Well-dispersed (pH = 8.0) suspensions were prepared from NSD
powder at solid loadings of 3 vol%, 10 vol%, 30 vol% and 45 vol%. It was

established that there was no change in the green density of cast samples
up to a solids loading of 30 vol%. Hence, the solids loading for

suspensions prepared for packing study (NSD powder) was maintained at
20 vol%. However, it is desirable to use high solids loading in case of

suspensions with polydisperse powders in order to avoid segregation of
particles. Hence, for the particle size distribution study, since the ISD and

BSD powders comprised particles of different sizes, the suspension solids
loading was increased to 45 vol%.

Suspensions for the particle packing study were prepared by the
following procedure. Two suspensions, one well-dispersed and one
flocculated, were prepared at 20 vol% solids loading with deionized water.

For the well-dispersed suspension pH adjustment was done with 1N

ammonium hydroxide solution*. This was followed with extensive
ultrasonication (3 to 4 hours) to break down the agglomerates. The
flocculated suspension was sonicated for about an hour before adjusting

the pH with IN nitric acid**. In addition to these two suspensions,
another suspension at a solids loading of 10.8 vol% (38.5 grams powder in

147.5 ml deionized water) was prepared. The suspension was sonicated for

30 minutes and pH adjusted to = 3.6. This suspension was then added to




* Fisher Scientific Co.
** Fisher Scientific Co.








18.5 ml of a 200 ppm poly (ethylene oxide) (PEO)* solution in deionized
water under conditions of constant stirring. The mixing of the suspension
to the polymer solution resulted in a lowering of the suspension solids
loading to 10 vol%. The final concentration of PEO in the suspension was
20 ppm. All suspensions were aged for 24 hours prior to casting.
Suspensions for size distribution study were prepared by the
following procedure. Well-dispersed suspensions at a solids loading of 45
vol% were prepared from broad-CSA and BSD powders. A small quantity
of powder (equivalent to approximately 15 vol% solids) was initially added
to the deionized water. After adjusting the pH to = 8.0, the suspension was

sonicated for 15 minutes. Again, a small quantity of powder was added to
the suspension followed by pH adjustment and 15 minutes of
ultrasonication. This procedure was repeated (approximately 4 or 5 times)
until all the powder was added to the suspension. Finally, the
suspensions (now 45 vol%) were sonicated for 2 hours and aged for 24
hours prior to casting.

Suspensions for theological measurements were prepared from
NSD and BSD powders. Well-dispersed suspensions at 44 vol% solids
loading were prepared by the procedure described above for the BSD
powder. Both suspensions were aged for 24 hours and sonicated for
additional 2 hours before the theological measurements. The solids
loading of both suspensions was accurately measured using the procedure
described by Yeh [Yeh89]. The measurements were done for a minimum
of two times for each suspension.




* Average M.W. 5,000,000, Cat. # 4031, Polysciences, Inc.








Rheological characteristics of the suspensions were determined
using a concentric cylinder viscometer*. All measurements were done
using the same sensor system (ZB 30 with inner cylinder O. D. = 29.36 mm,
outer cylinder I. D. = 30 mm and the gap size = 0.32 mm). Approximately 2
ml of suspension was used for each measurement. The shear rate was
increased from 0 to maximum in 2 minutes (up curve) and decreased
from maximum to 0 in another 2 minutes (back curve). Plots of shear
stress vs. shear rate were obtained at maximum shear rate settings of 10 s-

1 100 s- and 1000- Viscosities at each shear rate were calculated using
the relationship :

viscosity = shear stress / shear rate (3.1)


Preparation and Characterization of Green Compacts
Green compacts for the particle packing study were formed using
the following three methods: (1) gravity sedimentation, (2) slip casting and
(3) dry pressing. Green compacts for particle size distribution study were
formed by slip casting. The suspensions (after aging for 24 hours) were
sonicated for 30 minutes prior to casting. The pH values were checked and

adjusted, if necessary.

Suspensions prepared from NSD powder at pH = 8.0, pH = 3.6 and
pH = 3.6 with PEO were consolidated by gravity sedimentation. In this
method, 2.6 ml (5.2 ml in the case of PEO) of suspension (corresponding to
1.1 gram silica) was poured into 3/4 inch I.D. plastic tubes set on a glass

plate.The tubes were partially covered with a plastic cover slip to avoid
dust contamination. The suspensions were then allowed to settle


* Model RV-100/CV-100 Viscometer, Fisons, Inc., Saddle Brook, NJ.








undisturbed in an isolated area. A maximum of one week was required to
achieve complete settling (this was determined when the liquid in the top
portion of the tube appeared very clear). A portion of the clear liquid was
then drawn off with a transfer pipette and the remaining liquid was
allowed to air dry. The samples were then removed from the tubes and

further dried in an oven at 900C.

Another suspension prepared from NSD powder at pH = 8.0 was
consolidated by slip casting. For slip casting the plastic tubes were placed
on a flat surface of a plaster of paris mold. A 0.22 gim nylon filter paper*
was placed between the tubes and the mold to avoid contamination of the

sample as well as to prevent the powder particles from getting inside the

plaster mold (the pore size of plaster mold was much greater than the
particle size of the powder). Complete water removal was achieved in

about an hour. The samples were allowed to dry in air for 6-8 hours before
they were removed from the tubes. Further drying was done in an oven
at 900C.

For dry pressing, 1.1 grams of powder (NSD) was cold compacted
in a cylindrical tool steel die (3/4 inch I.D.). Thin teflon sheets were

attached to the surface of the top and bottom punches to avoid

contamination from the die. Various compaction pressures were tried in

order to match the green density of dry pressed samples to that obtained in
the samples with 20 ppm PEO. After preliminary experiments, it was
decided to use a compaction pressure of 12.4 MPa (1800 psi).

For the particle size distribution study, suspensions prepared from
broad-CSA and BSD powders were consolidated by slip casting. The slip


* Fisher Scientific Co.








casting procedure was similar to the one described in this section except

that due to the higher solids loading (45 vol%) of the suspensions, 1.2 ml

of suspension was used per sample. After removal from the tubes, the

samples were dried in the oven at 900C.

Total porosity and pore size distributions of the green compacts

were determined by mercury porosimetry*. Plots of applied pressure

versus intruded volume were obtained up to a maximum applied

pressure of 414 MPa (60000 psi). In the case of dry pressed samples,

mercury intrusion was observed at the lowest applied pressure. Hence,

data points were also obtained using low pressure (0 to 0.96 MPa. i.e., 0 to

14 psi) intrusion. Porosity (P) was calculated using the equation :


V
% P= X 100 (3.2)
W
-+V
p
where W is the weight of the sample, V is the intruded volume and p is

the theoretical density of the powder. Density value obtained by helium

pycnometry on loosely packed powder calcined at 2000C was used as the

theoretical density. The pore channel radius distribution was obtained

using the relation :

Pore radius (nm) = 735 / applied pressure (MPa) (3.3)

The median pore radius was calculated from the pressure corresponding

to 50% of the maximum intruded volume.

A minimum of three measurements were done on each set (i.e.,

pH = 8.0 gravity sedimentation, pH = 8.0 slip cast etc.) of samples. Two

measurements were done on a sample by breaking up the sample into two


* Model SP 100, Quantachrome Corp.








parts. A third measurement was done on a different sample in order to
determine the variation of porosity from sample to sample. In the case of
dry pressed samples, measurements were done on four different samples.
Specific surface area of slip cast sample (NSD, pH = 8.0) was
determined using the multipoint B.E.T. method. The sample was
outgassed at 1500C for 8 hours. SEM was used to observe the top surfaces of
the green compacts. Samples were coated with a thin gold-palladium
coating prior to observation in the SEM.


Pre-Sintering
Preliminary experiments were carried out to determine the
heating rate and the pre-sintering temperature for all the samples.
Prevention of crack formation during the heating cycle was the criterion
used for establishing the optimum heating rate. For pre-sintering
temperature, the objective was to determine the maximum temperature at
which no significant densification took place.

Samples (NSD powder, gravity sedimentation at pH = 8.0) were
sintered at 7500C for 6 hours in static air atmosphere at the following
heating rates : (1) 5C/ minute (2) 10C/minute (3) 10C/minute with a 2
hour hold at 2000C and (4) 1C/minute with 2 hour holds at 2000 and
4000C. The cooling rate for all samples was 30C/minute. In all cases the
samples showed crack formation. However, the severity of cracking
decreased with slower heating rates and also with the incorporation of
hold periods in the heating cycle. Hence, it was decided to use an
extremely slow heating rate with longer hold periods for pre-sintering.

In order to determine the pre-sintering temperature, samples were
sintered at 50C/minute in static air atmosphere for 6 hours at the








following temperatures : (1) 9500C (2) 8000C (3) 7500C and (4) 6750C.
Relative densities were determined for each sample by mercury

porosimetry as well as by the Archimedes method. The density values
obtained by helium pycnometry on loosely packed powders calcined at
corresponding temperatures were used as theoretical densities. The
relative density values were then compared with the density values
obtained for the green compacts. It was concluded based on the stated
objective to pre-sinter the samples at 6750C. The pre-sintering schedule
used for all samples is shown schematically in figure 3.1.


Sintering
Experiments were carried out to determine the sintering
temperature that can be used for all the samples. The objective was to
select an optimum sintering temperature that would produce the full
range of densities within reasonable times. Samples were sintered in static

air under isothermal conditions at 11000, 11500C in a resistance furnace*.

The furnace was equipped with a microprocessor" to control the sintering
schedules. A Type B thermocouple was used to read the temperature.
Samples were sintered for 30 minutes and 24 hours at each temperature.
Bulk densities were measured by the Archimedes method. After
examining the results, 11500C was chosen as the sintering temperature for
all the samples.

All samples were sintered in static air under isothermal
conditions for 5 minutes to 24 hours. For the particle packing study,


* Model DT 31 S, Deltech, Inc., Denver, CO.
** Model Micricon 82300, Research, Inc., Minneapolis, MN.






















675






300


Time (Hours)


Pre-sintering schedule used for all samples.


Figure 3.1








samples were sintered in batches of five (one sample for each
consolidation condition) for specific times. A batch of samples was
sintered for 144 hours (6 days) to determine if crystallization would occur.
In case of the samples prepared from broad-CSA and BSD powders
(particle size distribution study) each sample was sintered individually for

a specific time. Bulk densities and open porosities of the samples were
measured by the Archimedes method. Density value obtained by helium
pycnometry for loosely packed powder at 11500C was used as theoretical
density to calculate relative densities from bulk densities.


Sample Preparation for Quantitative Microscopy
To study the microstructural evolution during sintering, polished
sections were prepared by the following procedure. Small representative
samples were obtained by breaking the sintered samples. These samples
were then glued with a commercial adhesive* to the bottom (the side to be
polished facing down) of 20 ml glass scintillation vials**. A mixture of
monomer (methyl methacrylate) and initiator (methyl propionitrate)***
was prepared in the ratio 9 mg of initiator to 5 ml of monomer. The
mixture was stirred for 5 minutes to ensure complete dissolution of the
initiator in the monomer. This mixture (3 ml) was poured into the
scintillation vials. The vials were closed with a plastic cap lined with an
aluminium foil and placed in an oven at 650C. After about 6 hours, the
monomer was completely polymerized resulting in solid, hard mounts.


*Super Glue, Loctile Corp., Cleveland, OH.
*Fisher Scientific Co.
*** Fisher Scientific Co.








The vials were removed from the oven and 5 ml of quickmount* solution
was poured on the polymerized mount. The quickmount solution
solidified in 45 minutes at room temperature, thus increasing the height
of the sample mounts. The sample mounts were then removed from the
vials by breaking the vials.

Mounted samples were ground with silicon carbide powder
slurries on glass plates. The following grit sizes of powders were used in
succession. 120, 180 240, 320, 400, 600 and 1000. After fine grinding,
samples were hand polished on a polishing wheel** with alumina
powders using a microcloth***. Alumina powders with average particle
size 1.5 tgm*** and 0.05 gmtt were used. Final polishing was done on an
automatic polisherttt with 0.01 gmtttt alumina using a microcloth.
After polishing, the samples were cleaned in an ultrasonic
cleanerttttt with a dilute soap solution. The mounted samples were then
placed in an oven at 2000C for 30 minutes to soften the mounts. Samples
were removed from the mounts with a tweezer and the mounts were




* Fulton Metallurgical Products Corp., Saxonburg, PA.

t Buehler Ltd.
*Model Ecomet III, Buehler Ltd.
Buehler Ltd.
CR1 Alumina, Baikowski International Corp., Charlotte, N.C.
tCR30 Alumina, Baikowski International Corp.

ttt Model Minimet, Buehler Ltd.
tttt CR125 Alumina, Baikowski International Corp.

ttttt Fisher Scientific Co.








discarded. Finally, the samples were slowly (approximately 5C/minute)
heated to 6500C for 6 hours in order to burn the polymer out.
The polished sections were then cleaned in the ultrasonic cleaner
with a dilute soap solution and mounted on aluminum SEM specimen
holders. All samples were coated with a thin gold-palladium coating
prior to observation in the SEM. A minimum of 20 micrographs (scanned
over the entire cross-section) were taken for each sample at magnifications
in the range 10000 to 20000. Negatives of each micrograph was used to

obtain enlarged (8.5 in. x 11in.) prints for better accuracy during
microstructural characterization.


Quantitative Microscopy
Standard techniques of quantitative microscopy were used to
obtain quantitative values of microstructural features. The following
microstructural features were measured : (1) volume fraction of porosity
(2) average pore intercept size and distribution (3) specific pore-solid
interfacial area and (4) Number of pores per unit area.


Porosity (Relative Density)
A transparent plastic sheet with a 10 x 10 square grid (100
intersecting points) was overlaid on the enlarged prints. Points
intersecting the pore regions were counted. A minimum of 100 different

fields were measured. The average point fraction equals the porosity (P) of

the sample. The % relative density was obtained from the relation :

% relative density = (1 P) X 100 (3.4)
The relative density values for all the samples obtained by this method
were compared with those obtained by the Archimedes method.








Whenever the values differed by more than 2%, the samples were
rejected. The polishing procedure was repeated and a new set of
micrographs were taken.


Pore Intercept Size
A transparent plastic sheet with equally spaced parallel lines was
overlaid on the enlarged prints. The length of every pore intercept was
measured using a digitizing tablet interfaced with a personal computer*.
Average pore intercept size, and pore size distribution histograms were
obtained from the digitized measurements. A minimum of 750 intercept
sizes were measured. Due to microstructural inhomogeneities in the dry
pressed samples, a minimum of 1000 pore intercepts were digitized.


Pore-Solid Interfacial Area

The transparent plastic sheet with equally spaced parallel lines was
once again overlaid on the enlarged prints. The number of intersections

made between the lines and the pore-solid interface were recorded. A
minimum of 1500 intersections were recorded for each sample. Average
value of the intersections (NL) was obtained by dividing the number of

intersections with the total length of the test line (a correction for
magnification was done in determining the total length of the test line).
The specific pore-solid interfacial area (SV) was calculated using the

relationship :

SV = 2NL (3.5)




* Model H-P 86, Hewlett-Packard.








Number of Pores Per Unit Area

The total number of pores on enlarged prints were counted for
each sample. Number of pores per unit area (NA) were determined by

dividing the total pore count by the total test area (after correcting for
magnification).


Sample Preparation for Beam-Bending
For measuring viscosity by the beam-bending method, beams of
square cross-section were prepared from the following powders : (1) a

narrow size distribution powder with average particle size = 0.15 gpm (fine)
(2) NSD (3) broad-CSA and (4) BSD.
Initially, a well-dispersed suspension (35 vol% solids) in deionized
water at pH = 8.0 was prepared from NSD powder. Ultrasonication was
done for 3-4 hours to break down the agglomerates and the suspension
was aged for 24 hours. After aging, the suspension was again sonicated for
2 hours and the pH adjusted to = 8.0. The suspension (3.1 ml per sample)

was consolidated by slip casting (slip casting procedure has been described
earlier in this chapter) into five rectangular (5.1 cm length x 0.6 cm width)

teflon molds. A 0.22 gpm nylon filter paper was placed between the teflon
molds and the plaster. Complete water removal was achieved in less than
30 minutes. The compacts were allowed to dry in air for 6-8 hours before
they were released from the molds. All five samples were extremely
fragile and large cracks were evident over the sample surfaces. The entire

procedure was repeated with no apparent success. The samples remained
fragile and the cracks persisted. It was concluded that (1) the use of a
binder was necessary to increase the green strength of the compacts and (2)








it was necessary to optimize the drying rate to preclude crack formation
during drying.
Suspensions were prepared by adding poly (vinyl alcohol), PVA*,
(average M.W. 11,000) as a binder by the following procedure.

Approximately 60 grams of NSD powder was calcined at 7000C for 6 hours
in a high purity alumina crucible. Also, a polymer solution was prepared
by dissolving 6 grams of PVA in 100 ml of deionized water. In order to
facilitate dissolution, the solution was continuously stirred and heated at =
800C on a hot plate**. A suspension was prepared by mixing 10 grams of

powder, 2.8 ml of deionized water and 3.3 ml of polymer solution. The
powder was added to the polymer solution- deionized water mixture in
small quantities (i.e., a small quantity of powder was added to the polymer
solution-deionized water mixture, pH was adjusted to = 8.0, sonicated for
15 minutes, again a small quantity of powder was added followed by pH
adjustment and 15 minutes of sonication. This procedure was repeated 4
to 5 times until all the powder was added). Finally, the suspension was
sonicated for 2 hours and aged for 24 hours. The final solids loading of the
suspension was 35 vol% and the polymer concentration in the suspension
was 1% by weight of silica. After aging, the suspension was again
sonicated for 2 hours and pH adjusted to = 8.0.
The suspension (3.1 ml per sample) was then consolidated into
three teflon molds by slip casting. Moist paper towels were placed next to
the plaster to increase the relative humidity around the sample, thereby
decreasing the drying rate. The slip casting setup was covered with a


* Vinol 203, Air Products and Chemicals, Inc., Allentown, PA.

*Fisher Scientific Co.








plastic dome to minimize the effects due to variation in room
temperature. A small opening was created to allow the passage of air.
After 24 hours, the samples were released from the molds. All three

samples had very good green strength (they could be handled very easily)

and there was no evidence of crack formation.

The samples were pre-sintered (binder removal was also
accomplished at the same time) at 6750C for 6 hours in static air in a tube
furnace*. The samples were placed on a high purity alumina brick and

loaded into the furnace. The pre-sintering schedule was identical to the

one used earlier for all samples (figure 3.1). After pre-sintering, the
samples were visually examined for crack formation.

One of these samples was then sintered at 11500C in static air for 24
hours in the resistance furnace. A heating rate of 1C/minute was used.
During sintering, the sample broke into several pieces. It was also

observed that the broken pieces were not transparent (small disk shaped
samples prepared with the same powder without the addition of PVA and

sintered under similar conditions were transparent). One explanation for
this observation is the transformation of silica from amorphous phase to
crystalline phase. To verify this speculation, X-ray diffraction (XRD)
patterns were obtained with a diffractometer** using Ni-filtered CuKa
radiation and a scanning rate of 50C/minute. XRD measurements

confirmed the presence of cristobalite in the sample.

The remaining two samples were sintered at 11500C for 24 hours
at different heating schedules (0.50C/minute and 1lC/minute with a 2


*Model 59344-C10, Lindberg, Watertown, WI.
** Model APD 3520, Philips Electronic Instrument Corp., Mt. Vernon, NY.








hour hold at 6000C). The samples did not sinter to full density and
remained opaque. XRD measurements confirmed the transformation to
cristobalite.

Samples were prepared using another type of PVA* with a higher
(average M.W. 80,000) molecular weight. Suspension preparation, pre-
sintering and sintering were done under conditions identical to those
described above. The results showed no improvement over those obtained
previously with PVA addition.

It was then decided to use Daxad (CP2)** polyelectrolyte as a
binder. The advantage in using CP2 as a binder is that in addition to
increasing the strength of green compacts, it also stabilizes the suspensions
(when used in optimum concentrations). Hence, suspension pH
adjustments are not necessary. The suspension pH after the addition of
CP2 was = 3.6. A relatively simpler and cleaner burn out is also possible
due to its very low molecular weight (= 700).

Suspensions were prepared by the following procedure. All
powders were calcined at 7000C for 6 hours. A solution was prepared by
mixing 10 grams of CP2 in 100 grams of water(i.e., 0.1 gram CP2 per gram
of water). For narrow size distribution powders (i.e., NSD and fine),
suspensions were prepared at a solids loading of 35 vol% in deionized
water. For broad-CSA and BSD powders, suspensions were prepared at a
solids loading of 45 vol%.

Suspension from NSD powder (average particle size 0.65 gim) was
prepared by adding 12 grams of powder to a mixture of 10 ml deionized


* Vinol 523, Air Products and Chemicals, Inc.
*W. R. Grace and Co., Lexington, MA.








powder and 0.6 gram CP2 solution. The powder was added in small
quantities as described previously in this chapter. The concentration of
CP2 in this suspension was 1 mg/m2 of the surface area of the powder (the
surface area of NSD powder was 5 m2/gram. Since 12 grams of powder

was used, the total surface area of the powder was 60 m2. Hence 60 mg of
CP2 was added by adding 0.6 gram of CP2 solution). The suspension was
sonicated for 2 hours and aged for 24 hours. After 24 hours, the suspension
(3.1 ml per compact) was consolidated by slip casting in rectangular (5.1 cm
length x 0.6 cm width) teflon molds. The slip casting setup was identical to
the one used for samples with PVA described in this section. After
complete water removal and drying for 24 hours, the samples were
released from the molds. The dimensions of the green compacts were 5.1
cm length x 0.6 cm width x 0.6 cm thickness.
The samples were pre-sintered at 7000C for 6 hours in static air
atmosphere in the tube furnace. The samples were placed on a high purity
alumina brick and loaded into the furnace. The pre-sintering schedule is
shown schematically in figure 3.2.

The samples were then heated at 50C/minute and sintered in
static air at 11500C for 24 hours in the resistance furnace. A cooling rate of
3C/ minute was employed. During the sintering treatment, the samples
were placed on a bed of loosely packed calcined silica powder spread on the
furnace stage. The samples were then totally covered with the same silica
powder. This arrangement was utilized to maintain uniformity of
temperature over the length of the sample. The samples sintered to full
density, were transparent and there was no evidence of any crack

formation. The following dimensions were obtained for the sintered
samples: 4 cm length x 0.5 cm width x 0.4 cm thickness. Sample width and






















700



C.



S 300


















Figure 3.2


4


Time (Hours)


Pre-sintering schedule used for samples with CP2 as a
binder.








thickness were both reduced to 0.3 cm by polishing with 0.6 p.m diamond
paste on a polishing wheel.
Samples with fine size (average particle size 0.15 gm) powder were
prepared using the same procedure described above. The amount of CP2
solution to be added was calculated based on the surface area (= 18 m2/g)
of this powder measured by the multipoint B.E.T. method.
Samples with broad-CSA and BSD powders were also prepared by
the same method. Suspension solids loading was increased to 45 vol%
and hence 2.5 ml suspension per sample was used for consolidation.


Viscosity Measurements by Beam Bending
The measurement of viscosity by the beam bending technique was
done by the method of Hagy [Hag63] using a high temperature furnace*
attached to a materials testing system**. The feasibility of this assembly for
viscosity measurements, was demonstrated by carrying out experiments
with beams of standard glass. Viscosity measurements were then done
at 11000C and 11500C for beams prepared from fine size and NSD powders
and at 11500C for beams prepared from broad-CSA and BSD powders.
The sample (beam of square cross-section) was placed on the
supports of a specially designed silicon carbide three-point bend fixturett
with a span of 3.5 cm. The furnace was heated at a rate of 200C/minute to
the test temperature. A type B thermocouple (placed at a distance = 1mm


* Model 1600, CM Furnaces, Inc., Bloomfield, NJ.

*Model MTS 810, MTS Systems Corp., Minneapolis, MN.
t ASTM Standard Glass #712, ASTM, Philadelphia, PA.
tt Bomas Machine Specialities, Inc., Somerville, MA.








from the sample) was used to read the temperature. After the test

temperature was reached, the furnace was allowed to equilibrate for 10
minutes. A constant load (0.5 lb to 3 lbs) was then applied on the beam
and a plot of the mid-point deflection of the beam as a function of time
was obtained. During the test, the temperature was controlled with a
precision of + 1C and the deflection was measured with an accuracy of 1
gtm. Total deflections up to 2 mm were measured. A minimum of two

measurements were done on each sample. Viscosity was calculated using
the formula :


3 pAL
gL (M -)
T = 6(3.6)
2.4 IV

where in is the viscosity (poise), g is the acceleration due to gravity
(cm/sec2), L is the support span (cm), M is the centrally applied load

(grams), p is the density of the glass (g/cc), A is the cross-section area of the

beam (cm2), I is the cross-section moment of inertia (cm4) and V is the

midpoint deflection rate of the beam (cm/minute).














CHAPTER 4
RESULTS AND DISCUSSION


Effect of Particle Packing
Characterization of Powders

In order to unambiguously determine the effects of particle packing
on sintering behavior and microstructural evolution, silica powder with a

narrow particle size distribution was used. As described previously, the
silica powder was prepared using the Stober method [Sto68]. In this
process, ammonia acts as a catalyst for hydrolysis reaction and also as a
morphological modifier by making the particles spherical. The final
particle size depends on the initial water and ammonia concentrations,
the type of alkoxide (ethyl, methyl, etc.) and alcohol (ethyl, methyl, etc.)

used as well as on the reaction temperature [Sto68].

Figure 4.1 shows a micrograph of the silica powder used in this
study. It is clearly seen that the particles are spherical and nearly
monosized. The particle size distribution histogram determined from
SEM micrographs (size distribution based on number) is shown in figure
4.2. The median particle diameter was 0.62 gim and the geometric standard

deviation was only 1.07. The low value of geometric standard deviation

indicates that the particle size distribution was extremely narrow (for

comparison, the geometric standard deviation for perfectly monosized
spheres is 1).




64


SEM micrograph of silica particles.


Figure 4.1




















U


W 20-

S Median Diameter a 0.61 pm

10-





0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
PARTICLE DIAMETER (pm)


Histogram plot of the particle size distribution (number based) determined by SEM.


Figure 4,2









Figure 4.3 shows the particle size distribution (mass-based) obtained
by x-ray sedimentation. The median particle diameter (since the particles
are spherical, the Stoke's diameter obtained in x-ray sedimentation
represents the actual particle diameter) was 0.65 gpm and the geometric
standard deviation was 1.25. The x-ray sedimentation result (figure 4.3)
shows presence of larger particles than those observed in the SEM (i.e., >
0.75 grm). This can be attributed to the formation of doublets (temporary

or permanent) in the suspension. As shown in figure 4.4 the particle size
distribution had a very good fit to the log-normal distribution function
over the entire range.
The powder specific surface area was = 5 m2/g. This was in close
agreement with surface area value (= 4.7 m2/g) calculated from the
average particle diameter and the powder true density (2.08 g/cc). No
significant changes in specific surface area with increasing calcination
temperatures were observed by Sacks and Tseng [Sac84a] and Khadilkar
[Kha88], indicating absence of micropore formation during calcination.

The variation of powder true density as a function of calcination
temperature is listed in table 4.1 and illustrated in figure 4.5. Each data
point in figure 4.5 is an average value of a minimum of five
measurements. Density measurements were made on powders which
were calcined for 6 hours at temperatures indicated in a loose-stack
uncompactedd) arrangement. The powders retained the character of a

loose stack (as opposed to becoming a sintered mass), up to the highest
calcination temperature (11500C). This indicated that sintering had not

progressed beyond the initial stage and thus, it is unlikely that closed pores

developed during calcination. Therefore, gas pycnometry results in figure
4.5 represent true densities (as opposed to apparent densities).









100


z 8
60






40-
:.









o 20
01 1


0 I I IlI I _______I I I I I .1.. .
10 1.0 0.1
EQUIVALENT SPHERICAL DIAMETER (pm)
Figure 4.3 Particle size distribution (mass-based) obtained by gravitational X-ray sedimentation.











Median Size = 0.65 pm
Geometric Standard Deviation = 1.2 Am


I I I I I


10 30 50 70


99 99.9 99.99


CUMULATIVE MASS PERCENT
Particle size distribution plotted on a log probability scale:


5.0
4.0

3.0


2.0




1.0
0.9
0.8
0.7
0.6
0.5
0.4

0.3


0.2


0.1 L
0.c


Figure 4.4


II t 1 1


1













Table 4.1 Powder true density values determined by helium
gas pycnometry at various temperatures.


TEMPERATURE
(C)


200

675

750


800

950

1150


TRUE DENSITY
(g/cc)


2.081 0.001

2.170 0.005


2.197 + 0.024

2.204 0.003

2.224 0.016

2.235 0.009


































1 I


200


, 1


400


600


SI I


800


1000


1200


TEMPERATURE (oC)
Helium gas pycnometry density versus calcining temperature for silica powders.


2.5




2.4




S2.3



z
m 2.2
QI


2.1




2


Figure 4.5


I I I I I I


1 I









Calcination results in = 12% total weight loss which is primarily
associated with the removal of hydration water and hydroxyl groups
[Sac84a]. Dehydroxylation is accompanied by small increments in true
density with increasing calcination temperature (figure 4.5).
However, density values for powders calcined at T>8000C are
slightly higher (2.235 g/cc at 11500C) than the value (2.20 g/cc) usually

reported for fused silica [Ile79]. A similar observation was also made by
Sacks and Tseng [Sac84a]. They proposed that structural rearrangements
leading to a more ordered (on a scale small enough to be undetectable by
ordinary x-ray procedures), dense packing of SiO4 tetrahedra occur prior to

devitrification. These would explain the observed increase in density
beyond 2.20 g/cc. Transmission electron microscopy on powders calcined
at high temperatures could possibly confirm this interpretation.


Characterization of Green Compacts
In order to determine the optimum suspension solids loading for
casting, green compacts were prepared by consolidating (by gravity
sedimentation) well-dispersed suspensions at different solid loadings, viz.,
3, 10, 30 and 40 vol%. Figure 4.6 shows pore size distribution plots (i.e.,
specific volume frequency versus pore radius) obtained by mercury
porosimetry for these samples. It can be seen that the pore size
distributions are almost indistinguishable for 3, 10 and 30 vol% samples,
whereas considerably higher porosity was obtained for the 40 vol%
sample. This is consistent with Khadilkar's [Kha88] results on the
variation of suspension viscosity with solids loading. For well-dispersed

suspensions prepared from monosized silica powders, he observed
relatively small amounts of increase in viscosity with increasing solids









.02


.015


.01


.005


10 100


1000


PORE RADIUS (nm)


Plots of specific volume frequency versus pore radius obtained by mercury
porosimetry for samples prepared by sedimenting well-dispersed suspensions at solid
loadings of 3, 10, 30 and 40 vol%.


Figure 4.6








concentration up to = 25 vol% solids loading. This indicated that the
particles remained well-dispersed in the suspension. The viscosities
increased rapidly with further increases in the solids concentration.
Hence a solids loading of 20 vol% was chosen as the optimum for all the
samples used in the particle packing study.
Green compacts with five different packing characteristics were
prepared by varying suspension properties (i.e., well-dispersed and
flocculated) and consolidation methods (i.e., slip casting, sedimentation
and dry pressing).
The pore size distribution plots of samples prepared by gravity
sedimentation of well-dispersed and flocculated suspensions are shown in
figure 4.7. The sample prepared from well-dispersed suspension had a
higher green density (= 64% relative density) and finer average pore
channel size (= 90 nm) compared with the sample prepared from
flocculated suspension (= 55% relative density and = 125 nm average pore
channel radius). These microstructural characteristics can also be seen
from the SEM micrographs (figures 4.8A and 4.8B) of the top surfaces of
both compacts. The green compact prepared from well-dispersed
suspension showed a highly ordered structure with high packing density.
The green compact prepared from flocculated suspension showed fairly
uniform microstructure (i.e., no long range inhomogeneities were
observed) with formation of flocs composed of several particles. The size
as well as volume fraction of intrafloc pores was small (figure 4.7). The
relatively larger interfloc pores seen from the micrograph contributed to

the majority of the pore volume and were observed as a single peak in the
pore size distribution plot.









.02


0 50


Figure 4.7


100
PORE RADIUS (nm)


150


200


Plots of specific volume frequency versus pore radius obtained by mercury
porosimetry for samples prepared by sedimenting well-dispersed and flocculated
suspensions.





75


Figure 4.8


SEM micrographs of the top surfaces of green compacts
prepared by sedimenting (A) well-dispersed suspension and
(B) flocculated suspension.









The samples prepared by slip casting well-dispersed suspension also

showed high packing densities and fine pore channel radii. Figure 4.9

shows plots of specific volume frequency versus pore channel radius for
samples prepared by slip casting and sedimentation. Both samples had
similar green densities (= 62% relative density for slip cast and = 64%
relative density for sedimentation) and average pore channel radii (= 90
nm for both). However, the particle packing arrangements were distinctly

different. This can be seen by comparing the SEM micrographs, of the top
surfaces of these two compacts (figure 4.8A and 4.10). In case of the sample

prepared by sedimentation, the packing was highly ordered. This is

because in gravity sedimentation, particles settle over a long period
(usually one week) and hence there is sufficient time for particles to
arrange themselves in a close-packed order. In case of the sample

prepared by slip casting, the packing arrangement was also ordered, but the
domains of ordered regions were relatively smaller in size compared with
the sedimented sample.

Figure 4.11 shows pore size distribution plots for flocculated (pH

3.6) and PEO samples. Due to increased flocculation caused by the addition
of PEO, the PEO samples had slightly lower green densities ( 52.8% relative

density) and larger average pore channel radii (130 nm) compared with
the flocculated samples (54.5% relative density and 125 nm average pore
channel radius).

Figure 4.12 shows pore size distribution plots for PEO and dry

pressed samples. It should be pointed out that both these samples had

very similar green densities (= 53%) but different median pore radii (120
nm for dry pressed versus 130 nm for PEO) and highly dissimilar pore
characteristics. Due to the presence of agglomerates in the dry pressed


































50 100
PORE RADIUS (nm)


150


200


Plots of specific volume frequency versus pore radius obtained by mercury
porosimetry for samples prepared by sedimenting and slip casting well-dispersed
suspensions.


.02


.01










0


0

Figure 4.9




78


Figure 4.10 SEM micrograph of the top surface of green compact
prepared by slip casting a well-dispersed suspension.

































0


Figure 4.11


50 100 150 200
PORE RADIUS (nm)
Plots of specific volume frequency versus pore radius obtained by mercury
porosimetry for pH = 3.6 sedimentation and PEO samples.


.02


.01










0










.02


z









0

U
tz
.3








01





P-4
U
W


0


Figure 4.12


100 200 300
PORE RADIUS (nm)
Plots of specific volume frequency versus pore radius obtained by mercury
porosimetry for samples prepared by dry pressing and frbm a suspension flocculated
with PEO.









sample, it had a bimodal pore size distribution. The bimodality was due to
two types of pores, viz., smaller intra-agglomerate pores and larger inter-
agglomerate pores. It should be noted that the scale of the intra-
agglomerate porosity was similar to that obtained in samples prepared
from well-dispersed suspensions. This could be explained on the basis
that the powder used for dry pressing was prepared by grinding powder
cakes obtained from the filtration of well-dispersed suspensions. Due to
incomplete grinding of the powder cakes, granules with dense particle
packing remained in the powder, resulting in finer intra-agglomerate
pores. Also, the peak corresponding to intra-agglomerate porosity in the
dry pressed sample was for the same pore size (90 nm) as the peaks
observed in the pore size distribution plots of the samples prepared from
well-dispersed suspensions. The PEO samples had a unimodal but broad
pore size distribution. The pore size distribution was similar to that
obtained in the sample prepared from flocculated suspension, except that
the peak was shifted to a larger size due to increased flocculation caused by

the addition of PEO.
Figure 4.13 shows the SEM micrograph of the dry pressed sample
sintered at 11500C for 30 minutes to a relative density of = 59%. It can be
seen that the dry pressed sample had an extremely inhomogeneous green
microstructure. Large inter-agglomerate pores are clearly evident.


Pre-Sintering

The samples were pre-sintered for two reasons. First, a majority of
'water' could be removed by heat-treating the samples at temperatures

above 600C [Sac84b]. This would facilitate a constant viscosity at the
sintering temperature. The changing viscosity at the sintering





82


Figure 4.13 SEM micrograph of a dry pressed sample.








temperature also would complicate data analysis. Secondly, removal of
'water' would also aid in delaying crystallization which is detrimental to

sintering [Wag64, Wag66]. Thirdly, since the compacts were too fragile to
withstand thermal shocks, pre-sintering the samples for subsequent
isothermal sintering was imperative. Pre-sintering would impart strength
to the compacts by initiating neck formation between particles.
Two factors played a very important role in determining the pre-
sintering temperature and the heating rate. Firstly, to minimize
densification, the use of a lower pre-sintering temperature was necessary.
Secondly, due to significant amounts of water loss associated with heating,
it was essential to employ a slower heating rate to avoid formation of
cracks in the samples. In the light of these two criteria, experiments were
designed to determine the optimum pre-sintering schedule.
Samples prepared by sedimentation of well-dispersed suspension
(pH = 8) were chosen for trial experiments. Since these samples had
homogeneous green microstructures and fine average pore sizes, they
were the most suitable in determining the minimum temperature
required for densification. Thus, 6750C was selected as the pre-sintering

temperature. Figure 4.14 shows plots of pore radius versus specific
volume frequency for the green compact and the sample pre-sintered at
6750C for 6 hours. It can be seen from the plots that within experimental
error, the two pore size distributions are similar. All compacts were pre-
sintered under identical conditions to maintain consistency.


Sintering Kinetics

Table 4.2 shows relative density values for samples sintered under
isothermal conditions at 1100 and 11500C for 30 minutes and 24 hours.










.02


.01


100
PORE RADIUS (nm)


Figure 4.14


Plots of specific volume frequency versus pore radius obtained by mercury
porosimetry for a green compact and a sample pre-sintered at 6750C for 6 hours.


150


200












Table 4.2 Relative density values for samples sintered at 1100 and
11500C.


Sintering Condition


pH = 8, Sedimentation pH = 3.6, Sedimentation


11000C, 30 Min. 69% 59.2

11000C, 24 Hours 88.5% 64.6

11500C, 30 Min. 71.2% 61.1

11500C, 24 Hours 98.9% 94.1









Since, the samples prepared by sedimentation of well-dispersed
suspension reached only = 88% relative density after sintering at 11000C
for 24 hours, 11500C was chosen as the sintering temperature.

Plots of relative density versus sintering time at 11500C for samples
prepared from sedimentation of well-dispersed and flocculated

suspensions are shown in figure 4.15. For short sintering times, the well-
dispersed samples densified much faster compared with the flocculated
samples. For example, after 1 hour of sintering, the relative density for
the well-dispersed sample increased by 11.8% (i.e., from 63.5% to 75.3%
relative density), whereas the relative density for the flocculated sample
increased by only 7.5% (i.e., from 54.7% to 62.2%). Well-dispersed samples
retained higher densities over the entire range of densification. The
enhancement in densification for the well-dispersed samples was due to
higher particle packing densities and smaller pore channels observed in
the green bodies. Uniform green microstructures and small pore sizes
also resulted in uniform shrinkage at each particle-particle contact and
differential microdensification (which produce regions with large pores
and lower shrinkage rates) was minimized.

Plots of densification rate versus sintering time and densification
rate versus relative density for these samples are shown in figures 4.16
and 4.17 respectively. It can be seen from figure 4.16 that at short sintering
times, the well-dispersed sample shows a higher densification rate. This is
consistent with the higher particle packing density and smaller average
pore channel size observed in the green compact. However, at longer
sintering times, the densification rate for the well-dispersed sample is

lower than the flocculated sample. This is because densification rates fall
off rapidly with increasing densities ( a sample with high density contains











100



90


SINTERING TIME


Figure 4.15


Plots of relative density versus sintering time at 11500C for samples prepared by
sedimenting well-dispersed and flocculated suspensions.


(HOURS)




































0 5 10 15


Figure 4.16


SINTERING TIME (HOURS)
00
Plots of densification rate versus sintering time for samples prepared by sedimenting oo
well-dispersed and flocculated suspensions.



































70 80


Figure 4.17


RELATIVE DENSITY (%)
00
Plots of densification rate versus relative density for samples prepared by sedimenting O
well-dispersed and flocculated suspensions.


100









relatively small number of pores. Hence, the distances between pores are
large. Due to slower kinetics of long range diffusion, the densification
rate rapidly decreases.). Since the well-dispersed sample had high

densities at longer sintering times, the densification rate was lower. It can

be seen from figure 4.17 that the densification rate for the well-dispersed

sample is higher than the flocculated sample over the entire densification
range (when compared at constant sintered densities).
Figure 4.18 shows plots of relative density versus sintering time at

11500C for samples prepared by sedimentation and slip casting a well-

dispersed suspension. The sintering behavior for these two sample series

was essentially similar with the exception that the sedimentation samples

showed a slight enhancement in densification at short sintering times.
For example, after sintering for 2 hours, the relative density of the

sedimented sample increased by 11.8% (from 63.5% to 75.3%) whereas the

relative density for the slip cast sample increased by 11.1% (from 62% to
73.1%). Both these samples showed homogeneous green microstructures

with small average pore sizes. Hence, it is not surprising to observe

similar trends in their densification behavior. Plots of densification rate

versus sintering time and densification rate versus relative density

(figures 4.19 and 4.20 respectively) also show similar behavior. The

enhancement in densification of the sedimented sample in the very early

stage can be attributed to the highly ordered packing with less packing

defects.

Plots of relative density versus sintering time at 11500C for
flocculated and PEO samples are shown in figure 4.21. It can be seen that

the sintering behavior of these samples is also essentially similar. This

could be attributed to the fact that there were no significant differences in










100


5 10 15 20


SINTERING TIME (HOURS)


Figure 4.18


Plots of relative density versus sintering time at 11500C for sedimentation and slip
cast samples.

































5 10 15


SINTERING TIME


(HOURS)


Figure 4.19


Plots of densification rate versus sintering time for sedimentation and slip cast
samples.

































70 80 90


RELATIVE DENSITY (%)


Figure 4.20


Plots of densification rate versus relative density for sedimentation and slip cast
samples.


100









100


40 60


Figure 4.21


SINTERING TIME (HOURS)
Plots of relative density versus sintering time at 11500C for pH = 3.6 sedimentation
and PEO samples.




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