Title Page
 Table of Contents
 List of Tables
 List of Figures
 Theoretical aspects involved in...
 Solid state reactions and mass...
 Objective and accomplishments
 Experimental procedures
 Summary and conclusions
 Future work
 Biographical sketch

Title: Effect of microwave heating on the solid state reactions and mass transport in ceramics
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Permanent Link: http://ufdc.ufl.edu/UF00090181/00001
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Title: Effect of microwave heating on the solid state reactions and mass transport in ceramics
Series Title: Effect of microwave heating on the solid state reactions and mass transport in ceramics
Physical Description: Book
Creator: Ahmad, Iftikhar,
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Bibliographic ID: UF00090181
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Table of Contents
    Title Page
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    Table of Contents
        Page iv
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    List of Tables
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    List of Figures
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    Theoretical aspects involved in microwave heating
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    Solid state reactions and mass transport
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    Objective and accomplishments
        Page 72
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    Experimental procedures
        Page 74
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    Summary and conclusions
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    Future work
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    Biographical sketch
        Page 192
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        Page 194
Full Text








The author wishes to express his sincere gratitude to Dr. David E. Clark,

chairman of his supervisory committee, for his guidance, understanding and

supervision throughout all the phases of his graduate work. Appreciation is also

expressed to Drs. J.H. Simmons, R.T. DeHoff, E.D. Whitney and R.J. Hanrahan for

their suggestions, time and academic advice as members of the supervisory

committee. Special thanks go to Dr. A. Loddings of the Chalmers University of

Technology in Sweden for the SIMS analysis, providing me with the conclusive data

for this study.

The author is very grateful to Amy Hoelzer, Wayne Acree, Eric Lambers and

Richard Crockett of the Major Analytic Instrumentation Center (MAIC), Department

of Materials Science and Engineering, University of Florida, for the cheerful

assistance and characterization of numerous samples.

Special recognition is extended to the faculty, staff and fellow students for

their cooperation, assistance and contribution to my professional achievements. No

less was the goodwill and friendship of Alex, Ali, Arindam, Becky, Bob, Bruce, Craig,

Diane, Edmund, Greg, Jipin, Kim, Lorie, Salwan, Soo Man and Zak, for making a

delightful and memorable time as a graduate student.

The author acknowledges, with gratefulness, the financial support from United

States Agency for International Development (USAID) and the Defense Advanced

Research Project Agency (DARPA), without which the graduate studies and research

would not have been possible.

Last but not the least, the author wishes to express his deepest and most

sincere gratitude to his entire family, especially his father for inspiring the craving for

knowledge and wisdom; his mother for her persistent prayers for this

accomplishment; his wife for her patience, understanding and encouragement; and

his curious school-going son (why does daddy have to go to school at night?), for

their continuous support during this academic endeavor.


ACKNOWLEDGEMENTS ..................................... iv

LIST OF TABLES ............................................ ix

LIST OF FIGURES ............................. ........ ....... x

ABSTRACT ...................................... ......... xvii


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

Ceramic Processing ................................ ....... 2
M microwave Processing ..................................... 5

2 BACKGROUND ............................... ............ 7

M icrowaves ............................... .... ......... 7
Characteristics of Microwaves .......................... 7
Microwave Power Generation ......................... 11
M microwave Heating ...................................... 11
H history .......................................... 11
Industrial Microwave Heating Applications. .............. 13
Microwave Processing of Ceramics ........................... 16
Applications ...................................... 20
Radiation Safety and Hazards of Microwave Heating ............ 26


Dielectrics and Mechanisms of Losses ........................ 31
The Molecular Origins of Permittivity ................... 31
Polarization ............................. ....... . 32
The Complex Form of Dielectric Constant ............. 37
Dipolar or Orientation Loss Mechanism ................ 38
Interfacial or Maxwell-Wagner Loss Mechanism .......... 49

Combined Effects.................................. 52
Magnetic Loss Factor .................................. 52
Microwave Power Dissipated .............................. 54
Penetration Depth ..................................... 55
Rate of Rise of Temperature............................... 56


Solid State Reactions.......................... ........ 58
The ZnO-Al203 System ............................. 59
Kinetic M odels ........................ .......... 61
Diffusion-controlled Reactions .................. ...... 62
Phase-boundary Controlled Reactions. ................. 65
Reactions Controlled by Nuclei Growth. ................ 65
M ass Transport............................ ........ ... 65
Diffusion and Fick's laws........................... 66
The Nernst-Einstein Equation ....................... 67
Random-walk Diffusional Processes. ................... 67
Diffusion as a Thermally Activated Process .............. 68
Ionic Conductivity and Diffusion ...................... 68

5 OBJECTIVE AND ACCOMPLISHMENTS ...................... 72

6 EXPERIMENTAL PROCEDURES............................ 74

M materials ............................................ 74
Sample Preparation ....................... ......... 75
Experimental Set Up ...... .. .................. ....... 76
Characterization ...................................... 78
Quantitative X-ray Analysis........................... 78
Differential Thermal Analysis (DTA). ................... 79
Contact Angle .................................... 80
FT-IR/ATR ...................................... 82
Scanning Electron Microscopy and X-ray Mapping ........ 83
Secondary Ion Mass Spectrometry. ................... 84

7 RESULTS ............................................... 86

Microwave Hybrid Heating ............................... 86
Quantitative X-ray Analysis ............................... 88
Solid State Reaction Between Zinc Oxide and Aluminum Oxide ... 90
Microwave Heated Samples ......................... 93
Conventionally Heated Samples. ...................... 97
Comparison............................... 103
Effect of Particle Size on the Reaction Rate ............. 106
Effect of Compaction Pressure on Reaction Rate......... 126

Reaction and Diffusion of Zinc Oxide in Crystalline Alumina ..... 126
Polycrystalline Alumina. .................. .......... 129
Single Crystal Alumina ............................. 132

8 DISCUSSION............................................ 148

Solid State Reactions of Powders........................... 148
Enhanced Diffusion! .................................... 153
Physical M odel ................................... 154

9 SUMMARY AND CONCLUSIONS ............................ 167

10 FUTURE W ORK ......................................... 171

APPENDIX.............................................. 173

REFERENCE LIST .......................................... 183

BIOGRAPHICAL SKETCH ................................... 192


Table 7.1 Comparison of the synthesized and experimental
values ................................... 89

Table 7.2 Contact angle measurement on as-received single crystal
alumina, crystals conventionally and microwave heated
in zinc oxide, and on a sintered zinc oxide pellet . 133


Figure 2.1

Figure 2.2

Figure 3.1

Figure 3.2

Figure 3.3

Figure 3.4

Figure 3.5

Figure 3.6

Figure 3.7

Figure 3.8

The entire frequency spectrum ..................

Qualitative representation of the loss factor as a function
of the temperature ...........................

Schematic of polarization mechanisms in glass and
ceramics. .....................................

Frequency dependence of the polarization mechanisms
in dielectrics................... .......... ...

(a) Potential energy diagram for dipole rotating in a
crystal lattice with energy barrier AEb and equilibrium
positions of equal energy. (b) Potential energy diagram
for a complex system having unequal potential

Ideal Debye loss factor versus frequency response
(dotted lines) and multirelaxational response due to
hindered dipole redistribution (solid line) ..........

Qualitative representation of the Cole-Cole diagrams for
an ideal Debye relaxation (dotted line) and for a real
dielectric (solid line)..........................

Shift of the dielectric loss peak in lithium silicate glass
due to increasing temperature. ..................

Dielectric absorption at various temperatures for sodium
bromide with calcium impurity ..................

Influence of dc conductivity on the losses in interfacial
polarization dc conductivity increasing between I and
IV . . .. .. .. . . .. . .. .. . . . . . .

Figure 3.9

Figure 4.1

Figure 4.2

Figure 4.3

Figure 6.1

Figure 6.2

Figure 6.3

Figure 7.1

Figure 7.2

Figure 7.3

Figure 7.4

Figure 7.5

Effective loss factor of a heterogeneous dielectric
exhibiting dipolar and tail end conductivity losses .....

Phase diagram of the ZnO-Al203 system showing the
liquidus curve. ..............................

Propagation of the reaction in a spherical particle. ....

(a), (b), and (c) are schematic drawings showing the
sequence of configurations involved when an atom jumps
from one normal site to a neighboring one. (d) shows
how the free energy of the entire lattice would vary as
the diffusing atom is reversibly moved from
configuration (a) to (b) to (c)...................

The Raytheon Radarline Microwave Oven (2.45 GHz,
6.4 kW Max.) showing the installation of the
thermocouple and the optical pyrometer temperature
controllers. The sample is placed inside the susceptor.

Interface energies for a liquid on a solid surface .....

A typical optical illustration for attenuated total
reflectance (ATR) spectroscopy. .................

Heating profiles for microwave hybrid heating of
samples and thermocouple inside the insulation line with
susceptor .................................

Micrographs of reaction between zinc oxide and
aluminum oxide. The spinel forms on the alumina grain
leaving a gap between zinc oxide and spinel. Z, ZA, A
and R indicate ZnO, ZnAl204, A1203 and resin
impregnation into voids.......................

Graphical illustration of the validity of the Valensi
Reaction Rate model. ..........................

Microwave heating of the mixture of alumina AKP-50
and zinc oxide at different temperatures. The spinel
formation with increasing heating time is shown for each

Microwave heating of mixture of alumina and zinc oxide.
Attempt to fit the experimental data to Jander's model

Figure 7.6

Figure 7.7

Figure 7.8

Figure 7.9

Figure 7.10

Figure 7.11

Figure 7.12

Figure 7.13

Figure 7.14

Figure 7.15

Microwave heating of mixture of alumina and zinc oxide.
Attempt to fit the experimental data to Valensi-Carter

Microwave heating of reactants. Experimental data fit
to Jach's model of phase-boundary controlled reactions

Microwave heating of reactants. Experimental data fit
to the model for reactions controlled by nuclei growth
presented by Hulbert and Klawitter's ............

Conventional heating of the mixture of alumina AKP-50
and zinc oxide at different temperatures. The spinel
formation with increasing heating time is shown for each
temperature. .................................

Conventional heating of mixture of alumina and zinc
oxide. Attempt to fit the experimental data to Jander's
m odel. .............. ....................

Conventional heating of mixture of alumina and zinc
oxide. Attempt to fit the experimental data to Valensi-
Carter m odel ...............................

(a) Cubic array of particles of alumina and zinc oxide.
(b) Geometric arrangement showing formation of layers
of zinc aluminate spinel on alumina particles within an
aperture 20 ................................

Thirty minutes of microwave and conventional heating
of the mixture of alumina AKP-50 and zinc oxide,
showing the spinel formation versus temperature. For
most temperatures conventional heating forms more

Arrhenius type plot for natural log of reaction rate for
Valensi-Carter model versus 1/T for both the
microwave heating and conventional heating reactions.

Weight percent zinc aluminate spinel formed as a
function of the particle size of alumina with average
particle size of zinc oxide being 0.3 p. The average
particle sizes of alumina were 0.181, 0.41 and 0.68p.
The heating was at 1000'C for 30 minutes in both the
conventional and microwave case ................

Figure 7.16

Figure 7.17

Figure 7.18

Figure 7.19

Figure 7.20

Figure 7.21

Figure 7.22

Figure 7.23

Figure 7.24

Thirty minutes of microwave and conventional heating
of the mixture of alumina AKP-30 and zinc oxide,
showing the spinel formation versus temperature. At
almost all temperatures microwave heating forms
comparable product to that of conventional heating...

Thirty minutes of microwave and conventional heating
of the mixture of alumina AKP-15 and zinc oxide,
showing the spinel formation versus temperature. At all
temperatures microwave heating forms more spinel than
that formed by conventional heating. At 1000C in
microwave heating reaction reaches completion ......

Spinel formation as function of temperature for all three
particle sizes of alumina for 30 minutes of conventional

Spinel formation as function of temperature for all three
particle sizes of alumina for 30 minutes of microwave
heating ...................................

Weight percent zinc aluminate spinel formation as a
function of time for AKP-15 and AKP-50 in both
conventional and microwave heating at 8000C.......

Weight percent zinc aluminate spinel formation as a
function of time for AKP-15 and AKP-50 in both
conventional and microwave heating at 9000C .......

Weight percent zinc aluminate spinel formation as a
function of time for AKP-15 and AKP-50 in both
conventional and microwave heating at 10000C. AKP-15
shows higher product formation and reaches completion
of reaction whereas AKP-50 forms less spinel and does
not reach completion in the time and temperatures

Weight percent zinc aluminate spinel formation as
function of particle size of alumina at 900C and 1000C
for 30 minutes of conventional and microwave heating.

Differential thermal analysis at a heating rate of
100C/minute for the reaction between AKP-50 and zinc



Figure 7.25

Figure 7.26

Differential thermal analysis at a heating rate of
100C/minute for the reaction between AKP-15 and zinc
oxide ....................................

SEM micrographs of alumina AKP-50 and zinc oxide
heated for 45 minutes at 1100C, (a) microwave heated
(b) conventionally heated .......................

Figure 7.27

Weight percent spinel formation
compaction pressure for both
microwave heating at 10000C for 30

as a function of
conventional and
minutes ........ 127

Figure 7.28

Figure 7.29

Figure 7.30

Figure 7.31

Figure 7.32

Figure 7.33

Figure 7.34

Figure 7.35

Figure 7.36

Effect of the initial porosity on the microwave heating of
strontium titanate and alumina ..................

(a) SEM micrograph of polycrystalline alumina substrate
conventionally heated in zinc oxide for 1 hour at 1000C
(b) The x-ray map for zinc concentration indicating the
depth penetrated.............................

(a) SEM micrograph of polycrystalline alumina substrate
heated in zinc oxide for 1 hour at 1000C by microwave
energy (b) The x-ray map for zinc concentration
indicating the depth penetrated. .................

Spectrum of the as-received single crystal alumina. ....

Infrared spectrum of ZnAl204 ...................

IR spectrum of alumina single crystals heated at 1100C
for 3 hours in zinc oxide by conventional and microwave

Difference spectrum indicating excess of spinel and lack
of alumina in the crystal heated in zinc oxide by
microwave energy ............................

SEM micrographs of the single crystal alumina heated in
zinc oxide for 3 hours at 11000C (a) microwave heated
(b) conventionally heated....................

Backscattered electron image showing the contrast of the
reaction layer or the depth of penetration of zinc oxide
in the single crystal alumina (a) microwave heated
crystal (b) conventionally heated specimen .........






Figure 7.37

Figure 7.38

Figure 7.39

Figure 7.40

Figure 7.41

Figure 8.1

Figure 8.2

Figure 8.3

Figure 8.4

Figure 8.5

Figure 8.6

Figure 8.7

Figure 8.8

X-ray map for zinc concentration in the single crystal
alumina, (a) shows a much wider band in the microwave
heated sample as compared to the crystal shown in (b)
for conventional heating. ................... ...

Depth profile curves for aluminum and zinc isotopes in
the single crystal alumina (HEMLUX) heated at 11000C
in zinc oxide for 3 hours by conventional method .....

Depth profiles curves for aluminum and zinc isotopes in
single crystal alumina (HEMLUX) heated at 11000C in
zinc oxide for 3 hours by microwave energy.........

Depth profile curves for aluminum and zinc isotopes in
the single crystal alumina (HEMCOR) heated at 11000C
in zinc oxide for 3 hours by conventional method .....

Depth profiles of aluminum and zinc isotopes in single
crystal alumina (HEMCOR) heated at 1100C in zinc
oxide for 3 hours by microwave energy ............

The different particle sizes of aluminum oxide and zinc
oxide and one of the possible arrangements in contact
with each other shown in two dimensions .........

A number of isolated systems brought together in two
dimensions (a) AKP-50 and zinc oxide (b) AKP-15 and
zinc oxide. ..................................

An isolated dipole and its rotation in presence of an
electric field. ................................

The dipole attached to another neutral mass and their
movement in an electric field. .................

The dipole at different position in chains of neutral
masses........ ........ .....................

Microwave absorption at 20C for esters with polar
groups in different positions of molecular chain ......

Dielectric absorption in aliphatic methyl esters with
three different molecular chain lengths ............

Various ways of joining two tetrahedral carbon atoms.



A two dimensional representation of a number of masses
connected by springs...........................

Figure 8.9


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




August 1991

Chairman: Dr. David E. Clark
Major Department: Materials Science and Engineering

The use of microwave energy to process a wide range of ceramic materials

offers an alternative to the conventional heating of ceramics. With microwave

energy, heat generation is internal and volumetric, making it possible to rapidly and

uniformly heat even large ceramic bodies. Conventional heating is carried out by

placing the ceramics in furnaces with external heat sources. Heating of ceramics is

completely dependent on the thermal conductivity of the material. Unfortunately,

most ceramics are poor thermal conductors and can not be heated rapidly.

Microwave processing has so far been mainly focused on the sintering of

ceramics and composites. The reduction in processing time and temperature (higher

sintering rates) has resulted in a common speculation of higher diffusion rates with

microwave heating.


This research is concerned with the effect of microwave heating on solid state

reaction between zinc oxide and aluminum oxide. The reaction between zinc oxide

and aluminum oxide has been reported to be diffusion controlled and it proceeds

only on the alumina particle by one-way transfer of zinc oxide through the product

layer. If microwave heating results in enhanced diffusion, it should enhance the

reaction rates of zinc oxide and aluminum oxide.

It has been demonstrated in this work that microwave heating results in more

product formation with large particles of alumina reacting with zinc oxide. The

reaction of zinc oxide with polycrystalline and single crystal alumina also results in

larger thickness of product layer with microwave heating. However, with a small

particle size of alumina conventional heating resulted in more product formation at

lower temperatures, which needs further investigation.



The art of making pottery by forming and burning clay has been practiced

from the earliest civilizations. To most people ceramics mean the articles shaped

from moist clay and heated in kilns, which includes flower pots, cookware, bricks,

bathtubs, tiles and cement. Perhaps some others may realize that insulators on

power lines, false teeth and sandpaper are also made of ceramic materials.

But, in the recent decades people are becoming aware of the revolution that

is brewing quietly in materials engineering generally and in the field of advanced

ceramics specifically. The diversity of ceramic products now range from the

traditional ceramics comprising of clay products to refractories that can withstand

extreme temperature and further on to the high-temperature ceramic

superconductors. Superconductivity is a phenomenon earlier known to be exhibited

by metals only and that also at exceptionally low temperatures.

Although, presently the largest segments of the ceramic industry is the

manufacture of various glass and cement products, there is a growing demand for the

refractories as advanced structural materials. This family of materials exhibits a

combination of high strength at elevated temperatures, high hardness, good corrosion

and erosion resistance, low mass density and generally low coefficient of friction.

Major applications of advanced structural ceramics include cutting tools, wear

resistant insertions for automobile, ships, aircraft engine and propulsion components

and other aerospace applications. The resistance to corrosion and oxidation allows

use of some ceramics in heat exchangers, chemical and nuclear plants. Advanced

structural materials comprising of monolithic ceramics include, but are not limited

to, alumina, zirconia, silicon carbide and silicon nitride. Ceramic composites

comprising of ceramic matrices reinforced with particulates, whiskers, fibers or

platelets of different ceramics or metals, are also under investigation to achieve

enhanced mechanical properties.

Ceramic materials also contribute as passive components for a wide range of

electronic applications related to device packaging, sensors and magnetic uses such

as recording, memory storage and communication. The major categories of ceramics

for electronics use include piezoelectrics, capacitor dielectrics, thick film hybrid

components, ferrites, ceramic substrates as well as temperature, voltage, humidity and

gas sensors. Use of these materials as finished products, because of their integral

association with the dynamic growth in electronics, constitutes a major growth area

within the ceramics field. However, much of this expanding use for ceramics tends

to be masked by their application as components rather than as end use products


Ceramic Processing

In order to be able to use advanced ceramics with superior performance and

reliability, emphasis is placed on improvements in ceramic processing technology.

Ceramic processing has traditionally been discussed in terms of the material

formulations and industrial arts used in the manufacture of various products. This

empirical approach was understandably necessary, because the materials systems

were complex and not well characterized. But as the characterization of materials

has improved and the scientific principles underlying ceramic processing have been

elucidated, especially in the past twenty years, ceramic processing can now be

explained in the context of general principles and the engineering processes involved.

Ceramic processing is an increasingly important aspect of ceramic engineering;

therefore, innovative processing techniques and advances in the understanding of

principles will be essential for more advanced ceramic products.

Ceramic processing commonly begins with one or more ceramic materials, one

or more liquids and special additives called processing aids. The starting materials

may be beneficiated chemically and physically using operations such as crushing,

milling, washing, chemical dissolving, settling, flotation, magnetic separation,

dispersion, de-airing, filtration and spray-drying. The forming technique used

depends on the consistency of the system (i.e. slurry, plastic body or granular

material) and produces a particular unfired shape with a particular composition and

microstructure. Drying removes some or all of the residual processing liquids. In

certain case additional operations may include green machining, surface

grinding/smoothing and application of surface coatings [Ree88].

These green products are then heat treated, pretty much similar to the

practices used by a pot maker for centuries, in a kiln or furnace to develop the

desired microstructure and properties. This process, called firing (or sintering to

describe consolidation of product) may be considered to proceed in three stages:

(a) reaction preliminary to sintering which includes binder burnout and elimination

of gaseous products of decomposition and oxidation, (b) sintering and (c) cooling,

which may include thermal and chemical annealing.

According to an increasingly popular approach, the secret to improving a

ceramic material is to control its microstructure in an early stage of fabrication. This

prompts the notion -- physics has had its crack at ceramics -- now a chemical route

to advanced ceramics [Rob86]. The symposia titled "Better Ceramics Through

Chemistry" that are part of the Spring Meeting of the Materials Research Society

(published as MRS Symposia Proceedings) provide a partial look at this idea.

An extensive amount of effort and research work has resulted in

understanding the scientific principles involved in various aspects of ceramic

processing. These include surface chemistry, characterization and specification of

particulate materials, binders, deflocculants and coagulants, particle mechanics and

rheology, sol-gel processing and chemical vapor deposition.

After all this processing the carefully prepared green ceramic body has to be

fired to consolidate the particles within the body, so that it has good strength and can

be used as a finished product. Sintering is carried out in conventional furnaces,

generally a well insulated enclosed chamber equipped with a source of heat. The

ceramic body placed inside the furnace starts heating from the surface and the heat

is conducted into the ceramic depending on its thermal conductivity. Unfortunately,

most ceramics are poor thermal conductors and, especially in larger bodies, it can

take a while before the interior reaches the same temperature. The nonuniform

heating and the slow heating rates may not always produce the desired microstructure

and properties. No matter how much effort is put into ceramic processing (before

sintering), there is going to be an upper limit defined by the conventional sintering

methods. Although chemistry took advanced ceramics a long way to where they are

now, physics (and engineering) came to join hands with chemistry (materials science

and engineering) to find alternative ways to conventional heating. The interaction

of electromagnetic energy with materials results in heating the material and can

potentially be used to process ceramics more efficiently.

Microwave Processing of Ceramics

Although still in an early stage of development, the use of microwave energy

to process a wide range of ceramic materials offers many new and exciting

opportunities. Microwave heating is fundamentally different from conventional

processes. Heat generation is volumetric and within the material instead of

originating from external heating sources. Consequently, microwave processing

makes it possible to heat both small and large shapes very rapidly and uniformly,

reducing the thermal stresses that may cause cracking. There are a number of

reasons for the growing interest in microwave processing over conventional

processing. These include the potential for significant reduction in manufacturing

costs due to energy saving and shorter processing times, improved product uniformity

and yield, improved or unique microstructure and properties and synthesis of new

materials [Sut89].

This work involves the use of microwave heating for reactions in ceramics.

Chapter 2 provides some background on microwave radiation and its use in

processing various materials with some emphasis on ceramics. Chapter 3 discusses

the theoretical aspects involved in microwave heating. Since the effect of microwave

heating on the solid state reaction and mass transport is the main concern, Chapter

4 reviews some of the most widely accepted models involving these processes.

Chapter 5 states the main objective and accomplishments of this work and the

materials and methods involved are outlined in Chapter 6. Chapter 7 presents the

results obtained in this study, which are discussed in Chapter 8. Conclusions drawn

from this work and some suggestions for future work are presented in Chapter 9 and

10, respectively.



Characteristics of Microwaves

Microwaves, like visible light, UV, IR and radio waves are a part of the

electromagnetic spectrum. Microwaves cover a broad spectrum of frequencies,

usually ranging from 0.3 GHz to 300 GHz, that corresponds to wavelengths of 1m

to 1mm. Figure 2.1 shows the whole frequency spectrum including the microwave

region. Microwaves have the same characteristics as the other forms of radiation

mentioned above. All travel in a straight line at the speed of light, all can be

generated, reflected, transmitted and absorbed. In general, microwaves are reflected

by metallic objects, absorbed by some dielectrics and transmitted without significant

absorption through insulators.

Owing to the reflection from metals, microwaves can be transmitted through

hollow metallic tubes (waveguides). Glass, some ceramics and most polymeric

materials allow microwaves to pass with little or no absorption. Water and food with

high water content are good microwave absorbers. Other good microwave absorbers

include C, SiC, CuO, Co203, MnO2, NiO and WO3.

F10 Hz


Cancer Treatment


Gamma Ray Therapy

X-Ray Examination


Heating Lamp


10 2Hz





10 SHz


Figure 2.1. The entire
wall chart and [Str54]).

Secondary Cosmic Ray

Gamma Ray













10 1

-Nuclear States



Core Electronic
States of Atoms



Outer Electronic States
of Atoms & Molecules

10 m

frequency spectrum (adapted from a Kodak

10 Hz

Human body radiation


Microwave Spectrosocpy

Rotational Spectra


Water Resonance

Weather Radar

Police Radar


10 Hz


10 Hz




10 Hz







Radio Frequency

10 m

10 m

10 m

10 m

10 m


*' **

Vibration of

Internal Rotation
of Molecules

Free Rotation
of Molecules

Microwave Ovens

Space Research

10 m

Marine Radiophone

Figure 2.1. Continued.

10 Hz

Ultrasonic cleaning -

Highest Voice
Fish Sound

Human Hearing

Lowest Voice

Brain waves

Seismic Exploration




10 Hz



10 Hz

Resonance of Earth

< Hz
< 10 Hz

10 2Hz





Radio Frequency




10 m

10 m

10 m

One Mile

Induction heating

Maximum Lightning
Energy Pulse

Electrical Anesthesia

10 m

10 m

Diameter of Earth

10 m

Distance to Moon

10 m

Diameter of Sun

10 m

Distance to Sun

>10 m

Figure 2.1. Continued

Microwave Power Generation

High power microwaves are generated by vacuum tubes. Magnetron tubes are

most commonly used for generating continuous wave (CW) power at low capital cost.

Other microwave valves (tubes) are too expensive and complex to be used in

industrial processes. The klystron is an amplifier of microwave signals and has

excellent frequency stability. Although it is relatively less expensive, klystrons with

output of more than 1 kW CW usually require liquid cooling, which limits the

feasibility in some installations. Solid-state devices are also used to generate

microwaves but the power level is too low for industrial heating even when used in

large arrays [Met83, Dec86 and Vel87].

Microwave Heating


The applications of microwaves have in the past been mainly confined to

communication. Non-communication applications of microwave power include

medical and biological applications as well as heating. Iskander [Isk88] describes, in

detail, the medical applications in both the diagnostics and therapeutic areas.

Heating applications exist in the consumer, commercial, industrial and scientific

areas. The outstanding application area is that of heating food in the consumer

microwave oven.

A comprehensive historical review of microwave heating is given by Osepchuk.

There is little evidence of RF heating, and even less on microwave heating, before

the second world war. However, patent literature shows some loose reference to

using microwave energy to affect materials for industrial purposes. Kassner (who has

patents on a spark-gap microwave generator) believed that he could achieve useful

changes in molecular state and hence the chemistry of materials without heating


During the world war there were efforts to measure dielectric properties of

various materials. This work was done as a necessary task in the development of the

telephone and communication systems as well as radar. The work begun under Von

Hippel at the MIT Laboratory for Insulation Research, and the relevant lectures

given by experts in this area appeared as a book "Dielectric Materials and

Applications" [Von54]. This work is an important contribution to forming the

grounds for radio frequency and microwave heating.

After the world war the microwave tube market went in depression. Despite

the pessimistic view in the professional literature, people in the microwave tube

industry were examining microwave heating applications [Ose84]. The companies that

expressed interest in this area include GE, Raytheon, RCA and Westinghouse.

The Federal Communications Commission (FCC) was establishing a frequency

allocation procedure. Raytheon and GE petitioned the FCC for a microwave-oven

frequency. Raytheon favored higher frequency (2450 MHz), because this would

permit better coupling to smaller loads, and the greater number of modes in a given

cavity will allow better uniformity of heating pattern. GE preferred lower frequency

(915 MHz) because of the advantage of deeper penetration and less thermal

runaway. Both the frequencies were allocated by FCC, and ovens operating at these

frequencies were made commercially available. However, the 915 MHz ovens

phased out because the 2450 MHz units were more compact and convenient for

domestic use. The lower frequency (915 MHz) is still being used in the high power

large industrial systems mainly for food processing.

Industrial Microwave Heating Applications

Microwave processing until recent years has been dealing only with food

processing [Dec86], but this is now expanding drastically to include almost all

materials. The interest in this emerging technology, just recently, gave rise to the

first major international symposium on the use of microwave energy as applied to

materials processing. This Symposium organized by the Materials Research Society

was held at Reno in April 1988. Many important and interesting applications of

microwave energy were presented which were published in the proceedings [Sut88].

Since then more symposia have been held at other meetings as well.

Applications of microwave energy currently being explored are growing

tremendously. Some of them are briefly described.

1. Food industry. Microwave energy is utilized for numerous processes including

tempering of frozen foods, pasta drying, poultry processing, potato processing, baking,

cocoa bean roasting and sterilization of food [Dec86].

2. Polymer industry. Microwave energy is used for curing rubber tires and

bonding of composites, thermosets and thermoplastics in the automobile industry

[Rai88]. Litton has used microwaves for heating of the urethane foam, whereas

DuPont has been successful to dry Nylon fibers in a resonant cavity system [Ose84].

3. Medical applications. Medical applications include both treatment and

diagnostic techniques. Medical treatment deals with hyperthermia (deliberate

elevation of body temperature) to produce beneficial effects such as killing cancerous

tumors. The main advantage of this technique is the ability of the electromagnetic

energy to penetrate the human body (regardless of the thermal conductivity) and heat

deep-seated tumors. The medical diagnostics area includes measuring the changes

in lung water content, blood flow measurements and microwave imaging [Isk88].

In another application, an apparatus and process has been developed which

facilitates the exposure of all external surfaces to microwave radiation and

accomplishes sterilization. The standard 2.45 GHz microwave irradiation achieved

sterilization of dental instruments, artificial dentures, anesthesia nasal hoods and

hydrophilic contact lenses contaminated with a variety of bacteria, fungal and viral

pathogens. Microorganisms were totally killed in as little as 30 seconds to 8 minutes,

depending on the organism and the contaminated item [Roh90].

4. Electronic industry. Superwave Technology (Santa Clara, California) is

pioneering microwave heating in the electronics industry. The Supertherm line of

automated ovens is designed for a variety of thermal processes which include curing

wafer coatings, drying and reflowing solder, and fusing laminated printed circuits.

The Supertherm ovens are expensive, but the increased production rate justifies the

expense. The ovens reduce the curing time from one or two hours to less than six

minutes [Zyg87].

5. Mineral processing. The U.S. Bureau of Mines is looking into means to

reduce energy for grinding of minerals, which currently consumes 50 to 70% of the

total energy used for mineral extraction. The Bureau has demonstrated that many

minerals absorbs microwave and are rapidly heated. Research shows that

microwaves induce thermal stress cracking and improves the grindability [Wal88].

Reduction of metal oxides with carbon is an important metallurgical process

worldwide. An Australian group has irradiated mixtures of ores and appropriate

reducing agents, and metals produced by pyrometallurgical processes have been

rapidly smelted [Sta90, Bar90].

6. Asphalt recycling. A bright near-term financial prospect is a microwave

system for onsite recycling of asphalt. The microwave recycler reduces the expenses

for transporting asphalt and is smokeless, whereas other recycling operations must

add pollution-control equipment to meet federal regulations [Zyg87].

7. Waste treatment. Microwave energy is being investigated for the treatment

and disposal of waste materials. This includes daily life garbage as well as

radioactive waste. The Living Environmental Systems Research Laboratory,

Matsushita Company of Japan has developed a burning processor where the waste

material is dried and decomposed into gas by means of microwave energy. The gas

generated is burned in a sanitary way, leaving only a small amount of ash [Suz90].

Similar processes are under investigation for the treatment and disposal of

radioactive waste [Shi90, Dau90 and Var90].

8. Ceramic processing. Since this is the area of our interest, it will be discussed

in details in the following section.

Microwave Processing of Ceramics

Realizing the importance ofprocessing-microstructure-properties relationships,

researchers have begun studying the important aspects of processing. The study

includes the surface chemistry, materials characterization, processing additives and

rheology. Some other methods such as sol-gel processing and chemical vapor

deposition are also under investigation [Ree88]. These processing methods can

improve the microstructure of the ceramic and hence its properties.

After the ceramic has been formed, it has to be dried and fired to be useful

as a finished product. Drying and firing of these potentially improved ceramic is so

far carried out mainly in the conventional furnaces. So, whatever improvement one

may get from the studies mentioned above, there is an upper limit determined by the

capabilities of heat-treatment in the conventional furnaces.

Researchers have now recognized from various application of microwaves to

materials processing that this technology provides a powerful new tool and energy

source. Besides the savings in energy and cost (because of rapid processing cycle),

the greatest advantage is the novel rapid internal heating pattern that results in a

unique microstructure that can provide superior product quality [D690a, D690b,

D690c, Cla91].

The use of microwave energy in the ceramic industry is the first major

breakthrough that enables a change in the basic processes in heating. In order for the

ceramic to be heated effectively and to high temperatures it must couple with the

microwave energy, and this coupling must exhibit significant loss at that frequency.

The penetrating action of the microwave energy into the material results in the

internal and uniformly heating of large masses in relatively short periods of time.

Conventional heating starts from the surface of the body and is completely dependent

on the heat transfer characteristics of the material. Microwave heating is based on

internal heating mechanism that allows sintering large ceramic volumes with

uniformity of microstructure and properties throughout the entire volume [D690a,

D690b, D690c, Cla91]. (This is debateable because it is observed that hot spots exist

within the microwave oven. With appropriate mode stirrers that perturb the field

distribution continuously, although the analysis of the field distribution becomes

extremely complicated, it is possible to achieve nearly uniform heating). Another

advantage of internal heating is the inverse temperature gradient, which significantly

reduces the thermal stresses that cause cracking during the processing of large


Another important aspect is that different constituents (as well as phases)

absorb microwave at different rates. Thus, the possibility of controlled selective

heating has promising implications for improving the properties of ceramics,

especially in the area of composites. Generally, dielectric materials become more

receptive to microwave energy with increase in temperature, and as a consequence

absorb greater amount of energy as the temperature increases. A typical example of

the response is given in the Figure 2.2. The critical temperature T, gives an

approximate indication of the point at which the dielectric loss (absorption) increases


Coupling agents can be added to materials that cannot be efficiently heated

with microwave energy. The coupling agent preheats the entire sample which at


Figure 2.2 Qualitative representation of the loss factor as a function
of the temperature [Met83].


higher temperature starts to couple with microwave radiation. A common example

is that of the SiC whiskers in a low loss matrix. SiC is an excellent absorber of

microwave energy, which can heat the entire composite sample, which makes

sintering of the composite possible.

Alternatively, the sample may be preheated to temperatures where it

efficiently couples with microwave energy. This has been conveniently achieved in

our laboratory by placing the sample inside a susceptor (low loss insulation lined on

the inside with high loss silicon carbide). The heat generated in the silicon carbide

is retained within the insulation which preheats the sample to above its critical

temperatures where microwave losses become substantial. This is termed as

"Microwave Hybrid Heating." Usually with microwave heating alone there is an

inverse temperature gradient with higher temperatures in the interior of the sample

and lower temperatures on the surface because of the energy radiated from the

surface. Microwave hybrid heating, in addition to preheating the low loss materials,

provides an external heat source and compensates for radiation losses from the

surface. Microwave heating is generally much faster than conventional heating, but

for low loss materials heating rapidly with microwave energy alone (without

susceptor) may be difficult. This problem is overcome with hybrid heating. Heating

rates of 750C per minute have been achieved by microwave hybrid heating in our

laboratory. The sintering of alumina with this method has resulted in fine and

uniform microstructures [D690a, D690b, D690c, Cla91].


Although this technology is still in an early stage of development, microwave

energy is being explored to process a wide variety of ceramics, which offers exciting

opportunities. An excellent summary of almost all the applications in the area of

microwave processing of ceramics is presented by Sutton [Sut89]. Some of these will

be briefly discussed here to highlight the advantages obtained by microwave


1. Process control. Many ceramics are transparent to microwaves at ambient

temperatures. Campbell and Shivers [Cam73] have discussed the use of microwave

energy for process control applications such as moisture content measurements,

contact-free thickness gaging and flaw detection.

2. Liquid-state processing. Microwaves can be used for processing liquids in the

form of solutions or suspensions to analyze or synthesize materials. The U.S. Bureau

of Mines has been able to reduce time for wet-chemical analysis of minerals,

ceramics and alloys by greatly increasing their dissolution rates in acids.

Microwaves have also been used in several of the processing steps for slip

casting of ceramics [Cha86, Oda88].

3. Ceramic drying. Drying of ceramics with microwave energy is particularly

effective in removing low water contents from thick ceramic bodies where the

volumetric heating drives the water out from the interior. A hybrid system, in which

both conventional and microwave heating is used, is often the most efficient to dry

materials having high (>10%) water contents [Smi88].

4. Binder burnout. Binders are normally used in the ceramic forming process,

which are eventually to be removed, especially when high purity is desirable. These

can be removed by microwave either by directly coupling (if lossy material) or by the

heat generated in the ceramic. Binders have been burned out of polycrystalline lead

zirconate titanate (PZT) and lead-based lanthanum-doped zirconate titanate (PLZT)

during early stage of sintering of these materials [Har88].

From the above mentioned applications process control with microwaves does

not significantly increase the temperature of the sample. Liquid state processing and

drying are carried out at much lower temperatures, whereas in binder burnout

applications the temperatures can go up to a few hundred degrees (Celsius)

depending upon the binder used. The applications that follow require high

temperatures for processing. These applications are primarily in the research stage,

although some commercial processes have been investigated on a pilot scale [Sut89].

5. Sintering of ceramics and composites. Numerous ceramics and composites

have been sintered with microwave energy, mostly at 2.45 GHz, with a few at higher

frequencies. These include, but are not limited to, sintering of ferrites [Kra81], lead-

based perovskite ceramics [Ali87], boron carbide [Kat88a], titanium boride [Kat89]

and sintering of partially stabilized zirconia [Wil88]. Microwave sintering has been

performed under high gas pressure [Tia88] as well as in vacuum [Jan89]. The most

common ceramic "alumina" has been sintered at different frequencies which include

2.45 GHz [D690a, D690b, D690c, Swa88], 28 GHz [Jan88] and at 60 GHz in form

of A1203 and Al203/SiC composite [Mee87, Kat88b]. Other sintering of composites

deals with A1203/TiC [Tia87] and ZrO2/SiC, ZrO2/Si3N4 and AI203/Si3N4 [Bla86].

6. Joining of ceramics. Microwave energy has been used for joining of ceramics

at Quest Research Corporation [Pal88, Pal89] and Toyota R&D Labs. [Fuk88]. The

joints exhibited greater strength than the as received material and did not fail at or

near the joint. The joints were not detectable in microscopic observations and the

microscopic homogeneity in the vicinity of the joints was retained. There was little

difference in the microstructure before and after joining.

The properties of the joints are excellent; however, a complete physical and

chemical picture of the underlying bonding mechanism has yet to be developed.

According to the authors, their data supports the contention that the electromagnetic

energy contributes important nonthermal effects to the process.

7. Heating of fused quartz for the fabrication of optical fibers. Optical fibers for

telecommunication are most widely fabricated in a Modified Chemical Vapor

Deposition (MCVD) station. In a standard MCVD preform station the oxy-hydrogen

torch is replaced by a microwave cavity. Fused quartz has a small loss factor at lower

temperatures, so the oxy-hydrogen torch is used to preheat quartz that increases the

microwave absorption. Temperatures up to 20000C are achieved and the productivity

significantly increases with the microwave enhanced MCVD processing [Has88].

8. Processing and sintering of PZT and PLZT. Microwave energy has been

shown to be feasible for drying, binder burn-off, calcining and sintering of PZT and

PLZT samples. PZT samples with an average grain size of 1.7 to 2.8 micrometers

were obtained with the densities as high as 99% of the theoretical values. Unique

PZT was obtained with microwave processing where the piezoelectric voltage

constant was 0.023 versus 0.020 V-m/N for conventionally processed PZT [Har88].

9. Processing of Superconducting Ceramics. Superconducting ceramics have

been successfully prepared using microwave energy [Cla88, Ahm88]. The

superconducting powder mixture couple well to microwave energy. This is attributed

to the excellent coupling of one of most common constituents, CuO. Thus, all

superconducting ceramics based on CuO are excellent candidates for processing using

microwave energy. Sintering and annealing [Ahm89a] have been shown, not only to

be feasible, but superior to conventional methods. However, more investigation on

calcining (elimination of volatile constituents) is required. The samples prepared by

microwave processing had an onset T, of 93 K as compared to 90 K for conventional

processing. The superconducting fraction and diamagnetism were respectively 31.2%

and 24% for microwave processed samples as compared to 30% and 11% for the

conventionally processed samples. The conventionally processed samples exhibited

higher porosity as compared to the microwave processed samples.

10. Combustion synthesis of ceramics and composites. Microwave energy provides

an alternate, yet distinct way of igniting and sustaining controlled combustion of the

reactants [Cla89, Ahm89b]. Microwave energy, because of its novel internal heating

mechanism, tends to heat the entire sample nearly uniformly. The surface of the

sample radiates energy, resulting in a higher temperature at the interior of the

sample. In MICOM (Microwave Ignition and Combustion) because of the higher

internal temperatures, the sample ignites in the center and a combustion wavefront

propagates outward in a radial manner. This reduces the thermal gradient on the

sample. With other methods, ignition and combustion are initiated at the surface

and can result in a severe thermal gradient. In conventional ignition, the

propagation of the combustion wavefront is strongly dependent on the thermal

conductivity, the reactant-powder-compact density and the composition of the sample.

At high compaction densities, the propagation rate may decrease or terminate due

to self-extinction. In certain cases it may even fail to ignite. Thus, one expects a non-

uniform wavefront or no wavefront at all.

In contrast, with microwave ignition, energy is constantly absorbed within the

material. This absorption ensures that the ignition temperature is sustained. As the

temperature of the material is increased, the absorption of microwave energy by the

material is increased. Higher absorption leads to increased dissipation of energy,

resulting in a corresponding increase in temperature. Ignition temperature is reached

first in the center of the sample, leading to an even higher combustion temperature,

which further increases the absorption of microwave energy. So, microwave energy

and combustion synthesis assist each other in sustaining the reaction. The high

temperature in the interior of the sample forces propagation of a relatively uniform

radial combustion wavefront to the exterior of the sample, which ensures complete

combustion of the material. Thus, with microwave ignition and combustion, the

dependence of the reaction on the thermal conductivity and the density of the

compact is greatly reduced, compared to those samples ignited with conventional

methods. Samples pressed to compact densities in excess of 80 percent, which are

reported difficult to ignite with conventional methods, have been easily ignited using

microwave energy.

In addition to the above advantages, control of the propagation of the

combustion wavefront is also possible with microwave energy. This is termed as

MICROCOM (Microwave Ignition and Controlled Combustion). Having control on

the wavefront propagation allows for a gradual release of volatiles, which is very

important for fabricating dense products. With conventional ignition, if the density

and the thermal conductivity are high, the combustion wavefront may not be able to

propagate at all. Using microwave energy is especially favorable in this situation

because the wavefront can be forced to propagate by constantly dissipating

microwave energy in the sample.

As mentioned above, high compact density and high thermal conductivity

limit, or inhibit, the wavefront propagation. Further, a high value for density reduces

microwave heating rates of the sample. These two factors combined provide control

of the propagation of the combustion wavefront. The rate of propagation of the

wavefront can also be controlled by the incident power. Turning the power off will

terminate the propagation of the combustion wavefront. Pulsing the incident power

by altering the duty cycle will give even more precise control on the velocity of

propagation of the combustion wavefront.

As the wavefront propagates radially outward, more surface (4rir2, increases

with r) is encountered, which absorbs the heat generated at the smaller adjacent

surface (smaller r). This is another factor contributing to controlled propagation. In

planar wavefront propagation (from one end of the sample to the other) the cross-

sectional area remains constant, and the heat absorbed per unit area is larger than

that of radial propagation. Thus, radial wavefront propagation is slower, allowing for

more control than planar wavefront propagation.

Other parameters, such as addition of a diluent into the reactant powders

may also be used in MICROCOM. The major advantage of having control of the

reaction, especially the combustion wavefront propagation, is the capability of

forming dense monoliths. Controlled combustion allows for a gradual release of

volatile species, which reduces expansion and increases the density of the product.

These types of property improvements cannot be easily obtained with conventional

methods unless pressure is applied during the reaction process.

Radiation Safety and Hazards of Microwave Heating

Although there had been some fear of the use of microwave energy since the

World War II, the subject of microwave hazards was not generally known to public

until Congress passed the Radiation Control for Health and Safety Act of 1968. The

safety act resulted because of the scare of radiation from color TV, but was

broadened to include all kinds of potential radiations from electronic products,

including microwave/RF and acoustic energy. This step was taken as a cautious

safety measure and not because of any practical health or safety problem involving

microwave/RF energy. Details on this issue have been published by Osepchuk

[Ose79, Ose82 and Ose84] and are summarized in this section.

The Bureau of Radiological Health (BRH), having the charter to develop

safety or performance standards relating to electronic product radiation, decided to

develop a performance standard on leakage of microwave energy from microwave

ovens. The focus was on the power density of leakage measurement at 5 cm from

the oven which is a measure of "emission" rather than "exposure" and there was

confusion between these values. The consensus standard on safe "exposure" limit was

10 mW/cm2. A very conservative application of this limit was made by proposing the

same emission value at 5 cm because that was as close as the human eyeball could

typically be located to an oven. Other medical scientists proposed a higher

permissible leakage at 5 cm because of the inverse-square law which would dictate

much lower exposure values at several feet from the oven. A final choice of 1

mW/cm2 at 5 cm when the oven is new and 5 mW/cm2 at 5 cm thereafter, with an

arbitrary standard load of 275 ml of water was made for the emission standard on

microwave ovens. This was recognized as very conservative, having a safety factor

of 10,000 or more, mentioned in medical literature.

According to Osepchuk [Ose82], a large part of the risk of microwave

radiation in the United States is perceived, but not real. The perceived risk of

microwaves increased for various reasons in the early 70's. There were series of

articles questioning the safety of microwave ovens. A meeting of the U.S. Surgeon

General, BRH and manufacturers was called to deal with the fact that a large

percentage of old microwave ovens manufactured before 1970 leaked more than 10

mW/cm2 under standard test conditions. Although the manufacturers agreed to

repair such ovens, the perception of risk was heightened because some

noncompliance with a conservative leakage limit was equated with unacceptable risk

and hazard.

The misinformation in the popular media and microwave/RF hazards were

generally exaggerated. There were discussions within Institute of Electrical and

Electronics Engineers (IEEE) on the need to correct this misinformation and to

provide factual information to media, legislators and the general public.

A well-known event was the coincidence of allegations in 1973 by Consumer's

Union and others that microwave ovens were a significant radiation hazard and that

there is an ever-increasing danger to the entire population of our country from

exposure to the non-ionizing portion of the electromagnetic spectrum. These

allegations were widely publicized by television and radio, and the growth in sales of

microwave ovens was temporarily slowed, but these allegations were swiftly rebutted

by many scientists involved in relevant bioeffect research.

Since 1973, there have been occasional media campaigns stimulating new fears

of microwave radiation. These have probably contributed significantly to slow down

the acceptance of microwave heating in some industrial situations where the

management is sensitive to employee fears. Eventually, even the Consumer's Union

accepted the microwave oven and dropped its generalized warning against its use.

However, some suspicion still remains, even in some semi-professional literature,

about possible non-thermal effects that might invalidate U.S. safety standards.

Furthermore, the generalized fear of microwaves that developed in the 70's,

and the publication of a report concerning the interference with implanted cardiac

pacemakers by microwave ovens, prompted the U.S. Army and other agencies to

require warning signs around microwave ovens. It is believed that the original

incident involved significant spurious-signal radiation from early microwave ovens at

around 200 MHz and not 2450 MHz.

Real hazards of microwave ovens include, in addition to usual hazards of

electricity and heat, the hazards associated with the explosions of certain materials

super-heated in microwave ovens because of possible internal hot spot phenomenon.

The malfunction in ovens equipped with microprocessor control with a failure to shut

off ovens could cause food- or oven-fire, or by the use of arc-provoking metallic

objects inside ovens.

For information on real risks of microwave exposure one needs to refer to

data banks on microwave injuries. The data on confirmed injuries due to microwave

exposure is limited only to RF burns, caused either with diathermy treatment or

accidental contact with concentrated leakage sources (such as loose joint of

waveguide flanges in a high power system). Reports show no association of

significant health problems under typical microwave exposures in various

occupational settings [Ose82].

There is difference in the scientific facts on the hazards of ionizing and

nonionizing radiation. Opponents of nuclear power believe that natural background

ionizing radiation causes thousands of deaths per year and any addition to this

number, no matter how small, is unacceptable. For ionizing radiation, people believe

that there is no evidence for a safe level of radiation. However, the properties of

nonionizing radiation are different and safe levels of nonionizing radiation do exist.

Practically as well as scientifically one knows that there are safe levels of heat

radiation and safe levels of radiation that carries radio, TV and radar signals in the

air. From the scientific literature on the biological effects of nonionizing radiation

one can conclude that there are thresholds. Thresholds in frequency separating


ionizing and nonionizing radiation, and thresholds in exposure levels or duration of

exposure separating no effect or no harm from effect or harm.


Dielectrics and Mechanisms of Losses

The Molecular Origins of Permittivity

When a dielectric material is placed in an electric field it becomes polarized

due to the relative displacement of the positive and negative charges in the material.

The ratio of the permittivity of the dielectric material to the permittivity of free

space is called the dielectric constant or the relative permittivity of the material. The

phenomenon of dielectric dispersion which occurs in materials containing polar

molecules was first elucidated by P. Debye [Deb29]. A dielectric may have

permanent electric dipoles or induced dipoles which may arise due to the presence

of an applied field. The magnitude of the dipole moment depends on the size and

symmetry of the molecule. Molecules having a center of symmetry are non-polar

(zero dipole moment) while molecules having no center of symmetry are polar. The

dipole moment of the molecules influences the permittivity or the dielectric constant

of a material [Hil69]. The permittivity of the material will be higher, the greater the

polarizability of the molecules.


In a non-polar molecule the displacement of charge particles from their

equilibrium positions gives rise to induced dipoles which respond to the applied field.

Such induced polarization include electronic and atomic or ionic polarization.

Electronic polarization. Electronic polarization is due to the shift of the

valence electron cloud with respect to the nucleus (Figure 3.1a). This polarization

mechanism occurs at very high frequencies (1015 Hz) in the ultraviolet optical range.

This mechanism of polarization gives rise to a resonance absorption peak as shown

in Figure 3.2. The index of refraction of the material depends on the electronic

polarization [Hen90].

Atomic or ionic polarization. Atomic polarization is the displacement of the

positive and negative ions in the material with respect to each other (Figure 3.1b)

and occurs in the infrared frequency range (1012-1013 Hz). A resonance absorption

occurs at frequencies characteristic of the bond strength between the ions. If there

are several types of ions or a distribution in bond strengths, the infrared absorption

can be quite broad.

In addition to induced dipoles some dielectrics, known as polar dielectrics,

contain permanent dipoles due to the asymmetric charge distribution of unlike charge

in a molecule. In this case the dipoles tend to reorient under the influence of a

changing electric field, thus giving rise to orientation polarization.

Orientation polarization. This type of polarization, also referred to as dipolar

polarization, involves the perturbation of the thermal motion of ionic or molecular

dipoles, producing a net dipolar orientation in the direction of the applied field.

+ -

in Electron


atom M atom N

= E


(d) -

- ()

Na *



Figure 3.1 Schematic of polarization mechanisms in glass and
ceramics. (a) Electronic. (b) Atomic or ionic. (c) High-frequency
oscillatory dipoles. (d) Low frequency cation dipole. (e) Interfacial
space charge polarization at electrodes. (f) Interfacial polarization at
heterogeneities [Hen90].

Interfacial polarization

Dipole polarization
(low freq.) (high frequency)

1O-3 10-' 10 10o 10" lO0 10' 1 0"- 10 ,,0i (
o 10 (a)

10-' i0-' 10 103 105 10' 10 10 10 10'5
10 frequency

10-1 10'1 10 Jo3 1O1 1 1 10' IOV' 10'1

Figure 3.2 Frequency dependence of the polarization mechanisms in
dielectrics. (a) Contribution to the charging constant (representative
values of Ki'). (b) Contribution to the loss angle (representative
values of tan 6) [Hen90].

Dipolar polarization mechanisms can be divided into two categories. First, the

molecules containing a permanent dipole moment may be rotated against an elastic

restoring force about an equilibrium position. Under an applied sinusoidal ac field

the bond can oscillate about an equilibrium position (Figure 3.1c). The frequency

of relaxation of such a mechanism is very high, 1011 Hz at room temperatures.

The second mechanism of dipolar polarization is an especially important

contribution to the room temperature dielectric behavior of glasses and ceramics. It

involves the rotation of dipoles between two equivalent equilibrium positions. This

type of polarization occurs largely as a result of motion of charged ions between the

interstitial positions within the ionic structure of the material (Figure 3.1d). Since

an appreciable distance is involved in such an ionic transition the polarization occurs

at a frequency range of 103-106 Hz, at room temperature. Because of the

involvement of the same mobile cations that contribute to the dc conductivity, this

mechanism is sometimes referred to as migration losses.

Interfacial. Space Charge or Maxwell-Wagner Polarization. This is another

type of polarization which occurs in heterogeneous dielectrics when one component

has a higher electrical conductivity than the other. It results from the charge build-

up in interfaces between components in heterogeneous systems. It is usually

associated with the presence of impurities which form a separate and somewhat

conducting phase. If the density of the charge contributing to the interfacial

polarization is sufficiently large, the frequency range of sensitivity for interfacial

polarization, though usually quite low (10-3 Hz), may extend to fairly high frequencies

in the kilocycle range (103 Hz).

Polarizability. Polarizability is a measure of the average dipole moment in

presence of an electric field. If the average electric field acting on a molecule is Eint,

the average moment ji will be

T = aTEint (3.1)

where aT is the total polarizability of the molecules and

aT = ae + ca + ao + i (3.2)

where a., aa, ao and ai are the electronic, atomic, orientation and interfacial

(Maxwell-Wagner) contributions to the polarizability.

Suppose there are N molecules per unit volume and that the average moment

fu is induced in each of them as a result of the polarization (P), then

P = pN (3.3)

The polarization (P) is also related to permittivity (e') by

P = e'Eapp- %Eapp (3.4)

where eo is the permittivity of free space and Eapp is the applied electric field. Using

equation (3.1) and (3.3) it can be written as

eo(K'-l)Eapp = NaTEi, (3.5)

where K' (= e'/e0) is the relative dielectric constant of the material. This equation

links the macroscopic quantities to the molecular parameters in the dielectric. Using

Mosotti's equation for the two fields

Eint = (1/3)(K' + 2)Eapp (3.6)

in equation (3.5)

NaT (K'- 1)
= (3.7)
3eo (K'+ 2)

The number of molecules per unit volume is related to the number of molecules per

mole by Avogadro's number by

N = Nop/M (3.8)

where M is the molecular weight and p the density. This gives

3Meo(K' 1)
aT = (3.9)
Nop(xK'+ 2)

showing the dependence of the total polarizability on various parameters.

The Complex form of Dielectric Constant

The losses arising from various forms of polarizations are better understood

by considering the complex form of the dielectric constant, given by

K* = e*/o = K' iK" and e* = e' ie" (3.10)

where e' is the dielectric permittivity (real or storage part), and e" is the dielectric

loss (imaginary part). In the presence of an electric field there is some current flow

(conductivity), and some losses associated with it. Since, with most dielectric

measuring techniques, it is difficult to separate the losses due to conduction from

those due to polarization, all form of losses can be grouped together, defined as an

effective loss factor, e"f,. The complex dielectric constant is thus given by

K* = e*/eo and e* = e' ieeff (3.11)

where the loss factors includes the contribution from polarization as well as

conductivity. The ratio of the effective loss factor to that of permittivity

tanSeff = e'ff /e = K'ff/K' (3.12)

is called the effective loss tangent.

Dipolar or Orientation Loss Mechanism

Among all the possible forms of loss mechanisms, orientation polarization is

probably the most significant in industrial microwave heating applications at

frequencies above 1 GHz. However, there is influence on the lower frequencies as

well, because for many polar materials the time constants for the establishment and

decay of the polarizations occur at times comparable to the periods of oscillations

of these frequencies [Met83].

Debye equations. The classical approach to the treatment of permanent

dipoles in liquids (or polar molecules dissolved in non-polar solvents), is to consider,

in the presence of an alternating field, the rotation of a spherical dipole in a viscous

medium dominated by friction. Debye [Deb29] working on electrolytes deduced the

well-known equation

(;- ea,)
e* =e ie' = + +( (3.13)
(1 + io't)

where es and e, are the dielectric permittivities at dc and very high frequencies,

respectively, e" is the dipolar loss factor, the factor (e, e.) being termed as the

dispersion of the permittivity, r is the relaxation time of the system which controls

the build-up and decay of the polarization, and (to = 2ntf) is the angular frequency

of the field applied. The real (or storage) and imaginary (or loss) parts are given by

e' = e, + ( (3.14)
(1 + o2 2)

(eS eoo)WT
e = 1 (3.15)
(1 + 02 2)

The loss factor is maximum when or = 1 and is given by

e' = (1/2)(e, e ) (3.16)

Frequency dependence of the polarization. When an applied field is

alternating at sufficiently low frequencies, near dc, the dipoles have ample time to

follow the variation of the applied field. With increasing frequency, the polarization

will not have time to attain its full value before the field reverses: i.e. polarization

lags behind the alternating field. In this frequency range the permittivity decreases

and there is loss, or absorption of the electrical energy which causes heating in the


The absorption regions associated with the different mechanisms of

polarization occur in different parts of the electromagnetic spectrum. The electronic

and atomic polarizations usually result in resonance absorption peaks. However, in

dipolar and interfacial polarization, the resistance to dipolar motion is large, which

result in relaxation type absorption [Mea61]. This was illustrated earlier in Figure


Debye's interpretation of this relaxation is given in terms of dipolar rotation

against frictional forces in the medium. He derived an expression for the relaxation


r = 47tr3/kbT (3.17)

where tr is the viscosity of the medium, r is the radius of the rotating dipole and kb

is Boltzmann's constant. In practice, many liquids and solid dielectrics possess

relaxation times which are much longer than those derived from the above equation,

i.e., the response is much flatter than that indicated in Figure 3.2. The remedy lies

in substituting the applied field used in Debye Theory by the Mosotti local field

introduced earlier. The new effective relaxation time constant for the dipoles


(es + 2)
te (3.18)
(ea + 2)r

Despite this correction for the relaxation times of dipoles, the Debye

interpretation is fairly inaccurate. It is difficult to imagine, particularly in solid

dielectrics, the dipoles as spheres in a medium where viscosity is the dominant

mechanism. Moreover, when many atoms and molecules are bonded together to form

a dielectric, the dipoles are influenced by the forces of all the neighboring particles

which must be taken into account in the theory. The Mosotti field approximation,

although it is in many circumstances a very useful concept, leads to catastrophic

situations when applied to polar molecules, in that the polarization tends to infinity

when the polarizability term, a, approaches a certain critical value. Debye

recognized this shortcoming and introduced the notion of hindered motion of polar

molecules in an environment of other particles exerting an influence which cannot

be ignored.

Model for dielectric absorption. To account for the presence of dielectric

losses because of the hindered motion, Debye suggested the following simple

mechanism. Each dipole possesses two positions of equilibrium, equal in energy and

opposite in direction, separated by an energy barrier AEb. This is illustrated in Figure

3.3a. The dipoles oscillate with a frequency fo about the equilibrium positions and


Angle of rotation of dipole




Dipole rotation


Figure 3.3 (a) Potential energy diagram for dipole rotating in a
crystal lattice with energy barrier AEb and equilibrium positions of
equal energy. (b) Potential energy diagram for a complex system
having unequal potential minima [Mea61].

occasionally acquire enough energy to rotate from one equilibrium position to the

other, but at any instant there are equal number of dipoles occupying each position.

If an electric field is applied, a small excess of dipoles will rotate into more favorable

positions, thus giving rise to polarization.

The energy barrier between the equilibrium positions of the dipoles can be

obtained from the temperature dependence of the frequency of maximum absorption

by the equation

fmax = 1/27T = Aexp(-AEb/kbT) (3.19)

where the frequency factor A is a constant.

Generally, A is found to vary from one system to another, and can be replaced

by the product of frequency and entropy terms as

fmax = (fo/2n) exp(AS/kb) exp(-AEb/kbT) (3.20)

where AS is the entropy of activation and fo is the frequency of oscillation of the

dipole in its potential trough (of the order of 1012 1013 sec'l).

In the above discussion no reference is made to the magnitude of the

absorption. In polycrystalline solids possessing the simple mechanism illustrated in

Figure 3.3a, the equations for the magnitude of the absorption would be the same

as those for liquids. The general form of Onsager's equation for the liquids has been

found to apply [Mea61] to a number of solid systems

47iNg2 e,(eo + 2)2
(e, e.) = (3.21)
9kbT 2e, + eo

where N is the number of dipoles per unit volume and p. is the dipole moment. The

number of equilibrium positions may not necessarily be restricted to two, provided

they are all equal in energy. Further, in most solids, the equilibrium positions of the

dipoles are unequal. In such cases, the molecular relaxation time is approximated

by the expression

fmax = 1/(27x) = Aexp[-AEl/kbT] (3.22)

where AE1 is approximately equal to smaller energy barrier shown in Figure 3.3b.

If the energy difference between two equilibrium positions AEo>kbT, the magnitude

of absorption is approximately given by

(e', e'.) = (B/T)exp[-AE,/kbT] (3.23)

where B is a constant.

When AEb<
surrounding molecular particles do not play a very important role in the ensuing

polarization mechanism, as is the case for some gaseous substance, where the

interatomic forces are much smaller than kbT. However, in solid dielectrics

(AEb>kbT) the interatomic forces dominate, resulting in deviations from the simple

Debye theory.

The concept of more than one activation energy and spread of relaxation

times can be envisaged in an inhomogeneous solid dielectric, where hindered dipole

redistribution results in multi-relaxation spectra as shown qualitatively in Figure 3.4.

This is confirmed experimentally where e' as a function of frequency is much flatter

and broader than the response obtained from the simple Debye equations where the

time constant is viscosity dependent. To account for the broadening of the relaxation

response, Cole and Cole [Col41] introduced a spreading factor "s", modifying the

complex permittivity to

I / \ i\ Ideal Debye responses
/ VI I I
/ ^/. \( c__


Figure 3.4 Ideal Debye loss factor versus frequency response (dotted
lines) and multirelaxational response due to hindered dipole
redistribution (solid line) [Met83].

e* = e' ie" = eo + (3.24)
(1 + io~m(1-))

where rM is the mean of different relaxation times which correspond to transitions

between the different dipole positions. Any deviations from the pure Debye theory

can be readily seen if e" and e' are plotted for a real dielectric (solid line) on the

Cole-Cole diagram. A Cole-Cole plot is a measure of the various relaxation times

of a specific dielectric material (Figure 3.5). If a perfect semicircle is produced,

there exists a very narrow distribution of relaxation times (dotted line). This

indicates that only one primary mechanism exists for the polarization within the

material. A large range of relaxation times, on the other hand, indicates multiple

polarization mechanisms, but it can also indicate the losses due to conduction. The

factor "s" is a measure of this deviation, being zero for a purely Debye response

(dotted line).

Temperature dependence of orientation polarization. The development of the

above model also provides a basis for understanding the temperature dependence of

the dielectric properties of a material. Equation (3.19) gives the temperature

dependence of the frequency of maximum absorption. Combining the exponential

dependence of fmx or relaxation time r on temperature, with the Debye equations

it is possible to describe the temperature variation in the location of the tan6 loss

peak. Figure 3.6 [Hen90] shows the shift of the dielectric loss peak in a lithium

silicate glass to the higher frequency side due to increasing temperature. Likewise,

Figure 3.7 shows the shift in the dielectric loss with increasing temperature for

sodium bromide containing calcium impurity. At each temperature in Figure 3.7 the

Ideal Debye response

E' n r --.

(es- )/2
/ 0 \
/ I U. increasing

T /12 0



Figure 3.5 Qualitative representation of the Cole-Cole diagrams for
an ideal Debye relaxation (dotted line) and for a real dielectric (solid
line) [Met83].

10 hr 500C
-..o-.- 198C
-.0-- 1220C
-o 82"C
.....o..... 240C



S \ g \ _./" .

-..0- oS
o-^ ^>^-a" -" ."-. -

2 3 4 5 6
Logio frequency

Figure 3.6 Shift of the dielectric loss peak in lithium silicate glass due
to increasing temperature [Hen90].


= 0-03-
\3"4 o

0-02- \ \ .3-0
1 1

0 0 01
c VV

0 2I 3 4 5 6
log freQuency -- (c/s)

Figure 3.7 Dielectric absorption at various temperatures for sodium
bromide with calcium impurity [Mea61].

higher frequency part of the absorption conforms to a Debye curve, but at lower

frequencies the absorption is complicated by de conductivity. The dotted line curves

represent the resultant absorption after subtracting the part due to conductivity, and

in each case the resultant absorption is a Debye curve. In alkali halides at ordinary

temperatures there are some unoccupied lattice sites. These vacancies can diffuse

through the lattice and are the main cause of intrinsic electrical conductivity under

ordinary conditions. However, a small proportion of vacancies of opposite sign are

associated, thus forming dipoles which change direction by jumping of adjacent ions

into vacancies. This forms the basis of a simple dielectric absorption mechanism.

Thus, in the dielectric absorption mechanism for the alkali halides, the fundamental

process of jumping of a cation into a vacancy is the same, as in both the dc

conductivity and diffusion mechanisms [Mea61].

Interfacial or Maxwell-Wagner Loss Mechanism

Interfacial polarization is very important in heterogeneous dielectrics,

comprising of a small fraction of conducting phase in a non-conducting medium,

because it relates to the charge build-up at the interfaces of the heterogeneous

dielectrics. This certainly influences the total polarization of a heterogeneous

dielectric at the frequency band (less than 5x107 Hz) used in industrial high frequency

heating [Met83]. Wagner considered a simple model consisting of conducting spheres

distributed homogeneously throughout a non-conducting medium. For low

concentration of conducting material having a volume fraction v, the equations

describing the absorption are [Mea61]

9v(e'1)2 oT
e =- (3.25)
2e'1 + e'2 1 + 22 .2

fx (Hz) = 1.8 x 1012 (3.26)
2e'1 + e'2

where e'1 is the real part of the permittivity of the continuous phase, e'2 is the real

part of the permittivity of the conducting phase and 02 is the specific conductivity of

the conducting phase.

Equation (3.26) shows that the frequency of maximum absorption increases

with increasing conductivity of the conducting phase. For a system of metal spheres

included in an insulating material the absorption would occur at frequencies above

the normal range. An experimental system approximating the Wagner's model was

prepared [Ham53], which gave good agreement with the theory.

With higher concentrations of conducting impurity it is necessary to take into

account the interaction between the dipoles induced on the conductors. This has

been investigated experimentally and theoretically by Kharadly and Jackson [Kha53].

The agreement between the authors' theory and their experimental results was good

for concentrations up to about 30 per cent, the dielectric absorption being larger than

that indicated by Wagner's equation. Above 30 per cent the experimental values

were larger than either of the corresponding theoretical values.

Figure 3.8 shows qualitatively the contribution of dc conductivity on the losses

in interfacial polarization. For highly conductive dielectrics (such as foodstuff

containing large amounts of salts), the purely conductive term might dominate the

losses giving a response indicated by curve IV in Figure 3.8 [Met83].


Figure 3.8 Influence of dc conductivity on the losses in interfacial
polarization dc conductivity increasing between I and IV [Met83].

Combined Effects

Processing of many industrial materials with electromagnetic energy in the

frequency range 10 MHz
or interfacial absorption mechanisms. In mixtures containing very large amounts of

conductive phases (high losses due to dc conductivity), the interfacial polarization is

represented by

ed< = o/eo (3.27)

Therefore, in heterogeneous dielectric material containing some conductive phase,

the losses at higher frequencies combine with the dipolar losses to form an effective

loss factor e'f, as shown in Figure 3.9, where the rise at the lower end of the

radiofrequencies is attributable to effects of conductivity [Met83].

Magnetic Loss Factor

So far only with dielectric losses in materials were considered. However, in

microwave heating the magnetic losses can also contribute. Materials exhibiting high

magnetic losses at radio and microwave frequencies can also be effectively treated

[Eps54]. In analogy to the dielectric permittivity, the complex permeability of a

material under the influence of a high frequency field, can be given by the relation

B = op.**H (3.28)

where B is the magnetic flux density and H is the magnetic field. The complex

permeability is represented by

Conductivity losses

I Dipolar losses

Radio frequencies

Microwave frequencies

Log frequency
Log frequency

Figure 3.9 Effective loss factor of a heterogeneous dielectric
exhibiting dipolar and tail end conductivity losses [Met83].

E eff

(* = (0' i"'eff) (3.29)

where p.' is the permeability and peff is the effective magnetic loss factor due to

relaxation and resonance processes under the influence of the alternating magnetic


Consideration of the magnetic loss factor is important from the point of

microwave processing because lossy powder such as magnetite (Fe304) are added to

plaster molds to enhance the rates of microwave absorption.

Microwave Power Dissipated

Microwave heating results from the dissipation of the electromagnetic energy

in the material. The energy dissipated is derived from Maxwell's equations and has

been dealt in many books and papers [Cor62, Met83, Tin88]. Only the results are

presented here. The power through a closed surface can be calculated from the

integration of the Poynting vector

p = E xH W/m2 (3.30)

The average power absorbed is

Pav = O(eoefE2nsVb (3.31)

If the material exhibits magnetic losses the permeability term should be added to

equation (3.31), giving

Pav = oeoeeffE2rsVb + O)oteffH2rsVb (Watts) (3.32)

where o = 27tf (f in Hz) and Vb is the bulk volume of the sample being heated.

Penetration Depth

When microwaves penetrate through an absorbing material, they are

attenuated. The distance from the surface of the material at which the power drops

to 1/e of the value at the surface, is called the penetration depth. If 1, is the

wavelength in free space, the penetration depth with p' = 1 is given by

Dp = o2,) [(1 + (eff/e')2)1/2 1]-1/2 (3.33)
For low loss dielectrics e', /e' << 1, the penetration depth approximates to

Dp = (3.34)

Equation (3.34) shows that the penetration depth increases with larger wavelengths

or with decreasing frequencies. Usually ceramics such as A1203, SiO2, Si3N4, BN and

ZnO have values for relative dielectric constant e' ranging from 3 to about 9

[Sut89]. Loss tangent, tan6Sff (= e', /e'), has values from 0.002 to about 0.02 for

the ceramics mentioned above. Thus, at a frequency of 2.45 GHz, which corresponds

to a wavelength of 12.2 cm, the penetration depth exceeds 30 cm for ZnO and much

over 100 cm for Al2O3. This allows microwave heating of large ceramics bodies

much more efficiently than conventional methods.

The interaction of the electromagnetic wave at the metallic surface gives rise

to flow of currents and therefore some power is dissipated. The Maxwell equations

for the fields in the conductor are dealt by Jackson [Jac62]. For metals, the skin

depth, 6,, defined as the depth where the field is attenuated to 1/e of its surface

value, is given by

6, = [2/ooj1*]1/2 (3.35)

It can be seen that the skin depth decreases with the increase in conductivity and the

frequency of the applied microwave field. The skin depth of most of the metals

because of their high conductivity is in the order of few microns [Cor62] at the

commercially allowed frequency (2.45 GHz). The slight power dissipated occurs only

in a few microns depth, whereas most of the microwaves, since they can not

penetrate deeper, are reflected back from the metallic surface. Stainless steel has

lower conductivity (relatively higher losses) and is extensively used for domestic

microwave ovens to avoid magnetron damage when switched on without any food.

However, for industrial applications, although silver and gold have the least losses,

aluminum offers a good compromise of low cost and small skin depth [Met83].

Rate of Rise of Temperature

With the absorption of microwave energy in a material the temperature

increases. The rate of temperature increase is dependent on a number of

parameters. If the power absorbed is Pa, and the temperature of mass M kg of

material rises from ToC to TC in t seconds, then

Pav = Q/t = Mc,(T To)/t (3.36)

where Q is the heat generated and Cp is the specific heat (J/kg C) at constant

pressure. Using equation (3.31) for Pav

(T T,)/t = oeeffE2sVb /(Mcp) oC/s (3.37)

which may also be written as

(T To)/t = oeeffE2 s/(pbCp) C/s (3.38)

where Pb is the bulk density (kg/m3) of the material being heated. It can be seen

from equation (3.38) that as the bulk density of a sample decreases, i.e. it has more

porosity, the heating rate increases. However, this is true up to a certain extent only,

because with a lot of porosity the dielectric constant and the losses are going to

change. Varadan et.al. [Var88] have reported this and their data indicate higher

heating rates close to 50% porosity. The heating rates decrease as the porosity

changes significantly in either direction. The effect of porosity is a complicated issue

which in addition to the volume percent porosity includes the effect of the shape and

the distribution of the porosity as well.


In the previous chapters the area of microwave processing was introduced and

the theoretical aspects involved in microwave heating were described. Our interest

is to see how microwave heating affects the solid state reactions and mass transport

or diffusion in ceramics. It would be worthwhile at this point to briefly discuss solid

state reactions between various systems, the system selected, and a few models

proposed earlier for such reactions. Since the system selected for this study is

reported to be diffusion controlled, it seems necessary to briefly describe some of the

diffusion concepts as well. These concepts will be helpful later in the chapter on


Solid State Reactions

Solid state reactions are usually carried out by intimately mixing fine ceramic

powders and subjecting them to high temperatures. If the reaction is carried out

isothermally, the rate of formation of the reaction zone may depend on the rate of

diffusion [Kin76]. It may be the diffusion of one of the reactants or the

counterdiffusion of both reactants through the product layer. Solid state reactions

have also been studied by the formation of diffusion couples of ceramics in the

polycrystalline form as well as with single crystals. Various ceramic oxides have been

used for studying the solid state reactions either in the diffusion couple or the

powder form. These include NiO/A1203, ZnO/Al203, MgO/AI203, MgO/FezO3,

MgO/Cr2O3, MgO/TiO2 and CoO/TiO2 [Pet66 and Yam67]. The system selected

for this study is ZnO/Al203.

The ZnO-AQO3 System

The ZnO-Al203 system has appeared to be an interesting system and has been

used extensively in the powdered form for the solid state reactions studies [Bra65,

Yam67, Ram75, Ans81, Leb81 and Oka85]. Recently, the growth of zinc aluminate

on the surfaces of alumina single crystal has also been studied [Yam89]. The

reaction between zinc oxide and aluminum oxide forms a single phase compound

ZnAl204. The phase diagram (Figure 4.1 [Res64]) of these oxide ceramics shows no

solid solubility and the stable compound forms at an equimolar ratio. The reaction

proceeds according to the following equation.

ZnO + A1203 ZnAl204 (4.1)

This reaction occurs at moderately high temperatures (8000C and higher). It has

been reported by many investigators that the rate of formation of ZnAl204 from ZnO

and A1203 powders is controlled by diffusion. Furthermore, it has been demonstrated

that the overall reaction can be seen as a one-way transfer of zinc oxide to the

alumina grains with the reaction proceeding only on the alumina grains [Bra65,

Ram75, Ans81 and Leb81]. It is known that zinc oxide vaporizes at higher

temperatures [Mar67], so the reaction may be contemplated to proceed by the







0 10 20 30 40 50 60 70 80 90 100

AI 03



Figure 4.1 Phase diagram of the ZnO-Al203 system showing the
liquidus curve [Res64].

simultaneous action of solid state and evaporation-condensation mechanisms [Ans81].

However, the vaporization of ZnO may not be considered as the rate controlling step

in the formation of ZnA12O4 [Oka85].

Three types of diffusions are reported [Ram75] to be possible in the reaction

of zinc oxide and aluminum oxide powders. These are (a) bulk or volume diffusion,

occurring within the solid particles with the amount of diffusion increasing with

decrease in porosity of compacts, (b) boundary or interfacial diffusion, taking place

between the boundaries of two different solids, and (c) pore surface diffusion,

appearing predominantly on the surface of the solids, with the amount of diffusion

being directly proportional to the porosity of the compacts. In the reaction under

consideration, the percentage conversion to product is reported to increase with

decrease in particle size of aluminum oxide [Ram75]. It also increases with increase

in compaction pressure, reaction temperature and time. The decrease in the particle

size and increase in the compaction pressure correspond to a decrease in the initial

porosity of the compact. These observations indicate that bulk or volume diffusion

is prominent in the above mentioned reaction [Ram75].

Kinetic Models

The measurement of reaction rates in solid state was first attempted by

Janders [Jan27] who presented a detailed kinetic model for these processes. Since

his work many modifications of the model have appeared in the literature and new

approaches have been considered by various investigators. These models have been

described by Branson [Bra65] and Ramachandran [Ram75] and investigated for the

kinetic studies of the reaction between zinc oxide and aluminum oxide. Some of

these models which will be used later are briefly presented.

Hulbert reported [Hul69] that the growth of the product layer between two

solid reactants is generally controlled by any one of the following processes: (a)

diffusion of the reactants through the product layer, (b) phase boundary reaction and

(c) nuclei growth. The criteria of occurrence of these three processes, however, are

not very well understood.

Diffusion-controlled Reactions

The mathematical model for diffusion-controlled reactions reported in the

literature are based on the assumptions that (a) the reactant particles are spherical

and of uniform radius surrounded with the second reactant, (b) the reactant particles

are uniformly covered by a product layer and (c) the subsequent reaction proceeding

by bulk diffusion.

The earliest diffusion-controlled model was presented by Jander [Jan27]. If

r is the initial radius of the particle (Figure 4.2), y is the thickness of the product

layer, then the volume V of the unreacted material at time t, is

V = (4/3)7(r y)3 (4.2)

This volume may also be also given by

V = (4/3)7r3(1 x) (4.3)

where x is the fraction of the volume that has reacted. Combining the above two


y = r(1 (1 x)1/3)



Reactant A Reactant B

Figure 4.2 Propagation of the reaction in a spherical particle.

Using the parabolic rate law commonly observed for kinetic processes in which the

limiting step is mass transport through a reaction layer, the rate of reaction is given


K',t = (KD/r2)t = [1 (1- x)1/3]2 (4.5)

where K'j is the reaction rate constant and D is the diffusion coefficient. The

constant K is determined by details of the geometry and by the chemical potential

difference for the species diffusing across the reaction layer. The slope of the

function [1 (1 x)1/3]2 plotted against time t, gives the reaction-rate constant

equivalent to KD/r2 which is characteristic of the reaction conditions [Kin76].

There are two oversimplifications in the above model which limit the

applicability and the range over which it adequately predicts the reaction rates.

Firstly, it is valid only for a small reaction layer thickness y, because as the reaction

layer thickness increases the area at which the reaction occurs decreases. Secondly,

it does not consider the difference in volume between the reactants and the product

during the reaction process.

Valensi and Carter used the following equation to represent the rate of

formation of product taking into account the area and the volume change A.

K'vct = {A-[1+(A-1)x]2/3 (A-1)(1-x)2/3}/(A-) (4.6)

In the case of reaction between zinc oxide and aluminum oxide, the change in

volume of the product spinel is given by

A = (mass of spinel/density of spinel)/(mass of alumina/density of alumina)

and has a value of

A = (183.35/4.58)/(101.96/3.97) = 1.56.

Phase-boundary Controlled Reactions

The phase-boundary controlled model for a sphere reacting from the surface

inward, was suggested by Jach which relates the fraction of reaction completed with

time by the equation

K't = 1 (1-x)1/3 (4.7)

The solid state reaction is phase-boundary controlled when diffusion through the

product is so rapid that the reactants cannot combine fast enough at the reaction

interface to establish equilibrium.

Reactions Controlled by Nuclei Growth

Hulbert and Klawitter [Hul67] report a kinetic model based on nuclei growth

controlling the overall solid-state reaction for spherical particles. The equation for

the kinetic model for nuclei growth is given by

K't = In(1-x)2/3 (4.8)

This approach considers the nucleation of the product phase at active sites and the

rate at which the nucleated particles grow.

Mass Transport

In order for the chemical reaction to take place in condensed phases it is

essential that atoms be able to move about in the solid (single crystal or

polycrystalline). Since solid state reactions depend on the mass transport, it will be

beneficial to discuss briefly the diffusion processes and their equations which will be

useful in the chapter on discussion.

There are a number of mechanisms by which an atom can move from one

position to another in a crystal structure. It can move either by direct exchange of

positions between two atoms, or by a ring mechanism in which a closed circle of

atoms rotates. The process which is energetically more favorable is the movement

of an atom from a normal position to an adjacent vacant site. The rate of diffusion

of atoms by this process depends on the ease of moving atoms from their normal

sites to vacant sites, and on the concentration of the vacant sites. The mobility of the

atoms by this most probable mechanism in one direction is equivalent to the mobility

of vacancies in the other direction; occasionally referred to as vacancy diffusion.

Another process is the motion of atoms in interstitial sites, but the movement from

one interstitial site to another is energetically unfavorable [Kin76].

Diffusion and Fick's laws

According to Fick's first law the quantity of diffusing material which passes

per unit time through a unit area normal to the direction of diffusion is proportional

to its concentration gradient. This is represented by

J = -D(a c/ax) (4.9)

where J is the flux, D is the diffusion coefficient having dimensions of square

centimeters per second, c is the concentration per unit volume, and x is the direction

of diffusion. If D is constant and independent of the concentration, it can be written


(a c/a t) = D(d 2c/8 x2) (4.10)

which is Fick's second law.

The Nernst-Einstein Equation

Fick's laws were expressed above in terms of concentration. Einstein

suggested that the virtual force acting on a diffusing atom or ion is the negative

gradient of the chemical potential. If the absolute mobility (velocity obtained under

the action of a unit force) is B, the diffusion coefficient is given by

D = kbTB (4.11)

where kb is the Boltzmann's constant and T is the absolute temperature. The

mobility B, can be either due to chemical forces or electrical forces.

Random-walk Diffusional Processes

In the random-walk process where an atom jumps randomly in any direction

(three dimensional), if the jump frequency (average number of jumps per second) is

r and the jump distance is X, the diffusion coefficient is given by

D = (1/6) F 2 (4.12)

This result is strictly for a random-walk process with no bias or driving force in any

preferred direction. In addition to this process two more factors need consideration.

First is the geometric factor y, of the order of unity, which includes the number of

nearest-neighbor jump sites and the probability that the atom will jump back into its

original position. The second factor concerns the availability of a vacant adjacent

site. Using the fraction of vacant sites n, the diffusion coefficient is then given by


D = yx2n, P


Diffusion as a Thermally Activated Process

Consider the change in energy of an atom as it moves from one lattice site to

another by a diffusion jump across an intermediate position of high energy as shown

in Figure 4.3 [Kin76]. Only a certain fraction of atoms have sufficient energy to

overcome this barrier. The magnitude of the energy required to overcome this

barrier is called the activation energy AQ. With an increase in temperature there is

an exponential increase in the fraction of atoms which have sufficient energy to

surmount this barrier. The temperature dependence of diffusion can be represented


D = Do exp ( -AQ/RT ) (4.14)

where R is the molar gas constant and T is the absolute temperature. Considering

diffusion as a special case of more general reaction rate theory, the diffusion

coefficient D can be written as [Kin76]

D = yX2vexp (-AG/kbT) (4.15)

where AG is the free energy of formation and v is the frequency factor, which for

solids have a value of the order of about 1013/sec. Comparing it with D = y12n, r

we see that vexp(-AG/kT) is the jump frequency, r, showing an exponential

temperature dependence of the jump frequency as well as the diffusion coefficient.

Ionic Conductivity and Diffusion

Ionic conductivity and diffusion has been discussed in details in the literature

[She63, Gir64]. If an ionic crystal is placed in an electric field (or an electric

potential established across it), a current, I, flows through the crystal and the relation


0 0 0 OK
(a) (b) (c)

(a) (b) (c)

Figure 4.3 (a), (b), and (c) are schematic drawings showing the
sequence of configurations involved when an atom jumps from one
normal site to a neighboring one. (d) shows how the free energy of the
entire lattice would vary as the diffusing atom is reversibly moved from
configuration (a) to (b) to (c) [Kin76].

between the potential, E, and the current is governed by Ohm's law (I = aE). The

conductivity, a, is constant with respect to the current and the potential, but varies

with the temperature and the composition of the crystal.

The conductivity, a, for ionic crystals differs from that for metals in two

important respects. Firstly, a is much smaller for ionic crystals than it is for metals.

Secondly, a for ionic crystals increases rapidly with increasing temperature, whereas

for metals it decreases almost linearly with increasing temperature [Hum85]. Both

of these facts find their explanation in a consideration of the mechanisms responsible

for electrical conduction. In a metal, it is known that the current is the result of the

motion of the free electrons in the solid. The most important resistance to the

electronic motion arises from the vibrations of the atoms about their average lattice

positions. As the temperature increases the amplitude of the vibrating atoms

increases, thereby, colliding more with the electrons and effectively decreasing the


In ionic crystals there are no free electrons, and when the current does flow,

the charge carriers are the ions themselves. With a potential applied to the crystal,

positive ions are attracted to the cathode and the negative ions are attracted to the

anode. The current flow is based on the mechanisms for the motion of the ions,

which are provided by the point defects and are the same as for diffusion. Since

both the concentration of point defects and the mobility of point defects are low, the

conductivity in ionic crystals is much smaller than that of metals. The mobility and

the concentration of point defects rise rapidly with temperature, thus, rapidly

increasing the ionic conductivity with temperature. There is, therefore, an intimate

connection between diffusion and electrical conduction in ionic crystals and it is, in

fact, the knowledge of diffusion that allows us to understand the electrical conduction

in these crystals. The general equation relating the diffusion coefficient to

conductivity is given by [Gir64]

o/D = bCq2/kbT (4.16)

where C is the number of ions per cm3, q is the charge on the ion and b is some

numerical factor which depends on the particular mechanism of atomic migration

(for vacancy mechanism, b= 1.27, while for collinear interstitialcy mechanism, b=3,

and for noncollinear interstitialcy mechanism, b = 1.38).


Microwave energy is emerging as an attractive alternative method to

conventional heating of ceramics. So far, the emphasis has been mainly in sintering

of numerous ceramics and composites [Sut89]. The reduction in processing time and

temperature commonly reported in most papers indicate higher sintering rates.

These advantages with microwave heating are believed to be because of higher

diffusion rates induced by the microwave field [Jan88, Jan90a, Jan90b].

Although, calcination and reactions between solid are important in ceramic

processing, only a few references using microwave energy, are available in the

literature [Ahm88, Har88]. Solid state reactions, as described in Chapter 4, are

usually carried out by intimately mixing fine ceramic powders and subjecting them

to high temperatures. Under isothermal conditions, the rate of formation of the

reaction zone may depend on the rate of diffusion [Kin76].

It has been demonstrated that the reaction between ZnO and Al203 is

diffusion controlled and it proceeds only on the alumina particle by one-way transfer

of zinc oxide through the product layer [Bra65, Ram75, Ans81, Leb81]. If microwave

heating results in enhanced diffusion, it should alter the reaction rates as well. Thus,

the purpose of this work is to investigate whether there is any enhancement of the

reaction between alumina and zinc oxide using microwave energy.

The study was carried out by reacting powder mixtures of zinc oxide and

alumina by conventional as well as microwave heating. The particle size of alumina

was varied to see its effect on the reaction rate. This study also includes the reaction

of pressed pellets of zinc oxide with polycrystalline and single crystals substrates of

aluminum oxide.

The major accomplishment is the observation of an overall enhancement of

the reaction rate of zinc oxide and aluminum oxide heated with microwave energy.

Reaction of larger particle sizes of alumina with zinc oxide was more efficient with

microwave heating. However, smaller particle size of alumina did not react with zinc

oxide as efficiently as the larger particle sizes when heated with microwave energy.

The reaction layer on polycrystalline as well as single crystal alumina was

thicker with microwave heating as compared to conventional heating. There was no

difference in the reaction layer thicknesses between two different grades of single

crystal alumina heated in conventional furnace. However, by microwave heating, the

economical grade alumina single crystal having extensive lattice distortions resulted

in a thicker reaction layer.



Solid state reactions were studied in the powdered form of both alumina and

zinc oxide as well as between crystalline polycrystallinee and single crystal) alumina

and powder form of zinc oxide. For the reactions in the powder form, high purity

(>99.9%) alumina powders AKP-50, AKP-30 and AKP-15 were furnished by

Sumitomo Chemical Company, Limited. These powders have mean particle sizes of

0.18 p. (micron), 0.4 p, 0.68 pi and specific surface area of 10.6 m2/g, 7.1 m2/g and

3.6 m2/g, respectively.

The polycrystalline alumina substrates (99% pure) were furnished by 3M

company and the single crystal alumina (HEMLUX, HEMLITE & HEMCOR) were

purchased from Crystal Systems Inc. All these different grades are discs half an inch

in diameter and 0.020 inch in thickness, cut on the (0001) orientation and polished

on both sides. HEMLUX is the superior grade sapphire with minimal light scattering

and/or lattice distortion. HEMLITE is a standard optical grade with some light

scattering and/or lattice distortion. HEMCOR is a versatile economical grade with

extensive light scattering and/or lattice distortion.

Chemically pure (99.9%) laboratory grade zinc oxide which had average

particle size of 0.3 pi was purchased from Aldrich Chemical Company and used in the

reaction studies.

Sample Preparation

Equimolar mixtures of alumina and zinc oxide were prepared by wet mixing

in deionized water for 30 minutes. Small zirconia milling media was used to ensure

proper mixing of the powders. The mixture was then dried in a Blue M Stabil-Therm


The powder mixture was weighed in a fused quartz crucible and placed either

in the microwave oven or the conventional furnace for a specific amount of time at

a specific temperature.

Specimens weighing 4 grams were pressed in a Carver Laboratory Press to

pressures ranging from 2000 psi to 8000 psi to see the effect of compaction on the

solid state reaction of zinc oxide and alumina. In the microwave oven the

thermocouple was placed in contact with the pellets for temperature monitoring and


In case of the polycrystalline or single crystal alumina, the specimens were

sandwiched in pellets of 2 grams of zinc oxide pressed at 4000 psi. These were then

placed in 10 gms of zinc oxide powder in fused quartz crucible and placed in either

the microwave oven or the conventional furnace for the heating interval.

Experimental Set Up

Conventional heating of the specimens was carried out in a Lindberg box

furnace. The furnace was preheated to the desired temperature and the reactant

mixture was placed in the furnace. At the end of the reaction period, samples were

removed from the furnace and allowed to cool in air.

The thermocouple set up installed in the microwave oven was used in the

conventional furnace in contact with the sample to verify the temperatures read by

two thermocouples, which showed identical readings.

In case of the pressed samples, the actual sample was placed on another

similar pressed sample of the same composition to avoid any contamination on the

base of the sample.

Microwave heating was carried out in a Raytheon Radarline Multimode

Microwave oven Model QMP 2101A-6 operating at 2.45 GHz capable of delivering

a maximum power of 6.4 KW. The set up is shown in Figure 6.1. This unit is

basically similar to the kitchen model except that the number of operational

magnetron tubes (each delivering 800 watts) can be increased to eight (8x800= 6,400

watts) for high power industrial applications. The power from each magnetron tube

is delivered individually through eight port into the 32x32x24" cavity. Each port is

equipped with a mode stirrer to provide uniformity of microwaves in the cavity. The

power from all magnetron tubes can be pulsed to a desired duty cycle to have further

control on the power delivered. This unit was further modified in-house, in

consultation with the manufacturing engineers at Raytheon, to monitor the

temperatures with an inconel shielded K-type thermocouple and an optical


--=^------ 3---


Figure 6.1 The Raytheon Radarline Microwave Oven (2.45 GHz, 6.4 kW Max.)
showing the installation of the thermocouple and the optical pyrometer temperature
controllers. The sample is placed inside the susceptor.

pyrometer. Temperature controllers in conjunction to the thermocouple and the

optical pyrometer have been installed in-house to provide a feedback loop to control

the temperature defined by the temperature controllers. However, only the

thermocouple was used for this study, which was placed in contact with the sample.

The figure also shows a susceptor (alumina insulation lined on the inside with

SiC which is an excellent absorber) in the microwave oven. Since alumina and zinc

oxide do not couple very well at room temperature the susceptor assists the mixture

powder to attain higher temperatures. Once the sample mixture exceeds the critical

temperature defined in chapter 2, the sample starts coupling with microwave energy

and can be taken to the desired temperature. At this stage, although the main

contribution in heating the sample is by microwave energy passing through the

susceptor, there is still some contribution by the radiant heat from the susceptor.

Usually, the temperature on the surface of the sample is lower than the temperature

in the interior because of radiant losses at the surface. With the susceptor around

the sample one gets uniform heating with almost no temperature gradient within the

sample. This has been established in our laboratory on ultra-rapid sintering of

alumina with microwave hybrid heating [D690a, D690b, D690c, Cla91].


Quantitative X-ray Analysis

Quantitative x-ray analysis was used to ascertain the extent of reaction by

determining the amount of spinel formed. A Philips Automated Powder

Diffractometer System Model APD-3720 was used with the generator setting of 40

kV & 20 mA, copper radiation and a scan speed of 1.2 degree per minute.

A unified matrix-flushing method for quantitative multicomponent analysis

reported by Frank H. Chung [Chu74a-c, Chu75] was used. In this method the

calibration curve procedure is shunted and all components can be determined. The

weight fraction of any component in a multicomponent system is expressed in terms

of the intensity ratios Ii/Ij and k-ratios (ki/kj = Ii/Ij). The use of the intensity ratio

makes it immune to many sources of errors [Chu74a].

Zinc oxide and aluminum oxide powders were mixed in appropriate ratio,

heated in either the conventional furnace or microwave oven and the product

prepared for quantitative multicomponent x-ray analysis. Occasionally, preferred

orientation was observed in some samples. These samples were run again to

alleviate error in peak intensities. The intensities of the 002 plane, 104 plane and

311 plane were used respectively for zinc oxide, aluminum oxide and zinc aluminate


Differential Thermal Analysis (DTA)

Differential thermal analysis (DTA), as the name implies, is a techniques

which uses the difference in temperatures of a known inert material and the

specimen under investigation. The inert reference material and the sample are

heated at a fixed rate. The changes in the sample, such as the decomposition,

oxidation, crystallization, crystalline phase changes or chemical reactions result in

absorption (endotherm) or release (exotherm) of heat. Since the inert material

(reference) does not undergo any change, there is a difference in temperature of the

reference and the specimen, which helps to identify the phenomena mentioned


A Simultaneous Differential Thermal Analyzer/Thermogravimetric Analyzer

from Harrop Industries Model ST-736, was used to analyze the reaction between zinc

oxide and aluminum oxide. Equal amounts of both the mixtures AKP-50 + ZnO and

AKP-15 +ZnO were used for the thermal analysis of the reaction, with a heating

rate of 10C/minute for both the cases.

Contact Angle

Contact angle measurement is one of the simple, non-destructive techniques

which gives information on the outermost layers of solid surfaces. It is useful in

characterizing solid/liquid interfaces by the extent of wetting of solid surface by the

liquid. Figure 6.2 indicates the interfacial energies for a liquid on a solid surface.

The contact angle is related to solid-vapor (Ysv), solid-liquid (Ys,) and liquid-vapor

(y1,) interfacial free energies by the Young equation [Ree88]

coso = (sv Ysi)/Ylv (6.1)

Contact angle on single crystal alumina were measured on a Rame-Hart contact

angle Gonimeter at room temperature with distilled water. A microsyringe was used

to form the liquid drop on the surface of the sample. Typically six contact angles

were measured on both sides of the drop and were averaged.


Figure 6.2 Interface energies for a liquid on a solid surface.

To detector

Crystal (n ) 2 -
Sample (n1) ---. >

---- Sample (n)

From IR

Figure 6.3 A typical optical illustration for attenuated total reflectance
(ATR) spectroscopy.


The application of infrared spectroscopy to the identification of organic

compounds is well established and widely used. Infrared spectra of organic

compounds generally exhibit sharp well-defined bands, assignable to the vibrations

of individual functional groups of which the molecule is comprised. However, the

infrared spectra derived from inorganic compounds usually have absorption bands

that are broad and overlapping, making assignments and the specific identification

of a cation-anion pair more difficult. Nevertheless, IR spectroscopy has a long

history in characterization of numerous oxides [McD64], spinels [Pre71] and minerals

[Gad75]. The frequency at which a material absorbs infrared energy depends upon

the internal vibrations of the molecules and composition and hence can be

distinguished from one another.

Fourier-transform infra-red (FT-IR) with attenuated total reflectance (ATR)

was used to characterize the surfaces of the single crystal alumina, before and after

heating these single crystals in zinc oxide. Figure 6.3 shows a schematic optical

diagram for ATR spectroscopy. The capabilities of the FT-IR/ATR to analyze the

surface layer is due to the penetration of IR light and total reflection from the

internal reflecting element (IRE) crystal/sample interface into the sample. The

depth at which the IR beam decays to 1/e of its initial value is defined as the depth

of penetration Dp and given by the relation

D =2n(sn /2 (6.2)
2Kn,(sin2 -/nz/)1/2

where ; = wavelength of the IR radiation

n1 = refractive index of the IRE crystal (KRS-5 = 2.38)

n2 = refractive index of sample

0 = angle of incidence and exit of IR beam.

The surface depths probed usually range from 0.5 to 3 jI depending on 1, nj, n2 and

0, which is certainly more than expected depth of zinc oxide diffusion into the crystal.

The depth of penetration of IR radiation, because of the high frequency or shorter

wavelength, is much less than the microwaves (please see page 55).

The FT-IR/ATR spectra were obtained with a Nicolet 60SX spectrometer

using a parallelogram KRS-5 crystal. Two samples were pressed against the crystal

which had the entrance and exit face angle of 45. Typically 100 scans at a resolution

of 0.5 cm-1 were averaged. All data processing was done with the standard Nicolet

software provided with the instrument.

Scanning Electron Microscopy (SEM) and X-ray Mapping

It was intended to determine the width of the reaction layer by electron

microprobe analysis using the JEOL Superprobe 733. Since the reaction width was

only of the order of a micron, equivalent to the step for microprobe, the Jeol

Superprobe was used only for secondary electron images, backscattered electron

image and x-ray mapping for the concentration of zinc in the polycrstalline and single

crystal alumina.

Secondary Ion Mass Spectrometry

Secondary ion mass spectrometry (SIMS) is among the major techniques of

surface analysis and microstructural characterization of solids and is particularly

noted for its outstanding sensitivity of chemical and isotopic detection. Quantitative

or semi-quantitative analysis can be performed for small concentrations of most

elements (including the lightest) in the periodic table. However, the high versatility

of SIMS is mainly due to the combination of high sensitivity with good topographic

resolution both laterally and in depth.

Secondary ion mass spectrometry is based on the bombardment of the sample

surface by focused primary ions sputtering the outermost atomic layers. The ionized

secondary species (atoms, molecules, clusters) undergo mass spectrometric separation

according to their mass-to-charge ratio. The separated secondary ions are collected

as quantifiable mass spectra, as in-depth, along-surface profiles, or as distribution

images of the sputtered surface.

The primary ions are normally produced by a gas source (argon) which are

accelerated and focused to a selected area on the specimen. The collision cascade

following the incidence of a primary ions results in the emission of secondary ions

which are extracted into the mass spectrometer based on electric/magnetic deflection

fields. Secondary ions with given mass-to-charge ratio and within a certain interval

of kinetic energy are collected for pulse or current measurements and data


As indicated above, along-surface profiles and distribution images are possible,

however, the non-imaging ion probes are used for the depth profiling on laterally

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