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This is to certify that the

dissertation entitled

Microwave Processing of Ceramics and Ceramic Composites
Using a Single-Mode Microwave Cavity

presented by

Ki-Yong Lee

has been accepted towards fulfillment
of the requirements for

Ph.D. degree in Materials Science

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1m mm“

MICROWAVE PROCESSING OF CERAMICS AND CERAMIC
COMPOSITES USING A SINGLE-MODE MICROWAVE CAVITY

By

Ki-Yong Lee

A DISSERTATION

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Department of Materials Science and Mechanics

1998

ABSTRACT

MICROWAVE PROCESSING OF CERAMICS AND CERAMIC COMPOSITES
USING A SINGLE-MODE MICROWAVE CAVITY

By

KI-YONG LEE

This research seeks i) to use a single-mode microwave cavity to process ceramics
and ceramic based composites, ii) to study the conditions or parameters needed to
successfully apply the microwaves to processing of materials, and iii) to study the
interactions between materials and microwaves.

In sintering studies, alumina ceramics and alumina matrix 10wt% zirconia
composites were microwave-heated between 1500°C and 1600°C giving a density of
about 96% up to nearly 100% of theoretical without ‘thermal runaway’ or cracking. The
density, hardness, and toughness for individually- and batch-processed specimens were
relatively uniform with respect to the cavity mode and specimens’ location inside the
insulation called ‘casket’ during microwave heating. For example, the mean and standard
deviation of the hardness was 16.19 GPa i 0.58 GPa for a total of 24 alumina specimens
microwave-heated in batches of 6 specimens each. This corresponds to a coefficient of
variation of only 0.036.

Microwave power was successfully utilized to burn out organic binder from ceramic

powder compacts without cracking the specimens and without using any insulation

 

Lo

material to enclose the specimens. The extent of binder bum-out significantly depended
on material composition due to the dielectric properties of each material. For example,
A1203/10wt% SiC burned out the binder more successfully than either monolithic
alumina or alumina containing 10wt% zirconia.

In a joining study, ceramic materials and glass ceramics were successfully joined
using a spin-on material interlayer under ambient or low externally applied pressures.
Notches of submillimeter dimension were made in the specimens prior to joining. During
the joining process the notch dimensions changed by no more than a few percent.

In addition, this study revealed that compared to conventional heating, microwave
heating has remarkable effects in crack healing. For alumina specimens with initial
Vickers cracks about 350nm long, the cracks were nearly completely healed by
microwave heating at 1742K, while conventional heating healed the identical cracks by
only about 40% to 50% of the initial crack length.

In microwave hybrid heating utilizing a casket, the casket plays an important role.
The measured steady-state inner wall casket temperature, Ti, varied from about 1100°C to
1500°C depending on the casket geometry at 600 Watts input power. In addition, for a
microwave input power of 200 Watts to 700 Watts, Ti ranged from 740°C to 1574°C
depending on a combination of casket geometry and microwave power. Based on the
experimental data, a simple model equation was developed to describe Ti in terms of the
casket geometry and the microwave power level. A least-squares fitting indicated that
the model equation well described the experimental data obtained in this study. The R2,
coefficient of determination value was 0.954 for all 144 data used for fitting without

grouping the data.

To

the memory of my deceased father, Duk-Ho Lee.

ACKNOWLEDGMENTS

I would like to thank my adviser, Professor Eldon D. Case for providing me the
opportunity to perform this research and to continue my graduate studies under his
direction. His continuous encouragement, guidance, advice, and support were invaluable
to the completion of this work. It was a joy to work together with Dr. Case. Every
moment we spent on working together will be remembered in my heart forever.

My thanks are extended to Dr. Asmussen, Dr. Bieler, and Dr. Eick for being my
committee members. In particular, Professor Asumssen’s academic counsel and financial
support throughout this work are greatly appreciated.

Special thanks should go to Brett Wilson for the help with lab apparatuses and for
the instruction with lab skills. I would like to appreciate the help of Jong-Gi Lee,
Benjamin Tyszka, Martin Traub, Kiersten Seiber, Luke Cropsey, and Paul Dearhouse on
some of work included in this thesis. I also thank Ung-Sik Kim, Bo-Keun Kim, and
Mark Perin for the helpful discussion.

I gratefully thank my mother, Jung-Sook Kang and my deceased father, Duk-Ho
Lee who gave me their endless love, care and support. Finally, I wish to thank my wife,
Sun-Hee Lee, my daughter, Mee-Sul, and my son, Dong-Hoon for their love and
understanding. Especially, without my wife’s patience and encouragement, I could not

have completed this work.

TABLE OF CONTENTS

LIST OF TABLES

LIST OF FIGURES

INTRODUCTION
1. Goals of This Study
1.1. For Sintering
1.2. For Binder Bum-out
1.3. For Joining
1.4. For Crack Healing
1.5. For Thermal Etching
1.6. For Effect of Casket Geometry on Microwave Heating
2. General Literature Review
2.1. Differences between microwave and conventional heating
2.2. Fundamentals of microwave heating
2.2.1. Interactions between microwaves and materials
2.2.2. Variation of dielectric properties with temperature and
the relation between that variation and thermal runaway
2.2.3. Heating behaviors of dielectric materials
3. Theoretical Background for Microwave Heating
3.1. Flow of electromagnetic power and power dissipation within
a dielectric material
3.2. Skin depth and power penetration depth
3.3. Microwave applicators
3.4. Microwave cavity equivalent circuits and quality factor
3.5. Notation for microwave modes in a cylindrical microwave cavity
3.6. Mode diagram for 7" ideal cylindrical single-mode microwave
cavity

CHAPTER 1

SINTERING

Part I. Sintering of Alumina Ceramics in a Single Mode Cavity under
Automated Control

vi

Page

QGMA-waNNv-t

71

71

1. Introduction
2. Experimental Procedure
2.1. Experimental apparatus
2.2. Materials
2.3. Microwave sintering
3. Results and Discussion
4. Conclusions
Part 11. Grain Size, Density and Mechanical Properties of Alumina Batch
-Processed in a Single-Mode Microwave Cavity
1. Introduction
2. Experimental Procedures
3. Results and Discussion
4. Summary and Conclusions
Part III. Microwave Sintering of Alumina and Alumina Matrix Zirconia
Composites Using a Single-Mode Microwave Cavity
1. Introduction
2. Experimental Procedures
2.1. Materials and specimen preparation
2.2. Microwave sintering
3. Results and Discussion
3.1. Microwave sintering of alumina
3.2. Microwave and conventional sintering of alumina/10wt% zirconia
3.3. Grain size and mass density as a function of the cavity mode and
the radial position within the AKP30 alumina specimens.
3.4. Casket-microwave interactions
3.4.1. Local hot spots in the casket wall
3.4.2. Local melting in the casket end-plates
4. Summary and Conclusions

CHAPTER 2
BINDER BURN-OUT
Part I. Microwave Sintering of Ceramic Matrix composites and the Effect
of Organic Binders on the Sinterability
Introduction
Experimental Procedure
Results and Discussion
4. Summary and Conclusions
Part II. Binder Bum-out in a Controlled Single-Mode Microwave Cavity
1. Introduction
2. Experimental Procedure
2.1 . Materials and specimen preparation
2.2. Experimental apparatus
2.3. Microwave binder bum-out
3. Results and Discussion
3.1. Microwave binder bm'n-out using a fixed input power level

9’9)?"

vii

 

 

71
73
73
75
75
76
78
81

81
82
86
93
97

97
99
99
101
108
108
110

114
116
116
118
122

126

126

127
128
136
142
146
146
147
147
148
148
150
150

 

3.2. Microwave binder burn-out using a stepped input power level
sequence
4. Conclusions
Part III. Microwave Binder Burn-out for Batch Processing of A1203,
A1203/SiC Platelet, and Ale3/Zr02 Particle Powder COMPACTS
1. Introduction
2. Experimental Procedure
3. Results and Discussion
3.1. Binder removal using fixed input power
3.2. Binder removal using stepped input power
4. Conclusions

CHAPTER 3
JOINING
Part 1. Microwave Joining and Repair of Ceramics and Ceramic Composites
1. Introduction
2. Ceramic-Ceramic Joining: Background
2.1. Ceramic-ceramic joining using conventional heating
2.2. Ceramic-ceramic Joining via microwave processing
3. Experimental Procedure
3.1 . Materials and specimen preparation
3.2. Microwave joining and crack healing
4. Results and Discussion
5. Conclusions
Part II. Microwave and Conventional Joining of Ceramic Composites
Using Spin-On Materials
Introduction
Experimental Procedure
Results and Discussion
Summary and Conclusions

99’1”!"

CHAPTER 4
CRACK HEALING
Part I. Diffusive Crack Healing Behavior in Polycrystalline Alumina:
A Comparison Between Microwave Annealing and Conventional
Annealing
1. Introduction and Background
2. Experimental Procedure
3. Results and Discussion
4. Summary and Conclusions

viii

152

155
158

158
159
162
163
164
167

170

170
170
171
171
172
172
172
173
174
178
182

182
183
187
194

197

197

197

199

201
210

 

CHAPTER 5
EFFECT OF CASKET GEOMETRY AND MICROWAVE POWER ON
MICROWAVE HEATING
Part I. The Steady-State Temperature as a Function of Casket Geometry
for Microwave-Heated Refractory Caskets
1. Introduction
2. Relation to Previous Work
2.1. Caskets and insulation used in ceramic processing
2.2. Thermal modeling of microwave heating
2.3. Key innovations and differences from previous work
3. Experimental Procedure
3.1 . Materials
3.2. Refractory casket construction
3.3. The microwave cavity, power supply, and associated apparatus
3.4. Heating of microwave caskets
4. Model for the Dependence of Steady-State Casket Temperature
upon Casket Geometry
5. Results and Discussion
5.1 . Dependence of the steady-state casket temperature
on casket geometry
5.2. Comparison of steady-state temperature and heating rate
for empty casket and casket with a processed material
5.3. Dependence of heating characteristics on microwave
cavity modes
6. Conclusions
Part II. Steady-State Temperature of Microwave-Heated Refractories
as a Function of Microwave Power and Refractory Geometry
1. Introduction
1.1. Background
1.2. Authors’ previous analytical model for refractory casket heating
2. Experimental procedures
2.1. Casket construction
2.2. Microwave processing apparatus
2.3. Microwave heating of caskets and temperature measurements
3. Results and Discussion
3.1. The inner and outer wall steady-state casket temperatures
3.2. Further development of the refractory casket heating model
3.3. Least-squares fitting of the steady-state temperatures to the
extended model
4. Summary and Conclusions

 

 

215

215

216
217
217
218
220
222
222
225
226
231
233

247
247

259

261

262
270

270
270
271
276
276
279
280
281
281
285
286

290

 

Gilli
Hill;
iii 4

i

int“.

lU\il

CHAPTER 6
THERMAL ETCHING

Part I.

Part II.

An AFM Study of Thermally-Induced Grain-Boundary Grooving
in Polycrystalline Alumina: Part I, Groove Profile, Width, and Depth

An AFM Study of Thermally-Induced Grain-Boundary Grooving
in Polycrystalline Alumina: Part II, Groove Angle, Surface
Energy, Surface Diffusivity

CONCLUSIONS

5"?pr

SINTERING

BINDER BURN-OUT

JOINING

CRACK HEALING

EFFECTS OF CASKET GEOMETRY AND MICROWAVE POWER
ON MICROWAVE HEATING

297
297
299
300
301
302

.llllll

lPPlll

lPPiV.

APPENDICES

APPENDIX A. Microwave Processing Apparatus

APPENDIX B. Properties of Refractory Materials used for

Microwave Processing

Appendix B-l . Zirconia Insulating Cylinder, Type ZYC
Appendix B-2. Alumina Insulating Board, Type SALI
Appendix B-3. Alumina Insulating Board, Type SALI-2

APPENDIX 1. Sintering

APPENDIX 11. Ceramic/Binder Compact Specimens Heated

in a Micrwoave Cavity

Appendix II-l . Raw data for batch-processed binder burn-out

APPENDIX III. Joining

APPENDIX IV. Crack Healing

APPENDIX V. Data for Refractory Heating Study and Additional Study
Appendix V-l . Additional raw data for refractory heating study
Appendix V-2. Electromagnetic mode identification and heating

PPN!‘

5.

characteristics of caskets in various microwave modes in a
cylindrical single-mode microwave cavity

Reflected power measurements at low and high input power

Electric field probe measurements

Heating of microwave caskets

Results and discussion

4.1. Measurements of reflected power as a function of cavity
height, for low and high power levels

4.2. Determination of relative radial component of electric field
strength, 13,, around the cavity wall in various modes

4.3. Dependence of heating characteristics on microwave cavity
modes

Conclusions

APPENDIX VI. Thermal Etching

xi

304
305
307
307
308
309
310
312
315
316
317

318
321

322
325
328
329
331
334

334

LIST OF TABLES

Table Number Page
Introduction
Table 1. Frequency allocation for industrial, scientific, and medical 13
applications and areas permitted [3 9].
Table 2. Heating characteristics and resistivities for minerals, chemicals, 19
and metal powders heated by microwave power of 2.45 GHz
[50,51]. The materials were heated for 7 minutes or less at
microwave input power levels ranging from 500 Watts to 2000
Watts in a rectangular aluminum waveguide [51].
Table 3. Dielectric properties of various ceramics at room temperature 22
(25°C) [54].
Table 4. Dielectric properties of ceramics (at 1 MHz, room temperature) 23
[48].
Table 5a. Power penetration depth, Dp, for various ceramic materials [39]. 40
Table 5b. Effect of temperature on power penetration depth, Dp, in hot 42
pressed boron nitride with the critical temperature, Tc z 700°C [3 9].
Table 6. Values of (a) PM and (b) Q“m which are used to calculate resonance 62
frequencies for TM.“m and TE“m modes, respectively.
Table 7. Data for resonant frequency versus resonant length of idea] 7" empty 64
cylindrical cavity.
Chapter 1
Part I
Table 1. Results on microwave sintered alumina. 78
Part II
Table 1. Summary for microwave processing during batch processes. 85

xii

it»?

Table 2.

Density and grain size in terms of cavity modes and specimen
location.

Part 111
Table 1. Summary of microwave sintering of aluminas.
Table II. Summary for microwave processing of four AKP30 alumina
specimens each in different cavity mode.
Table 111. Summary of sintering of zirconia using microwave and
conventional means.
Table IV. Density and grain size measurements for alumina specimens in
terms of cavity modes and locations of individual specimens.
Chapter 2
Part I
Table 1. Summary of microwave processing done in this study.
Part II
Table 1. Summary of microwave binder burn-out done in this study
Chapter 3
Part H
Table 1. Thickness of the as-cured silica film as a function of spirming speed.
Table 11. Dimensions of notches before joining and afier joining.
Chapter 4
Part I
Table 1. For each of the three heating modes used in this study, the activation
energy, Q, and constant C (equations 2-4) calculated from the slopes
and intercepts of the curves in Figure 3.
Chapter 5
Part I
Table 1. Volume and dimensions of each casket used in this study.
Table 2. Composition, density, and porosity of the insulation used for
caskets in this study [3 8].
Table 3. Measured outer casket wall temperature, To, for caskets 5 - 12.
Table 4. Summary for the cavity short position (i.e. cavity height), L5,
as a function of the electromagnetic resonance cavity mode,
determined at a microwave input power of 50 Watts.
xiii

90

100

100

105

115

135

149

189

193

207

223

224

230

232

Table 5.

Table 6.

Table 7.

Table 8.

Table 9.

Table 10.

Part II
Table 1.

Table 2.

Table 3.

Appendices

Table B-l-l .
Table B-1-2.
Table B-1-3 .

Table B-2-1.

Input power, P, reflected power, P,, and power density, pubs,
for various caskets at a fixed input power of 600 Watts.

Least-squares coefficients and coefficient of determination (R2)
determined by fitting the casket heating data of the caskets
in Group 1, 2, and 3 to equation 14.

Least-squares coefficients and coefficient of determination (R2)
determined by fitting the casket heating data of the caskets
in Group 2 to equation 15.

Least-squares coefficients and coefficient of determination (R2)
determined by fitting the casket heating data of the caskets
in Group 1, 2, and 3 to equation 24.

Average heating rate, measured temperatures, temperatures
predicted by equation 24, and residuals for the least-squares fit
to the data for the entire set of empty caskets.

Comparison of the heating characteristics for two empty caskets
and the same two caskets with specimens.

Dimensions of the individual refractory caskets used in Paper 1 [1].

b, 3, LT, LSA, L2,, L2, are as defined in equation 5. V3,, and V2,
are the volume of the SALI aluminosilicate end plates and the
volume of the zirconia cylinder, respectively.

Dimensions of individual refractory caskets used in this study,
where b, a, LT, LSA, L2,, L2, are as defined in equation 5. VSA and
V2, are the volume of the SALI aluminosilicate end plates and the
volume of the zirconia cylinder, respectively.

Least-squares fitted constants C1, C2, and C3, and the coefficients

of determination, R2, values obtained by fitting the Ti, PC and
geometry data from this study and from Paper 1 [1] to equation 9.

General characteristics and properties
Thermal conductivity
Properties of zirconia fibers contained in Type ZYC

General characteristics & properties

xiv

236

239

239

243

258

260

277

279

288

307

307

308

308

— a

Ll.

 

Table B-2-2.
Table B-3-1.
Table B-3-2.

Table II-4-1.

Table II-4-2.

Table IV-l.

Table V-1-1.

Table V- 1 -2.

Table V-1-3.

Table V-2-1.

Table V-2-2.

Table V-2-3.

Table v-2-4.

Table V-2-5,

Thermal conductivity
Characteristics & properties
Thermal conductivity

Change in wt% of specimen using a fixed input power sequence
as a function of power and heating time.

Change in wt% of specimen using a stepped input power sequence
as a frmction of power and heating time.

Raw data for crack healing study. Anneal time is fixed at 1 hour.

The inner casket wall temperature, T,, and the casket outer wall
temperature, To, measured as a function of microwave input
power level, P,, for refractory caskets which has b/a = 1.33. L7 is
the total casket length.

The inner casket wall temperature, T,, and the casket outer wall
Temperature, To, measured as a function of microwave input power
level, P,, for refractory caskets which has b/a = 1.50. LT is the total
casket length.

The inner casket wall temperature, T,, and the casket outer wall
Temperature, To, measured as a function of microwave input power
level, P;, for refractory caskets which has b/a = 2.00. LT is the total
casket length.

Geometry and composition of the zirconia/aluminosilicate caskets
employed in this study

Summary for the cavity short position (i.e. cavity height), L5, as a

function of the electromagnetic resonance cavity mode, determined
at a microwave input power of 50 Watts.

Summary of the heating behavior of Casket 1 (Table V-2-2)
for various electromagnetic cavity modes.

Summary of the heating behavior of Casket 2 (Table V-2-2)
for various electromagnetic cavity modes.

Summary of the heating behavior of Casket 3 (Table V-2-2)
for various electromagnetic cavity modes.

XV

309

309

309

315

315

317

318

319

320

322

326

335

335

336

Table V-2-6.

Table V-2-7.

Table VI-l.

Summary of the heating behavior of Casket 4 (Table V-2-2) 336
for various electromagnetic cavity modes.

Temperatures and heating rates averaged for various cavity 337
modes tuned to heat each type of casket.

Surface diffusion coefficients, D5, calculated using equations 8 342
and 10 (Chapter 6, Part 11) based on measurements of the groove

depth & angle, the groove width, and the measured groove depth

& angle, calculated by equation 7 (Chapter 6, Part II), respectively.

xvi

LIST OF FIGURES

Figure Number
Introduction

Figure 1. Heating patterns in conventional (a) and microwave furnaces

(b) [28]-

Figure 2. Temperature gradients generated during conventional (a) and
microwave (b) heating of materials [29].

Figure 3. Density versus temperature of microwave (28 GHz) and
conventionally sintered MgO doped alumina [31].

Figure 4. (a) The apparent activation energies for microwave (28 GHz) and
conventionally sintered MgO doped alumina [31] and (b) the
apparent activation energies for microwave (28 GHz) and
conventional grain grth of MgO doped alumina [37].

Figure 5. Interaction of microwaves with materials at ambient temperature
[28].
Figure 6. Variation of (a) relative dielectric constant and (b) relative

effective dielectric loss factor with frequency [46-48]. Loss peaks
shown at frequencies of 102, 109, 1013, and 10 7 Hz correspond
to mechanisms, respectively.

Figure 7. Dipolar reorientation in an applied electric field can result in
heating [39].

Figure 8. Typical variations of e,’ (a) and tan8 (b) for aluminas as a function
of temperature [40,54].

Figure 9. Effect of microwave input power on heating rate of various

chemicals and minerals [51].

Figure 10. Schematic of the types of Response of materials to microwave
heating [28].

xvii

Page

10

11

15

15

18

21

26

27

or!

Figure 11.

Figure 12.

Figure 13.

Figure 14.

Figure 15.

Figure 16.

Figure 17.
Figure 18.
Figure 19.
Figure 20.
Figure 21.
Figure 22.
Figure 23.

Figure 24.

Chapter 1
Part I

Figure 1.

Figure 2.

Figure 3.

A volume V, enclosed by the closed surface S, containing fields
E, H, and current sources .73, 1171, [38].

E and I7 fields of a uniform transverse electromagnetic plane
wave [62].

Skin depth of electric field intensity and power penetration depth
[28,39].

Methods of exciting wave modes in a resonator [60].

(a) A series RLC circuit equivalent to a microwave resonator and
(b) a resonant circuit connected to an external load, RL [3 8].

Cylindrical coordinate system used for notation of microwave
cavity modes.

Notation for TMnm. modes for a cylindrical micrwavoe cavity.
Notation for TEN“. modes for a cylindrical microwave cavity.
Field distributions of TE)“, TEmz, TE; 1 1, and TE] [2 modes.
Field distributions of TE. 13, TEzn, TEm, and TE311 modes.
Field distributions of mo“, TM012, and TM013 modes.

Field distributions of mm and TM, 12 modes.

Bessel function of the first kind, for order n, where n = 1, 2, 3.

Mode diagram for 7" ideal cylindrical single-mode microwave
cavity.

Schematic of microwave sintering apparatus.

Heating schedule (a) and a plot of temperature vs. forward power
(b) for AKP-30 and AKP-SO.

Heating schedule (a) and a plot of temperature vs. forward power
(b) for Alcoa A16-SG.

xviii

29

34

38

43

44

52

53

54

56

57

58

59

62

63

74

77

77

Part II

Figure 1.

Figure 2.

Figure 3.

Figure 4.

Figure 5.

Part III

Figure 1.

Figure 2.

Figure 3.

Figure 4.

Figure 5.

Figure 6.

Schematics for electromagnetic field patterns of the indicated
microwave cavity modes. Solid lines represent electric fields (E)
and dotted lines represent magnetic fields (H).

Schematic for casket used for microwave heating showing the
positions of the six disc-shaped powder compact specimens
included in each processing batch.

Heat distribution inside empty casket (Figure 2) as determined by
thermally sensitive paper. The casket was heated in each cavity
mode (a) for 5 minutes at 130 Watts, (b) for 1.5 minutes at 90
Watts, (0) for 2 minutes at 90 Watts, and (d) 4 nrinutes at 170
Watts. The dark areas in (a)-(d) indicate regions of microwave
heating.

Hardness (a) and fracture toughness (b) for batch-processed
alumina specimens in terms of specimen position. Error bars
represent the standard deviation.

Hardness (a) and fracture toughness (b) for batch-processed
alumina specimens in terms of cavity mode. Error bars
represent the standard deviation.

Schematic of microwave processing apparatus.

Schematic of a casket and the disc-shape powder compact
specimen about 5 cm in diameter.

Heating schedules for (a) microwave heating of alunrinas, and (b)
microwave heating and conventional heating of AKP50/10wt%
zirconia composite specimens.

Schematic for microwave sintered AKP30 almnina specimen
used to examine the uniformity in grain size and density along
the diameter, showing the locations of sections A, B, and C.

Fracture surfaces of microwave sintered aluminas: (a) AKPSO,
(b) AKP30, and (c) A16SG.

Relative densities of AKP50/10wt% zirconia composites densified

by nricrowave heating and conventional heating as a function
of temperature.

xix

84

85

88

91

92

102

103

106

108

109

110

Figure 7.

Figure 8.

Figure 9.

Chapter 2
Part I

Figure 1.

Figure 2.

Figure 3.

Figure 4.

Figure 5.

Figure 6.

Part 11
Figure 1.

Fracture surfaces of AKPSO/l Owt% zirconia sintered (a) by
microwave at 1550°C for 20 minutes, (b) by microwave at 1450°C
for 20 minutes, and (c) by conventional furnace at 1450°C for 20
minutes.

X-ray diffraction patterns of AKPSO alumina powder, zirconia
powder, and microwave sintered AKPSO/ l Owt% zirconia.

Schematics of the caskets showing melted area of the SALI
insulation (a) when SALI was used as a specimen setter, and
(b) when SAFFIL was used as a specimen setter.

Schematic of the experimental apparatus.

For fixed input power level (without a susceptor), change in wt%
of the A1203/Zr02/binder compact specimens as a firnction of time
and input power level. The weight loss corresponds to binder
burn-out.

Electromagnetic field distribution for a single mode cylindrical
circular cavity [5, 11, 20].

For stepped power levels (with a susceptor), change in wt% of
specimens and the input microwave power schedule used to heat
the A1203/Zr02/binder specimens. The weight loss corresponds to
binder burn-out.

Heating schedule for binder removal and sintering of an A1203-Zr02
ceramic composite using the one-step process discussed in the
Experimental Procedure section. In Table 1, this specimen is
designated having a 10.26 wt% decrease.

Fracture surface of microwave sintered 90 wt% AKP-SO alumina and
10 wt% zirconia composite (Bar represents a length of one micron).
In Table 1, this specimen is designated having a 10.26 wt% decrease.

For fixed input power level, change in wt% of the A1203/binder
compact specimens as a function of time and input power level.
The weight loss corresponds to binder burn-out. The symbol ‘C’
indicates that the specimen cracked.

112

113

120

133

136

138

139

141

142

151

Figure 2.

Figure 3.

Figure 4.

Part 111
Figure 1.

Figure 2.

Figure 3.

Chapter 3
Part I

Figure 1.

Figure 2.

Figure 3.

Figure 4.

For fixed input power level, change in wt% of the A1203/SiC/binder
compact specimens as a function of time and input power level.
The weight loss corresponds to binder burn-out. The symbol ‘C’
indicates that the specimen cracked.

For stepped power levels, change in wt% of specimens and the
input nricrowave power schedule used to heat the A1203/binder
specimens. The weight loss corresponds to binder burn-out.

For stepped power levels, change in wt% of specimens and the
input microwave power schedule used to heat the A1203/SiC/
binder specimens. The weight loss corresponds to binder burn-out.

Schematic showing the setter material for binder burn-out and the
seven positions for powder/binder compact specimens.

Wt% of binder removed as a function of heating time using 80
Watts fixed ingpower in TE ,2 mode for both singly-
processed specimens [2,3] and batch-processed specimens.
The symbol ‘C’ denotes that the specimen cracked.

For a stepped input power sequence. average fraction of the binder
removed in wt% for six-specimen batches as a function of power
and heating time for (a) A1203/binder and A1203/Zr02 binder
specimens and (b) for A1203/SiC/binder specimens. For those data
points without error bars, the symbol size exceeds the standard
deviation. Figure (b) also includes data for A1203/SiC/binder
specimens for which the binder was removed by conventional
heating.

SEM micrograph of fracture surface of alumina discs joined at
1625°C for 10 minutes. Arrows indicate the joined interface.

SEM micrograph of polished surface of joined alumina discs heated
at 1625°C for 10 minutes. Arrows indicate the joined interface.

SEM micrograph of polished surface of joined alumina discs heated
at 1625°C for 10 minutes. Arrows indicate the joined interface.

An elemental map showing the position of aluminum ions near the
joint for joined alumina discs.

xxi

152

154

154

160

164

165

175

175

177

177

Hg-
~

 

Figure 5.

Part 11
Figure 1.
Figure 2.

Figure 3.

Figure 4.

Figure 5.

Figure 6.

Figure 7.

Chapter 4
Part I
Figure 1.

Figure 2.

Figure 3.

Micrograph showing Vickers indentation impression for 98
Newton Vickers indent, microwave-heated at 1500°C for 1 hour.
Radial cracks have healed.

Schematic showing notched specimen preparation.

Schematic for refractory casket used for microwave heating,
showing dead weights placed on the specimen for joining.

SEM images of silica film spun on alumina specimens at (a) 500
rpm and (b) 2000 rpm.

Silica film thickness as a function of spinning speed.

SEM images of notch made in MaCorT" specimen (a) before and
(b) afier joining.

SEM images of notch made in alumina specimen (a) before and
(b) after joining.

Total fraction of pores along the joint interface in joined MaCorT”
and alumina specimens as a function of film thickness.

Schematic of indented alumina specimens used for both the
conventional and the microwave heating experiments. The
indentation crack lengths are exaggerated.

The crack healing rates Aa/At for polycrystalline alumina specimens
with (a) 49 N and (b) 98 N indentation cracks, annealed by

(i) microwave heating, with a ramp rate of 75°C/min. (MWF),

(ii) microwave heating, with a ramp rate of 10°C/min. (MW S),

(iii) conventional heating, with a ramp rate of 10°C/min. (CV).

The solid lines represent a least—squares fit to quadratic polynomial
of the form Aa/At = a + bTmax + csz, where Tmax is the dwell
temperature for each annealing treatment.

A modified Arrenhius plot of ln[TmAa] versus l/Tmax (equation 4
[35, 49]) for polycrystalline alumina specimens annealed by

(a) microwave heating, with a ramp rate of 10°C/min. above 1000°C,
(b) microwave heating, with a ramp rate of 75 °C/min. above 1000°C,
(c) conventional heating, with a ramp rate of 10°C/min. The solid
lines represent a least-squares fit to equation 4.

xxii

179

‘ 186

186

188

189

191

192

193

200

202

206

Figure 4.

Chapter 5
Part I

Figure 1.

Figure 2.

Figure 3.

Figure 4.

Figure 5.

Figure 6.

Figure 7.

Figure 8.

Figure 9.

Figure 10.

Figure 11.

The calculated diffusivity ratios (equation 7) based on the values
of activation energies Q and constants C given in Table 1 for each
of the heating modes.

Schematic of the casket (specimen enclosure) used in this study.
The aluminosilicate (SALI) specimen setter was included in
Caskets 1-4.

Apparatus for microwave heating using a cylindrical single-mode
cavity.

Schematic of cylindrical single-mode microwave cavity. The
short position, L, (cavity height) and the probe position, Lp are
illustrated.

Schematic showing the measurement of the temperature of the
casket’s inner wall. The optical pyrometer is sited through
cavity viewport A and through a 5 mm hole in the casket wall.

Temperature versus microwave input power for microwave heating
of caskets with and without specimens.

The temperature dependence of the thermal conductivities of the
zirconia cylinders (ZYC) and aluminosilicate refractory board
(SALI) as specified by the vendor (Zircar, data taken from ref. [38],
curve fit done by the authors).

For various aluminas, e’ (a) and tan 8 (b) as a function of
temperature (after [1]).

A three-dimensional plot of the steady-state temperature T,
measured at the inner wall of the caskets' zirconia cylinder as a
function of total casket length and the radius ratio b/a.

Measured Ti versus the total volume of each casket included in this

study. Note the lack of correlation between T, and the total volume.

Measured Ti versus the ratio of total volume/total surface area of
the casket. Note the lack of correlation between T, and the volume/
surface area ratio.

Measured Ti versus the outer surface area of the casket. Note the
lack of correlation between T, and the outer surface area.

xxiii

208

224

228

229

230

240

245

246

248

248

249

249

Figure 12.

Figure 13.

Figure 14.

Figure 15.

Figure 16.

Figure 17.

Figure 18.

Figure 19.

Part1]
Figure 1.

Figure 2.

The inner wall temperature, T, as a function of the ratio b/a

a) = outer radius of zirconia cylinder, a = inner radius of zirconia
cylinder). The least-squares fit to equation 14 describes the data
well for the Group 1 caskets.

The inner wall temperature T, as a function of the ratio b/a

(b = outer radius of zirconia cylinder, a = inner radius of

zirconia cylinder). The least-squares fit to equation 14 (solid
curves) and to equation 24 (dashed curves) both describe the data
well for the Group 3 caskets.

Using equation 24 for several different b values, the predicted
values of casket steady—state temperature as a function of b/a for
several values of casket outer radius b, given L, = 4 cm, L3,, = 2.0
cm, and a fixed input power of 600 W.

The steady-state temperature, T,, as a function of the total casket
length for Group 2 caskets, for which the b/a ratio is fixed at 1.5,
the SALI thickness is fixed at 2.0 cm, and the input power is fixed
at 600 Watts.

For the Group 2 caskets, the temperature T, as a function of casket
length for three different input power levels: 540 W, 570 W, and
600 W.

The D, versus input power, where the D, values were obtained by
fitting the data in Figure 16 to equation 15.

The measured T, values versus the T, values predicted on the basis
of equation 24.

The total power absorbed, PT, versus the input power for two
sintering runs for Sumitomo AKP30 and AKP50 alumina in
Casket 1, compared to a heating run for Casket 1 with no
specimen included.

Schematic of a refractory casket, showing a cross-sectional view
of the hollow ZYC cylinder and the aluminosilicate disk-shaped
end plates [1]. The symbols a, b, LSA, L2,, and L, are as defined
in equation 5.

Schematic showing caskets with differing b/a ratios for inner

radius, a, and outer radius, b [after 1]. In this study, the length of
zirconia cylinder, L2,, ranged from 2 cm to 5 cm.

xxiv

251

252

252

254

254

255

257

260

272

278

Figure 3.

Figure 4.

Figure 5.

Figure 6.

Figure A1.

Appendices
Figure A-l.
Figure A-2.

Figure 1-1.

Figure I-2.

Figure 11-1.

Schematic of measurement of the casket inner wall temperature T,
and the outer wall temperature TO by an optical pyrometer.

The distance, u, from the bottom plate of the cavity to the center
of the hole made in the casket wall, is fixed at 2.5cm [after 1].

Measured outside casket wall temperature, T,,, as a function of
microwave input power level, P,. Trends in the T0 versus P, data
are highlighted by the solid curves that represent the least-squares
best fit to the empirical quadratic equation for T0 versus P,
(equation 8b). Note that in Figures (a) and (b), the data for

b/a = 1.33 is not fit to equation 8b, due to the “jump” in T0

at P, z 350 - 450 Watts, as discussed in Section 3.1.

Measured casket inside wall temperature, T,, as a function of
microwave input power level, P,. Trends in the T, versus P,
data are highlighted by the solid curves that represent the least-
squares best fit to the empirical quadratic equation for T,
versus P, (equation 8a).

Measured casket inside wall temperature, T,, as a function of total
absorbed microwave power, PC. The curves represent the least-
squares best fit of the data T,, PC, LSA, b, b/a, and L, in Group 4-7
to equation 9.

Schematic for electromagnetic field distributions of unloaded
TM,,, resonance microwave cavity mode.

Photo of microwave processing apparatus.
Photo of cylindrical single-mode microwave cavity.

Sem Images of Fracture Surface of Alumina Specimens Batch-
Processed in Various Microwave Cavity Modes.

Heat Distribution inside Empty Casket as Determined by
Thermally Sensitive Paper. The casket was heated in each cavity
mode (a) for 15 minutes at 80 Watts, (b) for 7 minutes at 90 Watts,
(c) for 15 minutes at 150 Watts, and (d) 5 minutes at 90 Watts.
The dark areas in (a)-(d) indicate regions of microwave heating.

Photo of A1203/binder compact specimens heated by microwave
heating.

280

282

283

289

293

305

306

310

311

312

Figure II-2.

Figure II-3.

Figure 111-] .

Figure V-2-l.

Figure V-2-2.

Figure V-2-3.

Figure V-2-4.

Figure V-2-5.

Photo of A1203/SiC/binder compact specimens heated by
microwave heating.

Photo of A1203/Zr02/binder compact specimens heated by
microwave heating.

SEM images of (a) mw-sintered AKP30 A1203 , (b) Mng,
(c) MaCor, and (d) mw-sintered TZ-3Y ZrOz.

Schematic of a cylindrical single-mode microwave cavity defining
the cavity height, Ls, (short position) and probe position, Lp.

Mode diagram for ideal 7 inch cylindrical single-mode microwave
cavity.

Schematic of single-mode microwave cavity and schematic of
electric probe for field strength determination.

Measurements of reflected power as a function of cavity height.

Change of short position, Ls, (i.e. cavity height) as a function of
time during microwave heating of Casket l at various modes.

Figure V-2-6a. Relative radial component of electric field strength, E,, around

the cavity wall in various modes.

Figure V-2-6b.Relative radial component of electric field strength, E,, around

Figure v1-1.

Figure VI-2.

Figure VI-3.

Figure VI-4.

the cavity wa_l_l_ in various modes.

Surface profile for sintered AKP30 alumina, thermally etched via
microwave heating for one hour at 1858K. (a) The surface profile
data as displayed on the Digital Instruments AF M used in this

study includes markers to analysis features such as the groove depth,
as shown here (part a). (b) Line L is the path along which the
surface profile data shown in (a) was collected. Triangular symbols
in both (a) and (b) designate the same points.

(a) AF M-measured groove width and (b) groove depth as a
function of temperature for ADS-995 polycrystalline alumina.

(a) AF M-measured groove width and (b) groove depth as a
function of temperature for AKP30 polycrystalline alumina.

(a) AFM-determined groove profiles of ADS-995 specimens

heated in a microwave cavity and (b) - (e) the groove profiles
determined by AFM and expected from least-squares fitting by

xxvi

313

314

316

323

326

327

330

331

332

333

338

339

339

340

 

,...
i

Figure VI-5.

Figure VI-6.

Figure VI-7.

equation 12 in Chapter 6, Part1, obtained from Mullins’ theory.

(a) AF M-determined groove profiles of AKP30 specimens heated 341
in a conventional furnace and (b), (c) the groove profiles

determined by AF M and expected from least-squares fitting by

equation 12 in Chapter 6, Part I, obtained from Mullins’ theory.

The ratio of AF M-measured groove depth to width, d/w as a 342
function of reciprocal temperature. The curves represent a least-
squares linear regression.

Linear thermal expansion coefficient as a function of temperature 342
for polycrystalline on alumina [Wachtrnan]. The curve in (a)

represents data fitting to a fourth order polynomial equation and the

curve in (b) represents a linear fit of the data as a function of

temperature, T.

xxvii

INTRODUCTION

For the last decade, microwave processing of materials (including inorganic and
organic materials) has been intensively developed and established since microwave
processing as a relatively new technology is known to provide many potential
advantages; energy savings, reduced processing time, and uniform and enhanced
physical properties of processed materials due to inherent heating characteristics of
microwave heating such as rapid, internal and volumetric heating characteristics.
However, unlike food processing by well-developed user-fiiendly microwave ovens,
microwave processing of materials encounters problems such as inability to heat low
dielectric-loss ceramics, thermal runaway, cracking, non-uniform heating, etc. Also,
compared to conventional heating, microwave heating can be relatively complex in that it
requires not only fundamentals of material processing but also various disciplines such as
electromagnetics, material science, physics, thermodynamics, etc. to better understand the
interactions between microwave energy and materials, and in turn to optimize a specific
material process. Thus without a high degree of technical knowledge and economic
consideration, one may not succeed in using microwave energy as versatile tools to
effectively process various types of materials.

The subtopics of the research included in this study are i) literature review and

theoretical background for microwave processing (Introduction), ii) sintering (Chapter 1),

iii) binder burn-out (Chapter 2), iv) joining (Chapter 3), v) crack healing (Chapter 4), vi)
effects of casket geometry and microwave power on microwave heating (Chapter 5), and
vii) thermal etching (Chapter 6). The experimental procedures, results and discussion
will be addressed under each subtopic.

Additional experimental data and results obtained in this study are included in
APPENDICES. In particular, Appendices A and B include photos of microwave
processing apparatus and material properties for microwave susceptor materials
(“caskets”) generally used for microwave heating in this study. Appendices I, II, III, IV,

V, and VI include additional data for Chapters 1, 2, 3, 4, 5 and 6, respectively.

1. GOALS OF THIS STUDY
This study explores various aspects of microwave processing of ceramics (sintering,
binder burn-out, and joining). In addition, the relationship between casket geometry and
steady-state temperature of the microwave-heated casket is studied in order to provide a
means of designing the microwave caskets required for sintering and joining. Also,
thermal etching is studied in order to obtain information on mass diffusion during
microwave heating, since diffusion is important in all high temperature processing of

ceramics.

1.1. For Sintering
The goal is to use a single-mode microwave cavity to sinter low dielectric-loss
ceramic materials such as aluminas and alumina matrix composites without problems

such as thermal runaway and cracking (Chapter 1) [1-3]. In addition, the

n‘

‘n

 

~.

alumina/zirconia particulate composites sintered in both the microwave cavity and the
conventional furnace are to be compared in terms of microstructures and densities as a

function of maximum hold temperatures for final densification.

1.2. For Binder Burn-out

Organic binders were burnt out from ceramic powder compacts without placing the
specimens in a refractory casket. The smoke and volatiles produced during burn-out
were removed more efficiently than would be the case if the specimens were enclosed in
a refractory casket (Chapter 2) [4-6]. Also, the binder burn-out research seeks to
maximize the binder burn-out rate without inducing cracking in the ceramic powder

compacts.

1.3. For Joining
Joining of monolithic and composite ceramic materials used a spin-on interlayer
(Chapter 3) [7,8]. Materials joined included alumina, alumina composites, and MaCorTM,
a commercial glass ceramic. The joints should be mechanically strong, such that the
bond strength is an appreciable fraction (say, at least 50%) of the strength of the bulk
material, where the bond strength will in part be assessed by an indentation crack
deflection at the interface. The work joined densified ceramic components, machining
holes and/or channels of submillimeter dimension in individual components, and then
joining the components while not modifying the dimensions of the channels or holes by

more than a few percent.

 

1.4. For Crack Healing

Distributed damage due to microcracks can affect a variety of material properties
such as elastic modulus, strength, and toughness. Reducing the size and/or the number
density of nricrocracks can enhance material properties. Also the gap between the
components to be joined can be considered as a crack. To better understand the
mechanism for joining ceramics using microwaves as well as to study crack healing
itself, a study was performed on crack healing of Vickers-indented polycrystalline
alumina via both microwave heating and conventional heating (Chapter 4) [9]. The crack
healing rates for both the heating methods were analyzed and compared utilizing a model

equation reported in the literature.

1.5. For Thermal Etching
Microwave sintering and joining (which are included in this study) are performed at
high temperatures, at which diffusion plays an important role. However, it is still
unknown what diffusion mechanism dominates during microwave heating. This study
includes AFM measurements of grooving width, depth and angles for both
conventionally- and microwave-etched polycrystalline alumina specimens (Chapter 6)
[10,11]. From the AF M data we should be able to calculate activation energies for
diffusion during microwave heating.
The thermal etching studies will be done in tandem with crack healing studies
(Crack healing in ceramics is an important potential processing step that might be
employed after components have been densified and has been ground to a final shape).

Crack healing itself is likely to be closely related to the joining process.

1.6. For Effect of Casket Geometry on Microwave Heating

In microwave hybrid heating which utilizes a casket composed of a microwave
susceptor material, the casket plays an important role by providing thermal insulation and
preheating a low dielectric-loss material to be microwave-processed. The effect of casket
geometry was investigated for caskets composed of hollow, partially stabilized zirconia
cylinder with aluminosilicate end plates (Chapter 5) [12,13]. The length of the casket
used in this study ranged from 4 cm to 7 cm. The inner radius, a, of the casket ranged
from 2.54cm to 3.8lcm, while the outer radius, b, ranged from 3.81cm to 5.08cm,
yielding the radius ratio, b/a of 1.27 to 2.00. Future study may include zirconia cylinders
having inner radii of 1.27cm and/or 5.080m.

The partially stabilized zirconia cylinders were selected for the casket
geometry/microwave heating study since sintering and joining work included in this
study used these materials. In addition, other researchers have used zirconia and/or

alurrrinosilicate specimen enclosures (caskets) [14-19].

2. GENERAL LITERATURE REVIEW
During the last decade, interest has grown in microwave processing of materials.
Many attractive advantages of the new and exciting technology of processing materials
utilizing microwaves have been well documented in the literature including MRS
Symposium Proceedings volumes 124 [20], 189 [21], 269 [22], 347 [23], and 430 [24],

and Ceramic Transactions, volumes 21 [25], 36 [26], and 59 [27].

2.1. DIFFERENCES BETWEEN MICROWAVE
AND CONVENTIONAL HEATING

Microwave heating is fundamentally different from conventional heating (Figure l)
[28]. Electrical furnaces used for conventional heating of materials are composed of
heating elements and insulation (Figure la). For microwave heating, the cavity used to
heat the material is composed of a metal shell and microwave port through which
electromagnetic waves are guided into the cavity from the microwave power supply
(Figure 1b). In conventional processing heat is generated by an external heating source
which deposits thermal energy on the surface of the material. Subsequently this thermal
energy is transferred to the center of the material by thermal diffusion. 1n microwave
processing, heat is created within the material through the interactions between
electromagnetic fields and the molecular and electronic structure of the material.

As a result of the inherent difference between microwave and conventional heating,
the thermal gradients and the heat flow in microwave processed materials are opposite to

those in conventionally heated materials (Figure 2) [29]. As a consequence, one can heat

Electrical Furnace

 

 

 

O O i I I

 

 

 

 

 

 

 

 

I
1 k
/f \\
(a) IHSUIaUOfl Heating element

Microwave Cavity

Microwave port

 

 

 

 

\_/ Specimen

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(1)) Metal shell Insulation

Figure 1. Heating patterns in conventional (a) and microwave furnaces (b) [28].

Conventional Heating

Temperature U

 

 

 

(a)

 

Microwave Heating

 

Temperature m

 

 

 

(b)

Figure 2. Temperature gradients generated during conventional (a) and microwave (b)
heating of materials [29].

materials very rapidly and uniformly by microwave processing. Due to these inherent
heating characteristics of microwave heating, many attractive advantages have been
proposed and proved in literature. For example, an Ontario Ministry of Energy study
[30] showed microwave drying and sintering uses less energy than conventional drying
and sintering by a factor of about two and ten, respectively. In addition to the energy
savings, the nature of microwave heating (i.e. internal and volumetric heating) results in a
set of “microwave effects,” including lower sintering temperatures and a considerable
decrease in processing time [31,32], smaller grain sizes [33], and lower diffusional
activation energies [32] compared to conventional processing. Also, several researchers
[34-36] report microwave processing improves microstructure and mechanical properties.

Janney and Kimrey [31] reported that A1203, doped with 0.1 wt% MgO and sintered
under vacuum by 28 GHz microwave energy was densified much faster than by
conventional sintering (Figure 3). The apparent activation energy calculated for
microwave sintering was 160 kJ/mol, which was much lower than 5 75 kJ/mol for
conventional sintering (Figure 4a) [31]. Janney and Kimrey [37] also compared grain
growth in microwave annealed alumina with conventional annealing results (Figure 4b).
The apparent activation energy for microwave grain growth using the Arrhenius rate
equation was 480 kJ/mol, which was about 20% lower than 590 kJ/mol for conventional
grain growth (Figure 4b) [37]. The activation energies for conventional annealing and
sintering agree well with each other, while the activation energy for microwave sintering
does not agree with the activation energy for microwave annealing. The difference in
activation energies may be due to different sintering mechanisms dominating the

microwave processes compared to conventional processes [37].

100

 

   
     
 
 
 

 

 

l I
90 * Microwave ‘
,3 Sintering
8E 80 - a
.33
m
5 7o _ _.
Q Conventional
6O _ Sintering g
50 l l l l 1

 

 

800 900 1000 l 100 1200 1300 1400

Temperature (°C)

Figure 3. Density versus temperature of microwave (28 GHz) and conventionally
srntered MgO doped alumina [31].

10

 

 

  

 
 
  

 

 

 

  

  
  

 

3 r r r
i
A 2 I-i
B 1
c6
:0 1 Microwave _
E 160 kJ/mol
8 i
w I. a
.9. _1 _ Conventional
575 kJ/mol
_2 4 l l r 1 r
0.5 0.6 0.7 0.8 0.9
1000/T (K)
(a)
I
-l9.0 - j
4% Microwave
:0 480 kJ/mol
E -200 - -
.E
m
:3 Conventional
.2 590 kJ/mol
-21.0 -
1 1 l

 

 

   

 

0.45

0.50

0.55 0.60 0.65
1000/T (°K")

(b)

Figure 4. (a) The apparent activation energies for microwave (28 GHz) and
conventionally sintered MgO doped alumina [31] and (b) the apparent activation energies
for microwave (28 GHz) and conventional grain growth of MgO doped alumina [37].

 

2.2. FUNDAMENTALS OF MICROWAVE HEATING
2.2.1. Interactions between Microwaves and Materials

The term ‘microwave’ refers to alternating current signals with frequencies between
300 MHz (3 x 108 Hz) and 300 GHz (3 x 10“ Hz) [38]. For a microwave signal, the
period, T = 10: ranges from 3 ns (3 x 10'9 sec) to 3 ps (3 x 10'12 sec), respectively. The
corresponding wavelengths range from A = c/f= 1 meter to A = l millimeter, respectively,
where c = 3 x 108 meter/sec, the speed of light in vacuum.

The frequency range used for microwave heating lies between 400 MHz and 40
GHz [39]. However, the allowed frequencies are restricted to discrete bands (Table 1)
[39]. Most microwave fi'equency bands are used for communications and radar, which is
regulated by the Federal Communications Commission (Internet address, httpzl/www.
fcc.gov). The FCC allocated 915 MHz, and 2.45, 5.85, and 20.2-21.2 GHz for industrial,
scientific, and medical (ISM) use [40]. Only 915 MHz and 2.45 GHz are significantly
applied for industrial and medical use because of the suitability of these frequencies for
such purposes. Other frequencies available on a limited basis as power sources are 28,
60, 140 GHz, and 500 MHz.

In using microwaves in various applications including processing of materials, one
must consider health effects of microwave radiation. Guidelines for human exposure to
radiofrequency electromagnetic fields are established by FCC (Internet address,
http://www.fggov/oet/info/documents/bulletini/#6j. The first exposure standard for
microwave radiation, based on the amount of radiation necessary to heat human tissue
one degree Celsius, was 10 mW/cm2 which was a tenth of the energy level required to

provide one degree heating [40]. The current revised standard, based on an exposure

12

Table 1. Frequency allocation for industrial, scientific, and medical applications and
areas permitted [3 9].

 

Frequency (MHz) Frequency tolerance Area permitted

 

 

Austria, Netherlands, Portugal, Switzerland,

433'” i 02% West Germany, Yugoslavia
896 i 10 MHz Great Britain
915 i 13 MHz North and South America
2375 i 50 MHz Albania’ Bmgfifinfifihaggl‘f‘da’ Hungary,
2450 i 50 MHz Worldwide except where 2375 MHz is used
3390 2|: 0.6% Netherlands
5800 i 75 MHz Worldwide
6780 :t 0.6% Netherlands
24150 i 125 MHz Worldwide

40680 Great Britain

 

l3

 

level of 0.4 W/kg, is 0.5 mW/cm2 at 2.45 G112, above which potentially hazardous
damage may occur.

Depending on the material, incident microwave energy can be transmitted,
absorbed, or reflected. During microwave processing, a waveguide transmits
microwaves from a microwave generator to a microwave cavity in which material is
heated. Thermal energy for heating materials can be directly produced inside materials
either by electrical current induction at high frequency for conducting materials or by
dielectric or magnetic energy absorption for non-conducting materials [41].

Sutton [28] schematically showed the interactions of microwaves with different
types of materials (Figure 5). As shown in Figure 6, metals are opaque to microwaves
(i.e. good reflectors) and thus metals are very difficult to heat by microwave power [28].
Low-loss ceramic materials such as A1203, MgO, SiOz, and'most glasses are transparent
to microwaves at ambient temperature [28]. For these low-loss materials, there is a
critical temperature, T,,, above which the materials begin to absorb and couple more
efficiently with microwave power. On the other hand, dielectrically lossy ceramic
materials such as C0203, MnOz, NiO, and CuO absorb microwaves at room temperature
[28]. For microwave-transparent ceramics, absorption of microwave energy can be
enhanced by adding conductive or magnetic phases in the form of fibers, particles, or
other additives [28,42]. The conductive or magnetic phases absorb microwave energy
more rapidly than the matrix and thus can be heated selectively and rapidly [28].

The interaction (or absorption) of microwaves by a dielectric material is related to
the material’s complex permittivity, 8* (Farad/meter), composed of real part, 6’, and

imaginary part, e”, by [28,43,441

14

Material Type Penetration

 

TRANSPARENT Total

 

 

 

(Low loss insulator)

 

 

 

 

 

 

 

 

 

 

 

2mg None
(Conductor)
M ABSORBER Partial to Total
' (Lossy insulator)
M °l . \ c," a, co ‘ ABSORBER Partial to Total
°\ 0" o, ‘0 (Mixed)

 

 

 

Matrix = low loss insulator
F rber/particles/additives = absorbing materials

Figure 5. Interaction of microwaves with materials at ambient temperature [28].

 

( a) 8, —F 7 l T l l l l

r

 

 

 

 

 

 

11111
1

10m Ion. low 10m; 10m

 

:
10° 102 10‘ 10‘ 10“

 

 

 

Frequency (Hz)
102 10‘ 10” 10”

Figure 6. Variation of (a) relative dielectric constant and (b) relative effective dielectric
loss falctor with frequency [46-48]. Loss peaks shown at frequencies of 102, 109, 1013,
and 10 Hz correspond to mechanisms, respectively.

15

£*=£'—je"=£o(£;—js:fl) (1)
where j =\/—1

so = permittivity of free space (so = 8.86 x 10'12 Farad/meter)

8’, = relative dielectric constant
81,,“ = effective relative dielectric loss factor.

When microwaves penetrate and propagate through a dielectric material, internal
electric fields are generated. These internal electric fields induce translational motions of
free or bound charges (e.g., electrons or ions) and rotational motions of charge complexes
such as dipoles [28]. The extent to which the charges and dipoles respond to the electric
fields is represented by 6",, which is in turn a measure of polarizability of a material in the
electric fields [28, 52]. The resistance of the induced motions due to inertial, elastic, and
frictional forces (which are frequency dependent) causes losses, attenuates the electric

fields, and results in volumetric and internal heating. All the loss mechanisms are

combined in one loss parameter, 5”“, , by (Figure 6) [43,4548]

0 _ It It It It CDC
8,], — as + a“, + a, + ac + _274f8 (2)
0
where a”, = Space charge polarization loss

(normally noted in heterogeneous materials)
6' d = Dipolar losses which are usually encountered in the
microwave region of the frequency band
= Ionic losses which are usually encountered in infrared
portion of the frequency band

r: c = Electronic polarization losses which are encountered in the

 

 

optical region of the frequency band
one = DC electrical conductivity of the material which is temperature
and material dependent (Siemens/meter)
f = frequency of the incident microwave energy (Hz).
Thus the effective dielectric loss factor, 5’25, measures the loss due to a summed effect of
the loss mechanisms in the frequency band and the loss due to DC conductivity.

Equation 2 thus can be rewritten as [43,45]

UDC
24st
= UAC

27%}

 

ajfl=sf+

(3)

where a: = a: + a; + a," + a: is a combined loss factor due to space charge polarization

loss, dipolar loss, ionic loss, and electronic loss for a given frequency band. Therefore,
we can express the AC (alternating current) conductivity, oAc, as [28,45]

O’AC = O’DC + 24508: = 271306;, (4)
where 0A,: is the total effective conductivity (Siemens/meter) caused by conduction and
displacement currents. Of all the loss mechanisms, dipolar losses (8’3) and conductive
losses (due to one) are two main physical loss mechanisms by which microwaves interact
with ceramics, resulting in internal heating [49]. At radio frequencies (1-100 MHz) the
dominant mechanism is due to conductive currents flowing within the materials, which in
turn is due to the movement of ionic constituents [39]. The CDC losses can be enhanced
by the presence of impurity constituents such as salts. For the frequencies ranging from 1

10 10 GHz the losses are due to the existence of permanent dipole molecules which tend

to re-orientate under the influence of an external electric field, E (Figure 7) [39]. Inertial,

17

—l

 

 

a ,,
J E
\V.\ )‘

i) 5;: t .
” - Alternatrng
k. “A i V electrical field

 

Figure 7. Dipolar reorientation in an applied electric field can result in heating [39].

elastic, and fiictional motions between adjacent dipoles can lag the polarization in the
extremely rapidly alternating electric field. Therefore, power can be dissipated in the
dielectric material by such motions as depicted in Figure 7.

Walkiewicz, Kazonich and McGill studied conduction losses in microwave heating
[50]. Walkiewicz et a1. heated various metal powders, inorganic chemicals, and minerals
in a microwave oven at power levels near 1 kW and recorded the temperatures after a few
minutes of heating (Table 2 shows the results [50]). Conduction plays an important role
in microwave heating (Table 2). In general, as the resistivity decreases (that is, the
conductivity increases), materials absorb microwaves more easily and thus heating
becomes easier. It is not easy to heat insulators like alumina and silica, while transition
metal oxides and sulfides such as magnetite and pyrite are easy to heat to higher
temperature [50]. However, in spite of their high electrical conductivity, metals are not
heated as well as semimetals and narrow-band semiconductors because electric fields
cannot penetrate much below the surface of metals [50].

When a material exhibits dielectric losses in the microwave frequency range, we can

18

expect very efficient energy conversion (90% in the conversion process of microwaves to
thermal energy). If a suitable microwave applicator is used, refractory materials can be
heated to high temperature [41]. An alternative expression frequently used to describe
dielectric losses, is the loss tangent, tanci, defrned as the ratio of the effective relative loss

factor to the relative dielectric constant [28,49]

8"
tanr‘)‘ = eff = 04C
I r ’
5, 2790906,

 

 

(5)

Table 2. Heating characteristics and resistivities for minerals, chemicals, and metal
powders heated by microwave power of 2.45 GHz [50,51]. The materials were heated
for 7 rrrinutes or less at microwave input power levels ranging from 500 Watts to 2000
Watts in a rectangular aluminum waveguide [51].

 

Material Type Materials Resistivity Range Heating Characteristic

 

 

SiOz, A1203, Very little heating

Oxide minerals 104 - 10l4 (Q-m)

KAlSi3Og, CaCO3 only about 80°C
r -
Carbon and graphite C ~10 (Q-m) EaSilllbggggd 10
Mixed valent oxides 263%;(fig’ 10-2 _ 104 (Q-m) Easily 116833350 3130111
semiscldlnfidciritors FCSZ’ PbS: CuFeSz 10'3 - 10'5 (Q-m) EaSily 1113;161:1330 about
M... Wm M: ii: 1,. a... “in: 2332s ‘°

 

19

 

2.2.2. Variation of Dielectric Properties with Temperature and the Relation
Between that Variation and Thermal Runaway

The dielectric constant, 5",, and loss tangent, tané', are not temperature independent
(Figure 8). Since the value of 8’, is a measure of polarizability of a material in an electric
field, a,’ increases with temperature due to an increase in polarizability caused by
volumetric expansion [28]. On the other hand, the loss factor, 5’2”, measures the extent
to which electric charges and dipoles dissipate the energy stored in the electromagnetic
field as heat in the material [52]. Thus the value of tan6 which is defined in equation 5 is
a measure of dielectric loss (or absorption) of microwave energy within the material [52].
Von Hippel [53] and Westphal, et al. [48,54] determined room-temperature dielectric
properties of various materials including organics and inorganics (Tables 3 and 4). At
room temperature tané’ for the low-loss ceramics such as alumina is very low and the
ceramics are essentially transparent to microwave radiation (Figure 8) [49,54]. However,
as temperature increases, the total electromagnetic loss for a ceramic increases. While
each loss mechanism contributes separately to the overall increase, conduction losses
typically predominate at high temperatures [55]. Although conduction losses of dielectric
materials are normally small near room temperature due to low conductivity, the
exponential increase in conductivity (in particular due to ionic conductivity) with
temperature results in a corresponding increase in the loss tangent [41,49,55]. Therefore
the loss tangent initially rises slowly with increasing temperature, until some critical
temperature, T,,“, is reached, beyond which tané‘ rises rapidly, resulting in more effective
heating [28,49]. For alumina, To,“ is roughly 1000°C. Heating of low dielectric-loss

ceramics from low temperatures to the point where it becomes more lossy often requires

20

 

 

14.0 I ' l ' l ' l ' I

/ Alba-ox Co. 11.950

 

 

 

 

1 3 .0 _ ““n— American Lava Co. AlSlMag 614 _
_ / Coors Porcelain Co. AD-99 ,,
"‘”"""' Coors. AD-995
12.0 - _
Sumitomo. AKP-so

‘° 11.0 — _
10.0 - _
9.0 - _

l , l . l ‘ 1 .
0 400 800 1200 1600

Temperature (° C)
(a)
0.010 I

 

 
  
  
  
    
  

/ Albemx Co. A-950

--- American Lava Co. AlSiMag 614
0008 ' / Coors Porcelain Co. AD—99

’ «wr‘M' Coors. AD—995

0006 _ —— Sumitomo. AKP-so

tans

 

 

 

 

0.004 r
0.002 "
0.000 I ...,.....-— 1 1 _,,.-....--l ......... 1 1 r
0 400 800 1200 1600
Temperature (° C)
(b)

Figure 8. Typical variations of a,’ (a) and tan8 (b) for aluminas as a function of
temperature [40,54].

21

Table 3. Dielectric properties of various ceramics at room temperature (25°C) [54].

 

Density

Freq.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Material (g/cm3) (GHz) 6", tan6
AlN (Carborundum) 8.5 ~8 ~0.003
A1203 (Coors Co. AD-995) 3.840 3.33-3.80 9.63 0.00008
BeO (99.5%)
(Amer. Lava Co. AlSiMag 754) 2.851 8.52 6.86 0.00031
BN (Carborundum Co.) 2.065 4.99-5.08 4.777 0.00033
CeF4 (MIT, Lab. for Ins. Res.) 0.06 15.8 0.253
CoO (MIT, Lab. for Ins. Res.) 0.001 12.9 0.0005
PbBr2 (MIT, Lab. for Ins. Res.) 0.001 52.7 0.0052
MgOAl2O3 (Union carbide) 3.574 4.07-4.23 8.28 0.0001
MgO (Kodak) 8.5 9.72 0.00045
MnF2 (Columbia Univ.) 0.01 6.7 0.004
HgI2 5.49 8.5 13.9 0.003
NiO 0.001 11.9 0.0154
Si crystal (MIT, Lab. for Ins. Res.) 14 12 0.0090
SiC (Carborundum) 3 60 0.58
Si02 (fused silica) (Amer. Opt. Co.) 2.196 5.37-5.50 3.818 0.00015
Si3N4 (Admiralty Materials Laboratory) 2.449 8.52 5.54 0.0036

 

22

 

Table 4. Dielectric properties of ceramics (at 1 MHz, room temperature) [48].

 

 

Material tan6 8r ’ 8cm”
Alumina (A1203) 0.0003 - 0.002 8.2 - 10.2 0.002 - 0.03
Spine] (MgO-Al203) 0.0004 7.5 0.0003
(3 11111401335102) 0.004 - 0.005 6.2 - 6.8 0.025 - 0.034
Magnesia (MgO) 0.001 8.2 0.002 - 0.01
Beryllia (BeO) 0.001 5.8 0.006
Zirconia (ZrO2) 0.01 12.0 0.12
Thoria (ThO2) 0.0003 13.5 0.004
Hafnia (HfO2) 0.01 12 0.12
Ceria (CeO2) 0.0007 15 0.011
Boron nitride (BN) 0.001 4.2 0.004
Silicon nitride (Si3N4) 0.0001 6.1 0.0006
Pyroceram 0.0017-0.013 5.5-6.3 0.01-0.07
Glass-bonded mica 0.0015-0.003 6.4-9.2 0.011-0.023
Mica 0.0002 5.4-8.7 0.001-0.002
(I‘la203izsg-Si02) 0.0005-0.01 4.0-8.0 0.002-0.08
Quartz (SiO2) 0.0003 3.8-5.4 0.0015
Pb-Al silicate 0.001 8.2-15 0.0080015
Alm’g‘fimmde 0.0001 8.8-8.9 0.001
Silicon (Si) 11.9

 

 

 

 

either external preheating by using a microwave susceptor material as insulation or
adding a material with high loss at room temperature to the green body.

A material absorbs microwave energy more efficiently as the temperature increases
above the critical temperature, Tom, and the absorption of energy accelerates the increase
in tanfi. Consequently, the net result is an exponential increase in temperature, which is
called ‘thermal runaway’ or ‘thermal breakdown’ [48].

Thermal runaway depends on (1) the dielectric constants, (2) the porosity, (3) the
shapes and the sizes of ceramic particles, and (4) the shapes and the sizes of the pores
[56]. Thermal runaway is generally attributed to local heating or conduction losses,
which generate heat faster than it can be removed. Thermal runaway can cause
undesirable hot spots within a material, raising the local temperature to the point of
melting or evaporation [48]. Also, around the local hot spot, cracks may develop
depending on the material and the thermal gradients present.

If the cracking that may accompany thermal runaway is avoided, we may use the
thermal runaway phenomenon to heat materials very rapidly. Thermal runaway (and
cracking) can be controlled or prevented by two approaches [57]. Firstly, thermal
runaway can be avoided by increasing the materials’ thermal conductivity [57]. Thermal
runaway does not occur in ceramics having high thermal conductivity such as SiC and
Zl'Oz- Adding thermally conductive fiber or powder to a low thermal conductive matrix

not only improves the microwave absorption of the material, but also eliminates the
thermal runaway (e.g. addition of 20 wt% TiC into A1203 [58]) [57]. Secondly, when
changes in the power cause an instantaneous response in a given material, thermal

runaway Can be prevented by varying or pulsing the microwave input power [5 7]. As an

24

 

 

 

example, or-Al2O3 was sintered without thermal runaway by controlling the input power

[33,57].

2.2.3. Heating Behaviors of Dielectric Materials
The heating rate and the triggering temperature (Tag) for the efficient absorption of
microwave power vary widely from material to material. McGill et a1. [51] investigated
the effects of microwave input power on the heating rates of selected chemicals and
minerals, using input power levels ranging from 500 W to 2000 W (Figure 9). In general,
as the input power increased, the heating rates increased. However, McGill et a1. [51]
observed that very low-loss materials such as SiO2, CaCO3, and CaCl2 did not beat well
at any of the power levels tested. Very high-loss materials such as Fe304 and CuO heated
rapidly at all power levels tested. For some oxides such as A1203, Fe2O3, T102, and ZnO,
the temperature increased steadily as the input power increased [51]. On the other hand,
Cr2O3, FeCr2O4 and some chlorides such as CuCl and ZnCl2 showed very rapid and
uncontrolled increase in temperature which is known as the ‘thermal runaway’ [51].
Sutton schematically showed the response of two different materials to microwave
heating (Figure 10) [28]. Material A absorbs the microwave energy efficiently at room
temperature and thus thermal runaway occurs as soon as the material is exposed to
microwaves at a given power level. On the other hand, material B is less absorptive (i.e.
low tan 8), so that the thermal runaway does not occur at the same power level used for
material A. However, if we increase the power sufficiently, the initial rate of heating can
be increased to the point where thermal runaway can be triggered [28]. Microwave

heating of F e304 at 2.45 GHz shows type A heating behavior [51], while A1203 shows

25

 

 

  
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

300 ~
A A
.0 u
v ‘Lz
% a 200 -
a a
100 -
1- 3
0
0 l 2 3 4 5 6 7
Time (min) Time (min)
(a) For CuCl (b) For ZnO
'2‘” 14m I I I I
1000 1200 r -
G 6 1000 l- -
°v 800 1.2
g 300 L 4
60° 8
a 600 L .
40° 1 l
i rm
0 O l l I 1
0 l 2 3 4 5 6 7 0 l 2 3 4 11 12 l3 14
Time (min) Time (min)
(c) For Fe304 (d) For Cr203
80 I 1 1 r T r w
800
A 60 _ _ A
8 ,8 600
0
a 4° ' ‘ g 400
a ‘ i
i . new I ”new A laoow 0 new)
0 r r r *1 r I 1 0
0 l 2 3 4 5 6 7 0 1 2 3 4 5 6 7
Time (min) Time (min)
(e) For Si02 (1‘) For FeSz

Figure 9- Effect of microwave input power on heating rate of various chemicals and
minerals [51].

26

   
      
 

 

 

(a)

<13 Material A (b)
E: Material B
cc
H
a £82
8
13

RT ggggggggggg Power level (b) > (a)

 

 

 

0 Time

Figure 10. Schematic of the types of Response of materials to microwave heating [28].

type B heating behavior [59].

27

3. THEORETICAL BACKGROUND FOR MICROWAVE HEATING

3.1. FLOW OF ELECTROMAGNETIC POWER AND POWER DISSIPATION

WITHIN A DIELECTRIC MATERIAL
Electromagnetic waves (including microwaves) carry electromagnetic power. The
power dissipated in a ceramic material heated by microwaves can be estimated from a

relation between energy transfer rate and the electric and magnetic field intensities. The

derivation begins by considering Maxwell’s equations [3 8,60-63]

V x E = -% Faraday’s law (6)

— — — 6D , . .

V x H = J + —6t_ Ampere s elrcultal law (7)
where E = electric field intensity (Volt/meter)

H = magnetic field intensity (Ampere/meter)
E = magnetic flux density (Tesla = Volt-sec/meterz)
.7 = electric current density (Ampere/meterz)
D = electric flux density (or electric displacement)
(Coulomb/meterz)
t = time (see).
In general, a source of electromagnetic energy sets up fields which store electric and

magnetic energy and carry power which may be transmitted or dissipated as heat loss.

We can now consider a free space or any medium of volume V enclosed by a closed
surface S containing fields E, F] and current sources .73, 1171, (Figure 11) [38]. To

allow the power loss, the electric permittivity, a, and the magnetic permeability, ,u, are

28

 

 

 

 

Figure 11. A volume V, enclosed by the closed surface S, containing fields E , I? , and
current sources 7,, 1171, [38].

often considered to be complex, such that a = a" — jg” and ,u = ,u’ -j;1”. Then the power
balance equation known as Poynting’s theorem (after the physicist J.H. Poynting, 1852-
1914) is expressed as [38]

1 .. .. _ . _
—§ [(E-J, +H -M,)dv

__1_ -‘ --0 60C -‘ ‘0 a) ”- -a ,- -a .w ,- ‘0 ,-‘ ‘0
—2i(ExH )-ati+T[E.Edv+3[(eE.E +pH-H )dv+}3[(/rH-H -£E-E )dv

 

 

 

I - - . . — .. .. .. _
=§i(ExH yang? “Elzdv+% [ta-'132 +p'Hl2)dv+j% [(2111142 —a'|E|‘)dv
(3)
where .7, = electric source current (Ampere/meterz)
.7; = conjugate complex of .75

M, = magnetization of source (Ampere/meter)

29

E ° = conjugate complex of E
17' = conjugate complex of H
(o = 2717r = angular frequency,
here f = frequency of electromagnetic waves (Hz)
j = J—_1 .
The integral on the left-hand side of equation 8 represents the complex power, Psomce,

delivered by the sources .7 S and A715 , inside S, which is [3 8]
P... =5 [ta-J:+H'-a.>dv. (9)

The first term on the right-hand side of equation 8 represents complex power flow out of
the closed surface S. The vector E x IT represents the power flow per unit area. The
quantity is defined as [38,60-63]

P = E x H‘ (W/mz). (10)
F is the Poynting vector, which is a power density vector associated with an
electromagnetic field. Then the first integral on the right-hand side of equation 8 can be
expressed as

1 - -. 1
g,,=§<[(ExH)~d§=-2-<[F.d§. (11)

The real parts of Psom, and Pom in equations 9 and 11 represent time-averaged total
complex power supplied by a source within a region and the time-averaged complex
power transmitted fi'om the region, respectively.

The second and third integrals in equation 8 are real quantities representing the

time-average power dissipated in the volume V due to conductivity, dielectric, and

30

magnetic losses. Defining this power as Pm, then

130,, =%HE|2dv+% [(5132 +p"H|2)dv (12)

 

 

 

which is sometimes referred to as Joule’s law.
The last term in equation 8 includes the time-averaged stored magnetic energy, Wm,

and the time-averaged stored electric energy, We, which are defined as
W =—’i[H.FI‘dv (13)
"' 4
and
a - 4.
WC=Z£E.Edv (14)

where ,u and a are real scalar constants. Therefore, Poynting’s theorem can be rewritten
as [38,60,61]

P =P

source Ollf

+P

a. + 2160(W. - W.) (15)
Thus this complex power balance equation can be interpreted as that the power delivered
by the sources (Psoum) is equal to the sum of the power transmitted through the surface S
(Pom), the ohmic power dissipated as heat in the volume V (floss), and 20) times the net

reactive energy stored in the volume V [3 8].
For a source fiee region in which .75: 0 and 11715= O (that is, in which power is
supplied from a remote space by electromagnetic waves), Psoum = 0, and the power
transmitted into the volume, P,., = — out, so that equation 15 becomes [60-63]

P’ =-I)0ut=I)l

In

+ZJ'0)(W.. “W.)- (16)

Assuming low or no magnetic loss for a dielectric material (i.e. u" z 0), the time-average

Power dissipated as heat in the volume V, PM, can be written as

31

-.

 

 

 

1,10” = 9'2?— LlElde'I'fl £8771?de
2 2
1 (17)
a —.2
=EI/(0'DC +608 )El dv
From equation 4,
(T,,,: = O'DC + 271505". (18)
Thus equation 17 becomes
1 - 2
P103: = E iaAClEi dv ' (19)

Since Pm, is the time-average power dissipated in the volume V, the power absorbed and

dissipated as heat per unit volume of ceramic materials, Pab, (W/m3), which provides the
basis for microwave heating, is related to the dielectric properties of the material from

equations 4, 5, and 19 by [28,43,45,49]

—- 2
Pubs = aAClEl

= 271505;,
= 27y‘6'os; tan6lE|2

if (20)

 

where f = frequency of the incident microwave energy in Hz
80 = 8.854 x 10'12 Farad/meter
= permittivity of free space

a , = relative dielectric constant

tan 8 = loss tangent

IEl = magnitude of internal electric field strength in Volt/meter.

32

3.2. SKIN DEPTH AND POWER PENETRATION DEPTH

As expected from equation 20, the microwave energy dissipated in a ceramic
dielectric and the conduction losses increase by amplifying the electric field of the
microwaves within the material [55]. However, depending on the material (Section
2.2.1), the internal electric field is not the same as the electric field at the surface of the
material, since it is attenuated as the microwaves penetrate the material, reducing the
electromagnetic power (Figure 5).

Therefore, to better understand the interactions between dielectric materials and
microwaves that result in internal heating within the material, one can consider
penetration depth of the electromagnetic power into the material (as measured by the skin
depth).

As electromagnetic energy penetrates the material, its attenuation depends on the
materials’ dielectric properties. To obtain the expressions for the skin depth and the
penetration depth, we begin with considering time-harmonic electromagnetics (i.e.
sinusoidal variations of electromagnetic waves with time).

For spatially varying electric and magnetic fields that are sinusoidal functions of
time (i.e. time-harmonic fields), the field vectors are typically represented by vector

Phasors that depend on space coordinates but not on time. The time-harmonic B field and

H field can be written as [62]
E(x9yszat) =3 [E(x,y,z)e’°"] (21)
f7(x, y, z,t) = £0 [17(x, y, z, )e’“] (22)

where E (x, y, z) and 17 (x, y, z) are vector phasors that contain information on direction,

magnitude, and phase. Phasors are, in general, complex quantities [62]. For simplicity,

33

consider a uniform plane wave propagating in +z direction which is characterized by

phasor electric field E = (LE, and associated phasor magnetic field H = (3,111,. Thus E

and 17 are perpendicular to each other and both are transverse to the direction of
propagation (Figure 12). This wave propagation pattern is a particular case of a
transverse electromagnetic (TEM) wave. The phasor field quantities are functions of

only the distance 2 along a single coordinate axis expressed as [62]

E = 8,18, = deoe": (23)

where E0 = peak magnitude of the electric field wave. A propagation constant, 7, is

defined as

7 = jk' = 7011/ ”3' (meter") (24)

 

 

 

 

 

 

Figure 12. E and 17 fields of a uniform transverse electromagnetic plane wave [62].

34

O 0
where k = a) pa = complex wavenumber.

Since 7 is complex, we can write [62]

7 = a + 173 (25)
where a and ,B are the real and imaginary parts of 7, respectively. Thus the propagation
factor e'” can be written as a product of two factors, such that

E, = Eoe”: = Effie—m: (26)
where both a and ,6 are positive quantities. The first factor, e’az, decreases as 2 increases
and thus is an attenuation factor. or is called an ‘attenuation constant’ with units of neper
per meter (Np/m). The second factor, 6“”, is a phase factor, and ,6 is called a ‘phase
constant’ and is expressed in radians per meter (rad/m).

On the other hand, from equations 1 and 3, it can be shown that

‘ I - n r A?"
8 =8 —16 =8(1-]—']
8

: £'[1+—éAC']
1605

Therefore, from equation 24, the propagation constant, 7, is expressed in terms of

(27)

dielectric properties such that

,, 1/2
. . , .6‘
7=a+1fl=1wdfls (1-1?) (28)
or
1/2
7 = a+jfl = fan/pip +fi‘7] . (29)

NOW we define the skin depth, 6,, as the distance through which the amplitude of a

traveling plane wave decreases by a factor of e'1 or 0.368, such that from equation 26

35

[39,62] at 5,,

E,,e"°°’ = e413, . (30)
Thus

a5, =1. (31)
Therefore,

6, = ~21— (meter). (32)

For a low-loss dielectric material, 5" << 5’ or 0'31..- / 606' << 1 [62], thus the propagation

constant, 7, can be approximated by using the binomial expansion on equation 29 such

that

 

2
. . , .6" 1 a"
7=a+jflsjar,/,u£ 1—1 ,+—(—') . (33)
26‘ 8 6‘

Thus the attenuation constant is [62]

 

a 5 a): J2, (Neper/meter). (34)
a

The skip depth for the low-loss ceramic is [62]

2,\/-;—= 2 ,i—gog' (meter). (35)
(05 .11 OAC #

From equation 35, the skin depth for low-loss ceramics increases as the AC conductivity,

65.;

 

 

O'Ac, decreases or the dielectric constant, 5;, increases.
In a ceramic for which dielectric conductivity dominates the losses, as in very wet

ceramics (or good conductors such as metals) [39,62], then 0' AC / (06' >> 1. Under this

condition, in equation 29, 0',“7 / jwa' << 1.111611 [62]

36

 

y=a+jszwpr,/;jg, =fit/ww... (36)

Also J7=(e’i’”2)”2 = e”"4 =(1+j)/s/2 and a) = 2717’.

Thus

0: =P=W . (37)
Therefore, the skin depth is [3 9,62]

of, = __1—_ (38)

047710 AC .
The skin depth increases as J7 and Jo“. decrease for a ceramic with dielectric losses

dominated by conductivity. However, for a lossy ceramic material in which both dipolar
and conductivity losses are present, approximations given by equations 33-37 are no
longer valid [39].

In Section 3.1, equation 20 shows that the power density, P3,,- (W/m3), is
proportional to the square of the internal electric field strength. Thus for a material in
which electromagnetic waves propagate in + z direction, the power attenuation can be

expressed in terms of the distance from the surface of the material as (Figure 13) [39]

P

abs

: Poe-2a: : Pe~2:/6, (39)

0

where P0 is the power at the surface and a = 1/55 from equation 32.

Analogous to the definition of the skin depth, 8,, the penetration depth, DP, is

defined as a depth at which the power at the surface is reduced by l/e, such that at z = Dp
[3 9]

1’06“)” = P e" . (40)

0

37

 
 
 
 

 

 

 

 

 

 

E/E" Electric field
or ,
Pabs/Po Power densrty
0.37 ,
0.14 ------ T124...
0 45 ' > Z
0 85,72 =5.
M Dielectric
i material
le—>7 l
l<——-l 5s

Figure 13. Skin depth of electric field intensity and power penetration depth [28,3 9].

38

 

 

 

2aDp=1. MD
Therefore, the power penetration depth is

l 5
D =—=—s_. 42
p 20: 2 ( )

Therefore, from equations 26 and 39, at z = 5,, the magnitude of the internal electric field

and power density within the material are
E: = Eoe" = 0.37E0 (43)
giving 63% attenuation of the electric field and

P = Poe’z = 0.1410, (44)

abs
giving 86% dissipation of power (Figure 13) [3 9].

Metaxas and Binner [3 9] found the power penetration depth, Dp depended on
dielectric properties for various ceramics (Table 5a). At the microwave band frequencies
allocated for industrial uses, the power penetration depth could be very small. The size
of the ceramic to be heated, in particular when the ceramic is very lossy, could be many
times larger than DP, resulting in unacceptable temperature non-uniformities [3 9].

The dielectric properties vary with temperature. Therefore the power penetration
depth also changes as a function of temperature. For example, for hot pressed boron
nitride with critical temperature, Tc z 700°C, as temperature increases from 600°C to
950°C, Dp decreases from 7.62 m to 0.45 m (Table 5b) [399]. In particular, Dp rapidly

decreased as the temperature increased above the critical temperature.

39

Table 5a. Power penetration depth, Dp, for various ceramic materials [3 9].

 

Temperature Frequency 8,

 

 

Material (°C) (MHz) , 6‘ eff tan 5 Dp (m)
Pym”? ”0’0“ 800 2450 3 2 x 10“ 169
mtrrde
Calcium titanate 25 2450 180 2 x 10'3 131
Steatite 25 2450 6 2 x 10'3 23.9
I‘m“? f’l‘m‘ma 25 2450 7 6 x 10'3 8.6
srllcate
Porcelain 25 2450 5 1.5 x 10'2 2.9
Barium/strontiu
m timte 25 2450 2000 0.5 1.74
Barium titanate 25 2450 700 0.3 1.72
-3
Hot pressed 500 8500 9 4 x 10 0.47
”mum mmde 700 8500 9 1.5 x 10'2 0.12

 

Table 5b. Effect of temperature on power penetration depth, Dp, in hot pressed boron
nitride with the critical temperature, Tc z 700°C [3 9].

 

 

 

Temperature (°C) 8’, tan 6 Dp (m)
600 4.22 6 x 10‘4 7.62
700 4.25 8 x 10'4 5.70
800 4.28 20 x 10“ 2.27
900 4.35 70 x 10“ 0.64
950 4.4 100 x 10“ 0.45

 

 

 

3.3. MICROWAVE APPLICATORS

The term ‘microwave applicator’ or ‘microwave cavity’ indicates a device that
applies the microwave energy from the generator (such as magnetron or klystron
microwave sources) to the workpiece (material to be heated). Industrial microwave
applicators for materials processing (including ceramics), fall into three categories;
traveling wave, single and multimode applicators [39]. This section gives brief
descriptions for the single and multimode applicators.

Microwave cavities are simply metallic enclosures which confine the electro-
magnetic waves and cause multiple reflections of the waves from the cavity walls,
establishing a standing wave pattern. Depending on the dimensions of the cavity and/or
the operating microwave frequency, a fundamental standing wave pattern can be set up
within the cavity [40]. Such a cavity is called a ‘single-mode’ cavity. The term ‘mode’
indicates a specific electromagnetic field standing wave pattern. Compared to the single-
mode cavity, in a ‘multimode’ cavity, several fundamental standing waves or modes are
superimposed to produce a standing wave pattern that consists of several modes [40].

The multimode applicators are most common type of applicators. For example,
home microwave ovens are multimode applicators designed for in particular, food
processing. In addition to domestic use, the multimode cavities are widely used in
industry since the applicators are relatively inexpensive, simple to construct, easy to
adapt to a wide range of material loads of different effective loss factors and sizes
[28,39,64]. When microwaves are introduced into a multimode cavity, the microwaves
reflect from the cavity wall to form a complex pattern of multiple standing wave patterns

(i.e. modes), such that the electric field distribution in the multimode cavity is given by

41

the sum of all the modes excited at a particular frequency. Due to non-unifonn field
distributions formed in the multimode cavity, heating efficiency and turiformity vary
depending on (1) the location of material within the cavity and (2) the size of the material
to be processed. The lack of homogeniety in the electromagnetic field can lead to
inhomogeneous heating and hot spots [28]. To improve the uniforrrrity of heating, a
turntable which rotates at a constant speed can move the load through the nodes and
antinodes [39]. Another way to improve the heating uniformity is to use a mode stirrer
which is a structure such as a metallic multiblade fan [39]. The mode stirrer rotates
continuously and the resulting reflections of the field continuously perturbs the spatial
distribution of the electromagnetic fields which yields a better unifornrity inside the
multimode applicator.

Compared to multimode cavities, the unloaded single-mode cavity is characterized
by a standing wave pattern or mode that is well defined in space. Knowing how the
electromagnetic field is distributed within the resonant cavity enables the material to be
placed in the position of maximum electric field for optimtun electromagnetic energy
transfer, yielding high heating efficiency [28,39,52,65]. Therefore, maximizing the
electric field strength at the processed specimen location yields rapid and uniform
heating.

In exciting a specific mode in a single-mode microwave resonator cavity, two basic
methods are used (Figure 14). In general, either a loop wire (or antenna, Figure 14a) or a
straight wire (or antenna, Figure 14b) coupling probe placed at the position of maximum
magnetic field or electric field intensity, respectively, can be used to excite a specific

standing wave pattern (i.e. cavity mode) [3 8,60]. The maximum standing wave

42

——;—— 4A

 

 

antenna

E H E H probe

 

<— Input

 

 

 

 

 

 

 

 

\/

Resonator

(a) (b)

Figure 14. Methods of exciting wave modes in a resonator [60].

amplitude occurs when the frequency of the input electromagnetic waves is equal to the

resonant frequency [60].

3.4. MICROWAVE CAVITY EQUIVALENT CIRCUITS AND QUALITY
FACTOR
A series or parallel RLC lumped-element circuit often can be used to better
understand and model the resonance and quality factor in a microwave resonator cavity

[38,60]. In this section, as an example, a series RLC equivalent circuit will describe the

resonance and quality factor (Figure 15).

43

 

+9

 

 

 

 

 

 

 

 

‘
Zin
(a)

I Resonant circuit I
i Q I

I
I R L I
l a I‘m—rim" ,
l + I
I I
: l
I v _. :: CI RL
I I
l I l
I I
I — I
I 4 i
I I
I I
I I
I I

b-_——————————————————————————

Figure 15. (a) A series RLC circuit equivalent to a microwave resonator and (b) a
resonant circuit connected to an external load, RL [3 8].

44

‘—4__I

 

As discussed in Section 3.1, a cavity resonator stores energy in the electric and the
magnetic fields for any particular mode pattern. In any practical cavity the cavity walls
have a finite conductivity, resulting in nonzero surface resistance, which in turn causes
power loss by resistance heating [62]. The stored electric and magnetic energies inside
the cavity determine its equivalent inductance and capacitance. Also the energy
dissipated by the finite conductivity of the cavity walls determines its equivalent
resistance. For a series RLC lumped-element resonant circuit (Figure 15a), the input

impedance is expressed as [3 8]
1
Z.=R+ 'wL— '— 45
m J 1 (0C ( )

where Z,n = input impedance (Q)
R = resistance ((2)
L = inductance (Henry = Weber/Ampere = Volt-sec/Ampere)

C = capacitance (F arad = CoulombNolt).

Then the power delivered to the resonant circuit, P,,,, is [3 8]

 

 

 

 

2
P,., =1V1‘ =12, 12 =12, —V—
2 2 2 Z m (46)
= %|1|2(R + ij — 1.216)
where V = source voltage (Volt)
1 = current (Ampere)
1‘ = conjugate complex of I (Ampere).
The power dissipated by the resistor, R, is given by
130,, = 51F R . (47)

45

#44

The average magnetic energy stored in inductor, L, is
1 2
Wm = 4 |11 L - (48)

and the average electric energy stored in capacitor, C, is

W,=l
4

 

I
wZC

 

VC

 

2C = fi|1|2 (49)

where V, is voltage across the capacitor. Equivalently, for electromagnetic waves [60]

l 2
W=—qu 50
”,Izllv ()

1
W = [53|E|2dv. (51)

e V
Then substituting equations 47-51 into the complex power relation (equation 46) gives
[3 8,60]

P.=P

m loss

+2ja)(Wm —W,). (52)
Also, equation 45 can be rewritten as

+ zjw(W., - W.) .
III’

|1|’/2

_ loss-

(53)

in

For the given RLC circuit (or microwave resonator) (Figure 15a), resonance occurs when

the average stored magnetic and electric energies are equal, or

Wm = We. (54)
Then at resonance
m = 33593,; = R , (55)
|1| /2

That is, the input impedance at resonance is purely real impedance. Since at resonance

W”, = We , thus from equations 48 and 49 the resonant frequency must be given by

46

98606u

 

 

090 = 2 0 = — (56)
4f JLC
or

f _ 1 (57)

° 2zJLC'

Equivalently, for electromagnetic waves,

1 v

G = — - G (5 8)

a = 27: ,ua . 27!

where v is wave propagation velocity in a medium with p and a. Geometric factor, G,
depends on the geometry and dimensions of the cavity and/or cavity mode type
(Transverse Electric, TE, or Transverse Magnetic, TM, modes). When the frequency of
an impressed signal equals a resonant frequency, a maximum-amplitude standing wave
occurs [60]. Theoretically, a given resonator has an infinite number of resonant modes
where each mode corresponds to a definite resonant frequency. The mode having the
lowest resonant frequency is known as the dominant mode.

Quality factor, Q, of a resonant circuit or microwave resonator is defined as [3 8,43,
52,60-62,66]

_ (time-averaged energy stored at a resonant frequency)

 

— 27:
Q (energy dissipated in one period of this frequecy)
(59)
_ 22:22
0 P

loss

Thus Q (dimensionless) is a measure of the electromagnetic energy loss per cycle for a
cavity resonator. A lower loss implies a higher Q. In the absence of any loading effects

caused by external circuitry, the unloaded Q, Qumad is a characteristic of the resonant

47

 

 

circuit (or cavity resonator) itself. At resonance W”' = We, such that from equations 48,

49, and 55

2Wm_w 2W,_ar,L_ 1
P “P R roORC'

loss loss

 

 

(60)

thload = 00

If a resonant circuit is coupled to an external load resistor, RL, in series, the effective
resistance in equation 45 is R+RL, shown in Figure 15b. Then loaded Q, QM“, can be

expressed as

 

 

 

 

a) L l l
= 0 .—. = . 61
Qload R + RL R + RL R + RL ( )
wOL wOL (00L
From equation 60, QM”, = {of} and if we define an external Q, QM, as
a) L . . .
Q“, = 0 for series c1rcu1t. (62)
RL
Then the loaded Q can be expressed as
Qload Qext Qunload

Equivalently, for a resonant microwave cavity made of a conductive wall in the presence
of a dielectric material, Qummd = Qcav, and Q“, = Qd,.,, so that [3 8]

l l l
= +
Q load thcl Qcav

 

(64)

Where QM = 260on 2 cool. = 1
P... R 0).R C

 

= quality factor for a resonant cavity without a load

P103, = power dissipated by the conducting cavity wall

48

 

 

Q _ 200W, _ s_' _ 1
M P, 3" tané‘

= quality factor of the cavity with a dielectric material, but
with perfectly conducting walls
P2,, = power dissipated in the dielectric material.
When both wall losses and dielectric losses are present, the total power loss is Pm, + Pdm,

so equation 64 gives the total Q for the resonant cavity loaded with dielectric material as

1 1 "
load = . 65
Q [leel + Qcav ] ( )

 

 

Then the power dissipated inside the dielectric, Pd,e,, is given by [41,42]

Pdlel °C filng/oadifl2 (66)
where quality factor Q,,,ad, electric field E and dielectric losses s’gff are not independent
parameters.

As microwave energy is absorbed in a dielectric material, the material’s temperature
increases at a rate depending upon a number of distinct parameters. The heating rate is
determined by competition between the loss due to the motion of charges and dipoles and
conductive and radiative heat loss from the material [52]. For a single mode resonant

cavity, Palaith and Silberglitt [52] gave a simplified equation for the heating rate in terms

of incident power, and temperature of the material such that

 

 

 

8"
£=4QIOML efl' i1," _ 60'( area J T4 (67)
dt d: p «’8; Vc pCp VOIume material

where p is the mass density of the material, Cp is the specific heat capacity, V, is the

cavity volume, P,. is the microwave power incident on the cavity and T is the specimen

49

 

surface temperature expressed in Kelvins. e is the surface emissivity of the material and
0’ is the Stefan-Boltzrnann (or radiation) constant which has the value 5.67 x 10"2 joule
cm'2 K4.

Therefore, high Q factors coupled with high electrical field strengths can cause very
high heating rates [42]. Single-mode, resonant cavities with high Q values of several
thousands are common and have been used by several investigators to heat ceramic
materials [42,52]. Since most ceramics of interest are not strong absorbers until a
temperature over 1000°C is reached, based on equation 66 this three-order-of magnitude
enhancement of the power in the cavity is crucial in microwave heating of ceramics [52,

28].

3.5. NOTATION FOR MICROWAVE MODES IN A CYLINDRICAL
MICROWAVE CAVITY
In this study a cylindrical resonant microwave cavity [64,65] has been used for
various researches. The cavity can be internally tuned to various electromagnetic modes
by adjusting the cavity height and position of the power launch probe. Thus this section
and Section 3.6 will discuss fundamentals about a cylindrical microwave cavity such as
notation for the electromagnetic resonance modes and a ‘mode diagram’ which shows
resonance fi'equencies of each mode theoretically expected for given cavity dimensions.
For microwave cavities with either rectangular or circular cross sections, two sets of
electromagnetic modes are admissible: transverse magnetic (TM) modes and transverse
electric (TE) modes [38,60-63]. Since a microwave cavity is a hollow metallic enclosure

which confines the electromagnetic fields, the electromagnetic waves are reflected from

50

wall to wall. This process results in a component of either electric or magnetic field
being parallel to the axial direction of the cavity. Therefore transverse electromagnetic
(TEM) modes (i.e. E2 = Hz = 0) are not admissible for hollow metallic microwave
cavities. The system in which TEM modes can exist should involve two conductors, for
example, coaxial lines and two-open-wire transmission line systems [3 8,60-63].
Customarily, for notation of cavity mode in a cylindrical cavity, a cylindrical coordinate
system is used as shown in Figure 16. In Figure 16, a is a radius of the cavity and d is a
cavity height.

For the TM modes, there are no axial magnetic fields (i.e. Hz = 0) but axial electric

fields E2 #0, such that [60]

 

E, = Eonn[P””' r}os(n¢)cos[g£z) (TM,,m, modes) (68)
a
where Eoz = amplitude of the electric field

Jn = Bessel function of the first kind
PM, = mg, x value at which J.,(x) = 0
n = number of periodicity in 111 direction (11 = 0,1,2,3...)
m = number of zero fields in radial direction (m =1 ,2,3...)
I = number of half-waves in axial direction (1 = 0,1 ,2,3...).
TE modes have no axial electric fields (i.e. E2 = 0) but axial magnetic fields (Hz at 0),

such that
Q... - 17!
Hz =H0an ——r os(n¢)srn 72 (TEnm, modes) (69)
a

where Hoz = amplitude of the magnetic field

51

 

 

 

 

 

 

 

X

Figure 16. Cylindrical coordinate system used for notation of microwave cavity modes.

J.1 = Bessel function of the first kind

Qnm = 1m, x value at which J,,'(x) = 0

n = ntnnber of periodicity in ([1 direction (n = 0,1,2,3...)

m = number of zero fields in radial direction (m = 1,2,3...)

1 = number of half-waves in axial direction (1 = 1,2,3,4...).
Using equations 68 and 69, relative distributions of electric field, E,, and magnetic field,
H2, can be depicted for a given TM,,,“, mode (Figure 17) and TEM, mode (Figure 18),
respectively, as a function of angular position, 11), radial position, r, and axial position, 2.

In considering the distributions of electromagnetic fields within the cavity which

consists of good-conductive walls, there are fundamental boundary conditions to be

52

TMnm, Modes

 

 

 

 

 

 

 

 

 

 

o
-e-
l
N
:1
o
"1
I
A)
o
N
l
a. .—

 

 

21 I
Q.

 

 

 

 

 

 

 

Figure 17. Notation for TM,,,“, modes for a cylindrical microwave cavity.

53

TE nm, Modes

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

H n=0 H m=1 H I
3 ;\\ 3
H n=l H “1:2 H 1
SN ‘ f ;\ /' (z)
V V
H n=2 H m=3 H l
;\ /\ / ;\ /\ f,
V V \/
0 (IF—t 271: 0 I” a 0
Z
A
Hz=0

 

 

 

 

 

 

 

 

 

Figure 18. Notation for TEM", modes for a cylindrical microwave cavity.

54

 

satisfied. For time-varying electromagnetic waves, following boundary conditions
between two mediums should be satisfied [61,62]; i) the tangential component of an E
field is continuous across an interface, ii) the tangential component of an [7 field (I? =
I? /,u) and thus the tangential component of the B field are discontinuous across an
interface where a surface current exists, iii) the normal component of a D field (D = 81? )
and thus the normal component of E field are discontinuous across an interface where a
surface charge exists, and iv) the normal component of a B field (B = ,uH ) and thus the
normal component of H field are continuous across an interface. In order to simplify the
analytical solution of field problems, good conductors are often considered perfect

conductors in regard to boundary conditions. In the interior of a perfect conductor the
electric field is zero and any charges the conductor will have will reside on the surface
only. Subsequently, from Maxwell’s equations (equations 6 and 7), B and H are zero in
the interior of a conductor in a time-varying situation. Therefore, at the surface of the
cavity walls, the tangential component of an E field should be zero. For example, E, = O
and E, at 0 at the side wall of the cavity for a given TM,,,,“ mode (Figure 17). Also, at the
top and bottom plates of the cavity, Ez ¢ 0 and E, = 0 for a given TM,,,,“ mode. Likewise,
for a given TEM. mode, Hz ¢ 0, H, = O at the side wall and H2 = O, H, :t O at the top and
bottom plates of the cavity (Figure 18).

Figures 19, 20 and Figures 21, 22 show three-dimensional views of field
distributions for various TE and TM modes established within a cylindrical circular

microwave cavity [61,62,64,67].

55

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 
 

 

 

56

 

 

 

 

 

 

 

6 II. fillllll I . 190V I/ \III I/
d a , z \ I I
, . . , . 0 z , , , x
o , ¢ . r ’ . M I, I; z z I;
M 1| t, r III! i .1, / , ,
l l r a l |# l l x
0 ’ a ’ 1 I I
, , , , ,
E 2. . . x .. 2 E x x ,
T 1111. r111 11. T 1.111111. / 111 11..
\ \ \ i
x \ i
H E H E
C C IIIIIIIIIIIIIIIII
d d x x uuuuuuuuuuuuuu J
O O , , ,
M M , ,
1 1 I
m 11.. ,
,
m m .............
\n /,
x. /
.i x
\ ,,
H E

 

Figure 19. Fleld diStl'ibuthl’lS 0f TEon, TE012, TE111, and TEnz modes.

TE113 Mode

 

 

 

 

 

 

TE311 Mode

TE212 Mode

 

 

 

 

 

 

 

 

Figure 20. Field distributions of TE 13, TE211, TEm, and TE311 modes.

57

TMO11 Mode

 

 

 

 

 

 

 

‘___________, )
QW-‘ty
E
H .
TM012 Mode "I‘M013 Mode

 

 

 

 

 

 

 

 

Figure 21. Field distributions Of TMOI 1, TMmz, and TM013 modes.

58

TM112 Mode

TM111 Mode

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 22. Field distributions of TM1 11 and TM1 12 modes.

59

3.6. MODE DIAGRAM FOR 7" IDEAL CYLINDRICAL SINGLE-MODE

MICROWAVE CAVITY

A mode diagram is a diagram which allows one to expect which mode is admissible
for a given geometry and dimension of a resonant cavity. Equation 58 states that the
resonance fi'equency for an electromagnetic mode depends on the geometry and
dimensions of a microwave cavity. The microwave used in this study is a cylindrical
circular resonant cavity of 17.78 cm (7 inches) in diameter. The cavity has a movable top
plate which determines the actual cavity height. The actual cavity height can be adjusted
in the range of 7.3 cm to 21.95 cm. Thus various cavity modes can be established for a
given cavity height of the cylindrical cavity.

The exact equation for a resonance frequency of a cylindrical circular single-mode

resonant microwave cavity is [60]

 

(f0 )m = :2v_ \/(-}i"-) + [[1] for TM,,,,“ modes (70)
7t

 

a d
and
2 2
(.fo)nml = L (949-) + ([1) for TEM“ modes (71)
27! a d
where v = velocity of EM waves in a medium = l/ ,/ p8

= c, speed of light in a vacuum = 1/ #08,,
= 3 x 108 m/sec

a = radius of a cylindrical cavity

d = cavity height

P,.m = mu. x value at which J n(x) = 0

6O

QM, = mm x value at which Jn'(x) = 0
Thus for the cavity used in this study the value of a is fixed to 8.89 cm, while the cavity
height, d, varies from 7.3 cm to 21.95 cm. Pm and Qnm can be determined from the
Bessel Function of the first kind as shown in Figure 23 (Table 6).

Based on equations 70 and 71, resonant frequencies for various modes were
calculated for the cavity heights ranging from 4 cm to 24 cm which include the allowed
cavity heights for the cylindrical cavity used in this study (Figure 24, Table 7). Since the
frequency of the microwave power source is 2.45 GHz, at which the present cavity is
designed to operate, the frequency range is confined to 2 GHz to 3 GHz for plotting a
mode diagram.

From the mode diagram, it can be assumed that TMon, TEzn, TEon (TMm), TE112,
TMmz, T1331], TEm, TE113, and TM013 modes are theoretically admissible for the present
7" empty cylindrical resonant cavity operated at 2.45 GHz (Figure 24, Table 7). Thus the
cavity without a material load can be tuned to one of those resonant modes by adjusting
the cavity height by changing the position of the movable top plate of the cavity.
However, it has been reported that once the cavity is loaded with a material to be heated,
the empty cavity modes are modified and may become hybrid modes or even new modes
may be introduced depending on the dielectric properties and location of the material
[65]. In spite of this discrepancy between the theoretically expected modes and the
practically operating modes, the mode diagram will be useful to predict, understand and
analyze the interactions between the material and microwaves during microwave heating

in a single-mode microwave cavity.

61

Table 6. Values of (a) P,.... and (b) Qum which are used to calculate resonance frequencies
for TM,,,. and TEM, modes, respectively.

(a)

(b)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

m
P"'" 1 2 3
0 2.405 5.520 8.654
1 3.832 7.016 10.174
n 2 5.135 8.417 11.620
3 6.380 9.761 13.015
m
9"“ 1 2 3
0 3.832 7.016 10.174
1 1.841 5.331 8.536
n 2 3.054 6.706 9.970
3 4.201 8.015 11.346
1.0 _ J0
‘ J1
' g' J2
0.5 - '

 

 

 

Figure 23. Bessel function of the first kind, for order n, where n = 1, 2, 3.

 

 

 

 

f0, GHz (resonant freqency)

 

 

 

 

Lo, cm (resonant length)

Figure 24. Mode diagram for 7" ideal cylindrical single-mode microwave cavity.

63

 

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REFERENCES

K.Y. Lee, E.D. Case, J. Asmussen, Jr., and M. Siegel, “Sintering of Alumina
Ceramics in a Single Mode Cavity under Automated Control,” Microwaves: Theory
and Application in Materials Processing III. Cer. Trans, vol. 59, The American
Ceramic Society Inc., Westerville, Ohio, pp. 473-480 (1995).

K.Y. Lee, L.C.G. Cropsey, B.R. Tyszka, and ED. Case, "Grain Size, Density and
Mechanical Properties of Alumina Batch-Processed in a Single-Mode Microwave
Cavity," Mat. Res. Bull., vol. 32, no. 3, pp. 287-295 (1997).

Additional research report for sintering by K.Y. Lee, P.H. Dearhouse, E.D. Case,
“Microwave Sintering of Aluminas and Alumina Matrix Zirconia Composites Using
a Single-Mode Microwave Cavity.”

K.Y. Lee, E.D. Case, J. Asmussen, Jr., and M. Siegel, “Microwave Sintering of
Ceramic Matrix Composites and the Effect of Organic Binders on the Sinterability,”
Proceedings of the 11th Annual ESD Advanced Composites Conference, ESD, The
Engineering Society, Ann Arbor, MI, pp. 491-503 (1995).

K.Y. Lee, E.D. Case, J. Asmussen, Jr., and M. Siegel, “Binder Burn-out in a
Controlled Single-Mode Microwave Cavity,” Scripta Materialia, vol. 35, no. 1, pp.
107-111 (1996).

K.Y. Lee, E.D. Case, and J. Asmussen, Jr., “Microwave Binder Burn-out for Batch
Processing of A1203, Aleg/SiC Platelet, and A1203/Zr02 Particle Powder
Compacts,” Microwaves: Theory and Application in Majerfim Proceging V,
Ceramic Transactions Vol. 80, pp. 539-546, Edited by D.E. Clark, W.H. Sutton, and
D.A. Lewis, The American Ceramic Society, Westerville, Ohio (1997).

K.Y. Lee, E.D. Case, and D. Reinhard, “Microwave Joining and Repair of Ceramics
and Ceramic Composites,” Ceramic Engineering and Science Proceedings, vol. 18,
pp. 543-550 (1997).

K.N. Seiber, K.Y. Lee, and ED. Case, “Microwave and Conventional Joining of
Ceramic Composites Using Spin-On Materials,” Proceedings of the 12th Annual
ASC Technical Conference on Composite Materials, Dearborn, MI, pp. 941-949
(1997).

B.A. Wilson, K.Y. Lee and ED. Case, “Diffusive Crack Healing Behavior in
Polycrystalline Alumina: A Comparison Between Microwave Annealing and
Conventional Annealing,” Materials Research Bulletin, vol. 32, no. 12, pp. 1607-
1 616 (1997).

65

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

21.

K.Y. Lee, J .G. Lee, and ED. Case “An AF M Study of Therrnally-Induced Grain-
Boundary Grooving in Polycrystalline Alumina: Part I, Groove Profile, Width, and
Depth,” to be submitted for publication in Journal De Physique III (1998).

K.Y. Lee, J .G. Lee, and ED. Case, “An AF M Study of Thermally-Induced Grain-
Boundary Grooving in Polycrystalline Alumina: Part II, Groove Angle, Surface
Energy, Surface Diffusivity,” to be submitted for publication in Journal De
Physique III (1998).

K.Y. Lee, E.D. Case, and J. Asmussen, Jr., “The Steady-State Temperature as a
Function of Casket Geometry for Microwave-Heated Refractory Caskets,” Mat.
Res. Innovat. 1(2): 101-116 (1997).

K.Y. Lee, E.D. Case, “Steady-State Temperature of Microwave-Heated Refractories
as a Function of Microwave Power and Refractory Geometry,” submitted for
publication in Materials Science & Engineering A (1998).

M.C.L. Patterson, P.S. Apte, R.M. Kimber, and R. Roy, “Batch Process for
Microwave Sintering of Si3N4,” Mat. Res. Soc. Symp. Proc. vol 269, pp. 291-300
(1992).

J .D. Katz, and RD. Blake, “Microwave Sintering of Multiple Alumina and
Composite Components,” Am. Cer. Soc. Bull. 70[8], 1304-1308 (1991).

D.K. Agrawal, Y. Fang, D.M. Roy, and R. Roy, “Fabrication of Hydroxyapatite
Ceramics by Microwave Processing,” Mat. Res. Soc. Symp. Proc. vol. 269, 231-236
(1992)

Y. Fang, D.K. Agrawal, D.M. Roy and R. Roy, “Rapid Sintering of Hydroxyapatite
Ceramics by Microwave Processing,” Cer. Trans. 21, Amer. Cer. Soc., 349-356
(1991).

T.T. Meek, R.D. Blake, and J .J . Petrovic, “Microwave Sintering of A1203 and A1203
- SiC Whisker Composites,” Cer. Eng. Sci. Proc., vol. 8 (7-8), 861-71 (1987).

J. Cheng, J. Qiu, J. Zhou, and N Ye, “Densification Kinetics of Alumina During
Microwave Sintering,” Mat. Res. Soc. Symp. Proc. vol. 269, 323-328 (1992).

Materials Research Society Symposium Proceedings Volume 124, Microwave
Processing of Materials, Editors: W.H. Sutton, M.H. Brooks and U. Chabinsky,
Materials Research Society, Pittsburgh, Pennsylvania, 1988.

Materials Research Society Symposium Proceedings Volume 189, Microwave

Processing of Materials 11, Editors: W.B. Snyder, Jr., W.H. Sutton, M.F. Iskander
and D.L. Johnson, Materials Research Society, Pittsburgh, Pennsylvania, 1990.

66

22.

23.

24.

25.

26.

27.

28.

29.

30.

31.

32.

33.

Materials Research Society Symposium Proceedings Volume 269, Microwave
Processing of Materials III, Editors: R.L. Beatty, W.H. Sutton and M.F. Iskander,
Materials Research Society, Pittsburgh, Pennsylvania, 1992.

Materials Research Society Symposium Proceedings Volume 347, Microwave
Proces_sing of Materials IV, Editors: M.F. Iskander, R.J. Lauf and W.H. Sutton,
Materials Research Society, Pittsburgh, Pennsylvania, 1994.

Materials Research Society Symposium Proceedings Volume 430, Microwave
Proceging of Materials V, Editors: M.F. Iskander, J .O. Kiggans, Jr., J .C. Bolomey,
Materials Research Society, Pittsburgh, Pennsylvania, 1996.

Microwaves: Theog and Application in Materials Processing, Ceramic
Transactions vol. 21, Edited by D.E. Clark, F.D. Gac, and W.H. Sutton, The

American Ceramic Society Inc., Westerville, Ohio, 1991.

Microwaves: Theog and Application in Materials Processing 11, Ceramic
Transactions vol. 36, Edited by D.E. Clark, W.R. Tinga, and J .R. Laia, Jr., The

American Ceramic Society Inc., Westerville, Ohio, 1993.

Microwaves: Theory and Application in Materials Processing III. Ceramic
Transactions vol. 59, Edited by ???, The American Ceramic Society Inc.,
Westerville, Ohio, 1995.

W.H. Sutton, “Microwave Processing of Ceramic Materials,” Am. Ceram. Soc.
Bull. 68[2], pp. 376-386 (1989).

MA. Janney, H.D. Kimrey, and J .O. Kiggans, “Microwave Processing of Ceramics:
Guidelines Used at the Oak Ridge National Laboratory,” in Microwave Processing
of Materials, III, R.L. Beatty, W.H. Sutton, and M.F. Iskander, eds., MRS Symp.
Proc., vol. 269, pp. 173-85 (1992).

L.M. Sheppard, “Manufacturing Ceramics with Microwaves: The Potential for
Economical Production,” Am. Cer. Soc. Bull., 67[10], 1656-1661, 1988.

MA. Janney, H.D. Kimrey, “Microwave Sintering of Alumina at 28 GHz,” Ceramic
Powder Science, 11, B, Ceramic Transactions, vol. 1, pp. 919-24 (1988).

MA. J anney and H.D. Kimrey, “Diffusion-Controlled Processes in Microwave-
Fired Oxide Ceramics,” Mater. Res. Soc. Symp. Proc., vol. 189, 215-227, 1991.

Y.L. Tian, D.L. Johnson and ME. Brodwin, “Ultrafine Microstructure of A1203

Produced by Microwave Sintering,” Ceramic Powder Science 11, B, Ceramic
Transactions, vol. 1, pp. 925-932 (1988).

67

34.

35.

36.

37.

38

39.

40.

41.

42.

43.

44.

45.

46.

A. De, I. Ahmad, E.D. Whitney, and BE. Clark, “Microwave (Hybrid) Heating of
Alumina at 2.45 GHz: I. Microstructural Uniformity and Homogeneity,”
Microwaves: Theory and Application in Materials Processing, Ceramic
Transactions, vol. 21, pp. 319-28 (1991).

CE. Holcombe, T.T. Meek, and N.L. Dykes, “Enhanced Thermal Shock Properties
of Y203-2 wt% ZrOz Heated Using 2.45 GHz Radiation,” Mat. Res. Soc. Symp.
Proc. vol. 124, 227-234, 1988.

M.C.L. Patterson, P.S. Apte, R.M. Kimber, and R. Roy, “Mechanical and Physical
Properties of Microwave Sintered Si3N4,” Mat. Res. Soc. Symp. Proc. vol 269, 301-
310, 1992.

MA. Janney, H.D. Kimrey, M.A. Schmidt, and J .O. Kiggans, “Grain Grth in
Microwave-Annealed Alumina,” J. Am. Ceram. Soc., 74 [7] 1675-81 (1991).

D.M. Pozar, Microwave Engineering, p. 34-3 8, p. 330-354, Addison-Wesley
Publishing Company, Inc., Reading, Massachusetts (1990).

A.C. Metaxas and J .G.P. Binner, “Microwave Processing of Ceramics,” in
Advanced Ceramic Processing and Technology, vol. 1, chap. 8, pp. 285-367, edited
by J .G.P. Binner, Noyes Publications, Park Ridge, New Jersey, USA. (1990).

J .D. Katz, “Microwave Sintering of Ceramics,” Annu. Rev. Mater. Sci., 22: 1 53-
70, 1992.

A.J. Berteau and J .C. Badot, “High Temperature Microwave Heating in Refractory
Materials,” J. Microwave Power, 11[4] pp. 315-320 (1976).

W.R. Tinga, “Fundamentals of Microwave Material Interactions and Sintering,”
Mat. Res. Soc. Symp. Proc., vol. 124, pp. 33-43 (1988).

A.C. Metaxas and R.J. Meredith, Industrial Microwave Heating, Peter Peregrinus,
Ltd., London, UK (1983).

AR. von Hippel, ed., Dielectric Materials and Applications. pp. 3-46, MIT Press,
Cambridge, MA (1954).

Ralph W. Bruce, “Activation Energies for the Dielectric Loss Factor/AC
Conductivity of Some Polycrystalline Ceramics,” Microwaves: Theory and
Application in Materials Processing, Cer. Trans. 21, Amer. Cer. Soc., 107-116
(1991)

Barsoum, Fundamentals of Ceramics, p. 543, The McGraw-Hill Companies, Inc.,
New York (1997).

68

47.

48.

49.

50.

51.

52.

53.

54.

55.

56.

S7.

58.

59.

60.

W.D. Kingery, H.K. Bowen, and DR. Uhlmann, Introduction to Ceramics, 2nd
edition, p. 923, Wiley-Interscience Publication, New York (1976).

 

R.C. Buchanan, Ceramic Materials for Electronics, p. 33, 47, Marcel Dekker Inc.,
New York, NY. (1986).

J. Samuels and J .R. Brandon, “Effect of Composition on the Enhanced Microwave
Sintering of Alumina-Based Ceramic Composites,” J. Matls. Sci., 27, 3259-65
(1992)

RE. Newnham, S.J. Jang, Ming Xu, and Frederick Jones, “Fundamental Interaction
Mechanisms Between Microwaves and Matter,” Microwaves: Theory and
Application in Materials Processing, Cer. Trans. 21, Amer. Cer. Soc., 51-67 (1991).

S.L. McGill, J .W. Walkiewicz, and GA. Smyres, “The Effect of Power Level on the
Microwave Heating of Selected Chemical Minerals,” Microwave Processing of
Materials, Matls, Res. Soc. Proc., vol. 124, pp. 247-252 (1988).

D. Palaith, R. Silberglitt, “Microwave Joining of Ceramics,” Am. Cer. Soc. Bull.,
vol. 68, no. 9, 1601-1606 (1989).

AR. von Hippel, ed., Dielectric Materials and Applications, pp. 3-46, M.I.T. Press,
Cambridge, MA (1954).

W. B. Westphal and A. Sils, “Dielectric Constant and Loss Data,” Technical Report
AFML-TR-72-39, Massachusetts Institute of Technology, Cambridge, MA (1972).

T.T. Meek, R.D. Blake, and J .J . Petrovic, “Microwave Sintering of A1203 and A1203
- SiC Whisker Composites,” Cer. Eng. Sci. Proc., vol. 8 (7-8), 861-71 (1987).

V.K. Varadan, Y. Ma, A. Lakhtakia and V.V. Varadan, “Microwave Sintering of
Ceramics,” Mat. Res. Soc. Symp. Proc. Vol. 124, pp. 45-55 (1988).

Y-L. Tian, “Practices of Ultra-Rapid Sintering of Ceramics Using Single Mode
Applicators,” Microwaves: Theory and Application in Materials Processing, Cer.
Trans. vol. 21, Amer. Cer. Soc., 283-300 (1991).

M.A. Janney, H.D. Kimrey, “Microwave Sintering of Alumina at 28 GHz,” Ceramic
Powder Science, II, B, Ceramic Transactions, vol. 1, pp. 919-24 (1988).

W.H. Sutton, “Microwave Firing of High Alumina Castables,” Mat. Res. Soc. Proc.
vol. 124, pp. 287-295 (1988).

S.Y. Liao, Microwave Devices and Circuits, 3rd ed., p. 16-21, p. 133-141, Prentice
Hall, Englewood Cliffs, New Jersey (1990).

69

61.

62.

63.

64.

65.

66.

67.

S. Ramo, J .R. Whinnery, and T. Van Duzer, Fields and Wayes in Communication
Electronics, 2'”d ed., p. 146-147, p. 279-283, p. 411-444, p. 486-512, John Wiley &
Sons, New York (1984).

D.K. Cheng, “Field and Wave Electromagnetics,” 2"d edition, p. 307-387, p. 582-
592, Addison-Wesley Publishing Company, Inc., Reading, Massachusetts (1989).

NJ. Cronin, Microwave and Optical Wavegpides, p. 79-90, Institute of Physics
Publishing, Bristol and Philadelphia (1995).

J. Asmussen and R. Garard, “Precision Microwave Applicators and Systems for
Plasma and Materials Processing,” Mat. Res. Soc. Symp. Proc. 124, 347-352
(1988).

J. Asmussen, H.H. Lin, B. Manring, and R. Fritz, “Single-mode or controlled
multimode microwave cavity applicators for precision materials processing,” Rev.
Sci. Instrum., 58 [8] 1477-1486 (1987).

J .D. Jackson, Classical Electrodvn_amics, pp. 255-259, Wiley, New York, 1962.

Helszajn, Microwave Engineering: Passive, Active, and Non-Reciprocal Circuits,
p. 140-141 , McGraw-Hill, New York (1992).

70

CHAPTER 1

SINTERIN G

Part I. SINTERING OF ALUMINA CERAMICS IN A SINGLE MODE

CAVITY UNDER AUTOMATED CONTROLl

ABSTRACT
An automated processing system featuring a single-mode microwave cavity
operated at 2.45 GHz has been used to sinter a series of alumina powder compacts. The
automated control allows repeatable heating schedules for the processing. The resulting

sintered alumina specimens were crack-free and had small, uniform grain sizes.

1. INTRODUCTION

Microwave sintering can be an attractive processing technique since materials can
be heated directly and/or indirectly via the interaction with electromagnetic fields.
Typically microwave processing yields ceramic specimens having high densities and fine
grain sizes. Also, microwave processing allows high heating rates (short processing times),

compared to conventional heating.

 

l Ki-Yong Lee, Eldon D. Case, Jes Asmussen, Jr. and Marvin Siegel, Microwaves: Theog and

Application in Materials Processing III, Cer. Trans, vol. 59, Am. Cer. Soc. Inc., Westerville, Ohio, pp.
473-480 (1995).

71

Multimode microwave cavities [1-6] require very high power due to the relatively
low coupling efficiency of microwave energy with materials. Also, a multimode cavity’s
nonuniform electromagnetic field distribution can result in inhomogeneous heating and hot
spots depending on the volume of the processed material and the location of the material
within the microwave cavity [7]. Nevertheless multimode cavities are frequently used due
to their low cost, ease of construction and adaptability [8].

To improve process control and heating uniformity, several investigators have
designed and used single-mode microwave cavities [8-13]. Single mode cavities can
maximize the elecuical field strength at the location of processed material, potentially
yielding higher heating rates and more uniform heating than is the case for conventional
multimode cavities [7-9, 14]. Using an intemally-tuned single-mode circular cylindrical
cavity, Asmussen et a1. [8, 14] demonstrated that microwave energy can be coupled
efficiently into either low loss or lossy materials.

Most single mode cavities used for microwave processing ceramics are tuned by
manually adjusting the positions of the electrical short and the probe to maximize the
energy absorbed by the process material. Since the dielectric properties of material are
functions of both porosity and temperature, the dielectric properties of the ceramic change
during processing. This change in dielecuic properties requires that the cavity be tuned
continuously to maintain efficient microwave coupling and an optimum heating rate.
Manual cavity tuning, however, is too slow and cumbersome to allow one to precisely tune
the cavity as the material's dielectric properties can change rapidly during processing.

Recently Asmussen and Siegel [15] developed a single-mode cylindrical cavity that

is tuned by computer-automated adjustments of the sliding electrical short and probe

72

positions. Two computer-driven controllers (Microstep Drive Sx Series, Compumotor,
Fauver, MI) allow a rapid fine-tuning of the short and the probe positions to with an
accuracy of i0.1 mm. In this study Asmussen and Siegel’s computer-controlled microwave
processing system was used to obtain very similar heating schedules during processing of a
series of alumina powder compacts. Such repeatability would be diffith using manual

tuning techniques.

2. EXPERIMENTAL PROCEDURE

2.1. Experimental Apparatus

Figure 1 is a schematic of the microwave sintering apparatus. The microwave
power supply (Sairem, Model MWPS 2000, Wavemat Inc., Plymouth, MI, ) used in this
study can supply fiom zero to 2000 Watts of continuous wave microwave power at 2.45
GHz. Microwave power is generated by a magnetron. Waveguides then feed the
microwave power into the cavity through an adjustable tuning probe. Analog power meters
connected to the waveguide through attenuators indicate the forward and reflected power
levels.

The single mode microwave cavity (Model CMPR-250, Wavemat Inc., Plymouth,
MI.) used in the study can be internally tuned to resonate in many different microwave
cavity resonant modes by adjusting the short and the power launch probe (Figure 1). Cavity
tuning was performed by continuous adjustments of the probe positions in order to
minimize the reflected power after every change of forward power.

An optical pyrometer (Accufiber Optical Fiber Thermometer, Model 10, Luxtron

Co., Beaverton, Oregon) was used to measure temperatures ranging from 500°C to 1900°C

73

 

    
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

‘— Short Position

(15' 0 ml 0 Adjusting Motor
0 Q o o 9 o J

\L

Attenuators
; I: WAVEMATJ
B - I: CMPR 25° Probe Position
Power Supply Controller Adjusting Motor

 

 

 

 

 

“mm“ \ Ti:

_\ /

Crrculators L
t a

l I

12.9" E???

Motor Controllers

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 1. Schematic of microwave sintering apparatus.

with an accuracy of 11°C. A 5 mm diameter hole through the wall of the insulation casket

allowed the pyrometer to be sited on the specimen during the experimentation.

2.2. Materials

Using the computer controlled single mode cavity, powder compacts of three
different commercial alumina powders (Alcoa A-16 SG, Sumitomo AKP-30, and
Sumitomo AKP-SO) were processed. The average particle size for each of the powders is
listed in Table 1. Each powder compact was cold pressed at about 20 MPa into a disk about
22 mm in diameter and 1.7 mm thick. The initial green densities of the compacts were

approximately 50 percent with respect to the theoretical density of 3.987 g/cm3 for alumina

[16].

2.3. Microwave Sintering

Each of the alumina powder compacts was heated to 1575°C using the mm 2
microwave cavity resonant mode and then held at 1575°C for 30 minutes. Alumina, which
is a low loss material, has a loss tangent ranging from 0.0003 to 0.002 [17]. The low loss
tangent of alumina at or near room temperature limits direct microwave coupling to the
alumina. However, the alumina specimens were placed in a casket composed of a zirconia
cylinder (Type ZYC, Zircar Products Inc.) 10 cm diameter and 7 cm height. Top and
bottom discs for the casket were made from alumina insulating board (SALI, Zircar
Products Inc.). The typical loss tangent value of zirconia is about 0.01 at room temperature
[17]. Thus the zirconia casket helped to heat the alumina by radiant heating as well as

providing thermal insulation.

75

3. RESULTS AND DISCUSSION

Under computer-automated control, the heating schedule from about 800 degrees to
the maximum temperature of 1575 C was very similar for specimens of each of the alumina
powder types (Figures 2 and 3). Over this temperature range, the heating schedule for the
alumina also was very similar to the “empty casket” (no alumina specimen present) runs.
However, the power level at which significant coupling first occurred (as evidenced by an
initial, rapid temperature rise) did vary in the following way. For the AKP-30 and AKP-50
coupling became significant at about 600 Watts of input power, while the A16-SG and the
empty casket first coupled at a input power of about 300 Watts and 275 Watts, respectively
(Figure 3).

The rapid temperature rise subsequent to the initial coupling with the microwave
power may be due to hot spots in the zirconia casket cylinder, which were observed as
bright spots with the unaided eye. The differences in the initial heating of the AKP grade
powders and the A16 powders may be due to differences in the dielectric properties of the
powders.

The sintered alumina specimens had densities ranging fi'om 97.1 to 99.6 percent of
theoretical (Table 1), as measured by Archimedes method. Average grain sizes (Table 1)
were determined by the linear intercept method using SEM micrographs of fracture

surfaces.

76

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1600 k , _ - 1600 _
T q
. .. . i
6 1200 - 1 a 1200 -
b b ’
8 800 — - g 800 -
g. - + CL
s + s
E— . ,1 . i— .
400 " 7 400 " —+—+-; AKP-30 ‘ d
. . v 1
—E1— AKP-$0 .
1 4
0 L4 1 A L A A l 1 l r 1 l . O L J l I
0 30 60 90 120 150 400 800 1200
Time (min) Forward power (Watts)
(a) (b)

Figure 2. Heating schedule (a) and a plot of temperature vs. forward power (b) for AKP-
30 and AKP-50.

 

 

 

 

 

 

 

 

 

 

 

 

 

1600 r 1600 ‘
l- 4
t .1
L- A -t
G 1200 o 1200
b ‘L, '
2 > a)
B - 5 - .
8 800 - g 800 -
8. Q .
s g 4
400 - -‘%*- mesa,“ - 400 - —+—+— A16-$0.111 1
—B— A16-$0.112 i * —El— A16-SG, #2 ‘
i —:’=— Insulation , WA Infill-lion
0 1 1 I n A I L A I A 1T 1 A J , 0 j 1 n 1 L I , A 4 F A
0 30 60 90 120 l 50 400 800 1200
Time (min) Forward power (Watts)
(3) (b)

Figure 3. Heating schedule (a) and a plot of temperature vs. forward power (b) for Alcoa
A16-SG.

77

Table 1. Results on microwave sintered alumina.

 

Average particle Average grain size

Material % Densification

 

size (pm) (pm)
A16-SG 0.52 1.94 r 99.6
AKP-30 0.41 4.85 * 98.4
AKP-50 0.23 3.68 * 97.1

 

* Average intercept length was multiplied by a stereographic correction factor
1.5 to obtain the average grain size [18].

4. CONCLUSIONS
This study has demonstrated that an automated processing system featuring a
single-mode microwave cavity can be controlled to provide repeatable heating schedules
for a series of alumina powder compacts. The resulting alumina specimens were near
theoretical density with a uniform, small-grain sized microstructure. Future studies will
employ the automated processing system to sinter other ceramics and ceramic

composites.

78

10.

ll.

12.

13.

14.

15.

16.

REFERENCES

A. De, I. Ahmad, E.D. Whitney, and DE. Clark, Cer. Trans., vol. 21, pp. 319-28
(1991).

Y. Fang, D.K. Agrawal, D.M. Roy and R. Roy, Cer. Trans., vol. 21, pp. 349-356
(1991)

M.A. Janney, C.L. Calhoun, and H.D. Kimrey, Cer. Trans., vol. 21, pp. 311-318
(1991)

H.D. Kimrey, J .0. Kiggans, M.A. Janney, and R.L. Beatty, Mat. Res. Soc. Symp.
Proc. vol. 189, pp. 243-256 (1991).

M.C.L. Patterson, P.S. Apte, R.M. Kimber, and R. Roy, Mat. Res. Soc. Symp. Proc.
vol 269, pp. 291-300 ( 1992).

R.L. Smith, M.F. Iskander, O. Andrade, and H. Kimrey, Mat. Res. Soc. Symp. Proc.
vol 269, pp. 47-52 ( 1992).

W.H. Sutton, Am. Ceram. Soc. Bull. 68[2] pp. 376-386 (1989).
J. Asmussen and R. Garard, Mat. Res. Soc. Proc. vol. 124, pp. 347-352 (1988).
Y-L. Tian, Cer. Trans. vol. 21, Amer. Cer. Soc., pp. 283-300 (1991).

HQ. Tian and W.R. Tinga, Cer. Trans. vol. 21, Amer. Cer. Soc., pp. 647-654
(1991)

J .F. Gerling and G. Foumier, Cer. Trans. vol. 21, Amer. Cer. Soc., pp. 667-674
(1991)

HS. Sa’adaldin, W.M. Black, I. Ahmad and R. Silberglitt, Mat. Res. Soc. Symp.
Proc., vol. 269, pp. 91-96 (1992).

D.S. Patil, B.C. Mutsuddy, J. Gavulic, and M. Dahirnene, Cer. Trans. vol. 21, Amer.
Cer. Soc., pp. 301-309 (1991).

J. Asmussen, H.H. Lin, B. Manring, and R. Fritz, Rev. Sci. Instrum., 58 [8] 1477-
1486 (1987).

J. Asmussen, Jr. and M. Siegel, to be published.

National Bureau of Standards (U .S.), Circ. 539, vol. 9, page 3 (1959).

79

 

 

17. RC. Buchanan, ed., Ceramic Materials for Electronics, Marcel Dekker, Inc., N.Y.,
N.Y., page 4 (1986).

18. E. E. Underwood, A. R. Colcord, and R. C. Waugh, pages 25-52 in R. M. Fulrath and
J. A. Pask, eds., Ceramic Microstructur_es_, John Wiley and Sons, New York (1968).

 

80

 

Part II. GRAIN SIZE, DENSITY, AND MECHANICAL PROPERTIES OF

ALUMINA BATCH-PROCESSED IN A SINGLE-MODE

MICROWAVE CAVITY2

ABSTRACT
Four different microwave cavity modes, namely, TMm, TEnz, TE113, TM013,
were used to sinter alumina powder compacts in a batch process using a cylindrical
single-mode microwave cavity. The grain size, mass density, hardness, and fracture
toughness of the final densified products were examined in terms of (i) the position of the

specimen within the microwave casket and (ii) the cavity mode.

1. INTRODUCTION

Although microwave processing of ceramics typically involves specimens processed
one at a time, Katz et a1. (1) and Patterson et a1. (2) are among the researchers that have
batch-processed ceramics using microwaves. Katz et a1. (1) used a resonant microwave
cavity to sinter 12.5 gram cylindrical powder compacts of alumina or alumina-5 vol% SiC
in batches of 20 specimens each. A maximum microwave input power of about 4 kWatts
yielded a sintering temperature of 1600°C. Using a multimode cavity at 2.45 GHz
Patterson et a1. (2) sintered 12, 24, and 90 specimen batches of Si3N4-5% A1203 and
Si3N4-5% Y203 powder compacts. Specimens were placed in a powder bed of 40wt%

SiC, 30wt% BN, and 30wt% Si3N4 held with an alumina crucible. The results of this

 

2 Ki-Yong Lee, Luke 00. Cropsey, Benjamin R. Tyszka, and Eldon D. Case, Materials Research Bulletin,
vol. 32, No. 3, pp. 287-295 (1997).

81

 

 

study and the work of Katz et a1. (1) and Patterson et a1. (2) will be compared in the
Summary and Conclusions section of this paper.

In this study, we used a circular, cylindrical single-mode microwave cavity for
batch-processing alumina powder compacts. First, at low temperatures and low
microwave input power, the heat distribution for various microwave cavity modes was
directly determined using thermally—sensitive paper within a casket (zirconia/alumina
enclosure). Next, alumina powder compacts were sintered and the grain size, mass
density, hardness, and fiacture toughness were determined as a function of (i) the

specimen position within a casket and (ii) the cavity mode.

2. EXPERIMENTAL PROCEDURES

Disc-shaped compacts about 2.2 cm in diameter, 2 mm thick, and with a mean mass
of 1.993 i 0.003 grams were pressed from Sumitomo AKP30 alumina powder. Details of
ball-milling and pressing the powders are given elsewhere (3,4). A cylindrical single-
mode microwave cavity (CMPR-250, Wavemat Inc., MI) was used with a microwave
power supply (Sairem, MWPS 2000, Wavemat Inc., MI) which generates microwaves of
2.45 GHz and maximum power of 2000 Watts (3-5).

The microwave modes identified for the cavity loaded with the casket were TEzr 1,
mm, TEnz, TMmz, TE311, TEm, TEm, and TM013 modes. These modes are standing-
wave electromagnetic field patterns that are a function of cavity geometry and microwave
frequency (6). The microwave cavity used for this study had a movable top plate,
enabling one to change the cavity height and thus ttme the cavity to either TM (transverse

magnetic) or TE (transverse electric) modes (3-5). Two TM modes and two TE modes,

82

 

namely; TMur, TEnz, TE113, TM013, were selected for microwave heating in this study,
since TM“; and TE“; modes were separated from TEn3 and Nora modes by at least 6
cm in cavity height (Figure 1).

For low temperatures, the heat distribution inside the empty casket (without the
alumina specimens) was investigated using a thermally-sensitive paper (Graphic Controls
Corp., Buffalo, NY). Using a conventional electrical resistance fumace, it was
determined that at about 120°C the color of the paper changed from white to light blue
and that the paper turned to dark blue after an increase in time-temperature. The casket
containing a circular piece of the thermal paper about 7 cm in diameter was centered
along the axis of the microwave cavity. The microwave cavity was tuned to each of the
four cavity modes (3-5).

A different mode was used to sinter each of four batches of alumina powder
compacts, with six specimens per batch. The casket containing six specimens (Figure 2)
was centered along the cavity axis. Temperature measurement techniques in the
microwave cavity (via an optical pyrometer) are described elsewhere (4). For specimen
temperatures above 500°C, the microwave input power was increased by 50 Watts every
3 minutes and the cavity was re-tuned until the temperature reached 1500°C. The initial
input power for microwave coupling (4), the maximum input power, average heating rate
from 500°C to 1500°C, and the sintering time and temperature are summarized in Table 1
for each of the four modes.

After sintering, the mass density of the 24 individual specimens was determined by
Archimedes method. Fracture surfaces of each specimen were examined by SEM (JEOL,

J SM 6400V) to determine the grain size using a line intercept method on the

83

 

 

 

 

 

 

’ -_ \ /—--
/,’ 3 ~\\
\
~M «2 Q
s \ '—:”
f’ ’a i II
\ -‘-.
N
H\ 4%»
N / I
II ’/”’
I ’I /
i I” ’I’\
" I
I \l
\\ / ’1 ll

 

 

 

 

 

 

 

 

 

   

(a) TMu] mode (b) TE“: mode

 

 

 

 

 

(c) TE113 mode (d) TM013 mode

Figure l. Schematics for electromagnetic field patterns of the indicated microwave
cavity modes. Solid lines represent electric fields (E) and dotted lines represent magnetic
fields (H).

84

 

 

 

 

 

 

 

 

 

[A A]
r‘ '1
T C \
a / .
c: <—— Alumrna SALI
\l\ jl/F— Zirconia ZYC
a I,- §-———4-——;6 2r~|
.3 E5; _____ §._.:_;-31__Arumina SALI
l 2 IIIIIII 3 |
’,: ..... 1-——-:; ”Specimen
‘8’] \E: "g2: "gfij
m .
JL N \ 2— Alumina SALI
k—>1<————+l-—>|
1.3 cm 7.6 cm 1.3 cm

Figure 2. Schematic for casket used for microwave heating showing the positions of the
six disc-shaped powder compact specimens included in each processing batch.

Table 1. Summary for microwave processing during batch processes.

 

 

Microwave mgfiflgrt Maximum Average heating Sintering
cavity mode p . input power rate from 500°C temperature and time
couplrng
W111 130 Watts 1060 Watts 16.0 °C/min. 1500°C for 30 min.
TE 12 90 Watts 1250 Watts 14.0 °C/min. 1500°C for 30 min.
TE113 100 Watts 1220 Watts 14.0 °C/min. 1500°C for 30 min.
TM013 190 Watts 1130 Watts 17.3 °C/min. 1500°C for 30 min.

 

 

85

micrographs.

The sintered specimens were polished with consecutive grits of 17, 15, 10, 6, and 1
pm diamond paste compounds (Warren Diamond Powder Company) using a Leco VP-SO
polishing machine. Ten Vicker’s indentations were made on each specimen, with an
indentation load, load time, and loading rate of 98 Newtons, 5 seconds, and 60
jun/second, respectively, to determine the hardness and fracture toughness of the

specimens.

3. RESULTS AND DISCUSSION

At low input power, the nontmiform heat distribution observed for each cavity mode
(Figure 3) likely resulted from spatial variation of the microwave power densities
absorbed by the casket. The central portion of the SALI setter within the casket
apparently did not couple well with the microwave field (Figure 3). The microwave-lossy
zirconia cylinder did couple well and the interaction between the microwave field and the
zirconia cylinder likely modifies the local electric field pattern (Figure 3).

Although at low microwave input power and low temperature the heat distribution
within the empty casket was nonuniform, the specimens sintered at higher input power all
had mass densities greater than 98.3% (Table 2). The mean grain size of batch-processed
specimens was similar fiom mode to mode ranging from 6.00 pm for TE 12 mode to 8.00
pm for Win mode, although the grain size was a weak function of the position of
individual specimens within the casket (Table 2).

The hardness, H, of the sintered alumina was determined by (8,9) H = aP/az, where

2a is the diagonal length of the indent, P is load and or is 0.4636, based on the area of the

86

 

Vicker’s indenter contact (8,9). The fracture toughness, Krc, was calculated by (8,10) Krc
= BP(E/H)”2c'3/2, where 2c is the total radial crack length, B is a dimensionless constant
equal to 0.016 :1: 0.004, E is the elastic modulus (assumed to be 365.4 GPa, which
corresponds to sintered alumina at 95% of theoretical density (11)), and H is the hardness
determined at the load P.

For the 24 alumina specimens sintered in this study, the mean and standard
deviation of the hardness was 16.19 GPa :t 0.58 GPa which corresponds to a coefficient
of variation of only 0.036 (Figure 4a) The hardness values obtained in this study thus are
reasonably consistent with the literature values for hardness of polycrystalline alumina of
13 GPa to 23 GPa (9,12-14). The fracture toughness ranged from 2.34 MPam”2 to 3.03
MPa-m”2 with the average value of 2.70 MPa-mm. The standard deviation was $0.18
MPa-m"2 which was 6.7% of the average toughness value. The toughness values
determined in this study were somewhat lower than the literature values of about 3 to 5
MPa-mm (9,12-14).

The variations in the hardness and fracture toughness were examined in terms of (i)
the specimen position (Figure 2) and (ii) the operating microwave cavity mode (Figure 1).
The average hardness and fracture toughness values for the specimens heated at the same
position but in different batches (Figures 4a and 4b) differed by no more than 2.6% and
5.3%, respectively, from position to position. The hardness for the specimens heated at
positions 1 and 4 (Figure 2) were somewhat higher than for the specimens heated at
positions 2, 3, 5 and 6 (Figure 4a) The hardness of specimens heated at positions 3 and 6
were slightly lower than average (Figure 4a)

Unlike homogeneity in the hardness and toughness data as a function of specimen

87

 

(a) TM": mode (b) TEm mode

 

(c) TEm mode (d) TM013 mode

Figure 3. Heat distribution inside empty casket (Figure 2) as determined by thermally
sensitive paper. The casket was heated in each cavity mode (a) for 5 minutes at 130
Watts, (b) for 1.5 minutes at 90 Watts, (c) for 2 minutes at 90 Watts, and (d) 4 minutes at
170 Watts. The dark areas in (a)-(d) indicate regions of microwave heating.

position, there are small apparent differences in hardness and toughness between
specimens sintered in the four different cavity modes (Figures 5a and 5b). The average
hardness of the specimens sintered in TE112 mode was about 6.6% higher than the
average hardness of the specimens sintered in TEm mode, which is lowest. Also, the
toughness data differed from 2.45 MPam“2 for W111 mode to 2.84 MPam”2 for TEnz
mode by 15.9%.

Differing grain size among the sintered specimens is a potential source of hardness
or toughness variation. For large-grained alumina, fracture toughness reaches a
maximum for grain sizes of about 100 um ( 15,16), but for grain sizes below 10 pm the
trend is less clear. Fracture toughness may increase or decrease with the grain size
depending on the test method or the specimen type (17). Rice et al. (15,16) show a
relatively constant Krc for alumina with grains smaller than 10 mn, while for similar grain
sizes Claussen et a1. (18) indicate Kxc increases as grain size decreases. For fine-grain-
size alumina, Skrovanek and Bradt (19) found hardness was grain-size independent for
grain sizes between 2 pm and 4 am, but for the grain sizes larger than 4 pm, the hardness
decreased with grain size.

In this study, the grain sizes for the entire set of 24 sintered alumina specimens
ranged from only 5.7 pm to 9.4 pm (Table 2) and thus not surprisingly the hardness and
toughness data are scattered within a relatively narrow band, with no definitive
relationships between grain size and hardness or toughness. However, some possible
trends in grain size do appear. For example, specimens sintered in TEuz mode with
smallest average grain size, (Table 2) yielded relatively higher hardness and fracture

toughness values (Figures 5a and 5b). Specimens sintered in TM; 11 mode with largest

89

Table 2. Density and grain size in terms of cavity modes and specimen location.

 

 

 

 

$3212, TMln TE112 TE113 TM013
Position Density Grain Density Grain Density Grain Density Grain
of size size size size
Specimen (%) (pm) (%) (um) (%) (um) (%) (pm)
1 99.9 6.96 98.6 6.40 99.8 7.90 99.6 8.52
2 100.0 8.10 100.0 5.89 99.9 8.22 99.0 7.58
3 99.7 8.40 99.5 6.18 99.1 7.09 99.8 8.48
4 99.8 7.80 99.3 5.80 98.3 7.36 99.5 6.70
5 100.0 7.34 99.9 5.65 99.8 7.97 99.9 6.74
6 99.8 9.42 99.4 6.10 99.9 7.65 99.3 7.39
:3: :0: :9: :9: :9: :9: :3 :5:
grarnsrze . . _. . . . .

 

 

 

 

 

* Density (%) is relative with respect to the theoretical value of alumina (3.987 g/cm3)

(7)-

" Grain sizes were determined by multiplying the average intercept length from the
SEM micrographs of fracture surfaces by the stereographic correction factor 1.5.

90

 

—1
—I
—
—
u—
—q

17e a- -

—
OK
I
l

 

Hardness (GPa)

 

 

 

 

 

 

 

 

14 — —
L 1 1 l 1
1 2 3 4 5 6
Specimen position
(a)
“A 3-2 I I I I r I
.8
a
E 2.3 - —
V
m
V)
i.
a 2 4 - -
.9
E L
o 2.0 — -
5‘.
LL‘ 1 l l l l l
1 2 3 4 5 6
Specimen position
(b)

Figure 4. Hardness (a) and fracture toughness (b) for batch-processed alumina
specimens in terms of specimen position. Error bars represent the standard deviation.

91

 

17~ -

u—n
ON
I
i

Hardness (GPa)

 

 

 

 

 

 

 

14 - —
L l l l
TE112 TM013 TE113 TMlll
Cavity mode
(a)
“A 3.2 I T I T
‘fa
(U
E 2.8 — 4
v
9:
E.
3 2 4 - -
8
E
0 2.0 - -
8
m l l l 1
TE112 TM013 TE113 TMlll
Cavity mode
('0

Figure 5. Hardness (a) and fracture toughness (b) for batch-processed alumina
specimens in terms of cavity mode. Error bars represent the standard deviation.

92

average grain size have lower average fracture toughness than the specimens sintered in

the other three cavity modes (Figure 5b).

4. SUMMARY AND CONCLUSIONS

In this study and the studies by Katz (2) and by Patterson (3), relatively uniform
grain sizes and densities were achieved for batch-processed specimens under differing
microwave processing conditions. Each of the three studies involved microwave power
at a fixed frequency of 2.45 GHz, although Katz (2) and Patterson (3) each used about 4
kW of microwave power to achieve a sintering temperature of 1600°C, while this study
used considerably lower input power (from 1.0 to 1.25 kW) to achieve a sintering
temperature of 1500°C (Table 2). Two studies (this study and Katz (2)) used single-mode
microwave cavities while Patterson (3) used a multimode cavity.

Each of the three studies employed a casket (specimen enclosure) during sintering.
Patterson (3) used an alumina crucible, with a powder bed enclosing the specimens,
while Katz used a casket composed of cylindrical aluminosilicate surrounded by zirconia
board. At low temperatures, the temperature distribution in Patterson's (3) powder bed
was nonuniform, while at higher (sintering) temperatures hot-spots within the powder bed
were dissipated by thermal conduction, yielding isothermal conditions. Patterson's results
parallel this study's results; at low temperature the therrnally-sensitive paper indicated a
nonuniform heat distribution within the empty zirconia casket, but the uniform final grain
size and density of the sintered specimens (Table 1) indicate a relatively uniform
temperature field within the casket at the sintering temperature.

Unlike the studies by Katz (2) and Patterson (3), this study determined hardness

93

and fracture toughness for each of the batch-processed specimens. Also, this study
differed from those of Katz and Patterson in that four different microwave modes (Figure
1) were employed to heat the specimens. Despite the spatial variations in the
electromagnetic fields within the cavity for a given mode, and despite the differences
among electromagnetic field patterns from mode to mode (Figure 1), this study revealed
only relatively small differences in hardness and fracture toughness as a function of (i)
specimen position within the zirconia casket and (ii) the electromagnetic mode used to
sinter the specimens. Thus, the microwave casket (specimen enclosure) in this study and
in the studies by Katz (2) and Patterson (3) apparently can act to homogenize the
temperature field for batch-processed ceramics, such that the grain size, density (2, 3, and

this study), hardness, and fracture toughness (this study) can be relatively uniform.

ACKNOWLEDGEMENTS

The authors acknowledge the financial support of Research Excellence funds

provided by the State of Michigan.

94

 

 

10.

ll.

12.

l3.

14.

15.

16.

REFERENCES
J.D. Katz, and RD. Blake, Am. Cer. Soc. Bull. 70[8], 1304 (1991).
M.C.L. Patterson, P.S. Apte, R.M. Kimber, and R. Roy, in MRS Symp. Proc., ed.
R.L. Beatty et al., Vol. 269, p. 291, Materials Research Society, Pittsburgh, PA
(1992)

K.Y. Lee, E.D. Case, J. Asmussen, Jr., and M. Siegel, in Cer. T rans., Vol. 59, p.
473, The American Ceramic Society Inc., Westerville, Ohio (1995).

K.Y. Lee, E.D. Case, J. Asmussen, Jr., and M. Siegel, in Proceedings of the 11th
Annual ESD Advanced Composites Conference, p. 491, Ann Arbor, Michigan
(1995).

K.Y. Lee, E.D. Case, J. Asmussen, Jr., and M. Siegel, Scripta Mat, 35[1], 107
(1996)

K.Y. Lee, E.D. Case and J. Asmussen, Jr., submitted.
National Bureau of Standards (U .S.), Circ. 539, Vol. 9, p. 3 (1959).

J .B. Wachtrnan, in Mechanical Properties of Ceramics, p. 83, John Wiley & Sons,
Inc., New York (1996).

U. McCohn, in Ceramic Hardness, p. 10, Plenum Press, New York (1990).

G.R. Anstis, P. Chantikul, B.R. Lawn, and DB. Marshall, J. Amer. Cer. Soc. 64[9],
533 (1981).

W.D. Kingery, H.K. Bowen, and DR. Uhlmann, in Introduction to Ceramics, 2"d
ed., p. 777, John Willey & Sons, New York (1976).

RF. Cook and GM. Pharr, J. Amer. Cer. Soc. 73[4], 787 (1990).

D.W. Richerson, in Modern Ceramic Engineering, 2"d edition, p. 179, 360, Marcel
Dekker, Inc., New York (1992).

PS. Apte, R.M. Kimber and M.C.L. Patterson, in Structural Ceramics Processing,
Microstructure and Properties Proc. of the Riso Int. Symp. on Metallurgy and
Materials Science, p. 167, Riso National Lab., Riso Library, Roskilde, Den. (1990).
R.W. Rice, S.W. Freiman, and RF. Becher, J. Amer. Cer. Soc. 64[6], 345 (1981).

R.W. Rice and SW. Freiman, J. Amer. Cer. Soc. 64[6], 350 (1981).

95

17. E. Dérre and H. Hiibner, in Alumina, ed., B. Ilschner and NJ. Grant, p. 85,
Springer-Verlag, New York (1984).

18. N. Claussen, B. Mussler, and M.V. Swain, J. Amer. Cer. Soc. 65, CM (1982).

19. SD. Skrovanek and RC. Bradt, J. Amer. Cer. Soc. 62, 215 (1979).

96

Part III. IVIICROWAVE SINTERING 0F ALUMINA AND ALUMINA

MATRIX ZIRCONIA COMPOSITES USING A SINGLE-MODE

MICROWAVE CAVITY’

ABSTRACT
In this study, alumina and alumina-based zirconia particulate composites have been
successfully densified using 2.45 GHz microwaves in a cylindrical single-mode
microwave cavity. The ‘microwave effect,’ that has been demonstrated by many
researchers on a wide range of ceramics, was verified by comparing the densities and the
microstructure of alumina/zirconia composites densified by microwave heating and

conventional heating.

1. INTRODUCTION

Recently, researchers have successfully processed a variety of ceramics using
microwave energy [1-7]. Microwave processing of ceramics can have a number of
benefits, for example, an Ontario Ministry of Energy study [8] showed microwave drying
and sintering uses less energy than conventional drying and sintering by a factor of about
two and ten, respectively. In addition to the energy savings, the nature of microwave
heating (i.e. internal and volumetric heating) results in a set of “microwave effects,”
including lower sintering temperatures [1], smaller grain sizes [9], and lower diffusional

activation energies [10] compared to conventional processing. Also, several researchers

 

3 Additional report for sintering by Ki-Yong Lee, Paul H. Dearhouse, Eldon D. Case, and J es Asmussen Jr.

97

 

[1 1-13] report microwave processing can improve microstructure and mechanical
properties.

A number of researchers have encountered problems with microwave sintering,
including thermal runaway [14-16], inability to heat low dielectric loss materials without
a microwave susceptor [17], and cracking of the processed materials [18,19]. The
microwave sintering techniques used in this study employed a microwave susceptor
(casket) to sinter 5.1 centimeter diameter alumina and alumina/zirconia specimens
without thermal runaway and without cracking the specimens. However, the sintering
procedure was developed such that it accommodated two types of casket-microwave
interactions: (1) development of local hot spots in the cylindrical casket wall at
temperatures between about 800°C and 1100°C and (2) local melting of the casket end
plates at temperatures above 1550°C.

Recently Lee et al. [20] successfully densified alumina discs about 2 cm diameter
using a cylindrical single-mode cavity equipped with a computer-controlled tuning
system developed by Asmussen et a1. [20]. In this study, the same single-mode
microwave cavity [20,21] is used to densify 5.1 cm diameter disc-shaped ceramic powder
compact specimens in TMIII, TE112, TE113, and TM013 microwave cavity modes. The
ceramic materials used in this study included (i) three grades of alumina and (ii) alurnina-
matrix/zirconia particulate composites. In particular, we verified the advantages of
microwave heating by comparing the microstructure and densities of A1203/Zr02
densified by the microwave heating and the conventional means. X-ray diffraction
(XRD) of the sintered A1203/Zr02 composites showed the presence of both tetragonal and

monoclinic zirconia phases dispersed within the composite specimens. The mass density

98

and grain size of sintered specimens were found to be relatively uniform with respect to
both (i) the radial position within a given specimen and (ii) the cavity mode used to sinter

the specimen.

2. EXPERIMENTAL PROCEDURES
2.1. Materials and Specimen Preparation

For the alumina powder compacts referred to here as Group A (Table I), one
compact of each of three different grades of alumina powders (Sumitomo AKP30,
AKP50, and Alcoa A16SG) was prepared to determine the microwave sintering behavior
of each of the powder types. In addition, four Group B powder compacts (Table H) were
fabricated to examine the grain size and density uniformity across the disc-shaped
specimen afier microwave sintering in various microwave cavity modes. Also, nine
alumina/zirconia ceramic composites were made using AKP50 alumina powder and a 0.4
micron [21] zirconia powder (Fisher Scientific Company).

A hardened tool steel die was employed to form the disc-shaped powder compacts
51 millimeters in diameter. All alumina and alumina/zirconia powder compacts were
pressed uniaxially at about 4.4 MPa using a Carver hydraulic press.

For the AKP50/10wt% Zr02 powder compacts, a mixture of alumina and zirconia
powders were ball-milled in a plastic mill for 24 hours using alumina grinding media.
Group B AKP30 alumina powders were ball-milled for 48 hours. The mass of the three
Group A alumina specimens and the nine alumina/zirconia composite specimens was
10.031 :1; 0.064 grams. The Group A alumina powder compacts were about 2.8

millimeter thick, while the alumina/zirconia powder compacts were about 2.7 millimeter

99

Table 1. Summary of microwave sintering of aluminas.

 

 

Material Average Sintering Heating rate Average grain Relative
particle size temperature (°C/min.) size (urn)* density (%)
(pm) (° C)
AKP50 0.23 1600 12.5 9.50 96.6
AKP30 0.41 1600 - 1535 12.6 12.50 96.6
A16SG 0.52 1595 - 1580 12.1 6.74 96.1

 

"‘ Average intercept length was multiplied by a stereographic correction factor 1.5 to

obtain the average grain size [124].

Table II. Summary for microwave processing of four AKP30 alumina specimens each in
different cavity mode.

 

Microwave Initial input Maximum Average heating Sintering temperature

 

cavity mode power for input power rate from 500°C and time
coupling
TMlll 150 Watts 1275 Watts 14.3 °C/min. 1500°C for 30 min.
TE112 130 Watts 1180 Watts 15.2 oC/min. 1500°C for 30 min.
TEII3 100 Watts 1450 Watts 14.5 °C/min. 1500°C for 30 min.
TM013 200 Watts 1350 Watts 14.2 °C/min. 1500°C for 30 min.

 

100

thick. The four Group B AKP30 alumina specimens were 3.2 mm thick afier uniaxial
pressing, with average mass of 11.928 grams and a standard deviation of 0.0006 grams.
The green (unfired) densities of all the powder compacts included in this study

corresponded to about 45 percent of theoretical.

2.2. Microwave Sintering

All specimens were sintered in air using a 2.45 GHz microwave system that
included a 2000 Watt microwave power supply (Sairem, MWPS 2000, Wavemat Inc.,
MI) and a cylindrical single-mode microwave cavity 17.78 centimeters in diameter
(CMPR-250, Wavemat Inc., MI) (Figure 1). The microwave cavity was equipped with a
computer-controlled tuning system for precise and fast tuning [20].

The single-mode cavity used in this study allows the microwave sintering to be done
using a standing wave electromagnetic field pattern. Instead of single-mode cavities,
most microwave applicators used to process materials are multimode cavities similar to
domestic microwave ovens. Multimode cavities are relatively inexpensive and easy to
construct, but the electromagnetic field distribution within the cavity is not well defined
and the power efficiency is relatively low [22]. Also, the non-uniform field distribution
within the multimode cavity promotes thermal instability in the processed material, which
can lead to local melting or cracking in the specimen. Single-mode microwave cavities
provide well defined electric field and enhanced power dissipation by the processed
material [22]. Precise tuning of a single-mode cavity to a characteristic mode can
optimize power dissipation in the processed material.

Each specimen was sintered using a microwave casket [20,21] composed of a

101

Upper limit /

switch

  

Short position
adjusting motor

 

   
   

Lower limit ”’4_

    
   

 

 

 

 

III
switch I' ! I'Iill-i
IIII
I I
Viewmg WAVEMAT
wmdow [ CMPR 250 ]
Waveguide adjusting motor

 

 

 

.' .
1.-
v

v

 

 

 

 

 

 

 

 

 

 

Casket

 

 

 

 

 

 

 

Finger
stock

 

 

 

 

 

 

 

 

 

 

Figure 1. Schematic of microwave processing apparatus.

102

Probe position

cylindrical zirconia microwave susceptor (Type ZYC, Zircar Products Inc.) having a 10.2
centimeter outside diameter and a 7.6 centimeter inside diameter (Figure 2). The top and
the bottom plates of the casket (Figure 2), which were each about 2 cm thick, were cut
from aluminosilicate refractory board (SALI, Zircar Products Inc.) In addition,
aluminosilicate fiber (SAFFIL, K-Industrial Corp.) was used as a setter material for
specimen inside the casket. The SAFFIL, which was shaped into a disc of about 7.5
centimeter in diameter and 0.5 centimeter thick, was placed directly on the SALI casket
end plate, and the specimens were placed on the SAF F IL disk (Figure 2).

For the three Group A A1203 specimens and five AKP50/Zr02 specimens (Tables I
and III), the microwave input power initially was set at 50 Watts with the cavity tuned to
TM1 11 mode. Then the microwave input power was increased by 50 Watts every 3

minutes up to 150 Watts. The casket-specirnen system was held for about 15 to 25

 

 

 

 

 

 

 

 

 

10.2 cm
[L ‘1
1‘ '1
1V
5 <———Alumina SALI
N
__. I
i <—— Zirconia ZYC
E I
[3 I / Specimen
E if .. i ” :‘if'L‘ ““Alumina SAFFIL
O
2 <———-Alumina SALI
L
1.3 cm 7.6 cm 1.3 cm

Figure 2. Schematic of a casket and the disc-shape powder compact specimen about 5
cm in diameter.

103

minutes at 150 Watts. Within about 5 to 10 minutes after the power was increased to 150
Watts, the casket began to heat significantly (corresponding to a specimen temperature of
about 500°C). For further heating the microwave input power was increased, followed by
tuning the cavity after every change of the power.

During microwave heating of the three Group A alumina compact specimens (Table
I) the microwave input power was adjusted to maintain a heating rate of 10°C/min. for the
temperature range of about 700°C to 1600°C (Figure 3a). As a result, an average heating
rate of about 12.5°C/minute was obtained for the entire interval from room temperature
(25°C) to the sintering temperature (Figure 3a, Table 1).

Four A1203/10wt% Zr02 powder compact specimens were microwave processed;
one specimen at each of the following four temperatures: 1150°C, 1250°C, 1350°C, and
1450°C. Four additional A1203/10wt% Zr02 powder compacts were processed at an
identical set of temperatures using a conventional high temperature horizontal tube
furnace (Thermtec Furnace, MRL Industries, California) at a fixed heating rate of
10°C/minute. A ninth composite specimen was microwave-sintered at 1550°C using a
10°C/minute rate, the same heating rate as that of the conventional furnace. No
conventional sintering was performed at 1550°C since the maximum use temperature of
the conventional furnace was 1500°C. The Group A alumina specimens and the nine
AKP50/Zr02 composite specimens were each held at the maximum temperature for 20
minutes.

Unlike the three Group A alumina specimens and nine AKPSO/ZrOz specimens

104

Table III. Summary of sintering of zirconia using microwave and conventional means.

 

Processing Specimen Sintering Sintering Average Average Relative

 

 

temp. time heating rate grain size density
(° C) (min) (°C/min-) (pm? (%)
Al/Zr-l 1550 20 10 4.55 96
Al/Zr-2 1450 20 22 2.42 95
Microwave Al/Zr-3 1350 20 20 ** 94.2
Al/Zr-4 1250 20 19 ** 72.4
Al/Zr-S 1150 20 15 ** 52.3
CAl/Zr-l 1450 20 10 0.77 87.4
Conventional CAl/Zr-2 1350 20 10 ** 69.8
CAl/Zr-3 1250 20 10 ** 60.7
CAl/Zr-4 1 150 20 10 ** 52.3

 

* Average intercept length was multiplied by a stereographic correction factor 1.5 to
obtain the average grain size [24].
** Average grain size was not determined.

105

 

 

 

 

 

 

 

 

 

 

 

J
1600 - 4
,,\ .
U ..
b 1200 - -
g ..
N " .
g 800 - -
r ’ —+—_-t— m '1
E" 400 -
L —:r— AKP30
C -fiF— awm:
O I n I I I l I I I I I l I rfi l I
0 30 60 90 120 150 180
Time (min.)
(a)
I I r j I l I
- 4
1600 r p » “f1
A t g 4’ r
L) .
b 1200 r r
:0 9 ’ fl ”
g 800 — 9 ~
. lirw
F“ ‘ -’ —fi+- MWJflWCJWONm
400- A
_ —'—"—_ 4 MW,1450'C, ZYC/Illi- 1
(NJflWtJWOd; ‘
0 I I l I I I I I i I I 1 I I I I I

 

 

 

0 30 60 90 120 l 50 1 80
Time (min.)

(b)

Figure 3. Heating schedules for (a) microwave heating of aluminas, and (b) microwave
heating and conventional heating of AKPSO/ l Owt% zirconia composite specimens.

106

sintered in TM; 11 mode, the four Group B AKP30 alumina specimens were heated one at
a time in four different cavity modes, namely, the W111, TE112, TEI 13, and TM013 modes.
A fixed microwave input power was used to initially couple the zirconia casket with the
microwave field, where the magnitude of input power required for the initial coupling
depended on the cavity mode (Table II) [23]. Immediately after the casket began to heat,
the input power was increased by 50 Watts every 3 minutes until the temperature reached
1500°C. The Group B specimens were held at the 1500°C for 30 minutes for final
densification (Table II).

To determine which zirconia phases were present in the final microwave-sintered
alumina-matrix/zirconia specimens, the x-ray diffraction (XRD) pattern was examined for
specimen Al/Zr-l using Cu—Ka x-ray (A. = 1.5406 A) (Scintag XDS 2000, Scintag Inc.,
USA.) The specimen was scanned for the diffraction angle, 20, ranging from 20° to 70°
at step size of 003°, with an accelerating voltage of 35 kV and current of 25 mA. The
XRD patterns of AKP50 alumina powder and the pure zirconia powder also were
examined to allow direct comparison with the alumina and zirconia phases in the Al/Zr-l
pattern.

Using a diamond saw, a bar-shaped specimen about 4 cm long was cut from each of
the four sintered Group B alumina specimens (Figure 4). Each bar was fractured into
three sections A, B, and C (Figure 4) to determine the mass density and grain size
depending as a function of radial position within the specimen. Grain sizes of specimens
were determined using a line intercept method on SEM (J SM-6400V, JEOL) micrographs

obtained from fracture surfaces [24].

107

Top View

 

 

Sldé view I 2.5 mm

i
T

l
‘1
#1

7T

40mm

Figure 4. Schematic for microwave sintered AKP30 alumina specimen used to examine
the uniformity in grain size and density along the diameter, showing the locations of
sections A, B, and C.

3. RESULTS AND DISCUSSION

3.1. Microwave Sintering of Alumina

Using 3.987 g/cm3 for the theoretical density of alumina [25] (Table I), relative
densities of up to 96.6% of theoretical were calculated for the three different grades of
pure alumina. Figures 5a, 5b, and 5c show the microstructure of AKP50, AKP30,
A16SG, respectively. Figure 5a shows the pores trapped at grain boundaries typical of
densified ceramic materials. The fracture surface of the AKP30 specimen shows the
cleavage planes indicating regions of transgranular fracture (Figure 5b). Figure 5c

indicates that the fracture mainly occurred by intergranular fracture.

108

 

Figure 5. Fracture surfaces of microwave sintered aluminas: (a) AKP50, (b) AKP30,
and (c) A16SG.

109

3.2. Microwave and Conventional Sintering of Alumina/10wt% Zirconia

The theoretical density of alumina and zirconia (monoclinic) is 3.987 g/cm3 [25] and
5.82 g/cm3 [26], respectively, yielding a theoretical density of 4.17 g/cm3 for the
alumina/10wt% zirconia composites. Relative mass densities of the alumina/zirconia
composites are given in Table 111.

At a sintering temperature of 1150°C, the mass density was 52.3% of theoretical
(Table III and Figure 6) for both the specimen sintered in the microwave and the
specimen sintered by conventional means. However, as the sintering temperature
increased from 1150°C to 135 0°C, the density of the microwave heated specimens rapidly
increased compared to the densities of the conventionally sintered specimens (Table III

and Figure 6). Specimen Al/Zr-3 (microwave-sintered) and CAl/Zr-2 (conventionally

 

60

l

_

 

 

Relative density (%)
5‘

 

 

 

 

50- {—9— M.............. J]
r —A— Conventional heating 3
40 . l . 1 . L . 1 .
1 100 1200 1300 1400 1500 1600
Temperature (°C)

Figure 6. Relative densities of AKP50/10wt% zirconia composites densified by
microwave heating and conventional heating as a function of temperature.

110

 

sintered) both were sintered at 1350°C for 20 minutes, using heating rates 20°C/minute
and 10°C/minute, respectively. Final relative densities of 94.2% for the Al/Zr-3 and
69.8% for the CAl/Zr-2 indicate the improvement in densification afforded by microwave
processing the alumina-matrix/zirconia specimens. Specimens Al/Zr-2 and CAl/Zr-l
both were sintered at 1450°C for 20 minutes, but the microwave sintered Al/Zr-2 was
well densified (95% of theoretical) while the density of the conventionally sintered
CAl/Zr-l was 87% of theoretical density.

The microstructures for specimens Al/Zr-2 and CAl/Zr-l showed significant
differences (Figures 7b and 7c). The average grain size of Al/Zr-2 was 2.42 pm, while
the average grain size of CAl/Zr-l was 0.77 m (Table H1). The average particle size of
the AKP50 alumina powder was 0.23 pm and the particle size for the zirconia powder
used in this study was less than 0.4 pm (Experimental Procedure). Specimen CAl/Zr-l
(conventionally sintered at 145 0°C) was at the initial stage of sintering at that temperature
only three or four particles began to coalesce.

As is typical in both conventional and microwave sintering of ceramics [9], a higher
heating rate yields a smaller grain size. The smaller average grain size of specimen
Al/Zr-2 compared to specimen Al/Zr-l (Table III and Figures 7a-7c) likely results from a
heating rate of about 22°C/minute for the Al/Zr-2 in contrast to a heating rate of about
10°C/minute for the Al/Zr-l (Table HI and Figures 7a-7c) Microwave sintering can yield
smaller grain size than sintering with conventional furnaces due to fast heating and
enhanced densification at lower temperature which is so called the ‘microwave effect’
[1,9,10,16,22]. The well-known and widely-discussed microwave effect results from the

direct interaction of the processed material with the microwave field, resulting in internal

1]]

 

Figure 7. Fracture surfaces of AKPSO/ 10wt% zirconia sintered (a) by microwave at
1550°C for 20 minutes, (b) by microwave at 1450°C for 20 minutes, and (c) by
conventional fumace at 1450°C for 20 minutes.

112

volumetric heating. The typical loss tangent of alumina is about 0.0001 at ambient
temperature and thus does not absorb the microwave energy significantly [27]. However,
as the temperature increases to 1000°C, the loss tangent of alumina rapidly increases to
about 0.01 [27]. A loss tangent of 0.01 indicates significant interaction with the
microwave field. Although we heated the specimens using the casket composed of
microwave susceptor (zirconia), at high temperature the alumina itself absorbed the
microwave energy, yielding high densification even at the temperature as low as 1350°C
(Table HI and Figure 6).

The x-ray diffraction pattern for the zirconia powder matched the pattern for

 

 

 

 

 

 

 

 

 

 

l l l i I I 1 1 l I 1 J I I I l I I l J I I l l
a-Alumina
m
t:
8
E m-Zirconia
D
> or . .
u a 10wt% Zirconia
L.“ or
d.)
or
ad a a a
t (I.
m m Li.._.l ‘t" M
I I I j 1 I I I h I I I I l I I I I l I I I I
20 30 40 50 60 70
20 (deg.)

Figure 8. X-ray diffraction patterns of AKP50 alumina powder, zirconia powder, and
microwave sintered AKP50/10wt% zirconia.

113

 

monoclinic zirconia [26]. The XRD pattern for specimen Al/Zr-l indicated the presence
of both the monoclinic phase and the tetragonal phase of zirconia (Figure 8). The x-ray
pattern for tetragonal zirconia was identified based on the original work performed by
Ruff and Ebert [28]. Thus a partial transformation from monoclinic to tetragonal phase

occurred during microwave heating using the single-mode microwave cavity in this study.

3.3. Grain size and mass density as a function of the cavity mode and the radial
position within the AKP30 alumina specimens.

The four Group B AKP30 alumina specimens achieved an average mass density of
96.2% of theoretical with standard deviation of i 0.6%, as determined for the twelve
sections obtained from the four specimens (Table IV). The densities for sections, A, B,
and C (Figure 4) of individual specimens sintered in different cavity modes revealed no
significant variation in mass density as a function of the radial position within a given
specimen (Table IV). Also, fi'om mode to mode the average mass density differed by less
than 1%.

Compared to the mass densities, somewhat larger variations in the grain size were
observed (Table IV) in terms of both (i) the radial position within a given specimen and
(ii) the cavity mode used to sinter the specimen. For the twelve specimen sections
examined in this study, the grain size varied from 3.83 pm to 7.72 pm. For the three
sections obtained from each of the four individual specimens, the largest standard
deviation corresponding to 6.1% of the mean grain size occurred to the specimen

densified in mm mode. Grain sizes averaged over a given cavity mode ranged fiom

114

Table IV. Density and grain size measurements for alumina specimens in terms of cavity
modes and locations of individual specimens.

 

 

 

 

(:32: TMI 11 TE112 TE113 TM013

. Grain . Grain . Grain . Grain

Section Diggty size D32“), size D233” size D793”, size
‘ (pm) (tun) (pm) (It!!!)

‘ 7.42 4.26 7.72 6.05
A 96.0 10.35 94.9 21:0. 49 96.9 i0. 48 95.6 $03 6
7.35 3.83 7.36 6.23
B 97.0 i035 95.9 $0.68 97.0 $024 96.3 21:0.39
7.46 4.06 7.42 5.54
C 95.6 $033 96.3 i075 95.9 $012 96.5 1:032
(16:48?“ 96.2 7.41 95.7 4.05 96.6 7.50 96.1 5.94
. size $0.7 3:006 :07 i022 1:06 3:019 $0.5 i036

 

 

 

 

 

* Density (%) is relative with respect to the theoretical value of alumina (3.987 g/cm3)

[25].

* "' Grain sizes were determined by multiplying the average intercept length from the
SEM micrographs of fracture surfaces by the stereographic correction factor 1.5

[24].

115

 

4.05 pm for the TE112 mode to 7.50 pm for the TE113 mode (Table IV). We assume
relatively large variation in grain size depending on the cavity mode may be due to
differences in electromagnetic field strength from mode to mode [23], although similar
heating rates, sintering temperatures and times were used for each of the four cavity

modes used to heat the four AKP30 alumina specimens (Table II). However, more work

needs to be done to clarify this effect.

3.4. Casket-microwave interactions

During this study, we have observed both local hot spots in the ZYC zirconia cylinder
wall of the casket and local melting in the SALI refractory board casket end plates. The hot
spots in the cylinder wall tend to occur at intermediate temperatures while the local melting
occurs near the maximum (sintering) temperature. Both phenomena are associated with
strong local microwave-power absorption, which alters the way in which energy is
partitioned within the microwave cavity and can lead to transient drops in the specimen
temperature. The time-power sequence of the microwave processing was modified to
accommodate these absorptions so that despite these perturbations, the alumina and the

alumina/zirconia specimens were sintered to high densities.

3.4.1. Local hot spots in the casket wall

For the Group A alumina compacts and the alumina/zirconia composite specimens,
the specimen temperature (monitored by an optical pyrometer) began to increase rapidly
above 500°C within 11 to 17 minutes afier beginning heating in TMIII mode (see

Experimental Procedure). During each heating run, immediately after the casket began to

116

heat significantly at a fixed input power of 150 Watts, the reflected microwave power
increased, which indicates the cavity had become out of tune. Re-tuning the cavity only
(withou_t increas_ing the input power) raised the specimen temperature from about 500°C to
about 800°C (Figures 3a and 3b). At this point, the heating rate control became difficult,
apparently due to non-uniform heating of the casket during the initial heating. Thus the
input power was held at 150 Watts for about 5 to 10 minutes until the temperature dropped
by about 50°C to 60°C and became stable. Then to heat the casket-specimen system to
higher temperature, heating was resumed by tuning the cavity and increasing the input
power.

However, in each of the heating runs, the increase in microwave input power was
accompanied by the development of a red hot spot in the casket wall closest to the power
launch probe. The first hot spot appeared with an initial size of about 1 cm diameter at a
specimen temperature of about 900°C. The intensity of the hot spot increased until the
specimen temperature reached about 1000°C, at which time a second hot spot developed in
the opposite wall of the casket. The appearance of the second red spot was accompanied by
a decrease in specimen temperature of as much as 30°C despite a 50 watt increase in input
power (Figures 3a and 3b). The microwave input power was held at 370 Watts to 430
Watts for 7 nrinutes to 15 minutes, during which time the first hot spot became less intense
and the second hot spot became more intense. When the specimen temperature began to
increase again at fixed input power, the input power was increased and tuning the cavity
was resumed and continued until the temperature reached the specimen’s final densification
temperature. Lee et al. [20] previously observed similar temperature changes accompanied

by a hot spot in the casket wall during microwave heating of both (i) the casket loaded with

117

 

a 2 gram, 2 cm diameter alumina specimen and (ii) the empty casket. The hot spot
phenomenon is probably due to non-uniforrn heating of the zirconia cylindrical casket. In
particular, the location of the hot spot may be related to the power launch probe in the “side-
feed” microwave cavity used in this study and previous studies [20], although the details of
the material-microwave interaction are unknown.

The microwave sintering behavior of the A1203/Zr02 specimens was similar to that of
the alumina compacts; at about 1000°C the temperature decreased by as much as 60°C
although the heating rates ranged fiom 10°C/min. to 22°C/min. (Table III, Figures 3a and
3b). For Al/Zr-l and Al/Zr-2, heated with the average heating rate of 10°C/minute and
22°C/minute, respectively, a temperature drop of 50°C was observed at about 1000°C
(Figure 3b illustrates the 50°C temperature drop for specimen Al/Zr-l). Specimen CAI/Zr-
], which was heated in a conventional furnace with a heating rate of 10°C/minute, did not
show a temperature drop during heating (Figure 3b). Thus the temperature drop near
1000°C is apparently related to the microwave sintering process rather than some type of

endothermic process in the powder compacts themselves.

3.4.2. Local melting in the casket end-plates

The AKP50 powder compact was sintered at 1600°C i 2°C for 20 minutes by
controlling the microwave input power (Table I and Figure 3a). However, the AKP30
specimen temperature decreased to 1535°C within 20 minutes after the temperature reached
1600°C, although during this 20 minute interval the microwave input power was increased
by more than 50 Watts. The A16SG specimen’s temperature decreased from 1595°C to

1585°C within 20 minutes (Table I and Figure 3a).

118

 

The observed decrease in specimen temperature likely was due to local melting in the
SALI aluminosilicate refractory boards that formed the top and the bottom casket plates
(Figure 2). Local melting of the SALI, which was observed after cooling the casket-
specirnen system, apparently was caused by the microwave input power being absorbed
locally instead of increasing the specimen temperature. The local melting of the SALI
boards occurred despite the fact that the specimen temperature as measured by the optical
pyrometer was less than 1600°C and the vendor-specified melting temperature of the SALI
is 1870°C (SALI’s maximum use temperature is specified as 1700°C). For the 5.1
centimeter diameter alumina powder compact specimens used in this study, the melted area
of the SALI board was about 4 centimeters in diameter or larger. Local melting of the SALI
board also was observed during microwave sintering of 2-gram almnina specimens at
1600°C [20]. The size of melted area was about 2 cm, which was approximately the same
diameter or somewhat larger than the size of the alumina specimens. When the SALI of
about 7.5 centimeter in diameter and 0.5 centimeter thick was used as a setter material for a
processed specimen and the specimen temperature was increased to about 1600°C, severe
local melting of the SALI board occurred and ruined the specimen (Figure 9a). In this study
we used aluminosilicate fiber (SAF F IL, see Experimental Procedures) as a setter instead of
the SALI board. The maximum use temperature and melting temperature of the SAFFIL
were 1649°C and 1816°C, respectively, as specified by the vendor. Although the maximum
use temperature and the melting temperature of the SAFFIL were lower than the
corresponding temperatures of the SALI insulation material, the SAFF IL did not melt. The

SAFFIL disc separated the processed specimen from the local melting of the SALI bottom

119

 

 

Melted area __ Alumina SALI

 

— Zirconia ZYC

/ Specimen

R Alumina SALI

 

 

Melted area —-Alumma SALI

 

 

 

(a)

 

Melted area «_ Alumina s ALI

 

 

<——— Zirconia ZYC

/ Specimen

—.--—-fi

 

“ ' \Alumina SAFFIL

 

<——Alumina SALI

 

 

Melted area

 

(b)

Figure 9. Schematics of the caskets showing melted area of the SALI insulation (a) when
SALI was used as a specimen setter, and (b) when SAFFIL was used as a specimen setter.

.120

 

plate of the casket, yielding well-densified specimens without either melting or warping
(Figure 9b).

Based on the experimental observations of this study for 10 gram alumina specimens
and results of a previous study for 2 gram alumina specimens [20], we believe that the local
melting of the SALI boards is due to a local thermal runaway [14-16] of the SALI end
plates. When the specimen temperature monitored by the pyrometer reaches about 1600°C,
the dielectric loss tangent of the SALI probably increases rapidly, resulting in more
absorption of the microwave power and increasing the local temperature of the SALI.
Finally, the local melting may occur.

For the alumina/zirconia specimens, local melting did not occur in the SALI board,
which indicates that a sintering temperature below 1550°C (or corresponding microwave
power) was not high enough to cause the local melting. However, in a previous study [21]
alumina/zirconia specimens heated to 1600°C resulted in severe local melting in the SALI
boards. When a SALI board was used as a specimen setter [21] instead of the SAFFIL fiber
insulation used in this study (Figure 2), local melting resulted in a hole about 4 centimeter in
diameter in the SALI board and enclosed the specimen in the hole, causing the specimen
warping. The local melting confined in the area of the SALI bottom plate under the
alumina/10wt% zirconia specimen indicates that a processed specimen, in particular,
containing more dielectrically lossy material like zirconia probably promotes the local

melting in the SALI board.

121

4. SUMMARY AND CONCLUSIONS

In this study, relatively large (about 5 centimeter in diameter) disc-shaped alumina
and alumina base zirconia composites were successfully densified by a cylindrical single-
mode microwave cavity. The three different grades of alumina each about 10 grams
sintered in TM”: mode showed final densities of about 96% of theoretical with fine grain
sizes (Figures 5a—5c) (Table I).

The four Group B AKP30 alumina specimens sintered at 1500°C in the cavity tuned
to mill, TE112, TE 1 13, or TM013 modes yielded relatively uniform mass density and grain
size in terms of both (i) the radial position within a given specimen and (ii) the cavity
mode used to sinter the specimens (Table IV). The four Group B specimens had an
average density 96.2% i 0.6% of theoretical and an average grain size of 6.23 pm :1: 1.5
pm. respectively. The small variations in mass density and grain size are likely due to the
hybrid effect of the microwave heating and conventional heating using a casket composed
of microwave lossy material [11,17].

The advantages of microwave heating over conventional heating have been verified
by heating alumina/10wt% zirconia particulate composites. Microwave-sintered
composite specimen (Al/Zr-3) reached about 94% theoretical density at a sintering
temperature of 1350°C, while a specimen (CAl/Zr-2) conventionally sintered at 1350°C
reached only about 70% of theoretical density (Table III). The microstructures of the
composite specimens sintered at 1450°C also indicate that microwave heating enhanced
the densification over conventional heating (Figures 7b and 7c).

Although a microwave susceptor is required for preheating the specimens at low

temperature, a low loss material such as alumina can directly interact with the

122

microwaves at high temperature, yielding internal, volumetric heating.

ACKNOWLEDGEMENTS

The authors acknowledge the financial support of the Research Excellence Fund of
the State of Michigan, provided by the Electronic and Surface Properties of Materials

Center, Engineering College, Michigan State University.

123

10.

11.

12.

13.

REFERENCES

M.A. Janney, H.D. Kimrey, “Microwave Sintering of Alumina at 28 GHz,” Ceramic
Powder Science, 11, B, Ceramic Transactions, vol. 1, pp. 919-24, (1988).

H.D. Kimrey, J .0. Kiggans, M.A. Janney, and R.L. Beatty, “Microwave Sintering of

Zirconia-Toughened Alumina Composites,” Mat. Res. Soc. Symp. Proc. vol. 189,
243-256, 1991.

J .D. Katz, R.D. Blake, and J .J . Petrovic, “Microwave Sintering of Alumina-Silicon
Carbide Composites at 2.45 and 60 GHz,” Ceram. Eng. Sci. Proc., 9, 725-34 (1988).

M.K. Krage, “Microwave Sintering of F errites,” Am. Cer. Soc. Bull., 60(11), 1232-
34 (1981).

K. Bai and HG. Kim, “Microwave Sintering of BaTiO3 thick Films,” Journal of
Materials Science Letters, vol.13, p 806-809, 1994.

PA. Haas, “Heating of Uranitun Oxides in a Microwave Oven,” American Ceramic
Society Bulletin, vol.58, No.9, p 873- , 1979.

J .F . MacDowell, “Microwave Heating of Nepheline Glass Ceramics,” American
Ceramic Society Bulletin, vol.63, No.2, p282-286, 1984.

L.M. Sheppard, Am. Cer. Soc. Bull., 67[10], 1656-1661 (1988).

Y.L. Tian, D.L. Johnson and ME. Brodwin, in Cer. Trans., Vol. 1, p. 925-932, The
American Ceramic Society Inc., Westerville, Ohio (1988).

M.A. Janney and H.D. Kimrey, in Mat. Res. Soc. Symp. Proc., ed. W.B. Snyder, Jr.,
W.H. Sutton, M.F. Iskander'and D.L. Johnson, Vol. 189, p. 215-227, Materials
Research Society, Pittsburgh, Pennsylvania (1990).

A. De, I. Ahmad, E.D. Whitney, and DE. Clark, “Microwave (Hybrid) Heating of
Alumina at 2.45 GHz: 1. Microstructural Uniformity and Homogeneity,”
Microwaves: Theory and Application in Materials Processing, Ceramic
Transactions, vol. 21, pp. 319-28 (1991).

CE. Holcombe, T.T. Meek, and N.L. Dykes, in Mat. Res. Soc. Symp. Proc., ed.
W.H. Sutton, M.H. Brooks and 1.]. Chabinsky, Vol. 124, p. 227-234, Materials
Research Society, Pittsburgh, Pennsylvania (1988).

M.C.L. Patterson, P.S. Apte, R.M. Kimber, and R. Roy, in Mat. Res. Soc. Symp.

Proc., ed. R.L. Beatty, W.H. Sutton and M.F. Iskander, Vol. 269, p. 301-310,
Materials Research Society, Pittsburgh, Pennsylvania (1992).

124

14.

15.

16.

17.

18.

19.

20.

21.

22.

23.

24.

25.

26.

27.

28.

V.K. Varadan, Y. Ma, A. Lakhtakia and V.V. Varadan, in Mat. Res. Soc. symp.
Proc., ed. W.H. Sutton, M.H. Brooks and U. Chabinsky, Vol. 124, p. 45-55,
Materials Research Society, Pittsburgh, Pennsylvania (1988).

S.L. McGill, J .W. Walkiewicz, and GA. Smyres, in Mat. Res. Soc. Symp. Proc., ed.
W.H. Sutton, M.H. Brooks and U. Chabinsky, Vol. 124, p. 247-252, Materials
Research Society, Pittsburgh, Pennsylvania (1988).

V.M. Kenkre, L. Skala, M.W. Weiser, and J .D. Katz, “Theory of Microwave
Interactions in Ceramic Materials: the Phenomenon of Thermal Runaway,” Journal
of Materials Science 26 (1991) 2483-2489.

GB. Holcombe and N.L. Dykes, .1. Mat]. Sci. Lett, 9, 425-8 (1990)-

M.A. Janney, C.L. Calhoun, and H.D. Kimrey, in Cer. T rans., Vol. 21, p. 311-318
(1991).

B. Swain, Adv. Mtls. and Processes, l34[3], 76-81 (1988).

K.Y. Lee, E.D. Case, J. Asmussen, Jr., and M. Siegel, in Cer. Trans., Vol. 59, pp.
473-480, The American Ceramic Society Inc., Westerville, Ohio (1995).

K.Y. Lee, E.D. Case, J. Asmussen, Jr., and M. Siegel, in Proceedings of the 11th
Annual ESD Advanced Composites Conference, p. 491-503, Ann Arbor, Michigan
(1995).

Committee on microwave processing of materials: an emerging industrial
technology, “Microwave Processing of Materials,” National Academy Press,
Washington, DC. (1994).

K.Y. Lee, E.D. Case, and J. Asmussen, Jr., to be submitted for publication.

E.E. Underwood, A.R. Colcord, and RC. Waugh, in Ceramic Microstructure, ed.
R.M. Fulrath and J .A. Pask, p. 25-52, John Wiley and Sons, New York (1968).

National Bureau of Standards (U .S.), Circ. 539, Vol. 9, p. 3 (1959).

F. Larson, G. McCarthy, North Dakota State University, Fargo, North Dakota, USA.
JCPDS Grant-in-Aid Report (1985).

W. B. Westpal and A. Sils, in Dielectric Constant and Loss Data, p. 4-37,
Massachusetts Institute of Technology, Technical Report AFML-TR-72-39, Air
Force Materials Laboratory, Wright- Patterson Air Force Base, Ohio (1972).

O. Ruff and F. Ebert, Zeitschriftfuer Anorganische und Allgemeine Chemie, 180,
19—41 (1929).

125

CHAPTER 2

BINDER BURN-OUT

Part I. MICROWAVE SINTERING OF CERAMIC MATRIX COMPOSITES

AND THE EFFECT OF ORGANIC BINDERS ON THE SINTERABILITYl

ABSTRACT

A single mode microwave cavity operated at 2.45 GHz and equipped with an
automated tuning system has been used to process an alumina matrix, zirconia particulate
composites that contained ten weight percent of corn oil binder. This research shows that
binder burn-out can be achieved without using a susceptor and can depend greatly on the
electromagnetic cavity mode used. For example, nearly 100 percent of the binder was
removed fiom a disc-shaped A1203/Zr02/binder compact using TE112 mode, while the TM012
mode was quite unsuccessful at removing the binder. When a susceptor material was used,
binder bum-out and sintering was successfully performed as a one-step process, yielding a
highly densified ceramic composite with uniform, small-grained microstructure after a total

processing time of about 3.5 hours.

 

Ki-Yong Lee, Eldon D. Case, Jes Asmussen, Jr. and Marvin Siegel, Proceedings of the 11th Annual ESD
Advanced Composites Conference, ESD, The Engineering Society, Ann Arbor, MI, pp. 491-503 (1995).

126

 

1. INTRODUCTION

Microwave processing allows a rapid, uniform and volumetric heating of ceramic
materials [1]. Janney and Kimrey densified A1203 + 0.1 wt% MgO via microwave heating
far more rapidly than by conventional heating [2]. Tian et al. [3] achieved rapid
densification and ultra-fine microstructures in unreinforced almnina using a single mode
microwave applicator.

Once microwaves are produced by a generator, they are guided into a microwave
cavity which confines the electromagnetic fields. Upon proper tuning of the cavity, the
electromagnetic fields set up a pattern of standing waves (a resonance) within the cavity. If
the energy fiom the microwaves couples efficiently with the material to be processed, then
the material may be heated by the microwave energy.

Microwave cavities can be either single mode or multimode [4]. A single mode cavity
produces a unique standing wave pattern or mode for a specific cavity dimension. The
multimode cavity, such as a kitchen microwave oven, superimposes several fundamental
modes to produce a complex pattern of standing waves. Multimode cavities are more
commonly used than single mode cavities due to the low cost, ease of construction and
adaptability of multimode cavities [5]. However, the nonuniform electric field distributions
multimode cavities provide can cause inhomogeneous heating, resulting in low coupling
efficiency of microwave energy with materials.

To improve both the coupling efficiency and uniformity of heating, single mode
cavities have been designed and used by several researchers [5-10]. Either low loss or lossy
materials can couple efficiently with microwaves using an internally tuned single mode

cavity [5, 11]. In a single mode cavity, the internal electric field can be maximized at a

127

location of the processed material by tuning the cavity. Tuning minimizes the reflected
power by two adjustments. A sliding short located on a movable top plate of the cylindrical
cavity changes the cavity length. A sliding probe located in the microwave power launch
assembly (through which the microwaves are fed into the cavity) determines the microwave
fields in the region near the probe and the cavity wall. The complex dielectric constants are
a frmction of temperature, thus continuous cavity tuning is required during heating in order
to optimize the coupling efficiency, which is a cumbersome job if the tuning is done
manually.

Recently Asmussen et al. developed a system for automated tuning of single mode
cavities which employs computer-controlled stepper motors to adjust the sliding short
position and the power launch probe positions. Using the computer—controlled tuning
system for a single mode microwave cavity, Lee and Case [12] demonstrated that repeatable
heating schedules can be obtained for sintering various alumina ceramics to high densities.

This study investigates the feasibility of using the automated single mode microwave
timing system to sinter compacts of alumina/zirconia mixed with an organic binder. Several
researchers have sintered A1203-Zr02 composites using microwave power [10, 13]. Kimrey
et a1. [13] have reported that A1203-10 to 70 wt% Zr02 was successfully densified using
2.45 GHz and 28 GHz microwave. Patil et al. [10] sintered A1203-15 and 23 volume %
Zr02 powders without binders using a single mode cylindrical cavity operating in the mo 12
mode.

Ceramic powders are typically compacted into desired shapes by techniques such as
pressing, slip casting, and injection molding and then densified at high temperature to obtain

strongly bonded components. Such consolidation techniques often rely on organic binders

128

 

to play a role as binder, lubricant, plasticizer, and/or sintering aid etc. [14]. If the binders are
not removed prior to sintering at higher temperatures, the bum-out of the residual binder at
elevated temperature may result in cracking in the final component. Microwave power
allows rapid heating rates due to the interaction between electromagnetic fields and material
so that careful control of heating is very important to burn out the organic binders without
cracking material.

Several researchers [15-18] have removed organic binders from ceramic compacts
using multimode microwave cavities. Moore et al. [15, 16] developed 3 Microwave
Thermogravimetric Analyzer (MTGA) to investigate the binder removal mechanism. Using
a commercial microwave oven, Harrison et al. [18] fabricated lead zirconate-lead titanate
(PZT) and lanthanum containing PLZT ceramics by a series of thermal processing steps
including microwave drying, calcining, binder bum-off, and finally sintering at high
temperature.

According to Asmussen [11], a cylindrical circular single mode cavity TM012 mode is a
logical processing mode for a cylindrical billet of material located in the center of the cavity.
For a thin slab of material located in the bottom of the cavity [11], either the TE or TM
modes may be used to heat the material.

Despite the microwave processing research discussed above, the present authors were
not able to find references in the literature to research using a single mode microwave
cavity: (1) to remove binder from ceramic compacts, or (2) to sinter ceramics containing a
binder phase. This study focuses on microwave binder bum-out and sintering in a single

mode cavity.

129

 

In this study, two different processing procedures are used. In the first procedure, two
adjacent cavity modes, namely TE112 and TMm2 modes, are used to only remove the binder
from A1203-Zr02 powder compacts without using a microwave susceptor material. Both
fixed and stepped microwave input power levels were used during processing. In this first
procedure (without a susceptor) the specimens were not sintered.

In the second procedure for the A1203/ZrO2/binder composite specimens, the binder
was removed and the specimens were sintered in a one step process. The one-step binder
removal/sintering process used TE112 and TM012 modes with a susceptor (casket) composed

of a zirconia microwave absorber.

2. EXPERIMENTAL PROCEDURE

MATERIALS used to fabricate the alumina matrix/zirconia composites were Sumitomo
AKP-50 alumina powder and a purified zirconia powder (Fisher Scientific Company). The
average particle size for AKP-50, as specified by the vendor, was 0.23 pm. However, the
vendor did not specify the particle size for the zirconia powders. Using an SEM (Hitachi, S-
2500C), we determined that the average particle size for the zirconia was less than 0.4 pm.
A commercial corn oil was used for the organic binder, since it is readily available and non-

toxic when removed at high temperature.
The alumina powder, zirconia powder, and the binder were mixed by ball milling. The
ball milling also likely reduced the particle size somewhat, but the extent of particle size
reduction via ball milling was not detennined in this study. All specimens used in the study

were approximately 90 wt% alumina and 10 wt% zirconia before adding the corn oil binder.

130

The ball milling procedure was as follows. First, alumina powder and zirconia powder
were mixed in a plastic mill by ball milling for 24 hours using alumina grinding media. The
milled alumina/zirconia powder mixture was then heated overnight at 200°C to aid in
removing water that may have been absorbed by the powders. After adding ten wt% corn
oil, the 81 wt% alumina—9 wt% zirconia-10 wt% binder system was ball milled for another
24 hours. After removing the material from the ball mill, agglomerates were broken-up
using a mortar and pestle. The A1203-Zr02 powder/binder material was cold pressed at
about 20 MPa into discs approximately 22 mm in diameter and 2 mm thick.

Using an electronic balance (Model EA-lAP, The Torsion Balance Co., Clifton, NJ.)
with an accuracy of i 0.0001 grams, the mass was measured before and after heating the
individual specimens. For the twenty seven powder compact specimens used in this study,
the mean and standard deviation for the specimen mass before heating was 2.0036 grams
and :1: 0.0089 grams, respectively. The compacts were stored in a desiccator to reduce the

absorption of ambient moisture prior to processing.

EXPERIMENTAL APPARATUS for this study includes the microwave processing
system and temperature measurement devices. Continuous wave microwave power was
generated by a magnetron (Sairem, Model MWPS 2000, Wavemat Inc., Plymouth, MI)
which supplies power from zero to 2000 Watts at 2.45 GHz. A hollow metallic waveguide
feeds the microwaves into an internally tunable single mode cavity operated at 2.45 GHz
(Model CMPR-250, Wavemat Inc., Plymouth, MI). The cavity was tuned by adjusting a
sliding short and a power launch probe to an accuracy of :h 0.1 m using computer-

controller stepper motors (Microstep Drive Sx Series, Compumotor, Fauver, MI) [11, 12].

131

To reduce contamination of the microwave cavity walls by smoke produced during
binder burn-out, a brass tube 5.3 cm in diameter and 24 cm long was affixed to the top,
circular plate of the cavity. Also, in some experiments, the elimination of volatiles fi'om the
cavity was assisted by a stream of compressed air fed into the cavity through an unused
viewing port.

During microwave heating, the specimen temperature was monitored with an accuracy
of i 2°C using a digital thermometer (Accufiber Optical Fiber Thermometer, Model 10,

Luxtron Co., Beaverton, Oregon) (Figure 1).

MICROWAVE BINDER BURN-OUT AT BOTH FIXED AND STEPPED INPUT
POWER LEVELS, WITHOUT THE USE OF A SUSCEPTOR was performed on the
A1203-ZrO2/binder specimens. The compact specimens were placed in the center of a disc
of alumina insulating board (SALI, Zircar Products Inc.) about 10 cm in diameter and 2 cm
thick. No additional insulating or microwave absorbing material was placed around the
specimen. The SALI board, with the specimen on it was placed on the bottom plate of the
cavity, and centered along the cavity axis. Twenty specimens then were heated one at a time
at fixed input power levels of 80 to 150 Watts with the cavity tuned at either the TE112 or
TMm2 mode (Table 1 and Figure 2). An additional six specimens also were heated by a

stepped power sequence using the input power ranging fi'om 80 to 165 Watts (Table 1 and

Figure 4).

IN ADDITION, MICROWAVE BINDER BURN-OUT AND SINTERING WITH

THE USE OF A SUSCEPT OR was performed as a one-step process for the

132

Viewing Window

Optical Pyrometer

 
  

accufiber model 10
Optical Fiber

 

   

 

 

 

 

 

 

 
 

 

Gowave Cavity

 

 

 

Casket

Specimen

Viewing Hole
in Casket

Figure 1. Schematic of the experimental apparatus.

133

 

A1203/Zr02/binder specimens. The composite specimens in this study combine a low loss
material (alumina, whose room temperature loss tangent values range from 0.0003 to 0.002
[19]) with a relatively lossy material (zirconia, with a typical loss tangent value about 0.01 at
room temperature [19]). The nine weight-percent zirconia in the A1203/ZrO2/binder
specimens does not provide sufficient microwave power absorption to sinter the compacts.
Thus in addition to direct coupling with the specimens, heating must be supplemented by
radiant heating provided by a casket. The casket is composed of a zirconia cylinder (Type
ZYC, Zircar Products Inc.) 3 cm in height, with a 7.62 cm outer diameter and a 5.08 cm
inner diameter. Top and bottom discs for the casket were made Of alumina insulating board
(SALI, Zircar Products Inc.) about 2 cm in thickness. A hole approximately 5 mm in
diameter was drilled in the zirconia cylinder wall to allow measurement of the specimen
temperature with the optical pyrometer. We employed a ‘mode switching’ technique to
process the alumina/zirconia/binder composite specimens rather than using a single mode,
due to differences in the manner in which the two modes (the TE112 mode and the TM012
mode) heated the specimen. Differences in heating induced by the two modes will be
discussed in Section 3.

The rapid mode switching was made possible by the computer control of the sliding
short and power launch probe positions. Positions for the sliding short and the power launch
probe for the two resonant modes (the TE112 mode and the TM012 mode) were stored in the
computer. During processing, the cavity was quickly switched from mode to mode using
the computer-controlled stepper motors.

During binder burn-out and sintering as a one-step process, the heating rate needs to be

controlled. Tuning the cavity enhances coupling between the processed material and the

134

microwave power, yielding a high heating rate. However, rapid heating before complete
binder burn-out may crack the specimen. In contrast, detuning reduces the power absorption
by the specimen, lowering the heating rate. Thus in this study, we Obtained the desired
heating rates (which will be discussed in Section 3) at the binder removal stage and at the
sintering stage by using the computer-automated system to continuously tune or detune the

cavity at a given input power level.

Table 1. Summary Of microwave processing done in this study.

 

 

 

 

Binder burn-out Binder burn-out Sintering
Process at fixed power level at stepped power level (with
(without susceptor) + (without susceptor) ++ susceptor)
Maximum
mp‘l’éfgwer 80 90 120 150 150 80 100 130 150 165 900
(Watts) and a :1- t It! n :1- a a :1- e an
cavity mode
““999“ Of 5 5 4 4 2 2 1 1 1 1 1
specrmens
Maximum
dweasem 5.86 6.53 7.09 9.5 0.01 3.97 6.03 7.1 7.75 10.17 10.26
wt% Of
specimen

 

 

 

 

 

 

 

 

 

 

 

 

+ Maximum fixed power level
+1- Final power level after a stepped power change
'7 TE112 mode

7' * TMojz mode
* " Switching from TE112 mode to T'Mm2 mode.

135

 

 

 

 

 

 

 

 

 

 

O-l ' . I . . 9 a I I W?
5 . \“ -e— ”win-«rammed: r!
E 20 __ “ -B— 90WattsatTE112IIode j
o " .
a) —A— 120WatuatTE112-odc i
a" b —e— IsowIImIrerrz-odc
”5 “4.0" g + ISOWatuatTMmZ-che i
\° 1 . ‘
E “6.0 — :
.5 , =
0 E'—
C
g’ -8.0 — . C C
u: ¢ : C
U
40.0 . . 1 1 . 1 . 1 1
0 15 30 45 60
Time (min.)

Figure 2. For fixed input power level (without a susceptor), change in wt% of the
A1203/ZrO2/binder compact specimens as a function of time and input power level. The
weight loss corresponds to binder burn-out. The symbol ‘C’ denotes that the specimen is
cracked.

3. RESULTS AND DISCUSSION
MICROWAVE BINDER BURN-OUT AT A FIXED INPUT POWER LEVEL,
WITHOUT THE USE OF A SUSCEPTOR was attempted using both the TE112 mode
and the TM” mode. Using a fixed input power Of either 80, 90, 120, and 150 Watts,
individual zirconia/alumina/binder compact specimens were heated using TE112 mode for
time periods of 7.5, 15, 30, 45, or 60 minutes (Table 1 and Figure 2). At each power level, a
total of four to five specimens were heated to obtain binder burn-out. At a given input
power level the mass of the specimens changed relatively rapidly at the initial stage of
heating depending on the power level. After heating for about 15 minutes at the fixed power

level, the rate of binder burn-out decreased (Figure 2). For the compact specimens heated at

136

80, 90, and 120 Watts in the TE112 mode, the specimens’ mass changed by up to about 7
wt% without cracking (Table 1). For the specimens heated at 150 Watts using the TE112
mode, the specimens’ mass changed by up to 9.5 wt% (Table 1), however the specimens
cracked at the center of the top surface due to rapid binder removal.

Unlike heating in the TE112 mode, heating in the TM012 mode did not efficiently burn
out the binder from the ceramic compact specimens. For the two individual compact
specimens heated at 150 Watts input power for 30 and 60 minutes in the TM012 mode, the
mass decreased by no more than 0.01 weight percent (Table 1). Thus, hardly any binder
burn-out occurred during microwave heating using the TM012 mode without a susceptor
(casket), as shown in Figure 2.

The relative efficiency of binder removal using the TE112 and TM012 modes may be
related to the spatial distribution of electric fields inside a single-mode cylindrical cavity
(Figure 3) [5, 11, 20]. For the TE112 mode, electric field lines are perpendicular to the cavity
axis, thus the electrical field lines are oriented parallel to the disc-shaped powder compact
specimen used in this study. In contrast, the TM012 mode’s electric field lines are parallel to
the cavity axis, and thus the electric field lines are oriented perpendicular to the surface of
the powder compact specimens. The differing relative orientations of the electric fields may
lead to the result that the organic binder was much more readily removed from the

alumina/zirconia/binder compacts by heating at TE112 mode compared to the man mode.

MICROWAVE BINDER BURN-OUT AT A STEPPED INPUT POWER LEVEL,

WITHOUT THE USE OF A SUSCEPTOR, can yield more complete binder removal

from compact specimens without cracking the specimen (Table 1). Heating was done in the

137

TE 112 Mode

. 1 Specrmen /, Specimen

 

 

 

 

 

Figure 3. Electromagnetic field distribution for a single mode cylindrical circular cavity
[5, l 1, 20].

TE112 mode using a stepped power sequence (Table 1 and Figure 4). Initially the specimen
was heated for 20 minutes at 80 Watts input power. The input power then was increased by
20 to 30 Watts every 10 minutes until the power reached 150 Watts. At about 160 or 165
Watts input power the temperature began to increase rapidly above 5 00°C. Fast heating at
such input power levels caused the binder to burn out too quickly. In one instance, a flame
appeared on the specimen surface. The rapid temperature rise induced cracks in the
specimens. The binder was burned out when the input power was held at 160 Watts for 40
minutes and subsequently increased to 165 Watts. The maximum temperature obtained at
165 Watts was about 550°C. The mass of a particular compact specimen decreased by as

much as 10.17 wt% (Table 1) which was greater than mass fiaction of binder initially added

138

to the compact. The mass decrease in excess of 10 weight percent likely resulted from the
loss of water absorbed by the specimen.

To investigate the possibility of binder residue in the specimen that showed the 10.17
weight percent decrease (Table 1 and Figure 4), the specimen first was heated in a
conventional furnace at 200°C for 1 hour to eliminate the absorbed water. Then the mass of
the specimen dried at 200°C was measured. When the specimen was reheated in the same
furnace at 850°C for 8 hours, its mass decreased by 0.1 wt%. Thus, approximately 99
percent of the binder originally added to the alumina/zirconia compact was removed by the
microwave heating using a stepped input power sequence in the TE112 mode, without using

a microwave susceptor (casket).

    
  
   

 

 

 

 

 

 

 

 

 

 

 

. . . 1 4 . . . i i . 180
a ' ' ‘ ‘ 165 Watts -
d) I '9 160
E —J . . 1 A
8 Change In Input power ‘1 140 §
:6
8* 4 120 g
“a 1 v
g ~ 100 a;
\ ‘ a
E - 80 O
. o.
E — 60 g
g)” d 40 8‘
§ 9 "‘
6 Change in wt% of specimen j 20
'10 r . . 1 1 . 1 . . 1 . A I . . I . i 1 r 0
0 15 30 45 60 75 90 105

Time (min.)

Figure 4. For stepped power levels (with a susceptor), change in wt% Of specimens and the
input microwave power schedule used to heat the A1203/Zr02/binder specimens. The
weight loss corresponds to binder burn-out.

139

FOR MICROWAVE BINDER BURN-OUT AND SINTERING OF THE ALUMINA]
ZIRCONIA/BINDER SYSTEM USING THE CASKET, we used a mode switching
technique for efficient coupling and heating. For the TM012 mode, the casket coupled with
the microwaves at an input power level Of 260 Watts or greater. For the TE112 mode, the
casket coupled at an input power of 80 Watts or greater. The TM012 mode heated the casket
better in the temperature range required for sintering. Due to these differences in mode
coupling, at the start of the binder bum-out/sintering procedure the microwave cavity was
tuned to the TE112 resonant mode with 80 Watts input power. A rapid temperature increase
(due to the coupling of the zirconia insulation cylinder with the microwaves) occurred
within about 12 minutes (Figure 5). When the temperature reached about 620°C at 125
Watts input power, the operating mode was quickly switched from TE112 to TM012 for
further heating. This switch from the TE112 mode to the Mn mode is the ‘mode switching’
referred to in this section and in the Experimental Procedure. Differences in the coupling
behavior for the two microwave cavity modes will be explored in a later publication [21].

After coupling, the heating rate was precisely controlled during the entire processing
sequence by continuously tuning or detuning the cavity at a given input power level. In the
temperature range from 550°C to 850°C the heating rate of about 33°C per minute during
binder burn off did not crack the specimen (Figure 5). After the binder had burned out, the
heating rate was increased to about 9°C per minute. The temperature was held at 1500°C for
20 minutes, during which time final densification occurred. The resulting total processing
time was about 3.5 hours.

The mass of a particular sintered A1203/ZrO2/binder specimen decreased by 10.26 wt%

140

 

 

l 600

 

 

 

 

6 1200 - -
‘L/
G)
g 8009- _
I-t
8. ’ 1
g . .
{-1 400- .-
9 1
0 I l L l l l l I I I m 1 J l
0 60 120 180 240

Time (min.)

Figure 5. Heating schedule for binder removal and sintering of an A1203-Zr02 ceramic
composite using the one-step process discussed in the Experimental Procedure section. In
Table 1, this specimen is designated having a 10.26 wt% decrease.

(Tablel), giving a final as-sintered density 4.04 g/cm3, as measured by the Archimedes
method. The theoretical densities of alpha alumina and zirconia (monoclinic) are 3.987
g/cm3 [22] and 5.82 g/cm3 [23], respectively, yielding a theoretical density of 4.12 g/cm3 for
the 90 wt% A1203-10 wt% Zr02 composite. Thus the measured value of 4.04 g/cm3
corresponds to 98.1 percent of the theoretical composite density.

The fracture surface Of the resulting composite was examined with an SEM (JEOL,
J SM 6400V) (Figure 6). The composite has a uniform, small-grain sized microstructure
with an average grain size 2.7 urn, as determined by the linear intercept method on SEM

micrographs. A stereographic correction factor 1.5 was used to compute the grain size [24].

141

 

Figure 6. Fracture surface of microwave sintered 90 wt% AKP-50 alumina and 10 wt%
zirconia composite (Bar represents a length of one micron). In Table 1, this specimen is
designated having a 10.26 wt% decrease.

4. SUMMARY AND CONCLUSIONS

Two processing procedures were used in this study. One procedure only burned out
the binder material, without using a susceptor (casket). The second procedure used a casket
and combined binder removal and sintering as a one—step process. Both processing
procedures were applied to alumina/zirconia/binder compacts consisting of 81 weight
percent alumina, 9 weight percent zirconia, and 10 weight percent corn oil binder.

Without using a susceptor material, the first procedure employed the TE112 and the
TMm2 cavity modes to attempt binder burn-out only. For example, a fixed input power of
120 Watts in the TE112 mode removed about 71 percent of the binder (which corresponds to
7.09 wt% mass decrease, as shown in Table 1) without cracking the specimen. In contrast,

the two specimens heated at 150 Watts fixed power level in the Mn mode showed a

142

maximum binder removal of only 0.01 weight percent (Table l and Figure 2). The
effectiveness of the TE112 mode in binder burn-out was enhanced by changing from a fixed
input power to a stepped input power sequence. In particular, nearly 100 percent of the
binder was removed using a stepped input power sequence in the TE112 mode (Table 1 and
Figure 4). Thus, this research shows that for microwave heating the extent of burn-out of an
organic binder can differ dramatically fi'om one cavity mode to another. In addition, binder
bum-out can be made more complete by using a stepped input power sequence rather than a
fixed input power level.

Using a susceptor material, the second procedure employed mode switching from the
TE112 mode to the TM012 mode to burn out the binder and sinter as a one-step process. For
an A1203/ZrO2/binder powder compact, the binder was removed and the specimen was
sintered by the one-step process in a total processing time of 3.5 hours by switching fiom
the TE112 mode to the TM012 mode and controlling the heating rate (Table 1 and Figure 5).
The final sintered alumina/zirconia composite specimen had mass density of 98.1 percent of
theoretical with a uniform and fine microstructure with an average grain size 2.7 pm (Figure

6).

143

10.

11.

REFERENCES

W.H. Sutton, “Microwave Processing of Ceramic Materials,” Am. Ceram. Soc. Bull.
68[2] pp. 376-386, 1989.

M.A. Janney, H.D. Kimrey, “Microwave Sintering of Alumina at 28 GHz,” Ceramic
Powder Science, 11, B, Amer. Cer. Soc., Cer. Trans., vol. 1, pp. 919-924, 1988.

Y.L. Tian, D.L. Johnson and ME. Brodwin, “Ultrafine Microstructure of A1203
Produced by Microwave Sintering,” Ceramic Powder Science H, B, Amer. Cer. Soc.,
Cer. Trans., vol. 1, pp. 925-932, 1988.

ID. Katz, “Microwave Sintering of Ceramics,” Annu. Rev. Mater. Sci., 22:153-70,
1992.

J. Asmussen and R. Garard, “Precision Microwave Applicators and Systems for
Plasma and Materials Processing,” Mat Res. Soc. Symp. Proc., vol. 124, pp. 347-352,
1988.

Y-L. Tian, “Practices of Ultra-Rapid Sintering Of Ceramics Using Single Mode
Applicators,” Microwaves: Theory and Application in Materials Processing, Amer.
Cer. Soc., Cer. Trans. vol. 21, pp. 283-300, 1991.

B0. Tian and W.R. Tinga, “A Wide Range Tunable and Matchable High Temperature
Applicator,” Microwaves: Theory and Application in Materials Processing, Amer. Cer.
Soc., Cer. Trans. vol. 21., pp. 647-654, 1991.

J .F. Gerling and G. Foumier, “Techniques to lrnprove the Performance Of Microwave
Process Systems Which Utilize High Q Cavities,” Microwaves: Theory and
Application in Materials Processing, Amer. Cer. Soc., Cer. Trans. vol. 21., pp. 667-
674, 1991.

HS. Sa’adaldin, W.M. Black, 1. Ahmad and R. Silberglitt, “Coupling with an
Adjustable Compound his in a Single Mode Applicator,” Mat. Res. Soc. Symp. Proc.,
vol. 269, pp. 91-96, 1992.

D.S. Patil, B.C. Mutsuddy, J .Gavulic, and M. Dahirnene, “Microwave Sintering of
A1203:Zr02 Ceramics,” Microwaves: Theory and Application in Materials Processing,
Amer. Cer. Soc., Cer. Trans. 21, pp. 565-575, 1991.

J. Asmussen, H.H. Lin, B. Manring, and R Fritz, “Single-mode or controlled

multimode microwave cavity applicators for precision materials processing,” Rev. Sci.
Instrum., 58 [8] 1477-1486, 1987.

144

12.

13.

14.

15.

16.

17.

18.

19.

20.

21.

22.

23.

24.

K.Y. Lee, E.D. Case, J. Asmussen, Jr. and M. Siegel, “Sintering of Alumina Ceramics
in a Single Mode Cavity under Automated Control,” to be published in Microwaves:
Theory and Application in Materials Processing, Amer. Cer. Soc., Cer. Trans., 1995.

H.D. Kimrey, J.O. Kiggans, M.A. Janney, and RL. Beatty, “Microwave Sintering of
Zirconia-Toughned Alumina Composites,” Mat. Res. Soc. Symp. Proc., vol. 189, pp.
243-256, 1991.

D.W. Richerson, Modern Ceramic Engineering, page 170-175, Marcel Dekker, Inc.,
New York, 1982.

EH. Moore, 1. Ahmad, and DE. Clark, “Microwave Thermogravimetric Analyzer
(MTGA),” Microwaves: Theory and Application in Materials Processing, Amer. Cer.
Soc., Cer. Trans. 21, pp. 675-681, 1991.

EH. Moore, D.E. Clark, and R. Hutcheon, “Polymethyl Methacrylate Binder Removal
from an Alumina Compact: Microwave versus Conventional Heating,” Mat. Res. Soc.
Symp. Proc., vol. 269, pp. 341-346, 1992.

X.D. Yu, F. Selrni, V.V. Varadan and V.K. Varadan, “Binder burn out Of tape cast
ceramics by microwave energy,” Materials Letters 14, 245-250, North-Holland, 1992.

W.B. Harrison, M.R.B. Hanson and HG. Koepke, “Microwave Processing and
Sintering of PZT and PLZT Ceramics,” Mat. Res. Soc. Symp. Proc., vol. 124, pp. 279-
286, 1988.

RC. Buchanan, Ceramic Materials for Electronics, Marcel Dekker, Inc., N.Y., N.Y.,
pages 4-5, 1986.

L.J. Mahoney, The Desigp and Testing of a Compact Electron Cyclotron Resonapt
Microwm-Cavitv Ion Source. Thesis for the Degree of MS, Michigan State
University, page 36, 1989.

K.Y. Lee, E.D. Case, J. Asmussen, Jr., and M. Siegel, to be published.

National Bureau Of Standards (U .S.), Circ. 539, vol. 9, page 3, 1959.

F. Larson, G. McCarthy, North Dakota State University, Fargo, North Dakota, USA.
JCPDS Grant-in-Aid Report, 1985.

EB. Underwood, A.R. Colcord, and RC. Waugh, Ceramic Microstructurg, pages 25-
52, R.M. Fulrath and J .A. Pask, eds., John Wiley and Sons, New York, 1968.

145

Part II. BINDER BURN-OUT IN A CONTROLLED SINGLE-MODE

MICROWAVE CAVITY2

1. INTRODUCTION

Organic binders are added to provide sufficient green strength to an unfrred ceramic
body to permit handling and machining (1). However, the organic binders must be
removed from the ceramic bodies prior to sintering at high temperature. The volatile
products produced during binder burn-out can cause cracking if the binder is removed too
quickly or if the sintering process (at high temperatures) begins before binder removal is
complete.

Several researchers (2-4) have investigated microwave binder bum-out for ceramics.
Moore et al. (3) removed PMMA binder from PMMA/almnina compacts using
conventional heating, microwave heating and microwave hybrid heating. 100% Of the
binder was removed from specimens (524 grams, containing _<_8wt% binder) heated to
470°C with 3200 Watts of microwave power. Yu et a1. (4) completed binder burn-out of
tape cast barium strontium titanate ceramics using a single-mode microwave cavity at
lower temperature and less time than in a conventional furnace.

This study focuses on microwave binder burn-out of A1203/binder and
A1203/SiC/binder systems in the single-mode cavity using: (i) fixed input power levels

and (ii) stepped input power level sequences.

 

2 Ki—Yong Lee, Eldon D. Case, Jes Asmussen, Jr. and Marvin Siegel, Scripta Materialia, vol. 35, no. 1, pp.
107-111 (1996).

146

2. EXPERIMENTAL PROCEDURE
2.1. Materials and Specimen Preparation

The organic binder used in this study was commercial corn Oil. Sumitomo AKP-50
alumina powder with a vendor-specified average particle size Of 0.23 run was used for
the alumina phase for all specimens. For alumina/silicon carbide composites, AKP-50
alumina powder and silicon carbide platelets (C-Axis Technology, Canada) were used.
Prior to fabricating the alumina/binder compacts, the AKP-50 powder was heated
overnight at 200°C in a conventional fumace to remove absorbed moisture. The dried
almnina powder was ball milled with the corn Oil binder for 24 hours. For the
alumina/silicon carbide/binder specimens, first 90wt% alumina and 10wt% silicon
carbide were ball milled together for 24 hours. The mixture was dried overnight at 200°C
in a conventional furnace, then 10wt% of corn oil binder was added and the mixture was
ball milled for 24 hours.

Agglomerates created during ball milling were broken-up using a mortar and pestle.
Both the alumina/binder and the alumina/silicon carbide/binder specimens were
uniaxially pressed at about 20 MPa, resulting in disc-shaped powder compacts
approximately 22 mm in diameter and 2 mm thick. The powder compacts were stored in
a desiccator to reduce moisture absorption prior to microwave heating.

Before and after heating the specimens in the microwave cavity, the mass of
individual compact specimens was measured to an accuracy of i 0.0001 grams using an
electronic balance (Model EA-lAP, The Torsion Balance Co., Clifton, NJ). For the 41
specimens used in this study, the mean mass before microwave heating was 2.0000 grams

with a standard deviation 0.0042 grams.

147

2.2. Experimental Apparatus

Microwave power was produced by a 2000 Watt, 2.45 GHz power supply (Sairem,
Model MWPS 2000, Wavemat Inc., Plymouth, MI). The microwaves were guided into a
circular cylindrical single-mode cavity 17.78 centimeters in diameter (Model CMPR-250,
Wavemat Inc., Plymouth, MI) (5, 6). Cavity tuning via the computer automated system
is discussed elsewhere (5, 6). During microwave heating, the specimen temperature was
monitored with an accuracy of at 2°C using an Accufiber Optical pyrometer and

thermometer (Model 10, Luxtron Co., Beaverton, Oregon).

2.3. Microwave Binder Burn-out

The individual compact specimens were placed in the center of a disc of alumina
insulating board (SALI, Zircar Products Inc.) about 10 cm in diameter and 2.5 cm thick.
No additional insulating material or microwave susceptor material was used in this study
(6). Seventeen alumina/binder specimens were heated using a fixed input power ranging
from 70 to 120 Watts (Table 1) (Figure 1), while 50 to 80 Watts of fixed input power
heated 14 A1203/SiC/binder compact specimens (Table 1) (Figure 2). Using a stepped
input power level sequence, an additional 5 A1203/binder specimens were heated by
microwave input power ranging from 80 to 150 Watts (Table 1) (Figure 3). Stepped
input power between 45 and 130 Watts was used to process 5 A1203/SiC/binder

specimens (Table 1) (Figure 4).

148

Table 1. Summary of Microwave Binder Burn-Out done in this study

 

 

 

 

 

 

 

 

 

 

 

Material Alumina/binder Alumina/silicon carbide/binder
Maximum Number of Maximum Maximum Number of Maximum
input specimens decrease in input specimens decrease in
Process power level and cavity wt% of power level and cavity wt% Of
(Watts) mode specimen (Watts) mode specimen
70 4 * 3.48 50 4 * 5.48
Fixed 80 4 * 6.31 60 4 * 7.27
input
power 100 4 * 7.21 80 4 * 9.56
level +
120 3 * 10.35 80 2" -0.18
100 2 ** 0.06
80 1 * 2.36 45 1 * 2.52
Stepped 90 1 * 5.84 55 1 "' 4.55
input
power 110 1 * 6.77 75 1 * 6.38
level H-
140 1 * 9.21 105 1 * 8.52
150 1 * 10.05 130 l * 10.47
+ Maximum fixed input power level
H- Final power level after a stepped input power change
* TE112 mode
** TM012 mode

149

3. RESULTS AND DISCUSSION
3.1. Microwave Binder Burn-out Using a Fixed Input Power Level

Individual powder compacts were heated in the TE112 mode one at a time for 7.5,
15, 30, and 60 minutes using fixed input power levels of 70, 80, 100, 120 Watts for
A1203/binder and 50, 60, 80 Watts for A1203/SiC/binder compacts (Table 1) (Figures 1
and 2). For alumina/binder compact specimens heated at input powers of 70 to 100 Watts
in the TE112 mode, the specimens’ mass decreased by up to 7.21wt% without cracking the
specimens (Figure 1). An input power of 120 Watts heated both the SALI board setter
and the specimen, accelerating the binder burn-out, cracking the specimens, and resulting
in a mass decrease of up to 10.35 wt%. This indicates nearly all of binder was removed
from the altunina/binder specimens (Figure 1).

At input powers of 100 Watts or less, the SALI did not appear to heat appreciably.
However, at 120 Watts, a flame and a red hot zone appeared on the SALI board and the
pyrometer temperature rose to a maximum of about 600°C within about 10 minutes.
After reaching 600°C, the temperature decreased such that it could no longer be sensed
by the pyrometer (the minimum temperature the pyrometer can detect is 500°C). When
the input power was 100 Watts or less, the SALI board was discolored afier microwave
heating. Smoke penetrating into the SALI likely assisted the heating of the SALI board
during microwave heating.

The mass decreased by up to 9.56 wt% for the 12 A1203/SiC/binder compacts heated
at powers of from 50 to 80 Watts in the TE112 mode (Table 1). Of the eight specimens

heated at 60 and 80 Watts, six of them cracked (Figure 2). Unlike the microwave heating

150

 

 

 

 

 

 

 

Y T I T I l I I I I I
‘3 0.147 i
9 = . 100 Watts at TM012
E - .
.8 5‘
8'. '2.0 '— .\ e -‘
U) .- «ID
«a 4.0 1. 70 Watts atTEllZ _1
o L. “
I“ i = 80 Watts at TEl 12
I; -6.0 e A
.5 ’
a, -8.0 __ ‘x C 100 Watts at TE112 4
m L It
: c
.c: '10-0 ' ‘ i? 120 Watts arr-2112 ‘
U 1 I I 1 1 l l l 1 l
O 15 30 45 60

Time (min.)

Figure 1. For fixed input power level, change in wt% of the A1203/binder compact
specimens as a function of time and input power level. The weight loss corresponds to
binder burn-out. The symbol ‘C’ indicates that the specimen cracked.

 

 

 

 

 

 

 

 

 

I I 1' r I I I 1 I j

‘3 0.19 A
0 80 Watts at TM012
.13. 1 e
8 -2.0 - a —
O. O ,
In
”6 “LOL— : 50 WattsatTEllZ ‘
N D
T; -6.0 - ‘ -
q 5 60 Watts at TE112 an
0F.
m ‘8.0 '— LC C C '1
w . A 80 Watts at TE112 .
8 “ C9:
3: -10.0 - -
o 1 l l 1 l l l l l l

0 15 30 45 60

Time (min.)

Figure 2. For fixed input power level, change in wt% of the A1203/SiC/binder compact
specimens as a function of time and input power level. The weight loss corresponds to
binder burn-out. The symbol ‘C’ indicates that the specimen cracked.

151

of the alumina/binder specimens, the temperature during the binder removal process
always was below 500°C and there was no indication for heating of the SALI board. An
input power of about 50 Watts in the TE112 mode was required for approximately 6wt%
binder burn-out within one hour for the alumina/silicon carbide/binder composites
compared to about 80 Watts in the TE112 mode for the alumina/binder compacts. Since
the loss tangent of alumina is 0.0003 to 0.002 at room temperature at 1 MHz (7) and the
loss tangent of silicon carbides is 0.14 at about 25°C at 8 GHz (8), likely the 8lwt%
A1203/9wt°/o SiC/10wt% binder compacts coupled better with microwave energy at low
power than did the 90wt% A1203/10wt% binder specimens.

An additional 2 specimens each of A1203/binder and A1203/SiC/binder systems were
heated in the TMon mode using a fixed input power level of 100 Watts for
alumina/binder and 80 Watts for alumina/silicon carbide/binder specimens (Table 1)
(Figures 1 and 2). The negligible binder burn-out for the Mn mode is likely related to
the spatial distributions of electric fields inside a single-mode cavity (6). For the Mn
mode the electric fields are parallel to the surface of the disc-shaped powder compacts,

whereas for the TMon mode the field lines are perpendicular to the specimen surface.

3.2. Microwave Binder Burn-out Using a Stepped Input Power Level Sequence
Using a fixed input power level, a complete or nearly complete binder burn-out

always resulted in cracking the specimens (Section 3.1). However, specimen cracking

was avoided when stepped input power sequences in TE112 mode was used to heat both

the alumina compacts and the alumina/silicon carbide composites. The change in wt% of

152

individual specimens and the input power sequence (Table 1) are shown in Figures 3 and
4 for the A1203/binder and the A1203/SiC/binder specimens, respectively.

Alumina/binder specimen A/Bl was heated for 75 minutes by a stepped input power
sequence up to 145 Watts (Figure 3). The input power then was increased to 150 Watts,
and the SALI board coupled with microwave energy within 10 minutes. The temperature
indicated by the pyrometer stayed at about 550°C for another 15 minutes. After 100
minutes of heating, the specimen’s mass decreased by 10.05wt% (Table 1) without
cracking the specimen.

For alumina/silicon carbide platelet composite specimen AIS/Bl heated for 105
minutes by a stepped input power level sequence ranging from 45 to 130 Watts, the
specimen’s mass decreased by 10.47wt% (Table 1) and the specimen did not crack
(Figure 4).. There was no indication of microwave coupling with the SALI board (the
temperature was below 500°C) during heating of the alumina/silicon carbide composites.
A final maximum power of 130 Watts removed nearly all of the binder from the
A1203/SiC/binder specimen while 150 Watts was needed to entirely remove the binder
from the A1203/binder compacts. The lower power to complete the binder burn-out for
the A1203/SiC/binder composite specimen is likely due to SiC’s higher loss tangent
(Section 3.1).

For specimen A/Bl (alumina/binder specimen, Figure 3) and specimen AIS/B1
(alumina/SiC/binder composite, Figure 4), we quantitatively determined the amount of
binder residue left in each specimen after microwave heating. Following microwave
binder burn-out (Figures 3 and 4), the specimens were heated at 200°C for one hour in a

conventional furnace. The dry mass of each specimen was measured, then the specimens

153

   
 
   

 

 

 

 

 

T I r I r r 1 r I I r I f T f I I I 160
5 ___t——' 150 Watts _, 140
E
3 '2 ‘ Change in input power 1 120 1,?
0 +3
3* * d
“5 4 — f 100 5
. r...
- 80 a.)
go -6 _80 Watts . g
G - 60 Q.
.,.. - +3
In -8 - - 40 a
DD .1 5
5 ‘ . . — 20
,r: 10 __ Change in wt% of specunen .
U - P4 1 J 1 I l 1 l 1 1 I 1 4 L L n l l n 0

 

 

 

O l 5 30 45 60 75 90 105
Time (min.)

Figure 3. For stepped power levels, change in wt% of specimens and the input
microwave power schedule used to heat the A1203/binder specimens. The weight loss
corresponds to binder burn-out.

 

   
   

 

 

 

I l I I l T j I 7 I I ' I 160
a .1
g 130 Watts‘ 140
.pa A
8 —'__,———‘_—'r: 120 15’
a. - *3
m . . - 100 SE
“5 Change in 1nput power . h
N 4 80 g

o

F - 60 a.
.5 ‘ ...>
a, - 40 a
2" 5
3 Change in wt% of specimen 20
U '10 b I . . l . . 1 . . 1 .

 

 

 

O 15 3O 45 60 75 90 105
Time (min.)

Figure 4. For stepped power levels, change in wt% of specimens and the input
microwave power schedule used to heat the A1203/SiC/binder specimens. The weight
loss corresponds to binder burn-out.

154

were heated at 850°C in the conventional firrnace for 8 hours. After the burn-out in the
conventional furnace, the mass of the two specimens decreased by 0.1 1wt% with respect
to the dry mass. Therefore, approximately 99% of the binder originally added to the
alumina powder and the alumina/silicon carbide platelet compact was removed by the

microwave heating using stepped input power in the TE112 mode.

4. CONCLUSIONS

This study attempted com-oil binder removal from alumina/binder and the
alumina/silicon carbide/binder compacts by microwave heating in the TE112 and the
TM]; mode of a computer controlled single-mode cavity. In the TE112 mode when the
fixed input power level was relatively high, the binder removal was nearly complete but
the specimens cracked due to the rapid binder removal. The fixed input power level
required to decrease the specimens’ mass by about 6wt% was 50 Watts for the
A1203/SiC/binder specimens compared to 80 Watts for the A1203/binder specimens
(Table 1). The A1203/SiC/binder composite compacts coupled better with the microwave
energy due to the high loss tangent of the silicon carbide itself. In contrast to heating in
the TE112 mode, almost no binder burned out in the TMmz mode for any of the
A1203/binder or the A1203/SiC/binder specimens heated (Figures 1 and 2).

A stepped input power level sequence burned out in the TE112 mode almost 100
percent of the binder from both the alumina/binder and the alumina/silicon carbide/binder
systems without cracking the specimens (Table 1) (Figures 3 and 4). For the
A1203/binder specimens, microwave coupling with the SALI board at 150 Watts assisted

the binder removal. In contrast, the alumina/SiC/binder compacts coupled better with the

155

microwave energy, completing the binder burn-out at an input power low enough (130

Watts) that the microwave heating of the SALI board was apparently negligible.

ACKNOWLEDGEMENT
This study was financially supported by the Research Excellence Fund of the state

of Michigan.

156

 

REFERENCES

D. W. Richerson, Modern Ceramic Engineering, p. 170, Marcel Dekker Inc., NY
(1982)

W. B. Harrison, M. R. B. Hanson and B. G. Koepke, Microwave Processing of
Materials, Materials Research Society, 124, p. 279, Pittsburgh, Pennsylvania (1988).

E. H. Moore, D. E. Clark and R. Hutcheon, Microwaves: Theory and Application in
Materials Processing 11, Ceramic Transactions, 36, p. 325, The American Ceramic
Society Inc., Columbus, Ohio (1993).

X. D. Yu, F. Selmi, V. V. Varadan and V. K. Varadan, Materials Letters 14, p. 245
(1992)

K. Y. Lee, E. D. Case, J. Asmussen, Jr. and M. Siegel, accepted for publication in
Microwaves: Theory and Application in Materials Processing, Ceramic
Transactions, The American Ceramic Society Inc., Columbus, Ohio (1995).

K. Y. Lee, E. D. Case, J. Asmussen, Jr. and M. Siegel, Proceedings of the 11th
Annual ESD Conference on Advanced Composites, p.491, ESD-The Engineering
Society, Ann Arbor, MI (1995).

R. C. Buchanan, Ceramic Materials for Electronics, p. 4, Marcel Dekker Inc., NY
(1986)

R. D. Hollinger, V. V. Varadan, V. K. Varadan and D. K. Ghodgaonkar,
Microwaves: Theory and Application in Materials Processing, Ceramic

Transactions, 21, p. 243, The American Ceramic Society Inc., Columbus, Ohio
(1991)

157

Part III. MICROWAVE BINDER BURN-OUT FOR BATCH PROCESSING OF

A1203, A1203/SiC PLATELET, AND A1203/Zr02 PARTICLE

POWDER COMPACTS’

ABSTRACT
A cylindrical 2.45 GHz single-mode microwave cavity was used for organic binder
burn-out of batch processed ceramic compacts. The burn-out was accomplished without
enclosing the specimens in a microwave susceptor material. Strategies are discussed for

controlling cavity mode and input power to avoid specimen cracking during burn-out.

1. INTRODUCTION

Organic binders are ofien used in industrial processing of ceramics. The binders
add green strength to ceramic powder compacts, reducing the damage induced by
handling the compacts prior to sintering [1]. However, the binders must be burned out
(eliminated) from the powder compacts prior to densification. The binder burn-out
process may take up to 24 hours, thus the time needed for binder burn-out of large parts
can exceed the sintering time.

In this study, a 2.45 GHz single-mode microwave cavity was used to burn organic
binder from ceramic powder compacts processed in a batch process mode (six to seven
specimens processed simultaneously). The results of previous studies done by the

present authors on binder burn-out of individually-processed specimens [2,3] will be

 

3 Ki-Yong Lee, Eldon D. Case, Jes Asmussen, Jr., Microwaves: Theog and Application in Materials
Processing V, Cer. Trans. vol. 80, pp. 539-546, Edited by DH. Clark, W.H. Sutton, and D.A. Lewis,
American Ceramic Society, Westerville, Ohio (1997).

158

compared with this batch processing study.

2. EXPERIMENTAL PROCEDURE

To facilitate comparison with a previous binder-bum-out study done by the current
authors for individually-processed specimens [2,3], this binder-bum-out study for batch
processed specimens employed specimens of the same composition and binder type as
the study of individually processed specimens 2,3]. Materials used for both the batch-
processed and individually-processed specimens were A1203, A1203/SiC platelet, and
A1203/Zr02 particle with 10 wt% corn oil binder in each compact. Identical processing
methods, including the ball milling and dry pressing were used for both studies.
Furthermore the dimensions and mass of the specimens were nominally identical. In both
studies, the same 2.45 GHz single-mode microwave cavity and power supply were used
for binder burn-out.

For the two composite compositions (A1203/SiC platelet and A1203/Zr02 particle)
the ratio of reinforcing phase to the A1203 matrix was 1:9 afier binder burn-out.
Sumitomo AKPSO powder, having an average particle size of 0.23 pm (as specified by
the manufacturer) was used as the A1203 phase in every specimen in this study. SEM
examination revealed that the Zr02 particles (Fisher Scientific Company) were
approximately equiaxed, with a mean diameter of about 0.4 microns, while the SiC
platelets (C-Axis Technology, Canada) were about 2 microns thick with irregular shapes.

The A1203/Zr02 particle and A1203/SiC platelet powders were mixed by dry ball
milling for 24 hours. No dry ball milling was done for the monophase A1203 specimens.

Each of the three compositions then were ball milled with 10 wt% corn oil for 24 hours.

159

The specimens were uniaxially hard-die pressed at 32 MPa, yielding disc-shaped
compacts about 22 mm in diameter with an average thickness of about 2 mm. Each
specimen mass was measured before and after microwave heating by an electronic
balance (Model EA-lAP, The Torsion Balance Co., Clifton, NJ) with an accuracy of i
0.0001 grams. Prior to binder burn-out, the specimens' mean mass and standard
deviation were 1.9988 grams and i 0.0068 grams, respectively, for a total of 269
specimens included in this study.

The 2.45 GHz single-mode microwave cavity and the microwave power supply are
described in detail elsewhere [2,4,5]. A brass tube 5.3 cm in diameter and 24 cm long
attached to the movable short plate of the cavity allowed smoke generated during binder
burn-out to exit the cavity into a fume hood. This avoided contamination of the cavity
wall and allowed better monitoring of the specimen through a viewing port in the

microwave cavity.

7
l |
5 Q 1 .\‘/ Specimen
. - 3 -
- ./ '\ Aluminosilicate
e 4%

2.5 cm

 

 

 

 

 

Figure 1. Schematic showing the setter material for binder burn-out and the seven
positions for powder/binder compact specimens.

160

The batch-processed powder compacts were placed on disc-shaped SALI or SALI-2
aluminosilicate (Zircar Products, Inc.) refractory board setters (Figure 1). No further
insulation was placed around the specimens, and the specimens were not enclosed in a
“casket” of susceptor material.

Microwave power level was controlled by one of two protocols [2,3]: (1) fixed

microwave power or (2) stepped microwave power. The fixed input power levels ranged
from 50 Watts to 150 Watts depending on the material composition.
The stepped power procedure involved microwave power increments 5P (where 8P 5 50
Watts) made at 5 to 15 minute intervals. For both the fixed power and the stepped power
protocols, binder burn-out was monitored as a fimction of heating time (Figures 2 and 3)
by heating a series of initially nominally identical powder/binder compacts for
successively longer times. For example, for the A1203 compacts heated at a fixed input
power of 80 Watts, a total of three batches of seven specimens each were heated (Figure
2).

The processing temperatures, measured via an optical pyrometer system (Accufiber
Optical Fiber Thermometer, Model 10, Luxtron Co., Beaverton, OR), were obtained by
sighting on the side of the central specimen when seven specimens were present or on the
central region of the refractory setter disk when six specimens were present. (When six
specimens were used, the central specimen was removed.) The pyrometer is capable of
measuring temperatures ranging from 500°C to 1900°C with an accuracy of i 2°C.

The persistent differential heating between the central specimen and six
circumferential specimens lead us to attempt binder burn-out using only six specimens,

omitting the central specimen. Each of the three types of powder compacts was heated

161

using six-specimen batches. Four sets each of A1203/binder and A1203/Zr02/binder
specimens were heated by increasing the input power from 70 Watts to 460 Watts in
increments of 10 to 20 Watts every 5 minutes. At an input power of about 300 Watts the
center region of the setter began to heat above 500°C. Three batches of
alumina/SiC/binder powder compacts (six specimens per batch) were heated using a
stepped input power that was increased from 40 Watts to 250 Watts in increments of 10
or 20 Watts every 5 minutes.

In addition to the microwave heating, an electrical resistance furnace (Eurotherm
Limited, England) was used for conventional heating and binder burn-out of seven
alumina/SiC/binder compacts (Figure 3b). The furnace temperature was increased from
room temperature to 545°C at a heating rate of 5°C/minute. In order to determine the weight
% binder burn-out, one specimen was removed fi'om the furnace every 15 minutes during

conventional heating.

3. RESULTS AND DISCUSSION
During this batch processing study and the individual specimen burn-out study
[2,3], the principal microwave parameters that were found to be important to binder bum-
out are: (1) the electromagnetic cavity mode, (2) the magnitude of the microwave power,
(3) the control of microwave power level (fixed or stepped input power) during the
processing, and (4) the cavity "load", including the mass of material being processed and

its dielectric nature.

162

3.1. Binder Removal using Fixed Input Power

For both individually [2,3] and batch processed powder compacts, the choice of
electromagnetic mode can greatly affect the burn-out results. For each of the three types
of ceramic compacts (A1203/binder, A1203/Zr02/binder, and A1203/SiC/ binder), the
individually processed specimens [2,3] showed a maximum binder burn-out of only 0.6
wt% after heating at 100 to 150 Watts (fixed power) for 1 hour in TMmz mode. For the
batch-processed specimens, the maximum binder burn-out was 1.4 i 0.4 wt% in the mom
mode at 150 Watts and a heating time of one hour. In contrast to the TMmz mode, we were
able to achieve essentially complete binder burn-out using the TE112 mode. Therefore,
the remainder of the experimentation performed in this study with both fixed and stepped
power levels was done using the TE112 mode.

For low microwave input power (80 Watts, TE112 mode) the average percentages of
the binder burned out after 60 minutes during batch processing were 22.6 wt% for the
A1203/binder specimens, 20.9 wt% for A1203/Zr02/binder specimens, and 40.1 wt% for
alumina/SiC/binder specimens (Figure 2). Each batch for each material included seven
specimens, where the relative specimen locations are illustrated in Figure 1. In each case
(Figure 2) little additional binder burns out during the elapsed time interval from 30
minutes to 60 minutes. The trends for the individually processed specimens are quite
similar to the trends for the batch processed specimens, except that the overall binder
burn-out is higher for the individually processed specimens than for the batch processed
specimens (Figure 2). When the microwave input power was increased from 80 Watts to

150 Watts, the mean binder burn-out for a given batch increased by up to a factor of five.

163

 

 

 

 

 

 

100.0 __ I r ' I ' ' I 1 1 t Y ' r d
'e C C C 4 ‘9— A1203
E 80.0 ~ ,. L ‘ _ “B— A1203/m2
g l —A— A1203/SiC
t— 9
g 60.0 ~ /3 = a '* Q A1203 (batch)
g 40 0 _ f 41 4 &- A1203rzt02 (batch)
“5 _ / . -§— A1203/SiC (batch)
i 20.0 — ' a) ‘: :§ -

0.0 — ~ . 1 . . . 1 . 1 1 . . 1 _

0 15 30 45 60

Heating time (min.)

Figure 2. Wt% of binder removed as a function of heating time using 80 Watts fixed
input mwer in TE112 mode for both singly-processed specimens [2,3] and batch-
processed specimens. The symbol ‘C’ denotes that the specimen cracked.

The extent of binder burn-out is similar for the alumina/binder and the
alumina/zirconia/binder systems (Figures 2 and 3a). The low temperature (monoclinic)
form of zirconia is not a susceptor, while the high temperature (above about 1000°C)
tetragonal form of zirconia is a susceptor material [6]. Since binder removal is mostly

done below 800°C, zirconia does not aid binder removal.

3.2. Binder Removal using Stepped Input Power

Using a stepped input power sequence, five batches of alumina/SiC/binder were
heated (7 specimens per batch) using SALI refractory board setters. At about 150 Watts
the setter temperature rapidly rose to about 600 to 700°C. Typically the center specimen

and three to four of the other six specimens cracked during binder burn-out.

164

Due to the local melting, the SALI refractory board was replaced with a SALI-2

refractory board, which has higher temperature capabilities. Using SALI-
2, five batches of alumina/zirconia/binder compacts (with 7 specimens per batch) were
heated using stepped input power. For the two experimental runs for which the final
input power was _>. 240 Watts, the central region of the setter heated above 500°C and the
central specimen cracked. For the central specimen nearly all of the binder burned out,
while only about 68 wt% of the binder burned out from the other circumferential
specimens (Figure 1). However, in the stepped-power experimentation on each of the
three types of ceramic compacts, when the center specimen was removed and the SALI-2
refractory was used, we were able to achieve nearly complete binder burn-out without
cracking the specimens (Figure 3), in contrast to the partial burn-out achieved for fixed
input power (Figure 2).

Although the microwave heating burned out the binder immediately after the power
was applied, the conventional heating did not burn out the binder until the temperature
reached about 175°C at heating time of 30 minutes (Figure 3b). At 545°C, about 90 wt%
of the binder was removed by the conventional heating, while the microwave heating
burned out about 95 wt% of the binder at 250 Watts.

Although in this study, no "casket" of susceptor material surrounded the specimens,
the authors have successfully removed corn oil binder in a one-step process in which the
binder was burned out in a casket, then the microwave power was increased and the
specimens were sintered [2]. Also, batch-sintering alumina specimens using a casket and
the same microwave cavity as in this study resulted in specimens of relatively uniform

grain size, mass density, fracture toughness, and hardness [7]. Especially at high

165

 

 

 

 

 

 

 

 

 

100
“U “ '1
g _
o 80
8 a
2
D
E
:9 40 _
CH
O
3: 20 _

O l 1 J 4 L m L 1 l l
0 20 40 6O 80 100 120
Heating time (min.)
(a)

100 Fr f I I l l l I l
-e 545°C
g a
o 80 — 0
E L 470 C *
{:3 250 Wa

393°C
:.2 40 t- -
‘b-t
O
9
a}; 20 L40 wa 325°C -
175°C 244°C
0 l n L 1 L L l l 4 l
0 20 40 60 80 100 120
Heating time (min.)
(b)

500

400 A
E
300 v
II-I
4)
E
200 a.
E.
100 .5
0
500
400 A
g
300 g
3
3
200 8,
‘2.
100 E.
0

 

A1203/Zr02/bmdcr

J‘J MW input power

‘_B'_ Conventional, 5 C/mir

ff— MW input power

Figure 3. For a stepped input power meme, average fraction of the binder removed in
wt% for six-specimen batches as a function of power and heating time for (a)
A1203/binder and A1203/Zr02 binder specimens and (b) for A1203/SiC/binder specimens.
For those data points without error bars, the symbol size exceeds the standard deviation.
Figure (b) also includes data for A1203/SiC/binder specimens for which the binder was

removed by conventional heating.

166

temperatures, the radiant heating and insulating qualities of the casket likely reduce
temperature gradients. However, an advantage of not using a refractory casket for binder
removal may be related to the level of residual carbon in the specimens after binder burn-
out. Moore et al. [8] found that for removal of polymethly methacrylate binder fi'om
alumina compacts, there was 2 to 3 times more residual carbon in the microwave heated
specimens than in conventionally heated specimens. Moore et a1. attributed the
differences in residual carbon to the oxygen-poor environment within the insulating
casket that enclosed the specimens [8]. Thus, binder removal without the use of

microwave casket may lead to more complete burn-out.

4. CONCLUSIONS

For both the singly processed specimens [2,3] and the batch processed specimens,
the extent of binder burn-out can vary widely with the electromagnetic mode. For
example, heating via the TM”; mode resulted in very little binder burn-out, while in
comparison, nearly complete binder burn-out was achieved in the TE112 mode (Figures 2-
3).

For both the individually-processed specimens [2,3] and the batch-processed
specimens (this study), a stepped input power sequence burned out the binder more
completely than a fixed input power without cracking the specimens. Among the three
types of ceramic compacts processed (A1203/Zr02 composites, A1203/SiC platelet
composites, and A1203) the binder burned out at lower power for the A1203/SiC platelet
specimens, under both fixed and stepped power conditions. This may have been due to

differing dielectric properties of the specimens.

167

For a given batch, the centrally-located specimens exhibited the most complete
binder burn-out. Thermally-sensitive paper indicated that (for low powers) the highest
temperatures on the specimen setter were at the central-specimen position, which agrees
with the binder burn-out results for low power (80 Watt) and higher power (440 Watt)
binder burn-out. Thus the temperatures (and likely the electromagnetic fields) were
highest along the cavity axis.

In this batch-processing study, no microwave casket enclosed the specimens (Figure
1). Future work should directly compare the residual carbon lefi in specimens as a
function of processing temperature for binder burn-out with and without a microwave

casket enclosing the specimens.

ACKNOWLEDGEMENTS

The authors acknowledge the financial support of the Michigan Research
Excellence Fund provided through the Electronic and Surface Properties of Materials

Center, Michigan State University.

168

REFERENCES

D.W. Richerson, Modern Ceramic Engineering, 2“° edition, p. 496-497,
Marcel Dekker, Inc., New York (1992).

K.Y. Lee, E.D. Case, J. Asmussen, Jr., and M. Siegel, Proc. 11th ESD Advanced
Composites Conf., Ann Arbor, MI, pp.491-503 ( 1995).

K.Y. Lee, E.D. Case and J. Asmussen, Scripta Mat., 35[1]: 107-111 (1996).

K.Y. Lee, E.D. Case, J. Asmussen, Jr., and M. Siegel, Cer. Trans., Vol. 59, Amer.
Cer. Soc., Columbus, OH, pp. 473-480 (1995).

J. Asmussen and R. Garard, Mat. Res. Soc. Proc. 124: 347-352 (1988).

P. S. Apte, R. M. Kimber, A. Pant, R. Roy, D. N. Mitchell, United States Patent
5,072,087, December 10 (1991).

K. Y. Lee, L. Cropsey, B. Tyszka, and E. D. Case, accepted for publication,
Materials Research Bulletin.

E. H. Moore, D. E. Clark, and R. Hutcheon, Mat. Res. Soc. Symp. Proc., 269: 341-
346 (1992).

169

CHAPTER 3

JOINING

Part I. MICROWAVE JOINING AND REPAIR OF CERAMICS

AND CERAMIC COMPOSITES‘

1. INTRODUCTION

The application of ceramics and ceramic composites is limited in part by the difficulty
in processing components with complex geometries. However, the processing difficulties
could be reduced considerably if the components were formed from subcomponents of
simpler geometries. This paper first briefly overviews some ceramic joining techniques and
then discusses work done on microwave joining of ceramics. Although ceramics may be
joined as green (unfired) billets [1], both literature review (Section 2) and the experimental
results of this paper will deal with joining of densified ceramics. Also, to address the repair
of ceramics, this study includes experimentation on the healing of Vickers indentation

cracks via microwave heating.

 

' Ki-Yong Lee, Eldon D. Case, and Donnie Reinhard, Ceramic Engineering and Science Proceedings, vol.
18, no. 4, pp. 543-550 (1997).

170

2. CERAMIC-CERAMIC JOINING: BACKGROUND
2.1. Ceramic-Ceramic Joining using conventional heating

Various researchers have utilized brazing techniques for ceramic-ceramic joining. In
the metallurgical context, brazing is defined as "a joining process in which a filler metal and
a flux are sandwiched between the workpieces" [2]. Subsequent heating of the component
converts the filler metal/flux system into a liquid that wets the joined surfaces. Ceramic-
ceramic joining via brazing uses oxide and oxynitride glasses as bonding media as well as
slurries of metal particles or metal layers between the ceramic pieces to be joined [3]. Using
zero applied stress, oxide glasses can bond alumina [4,5] and oxynitride glasses can join
silicon nitride [6]. However, the glass layer formed during such joining leads to relatively
low fracture toughness and poor high temperature properties for the joined component [3,5]
since the glass layers themselves tend to have low fracture toughness and soften at elevated
temperatures.

Sandage et al. used Ba-Al-Si metal tape, 200 microns thick, to join 1.0 cm x 0.5 cm
mullite plates [3]. Heating at 1230°C in air for 5 hours oxidized the Ba-Al-Si metallic tape,
converting it to a BaAlZSi208-rich layer that also contained crystalline alumina, mullite,
barium aluminate, and a glassy aluminosilicate phase [3].

Diffusion bonding joins materials at high temperatures and pressures, ideally via solid
state diffusion of atoms across the joined interface, although interlayers can be added which
promote local melting and hence enhance the mass diffusion rates [3 ,7]. Diffusion bonding

is enhanced when the stresses and temperature are high enough to induce creep [8,9].

171

2.2. Ceramic-Ceramic Joining via microwave processing

Ceramic/ceramic joining via microwave heating has been done for simple cross-
sectional geometries including bars [10], rods [11], discs [12], and tubes [13]. Applied
external loads have ranged from about 0.6 MPa to 9.0 MPa for joining mullite, alumina, and
silicon nitride [13], to 3 MPa for alumina (in air) and silicon nitride (in nitrogen gas) [11], to
no external load for plasma sprayed Si coated SiC disks [13].

When ceramic-ceramic joining is done without the use of an interlayer, the bonding
typically takes place via an intergranular glassy layer already present in the ceramic; such
intergranular phases can become viscous at elevated temperatures [11,13]. As an example
of the role of intergranular phases in microwave joining, Fukushima et al. [11] joined
alumina with 92 to 96 percent purity using microwave heating, but failed to directly join
specimens of 99 percent alumina, although inserting a sheet of the lower purity alumina

between the 99 percent purity alumina components gave a successful bond.

3. EXPERIMENTAL PROCEDURE
3.1. Materials and Specimen Preparation
Two materials (sintered polycrystalline alumina and a commercial mica platelet
reinforced glass ceramic) were used in the joining experiments. Coors ADS-995, a
commercial polycrystalline alumina, was used for the Vickers indentation crack healing
experiments.
The flurophlogopite mica platelet reinforced glass ceramic used was MaCorTM, a

machinable glass ceramic (Corning Code 9658) in the system SiOz-A1203-MgO-K20-F. As

172

received MaCor billets 7.8 cm x 7.8 cm x 0.18 cm were sectioned into specimens roughly 1
cm X 2 cm using a low speed diamond saw and polished prior to joining.

Sumitomo AKP50 powder alumina discs were uniaxially hard-die pressed at 32 MPa,
giving powder compacts about 22 mm in diameter and about 2 mm thick, weighing about
2.0 gm. The alumina discs were sintered using a 2.45 GI-lz single-mode microwave cavity
with an automated sliding short and launch probe position controls [14]. Seven alumina
powder compacts were sintered simultaneously at 1500°C for 20 minutes in a zirconia
refractory casket using the ml 11 cavity mode. After sintering, the alumina disks were

polished with a series of grit sizes, ending with 1 micron diamond paste.

3.2. Microwave Joining and Crack Healing

After polishing, both the alumina and the glass ceramic specimens were coated with
silica film (Emulsitone Company, Whippany, New Jersey) by spinning on a substrate
spinner at 3000 rpm for 20 seconds. The coatings were then cured by two methods: (1)
heating in a conventional furnace for 1 hour at 200°C or (2) heating in the microwave cavity
at low power.

The coated 'specimens were joined in the microwave cavity using a zirconia casket and
the TM] 11 microwave cavity mode with a stepped input power sequence typically starting at
100 Watts and increasing to about 1200 Watts in steps of 100 Watts every 3 minutes.
During both the sintering (Section 3.1) and joining, the specimen temperatures were
measured via an optical pyrometer system (Accufiber Optical Fiber Thermometer, Model
10, Luxtron Co., Beaverton, OR). The pyrometer is capable of measuring temperatures

ranging from 500°C to 1900°C with an accuracy of i 2°C.

173

The joined specimens were sectioned and polished, with the cuts oriented normal to
the specimen interface. The polished surfaces were examined both by optical microscopy

and scanning electron microscopy.

4. RESULTS AND DISCUSSION

The as-microwave-sintered AKP-50 alumina disks had a mean mass density of about
99% of theoretical and a mean grain size of about 6.3 microns. Alumina discs joined at
1625°C had a mean grain size of 16.4 microns (Figure 1).

For the AKP-50 alumina specimens, the crack path near the joint was determined since
crack deflections at an interface can indicate the relative magnitude of the interfacial fracture
energy compared to the matrix fiacture energy [15]. As reviewed by Lee et al. [15], crack
deflection at interfaces can occur for interfacial fracture energies < 0.25 the matrix fi'acture
energy [15]. If defects located at the interface extend before the primary crack reaches the
interface, then a crack approaching the interface will deflect if the interfacial fracture energy
is less than about 60 percent of the matrix fracture energy [15]. Three joined AKP-50
alumina specimens were selected for Vickers indentation, in which a series of 49 N and 98
N indentation cracks were placed across the specimen surface, where the radial crack
systems were oriented approximately normal to the joined interface. Except when a series
of pores were present at the interface, the indentation cracks were undeflected at the joint,
indicating a strong interface.

One of the joined alumina specimens (with an as-joined thickness of 4.2 mm) was
fractured by loading in bend. SEM examination of the joined region of the fractured

specimen shows no evidence of cracking or microcracking near the joint (Figure 1); thus the

174

 

Figure 1. SEM micrograph of fracture surface of alumina discs joined at 1625°C for 10
minutes. Arrows indicate the joined interface.

 

Figure 2. SEM micrograph of polished surface of joined alumina discs heated at 1625°C
for 10 minutes. Arrows indicate the joined interface.

175

macrocrack that fractured the specimen apparently did not damage the joint, again indicating
a very strong interface. Also, the grain structure near the joint does not differ from the grain
structure in the bulk of the specimen (Figure 1), indicating that the process of generating the
joint does not greatly perturb the specimen's microstructure, at least on a micron-size scale.
Future research should include a detailed TEM examination of the joint to analyze the
phases present.

Polished surfaces of the alumina-alumina joint region also show the continuity of the
microstructure (Figures 2 and 3, where arrows included in the micrographs mark position of
the interface). An elemental map generated by the SEM EDS facility shows a homogeneous
distribution of aluminum ions through the joined region (Figure 4).

The region of the joint covered by the elemental map of aluminum ions in Figure 4 is
identical to the area shown in Figure 3. An x-ray line scan across the joint also shows a
constant concentration of alumina ions across the joint.

For the coated and joined AKP-50 alumina specimens, the nature of the joint is related
to the silica-alumina phase diagram. For alumina fractions below about 60 mole percent,
the silica-almnina equilibrium phase diagram has an eutectic at 1587°C j: 10°C. Between
about 15 and 60 mole percent alumina, mullite and a 95% silica-5% alumina liquid are the
equilibrium phases from the eutectic temperature up to about 1800°C. For the temperatures
at which joining was successful (1605 to 1665°C), the silica and alumina should react, and
as the reaction continues, the alurnina/ silica ratio should increase and shift the equilibrium to
the alumina-mullite side of the phase diagram [17]. The siliceous liquid present is likely
very viscous in the joining temperature range, which might aid the joining process by

helping to hold the opposing faces together.

176

5*“

 

Figure 3. SEM micrograph of polished surface of joined alumina discs heated at 1625°C
for 10 minutes. Arrows indicate the joined interface.

 

Figure 4. An elemental map showing the position of aluminum ions near the joint for
joined alumina discs.

177

Polished and coated pairs of MaCorTM specimens failed to join when microwave-
heated for 20 minutes at temperatures of 1000°C and 1025°C. Additional polished and
coated specimens partly joined when heated at 107 5°C for 20 minutes and for one hour.
Polished and uncoated specimens were heated together with the joined specimens at
temperatures between 1000°C and 1075°C but the uncoated MaCorTM specimens did not
join during microwave heating. Coated and polished specimens joined at 1150°C but the
MaCorTM specimens warped at that temperature (the maximum recommended working
temperature for MaCorTM is 1000°C). A pair of specimens with coated but as—received
(unpolished) surfaces joined weakly when heated at 1050°C for 20 minutes.

In addition to the joining experiments, a 1 cm x 1 cm square of polished Coors ADS-
995 polycrystalline alumina was indented at 49 Newtons and 98 Newtons using a Vickers
indenter. The indented specimen was aged for 48 hours in laboratory air to stabilize against
slow crack growth, then the specimen was heated in the microwave
cavity for 1 hour at 1500°C. Both the 98 Newton cracks (12 radial cracks) and 48 Newton
indents (6 radial cracks) healed completely, leaving only the indent impression to mark to
indent locations (Figure 5). In contrast, for conventional heating of 48 Newton Vickers
indents in ADS-995 under the same conditions (one hour at 1500°C), the change in relative

crack length was only 45.4% 3: 7.9% for six radial cracks [16].

5. CONCLUSIONS
While nearly all of the ceramic-ceramic joining described in the literature involves
externally applied pressure, the present research involves only ambient pressure.

Microwave-sintered alumina discs were polished, coated with a silica film, and joined using

178

 

Figure 5. Micrograph showing Vickers indentation impression for 98 Newton Vickers
indent, microwave-heated at 1500°C for 1 hour. Radial cracks have healed.

microwave heating at temperatures between about 1605°C and 1665°C. Under SEM
examination, the best joints were essentially indistinguishable from the bulk material, except
for occasional small pores. Specimens of a mica platelet reinforced glass ceramic composite
also were polished, coated, and joined at 1075°C.

In order to explore the repair of ceramic components, Vickers indentation cracks were
placed in polished surfaces of Coors ADS-995 polycrystalline alumina (no coating was
applied to the indented surfaces). The dramatic healing observed in the indentation crack
healing experiment likely indicates an enhanced mass diffusivity, either via the "microwave
effec " or possibly by intense local heating caused by the interaction of the microwave fields
and the "air gap" formed by the crack. Due to the microscopic scale of the crack opening

displacement, the pyrometer used to measure the specimen temperature would likely be

179

insensitive to such local heating. This phenomena and its origins merits further study, since

during both joining and repair of ceramics, small air gaps would occur at the interface.

ACKNOWLEDGENIENTS

Funding was provided by the Electronic and Surface Properties of Materials Center

and Composite Materials and Structure Center, Michigan State University.

180

10.

11.

12.

13.

14.

15.

l6.

17.

REFERENCES

C. H. Bates, M. R Foley, G. A. Rossi, G. J. Sundberg, and F]. Wu, Amer. Ceram.
Soc. Bull., 69[3]: 350-56, 1990.

J. P. Schaffer, A. Saxena, S. D. Antolovich, T. H. Sanders, Jr., and S. B.
Waner, pp. 718-720 in The Science and Design of Eng'geering Materials,
Irwin Press, Chicago, 1995.

K. H. Sandhage, H. J. Schmutzler, R. Wheeler, and H. L. Fraser, J. Am.
Ceram. Soc., 79[7]: 1839-1850, 1996.

A. J. Moorhead, Adv. Ceram. Mater., 2:159-166, 1987.

W. A. Zdaniewski, P. M. Shah, and H. P. Kirchner, Adv. Ceram. Mater., 2:
204-208, 1987.

M. L. McCartney, R. Sinclair, and R. E. Loehman, J. Amer. Ceram. Soc., 68: 472-
488, 1985.

M. Santella, Am. Ceram. Soc. Bull., 71:947-54, 1992.

G. Elssner, W. Diem, and J. S. Wallace, pp. 629-639 in Surfaces and Interfaces
in Ceramic and Ceramic-Metal System_s, Edited by J. Pask and A. G. Evans,
Plenum Press, New York, 1981.

W. D. Kingery, H. K. Bowen, and D. R. Uhlmann, pp. 744-54, Introduction to
Ceramics, Second Ed., Wiley, New York, 1976.

J. C. Xiao-ming, L.-W. Zhang, X. Li, Y. Tian, T. Chen, and J. Guo, J. Am. Ceram.
Soc.,77: 1090-1092, 1994.

H. Fukushima, T. Yamanaka, and Matsui, J. Mater. Res., 5[2]: 397-405, 1990.
D. Palaith and R. Silberglitt, Ceramic Bulletin, 68 [9]: 1601-1606, 1989.

R. Silberglitt, D. Palaith, W. M. Black, H. S. Sa'adaldin, J. D. Katz and R. D. Blake,
Ceram. Trans., 21: 473-480, Amer. Ceram. Soc., Columbus, OH, 1991.

K.Y. Lee, E.D. Case, J. Asmussen, Jr., and M. Siegel, Scripta Mat. 107-111, 1996.
W. Lee, S. J. Howard, and W. J. Clegg, Acta Mater. 44[10]: 3905-3922, 1996.
B. A. Wilson and E. D. Case, unpublished data

Pages 304-307 in reference 9.

181

Part II. MICROWAVE AND CONVENTIONAL JOINING OF CERAMIC

COMPOSITES USING SPIN-ON MATERIALS2

ABSTRACT

Polycrystalline alumina, glass ceramic composites reinforced by mica platelets
(MaCorW), and alumina/zirconia composites were joined using a commercial spin-on
material which is also used as a passivation layer in semiconductor processing. The film
thickness was controlled by varying spin speed, spin time, and temperature for heat
treatment. Curing a coated specimen at 200°C produced a fihn thickness ranging from
about 0.2 micron to about 0.6 micron. Joining was performed in both a conventional
electrical resistance furnace and a single-mode 2.45 GHz cylindrical microwave cavity.
Effects of film thickness, joining temperature, and heating time on the joining of the

materials will be discussed.

1. INTRODUCTION
Ceramic components with complex geometric shapes are difficult to process.
Intricately shaped components are of interest in high temperature heat exchanger and engine
applications. Complex structures, however, can be fashioned by joining ceramic
components of simpler shape. Joining simpler ceramic subcomponents assists quality
control as well, by allowing flawed subcomponents to be rejected prior to joining.

Using conventional (radiant) heating, ceramic components have been brazed via oxide

 

2 Kiersten N. Seiber, Ki-Yong Lee, and Eldon D. Case, Proceedings of the 12th Annual Meeting of
the American Society for Composites, pp. 941-949 (1997).

182

or oxinitride glasses, slurries of metal particles, and metal layers (Sandage et al., 1996).
Oxide glasses have been shown to join alumina (Moorhead, 1987; Zdaniewski, Shah, and
Kirchner, 1987) and oxinitride glasses have been used to join silicon nitride (McCartney,
Sinclair, and Loehman, 1985). Diffusion bonding has also been utilized to join ceramic
components under high applied pressures and temperatures (Santella, 1992).
Ceramic-ceramic joining using the microwave system typically involves externally
applied pressures. An applied load of 3 MPa has been utilized to join alumina (in air) and
silicon nitride (in nitrogen gas) (Silberglitt et al., 1991), while loads ranging from 0.6 MPa
to 9 MPa have been used to join alumina, mullite, and silicon nitride.
(Fukushima,Yamanaka, and Matsui, 1990). The objectives of this study were to I) join the
subcomponents with the use of a spin-on film and 2) to use ambient or low externally
applied pressures in the joining process. A low external pressure, provided by dead weight
loading, avoided the use of loading systems (such as those using a piston and load cell)
which can be awkward and interfere with the microwave fields. In this study, a total of 15
pairs of MaCorT” specimens, five pairs of alumina specimens and 1 pair of alumina/zirconia

composite specimens were joined.

2. EXPERIMENTAL PROCEDURE
MaCorT”, polycrystalline alumina specimens, and alumina/zirconia particulate
composite specimens were joined in this study. MaCorT“ is a machineable glass ceramic
reinforced by mica platelets (Corning code 9658). The MaCorT" specimens were cut from

as received billets of the material into 1 cm x 1 cm components using a low speed diamond

saw.

183

To fabricate the alumina specimens, about 2 grams of alumina powder was hard-die
pressed at about 32 GPa from Sumitomo AKP-3O powders, resulting in a disc-shaped
powder compact of about 2.2 cm diameter and 2 mm thick. The specimens were sintered at
1550°C for 20 minutes using a 2.45 GHz single-mode microwave cavity (Ice et al., 1996;
Lee, Case, and Reinhard, 1997; Lee, Case, and Asmussen, 1997). The average grain size of
the sintered alumina specimens was about 8.6 pm after multiplying the average intercept
size by a stereographic factor of 1.5 (Fulhnan, 1953). The density determined by
Archimedes technique was about 3.806 g/cm3, which is about 95% of theoretical density of
alumina (National Bureau of Standards, 1959).

For alumina/zirconia particulate composite specimens, AKP30 alumina powder was
mixed with 15wt% of zirconia powder (Fisher Scientific Co.). The mixture was ball-milled
with alumina grinding media in a plastic container for 48 hours.

Approximately 2 grams of the A1203/15wt% Z102 powder mixture (pressed using
conditions identical to those used for the alumina compacts) was sintered at 1550°C for 20
minutes in the microwave cavity.

Using an automatic polisher (LECO Corporation, St. Joseph, MI), alumina and
alumina/zirconia particulate specimens were polished using a series of grits; 25, 17, 10, 6
and 1 pm diamond paste. MaCorT" specimens were polished using 17, 10, and 1 pm
diamond paste. After polishing, selected specimens of MaCorT", alumina, and
alumina/zirconia were coated with silica film by placing ten drops of the silica film
(Silicafilm, Emulsitone Co., Whippany, NJ) onto the specimens and spinning the specimens

on a substrate spinner. The specimens were spun for 20 minutes at spinning rates ranging

184

from 500 rpm to 2000 rpm. Curing the film in a conventional oven for 20 minutes at 200°C
yielded a high purity silica coating.

Notches were made in five MaCorT“ specimens and four alumina specimens with a
stationary sonic mill (Sonic-Mill, Rio Grande Jewelers Supply Inc., Albuquerque, NM). A
razor blade tool was made by silver soldering a commercial razor blade to a standard flat
sonic-mill screw. The sonic mill vibrated the razor blade tool in a slurry of boron carbide
particles, which in turn vibrated the boron carbide particles contacting the razor blade tool.
The specimen was cut (notched) by the vibration of the boron carbide media itself.

A portion of the specimen containing the notch was then sectioned and reserved for
scanning electron microscope (SEM) analysis, in order to examine the notch prior to joining
(Figure 1). The remaining section was used in the joining experiment.

Microwave heating was done in a single-mode, 2.45 GHz microwave cavity using the
TM“; mode (Lee et al., 1996; Lee, Case, and Reinhard, 1997; Lee, Case, and Asmussen,
1997).

The specimens were positioned in a refiactory casket (Figure 2) that was centered along the
microwave cavity axis. The refractory casket acted as a thermal insulator that coupled well
with the microwaves at low temperatures. Sintered alumina discs about 4 grams
(approximately 1.8 cm in diameter and 4 mm thick) and 20 grams (approximately 4.1 cm in
diameter and 4 mm thick) were used as dead weights (Figure 2). A total of 0 to 60 grams of
dead weight was applied to the specimens. The microwave input power, initially set at 100
Watts, was increased by 100 Watts every 3 minutes until the desired temperature was
reached, providing a heating rate of approximately 40°C/min. The temperature in the

microwave system was measured

185

 

Coated specimen
'/ . _!/

 

— _.-
Joined specimen

Razor blade with notch

tool attached

to sonic-millTM fl

Coated specimen Specimen
'/ with notch
—> ->
Notch Specimen out

along this line

Figure 1. Schematic showing notched specimen preparation.

7.6 cm

 

Alumina SALI

.1
'1

2cm
1-——-1

Zirconia ZYC

Dead weights

7cm

Specimen

Alumina SALI
specimen setter

Alumina SALI

 

2.5 cm

 

1.3 cm 5.1cm 1.3 cm

Figure 2. Schematic for refractory casket used for microwave heating, showing dead
weights placed on the specimen for joining.

186

using an optical pyrometer (Accufiber Optical Fiber Thermometer, Model 10, Luxtron Co.,
Beaverton, OR).

Conventional heating was performed using an electric box furnace (C-M Inc.) with
MoSiz heating elements. The specimens to be joined were placed on an alumina (Coors
high alumina) setter and covered with an inverted cylindrical alumina crucible (Coors high
alumina) 60 mm in height, 10 mm in diameter, and a wall thickness of 1 mm. The
temperature was sensed by a K-type thermocouple placed in contact with the crucible. The
heating rate was approximately 30-40°C/min. The crucible protected the specimens fiom

contamination by material from the furnace elements and insulation.

3. RESULTS AND DISCUSSION

Four MaCorTM specimens and four alumina specimens were coated using spinning
rates between 500 rpm and 2000 rpm. The specimens were then cured at 200°C for 20
nrinutes. The silica film thickness was a function of the spinning rate, such that the coating
thickness decreased with increasing spinning rate (Figures 3 and 4, Table I). For example,
an alumina specimen spun at 500 rpm had a coating thickness of approximately 0.61
microns (Figure 3a), while another alumina specimen spun at 2000 rpm had a coating
thickness of about 0.20 microns (Figure 3b). Over the range of spinning rates used in this
study, the as-cured silica film thicknesses for the MaCorT" and alumina specimens agreed to
within :1: 9% (TABLE 1).

Ten pairs of MaCorTM specimens were joined in the microwave cavity using 20 gram

dead weight loading at temperatures of 1050°C and 1075°C with an approximate joining

187

 

(b)

Figure 3. SEM images of silica film spun on alumina specimens at (a) 500 rpm and (b)
2000 rpm.

188

 

0.8 , . , I , . ,
i [ —e— Silica film on alumina ] .

—A— Silica film on MaCor

 

-

.9
Us
I

 

    

Film thickness (pm)
9 i

 

 

 

00 l i l t l i l
500 1000 1500 2000
Spinning speed (rpm)

Figure 4. Silica film thickness as a function of spinning speed.

Table L Thickness of the as-cured silica film as a function of spinning speed.

 

 

 

Spinning speed 500 rpm 1000 rpm 1500 rpm 2000 rpm
Silica film on alumina (pm) 0.61 0.44 0.35 0.20
Silica film on MaCorT" (pm) 0.58 0.40 0.32 0.21

 

189

 

time of 20 minutes. Conventionally, five pairs of MaCorT" specimens were joined at
1050°C with no externally applied load and with 20 gram dead weight loading, using an
approximate joining time of 20 minutes. Initial results indicated that heating times shorter
than 20 minutes may not be sufficient to join MaCorT“ specimens. For example, one pair of
MaCorTM specimens was tested with a joining temperature of 1050°C, a joining time of 10
minutes, and a 20 gram dead weight loading. The 10 minute heating time failed to join the
MaCorT“ specimens.

The width and depth of notches in the MaCorT" specimens changed by less than 5.7

percent during joining (Figure 5, Table 11), while for the alumina specimens the notch width
and depth changed by less than 4.1 percent (Figure 6, Table H). Note that the dimensional
stability observed for the notch geometries holds for a range of notch sizes (Table II).

For five alumina and for five MaCorTM specimens, the fraction of the interface that

included pores was evaluated by SEM observations, where Fp is defined as

total length of porous regions along specimen interface

Fp = (1)
total length of specimen interface

 

The fraction of Fp is a function of the silica film thickness (Figure 7) for both the MaCorTM
and alumina specimens. However, the functional dependence of F p is quite different for
alumina and MaCorT" specimens (Figure 7). One pair of microwave heated, polished, and
coated MaCorT” specimens was compared to a conventionally heated, polished and coated
MaCorT'“ specimen. Both the microwave and the conventionally heated specimens were

processed at a maximum temperature of 1050°C for 20 minutes, with a 20 gram dead-weight

190

{"‘ “ r." *5"‘"'9<‘vrr‘~.rrr*\ 4'— r W ~—---~:-—

I

500 pm _‘

50011111

 

(b)

Figure 5. SEM images of notch made in MaCorT'“ specimen (a) before and (b) after
joining.

191

225011111.

 

(b)

Figure 6. SEM images of notch made in alumina specimen (a) before and (b) after
joining.

192

Table 11. Dimensions of notches before joining and after joining.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Material MaCorTM Alumina
Dimension Depth Width Depth Width Depth Width
(um) (um) (Inn) (urn) (urn) (11111)
Before joining 619 321 331 228 531 907
After joining 585 312 314 215 528 870
% difference -5.5 -2.8 -5.1 -5.7 -0.6 -4.1
1.0 1 1 1 1 .
—e— MaCor
0.8 r —'A'- Alumina
0.6 r -
1.13
0.4 - ~
0.2 ~ —
0.0 L l i l l l
0.2 0.3 0.4 0.5 0.6
F ihn thickness ( um)

Figure 7. Total fraction of pores along the joint interface in joined MaCorTIM and alumina
specimens as a function of film thickness.

193

 

load. The coatings for both specimens were spun at 2000 rpm and cured for 20 minutes at
200°C. The Fp values were 0.14 and 0.25 for the conventional and microwave heated

specimens, respectively.

4. SUMMARY AND CONCLUSIONS

A total of five pairs of alumina specimens, fifteen pairs of MaCor” specimens and one
pair alumina/zirconia particulate composite specimens were successfully joined with low
externally applied pressure. The joining temperature for alumina was 1575°C with a joining
time of 20 minutes in the microwave system. The MaCor” specimens were joined using
both conventional and microwave heating techniques for approximately 20 minutes at
1050°C and 1075°C. The quality of the joins was assessed using Fp (equation 1). Figure 7
shows the functional dependence of Fp on the film thickness.

Notches in MaCorT" specimens changed dimension by less than 5.7% in width and
depth during joining (Figure 5, Table II). Alumina specimens changed by less than 4.1% in
width and depth (Figure 6, Table II). Notch shape retention indicates that ceramic
components with intricate features, such as small holes and channels, could maintain their
complex geometry during joining. Also for the MaCorTM specimens, the constancy of notch
geometry indicates a lack of wide-scale viscous flow.

Additional work needs to be done to compare the quality of the joins as a function of
the join temperature, time, coating thickness, and heating mode (microwave versus
conventional heating). Also, future research might include mechanical testing of the joined

region using techniques, such as compressive shear tests using a variety of loading

194

techniques. Transmission electron microscopy (TEM) analysis of phases present near the

joined region should also be investigated.

ACKNOWLEDGEMENTS
We acknowledge the financial support from the Electronic and Surface Properties of
Materials Center and the Composite Materials and Structure Center at Michigan State
University. We also acknowledge the use of the electron microscopes at the Center for

Electron Optics, Michigan State University.

195

REFERENCES

Fukushima, H., T. Yamanaka, and M. Matsui. 1990. “Microwave Heating of Ceramics and
Its Application to Joining,” J. Mater. Res., 5 (2): 397-405, 84.

Fullrnan, R. L. 1953. “Measurements of particle sizes in opaque bodies,” Trans. Met. Soc.
AIME 197(3): 447-452.

Lee, K. Y., E. D. Case, J. Asmussen, Jr., and M. Siegel. 1996. “Binder Burnout in a
Controlled Single-Mode Microwave Cavity,” Scripta Materialia, 35(1): 107-1 1 1.

Lee, K. Y., E. D. Case, and D. Reinhard. 1997. “Microwave Joining and Repair of Ceramics
and Ceramic Composites,” Ceramic Eng. and Sci. Proc. vol. 18.

Lee, K. Y., E. D. Case, and J. Asmussen, Jr. 1997. “Microwave Binder Burn-out for
Batch Processing of A1203, A1203/SiC Platelet, and A1203/Zr02 Particle Powder
Compacts,” Cer. T rans., 80:539-546.

Mecartney, M. L., R. Sinclair, and R. E. Loehman. 1985. “Silicon Nitride Joining,” J. Amer.
Ceram. Soc., 68:472-488.

Moorhead, A. J. 1987. “Direct Brazing of Alumina Ceramics,” Adv. Ceram. Mater. 2:159-
166.

National Bureau of Standards (US). 1959. Circ. 539, 9:3.

Sandage, K. H., H. J. Schmutzler, R. Wheeler, and H. L. Fraser.1996. “Mullite Joining by
Oxidation of Malleable, Akaline-Earth-Metal-Bearing Bonding Agents,” J. Am Ceram.
Soc., 79(7): 1839-50.

Santella, M. 1992. “A Review of Techniques for Joining Advanced Ceramics,” Am. Ceram.
Soc. Bull., 71 :947-54.

Silberglitt, R., D. Palaith, W. M. Black, H. S. Sa'adaldin, J. D. Katz and R. D. Blake. 1991.
“Investigation of interlayer Materials for the Microwave Joining,” Ceram. Trans., 21:487-
495.

Zdaniewski, W. A., P. M. Shah, and H. P. Kirchner, 1987. “Crystallization Toughening of
Ceramic Adhesives for Joining Alumina,” Adv. Ceram. Mater., 2:204-208.

196

CHAPTER 4

CRACK HEALING

Part I. DIFFUSIVE CRACK HEALING BEHAVIOR IN POLYCRYSTALLINE

ALUMINA: A COMPARISON BETWEEN MICROWAVE ANNEALING

AND CONVENTIONAL ANNEALINGl

ABSTRACT
Crack healing experiments via both conventional heating and microwave heating
were performed on Vickers-indented specimens of polycrystalline alumina (Coors ADS-
995). For the entire temperature range included in this experiment (1510 K to 1742 K),
the crack healing rate was enhanced for microwave heating compared to conventional
heating. The microwave crack-healing data was described well by a diffusive mass

transport model given by Stevens and Dutton.

1. INTRODUCTION AND BACKGROUND
Distributed damage due to microcracking can be induced by crystallographic phase

transformation [1], thermal expansion anisotropy (TEA) [2-7], thermal shock and thermal

 

1 B.A. Wilson, K.Y. Lee and ED. Case, Materials Research Bulletin, vol. 32, no. 12, pp. 1607-1616
(1997).

197

fatigue [8-14], mechanical fatigue [15-19], particulate impact [20], and machining
damage [21]. Also, microcracks affect a wide range of material properties, including
Young's modulus, shear modulus [2-5,7,9,10], Poisson’s ratio [22], fracture surface
energy [23], thermal diffusivity [6], thermal conductivity [24] and thermal expansion
[7,25], and strength [7,26-29].

Since microcracking occurs for a variety of mechanisms and since microcracking
can in turn affect a broad spectrum of material properties, there is interest in microcrack
"healing", that is, reversing to some extent the effects of microcracking by reducing the
size/number density of microcracks. While crack healing occurs near room temperature
in humid environments for glass [30,31] and in mica [32], microcrack healing is typically
accomplished by thermal annealing in conventional furnaces [33]. For example,
conventional heating has resulted in strength increases for a number of studies of
microcracked ceramics [7,26-29]. Also, there have been direct observations of a crack
length decrease as a function of thermal annealing time and temperature [34-37], again
for annealing in conventional furnaces.

During microwave processing, a number of researchers, beginning with J anney and
Kimrey [3 8], report an enhanced sintering rate compared to the sintering rate obtained by
heating in a conventional furnace, and other authors have reported an increase in grain
and diffirsivity during microwave heating, compared to conventional heating. However,
the present authors are not aware of a published study of crack healing in a microwave
furnace, except for a preliminary study of crack healing in alumina by two of the present
authors [3 9]. This study employs Vickers indentation cracks as model microcrack

systems [40-44].

198

2. EXPERIMENTAL PROCEDURE

Crack healing experiments were performed on commercial polycrystalline alumina
(Coors ADS-995) specimens. The cutting, polishing, and indentation was done in the
same manner for all specimens included in the study. The specimens were cut to nominal
dimensions of 10 mm x 10 mm x 1 m using a high speed cutting saw (K.O. Lee
Slicer/Dicer) and then polished using an automatic polisher (Leco VP-50 12" Wheel
Polisher with an AP-50 Auto Polishing Attachment). To mark specimen orientation, one
or two circular holes, 1.5 mm in diameter and about 0.4 mm deep (Figure l), were milled
in a specimen comer using an ultrasonic milling machine (Sonic Mill Co., Stationary
Sonic Mill). The specimens then were ultrasonicated in a de-ionized water bath for 10 to
15 minutes to remove debris produced by the polishing or the milling procedures.

Six indents per specimen, three at 49 N load and three at a 98 N load (Figure 1) were
made with a 70 microns/second loading rate and a loading time of 15 seconds. After
indentation, all specimens were aged for 24 hours in laboratory air to allow for slow crack
growth saturation of the indentation cracks [45]. Following the aging in air, the
specimens were thermally annealed either (i) in air in a conventional tube furnace or (ii)
in air in a single-mode microwave cavity. For both the conventional and the microwave
anneals, the specimens were heated to a maximum temperature between 1510 K and 1742
K, held for 60 minutes at the maximum temperature, and then cooled to room
temperature.

Conventional heating was performed in a tube fumace (MRL Therrntec Horizontal

Tube Furnace) with a heating and cooling rate of 10°C per minute. The time-temperature

199

4.0 mm 3.0 mm

3.0 mm

4.0 mm

2.0 mm

1.5mm

 

1<—>1<—>1

1.5 2.0
mm mm

Figure 1. Schematic of indented alumina specimens used for both the conventional and
the microwave heating experiments. The indentation crack lengths are exaggerated.

history for conventional heating was determined from a chart recording of an R-Type
thermocouple which was placed next to the specimens.

Microwave heating was done using a 2.45 GHz single-mode microwave cavity
(W avemat CMPR250) with an automated sliding short and launch probe position
controls. Details of the microwave cavity and power supply are given elsewhere [46,47].
During annealing, specimens were placed in a refiactory casket consisting of a zirconia
cylinder 3 cm high with an outer diameter of 7.6 cm and two aluminosilicate end plates,

each 7.6 cm in diameter and 2 cm thick. The specimens were heated using a TM111 '

200

electromagnetic microwave cavity mode. All rrricrowave-annealed specimens were
heated from room temperature to about 1000°C in 8 - 9 minutes. For temperatures above
1000°C, two different heating rates were used: a fast heating rate of about 75°C per
minute and a slow heating rate of approximately 10°C per minute. During the one hour
dwell period, the temperature remained within :t 2°C of Tm“.

Following the thermal anneal, the extent of healing was assessed using an optical
microscope and an Environmental Scanning Electron Microscope (ESEM). The optical
microscope used was equipped with moveable filars and a digital length readout to :1: 0.1
micron. An Electroscan Model 2020 Environmental Scanning Electron Microscope
allowed one to observe nonconducting specimens such as ceramics without applying a

conductive coating to the specimen surface [34,48].

3. RESULTS AND DISCUSSION

The observed crack healing rates (Figure 2) are functions of the dwell temperature,
Tmax, heating mode, and the applied indentation load. For the three heating modes used in
this study: (i) conventional heating with a ramp rate of 10°C/min. (CV), (ii) microwave
heating with a “slower” ramp rate of 10°C/min. (MWS), and (iii) microwave heating with
a “faster” ramp rate of 75°C/min. (MWF), the crack healing rate Aa/At was very similar at
about 1510 K (Figure 2). However, the healing rate curves diverge with increasing
temperature, such that for both the 49 N and 98 N indentation cracks, Aa/At is at least
double for microwave annealing MWS compared to conventional annealing CV (Figure
2). The healing rate Aa/At (Figure 2) was evaluated as Aa/At = (a: — a1)/At, where at = the

final crack length (after annealing), at = the initial crack length (after aging the

201

 

 

 

 

 

 

 

 

 

 

 

 

500 1 r 1 . 1
—G— CV,49N
400 fl —A- MWF,49N _
r: -9— MWS,49N
D 1-
O
E 300 '- —1
:7 200 - -
Q
R
Q
100 r -
O 1
1 5 00 1600 1700 1800
T,,... (K)
(a)
500 1 . I r u
- —.— CV,98N
400i + MWF,98N _
+ MWS,98N

 

 

 

Aa/At (um/hour)
8

 

 

 

 

200 - -
L
100 — ~
0 L i I 1 I 1
1500 1600 1700 1800
T... (K)
(b)

Figure 2. The crack healing rates Aa/At for polycrystalline alumina specimens with (a) 49
N and (b) 98 N indentation cracks, annealed by (i) microwave heating, with a ramp rate of
75°C/min. (MWF), (ii) microwave heating, with a ramp rate of 10°C/min. (MW S), (iii)
conventional heating, with a ramp rate of 10°C/min. (CV). The solid lines represent a least-
squares fit to quadratic polynomial of the form Aa/At = a + bTmax + cszsx, where Tm is the
dwell temperature for each annealing treatment.

202

indentation crack in air, but before annealing), and At = 1 hour = time at Tmax. In this
study the initial crack length was about 200 um and 350 pm for 49 N and 98 N
indentation cracks, respectively.

With increasing temperature, the “slower” microwave ramp rate heating, MWS,
(10°C/min) shows higher crack healing rates compared to the “faster” microwave ramp rate
heating, MWF (75°C/min), despite the fact that all microwave and conventionally annealed
specimens were held at Tm for one hour (Figure 2). At 1742 K, the MWS heating gives
Aa/At values that are higher than the MWF heating Aa/At values by a factor of 1.27 for the
49 N indentation cracks and a factor of 1.24 for the 98 N indentation cracks. The increased
Aa/At values observed for the MWS anneals may be due to differences in the time-averaged

diffusivity for the two anneals. For the integral [49]
[ambit = ‘1')? (1)
0

a slower heating rate is equivalent to a longer anneal time at Tm. Consider a time-
temperature history “A” with a heating ramp rate H from an initial temperature Tim up to a
maximum temperature Tm which is held for time Idwell, A and then cooled with rate H to
Tim. Let time-temperature history B be an idealized step-function change from Tim to the

same maximum temperature Tmax, which is held for time towe11,a, followed by a step-function
drop to temperature Tint. If towen, A = tawen, B, then by equation l D; for history A will be

somewhat greater than 5 for history B. The difference in 3! between the two histories
would increase as the ramp rate H decreases.
Equation 1 is consistent with the general trends observed in the crack healing rate data

(Figure 2). For a Tmax of 1510 K, the crack healing rate is low, hence the diffusivities are

203

low for both the “faster” and “slower” microwave heating rates. Given the Arrhenius nature

of the temperature dependence of D, the time spent in the ramp portion of the heating curve
< 1510 K will add little to Ft. However, as Tmax increases the ramp portion of the heating

curve will include increasingly significant contributions to 57. However, the time
dependence of the crack healing rate has not been studied.

Differences between Aa/ At for the 49 N indentation cracks and the 98 N indentation
cracks may be due to differences in the crack geometry or due to differences in residual
stress states resulting from the differing indentation loads. A diffusive mass transport
model by Stevens and Dutton [50] provides a fiamework for both understanding a possible
source of crack geometry- Aa/At relations along with providing a link between Aa/At data
and activation energies for crack healing. For the case of zero applied external stress,

Stevens and Dutton’s model [50] may be rewritten as [3 5]

6a C Q
_ = —e .. _ 2
at T ”’1 kT) ( )
where aa/at = the crack healing rate
T = temperature in Kelvin

Q = activation energy for diffusion
k = Boltzmann’s constant
The constant C in equation 2 is in turn given by [3 5]

n'Don

= R211 ln(Lo /R) (3)

 

where Do is the pre-exponential factor for the diffusivity D, y is the surface free energy, D
is the atomic volume, R is the equilibrium crack tip radius of curvature and Lo is the

distance from the crack edge to the external bulk surface [50]. For each alumina

204

specimen included in this study, the average aa/at was evaluated as Aa/At (Figure 2).

Equation 2 can be rewritten as

ln[Tm Aa] = ln(CAt) —%-. (4)

The healing data show different activation energies, Q, for each of three heating modes
used in this study (Figure 3 and Table 1). Note that the activation energy, Q, is
significantly higher for microwave heating compared to conventional heating (Table l),
and the intercepts are higher for microwave heating. For each heating mode, the healing
curves for the 49 N indentation cracks and the 98 N indentation cracks are approximately
parallel (Figure 3), giving activation energies, Q, which are not significantly different for
the two crack sizes (Table 1), indicating that the Q for healing is not a sensitive function
of crack size or applied load for the range of the crack size, indentation load, and
temperature employed in this study. In each case, the curves for the 98 N data were
displaced upward from the 49 N data (Figure 3, parts a-c), which may be related to the
crack geometry term R21n[Lo/R] in the denominator of the expression for the constant C
(equation 3). A careful electron microscopic study of the effective equilibrium crack tip
radii, R, as a function of crack size (indentation load) and temperature should be done to
quantitatively determine whether or not Stevens and Dutton’s [50] crack geometry term
can explain the observed effect of crack size upon healing rate (Figure 2).

If we assume that R and Lo are not sensitive functions of heating mode, heating
time, and temperature, then from equation 3, we can use the C values (Table 1) to

calculate the ratios of Do’s between two different heating modes by

D, c
D(MWS) = CMWS (5)
0(CV) CV

205

 

14*

 

 

 

 

 

 

 

  
   

 

 

 

 

 

 

 

 

12 9-
A
.— 10 -
E L1 1 l i l 1 l l i 1 l 1 l 1 Lil i L1 1 l i l l l L
:1.
14 r Q/OMWFAsN‘
a _ A--—"Z:MWI=,98N a
g: I
"v 12 i." _ f
'3' 9 ‘
a 111
< 10 —- (b) 1 -
H -1 1 MJLI 1 1 1 3 1+1; 1 1 1 1 1 1 1 1 1 l 1 1 1 1
1._1
: 1 4 :_ (Q/C )Cv,49N_:
1"" _. 1’1 cv,98N..
12 r —‘
\I
i 9M
10 f" (0) ~:
14 l l i L1 L1 i l l 1 l i l l l l i l l l l i L l l I

 

5.50 5.75 6.00 6.25 6.50 6.75 7.00
107T... (K')

Figure 3. A modified Arrenhius plot of 1n[Tmaan] versus 1/me (equation 4 [35, 49]) for
polycrystalline alumina specimens annealed by (a) microwave heating, with a ramp rate of
10°C/min. above 1000°C, (b) microwave heating, with a ramp rate of 75°C/min. above
1000°C, (c) conventional heating, with a ramp rate of 10°C/min. The solid lines represent a
least-squares fit to equation 4.

206

Table 1. For each of the three heating modes used in this study, the activation energy, Q,
and constant C (equations 2-4) calculated from the slopes and intercepts of the curves in

Figure 3.

 

 

 

 

Heating mode Indentation load Q (kJ/mol) C (m-K/sec)
Conventional 49N 69 :t 21 0.005
(10°C/min, CV) 98N 80 i 34 0.014
Microwave 49N 140 i 49 1.29
(75°C/min, MWF) 98N 137 j; 20 1.76
Microwave 49N 193 i 16 101
(10°C/min, MWS) 98N 197 i 17 190

 

for the particular example of the MWS and CV heating modes. In general, the diffusivity

Dcanbewrittenas
Q)
D=D ——. 6
.exp( k7. ()

Thus, combining equation 5 and equation 6 gives the diffusivity ratio DMWS/DCV as

 

DMWS _ CMWS .exp(—QMWS / kT) . (7)
Dev Coy crux-QC.» / kT)

The other diffusivity ratios were calculated (Figure 4) in a similar manner. In analogy

with Figure 2, the calculated diffusivity ratios for each heating mode are approximately

equal to 1 at low temperature (1510 K), implying that the effective diffusivities are

approximately equal for microwave and conventional heating. At higher temperatures

(1742 K) the diffusivity ratios increase, ranging from about 1.7 for DMws/DMWF to 4.1 for

DMWS/DCV (Figure 4).

207

The microwave enhancement of crack healing rates for the specimens included in
this study imply that mass transport via diffusion is enhanced during the microwave
annealing of the indented specimens. Although the literature does not include other
studies of microwave-enhanced crack healing in ceramics, there are numerous examples
of microwave heating enhancement of sintering and grain growth [38,51-53]. A recent
study by Nightingale et al [53] compared microwave and conventional processing for 3
mol% yttria zirconia specimens: (i) sintered at maximum temperatures, Tmax, of 1573 K
to 1773 K with no dwell time at Tmax and (ii) grain growth at 1773 K for 1 - 15 hours.

Microwave heating enhanced densification for Tmax = 1573 K, but the enhancement

 

5 I I I IiI I I I I I I I I I I I I I I I I I I I I I lfT

 

—— Dun/Dev, 49N
Duws/Da, 98N
DM‘IF/Dcv, 49N
DIM/Dev, 98N
Dims/Dun, 49N
Dawn/Du», 98N

 

 

 

Diffusivity ratio

 

I I I I I I I I I l L I 1 I I I 1 I l

I I I l I I If T r I I I I I I T I I r

 

 

OJAILIIIIILIIIIIIJIIIIIIIIIIIII

5.50 5.75 6.00 6.25 6.50 6.75 7.00
107T... (K')

 

Figure 4. The calculated diffusivity ratios (equation 7) based on the values of activation
energies Q and constants C given in Table 1 for each of the heating modes.

208

decreased as temperature increased such that at Tmax = 1773 K the densities were
essentially the same for microwave and for conventional heating. Also, there was a
modest increase in grain growth for microwave-heated specimens compared to
conventional heating. From analysis of the grain size-density trajectories of the yttria
zirconia specimens, Nightingale et al [53] inferred that microwave heating tends to
enhance lattice diffusion more than it enhances surface and grain boundary diffusion.
Thus Nightingale et al [53] found that the relative microwave enhancement for the
sintering process was a function of temperature, but the importance of grain boundary,
surface, and lattice difiusion changes as the sintering process evolves so that detailed
comparisons between the temperature dependence of sintering and the temperature
dependence of crack healing may be difficult.

At 1473 K, for alpha alumina powders doped with 0.21 wt% MgO, the ratio of
diffusivities D(microwave) / D(conventional) for microwave and conventional heating was 3,
based on linear shrinkage kinetics during sintering [51]. However, an analysis based on
sintering rates is not able to determine whether the net change in diffusivity D stems from
a change in Do, a change in Q, or changes in both Do and Q. Katz et al [54] studied
diffusion in microwave-heated chromia/alumina diffusion couples. The diffusion couples
were prepared from dense polycrystalline alumina plasma-sprayed with a 30 micron-thick
chromia layer. Comparison with chromia/alumina diffusion data from the literature
[55,56] showed the interdiffusivity for chromium in alumina was about 3 times higher for
microwave heating that for conventional heating. However, the slopes of the Arrenhius
plots of logD versus 1/T were approximately parallel for conventional- and microwave-

heated specimens, indicating that while the activation energies were similar for

209

microwave and conventional heating, Do(microwave) was three times higher than
Do(conventional). Katz et al [54] argued that the apparent increase in Do may result from
microwave-induced changes in the correlation factor and/or the entropy for defect
formation and ion movement.

The results of this study are roughly consistent with the results of Cheng [51] and Katz
et a1 [54], in that the apparent diffusivity due to microwave heating can be larger than that
for conventional heating by about a factor of up to about three or four (Figure 4), and that
microwave heating can induce changes in Do (Table l and equations 5 - 7). However, the

changes in D0 are far larger in this study compared to Katz et al’s work [54].

4. SUMMARY AND CONCLUSIONS

In this study, Vickers-indented specimens of a commercial polycrystalline
alumina (Coors ADS-995) were annealed both via microwave heating and by
conventional (radiant) heating for one hour at maximum temperatures ranging form 1510
K to 1742 K. The crack healing data was analyzed using equation 4, which is based on a
diffusive mass transport model by Dutton and Stevens [50]. The activation energies for
crack healing were significantly lower for conventional heating than for microwave
healing (Figure 3 and Table 1). However, based on the experimentally determined Q
values (Table l) and the Do ratios calculated from the C values (Table l), the net
difi‘usivities inferred from the healing data show that the microwave heating increased the
diffusivities by a factor of about 1 to 4 over the range of the temperature used in this
study (Figure 4). Regardless of the inferred diffusivities, the net crack healing rate for

microwave annealed indentation cracks was considerably higher than annealing by

210

conventional furnaces (Figure 2).

This research has observed differences between the crack healing rates Aa/At based on
(i) indentation load (crack size) and (ii) heating ramp rate for microwave annealing, and
mechanisms for each effect has been identified. The possible mechanism for the
indentation load/crack size effect is the geometric factor R21n[Lo/R] in the denominator of
equation 3, which arises in the Stevens and Dutton model [50]. A mechanism for the
heating rate effect is the time-averaged diffusivity (equation 1 [49]). Additional work needs
to be done to gather the data that allow one to quantitatively compare the effects of these
mechanisms with the crack healing rate data.

The microwave-enhanced healing rates observed for the Vickers indentation cracks
included in this study imply that for a microcracked specimen annealed for a given
temperature and time, the recovery of strength, elastic modulus, etc. would occur more
rapidly via microwave annealing than for conventional thermal annealing. Additional
research should be done to investigate such effects. In addition, although this study was
limited to the healing of microcracks (V ickers indentation cracks), further work should be
done to determine whether the microwave enhancement also applies to healing of

macrocracks.

ACKNOWLEDGEMENTS
The authors acknowledge the financial support of the Electronic and Surface
Properties of Materials Center and the Composite Materials and Structure Center,

Michigan State University.

211

10.

ll.

12.

13.

14.

15.

16.

17.

18.

REFERENCES
E.D. Case and C. Glinka, J. Mater. Sci. 9, 2962 (1984).

S.L. Dole, 0. Hunter, Jr., F.W. Calderwood, and DJ. Bray, J. Amer. Ceram. Soc.
61, 486 (1978).

ED. Case, J .R. Smyth, and 0. Hunter, Mater. Sci. and Eng. 51, 175 (1984).
ED. Case, J .R. Smyth, and 0. Hunter, J. Nuclear Mater. 102, 135 (1981).
J .J . Cleveland and RC. Bradt, J. Amer. Ceram. Soc. 61, 478 (1978).

J .J . Siebeneck, D.P.H. Hasselman, J .J . Cleveland, and RC. Bradt, J. Amer. Ceram.
Soc. 60, 336 (1977).

Y. Ohya, Z.E. Nakagawa, and K. Hamano, J. Amer. Ceram. Soc. 71, c232 (1988).
J .C. Coppola and RC. Bradt, J. Amer. Ceram. Soc. 56[4], 214 (1973).

W.J. Lee and ED. Case, Mater. Sci. and Eng. A119, 113 (1989).

W.J. Lee and ED. Case, J. Mater. Sci. 25, 5043 (1990).

W.J. Lee and ED. Case, Mater. Sci. and Eng. A154, 1 (1992).

ED. Case, Y. Kim, and W.J. Lee, 24th International SAMPE Technical Conference,
SAMPE, Covina, CA, p 1123 (1992).

ED. Case, Y. Kim, and W.J. Lee, Thermal Shock Behavior and Thermal Fatigue of
Advanced Ceramics, G.A. Schneider and G. Petzow, Editors, Kluwer Academic
Publishers, the Nederlands, p 393 (1993).

ED. Case, Proc. 1995 SEM Spring Conference on Experimental Mechanics, Soc.
for Experimental Mechanics, Inc., Bethe], CN, p 264 (1995).

M.J. Reece, F. Guiu, and M.F.R. Sammur, J. Amer. Ceram. Soc. 72, 348 (1989).

R.H. Dauskardt, M.R. James, J .R. Porter, and RD. Ritchie, J. Amer. Ceram. Soc.
75[4], 759 (1992).

S.Y. Liu and I.W. Chen, J. Amer. Ceram. Soc. 75[5], 1191 (1992).

B.A. Wilson and ED. Case, 1993, Proc. 9th Annual Advanced Composites Conf.,
The Engineering Society, Ann Arbor, MI, p 518 (1993).

212

19.

20.

21.

22.

23.

24.

25.

26.

27.

28.

29.

30.

31.

32.

33.

34.

35.

36.

37.

38.

B.A. Wilson and ED. Case, Scripta Mater. 28, 1571 (1993).

ED. Case, K.M. Louie, and A.G. Evans, J. Mater. Sci. Letters 10, 879 (1984).
DB. Marshall, Fracture in Ceramic Materials: T oughening Mechanisms,
Machining Damage, Shock, A. G. Evans, editor, Noyes Press, Park Ridge, New
Jersey, p 190 (1984).

ED. Case, J. Mater. Sci. 11, 3702 (1984).

ED. Case, and J .R. Smyth, J. Mater. Sci. 16, 3215 (1981).

D.P.H. Hasselman, J. Comp. Mat. 3, 403 (1978).

W.R. Manning, 0. Hunter, F.W. Calderwood and D.W. Stacey, J. Amer. Ceram.
Soc. 55, 342 (1972).

F .F. Lange and KC. Radford, J. Amer. Ceram. Soc. 53, 420 (1970).

T.K. Gupta, J. Amer. Ceram. Soc. 59[5-6], 259 (1976).

A.G. Evans and B.A. Charles, Acta Met. 25, 919 (1977).

G. Bandyopadhyay and CR. Kennedy, J. Amer. Ceram. Soc. 59[9-10] (1977).
T.A. Michalske and ER. Fuller, Jr., J. Amer. Ceram. Soc. 68, 586 (1985).
M.K.C. Holden and V.D. Frechette, J. Amer. Ceram. Soc. 72[11], 2189 (1989).
RB. Leonesio, J. Amer. Ceram. Soc. 55[9], 437 (1972).

ED. Case, J .R. Smyth, and 0. Hunter, Fracture Mechanics of Ceramics, vol. 5,
edited by R. C. Bradt, A.G. Evans, D.P.H. Hasselman, and FF. Lange, Plenum
Press, New York, p 507 (1983).

B.A. Wilson and ED. Case, J. Mater. Sci. 32, 3163 (1997).

Z. Wang, Y.Z. Li, M.P. Harmer, and Y.T. Chou, J. Amer. Ceram. Soc. 75[6], 1596
(1992)

R. Raj, W. Pavinich, and C.N. Ahlquist, Acta Metall. 23, 399 (1975).
J. Rodel and A.M. Glaser, J. Amer. Ceram. Soc. 73, 592 (1990).

M.A. Janney and H.D. Kimrey, Ceramic Transactions, Vol. 1, 919 (1988).

213

39.

40.

41.

42.

43.

45.

46.

47.

48.

49.

50.

51.

52.

53.

54.

55.

56.

K.Y. Lee, E.D. Case, and D.K. Reinhard, Cer. Eng. Sci. Proc. 18, 543 (1997).
ED. Case and Y. Kim, J. Mater Sci. 28, 1885 (1993).

Y. Kim, E.D. Case and S. Gaynor, J. Mater. Sci. 28, 1910 (1993).

Y. Kim and ED. Case, J. Mater. Sci. 28, 1901 (1993).

B.R Lawn, Fracture Mechanics of Ceramics, vol 5., edited by RC. Bradt, A.G.
Evans, D.P.H. Hasselman, and F .F. Lange, Plenum Press, New York, p 1 (1983).

DB. Marshall and B.R. Lawn, J. Mater. Sci., 14, 2001 (1979).

W.S. Kim and ED. Case, Proc. 11th Annual Advanced Composites Conference,
The Engineering Society, Ann Arbor, MI, p 505 (1995).

K.Y. Lee, E.D. Case, J. Asmussen, Jr., and M. Siegel, Cer. Trans., Vol. 59, Amer.
Cer. Soc., Columbus, OH, p 473 (1995).

K.Y. Lee, E.D. Case, J. Asmussen, Jr., and M. Siegel, Proc. 11th ESD Advanced
Composites Conf., ESD, The Engineering Society, Ann Arbor, MI, p 491 (1995).

S. F. Flegler, J .W. Heckman JR., K.L. Klomparens, Scanning and Transmission
Electron Microscopy: An Introduction, W.H. Freeman and Company, New York,
NY. (1993).

P. Shewmon, Diffusion in Solids, Second Edition, The Minerals, Metals, & Materials
Soc., Warrendale, PA, p 37 (1989).

R.N. Stevens and R. Dutton, Mater. Sci. Eng. 8, 220 (1971).

J. Cheng, J. Qiu, J. Zhou, and N. Ye, p 323 in Mat. Res. Soc. Symp. Proc., Vol. 269,
Microwave Processing of Materials 11, Materials Research Society (1992).

R. Wroe and A.T. Rowley, J. Mater. Sci. 31, 2019 (1996).
SA. Nightingale, D.P. Dunnie, and H.K. Womer, J. Mater. Sci. 31, 5039 (1996).

J .D. Katz, R.D. Blake, and V.M. Kenkre, Cer. Trans. Vol. 21, Amer. Cer. Soc.,
Westerville, Ohio, p. 95 (1991).

V.S. Stubican and J .W. Osenbach, Advances in Ceramics, 10, 406 (1984).

Y. Oishi and W.D. Kingery, J. Chem. Phys. 33, 905 (1960).

214

CHAPTER 5
EFFECTS OF CASKET GEOMETRY AND MICROWAVE POWER

ON MICROWAVE HEATING

Part I. THE STEADY-STATE TEMPERATURE AS A FUNCTION OF CASKET

GEOMETRY FOR MICROWAVE-HEATED REFRACTORY CASKETSI

ABSTRACT
This study demonstrates experimentally that for a fixed microwave input power, the
steady-state temperature for microwave “caskets” (specimen enclosures) can vary
significantly as the casket geometry changes. Also, the steady-state casket temperatures
are very similar for caskets with and without an included specimen, as long as the
specimen’s volume and mass are small compared to the casket’s volume and mass. In
addition to the experimental work, a simple model is presented that describes the
variation in steady-state temperature as a function of casket geometry. The model also
describes how the steady-state casket temperature scales with microwave input power
level. For the single-mode microwave cavity operated at 2.45 GHz that is used in this

study, the steady-state casket temperature at 600 Watts of input power ranged from

 

l K.Y. Lee and ED. Case, and J. Asmussen, Jr, Materials Research Innovation, vol. 1, no. 2, pp. 101-116
(1997).

215

1112°C to 1519°C as the casket geometry changed for caskets composed of porous

zirconia cylinders with aluminosilicate end plates.

1. INTRODUCTION

At room temperature, only a few ceramic materials such as silicon carbide and
zirconia couple well with microwave energy. Typically the dielectric losses increase
with increasing temperature, so that materials that do not couple well at low temperatures
can couple well at elevated temperatures. For example, alumina does not couple well at
room temperature, where the loss tangent is less than 0.001 for frequencies between 3.15
GHz and 4.13 GHz [1]. However, alumina does couple well at temperatures between
900°C to 1300°C, where the dielectric loss tangent increases to 0.01 for the same
frequency range [1].

The difficulty in heating many ceramics with microwaves (at least at low
temperatures) leads to the practice of hybrid heating, where the specimen to be heated is
enclosed in a “casket” consisting of thermal insulation and/or microwave susceptor
material. The casket typically serves the dual functions of (i) absorbing microwave
power, thereby heating the specimen via radiant heating and (ii) thermally insulating the
specimen [2]. The radiant heat supplied by microwave heating of the susceptor can in
turn boost the dielectric loss of the ceramic specimens and allow the specimens to

directly couple with the microwave energy.

216

2. RELATION TO PREVIOUS WORK
2.1. Caskets and Insulation Used in Ceramic Processing

A variety of casket/insulation materials and geometries have been used in
microwave processing of ceramics. Insulation or casket materials used during microwave
processing include alumina [3-8], boron nitride [2,9,10], zirconia [IO-17], and alumina-
silica [11,18,19]. Typical casket geometries include prismatic boxes [20] or cylindrical
crucibles [2-4,7,9,10]. Within the caskets, some researchers use powder beds containing
mixtures of insulating/susceptor materials, such as silicon nitride, silicon carbide, or yttria
[7,10,20,21].

Susceptor materials to provide hybrid heating also have been incorporated into the
casket via SiC rods inserted into the insulating materials, and the insulating materials
often are in turn surrounded by a box or cylindrical refiactory fiberboard enclosure
[6,13,22-24]. Alternatively, cylindrical susceptors, such as porous zirconia cylinders [12-
17] act both as insulators and susceptor materials. Thus, despite the variety in casket
geometry and material, typical casket design elements include (i) a cylindrical geometry
and (ii) inclusion of susceptor materials to provide hybrid heating. The caskets included
in this study consist of porous zirconia cylinders and aluminosilicate end plates, and the
systematic changes in the steady-state inner wall temperature are measured as a function
of casket geometry. In addition, we develop a simple model to describe this functional
dependence of steady-state casket temperature on casket geometry. Therefore, we shall

briefly survey the literature that deals with thermal modeling of microwave heating.

217

2.2. Thermal Modeling of Microwave Heating

In the literature, thermal runaway has received the most attention in terms of
thermal modeling of microwave processing of materials. Thermal runaway during
microwave heating has been explained in terms of a specimen temperature which is a
multivalued function of the absorbed microwave power density p31,, (or, alternatively the
magnitude of the local electric field strength), so that an instability develops during
heating [24-28]. When a critical temperature is exceeded, the instability allows the
specimen temperature to “jump” from the stable low-temperature branch to the stable
high-temperature branch of the temperature-pal,s curve. (An unstable branch of the
temperature-p31,, curve connects the two stable branches).

In addition to modeling thermal runaway, a number of authors have used finite
difference calculations to model the electromagnetic fields and the temperature
distribution within loaded cavities during microwave processing [24,29-3 5]. Johnson and
co-workers [34,3 5] used finite difference techniques to calculate temperature
distributions and thermal stability for microwave-heated ceramic specimens with a
convection/radiation condition along a vertical wall. For cylinders of alumina, Johnson et
al. determined the temperature gradients in the radial direction for varying thicknesses of
insulation surrounding a long cylindrical specimen [34]. Johnson et al. [34,35], thus
focused on the temperature distribution within the specimen and the thermal stability of
the specimen.

Tucker et al. [30,31] used a F inite-Difference Time-Domain (FDTD) technique to
model heating in a multimode rectangular waveguide for a cylindrical specimen encased

in insulating material. SiC rods inserted in the insulator acted as a susceptor material.

218

The absorbed power density in the specimen and the surrounding insulation was
calculated using a 3-dimensional finite-difference time-domain code, then the
temperature distribution was solved via a finite-difference heat transfer code [31]. Since
the dielectric properties of the specimen and insulation were functions of temperature, the
temperature distribution results were input to the absorbed power density, and the process
was continued iteratively. The field pattern in the cavity and the temperature distribution
in the specimen was computed with and without the insulation, and with the SiC rods in
various configurations.

While Tucker et al. [30,31] modeled susceptor materials in terms of SiC rods,
Skamser and Johnson [36] used a finite difference technique to model a cylindrical
bundle of alumina fibers surrounded by a cylinder consisting of a lossy susceptor
material. The electric field and temperature distributions were then calculated for the
specimens.

Jackson et al. [24,32,33] modeled heating a lossy dielectric sphere in a rectangular
resonant microwave cavity. The finite difference computations simultaneously solved
Maxwell’s equation and the heat balance equation using dielectric constants and thermal
conductivity that were temperature dependent (thus equations were mathematically
nonlinear). The sphere was modeled with homogeneous thermal and dielectric properties
in a given thin shell, but thermal and dielectric properties varied from shell to shell,
resulting in properties that changed as a ftmction of the radial coordinate. In addition to
the assumed symmetry for the material properties of the sphere, the mode (TM354
rectangular waveguide mode), the cavity dimensions, and the placement of the sphere

were selected to give an isotropic electric field near the sphere. Despite the simplifying

219

assumptions of material-property symmetry, isotropic local electric field, etc., the
calculations became extremely complex when the dielectric and thermal properties were
allowed to change as a function of temperature, as is highlighted by Jackson’s statement
that “Even with these simplifications, part of the calculations required the use of a Cray
computer” [24].

Thus, most of the effort in thermal modeling has been aimed at transient
temperature distributions including thermal runaway and temperature distributions as a
function of time for a given susceptor/specimen system. For the calculation of transient
or steady-state temperature fields in microwave-heated specimens and caskets, the
computational complexity of the thermal modeling has led most researchers to employ
numerical calculation techniques, such as finite difference or finite element. In this study
we concentrate on predicting the steady-state temperature of the inner wall of empty (no
specimens included with the casket) caskets. Steady-state temperatures are much easier
to model than transient temperatures, yet steady-state temperature conditions are ofien

employed in sintering, binder burnout, and joining.

2.3. Key Innovations and Differences from Previous Work

For a fixed microwave input power, the steady-state inner wall casket temperature,
T,, for an empty casket can vary dramatically as a function of casket geometry. In this
study, at a fixed input power of 600 Watts, we observed T, to change by more than 400°C
as the casket geometry changed. This study presents a set of simple heat transfer
equations that describe well this geometrical dependence of T3. In addition, we also show

how Ti scales with changes in the microwave input power, and the experimental

220

observations of this scaling agree well with the heat transfer equations given in this
paper. The authors were unable to find work in the literature that describes either the
dependence of T, on casket geometry or on scaling of T, with microwave input power.

In contrast to many other studies, this study focuses on the heating behavior of
empty caskets (no specimens included within the casket). Since the casket material often
has a relatively large volume and mass compared to the specimen volume and mass, if the
dielectric losses in the casket are high, the casket will dominate the heating process
(equations 1 - 6 in Section 4). In order to relate the heating behavior of the empty caskets
to the microwave processing of the ceramics, we performed additional experiments in
which we compared the inner wall temperature and the absorbed power for caskets with
and without a specimen present in the casket. When the specimen’s volume and mass
' was small compared to the casket’s volume and mass, the inner wall casket temperature
was nearly the same for both the empty casket and the casket with the specimen inside.

The simple and approximate models developed in this paper describe well the
dependence of T,, the steady-state inner wall casket temperature as a function of casket
geometry. As discussed in Section 2.2, other researchers have modeled casket
temperatures using finite element techniques, but such techniques can be cumbersome.
Parametric studies could potentially describe the dependence of the steady-state
temperature upon casket geometry, but even if the numerical modeling was successful,
one still would need to distill the functional dependence of the geometrical parameters
from the numerical results. The models presented here give analytical results which form
a basis for the rational design of microwave caskets, and the tools for such a casket

design strategy are not found now in the literature.

221

The computer database Compendex was searched using the following keywords:
microwave heating, microwave processing, microwave cavity, microwave sintering for
the years 1991-1996. The following keywords were searched by the Compendex as a
group: microwave, cylinder (cylinders, cylindrical), and ceramic (ceramics). In addition,
references were taken from the authors’ files of microwave heating and processing

papers.

3. EXPERIMENTAL PROCEDURE
3.1. Materials

In this study, the refractory caskets that were microwave-heated were nominally
identical to caskets used by the authors [14-16] for hybrid heating of ceramics and
ceramic composites. Each casket used for this research (Table l and Figure 1) was made
of aluminosilicate board end plates (SALI, Zircar) and zirconia cylinders (ZYC, Zircar).
The approximate compositions (as specified by the vendor) of the aluminosilicate
refractory boards and the zirconia cylinders are given in Table 2 [3 8].

The caskets were divided into three groups. Caskets in Group 1 (Caskets 1 - 4)
included a disc-shaped aluminosilicate (SALI) specimen setter (Figure 1) similar to those
setters used by the authors for microwave sintering and joining of ceramic materials [14-
16]. The specimen setters had a radius equal to the inner radius of the zirconia cylinder.
The setter thickness was 0.5 cm for Caskets l, 2, and 3, and 1.5 cm for Casket 4.

Group 2 (Caskets 5, 6, 7, and 8) and Group 3 (Caskets 9, 10, 11, and 12) included
only SALI end plates and zirconia cylinder; no specimen or specimen setter was

included. For Group 2, the b/a ratio (outer radius/inner radius) was fixed at 1.5 and the

222

Table 1. Volume and dimensions of each casket used in this study.

 

 

 

 

o t r Inn ma]
u. C . 61' L2,» b Ls A b VZr c VSA c volume
Group Casket radius, radius, b/ a 3 3
(cm) (cm) (cm ) (cm ) of casket

b (cm) a (cm) 3

(cm )

Casket 1 5.08 3.81 1.33 3 4 106 347 453 d

1 Casket 2 3.81 2.54 1.50 3 4 76 193 269 d

Casket 3 5.08 2.54 2.00 3 4 182 334 516 d

Casket 4 5.08 3.81 1.33 5 2 177 231 408 d
Casket 5al 3.81 2.54 1.50 2 2 51 91 142
2 Casket 6 3.81 2.54 1.50 3 2 76 91 167
Casket 7 3.81 2.54 1.50 4 2 101 92 193
Casket 8 3.81 2.54 1.50 5 2 127 91 218
Casket 5“1 3.81 2.54 1.50 2 2 51 91 142
Casket 9 5.08 3.81 1.33 2 2 71 162 233
3 Casket 10 5.08 2.54 2.00 2 2 122 162 284
Casket 11 3.81 3.00 1.27 2 2 35 91 126
Casket 12 5.08 3.00 1.69 2 2 106 162 268

 

‘ Same heating data for the casket used in analysis.
b Lzr and LSA are length of zirconia cylinder and total thickness of SALI end plates,

5"?”

ctivel .
and V3;

are volume of zirconia cylinder and volume of SALI, respectively.

d Volume included the volume of specimen setter (SALI) inside each casket in Group 1.

223

2b

IL kl

 

 

 

 

 

 

j
T a
'4 e— Alumina SALI
V!
O I I
: : <—— Zirconia ZYC
{- | I
i—l l l
l—Amm W
E ' specnnen setter
”2
JL N +—— Alumina SALI

 

T
L

2a

Figure 1. Schematic of the casket (specimen enclosure) used in this study. The
aluminosilicate (SALI) specimen setter was included in Caskets 1-4.

Table 2. Composition, density, and porosity of the insulation used for caskets in this

 

 

study [3 8].
Refi'actory Composition wt% Den“? Porosity
’ (g/cm ) (%)
Aluminosilicate, SALI 80% A1203 - 20% Si02 0.48 84
Zirconia, ZYC 87% Zr02 - 8% Y203 - 5% SiOz 0.48 91

 

224

total casket length ranged from 4 cm to 7 cm. For Group 3, the casket length was fixed at
4 cm (2 cm zirconia cylinder height and 2 cm total aluminosilicate board thickness), but
the b/a ratio ranged from 1.27 S b/a S 2.0 (Table 1).

In addition to heating the empty caskets, Casket 6 (Group 2) and Casket 9 (Group 3)
were reheated with a powder compact specimen added to the caskets. A 2 gram alumina-
15 wt% zirconia powder compact and a 20 gram alumina powder compact were heated in
Caskets 6 and 9, respectively, to compare the steady-state temperatures at 600 Watts to
the temperatures of the corresponding caskets without specimens at the same microwave
input power. The materials used for the 2 gram powder compact specimen were
Sumitomo AKP50 and zirconia powder (Fisher Scientific Company). For the 20 gram
specimen, Sumitomo AKP30 was used. Both the specimens were uniaxially pressed (the
2 gram specimen at 32 MPa and the 20 gram specimen at 4 MPa), yielding a 2 gram disc-
shaped A1203-15 wt% Zr02 powder compact, 2.2 cm in diameter and about 2 mm thick

and a 20 gram disc-shaped A1203 powder compact, 5.1 cm in diameter and 5.5 mm thick.

3.2. Refractory Casket Construction

The caskets were prepared from as-received billets of aluminosilicate board and
from as-received zirconia cylinders (Zircar SALI and ZYC, respectively). The boards
and cylinders were cut to the desired dimensions using a commercial saw. The cut
surfaces were finished by abrading the zirconia cylinder with a sheet of notebook paper to
reduce possible thermal losses from the gaps between the casket end plates and the
zirconia cylinder.

For each casket, the total casket height (zirconia cylinder plus the aluminosilicate

225

board end plates) ranged from 4 cm to 7 cm (Table 1 and Figure 1). The cylindrical
zirconia refractory was available in two types. One had 10.16 cm (4 inch) OD and 7.62
cm (3 inch) ID, while the other had 7.62 cm (3 inch) OD and 5.08 cm (2 inch) ID. The
caskets having b/a ratio equal to 1.3333 (Casket 1, 4, 9) or 1.5 (Casket 2, 5, 6, 7, 8) were
prepared from the as-received 10.16 cm OD or 7.62 cm OD cylinders, respectively (Table
l). Caskets 3 and 10 having a b/a ratio of 2.00 were made by inserting a 7.62 cm OD
cylinder into a 10.16 cm OD (7.62 cm ID) cylinder. For Casket 11, a b/a ratio of 1.27
was obtained by reaming a casket of an original inner diameter of 5.08 cm to a final inner
diameter of 6 cm. For Casket 12, a b/a ratio of 1.69 was obtained by inserting a casket
having an inner diameter of 5.08 cm into a casket having an inner diameter of 7.62 cm
and then reaming the inner diameter from 5.08 cm to a final inner diameter of 6 cm.
(Table 1). Therefore, each casket had an outer radius of either 3.81 cm or 5.08 cm and an
inner radius of either 2.54 cm, 3 cm, or 3.81 cm. The dimensions of the 12 caskets
constructed for this study are listed in Table l.

A maximum casket length of 7 cm was used in this study because the tuned
microwave cavity height varies from a lower limit of 7.3 cm to an upper limit 21.95 cm.
During heating, the cavity was tuned by adjusting the cavity height and launch probe
position. A casket height equal to or smaller than 7 cm avoids possibly crushing the

casket by the top plate of the microwave cavity.

3.3. The Microwave Cavity, Power Supply, and Associated Apparatus

The microwave cavity used in this study was an internally tunable, cylindrical

single-mode cavity operated at 2.45 GHz (CMPR-250, Wavemat, Plymouth, MI, Figure

226

2) [l4-17,39,40—42]. Continuous microwave power ranging from 0 Watts to 2 kWatts
generated by a magnetron power supply (Sairem MWPSZOOO, Wavemat, Plymouth, MI)
was transmitted to the cavity by a rectangular metallic hollow waveguide with
approximate internal dimensions of 7.2 cm by 3.4 cm (Figure 2). The power was fed into
the cavity through a power launch probe which determines the field distribution around
the cavity wall (Figure 3). The microwave cavity was tuned using two computerized
stepper motors which change the probe and short positions with an accuracy of 21:00] cm
(Figures 2 and 3) [14-17,41,42].

P,, the reflected power was measured by a Hewlett-Packard power meter (HP435B).
The total power, PT, absorbed by the cavity system was calculated from PT = Pi - P,,
where Pi is the microwave input power.

The temperature at the inner wall of the casket was measured via an optical
pyrometer system (Accufiber Optical Fiber Thermometer, Model 10, Luxtron Co.,
Beaverton, OR) (Figures 2 and 4) capable of measuring temperatures ranging from 500°C
to 1900°C with an accuracy of :t 2°C. For every casket used in this study, a 5 mm
diameter hole was drilled in the casket wall (Figures 2 and 4) [14,15] to allow the
temperature measurement. The hole was positioned 2.5 cm above the cavity bottom plate
during microwave heating of the caskets to allow the hole to be aligned with the
microwave cavity viewport A, which in turn permitted pyrometer observation (Figures 2
and 4).

In addition to the temperature measurement of the casket inner wall, the outer wall
temperature was measured for the caskets in Groups 2 and 3 (Table 3). Using cavity

viewport B (Figure 2), the outer casket wall temperature was measured by sighting the

227

Directional Power meter Cylindrical single-mode

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

   

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

coupler microwave cavity
0 ° ° Specimen
Magnetron Circulator
/ \.
: .\ / -_-
Dumm load *
Y QT: _ Casket
I E -
._ § e =
E 5 Optical
Power supply controller pyrometer
Motor controller
[ . for probe
accufiber model 10
l . f Optical Fiber
Motor controller
for short

Figure 2. Apparatus for microwave heating using a cylindrical single-mode cavity.

228

‘— Short Position

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Upper Limit Switch Adjusting Motor

[ _ _ j
i
E

II 7 11

f ‘ .
Finger Stock
fir—_— 'crc‘c‘c'c'c‘c'clc‘SB'J‘J’JBTy') 5

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

LT

Probe Position
Adjusting Motor

 

 

 

 

—

 

 

 

 

Figure 3. Schematic of cylindrical single-mode microwave cavity. The short position,
Ls (cavity height) and the probe position, Lp are illustrated.

229

Cavity wall

/ \ Viewing port

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Casket
l
- a: s :1ij J
32--.: ---------- mmm )
”lililwl—l 2.5cm ()t' 1
I p 1ca pyrometer
n \ I n
\
\
Cavity bottom plate

Figure 4. Schematic showing the measurement of the temperature of the casket’s inner
wall. The optical pyrometer is sited through cavity viewport A and through a 5 mm hole
in the casket wall.

Table 3. Measured outer casket wall temperature, To, for caskets 5 - 12.

 

 

Casket# 5 6 7 8 9 10 11 12
Max?“ T° 906 865 835 804 937 759 873 975

 

230

optical pyrometer on the casket’s cylindrical outer surface. The outer wall temperature
was measured when the inner casket wall temperature reached a steady-state at 600
Watts. Unlike the inner wall temperature measurement, where the pyrometer was sighted
through the 5 mm hole in the casket wall, the curved outer surface of the casket made
temperature measurement difficult. The uncertainty in outer wall temperature was
estimated as about i 50°C. In addition, the microwave cavity was set up in a firme hood
which made it difficult to maneuver the optical pyrometer near viewport B as it was
being sighted on the casket outer wall, but there was no similar space problem involved
in aligning the pyrometer near viewport A through which the inner wall temperature was

measured.

3.4. Heating of Microwave Caskets

The heating experiments were done in two stages. First, the caskets were heated to
500°C using a fixed power ranging from 100 to 130 Watts. After the casket temperature
reached 500°C, the microwave input power was increased by 30 Watts every three
minutes up to a maximum power of 600 Watts. This rate of power increase resulted in a
relatively slow heating rate ranging from 8°C/min. to 22°C/min. for the temperature range
from 500°C to the maximum temperature.

The caskets in Group 1 were heated in various cavity modes (Mode 1 - Mode 9
described in Table 4) [3 7]. The caskets in Groups 2 and 3 were heated in the cavity tuned
to Mode 3. The reason for identifying the cavity modes used in this study with a simple
one-digit label is as follows. For an empty cavity, ideally there are a set of pure TE and

TM electromagnetic cavity modes. When the cavity is loaded with a lossy dielectric, the

231

Table 4. Summary for the cavity short position (i.e. cavity height), L5, as a function of
the electromagnetic resonance cavity mode, determined at a microwave input power of

 

 

50 Watts.
Ls (cm) for L8 (cm) Ls (cm) L, (cm) L,- (cm) Ls (cm)
ideal 7” for for for for for
Mode cylindrical empty casket casket casket casket
empty cavity cavity 1 2 3 4
(mode)
Mode l 7.21 (TMon) 7.66 a a a 8
Mode 2 8.24 (TE211) 8.43 7.72 8.15 7.47 7.65
Mode 3 11.29 (TM: 11) 11.62 9.77 10.32 9.45 9.50
Mode 4 13.38 (TE112) 13.60 12.83 12.96 12.52 12.80
Mode 5 14.41 (TMorz) 15.13 14.43 14.63 14.30 14.35
Mode 6 15.71 (TE311) 16.63 15.31 16.26 15.10 15.35
Mode 7 16.48 (TE212) 17.19 16.20 16.71 16.00 16.17
Mode 8 20.07 (TE113) 20.46 19.79 19.92 19.49 19.70
Mode 9 21.62 (TM013) a 21.76 a 21.34 21.68

 

° Could not determine, outside the range of the adjustable cavity height.

232

electric field distribution can be greatly modified, so that a simple TE or TM mode
designation is no longer appropriate [43]. For example, the TB modes can be distorted to
include 2 (axial) field components. Table 4 lists the corresponding designations for the
ideal cylindrical empty cavity mode and the short positions for the actual empty cavity
and for the cavity loaded with Caskets 1 - 4.

When Caskets 6 and 9 were reheated with a specimen present, the powder compact
specimens were placed at the center on the casket bottom plate without a specimen setter.
The caskets with each specimen were heated in the microwave cavity by the same heating
procedure used for heating the corresponding empty caskets. As was the case for the
temperature measurements for the empty caskets, the casket inner wall temperature was
monitored by the pyrometer through cavity viewport A and the 5 mm hole in the casket

wall (Figures 2 and 4).

4. MODEL FOR THE DEPENDENCE OF STEADY-STATE CASKET
TEMPERATURE UPON CASKET GEOMETRY
The power dissipated per unit volume of microwave absorbing material is given by

pans, which is related to the dielectric properties of the material by

p... =27r/e.e:(i.T)tan6(r,Timer (1)
where f = frequency of the incident microwave energy in Hz
80 = 8.854 x 10'12 F/m

= permittivity of free space
e,'( F ,T) = relative dielectric constant as a function of position vector, F ,

and temperature, T

233

tan 8( r ,T)= loss tangent as a function of 7' and T
E( F ) = magnitude of internal electric field in V/m as a function of r ,
The total power, PT, absorbed by the cavity loaded with a casket and a specimen is
equal to the difference between the input power, P], and the reflected power, PR, which
can be expressed as
PT=P,-PR=PW+PC+PS (2)
where Pw = power dissipated by the cavity wall
PC = power absorbed by the casket
P5 = power absorbed by a processed specimen.

In turn, PC and P5 can be expressed in terms of power density

PC =< p573 > VC (3)
P. p3,. > V. <4)
where < p2” = spatial average for power density within a casket of volume VC

(heat energy per unit time per unit volume)
< pf,” > = spatial average for power density within a specimen of
volume V.
For microwave heating performed with the casket alone (no specimen) then the total
power absorbed by the specimen becomes
PT = PW + PC. (5)
The caskets used in this study consisted of zirconia cylinders with aluminosilicate

refractory board end plates which are very lossy materials [23]. In this study, at 600 W

input power the measured reflected power was 0.1% to 1.4% of the input power for the

234

caskets of various geometries included in this study (Table 5) so that the power is nearly
totally absorbed by the cavity system (the cavity walls and the casket). From equation 2,
since the measured reflected power is very small, the total absorbed power, PT, is well
approximated by the input power, P, for 600 Watts. In fact, we observed experimentally
that PT is very nearly equal to P, over the entire range of input power from about 500
Watts to 600 Watts.

For lossy casket materials, Pw << PC the wall losses can be neglected in this case
and we can approximate PT by [43]

PT z PC =< p5... > VC (6)
which is the heat per unit time generated within the cylindrical casket (due to microwave
heating), thus PC z the total absorbed power PT.

We shall now develop a simple model for the steady-state thermal energy balance
for the microwave heated casket. This energy balance will consider the thermal energy
per unit time generated in the casket as a function of microwave heating and thermal
energy per unit time that flows out from the cavity walls. At steady-state, the energy
fluxes must balance.

For the steady-state flow of heat energy in a hollow infinite cylinder of inner radius
a and outer radius b subject to the boundary conditions that

(i) Atr=a, T=T

inside

= T, (7)
(ii) Atr=b,—dI—=h(7}-To)=0. (8)
dr

Carslaw and Jaeger give [44] the outward radial heat flux per unit length of cylinder as

J, _ 27dc(T,- - T.)Hb

_ 1+ Hbln(b/a) (9)

 

235

Table 5. Input power, P, reflected power, P,, and power density, pass, for various caskets
at a fixed input power of 600 Watts.

 

 

 

 

GrouP Casket Reflecgfkdaptzyer, P’ 57:75. x 100 (%) Pabs (W/m3)

Casket 1 1.54 99.7 5.65

1 Casket 2 3.38 99.4 7.85
Casket 3 8.21 98.6 3.25

Casket 4 6.15 99.0 3.36

Casket 5 a 3.08 99.5 4.21

2 Casket 6 1.54 99.7 3.58
Casket 7 0.51 99.9 3.11

Casket 8 0.51 99.9 2.75

Casket 5 a 3.08 99.5 4.21

Casket 9 0.51 99.9 2.57

3 Casket 10 1.03 99.8 2.11
Casket 11 2.05 99.7 2.23

Casket 12 4.10 99.3 4.73

 

a Casket 5 is included in both Group 2 and Group 3.

236

where in equations 7 - 9
T, = temperature at inner wall of hollow cylinder
To = temperature at outer wall of hollow cylinder
H = M and
h = surface heat transfer coefficient for the cylinder

k = thermal conductivity of the cylinder.

For a total length LT of the cylinder, the flux J is thus given by

J = J'Lr = 271150} '70)er (10)
[1+Hbln(b/a)] .

 

Given units of watts/m °C for k, watts/m2 °C for h, and meters for the dimensions a,
b, LT, then H has units of rn'l and J has units of watts (joule/sec). Thus J measures the
heat energy per unit time that flows through a length L of the cylinder wall.

At steady-state, the production of heat energy per unit time with the cylindrical
casket will be balanced by the outflow of energy (equation 10) so that

278(73- — T. >th

(11)
[l+Hbln(b/a)]

 

_ C C-
PT -<pabs>V —

where for a length of zirconia cylinder, L2,, and a total thickness of SALI end plates
(Figure 1), the total length of the cylindrical casket is

LT = L2, + LS, .
If we include in the volume of the casket, VC, the volume of the SALI end plates and the

volume of the zirconia cylinder then

P, =< pg, > [7:022 —a2)Lz, + rzszSA] (12)

Upon solving for Ti from equation 5 we obtain

237

 

T _ P, .[1+Hbln(b/a)]+T

_ 13
' 27d: HbL, 0. ( )

Using the measured Ti data as the independent variable, with four dependent variables
(three measured geometrical parameters, b, a, and LT, along with PT, the measured total

absorbed microwave power) we can use the following candidate equation to fit the data.

 

 

I; :ClPT[1+C2bln(b/a)]+C;. (14)
be
In theory, the fitted coefficients (Table 6) should correspond to

CI, = 1 = 1

27ch 27:}: (14a)
C' = H = E

k (14b)
C5 = 7?) . (14c)

If for the casket, the inner radius a, the outer radius b, and the total length LT are
fixed, then equation 14 reduces to

z=%+m as

where LT = the total cylinder length and D1 and D2 are fitted constants of the caskets in
Group 2 (Table 7). Referring to equation 13, D1 is given by

[1+ Hb1n(b/a)]

Dl =PT- 2
(16)

 

and D2 = To.
In the case that the geometric variables b, b/a, and LT are fixed, and the material
parameters H and k are fixed, then the coefficient D1 in equation 16 should vary linearly

with P7.

238

Table 6. Least-squares coefficients and coefficient of determination (R2) determined by
fitting the casket heating data of the caskets in Group 1, 2, and 3 to equation 14.

 

 

Group C.’ (m’-°C/W) Cz' (m") C3' (°C) R’
1 0.0052 17.2 26 0.999
2 0.1238 -64.3 1149 0.999
3 0.0025 10.8 342 0.997
1, 2, and 3 0.0006 13.5 1128 0.196

 

Table 7. Least-squares coefficients and coefficient of determination (R2) determined by
fitting the casket heating data of the caskets in Group 2 to equation 15.

 

 

Input power (Watts) D1 (m-°C) D2 (°C) R2
600 12.9 1 149 0.999
570 12.0 1121 0.972
540 1 1.4 1095 0.942

 

239

Thus the observed casket temperature results from a balance of the power absorbed
(which is a function of casket volume) and the heat losses (which is a function of the
casket surface area). Therefore, the volume and surface area of the caskets, as well as the
dielectric properties of the casket, will be important in determining the casket
temperature. When the volume and mass of the casket is large compared to the volume
and mass of the microwave-heated specimens, and the dielectric losses of the casket and
specimen materials are comparable, the casket should dominate the heating process
(equations 1 - 6, Section 5.2, and Figure 5). If the casket dominates the steady-state
casket temperature, then the casket geometry will have an important impact on the
processing of ceramics and ceramic composites, since often materials are processed at a

steady-state temperature.

 

  

 

 

 

 

 

1600 1 ' 1 a 1 ' 1 ' 1 v I
1400 r "
A 1-
U
D 1200 *- ‘
g .
g 1000 r p
Q) ..
g‘ t
g 800 T ‘9— WCWIfioutlpod-el
E_‘ b + CaMCWKIZIsped-en
600 " —A— memo-imam-
+ Cums-1a zapped-a-
400 1 . 1 . 1 r r . r a 1
l 00 200 300 400 500 600
Input power (Watts)

Figure 5. Temperature versus microwave input power for microwave heating of caskets
with and without specimens.

240

Equation 14 considered the microwave-generated heat within the casket and
convective heat losses from the casket’s outer surface, resulted in amazingly high values
of the coefficients of determination, R2, when the caskets within a given Group (Group 1,
Group 2, and Group 3) were modeled (Table 6). However, for the full set of 12 empty
caskets (that is, Groups 1, 2 and 3 taken together), the R2 value was 0.196, indicating that
the entire data set can not be appropriately described by equation 14. The low R2 value
obtained from equation 14 led us to include the top and bottom surface areas of the
caskets’ aluminosilicate end plates.

For a plane wall of thickness L, the flux per unit area is expressed as [44]

_k(T.-T.)
L

J'

Then for a surface of area, A, the flux is

 

J=J' =fl'f—QA A=areaofendplates (17)
_ 2
Jzkm Law: (18)

For a circular cylindrical casket used in this study, the thickness of each end plate is 0.5

LSA. Thus the flux from two end plates of the casket is

k0,- — 7.)an _ 4km - 72W

 

 

 

J = 2- (19)
0.5L“ Ln:
From equations 10 and 19, a total heat flux for the circular cylinder with end plates,
_ _ 2
_ 27rk(T, To )HbL, + 47tk(T,. To )b (20)

W — 1+ Hbln(b/a) L,4

Thus at steady-state, the production of heat energy per unit time with the circular

cylindrical casket with end plates will be balanced by the outflow of energy so that

241

HbL, +2b2
1+Hbln(b/a) LS,

 

27817“. —T.)=[ ]=p...V =1". (21)

Solving for Ti gives

_ P, LSA[1+Hb1n(b/a)]

 

.— - 2 . (22)
271k HbL,LSA + 2b [1+ Hbln(b/a)]
where L1 = LSA + LZr .
On multiplying by l/H in both the nominator and denominator, then we obtain
L [1 +bln(b/a)]
SA _
, PT H + To (23)

 

2”“ bL,L,,, + 21,21};- + b 1n(b/a)]

Using the measured Ti data as the independent variable, with five dependent variables
(four measured geometrical parameters, b, a, L2,, and LSA along with PT, the measured

total absorbed microwave power) we can use the following candidate equation to fit the

 

 

data.
: P,LS,[C,+C,b1n(b/a)] (24)
' bL,LSA+jb2[C3+bln(b/a)] ‘
where CI = 1 = I
27ch 27111 (24a)
C, =_1_
Zak (24b)
Q=i=5
H h (24c)
C4 = To. (24d)

In equation 24, the factor f corresponds to the dimensionless coefficient 2 in the

term 2b2[C3+bln(b/a)] in the denominator of equation 23. During the least-squares

242

fitting, f was also varied. The value of f equal to 0.1728 gave an optimal least-squares fit
of equation 24 to the data for the 12 empty caskets (Table 8).

Equation 14 or 24 can be generalized by replacing the expression for the heat flow
per unit length in a hollow cylinder (equation 9) with the following equation for the heat
flow per unit length in a composite cylinder composed of a series of n coaxial cylindrical

shells where the in, shell has thermal conductivity k;, such that [44,45,47]

.1274];_];),l°zfl___(ark+1/ar+)+R§_rL-‘] (25)

r=l f=1 a

where T1, T2, T3, are the temperatures at the radii a1, a2, a3, and Ti equals the
temperature inside the composite cylinder and To is the temperature outside the
composite cylinder. R1 is the contact resistance per unit area for the cylindrical surface
located at radius a.

Equation 25 could be applied to composite casket systems described in the
literature, such as coaxial aligned crucibles with fiber or powder insulation between the
inner and outer crucibles [3,7]. If we let am equal the outer radius of the composite

cylinder and a1 equal the inner radius of the composite cylinder, then in the limit as

Table 8. Least-squares coefficients and coefficient of determination (R2) determined by
fitting the casket heating data of the caskets in Group 1, 2, and 3 to equation 24.

 

 

C1 C2 C3 C4 2
Gm” (m2-°C/W) (m-°C/W) (m) (°C) R
1, 2, and 3 a 0.0036 0.106 0.203 747 0.993

 

" Casket 1 was not included.

243

an+1/a1 ——) 1, the casket walls become infinitely thin while in the limit arm/a1 -—) co, the
casket approaches a solid cylinder. For awn/a1 large, equation 25 might be applied to the
case of a cylindrical casket filled with a powder bed [2,10]. In this particular study, we
shall not pursue the composite cylinder model further, although it could likely be applied
to a variety of caskets described in the literature [2,3,7,10].

This model (equations 14, 15, and 24) ignores the temperature and spatial
dependencies of both the thermal and dielectric properties of the casket material. For the
zirconia cylinders and aluminosilicate (SALI) refractory board used to construct the
caskets in this study, Figure 6 gives the temperature dependence of the thermal
conductivities as specified by the vendor (Zircar Inc. [38]). The solid curves fitted
through the data was fitted by the authors to a quadratic function of temperature.

In addition to the thermal properties of the material, the surface heat transfer
coefficient h, is a measure of the transport of thermal energy across the interface between
the casket and the ambient air, and in this case the surface heat transfer coefficient for
free convection should be appropriate for the heated caskets in this study. However, h is
a function of temperature, and h varies from point to point on a surface, and the form of h
varies considerably for vertical as opposed to horizontal surfaces [4547].

Information on the temperature dependence of the dielectric properties of the casket
materials was not available fi'om the vendor. However, Figure 7 shows the temperature
variation of 8' and tan 8 as a function of temperature for several different aluminas [1].
The temperature dependence for s’ and tan 8 for zirconia is broadly similar to that of

alumina [48]. In this study, we did not attempt to estimate the temperature dependence of

s' and tan 6 since PT was measured directly. (For the caskets, PT = < pf,” >VC where pabs

244

 

 

  
     

 

 

 

 

G I ' l " l T 1
ca 0.40 ”L O Aluminosilicate, SALI O ..
\ El Zirconia cylinder, zvc ,
3. 0.30 P O J
IE
’2
"C 0.20 *’ .—
I:
O
o
"g 0.10 — _
a)
.1:
H 0.00 ‘ l 1 1 1 L . 1 ,
0 400 800 1200 1600 2000

Temperature (°C)

Figure 6. The temperature dependence of the thermal conductivities of the zirconia
cylinders (ZYC) and aluminosilicate refractory board (SALI) as specified by the vendor
(Zircar, data taken from ref. [3 8], curve fit done by the authors).

is a function of 8' and tan 5, as shown in equations 1 - 6.)

Since the thermal conductivity, k, the surface heat transfer coefficient, h, and the
dielectric properties 8' and tan 6 all are functions of temperature, and since the
temperature changes as a function of position through the casket walls, then k, h, s', and
tan 5 also will depend on position within the casket. In addition, material
inhomogeneities in the casket material will contribute thermal local perturbations in the
thermal and dielectric properties of the casket.

Also, the model presented here ignores radiative losses from the outer surface of the
casket. The heat flow due to radiation goes as the fourth power of the surface

temperature, and the details of the heat flow involves shape factors (not included in our

245

 

12.0 1’ I L I I 1 I T r I I Y I

 

 

 

 

 

 

 

 

 

 

 

 

 

 

ll 5 l / AlbemeuA-950 ‘
° _ I ---"‘“ American Lava Co. AlSiMag 614 ‘
l 1.0 -1 / Coors Porcelain Co. AD-99 , .
10.5 _
’00 _ q
10.0 _
9.5 _
9.0 -
L It
3.5 ‘ 1 J ' . J 1 1 a 1 . l .
0 200 400 600 800 1000 1200 1400
Temperature (°C)
(a)
(1010 pier 1 . I . , ., 4,\ 5f ,2. 1
/ Alberox Co. A-962 2
0008 """a Amer. Lava Co. AlSiMag 614 / _
_ / Coon Porcelain Co. AD-99 / d
0.006 _
00
0.004 a
0.002 _
1
0.000 1 i 1 I I l 1 l r l n l l
0 200 400 600 800 1000 1200 1400
Temperature (°C)
(b)

Figure 7. For various aluminas, 8' (a) and tan 8 (b) as a function of temperature (after
[1])-

246

analysis) that are functions of the geometry of the radiating body [45].

Including the temperature dependence of the thermal or dielectric properties would
make the problem mathematically nonlinear. Also, the problem becomes nonlinear if the
radiative heat transfer is included. If the temperature and spatial dependencies k, h, 8',
and tan 8 were treated fully, along with the radiative heat transfer, the problem would be
analytically intractable and numerical techniques would be required. By treating the
problem in a very approximate and simplified fashion, we were still able to capture the
geometric dependence of the steady-state inner wall temperature, T,, for the cylindrical

caskets included in this study.

5. RESULTS AND DISCUSSION

5.1. Dependence of the Steady-State Casket Temperature on Casket Geometry

The steady-state temperature T, measured at the inner wall of the zirconia cylinder
in the casket (Figure 8) changes as the casket geometry changes (Figures 9-11), but the
trends in T, versus geometry are not immediately obvious based on a parametric study
alone. In particular, Ti is not correlated well with either the total casket volume (Figure
9) or with the ratio of total volume/total surface area of the casket (Figure 10). A plot of
Ti versus the outer surface area of the casket (Figure 11) shows somewhat less scatter
than Ti versus volume or T, versus volume/surface area, although Ti versus the outer
surface area shows considerable scatter. Clearly, any dependence of Ti upon casket
geometry is not merely a function of only the total volume, the total surface area, or the
volume/surface ratio. However, the simple heat transfer model presented in Section 4 of

this paper can relate the temperature T, to the casket geometry.

247

 

 

 

 

 

O t- l. 01 (- (1I_.l E- t—
\

 

 

(Cm)

 

 

 

 

 

x4 **** wxaka
/ \ HH\\M “Ax
,,/" \
\xwéi. —t ,W/ ‘ 1500
*‘u ~‘ ‘\‘ ‘NK ///
8 7” ~
~ 1400 E3,
W 2
fil— <> “ 1300 a;
L.
m
0..
r 1200 E
e
, a..- 2 e
,//’ - °°°° -—.
/l,./"/L’// h\\‘l\“‘ l 100
1
4
IT

Figure 8. A three-dimensional plot of the steady-state temperature Ti measured at the
inner wall of the caskets' zirconia cylinder as a function of total casket length and the
radius ratio b/a.

 

 

 

 

 

 

Total volume of casket (cm3)

1600 1 r I l l
6 1500 - e O -
a, “ + 0
g 1400 e 0 -
. 0
g 1300 O +
— 4
o _ +
8
1200 - -
E? p C) (kmml 4. C) 1
F" 1100 — <> 6.....2 O _.
T + Groap3
1000 I I I 17 I Li I l
0 100 200 300 400 500 600

Figure 9. Measured Ti versus the total volume of each casket included in this study.
Note the lack of correlation between T, and the total volume.

248

T. at 600 Watts (°C)

1 600

1500

1400
1300

1200

1100

1000 \

 

 

 

 

 

 

 

I I 1 l
_ O ..
0 O .
_. + o _
O
o + 1
1— + '4
)- 0 Group 1 ['- O
0 Group 2 O -
+ Groap3
I L ”l t l g 1
0.6 0.8 1.0 1.2 1.4

Volume/ surface area (cm)

Figure 10. Measured T1 versus the ratio of total volume/total surface area of the casket.
Note the lack of correlation between T; and the volume/surface area ratio.

T1 at 600 Watts (° C)

 

 

 

 

 

 

1600 1 1 I 1 1
1500 - e O 4
. O .
1400 - + 0 1
O .
O +
1300 '7 + .—
- 1
1200 _ -1
+
l- 0 Group 1 8 q
1 100 " 0 Group 2 '7
+ Group 3
1000 \ . 1 i ’1 m l . l . 1
160 200 240 280 320 360 400

Outer surface area (cmz)

Figure 11. Measured Ti versus the outer surface area of the casket. Note the lack of
correlation between T, and the outer surface area.

249

For the caskets in Group 1 (Caskets 1 - 4, Table 1) the total length, LT, was fixed at
7 cm and b/a ranged from 1.33 to 2.0. Caskets 1 — 3 had a total aluminosilicate end plate
thickness, LSA, equal to 4.0 cm and zirconia cylinder length, L2,, equal to 3.0 cm. For
Casket 4, LSA was 2.0 cm and L2r was 5.0 cm. A least-squares fit of the steady-state
temperature, T, to equation 14 for the Group 1 caskets gave a coefficient of
determination, R2, value of 0.999 (Table 6, Figure 12). In Figure 12, the lower curve was
plotted setting the outer casket radius, b, equal to 0.0508 meter and the upper curve was
plotted setting b equal to 0.0381 meter. Thus, although Figure 12 shows two solid
curves, both curves were obtained from a single set of fitted coefficients (Table 6).

For equation 14, the independent variable is the steady-state temperature, T, and the
four dependent variables are b, a, LT, and PT (outer casket radius, inner casket radius,
total casket length, and the measured total absorbed microwave power, respectively). For
equation 24, the independent variable is T; and there are five experimentally determined
dependent variables b, a, LSA, L2,, and PT (where L3,, = the total thickness of the
aluminosilicate end plates and L2r = the length of the zirconia cylinder). For the four
caskets in Group 1, only three caskets had a fixed value of LSA so that if equation 24 was
used to fit the data, we could only include three data points in the least-squares fit, and
equation 24 has four fitted coefficients. Thus we could not use equation 24 to attempt to
fit the Group 1 data. However, for equation 14, we can use each of the four data points in
Group 1 since equation 14 (which has three fitted coefficients) only requires that the total
casket length, LT, is fixed. Therefore, we used only equation 14 (Figure 12 and Table 6)
to fit the Group 1 data.

Consider the caskets in Group 3 (Table 1), which includes caskets with fixed values

250

 

 

 

 

 

 

2000 . 1 T m ' 1 f l
l 0 Measured for Group 1
’ L— Predicted from eq. 141
1800 - -
b = 0.0381 in
A 1600 r -
.0
v
F‘ 14001 a
1200 7 b = 0.0508 m 7
- 1
1000 r l r l r l r l
1.2 1.4 1.6 1.8 2.0
b/a

Figure 12. The inner wall temperature, Ti as a firnction of the ratio b/a (b = outer radius
of zirconia cylinder, a = inner radius of zirconia cylinder). The least-squares fit to
equation 14 describes the data well for the Group 1 caskets.

of LT = 4.0 cm, LSA = 2.0 cm, Pr = 600 Watts. The caskets include five different b/a
ratios, ranging from 1.27 to 2.0, which includes the entire range of b/a ratios included in
this study. A least-squares fit to equation 14 (solid curves) and to equation 24 (dashed
curves) to the casket heating data shows good agreement between the measured Ti and
predicted T, values for both equations (Figure 13, Tables 6 and 8). In addition, the two
equations predict very similar values of Ti over the plotted range of b/a (1.2 < b/a < 2.0).
To illustrate the functional dependence of equation 24 on the Ma ratio, Figure 14 shows
the predicted values of steady-state temperature as a function of b/a for 1 s b/a S 5 and

several values of outer radius b, given LT = 4 cm, LSA = 2.0 cm, and a fixed input power

of 600 Watts.

251

 

 

 

 

 

 

1800 f 1 r 1 fig 1 . 1
+ Measured for Group 3
. —- Predicted from eq. 14
‘— Predicted from eq. 24 b = 3.81 cm
1600 r —
A
.0
5.: 1400 - b=5.08 cm ‘
Fe
1200 r -
600 Watts 4
Lt = 4 cm, Lsa = 2 cm
1000 1 l 1 l 1 l 1 l
1.2 1.4 1.6 1.8 2.0
b/a

Figure 13. The inner wall temperature T1 as a function of the ratio b/a (b = outer radius
of zirconia cylinder, a = inner radius of zirconia cylinder). The least-squares fit to
equation 14 (solid curves) and to equation 24 (dashed curves) both describe the data well
for the Group 3 caskets.

 

2000 - 1 . 1 - I
- 600 Watts

1300—Lt=4cm,Lsa=2cm ..

1 600

 

 

 

 

 

 

G 1400
‘L/
[4: 1200
1000 f,
1'" f—b=3.81cm .
.-- b = 5.08 cm
800 _ — b = 6.35 cm
600 ’ 1 1 ---- b = 7.82 cm '
1 2 3 4 5

b/a

Figure 14. Using equation 24 for several different b values, the predicted values of
casket steady-state temperature as a function of b/a for several values of casket outer
radius b, given LT = 4 cm, Lsa = 2.0 cm, and a fixed input power of 600 W.

252

For the caskets in Group 2, the b/a ratio is fixed at 1.5, the SALI thickness is fixed
at 2.0 cm, the input power is fixed at 600 W, and the length of the zirconia cylinder
ranges from 2 to 5 cm in 1 cm increments, giving a total casket length ranging from 4.0
cm to 7.0 cm (Table 1). For the Group 2 data, decrease in the steady-state temperature T,
as a ftmction of l/LT is described very accurately by equation 15 (Table 7), corresponding
to the solid curve in Figure 15 . The least-squares fit of the Group 2 data to equation 24 is
shown as the dashed line in Figure 15.

During the microwave heating of the Group 2 caskets, the temperature was recorded
after incrementing the input power by 30 Watts, up to the maximum input power of 600
Watts. The temperature as a function of casket length for input powers of 540 W, 570 W,
and 600 W are shown in Figure 16, along with a least-squares fitted line to equation 15
for each of the three different power levels. Although the heating conditions are at
steady-state for the 600 W case, steady-state may not have been achieved for the
measurements taken at input powers less that 600 W. For an input power, Pi, of 600
Watts, the reflected power, P,, was only about 0.1% to 1.4% of Pi (Table 5). Thus the
total power absorbed, P1, is nearly identical to the input power, Pi (equation 2). Also, we
found experimentally that PT is very nearly equal to P, for input powers between about
500 Watts to 600 Watts. Thus in Figure 17, we plotted the D1 coefficients as a function
of P1 rather than PT, since for each curve in Figure 16 there are four slightly different
values of PT (one for each casket) for each of the three input power levels, but all of the
PT values are nearly the same as P,. The fitted coefficients D1 show a linear trend as a
function of input power for 600 W, 570 W and 540 W (Figure 17). The linear trend

between the coefficients D1 and PT (where PT z P1) is consistent with the predictions of

253

 

 

   
 
  

 

 

 

 

1550 . 1 1 1 A . 1 . 1 r
1 ‘ 0 Measured for Group 2 q
— Predicted from eq. 15
1500 - — Predicted from eq. 2;
1450 - _
6 .
‘L/ 1400 - -
14? _ .
1350 - _
L 600 Watts 1
Lsa = 2 cm
1300— b=3.81cm,a=2.54cm _
' b/a = 1.5
1250 r l r l r l L l
3 4 5 6 7 8
Total length of casket (cm)

Figure 15. The steady-state temperature, T,, as a function of the total casket length for
Group 2 caskets, for which the b/a ratio is fixed at 1.5, the SALI thickness is fixed at 2.0
cm, and the input power is fixed at 600 Watts.

 

 

 
  
   

 

 

 

 

1550 1 1 . 1 1 1 ,r 1 .
. [ 0 800 Watts 4
D 570 Watts
1500 ' A 540 Watts]‘
1450 - "
6 1400 - ‘
b t
{—1 1350 - ‘
1
1300 - ‘
' Group 2 ‘
1250-Lsa=2cm,b/a=l.5 A ‘
- b=3.81cm,a=2.54cm ‘
1200 1 l 1 l 1 l 1 l 1
3 4 5 6 7 8

Total length of casket (cm)

Figure 16. For the Group 2 caskets, the temperature T1 as a function of casket length for
three different input power levels: 540 W, 570 W, and 600 W.

254

 

 

 

 

 

 

—I ' I 1 1— r I
1' 0 D1 valuea from least-squares fit
12.8 11* Linear regression curve _ //0 -
A 12.4 - .1
CC) /’I -t
E of
\f 12.0 - _
G
11.6 - _ 1' " 3
O .1
11.2 J L 1 A 1 . l
540 560 580 600
Input power (Watts)

Figure 17. The D1 versus input power, where the D1 values were obtained by fitting the
data in Figure 16 to equation 15.

equation 16.

The fitting coefficients C1', C2' (obtained for equation 14) and C1, C2, C3 (obtained
for equation 24) are functions of thermal conductivity, k, and surface heat transfer
coefficient, h (equations 14a - 14b, 24a - 24c). However, the numerical values of these
fitting coefficients do not agree with values calculated from our estimates of kg and <h>,
the caskets’ effective thermal conductivity and average surface heat transfer coefficient,
respectively.

The surface heat transfer coefficient for free convection in air ranges fiom about 5
to 15 W/m2 °C [49]. We chose a value of 10 W/m2 0C for our estimate of <h> the mean
value of the surface heat transfer coefficient.

To estimate the effective thermal conductivity, km, for the caskets, we used the

255

relationship [50]

ketr = kSA VSA + kzt V21 (26)
where kSA = thermal conductivity of the aluminosilicate (SALI) end plates

VSA = volume fraction of the aluminosilicate end plates

k2r = thermal conductivity of the porous zirconia cylinders

V2r = volume fraction of the porous zirconia cylinders,
assuming that the heat flow takes place primarily parallel to the interfaces between the
end plates and the cylinder. Mean values of kSA = 0.30 W/m °C and k2r = 0.15 W/m °C
were selected from Figure 6 for the temperature range from about 800°C to 1400°C. The
values of V511 and V2, were calculated from the casket dimensions (Table 1). The values
of km— for the twelve caskets included in this study, as estimated from equation 26, ranged
from 0.213 W/m °C to 0.265 W/m °C, with a mean value of 0.242 W/m °C.

From equation 24a, C1 = 1/21rh. Using the <h> value of 10 W/m2 °C, C1 should be
0.016 m2 °C/W, but for equation 24 the least-squares fit to the data for the full set of the
twelve caskets gave a C1 value of 0.0036 m2 °C/W (Table 8). Thus the value of
coefficient C1 obtained from the least-squares fit of equation 24 differs by a factor of 4.4
from the estimate of C1 based on <h> = 10 W/m2 °C. The coefficient C2 = 1/2nk
(equation 24b) has a value of 0.65 m °C/W based on our estimate of the caskets’ keg,
while C2 obtained from the least-squares fitting was 0.106. These two values of C2
disagree by a factor of about 6.1. The coefficient C3 = k/h (equation 24c), but the value
of C3 obtained from the least-squares fit is different by a factor of about 8.4 from the
value obtained using keff and <h>. The lack of agreement likely is related to this study’s

exclusion of the temperature and spatial variations for the thermal and dielectric

256

properties. Nevertheless, the value of the coefficient C4 obtained for equation 24 was
747°C, where C; corresponds to T0 the outside casket wall temperature (equation 24d).
This value of C4 is in rough agreement with the average outer wall temperature of 869°C
obtained for eight caskets in Groups 2 and 3 (Table 3).

Despite the discrepancy between the fitted and the estimated coefficients, the least-
squares fit of equation 24 corresponds well with T1 data. For the entire set of 12 empty
caskets included in this study (Tablel), the overall correlation between the measured T1
data and the T1 predictions based on equation 24 is relatively good (Table 9 and Figure
18). Eleven of the twelve data points in Figure 18 lie very close to the straight line,

where the straight line corresponds to perfect agreement between the measured and

 

 

 

 

 

predicted values.
1600 1 I ' l ' I r I ' I 1 ,
r’i \
A - O G l / -
.9, 1500 - 1...... , -
B F 0 Group 2 fi
8 1400 —\ + Groups _ + a
‘o 1
*5 1300 - +/ _
CL 1 C) “6
e 1 100 — /O —1
D4 / .
1000 / 1 l 1 l 1 l 1 L 1 L

 

 

 

1000 l 100 1200 1300 1400 l 5 00 1600
Meas. temp. at 600 W (°C)

Figure 18. The measured T, values versus the T1 values predicted on the basis of
equation 24.

257

Table 9. Average heating rate, measured temperatures, temperatures predicted by
equation 24, and residuals for the least-squares fit to the data for the entire set of empty
caskets.

 

Average heating Measured Predicted Residual, Tm - T,,

 

 

 

Group Casket rfldetefrrri): £0333: terr(1(1)3é,)Tm terr(1012.:,)Tp T2103}, T x 100

Watts (°C/min.) (%)

1 Casket] 12.2 1133 1261 -128 -11.3
Casket2 19.8 1519 1519 0 -0.0
Casket 3 18.9 1446 1443 3 0.2
Casket4 12.1 1112 1110 2 0.2

2 Casket 5" 18.8 1470 1479 -9 -0.6
Casket 6 18.2 1407 1420 -13 -0.9
Casket 7 17.2 1362 1370 -8 -0.6
Casket 8 16.4 1333 1326 7 0.5

3 Casket 51 18.8 1470 1479 -9 -0.6
Casket9 13.5 1181 1194 -13 -1.1
Casket 10 16.3 1348 1343 5 0.3
Casket 11 15.5 1289 1284 5 0.4
Casket 12 18.0 1417 1396 21 1.5

 

a Casket 5 is included in both Group 2 and Group 3.

258

5.2. Comparison of Steady-State Temperature and Heating Rate for Empty Casket
and Casket with a Processed Material

In Section 5 .1, the T1 data that is fit to equations 14, 15, and 24 corresponds to: (i)
Group 1 caskets, which include an aluminosilicate refractory board setter and no
specimen and (ii) Groups 2 and 3 caskets, which do not include either a specimen or a
specimen setter. By reheating caskets 6 and 9 with powder compact specimens present,
we seek to determine how the steady-state casket temperature, T, differs for the empty
casket case compared to the casket loaded with specimens.

For Casket 6, the steady-state inner casket wall temperature T1 for the empty casket
was 1407°C, while T1 was 1416°C for reheating Casket 6 loaded with a 2.0 gram
alumina/ 15 wt% zirconia specimen (Table 10 and Figure 5). Furthermore, the heating
rate from 500°C to T1 was very similar for Casket 6, with and without the 2.0 gram
specimen present (Table 10). Thus for Casket 6, where the specimen-to-casket volume
ratio was 0.005 and the specimen-to-casket mass ratio was 0.02, the specimen did not
greatly perturb the value of T. from that obtained for the empty casket (Table 10).
However, for Casket 9, the steady-state inner casket wall temperature T; for the empty
casket was 1181°C, while T, was 1257°C for reheating Casket 9 loaded with a 20 gram
alumina specimen (Table 10 and Figure 5). Also, the heating rate from 500°C to T1 was
somewhat higher when Casket 9 was loaded with the 20 gram alumina specimen (Table
10). For Casket 9, where the specimen-to-casket volume ratio was 0.03 and the
specimen-to-casket mass ratio was 0.16, the 20 gram specimen did significantly perturb

the value of T; from that obtained for the empty casket (Table 10).

259

Table 10. Comparison of the heating characteristics for two empty caskets and the same
two caskets with specimens.

 

 

 

 

Casket Volume Casket Mass Total Heating rate Steady-
volume ratio of mass ratio of absorbed from 500°C state temp.
System (cm’) specimen (g) specimen power, to temp. at at 600 W
to casket to casket PT 600 W (°C)
(Watts) (°C/min.)
Casket ““3"“ 167.2 a 84 a 598.5 18.2 1407
specrmen
with 168.0 0.005 86 0.02 599.0 18.0 1416
specrmen
Casket ““9”“ 233.1 a 129 a 599.5 13.5 1181
specrmen
9 with 240.3 0.03 149 0.16 596.4 15.1 1257
specrmen
a Not available
' I r I g l . I I I
1200 ‘6— Empty casket J

1000

P1 (Watts)

 

800
600
400

200

 

1..”‘7
-i —-B— Sumitomo AKP-30

—A_‘ Sumitomo AKP-50

 

1—“

l-

 

 

600
P1 (Watts)

800

1

l 000

  
   

 

1200

Figure 19. The total power absorbed, PT, versus the input power for two sintering runs
for Sumitomo AKP30 and AKP50 alumina in Casket 1, compared to a heating run for
Casket l with no specimen included.

260

In addition, in separate sintering experiments using Casket 1, two microwave
sintering runs were done, each including either a single 2 gram specimen of Sumitomo
AKP30 or a single 2 gram specimen of Sumitomo AKPSO. The absorbed power versus
input power for the two sintering experiments were each nearly identical to the absorbed
power versus input power for a heating run done for an empty Casket 1 (no specimen
present) (Figure 19). For the two sintering runs and the empty casket, a steady-state
temperature of 1575°C was achieved with a 1200 Watts input power for AKP30 sintering
experiment and the empty casket, and with 1225 Watts input power for the AKP50
specimen. Thus in these sintering experiments where the specimen mass and volume is
small compared to the casket mass and volume, the steady-state inner wall casket
temperature, T,, is essentially identical whether or not a specimen is present. This is
important, since if we can predict T1 for an empty casket, then we can also predict the
steady-state (i.e. the sintering) temperature for caskets that include processed specimens.

Therefore, although the total absorbed microwave power may be partitioned
between the casket and the specimen, the casket can play a dominate role in microwave

hybrid heating. The effect of specimen mass or volume on microwave hybrid heating

should be studied filrther.

5.3. Dependence of Heating Characteristics on Microwave Cavity Modes

Since every microwave cavity resonance mode has a unique electromagnetic field
pattern [51, 52], and because p31,, and PT are functions of the local electric field strength
(equations 1 - 6), microwave heating using different cavity modes might give different

steady-state temperatures. To explore this effect [3 7], the authors heated Caskets 1, 2, 3,

261

and 4 using eight different cavity modes, corresponding to eight different resonance
lengths (cavity lengths) (Table 4). For example, with Casket 1 heated at 600 Watts, the
steady-state inner casket wall temperature ranged from 105 5°C to 1186°C for the entire
set of eight modes, which corresponds to a maximum difference of 131°C in the steady-
state temperature for heating in the various cavity modes. However, for the 12 caskets
included in this study (which were heated in a single mode) the differing casket geometry
resulted in a maximum difference of 407°C in the steady-state temperature. Thus the
temperature differences induced by changing modes for a fixed casket geometry can be
much less than the temperature differences induced by changing the casket geometry.
Details of the difference in heating behaviors as a function of changing the
electromagnetic mode will be discussed in a forth-coming paper by the present authors

[37].

6. CONCLUSIONS

Using simple heat transfer concepts, we have developed a model that captures the
geometric dependence of the steady-state inner casket wall temperature T1 as a function
of casket geometry.
For a fixed microwave input power, the steady-state temperature T1 for microwave
“caskets” (specimen enclosures) can vary significantly as the casket geometry changes.
For an input power of 600 Watts, the steady-state temperature ranged from 1112°C to
1519°C for caskets composed of porous zirconia cylinders with aluminosilicate end
plates.

Knowing that (1) the absorbed microwave power is proportional to the volume of

262

the dielectric material (equation 1 and references 34, 35, 44) and that (2) the heat flow out
from the cylindrical casket is proportional to the surface area of the casket [34, 35, 44] is
not sufficient to describe the geometrical dependence of the steady-state temperature, as
demonstrated by Figures 9 - 11, where T, does not correlate well with the surface area,
volume, or volume/surface area of the caskets. However, equations 14, 15, and 24 in
Section 4.0 can describe the geometric dependence of T1 (Figures 12, 13, 15, 16, and 18)
and the manner in which T1 scales with input power (Figure 17).

At a fixed input power of 600 Watts, (Figures 12, 13, 15 and Table 6) equation 14
fits the data very well for Group 1 (LT fixed, LSA, L2,, and b/a vary), Group 2 (b/a fixed,
LT varies), and Group 3 (LT, LSA, and L2, fixed, b/a varies). Equation 15, which is a
simplified version of equation 14 (Section 4), fits well the Group 2 casket data for the
case where three different values of input power were used. Also, the coefficients D1
obtained by fitting the data for the Group 2 caskets heated at three different input power
levels, follows the linear trend with P7 predicted by equation 16 (Figure 18). Thus, this
analysis shows how the steady-state casket temperature scales with input power.

Although equation 14 fails to describe the entire dependence of T; on casket
geometry for the entire data set of empty caskets where each of the geometric variables
(LT, L211, L511, a, b, and b/a can vary), equation 24 does describe the full data set well
(Table 9 and Figure 18).

In addition to presenting experimental evidence for the dependence of steady-state
temperature on casket geometry and developing simple equations to describe that
dependence, we have shown that for the lossy dielectric casket materials used in this

study, the casket temperature was only slightly perturbed by the presence of a specimen

263

with a volume and mass that was small compared to the casket volume and mass.
However, for a relatively “large” specimen, whose mass was about 0.16 of the casket
mass, the temperature perturbation was significant. The steady-state empty casket
temperature was 1181°C and the steady-state temperature of the casket plus the large
specimen was 125 7°C, which was a specimen-induced steady-state temperature shift of
76°C.

The simple models presented in this study ignore the temperature and spatial
dependencies of k, h, 3', and tan 8 along with ignoring the radiative heat losses. An
equation for heat flow in an infinite hollow cylinder (equation 9) was the starting point of
the analysis, thus end effects due to the finite cylinder length are neglected for the
equations given in Section 4. Also, the coefficients obtained fi'om the least-squares
fitting of the T1 data do not agree with the value of the coefficients calculated from our
estimates km and <h> (Section 5.1). The lack of agreement likely stems, at least in part,
fi'om neglecting the spatial and temperature dependencies of the thermal and dielectric
parameters. However, treating these dependencies in detail would require numerical
techniques, which lack advantage of providing a straightforward analytical expression for

the functional dependence of T1.

ACKNOWLEDGEMENTS
The authors acknowledge the financial support of the Michigan Research
Excellence Fund provided through the Electronic and Surface Properties of Materials

Center, Michigan State University.

264

10.

REFERENCES

Westphal WB and Sils A (1972) Dielectric Constant and Loss Data, Technical
Report AF ML-TR-72-39, Massachusetts Institute of Technology, Cambridge, MA.

Holcombe CE and Dykes NL (1990) J. Matl. Sci. Lett. 9:425.

Janney MA, Kimrey HD, Schmidt MA, and Kiggans JO (1991) J. Am. Ceram. Soc.
74[7]:l675.

McGill SL, Walkiewicz JW, and G.A. Smyres (1988) The Effect of Power Level on
the Microwave Heating of Selected Chemical Minerals. In: Sutton WH, Brooks MH
and Chabinsky IJ (eds) Microwave Processing of Materials, Mat. Res. Soc. Proc.,
vol. 124, Materials Research Society, Pittsburgh, Pennsylvania, pp. 247-252.

Patil DS, Mutsuddy BC, Gavulic J, and Dahimene M (1991) Microwave Sintering
of Alumina Ceramics in a Single Mode Applicator. In: Clark DE, Gac PD, and

Sutton WH (eds) Microwaves: Theory and Application in Materials Processing, Cer.
Trans. vol. 21, Amer. Cer. Soc., Westerville, Ohio, pp. 301-309.

Kimrey HD, Kiggans JO, Janney MA, and Beatty RL (1990) Microwave Sintering
of Zirconia-Toughned Alumina Composites. In: Snyder WB, Jr., Sutton WH,
Iskander MF and Johnson DL (eds) Microwave Processing of Materials 11, Mat.
Res. Soc. Symp. Proc. vol. 189, Materials Research Society, Pittsburgh,
Pennsylvania, pp. 243-256.

Lorenson CP, Patterson MCL, Risto G, and Kimber R (1992) The Effect of Particle
Size on Microwave Heated Carbon and The Subsequent Crystallite Growth. In:
Beatty RL, Sutton WH and Iskander MF (eds) Microwave Processing of Materials
III, Mat. Res. Soc. Symp. Proc. vol. 269, Materials Research Society, Pittsburgh,
Pennsylvania, PP. 129-136.

Boch Ph, Lequeux N, and Piluso P (1992) Reaction Sintering of Ceramic Materials
by Microwave Heating. In: Beatty RL, Sutton WH and Iskander MF (eds)
Microwave Processing of Materials 111, Mat. Res. Soc. Symp. Proc. vol. 269,
Materials Research Society, Pittsburgh, Pennsylvania, pp. 211-216.

Holcombe CE and Dykes NL (1991) Ultra High-Temperature Microwave Sintering.
In: Clark DE, Gac FD, and Sutton WH (eds) Microwaves: Theory and Application

in Materials Processing, Cer. Trans. vol. 21, Amer. Cer. Soc., Westerville, Ohio, pp.
375-386.

Patterson MCL, Apte PS, Kimber RM, and Roy R (1992) Batch Process for
Microwave Sintering of Si3N4. In: Beatty RL, Sutton WH and Iskander MF (eds)
Microwave Processing of Materials 111, Mat. Res. Soc. Symp. Proc. vol. 269,
Materials Research Society, Pittsburgh, Pennsylvania, pp. 291-300.

265

ll.

12.

13.

14.

15.

l6.

17.

18.

19.

20.

Katz JD, and Blake RD (1991) Amer. Cer. Soc. Bull. 70[8]: 1304.

Agrawal DK, Fang Y, Roy DM, and Roy R (1992) Fabrication of Hydroxyapatite
Ceramics by Microwave Processing. In: Beatty RL, Sutton WH and Iskander MF
(eds) Microwave Processing of Materials 111, Mat. Res. Soc. Symp. Proc. vol. 269,
Materials Research Society, Pittsburgh, Pennsylvania, pp. 231-236.

Fang Y, Agrawal DK, Roy DM and Roy R (1991) Rapid Sintering of
Hydroxyapatite Ceramics by Microwave Processing. In: Clark DE, Gac F D, and
Sutton WH (eds)_Microwaves: Theory and Application in Materials Processing, Cer.
Trans. vol. 21, Amer. Cer. Soc., Westerville, Ohio, pp. 349-356.

Lee KY, Case ED, Asmussen J, Jr., and Siegel M (1995) Sintering of Alumina
Ceramics in a Single Mode Cavity under Automated Control. In: Microwaves:
Theory and Application in Materials Processing 111, Cer. Trans., vol. 59, Amer. Cer.
Soc., Westerville, OH, pp. 473-480 .

Lee KY, Case ED, Asmussen J, Jr., and Siegel M (1995) Microwave Sintering of
Ceramic Matrix Composites and the Effect of Organic Binders on the Sinterability.
In: Proceedings of the 11th Annual ESD Advanced Composites Conference, Ann
Arbor, MI, pp. 491-503.

Lee KY, Cropsey L, Tyszka B, and Case ED (1997) Materials Research Bulletin
32[3]:287.

Lee KY, Case ED, and Asmussen J, Jr. ( 1997) Microwave Binder Burn-out for
Batch Processing of A1203, A1203/SiC Platelet, and A1203/Zr02 Particle Powder

Compacts. In: Microwaves: Theory and application in materials processing, IV,
Cer. Trans., vol 80, Amer. Cer. Soc., Westerville, OH, pp. 539-546.

Meek TT, Blake RD, and Petrovic JJ (1987) Microwave Sintering of A1203 and
A1203-SiC Whisker Composites. In: Cer. Eng. Sci. Proc. vol. 8 [7-8], pp. 861-71.

Cheng J, Qiu J, Zhou J, and Ye N (1992) Densification Kinetics of Alumina During
Microwave Sintering (1992). In: Beatty RL, Sutton WH and Iskander MF (eds)
Microwave Processing of Materials 111, Mat. Res. Soc. Symp. Proc. vol. 269,
Materials Research Society, Pittsburgh, Pennsylvania, pp. 323-328.

Kiggans JO, Jr., and Tiegs TN (1992) Characterization of Sintered Reaction-Bonded
Silicon Nitride Processed by Microwave Heating (1992). In: Beatty RL, Sutton WH
and Iskander MF (eds) Microwave Processing of Materials III, Mat. Res. Soc.

Symp. Proc. vol. 269, Materials Research Society, Pittsburgh, Pennsylvania, pp.
285-290.

266

21.

22.

23.

24.

25.

26.

27.

28.

29.

30.

Tiegs TN, Kiggans JO, Jr., and Kimrey HD, Jr. (1990) Microwave Processing of
Silicon Nitride. In: Snyder WB, Jr., Sutton WH, Iskander MF and Johnson DL
(eds) Microwave Processing of Materials 11, Mat. Res. Soc. Symp. Proc. vol. 189,
Materials Research Society, Pittsburgh, Pennsylvania, pp. 267-272.

Janney MA, Calhoun CL, and Kimrey HD (1991) Microwave Sintering of Zirconia-
8 mol % Yttria. In: Clark DE, Gac F D, and Sutton WH (eds) Microwaves: Theory
and Application in Materials Processing, Cer. Trans. vol. 21, Amer. Cer. Soc.,

Westerville, Ohio, pp. 31 1-318.
Janney MA, Calhoun CL, and Kimrey HD (1992) J. Am. Cer. Soc. 75[2]:341.

Jackson HW, Barmatz M, and Wagner P (1993) Transient Temperature Behavior of
a Sphere Heated by Microwaves. In: Clark DE, Tinga TR, and Laia JR, Jr. (eds)
Microwaves, Theory and Applications in Materials Processing 11, Cer. Trans. vol
36, Amer. Cer. Soc., Westerville, OH, pp. 189-199.

Kriegsmann GA (1991) Microwave Heating in Ceramics. In: Clark DE, Gac FD,
and Sutton WH (eds) Microwaves: Theory and Application in Materials Processing,
Cer. Trans. vol. 21, Amer. Cer. Soc., Westerville, Ohio, pp. 177-183.

Kriegsmann GA (1992) Thermal Runaway and its Control in Microwave Heated
Ceramics (1992). In: Beatty RL, Sutton WH and Iskander MF (eds) Microwave
Processing of Materials 111, Mat. Res. Soc. Symp. Proc. vol. 269, Materials
Research Society, Pittsburgh, Pennsylvania, pp. 257-264.

Kriegsmann GA (1993) J. Appl. Phys. 71:1960.

Reirnbert CG, Minzoni AA, and Smyth NF (1996) IMA Journal of Applied
Mathematics 57: 165.

Chapman B, Iskander MF, Smith RL, and Andrade OM (1992) Simulation of
Sintering Experiments in a Single-Mode Cavity (1992). In: Beatty RL, Sutton WH
and Iskander MF (eds) Microwave Processing of Materials 111, Mat. Res. Soc.
Symp. Proc. vol. 269, Materials Research Society, Pittsburgh, Pennsylvania, pp. 53-
59.

Tucker J, Smith R, Iskander MF, and Andrade CM (1992) Dynamic Model for
Calculating Heating Patterns During Microwave Heating (1992). In: Beatty RL,
Sutton WH and Iskander MF (eds) Microwave Processing of Materials 111, Mat.
Res. Soc. Symp. Proc. vol. 269, Materials Research Society, Pittsburgh,
Pennsylvania, pp. 61 - 67.

267

31.

32.

33.

34.

35.

36.

37.

38.

39.

40.

41.

42.

43.

Tucker J, Iskander MF, and Huang Z (1994) Calculation of heating patterns in
microwave sintering using a 3D finite—difference code. In: Iskander MF, Lauf RJ
and Sutton WH (eds) Microwave Processing of Materials IV, Mat. Res. Soc. Symp.
Proc. vol. 347, Materials Research Society, Pittsburgh, Pennsylvania, pp. 353-362.

Jackson HW and Barmatz M (1991) J. Appl. Phys. 70:5193.

Barmatz M and Jackson HW (1992) Steady State Temperature Profile in a Sphere
Heated by Microwaves (1992). In: Beatty RL, Sutton WH and Iskander MF (eds)

Microwave Processing of Materials III, Mat. Res. Soc. Symp. Proc. vol. 269,
Materials Research Society, Pittsburgh, Pennsylvania, pp. 97 - 103.

Johnson DL, Skamser DJ, and Spotz MS (1993) Temperature Gradients in
Microwave Processing: Boon and Bane. In: Clark DE, Tinga WR, and Laia JR, Jr.

(eds) Microwaves, Theory and Applications in Materials Processing 11, Cer. Trans.
vol 36, Amer. Cer. Soc., Westerville, OH, pp. 133-146.

Spotz MS, Skamser DJ, and Johnson DL (1995) J. Am. Ceram. Soc. 78[4]: 1041.
Skamser DJ and Johnson DL (1994) Simulation of Hybrid Heating. Iskander MF,
Lauf RJ, and Sutton WH (eds) Microwave Processing of Materials IV, Mat. Res.
Soc. Symp. Proc. vol 347, Materials Research Society, Pittsburgh, Pennsylvania, pp.
325-330.

Lee KY, Case ED and Asmussen J, Jr., to be pulished.

Zircar Fibrous Ceramics Catalog (December, 1995) Zircar Products Inc., Florida,
New York.

Asmussen J and Garard R (1988) Precision Microwave Applicators and Systems for
Plasma and Materials Processing. In: Sutton WH, Brooks MH and Chabinsky IJ
(eds) Microwave Processing of Materials, Mat. Res. Soc. Proc., vol. 124, Materials
Research Society, Pittsburgh, Pennsylvania, pp. 347-352.

Asmussen J ., Lin HH, Manring B, and Fritz R (1987) Rev. Sci. Instrum.
58[8]:1477.

Lee KY, Case ED, Asmussen J, Jr., and Siegel M (1996) Scripta Materialia
35[1]:107.

Lee KY, Case ED, and Reinhard D (1997) Microwave Joining and Repair of
Ceramics and Ceramic Composites. In: Cer. Eng. and Sci. Proc. 18:543-550.

Mak P and Asumssen J (1997) J. Vac. Sci. Technol. A15(1):154-168.

268

44.

45.

46.

47.

48.

49.

50.

51.

52.

Carslaw HS and Jaeger JC (1959) Conduction of Heat in Solids, 2nd ed., Oxford
University Press, Fair Lawn, NJ, pp. 19, 188-190.

Kreith F (1972) Chapters 2, 5, and 7 in Principles of Heat Transfer, Third Edition,
International Textbook Company, Scranton, PA,.

Beck JV, Blackwell B, and Clair CR, Jr. (1985) Inverse Heat Conduction, Wiley-
Interscience, New York, pp. 281-300 .

Gebhart B (1993) Heat Conduction and Mass Diffusion, McGraw-Hill, New York,
pp. 48-52, 64-71, 139-144.

Binner J, Cross T and Greenacre N (1997). In: Abstract Book for First World
Congress on Microwave Processing, Lake Buena Vista, Florida, pp. 47.

Karlekar BV and Desmond RM (1977) Engineering Heat Transfer, West Publishing
Co., New York, pp. 8, 14.

Kingery WD, Bowen HK, and Uhlmann DR (1991) Introduction to Ceramics, 2nd
edition, John Wiley & Sons, Inc., New York, pp. 634-637, 822.

Liao SY (1990) Microwave Devices and Circuits, 3'° ed., Prentice Hall, New Jersey,
pp. 136-138.

Pozar DM (1990) Microwave Engineering, Addison-Wesley Publishing Company,
Inc., New York, pp. 348-353.

269

Part II. STEADY-STATE TEMPERATURE OF MICROWAVE-HEATED

REFRACTORIES AS A FUNCTION OF MICROWAVE POWER AND

REFRACTORY GEOMETRY’

ABSTRACT

Using a simple energy balance model developed in a previous paper, this study
presents an improved least-squares fitting equation that relates T1 (the steady-state inside
wall temperature for hollow cylindrical refractory caskets) to microwave input power and to
casket geometry parameters. For microwave input power ranging fiom 200 Watts to 700
Watts, we measured 132 new casket/input power combinations, adding to the authors’
earlier data characterizing twelve different casket geometries at a fixed input power of 600
Watts. When such caskets are used for the microwave processing of ceramic materials, T1 is

very significant since it approximates the processing temperature within the casket.

1. INTRODUCTION
1.1. Background
The authors and co-workers have measured and modeled steady-state temperatures for
refiactory caskets heated in a single-mode microwave cavity [1]. Such refractory caskets
are widely used as insulation and/or susceptor materials for the microwave processing of
ceramics. While the previous study investigated trends in steady-state temperature mainly

as a function of casket geometry [1], this paper considers both geometrical effects and the

 

2 K.Y. Lee and ED. Case, submitted for publication, Materials Science & Engineering A (1998).

270

microwave input power level effects on the steady-state casket temperature. From this point
on in this paper, we shall refer to this previous study [1] as Paper 1.

The authors and co-workers have used refractory caskets consisting of porous zirconia
cylinders with refractory fiberboard end plates (Figure 1) for various types of microwave
ceramic processing, including sintering, joining, crack healing, thermal etching, and binder
burn-out of ceramics [2-12]. For example, the authors and co-workers have microwave-
sintered various aluminas [2,6], alumina/zirconia particulate composites [3], and yttria
stabilized zirconia [10] using such refractory caskets (Figure 1). In addition, the authors
have studied ceramic-ceramic joining for alumina [7,8], MaCor [7,8], and zirconia [10] as
well as crack healing behavior in alumina [7,9] and thermal etching in polycrystalline
alumina [11,12]. During binder burn-out studies for alumina and alumina/zirconia powder
compacts, the present authors and co-workers used refiactory caskets [3], but subsequent
binder burn-out work on A1203, A1203/SiC platelets, and A1203/Zr02 particle powder
compacts was done without a casket [4,5]. (Not using a refractory casket during binder
burn-out allows volatiles generated during burn-out to escape more effectively than when a
casket is used [4,5].) Other researchers have also used porous zirconia cylinders for

refractory casket materials during microwave sintering of ceramics [13,14].

1.2. Authors’ Previous Analytical Model for Refractory Casket Heating

In Paper 1 [1], a simple model for the steady-state temperature inside a microwave-
heated refractory casket was obtained by balancing the total power absorbed by the casket
and the thermal energy per unit time that flows out from the casket walls. This section

briefly summarizes that mode] [1].

27]

2b

 

 

   

 

   

 

 

1‘ ‘1
1‘ '1
71‘ <
,3 Aluminosilicate
,n. SALI
O
t" g 1 1
A 1—1 ercoma ZY C
.1:
fl ‘__ Aluminosilicate
.iL In. SALI
O

 

 

2a

Figure 1. Schematic of a refractory casket, showing a cross-sectional view of the hollow
ZYC cylinder and the aluminosilicate disk-shaped end plates [1]. The symbols a, b, L3,,
L2,, and LT are as defined in equation 5.

For a microwave cavity, the cavity “load” may be defined as those materials or objects
added to an ideal empty cavity that absorbs microwave energy (an ideal empty cavity would
not absorb energy even at the cavity wall). For a system consisting of a microwave cavity

loaded with a lossy refractory casket and a lossy ceramic specimen, the total power, PT,

absorbed by the system is [1]
P,=P,—PR=PW+PC+PS (1)
where P1 = microwave input power

PR = reflected microwave power
Pw = power dissipated by the cavity wall
PC = power absorbed by the casket

P5 = power absorbed by a processed specimen.

272

If we define p31,, as an absorbed energy per unit volume, then PC and PS are the spatial

averages of p31,, integrated over the appropriate material volumes, such that

PC = IVC pabs dV (23)

PS : IVS pabs dV (2b)

where in the above integrals, VC represents the casket volume and Vs represents the
specimen volume. For a dielectrically lossy cavity load, most of the microwave input
power is absorbed by the casket plus specimen combination, such that Pw can be
neglected.

When no specimen is present in the cavity, the total microwave power absorbed by the
casket alone may be approximated as

P, = PW + PC. (3)

If the relative wall loss << the power absorbed by the casket for the entire range of the
microwave input power, then the microwave power absorbed by the casket during
heating at a given input power level is

PC z P,. . (4)

During microwave heating, a steady-state refiactory casket temperature is achieved
when the power absorbed by the casket, PC, is balanced by the outflow of thermal energy,

such that

 

(5)

H L 2b2
P.:=27rk(T.—T.)[ b T ]

1+Hbln(b/a)+ L,,

where k = thermal conductivity

1 = temperature at inner wall of hollow cylinder

273

To = temperatm'e at outer wall of hollow cylinder
H = h/k

h = surface heat transfer coefiicient for the cylinder
LT = L51 + L2,: total length of the casket, where
L2, = length of zirconia cylinder

L51. = total thickness of the end plates

b = outer radius of the cylinder

3 = irmer radius of the cylinder.

In this paper we assumed that P,. = P, — PR . Rewriting equation 5 gives [1]

-1 -

LS, —+bln(b/a)

2:213. _H -1 ~ -+T, (6)
” bL,L,,+2112 F+bln(b/a)

h d

 

 

 

 

 

Equation 6 was derived using a number of simplifying assumptions [1]. For
example, the heat flow expression from Carslaw and Jaeger [15] used to derive equation
6 assumed an infinite hollow cylinder with heat generated within the cylinder wall. The
actual caskets are of finite length. Also, the heat flow through the end plates was
modeled in terms of a simple linear addition of terms describing heat flow through a
plate.

In addition to the simplifications involving the heat flow equations [1], equation 6
ignores that k, h, and the dielectric properties of the casket are each frmction of
temperature and position. (Since k is a fiinction of temperature and since the casket
temperature varies in a radial direction through the casket wall, k also will vary as a

function of spatial coordinates.) Also ignored are the radiation losses at the outer casket

274

wall which are functions of T4 and are expressed in terms of shape factors that are
functions of the geometry of the radiating body [16].

There are a number of physical and mathematical problems involved in directly using
equation 6 to predict the steady-state temperature T,. For example, the heat transfer
coefficients for convective heat transfer and for radiative heat transfer are difiicult to
measure and to model [16-19]. The derivation of equation 6 used an expression for heat
flow through the wall of an infinite hollow cylinder [1]. Real refractory caskets are finite so
that equation 6 neglects complicated end effects that may be expressed in terms of infinite
series of Bessel functions [15]. Even more important is the fact that the temperature and
spatial dependence of h, k and the radiative heat loss makes the problem mathematically
nonlinear. In fact, the temperature dependence of any one of the three factors (11, k, radiative
heat loss) is sufficient to make the problem nonlinear [20]. Such nonlinear problems
generally can be solved only by numerical techniques.

Given the nonlinearity and the other mathematical difficulties discussed above, the
refractory casket heating problem is analytically intractable. On the other hand, even
numerical solutions of such problems are extremely complex [21,22,23]. For problems
involving a large number of parameters (here 4 geometric variables and PC, the power
dissipated in the casket) it can be difficult to distill trends fi'om a collection of numerical
solutions. In Paper 1 [1], we chose to use a simple linear model (equation 6, which treats h
and k as constants) as the candidate function for a least-squares regression of the data T,, fit
the measured steady-state casket temperatures to the model (equation 6) we rewrite equation

6as[1]

 

P,L,,[C; +C§bln(b/a)] + C,

T =
' 61,8, + fb2[C; +bln(b/a)] ‘

(7)

275

where

 

‘ = 27111111 = 21111 (73)
C5 = __1_
271k (7b)
Q=L=£
H h (7c)
C3 = To. (7d)

For the least-squares fitting procedure, equation 6 was modified in the following
ways: (1) the free parameters C,’ , C; , C; , and C; replaced functions of k, h, and To as
defined in equations 7a-7d, and (2) the factor f in equation 7 replaces the numerical
coefficient 2 in the term 2b2[1/H+bln(b/a)] in the denominator of equation 6. In addition
to allowing C,’ , C; , C; , and C; to vary during fitting, f also varied [1]. For the 12 empty
caskets included in Paper 1 [1], the best least-squares fit of the data was obtained for f =
0.1728.

The data fitted to equation 7 in Paper 1 [1] consists of 12 ordered sextuples of the

form (T1, P1, L51, b, b/a, and LT). Although the casket geometry differed from casket to

casket in Paper 1 [1] (Table 1), P1 was 600 Watts for each sextuple [1].

2. EXPERIMENTAL PROCEDURES
2.1. Casket Construction
The refractory caskets used in this study (Figures 1 and 2) consisted of as-received
aluminosilicate boards (SALI, Zircar Products Inc.) and partially stabilized zirconia

cylinders (ZYC, Zircar Products Inc.). Using a commercial saw, the SALI board end plates

276

Table 1. Dimensions of the individual refractory caskets used in Paper 1 [1]. b, a, LT,
L51, L2,, L2, are as defined in equation 5. VSA and V2, are the volume of the SALI
aluminosilicate end plates and the volume of the zirconia cylinder, respectively.

 

 

 

 

Group b/a b (cm) a (cm) L1 L3,, L2, V5,, V2,
(cm) (cm (cm) (cm3) (cm3)

1.33 5.08 3.81 7 4 3 347 106

Group 1 1.50 3.81 2.54 7 4 3 193 76
2.00 5.08 2.54 7 4 3 334 182

1.33 5.08 3.81 7 2 5 231 177

1.50 3.81 2.54 4 2 2 91 51

Group 2 1.50 3.81 2.54 5 2 3 91 76
1.50 3.81 2.54 6 2 4 91 101

1.50 3.81 2.54 7 2 5 91 127

1.50 3.81 2.54 4 2 2 91 51

1.33 5.08 3.81 4 2 2 162 71

Group 3 2.00 5.08 2.54 4 2 2 162 122
1.27 3.81 3.00 4 2 2 91 35

1.69 5.08 3 .00 4 2 2 162 106

 

were cut into disks either 3.81 cm or 5.08 cm in radius with a fixed thickness of 1cm (Figure
2). In a given casket, the top and bottom plates were identical in dimension. The ZYC
cylinders were cut to a length of 2 cm, 3 cm, 4 cm, or 5 cm. The cut surfaces of the ZYC
cylinders were finished by abrading the cylinders with a sheet of notebook paper, in order to
planarize the cut cylinder surfaces and in turn reduce possible therrna] losses due to the gaps
between the ZYC cylinder and the end plates.

The as-received ZYC cylinders available for this study were either (1) 2.54 cm ID and
3.81 cm OD, or (2) 3.81 cm II) and 5.08 cm OD, giving a b/a ratio ofthe outer radius, b, to
the inner radius, a, of the 1.33 and 1.50. In addition, caskets of b/a = 2.00 were prepared by
inserting the smaller cylinders into the larger cylinders, yielding cylinders with a 2.54 cm ID

and a 5.08 cm OD.

277

‘___ Zirconia ZYC

*— Aluminosilicate

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 2. Schematic showing caskets with differing b/a ratios for inner radius, a, and
outer radius, b [after 1]. In this study, the length of zirconia cylinder, L2,, ranged from 2
cm to 5 cm.

278

Depending on the total casket length LT, the caskets used in this study were divided
into four groups; L1 = 7 cm for Group 4, L1 = 6 cm for Group 5, L7 = 5 cm for Group 6,
and LT = 4 cm for Group 7 (Table 2). The SALI thiclmess, 0.5L5A, was 1 cm for each of the

two endplates for each casket included in the present study (Figure 2).

2.2. Microwave Processing Apparatus

A 2.45 GHz single-mode cylindrical microwave cavity [1-9] heated the refractory
caskets. The cavity was internally tuned by two stepper motors, each interfaced to a
computer. The stepper-motor tuning adjusted the launch probe and the cavity short
positions to within an accuracy of 3:01 millimeter. A Sairem power supply generated
continuous microwave power of 0 to 2 kWatts at 2.45 GHz. The microwave cavity and the

power supply is further described elsewhere [1-9].

Table 2. Dimensions of individual refractory caskets used in this study, where b, a, L7,
L31, L2,, L2, are as defined in equation 5. V511 and V2, are the volume of the SALI
almninosilicate end plates and the volume of the zirconia cylinder, respectively.

 

 

 

 

 

Group b/a b (cm) a (cm) LT L5,, L2, V5,, V2,
(cm) 3cm) (cm) (6113) (an?)

1.33 5.08 3.81 7 2 5 162 177

Group 4 1.50 3.81 2.54 7 2 5 91 127
2.00 5.08 2.54 7 2 5 162 304

1.33 5.08 3.81 6 2 4 162 142

Group 5 1.50 3.81 2.54 6 2 4 91 101
2.00 5.08 2.54 6 2 4 162 243

1.33 5.08 3.81 5 2 3 162 106

Group 6 1.50 3.81 2.54 5 2 3 91 76
2.00 5.08 2.54 5 2 3 162 182

1.33 5.08 3.81 4 2 2 162 71

Group 7 1.50 3.81 2.54 4 2 2 91 51
2.00 5.08 2.54 4 2 2 162 122

 

279

2.3. Microwave Heating of Caskets and Temperature Measurements

Individual caskets were centered on the bottom plate of the microwave cavity. The
initial microwave input power was set to 100 Watts, and then the cavity was tuned to an
“apparent” TM; 11 cavity mode (Appendix A, Figure A1). When the microwave input power
level was increased to 200 Watts, the casket temperature rapidly increased above 500°C. An
optical thennometry system capable of measuring temperatures between 500°C to 1900°C
[1-9] monitored the casket’s inner wall temperature (Figure 3). In order to view the inner
casket wall, a hole, approximately 5 mm in diameter was drilled 2.5 cm from the bottom
endplates’ top surface (Figure 3). Aligning the hole with the optical pyrometer and one of

the cavity’s view ports allowed measurement of the inner casket wall temperature, T,

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Cavitywall
/ caSket \\ View port A
Vrew “Zr 1
130113 LT :: 1311i: LT'u T
T.--- --+ :<---;-- ---* 111111111 1
“t 11111“: I u Optical pyrometer
I \ i ‘ f ] r1 Silica window
I \ _
\

Cavity bottom plate

Figure 3. Schematic of measurement of the casket inner wall temperature T, and the
outer wall temperature TO by an optical pyrometer. The distance, u, fiom the bottom
plate of the cavity to the center of the hole made in the casket wall, is fixed at 2.5cm
[after 1].

280

(Figure 3). The outer casket-wall temperate, T0, was measured by the same optical
pyrometer used for the inner casket wall measurements, but through another cavity view
port (Port B, Figure 3). For outer casket wall temperature measurements no additional holes
were made in the casket wall.

Immediately after the casket began to heat, the cavity was tuned by changing the
launch probe position and the cavity short position. The steady-state inside wall and outside
wall temperatures were measured at microwave input power levels ranging fiom 200 Watts
to 700 Watts with 50 Watts power increments. The microwave input power level was
changed, the cavity was retuned, and within about 10 to 15 minutes after reaching a given
microwave power level, the inner wall casket temperature reached steady state. Once the
inner casket temperature reached a steady-state temperature, both the inner and outer casket

temperatures were measured.

3. RESULTS AND DISCUSSION

3.1. The Inner and Outer Wall Steady-State Casket Temperatures

This paper includes a vastly expanded data set compared to Paper 1 [1], with 132
new octuple data items (T,, P], PR, LSA, b, b/a, LT, To) where P1 for the new data set ranges
from 200 Watts from 700 Watts. For Paper 1, the data set consisted of 12 ordered
sextuples, (Ti, P1, LSA, b, b/a, and LT), where P1 = 600 Watts for all data [1]. Unlike Paper
1 [l], in this study we measured both (1) the steady-state casket outer wall temperatures, To
(Figure 4), and (2) the steady-state casket inner wall temperatures, T, (Figure 5). In Paper 1,

only limited To data was obtained [1].

281

 

 

 

 

 

 

 
 

 

 

  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1m T I I I L ' I ' I ' I
, -e— Lr-50I‘l'l, b/a-2.
—a— L:-5cm. lilo-1.50
900 ~ A Lw6cm. talc-1.33 *
1
4 A _
a U 800
L; La
a .2 700» -
» 1
a 600 e 7
, ‘ J
5‘” i 1 4r 4% I l l
200 300 400 $00 600 700
PI (Watts)
1m 4 fii f I I ' I r I I I I“ I f I T L ' I ' I ‘ T
. -e— um. b/a-z. 1 , -e— Lr-7em. bio-2.
-a- Lvsaem. bin-1.50 J —a— Lr-7cm, lulu-1.50
900 ~ + Lr-Bcrn. bin-1.33 900 — + Lv-‘Icm. b/a-1.33 ‘
1
O 300 ~ 6 800L -
b . g, ,
E" 700 ~ . E— 700 - _
. T t
600 v 4 600 ~ .
1 1 4
500 500

   

Figure 4. Measured outside casket wall temperature, To, as a function of microwave
input power level, P]. Trends in the T0 versus P1 data are highlighted by the solid curves
that represent the least-squares best fit to the empirical quadratic equation for To versus Pl
(equation 8b). Note that in Figures (a) and (b), the data for Na = 1.33 is not fit to
equation 8b, due to the “jump” in T0 at P; z 350 - 450 Watts, as discussed in Section 3.1.

282

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1600 I600 . - . . 1 ~ T , . ~
1400 »- 1400
A 1200 i A 1200 + .1
U » 0
b 1000 9" 1000
t; {-1 i
800 » 800 ~ «
—6- mm. b/asz. 1 -e— Lv-5cm. b/a-2.
—a— Lv-4cm. b/a=1.50 -e— Lvt60m. tale-1.50
600* . + Lr-4cm. b/a=1.33 600 + mammals-1.33 ‘
I - I A 1 "” ’fi—u;f ‘I—.—‘ l A _L . I I j . 1 - 1
200 300 400 500 600 700 200 300 400 500 600 700
P. (Watts) 1’1 (WattS)
(a) (13)
I600 T * T ‘ I V I ' I f T 1600 I ' I I I ' I fi' I
’ 1
I400 » I400 ~- 4
1200 - 1200 r 1
A A
U 1 U 1
b 1000 b 1000
E— F ‘
800 l’ _ _‘ 8m 1- _.
, —e— Lv86cm. b/a-z. —e— Lr-7cm. b/aaz.
—e— Lr=60m.b/881.50 —a— Lr-7cm. blu=1.50
600 ~ + L1I60m, tale-1.33 600 t + L.-7cm. tale-1.33 ‘

 

 

 

200 300 400 500 600
PI (Watts)

(C)

700

 

 

 

200 300 400 500 600 700

P1 (Watts)

(d)

Figure 5. Measured casket inside wall temperature, T,, as a function of microwave input
power level, P1. Trends in the Ti versus P1 data are highlighted by the solid curves that
represent the least-squares best fit to the empirical quadratic equation for T; versus P1
(equation 8a).

283

Recall that we can express the refractory heating problems in terms of four geometric
variables, LSA, b, b/a, and LT, where LSA is fixed at 2 cm in this study. In a 2-dimensional
plot it is impossible to simultaneously represent Ti, P1, and four geometric variables
(although a fixed value of LSA makes the effective number of geometric variables equal to
three).

The T, versus P; plots (Figures Sa-Sd) display two categories of geometric data, namely
(1) an outer radius b of 5.08 cm for Na values of 1.33 and 2, and (2) an outer radius b of
3.81 cm for b/a values of 1.5. For caskets with b = 5.08 cm, b/a = 1.33 or 2, the trends ofTi
versus P1 are very similar for a fixed LT value (LT is 4 cm, 5 cm, 6 cm, and 7 cm in Figures
5a-5d, respectively). Caskets with b = 3.81 cm and b/a = 1.5 show slightly different trends.
For example, for LT = 5, 6, and 7 cm, the Ti curves for b/a = 2.0 and b/a = 1.33 cross at
about 250 to 300 Watts. However, the Ti versus P1 plots are 2-dimensional “surfaces”
cutting through a 6—dimensional space (Ti, P1, and four geometric variables), thus it is
difficult to visualize the multidimensional surfaces over which the b = 5.08 cm and b = 3.81
cm data is distributed. This difficulty underscores the need for a theoretical model to help
us understand the interdependence of geometry, temperature, and power in the refiactory
casket heating problem.

Before fitting the inner and outer wall steady-state casket temperatures to a
theoretical model, we first consider the raw data trends in terms of (1) Ti versus P1 and (2)
T0 versus P1. Both the Ti versus P1 and To versus P1 data (grouped according to L1 and b/a

values) are described well by the empirical quadratic equations 8a and 8b, respectively

(Figures 4 and 5)

284

T, = a, + ,B,P, + 7,.P,2 (8a)

T. = a. + .601”, + m2 (sh)
where (1., Bi, 7;, a0, [30, and yo are least-squares fitted constants. Trends in T; versus P; were
discussed above. The T0 data (again grouped according to LT and b/a values) changes
smoothly as a function of P1, except that for LT = 4cm (b/a = 1.33) and 5cm (b/a = 1.33), T0
jumps by about 150°C to 200°C between P; = 350 Watts and P1 = 450 Watts (Figure 4).
These jumps in '1'() likely are due to inhomogeneous heating (hot spots) that occur in the
casket. (Hot spots have been fiequently observed during the microwave heating of ceramics
[24—27].) The observed differences in uniformity between the inside and outside wall

temperatures (Ti and To, respectively) may be related in part to emissivity differences

between the inside and outside of the casket, as discussed in Section 3.2.

3.2. Further Development of the Refractory Casket Heating Model
In addition to generating 132 new data items, this study presents an improved form

of model in equation 9 (Section 3, Results and Discussion) which uses only three free

parameters (C 1, C2, and C3) instead of 5 free parameters used in equation 7 (Cf , C; , C; ,
C; , and 1). Also, in Paper 1, we considered only the microwave input power P1, while in

this study, we use P1 and reflected power, PR, to compute the energy dissipated by the
casket PC by PC = P1 - PR.

Although it was not discussed in Paper 1 [1], the emissivity, e, is also a function of
temperature. Since the microwave casket is a closed cylindrical region with a single,
small (5 mm) hole in the casket wall (Figures 2 and 3), the volume inside the casket

should approximate a black body, so that e z 1 within the casket. (In the Second edition

285

of his textbook thi_c§ [28], E. Hecht notes that “Generally, one approximates a
blackbody in the laboratory by a hollow insulated enclosure... with a hole in one wall”,
which is a very good description of the refractory caskets used in this study.) In contrast,
the casket outer wall is not a black body and thus (as is the case for ceramics generally
[29]) the emissivity, e(T), for the outer wall can vary considerably as a function of
temperature [29].

Changes in the emissivity of the outer casket wall as a function of temperature mean
that T, and T0 are measured under differing thermal radiation conditions, thus fiirther
complicating the task of modeling To as a function of power and geometry variables.
However, Ti the steady-state inside wall casket temperature is by far the most important
temperature of the two temperatures (T; and To) to model. In terms of ceramic processing,
the black-body environment inside the closed refiactory casket means that Ti should

approximate the steady-state specimen temperature.

3.3. Least-Squares Fitting of the Steady-State Temperatures to the Extended Model

In this study, the data for: the steady-state inner casket wall temperature, T,, the power
dissipated in the casket, PC (PC = P1 - PR), and four geometric variables b, b/a, LT, and LSA,
were least-squares fit to equation 9 (Figure 6)

PCLS,,[Cl +C,bln(b/a)]

 

 

T =
' bLTLSA+2b2[C,/C2+bln(b/a)] 3 (9)
1 1
h C = =
W ere ' 2ch 27d: (9a)
1
C =—
2 Zak (9b)

286

2 H h (99)
C3 = To. (9d)

For the least-squares fitting to equation 9, the coefficient of determination, R2, was greater
than 0.984 for four individual data groups (Group 4-7, Table 3). For the entire 132-item
new data set obtained in this study (not grouped) the R2 value was 0.957 (Table 3). The R2
value was 0.954 for 144-item data set including the 12 data points at 600 Watts from Paper
1 [1] and 132 data items from this study (Table 3). For the individual data groups for LT =
4, 5, 6, and 7cm, the mean of the residuals for the T; residuals ranged from 16°C to 21°C for
the thirty three data points in each group (Figure 6).

Thus, equation 9 captures well the trends in the steady-state inner casket wall
temperature T; as a function of PC, the microwave power dissipated in the casket and the
four geometric variables (LSA, b, b/a, LT) that describe the refractory caskets used in this
study. However, according to the simple energy balance model (Paper 1 [1] and equation 6
of this study, the fitted parameters C1, C2, and C3 should correspond to C1 = 1/21th, C2 =
l/an and C3 = To, where h = surface heat transfer coefficient, k = thermal conductivity, and
To = outer wall temperature. The effective thermal conductivity, kg, for the caskets over the
temperature range included in this study, is roughly 0.21 W/m-°C - 0.26 W/m-°C [1], based
on the vendor-specified temperature-dependent k values for the casket materials. The keg
values computed from the fitted C2 values are about 0.45 W/m-°C - 0.54 W/m-°C (Table 3),
or about a factor of two different than the keg calculated fiom the vendor data.

In Paper 1 [1], we estimated h for free convection to range from very roughly fiom 5

W/m2-°C to 15 W/m2-°C, although that number is based on free convection. The actual h

287

Table 3. Least-squares fitted constants C;, C2, and C3, and the coefficients of
determination, R2, values obtained by fitting the T;, PC and geometry data from this study
and from Paper 1 [1] to equation 9.

 

 

 

Group Number of data C; C2 C3 R2
used for fitting (m2-°C/W) (m-°C/W) (°C)

Group 4 33 0.0021 0.2923 677.1 0.967
Group 5 33 0.0006 0.3267 693.1 0.977
Group 6 33 -0.0010 0.3519 729.4 0.984
Group 7 33 -0.0015 0.3569 745.9 0.988
Group 4 - 7 132 -0.0003 0.3426 705.8 0.957
Group 1 - 7 144 -0.0004 0.3396 711.3 0.954

 

value may be much larger than the free convection h, due to radiative contributions to h.
From c;, we obtain h values ranging from ~75 W/m2-°C to ~265 W/m2-°C for the Group 4
and Group 5 caskets (Table 3). However, the negative values of C; associated with Groups
6 and 7 are clearly unphysical. The mean of the measured To values for the caskets in this
study ranges from about 600°C to 800°C which roughly corresponds to T0 as inferred from
C3.

Thus the values of k and T0 obtained by fitting the T;, PC, LSA, b, b/a, and L; to
equation 9 correspond roughly to experimental values of k and To. In contrast, the h values
obtained from fitting the data to equation 9 is sometimes unrealistic, especially for negative
values of C;. However, equation 9 does an excellent job in describing the trends in T; as a
function of power and casket geometry, given the complex six-dimensional functional space
(T ;, PC, LSA, b, b/a, LT) being fitted and given the nonlinear nature of the problem

(Sections 1.2 and 3.2).

288

 

 

 

   
  

 

    

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

HAT. ,____l__fi_;___’_ T T T ' I Y 1 ' r 1 v r
- O ha4crn. b/n=2.0tfl 4 O h=5¢m. b/a=2.00
“500, cr 11-4cm.b/a-1.501 ”’00, o h-Scm. b/a-1.50
L_ A 1.=4em, b/u=1.33J . A h=5cm. b/a=l.33
I400 - I400 - e
A A 1
U U 1
La 1200 b 1200 4
f- E I; .
1000 - 1000 ~
1
l , 3
800 .- ., 800 - .
l r l r I A 1 l I A; l r l I l . l r l . l
200 300 400 500 600 700 200 300 400 500 600 700
Pc (Watts) Pc (MM)
(3) (b)
_ I ' I I/ I j I Y T I I .. T ' I '/ I ‘- I ' T ' I
P O h26cm. b a=2.00 . O In=7crn. b a=2.00 H
I600» O h-ch. b/l-1.50 ‘ J I600 D h-‘Icrn. b/a-l.50
l A h=6cm. b/a=l.33J , A I.=7cm. b/a=1.33
1 o .
1400 ~ I400 ~ 0
A A
U u .
La 1200 '- L/ 1200 r i
[— E-i 1
1000 - 1000 . ° 4
. 1 n
800 e . 300 r- o
l A l l _._i l r l j 9 L . l A 1 A I I
200 300 400 500 600 700 200 300 400 500 600 700
PC (Watts) Pc (Watts)

(C) ((1)

Figure 6. Measured casket inside wall temperature, T;, as a function of total absorbed
microwave power, PC. The curves represent the least-squares best fit of the data T;, PC,
LSA, b, b/a, and L; in Group 4-7 to equation 9.

289

4. SUMMARY AND CONCLUSIONS

In this study, we measured 132 new octuple data items (T;, P;, PR, LSA, b, b/a, LT, To)
for microwave heating of ceramic refiactory caskets of varying geometry (Figure 2 and
Table 2), where T; = steady-state inner wall casket temperature, P; = microwave input
power, PR = reflected microwave power, L5,; = thickness of SALI end plates, b = outer
radius of the casket, b/a = ratio of the outer casket radius/inner casket radius, L; = total
casket length, and T0 = steady-state outer wall casket temperature. Unlike Paper 1 [1],
where the data was taken almost exclusively at P; = 600 Watts, in this study the microwave
input power ranged from 200 to 700 Watts. The data set for this study also includes T0
measurements for every casket/input power combination but Paper 1 included only very few
T0 measurements.

Even more important than the expanded data set is the fact that equation 9, the fitting
equation introduced in this study (equation 9), represents a significant improvement over
equation 7, the fitting equation presented in Paper 1 [1]. While equation 7 involves five free
parameters, the new equation (equation 9) has three free parameters. In addition, equation 7
employed microwave input power P; in describing the energy balance relationship while in
equation 9 we used PC = P; - PR instead of P;. The PR term in PC accounts for the measured
microwave energy that is reflected during microwave heating, which brings the model
closer to physical reality. Using PC and the larger data set still results in an improved least-
squares fit to the data compared to Paper 1 [1].

Paper 1 discussed the numerous simplifications and assumptions involved in simple
energy balance model developed in that paper [1], where the final form of that model is

given here as equation 6. In addition to reviewing the simplifications noted in Paper 1, we

290

have also discussed difficulties in modeling the steady-state outside casket wall temperature,
To. One of the chief difficulties in integrating To data into the fitted equation (equation 9)
likely is that the radiative heat transfer at the inner wall and at the outer wall are subject to
different emissivity conditions.

The energy balance model [1] (equation 6) ignores many of the details of the
temperature dependence of material properties and thermal radiation Nevertheless when
the model is used as a candidate equation for least-squares fitting (equation 9), the high
values of R2 obtained (Table 3) indicate that it describes very well the dependence of the
steady-state inner wall temperature, T;, on the power dissipated in the casket and the
geometry of heated refractory caskets (Figure 6).

It is important to note that the most crucial temperature to measure is T; since inside
the refiactory casket T; likely approximates the specimen processing temperature. Thus for
practical applications such as sintering and joining of ceramics, equation 9 provides the

means for a rational design of microwave caskets of the type discussed here.

Future Work
Finite element and/or finite difference methods will be used to analyze both the steady-
state and transient heating behaviors for refractory caskets. We will attempt to integrate the
munerical results with the model that was given in Paper 1 [1] and extended in this study. In
collaboration with the present authors, a colleague has begun a finite element analysis of the
refiactory caskets included in this study. In addition, the authors will investigate microwave

heating using other casket materials and geometries, including powder filled caskets.

291

ACKNOWLEDGMENTS
The authors acknowledge the financial support of the Electronic and Surface Properties

of Materials Center, Michigan State University.

Appendix A. Differences between the resonant electromagnetic field patterns for
loaded and unloaded microwave cavities

An empty cavity mode refers to a resonant electromagnetic field pattern for an
unloaded microwave cavity (Figure A1). By “unloaded” we mean that there is no
external object within the cavity [A1]. When the microwave cavity is loaded with a
dielectric material, the presence of the dielectric perturbs the electromagnetic field
pattern, so that at the resonant condition the electromagnetic field pattern for the loaded
cavity case is different than for an unloaded cavity [A2]. The magnitude of the difference
between the electromagnetic field pattern for the unloaded and the loaded cavities
increases as the volume of the load (dielectric material added to the empty cavity)
increases. The perturbation is also a function of the complex dielectric constants of the
load.

As the temperature of the dielectric material increases due to microwave heating,
the complex dielectric constants also change with temperature. As the complex dielectric
constants change during heating, the electromagnetic nature of the cavity load changes
also, so that the cavity must be retuned to maintain the resonance condition. The
microwave cavity is retuned by adjusting the cavity height and the probe position to

minimize the reflected microwave power.

292

References for Appendix

A1. S.Y. Liao, Microwave Devices and Circfiuitg, 3rd ed., Prentice Hall, New Jersey, pp.
136-138 (1990).

A2. P. Mak and J. Asumssen, “Experimental Investigation of the Matching and
Impressed Electric Field of a Multipolar Electron Cyclotron Resonance Discharge,”
J. Vac. Sci. Technol. A15[1]: 154-168 (1997).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

‘ ‘—-”
‘~_—‘

Figure Al. Schematic for electromagnetic field distributions of unloaded TM;;;
resonance microwave cavity mode.

293

10.

REFERENCES

K.Y. Lee, E.D. Case, and J. Asmussen, Jr., “The Steady-State Temperature as a
Function of Casket Geometry for Microwave-Heated Refiactory Caskets,” Mat.
Res. Innovat. l[2]: 101-116 (1997).

K.Y. Lee, E.D. Case, J. Asmussen, Jr., and M. Siegel, “Sintering of Alumina
Ceramics in a Single Mode Cavity under Automated Control,” Cer. Trans., vol. 59,
Amer. Cer. Soc., pp. 473-480 (1995).

K.Y. Lee, E.D. Case, J. Asmussen, Jr., and M. Siegel, “Microwave Sintering of
Ceramic Matrix Composites and the Effect of Organic Binders on the Sinterability,”
Proceedings of the 11th Annual ESD Advanced Composites Conference, ESD, The
Engineering Society, Ann Arbor, MI, pp. 491-503 (1995).

K.Y. Lee, E.D. Case, J. Asmussen, Jr., and M. Siegel, “Binder Burn-out in a
Controlled Single-Mode Microwave Cavity,” Scripta Materialia, 35[1]: 107-111
(1996).

K.Y. Lee, E.D. Case, and J. Asmussen, Jr., “Microwave Binder Burn-out for Batch
Processing of A1203, A1203/SiC Platelet, and A1203/Zr02 Particle Powder
Compacts,” Cer. Trans. vol. 80, pp. 539-546 (1997).

K.Y. Lee, L.C.G. Cropsey, B.R. Tyszka, and ED. Case, "Grain Size, Density and
Mechanical Properties of Alumina Batch-Processed in a Single-Mode Microwave
Cavity," Mat. Res. Bull., 32[3]:287-295 (1997).

K.Y. Lee, E.D. Case, and D. Reinhard, “Microwave Joining and Repair of Ceramics
and Ceramic Composites,” Ceramic Engineering and Science Proceedings, vol. 18,
pp. 543-550 (1997).

K.N. Seiber, K.Y. Lee, and ED. Case, “Microwave and Conventional Joining of
Ceramic Composites Using Spin-On Materials,” Proceedings of the American
Society for Composites, 12th Technical Conference, Dearborn, MI, pp. 941-949
(1997)

B.A. Wilson, K.Y. Lee, and ED. Case, “Diffusive Crack Healing Behavior in
Polycrystalline Alumina: A Comparison Between Microwave Annealing and
Conventional Annealing,” Mat. Res. Bull., 32[12]:1607-l616 (1997).

J .G. Lee and ED. Case, “Microwave Joining of Zirconia by using Spin-On
Materials,” to be submitted, Materials Research Bulletin (1998).

294

11.

12.

13.

14.

15.

16.

l7.

18.

19.

20.

21.

22.

K.Y. Lee and ED. Case, “An AFM Study of Thermally-Induced Grain-Boundary
Grooving in Polycrystalline Alumina: Part I, Groove Profile, Width, and Depth,” to
be submitted, Journal De Physique III (1998).

K.Y. Lee, E.D. Case, and J .G. Lee “An AFM Study of Thermally-Induced Grain-
Boundary Grooving in Polycrystalline Alumina: Part II, Groove Angle, Surface
Energy, Surface Diffusivity,” to be submitted, Journal De Physique III (1998).

D.K. Agrawal, Y. Fang, D.M. Roy, and R. Roy, “Fabrication of Hydroxyapatite
Ceramics by Microwave Processing,” R.L. Beatty, W.H. Sutton and Iskander MF
(eds) Microwave Processing of Materials III, Mat. Res. Soc. Symp. Proc. vol. 269,
Materials Research Society, Pittsburgh, Pennsylvania, pp. 231-236 (1992).

Y. Fang, D.K. Agrawal, D.M. Roy and R. Roy, “Rapid Sintering of Hydroxyapatite
Ceramics by Microwave Processing,” D.E. Clark, F .D. Gac, and W.H. Sutton (eds)

Microwaves: Theory and Application in Materials Processing, Cer. Trans. vol. 21,
Amer. Cer. Soc., Westerville, Ohio, pp. 349-356 (1991).

HS. Carslaw and J.C Jaeger, Corgrction of Heat in Solicg, 2nd ed., Oxford
University Press, Fair Lawn, NJ, pp. 19, 188-190 (1959).

F. Kreith, Chapters 2, 5, and 7 in Principles of Heat Transfer, Third Edition,
International Textbook Company, Scranton, PA, (1972).

J .V. Beck, B. Blackwell, and CR. Clair, Jr., Inverse Heat Conduction, Wiley-
Interscience, New York, pp. 281-300 (1985).

 

B. Gebhart, Heat Conduction and Mass DiMon. McGraw-Hill, New York, pp. 48-
52, 64-71, 139-144 (1993).

B.V. Karlekar and R.M. Desmond, E_ngineering Heat Transfer, West Publishing Co.,
New York, pp. 8, 14 (1977).

MN. Ozisik, Finite Difference Methods in fiat Transfer, Boca Raton, CRC Press,
pp. 1-18, 61-65 (1994).

H.W. Jackson, M. Barmatz, and P. Wagner, “Transient Temperature Behavior of a
Sphere Heated by Microwaves,” D.C. Clark, T.R. Tinga, and J.R. Laia, Jr. (eds),
Microwaves: Theory and Applications in Materials Processing 11, Cer. Trans. vol
36, Amer. Cer. Soc., Westerville, OH, pp. 189-199 (1993).

H.W. Jackson and M. Barmatz, “Microwave Absorption by a Lossy Dielectric
Sphere in a Rectangular Cavity,” J. Appl. Phys. 70:5193-5204 (1991).

295

23.

24.

25.

26.

27.

28.

29.

M. Barmatz and H.W. Jackson, “Steady State Temperature Profile in a Sphere
Heated by Microwaves,” R.L. Beatty, W.H. Sutton and M.F. Iskander (eds),
Microwave Processing of Materials 111, Mat. Res. Soc. Symp. Proc. vol. 269,
Materials Research Society, Pittsburgh, Pennsylvania, pp. 97-103 (1992).

G.A. Kriegsmann, “Microwave Heating in Ceramics,” D.E. Clark, F .D. Gac, and
W.H. Sutton (eds), Microwaves: Theory and Application in Materials Processing,
Cer. Trans. vol. 21, Amer. Cer. Soc., Westerville, Ohio, pp. 177-183 (1991).

G.A. Kriegsmann, “Thermal Runaway and its Control in Microwave Heated
Ceramics,” R.L. Beatty, W.H. Sutton and M.F. Iskander (eds), Microwave
Processing of Materials III, Mat. Res. Soc. Symp. Proc. vol. 269, Materials
Research Society, Pittsburgh, Pennsylvania, pp. 257-264 (1992).

D.L. Johnson, D.J. Skamser, and MS. Spotz, “Temperature Gradients in Microwave
Processing,: Boon and Bane,” D.E. Clark, W.R. Tinga, and J.R. Laia, Jr. (eds),
Microwaves: Theory and Applications in Materials Processing 11, Cer. Trans. vol.
36, Amer. Cer. Soc., Westerville, OH, pp. 133-146 (1993).

MS. Spotz, D.J. Skamser, and D.L. Johnson, “Thermal Stability of Ceramic
Materials in Microwave Heating,” J. Am. Ceram. Soc. 78[4]: 1041-1048 (1995).

E. Hecht, Optics, Second Edition, Addison-Wesley Publishing Company, Reading,
Massachusetts, pp. 539 (1990).

Y.S. Touloukian, ed., Thermophysical Properties of High Temperature Solic_1_
Materials Volume 4: Oxides and Their Solutions and Mixtures, The Macmillan
Company, New York, pp. 28-31 (1967).

 

296

CONCLUSIONS

1. SIN TERING

This study demonstrated that a cylindrical single-mode microwave cavity equipped
with computer controlled tuning system can be used to provide repeatable heating
schedules and successfully densify alumina ceramics and alumina matrix zirconia
composites. For the specimens densified at 1500°C to 1600°C, the mass density as
determined by Archimedes was about 96% up to nearly 100% of theoretical density.

The advantages of microwave heating over conventional heating have been verified
by heating alumina/10wt% zirconia particulate composites. Microwave-sintered
composite specimen reached about 94% theoretical density at a sintering temperature of
1350°C, while a specimen conventionally sintered at 1350°C reached only about 70% of
theoretical density. The microstructures of the composite specimens sintered at 1450°C
also indicate that microwave heating enhanced the densification over conventional
heating.

In addition, in this study the variations in the density, grain size, and/or hardness,
fracture toughness of microwave-sintered ceramics were examined in terms of (i) the
radial position within individually-processed specimens, (ii) the specimen position within
the zirconia casket for the batch-processed specimens, and (ii) the operating microwave

cavity mode.

297

For alumina specimens sintered at 1500°C in the cavity tuned to four different
cavity modes, mass density and grain size examined in terms of both the radial position
within a given specimen and the cavity mode were relatively uniform with an average
density 96.2% i 0.6% of theoretical density and an average grain size of 6.23 um i 1.5
pm, respectively.

For batch-processed alumina specimens, the variation in mass density in terms of
both the specimen position and the cavity mode was negligible, which was less than
0.6% of theoretical density. However, the mean grain size ranged from 6 um up to 8 pm
depending on the operating cavity mode and for the specimens processed in a batch (i.e.
same cavity mode) the standard deviation was less than 1 pm. The average hardness
determined by Vickers’ indentation was 16 GPa and the calculated toughness was about
2.70 MPa-mm. The average hardness and fracture toughness values for the specimens
heated at the same position but in different batches (i.e. different cavity modes) differed
by no more than 2.6% and 5.3%, respectively, from position to position. However,
depending on the modes used to sinter specimens in batches, the variations in mean
hardness and toughness values were somewhat large, which were about 6.6% and 15.9%,
respectively.

Therefore, based on the obtained results, this sintering study revealed that the
microwave casket (specimen enclosure) used in this study can act to homogenize the
temperature field, such that the grain size, density, hardness, and fi'acture toughness can
be relatively uniform in terms of position within a given specimen and/or position of

specimens batch-processed within the casket.

298

2. BINDER BURN-OUT

The objectives of binder burn-out study was to burn out organic binders utilizing
three processing procedures; (i) binder burn-out and sintering as a one step process using
a casket, (ii) fixed input power sequence without using a casket, and (iii) stepped input
power sequence without using a casket. These three procedures were applied to burn out
the corn oil binder from the individual powder compacts or the powder compacts in a
batch. The materials used for the binder burn-out study were alumina, alumina/10wt%
zirconia, alumina/10wt% silicon carbide powders mixed with 10wt% corn oil binder.

Using a susceptor material, the binder was successfully burned out and sintered as a
one step process by controlling heating rate by cavity timing control, microwave power
control, and mode switching. The total processing time was relatively short, about 3.5
hours. The final sintered alumina/zirconia composite specimen had mass density of 98.1
percent of theoretical density with a uniform and fine microstructure with an average grain
size 2.7 pm.

In literature, binder bum-out studies which were performed by microwave energy
using caskets enclosing specimens to be heated have been reported but few reported on
binder burn-out without a casket. This study attempted to burn out the binder without using
any insulation material enclosing specimens. This study revealed that for both the
individually- and the batch-processed specimens, the extent of binder burn-out can vary
widely with the electromagnetic mode. For example, heating via the TM;;;2 mode
resulted in very little binder burn-out, while in comparison, nearly complete binder bum-
out was achieved in the TE; ;2 mode. In particular, for both the individually-processed

specimens and the batch-processed specimens, a stepped input power sequence burned

299

out the binder more completely than a fixed input power without cracking the specimens.
Among the three types of ceramic compacts processed (A1203/Zr02 composites,
A1203/SiC platelet composites, and A1203) the binder burned out at lower power for the
A1203/SiC platelet specimens, under both fixed and stepped power conditions. This may

have been due to differing dielectric properties of the specimens.

3. JOINING

Compared to typical ceramic-ceramic joining by conventional heating which
requires relatively high applied stress of several MPa’s, this study employed no or very
low applied stress ranging from 0 to 6 kPa to join alumina ceramics and glass ceramics
with spin-on film materials by using microwave energy.

Without a dead weight, alumina components were joined by heating at 1625°C for 10
minutes in a single-mode microwave cavity. SEM examination of the joined region of the
fractured alumina specimen showed no evidence of cracking or microcracking near the joint.
That is, the macrocrack that fractured the specimen apparently did not damage the joint.
This observation indicates that the joint is a very strong interface. Also, the grain structure
near the joint does not differ from the grain structure in the bulk of the specimen, indicating
that the process of generating the joint does not greatly perturb the specimen’s
microstructure, at least on a size scale of a few microns.

The maximum hold temperature for ceramic joining could be apparently lowered by
using dead weights. For example, alumina-alumina joining with dead weights of 60 grams
(about 2 kPa) lowered the joining temperature from 1625°C (corresponding to temperature

without a dead weight) down to 1575°C. For joining of MaCorTM specimens, the joining

300

temperature was lowered from 1150°C (corresponding to temperature without a dead
weight) to 1050°C by using dead weights of 60 grams (about 6 kPa).

Dimensional changes in notches made in alumina specimens or MaCorTM glass
ceramics were examined before and after joining. Alumina specimens heated at 1575°C for
20 minutes changed notch dimensions by less than 4.1% in width and in depth. Notches in
MaCorTM specimens changed dimension by less than 5.7% in width and in depth during
joining at a maximum hold temperature of 1050°C for 20 minutes. Notch shape retention
indicates that ceramic components with intricate features, such as small holes and channels,
could maintain their complex geometry during joining. Also for the joined MaCorTM
specimens, the constancy of notch geometry indicates a lack of wide-scale viscous flow

which might be a potential disadvantage for using spin-on silica or silicate film.

4. CRACK HEALING

Crack healing study for both conventional heating and microwave heating was
performed on Vickers-indented specimens of polycrystalline alumina (Coors ADS-995)
for the temperatures ranging from 1510 K to 1742 K. The crack healing rates were
studied as a function of i) heating mode, ii) dwell temperature, and iii) applied
indentation load.

The heating modes used in this study were i) conventional heating with a heating
rate of 10°C/min, ii) microwave heating with a “slower” heating rate of 10°C/min, and
iii) microwave heating with a “faster” heating rate of 75°C/min. For the three heating

modes, the crack healing rate Aa/At was very similar at about 1510 K. However, for both

the 49 N and 98 N indentation cracks, Aa/At was at least double for microwave annealing

301

(slower heating rate) compared to conventional annealing with increasing the dwell
temperature, indicating that microwave heating considerably enhanced the crack healing
rate.

The crack healing data analyzed based on a diffusive mass transport model by
Dutton and Stevens revealed that the activation energies for crack healing were
significantly lower for conventional heating than for microwave healing. However, the
net diffusivities inferred from the healing data showed that the microwave heating
increased the diffusivities by a factor of about 1 to 4 over the range of the temperature
used in this study.

The microwave-enhanced healing rates observed for the Vickers indentation cracks
included in this study imply that for a microcracked ceramic material, microwave heating
may recover mechanical properties such as the strength, elastic modulus, etc. faster than

conventional heating.

5. EFFECTS OF CASKET GEOMETRY AND MICROWAVE POWER ON
MICROWAVE HEATING

This study demonstrated that the steady-state inner-wall temperature of a casket
which is used to process ceramic materials by microwave energy, can vary significantly
as a function of casket geometry. For example, the steady-state casket temperature at 600
Watts of microwave input power ranged from 1112°C to 1519°C as the casket geometry
changed for caskets composed of porous zirconia cylinders with aluminosilicate end
plates. However, the variation of the steady-state casket temperature could not be

described by a function of only simple geometric variables such as volume, surface area,

302

11111L

 

 

etc. Based on thermal balance between the heat generated within the casket by
microwave energy and the heat dissipated from the outer surface of the casket, a simple
model equation was developed to describe the variation in steady-state temperature as a
function of casket geometry. The model also described well the dependence of the
steady-state casket temperature on the microwave power level.

This study also revealed that the steady-state temperature of the dielectrically lossy
casket was only slightly perturbed by the presence of a specimen with a volume and mass

that was small compared to the casket volume and mass.

303

APPENDICES

304

APPENDIX A. PHOTOS OF MICROWAVE PROCESSING APPARATUS.

Figure A-l. Photo of microwave processing apparatus.

 

305

Figure A-2. Photo of cylindrical single-mode microwave cavity.

 

306

APPENDIX B. PROPERTIES OF REFRACTORY MATERIALS USED FOR

MICROWAVE PROCESSING‘

Appendix B-l. Zirconia Insulating Cylinder, Type ZYC

Table B-l-l. General characteristics and properties

 

 

 

 

 

Property Data Property Data
Density 0.48 (gm/cm3) Moisture and organic content Nil
Porosity 91 (%) Outgassing in vacuum Nil

T ical com sition, wt‘V
Color White yp po 0
Zr02 87
Thermal expansion for Y2O3 8
RT—l425°C 9x104 (l/°C) Si02 5
Maximum service temp. 1650 (° C) Linear shrinkage isothermal
Melting temp. 2200 (°C) soak for 24 hrs at 1650°C 4% max.
Table B-l-2. Thermal conductivity
Mean temperature (°C) 400 800 1100 1400 1650
Thermal conductivity, k
(Watts/m-K) 0.09 0.1 l 0.14 0.19 0.23

 

 

‘ Catalog (1995) from Zircar Products Inc.,
1 10 North Main Street - PO. BOX 458, Florida, New York 10921-0458
TEL: 914-651-4481, FAX: 914-651-3192
Internet: www.2ircar.com, e-mail: zircarsa@zircar.com

307

Table B-l-3. Properties of zirconia fibers contained in Type ZYC

 

 

 

 

 

 

 

 

Property Data Property Data
Diameter 4 - 6 (pm) Stabilizer (Yttria) 4.5 (wt%)
Density (92-97% _ 3 Composition 0
dense) 5.6 5.9 (gm/cm ) (Z r02 +HfO2 +Y2O3) 99+ (/o)

< 1.0 max. . .
Surface area BE Meltm int 2590 C
Appendix B-2. Alumina Insulating Board, Type SALI
Table B-2-l. General characteristics & properties
Property Data Property Data
Typical composition, % Linear Shrinkage, %
A1203 80 24 hrs at 1650°C 1
SiO2 20 24 hrs at 1700°C 3
Moisture & organic
content, % 0 F lexural strength 2.07 (MPa)
' 0
Bond Silica Comp ”88.1% strength at 10/0 1.31 (MPa)
compressron
. 3 SAG/Distortion,
Densny 0'48 (gm/“n ) 152mmx25.4mmx25.4mm,
Open porosity 84 (%) 127mm Span,
Maximum use temp. 1700°C % after 24 hrs. at 1650°C 2
Melting temp. 1870°C Thermal expansion
Color White for RT-1000°C 5.0x10'°/°C
Table B-2-2. Thermal conductivity
Mean temperature (°C) 400 800 1100 1400 1650
Thermal °°°°°°°‘"ty’ 1‘ 0.20 0.25 0.31 0.34 0.39

(Watts/m-K)

 

308

Appendix B-3. Alumina Insulating Board, Type SALI-2

Table B-3-l. Characteristics & properties

 

 

 

 

 

 

 

Property Data Property Data
Typical composition, % Linear Shrinkage, %
A1203 80 24 hrs at 1650°C 0
SiO2 20 24 hrs at 1700°C 3.5
Moisture & organic
content, % 0 Flexural strength 2.14 (MPa)
' 0
Bond Compressive strength at 10 /o 1.04 (MPa)
compressron
. 3 SAG/Distortion,
Dms‘ty °'5 1 (gm/m ) 125mmx25.4mmx25.4mm,
Open porosity 84 (%) 100mm Span,
Maximum use temp. 1800°C % after 24 hrs. at 1700°C 2
. 0 Thermal expansion
Melting temp. 1870 C coefficient
Color White for RT-1000°C 6.0x1045/°C
Table B-3-2. Thermal conductivity
Mean temperature (°C) 400 800 1100 1400 1650
Thermal ”mummy: k 0.15 0.20 0.25 0.34 0.39

(Watts/m-K)

 

309

APPENDIX 1. SINTERIN G.

Figure I-l. Sem Images of Fracture Surface of Alumina Specimens Batch-Processed
in Various Microwave Cavity Modes.

u“. .. ‘ . / 1‘ y,’
'. \ K), J ”\x ., ‘
s. \x._\ \‘ Fl _
A; J -' 1' K. 10 11'“ _

(a) TM;;; mode (position 3) (b) TE;;2 mode (position 2)

 

 

(c) TE;;3 mode (position 2) (d) TM;;;3 mode (position 5)

310

Figure I-2. Heat Distribution inside Empty Casket as Determined by Thermally
Sensitive Paper. The casket was heated in each cavity mode (a) for 15 minutes at 80
Watts, (b) for 7 minutes at 90 Watts, (c) for 15 minutes at 150 Watts, and (d) 5 minutes at
90 Watts. The dark areas in (a)-(d) indicate regions of microwave heating.

   

(a) TEzn mode (1)) TE112 mode

 

(c) TM;;;2 mode ((1) TE2;2 mode

311

APPENDIX H. CERAMIC/BINDER COMPACT SPECIMENS HEATED IN A

MICROWAVE CAVITY.

Figure II-l. Photo of A1203/binder compact specimens heated by microwave heating.

 

312

Figure II-2. Photo of Al2O3/SiC/binder compact specimens heated by microwave

heating.

 

313

Figure II-3. Photo of A1203/ZrO2/binder compact specimens heated by microwave

heating.

 

314

Appendix II-4. Raw Data for Batch-Processed Binder Burn-Out

Table 114-1. Change in wt% of specimen using a fixed input power sequence as a
function of power and heating time.

 

 

 

 

 

 

 

Material Microwave Heating time (minutes)
input
power (Watts) 10 30 6O

80 -0.50¢0.44* -2.03i0.36 -2.30:t0.56
(-0.33i0.04)* * (-1.90:t0.13) (-2. 10:1:0.21)

A1203/binder 1 50 -2.70i3 .48 -5.50:l:2. l 9 -6.74:|:1.62

l-l .40i0.43) (4.684.034) (-6.13i0.30L

80 -0.47i0.27 -l .93i0.49 -2.12:t:0.50
(-0.39i~0.16) (-1 8210.43) (-1.95i0.21)

A1203/Zr02/binder 1 50 -2.84i3.31 -6.40:t:1.77 -6.7211 .56
(-1 59:0. 16) (-5.73i0.17) (-6.14i0.30)

80 -1.65i0.67 4.26:0.79 -4.51i0.79
(-l .40:t0.16) (-4.00:t:0.39) (-4.23:t0.32)

A1203/SiC/binder 120 -6.26i1.25 -6.64:t1.39 -7.69:tl .54
(-5.86i0.76) (-6.19i0.78) (-7.44:t:1.52)

 

 

 

 

 

 

* Data for batches of seven specimens.

** Centrally located specimens not considered in calculation.

Table II-4-2. Change in wt% of specimen using a stepped input power sequence as a
function of power and heating time.

 

 

 

 

 

Material Final microwave Heating time (minutes)
”123333“ 15 40 70* 120
“203%“ 46° 35.203 £37222 £33167 35.3.62
A120“ Z‘OZ/b ind“ 4°° 1.00.2034 £30.33: 32702146 30.1285
A1203/SiC/binder 250 300.7034 :3; 2 31(3)

 

 

 

 

 

 

"‘ For A1203/SiC/binder, the heating time was 75 minutes.

315

APPENDIX III. JOINING

Figure III-l. SEM images of (a) mw-sintered AKP30 A1203 , (b) MgF2, (c) MaCor,
and (d) mw-sintered TZ-3Y Zr02.

 

316

APPENDIX IV. CRACK HEALING.

Table IV. Raw data for crack healing study. Anneal time is fixed at 1 hour.

 

 

 

 

 

Annealing Anneal Anneal Change in crack length, dC (111“)
process temp. (°C) temp. (K) 49N indentation crack 98N indentation crack
1245 1518 50.021: 19.7 75.5 21:21.0
1309 1582 59.9 i 16.1 77.0 i 18.1
Conventional
1354 1627 53.3 i 9.5 60.1 :1: 18.3
(10°C/min.)
1426 1699 66.0 :1: 17.5 113.5 :1: 21.8
1469 1742 99.0 :1: 17.9 146.8 1: 31.7
1237 1510 22.0 :1: 14.2 59.2 :1: 17.6
1295 1568 68.3 i 18.3 96.4 i 33.5
Microwave
1353 1626 91.0 i 17.7 155.3 :1: 20.1
(75°C/min.)
1411 1684 136.9 :1: 27.8 216.0 :1: 16.4
1469 1742 157.1 :1: 53.2 273.0 i 30.6
1237 1510 46.9 :1: 17.7 72.1 i 23.4
1295 1568 84.1 i 14.4 114.3 i 9.0
Microwave
1353 1626 151.5:1:17.7 l75.6:1:21.8
(10°C/min.)
1411 1684 199.1 :1: 10.1 338.0 1 9.2
1469 1742 199.1 i 9.2 337.9 :1: 8.8

 

317

APPENDIX V. DATA FOR REFRACTORY HEATING STUDY AND
ADDITIONAL STUDY

Appendix V-l. Additional Raw Data for Refractory Heating Study

Table V-l-l. The inner casket wall temperature, T;, and the casket outer wall
temperature, To, measured as a function of microwave input power level, P;, for refractory
caskets which has b/a = 1.33. L; is the total casket length.

 

P; L;~=4cm LT=5cm LT=6cm LT=7cm

 

(W338) Ti (° C) To (° C) Tt(°C) To (°C) Tt(°C) To (°C) Ti (° C) To (°C)

 

200 924 583 895 566 867 567 850 562
250 955 606 934 587 898 587 875 587
300 986 626 967 607 932 614 91 1 610
350 1021 648 995 637 962 633 941 633
400 1063 674 1002 771 963 678 943 636
450 1078 864 1050 792 999 716 970 673
500 1 135 874 1096 814 1036 754 998 705
550 1173 987 1137 835 1083 773 1038 727
600 1229 923 l 187 842 l 130 793 1081 764
650 1274 928 1237 852 1175 810 1124 771
700 1318 944 1266 856 1205 813 1158 782

 

 

 

 

 

 

 

 

 

318

Table V-1-2. The inner casket wall temperature, T;, and the casket outer wall
Temperature, T;,, measured as a function of microwave input power level, P;, for
refractory caskets which has b/a = 1.50. LT is the total casket length.

 

P; LT=4cm LT=5cm LT=6cm LT=7cm

 

(WattS) Ti(°C) To(°C) Tt(°C) To(°C) Ti(°C) To(°C) Ti(°C) To(°C)

 

200 989 594 949 589 931 583 908 581
250 1037 699 1017 615 989 595 963 600
300 1 131 730 1075 721 1039 645 1005 606
350 1206 787 1 145 731 l 101 686 1062 624
400 1275 815 1201 763 1169 716 1130 662
450 1333 825 1272 786 1238 733 1 185 695
500 1398 843 1323 831 1297 764 1243 724
550 1456 858 1381 847 1353 778 1293 745
600 1514 898 1434 868 141 1 794 1345 772
650 1562 915 1471 875 1440 828 1386 797
700 1574 936 1507 894 1462 846 1409 816

 

 

 

 

 

 

 

 

 

319

Table V-l-3. The inner casket wall temperature, T;, and the casket outer wall
Temperature, T;,, measured as a function of microwave input power level, P;, for
refractory caskets which has b/a = 2.00. L; is the total casket length.

 

 

 

P; LT=4cm LT=5cm LT=6cm LT=7cm
(Watts) Ti (0C) To (0C) Ti (0C) To (0C) Ti (0C) To (0C) Ti (0C) To (0C)
200 899 520 878 543 778 * 740 51 1

250 1010 543 920 569 885 506 802 536
300 1054 581 993 586 956 544 896 547
350 l 106 636 1063 631 1007 591 969 569
400 l 179 656 1 132 653 1075 606 1026 603
450 1236 678 1192 669 1120 616 1071 612
500 1295 691 1269 657 1178 629 11 19 635
550 1355 701 1318 672 1228 646 1160 648
600 1415 727 1368 683 1281 674 1200 668
650 1471 747 1412 703 1316 698 1236 687
700 1505 754 1438 723 1354 712 1263 708

 

 

 

 

 

 

 

 

 

320

Appendix V-2. ELECTROMAGNETIC MODE IDENTIFICATION AND
HEATING CHARACTERISTICS OF CASKETS IN VARIOUS MICROWAVE
MODES IN A CYLINDRICAL SINGLE-MODE MICROWAVE CAVITY

Two methods were used to identify the particular electromagnetic modes present in
the cylindrical resonant cavity, namely: (1) reflected power measurements and (2)
electric field probe measurements. Mode identification was done on a microwave cavity

loaded with caskets of various dimensions (Table V-2-l) as well as on an empty cavity.

1. REFLECTED POWER MEASUREMENTS AT LOW AND HIGH INPUT
POWER

The reflected power was measured as a function of cavity height under (a) low
power conditions (50 Watts), and (b) higher power conditions, during the microwave
heating of the caskets.

For the low power measurements, the reflected power versus cavity height was
determined at a fixed microwave input power of 50 Watts and with the launch probe
position fixed at 1 cm from the inner wall of the cavity (Figure 1). The input power of 50
Watts were selected for the low power measurements since at 50 Watts the caskets used
in this study did not heat above 500°C. At higher input power levels, the caskets couple
with microwave energy and heat above 500°C depending on the cavity height,
accompanied by the rapid change of dielectric properties of the insulation materials. Thus
as the cavity height changes from the lower limit to the upper limit of the cavity height,

the temperature of the casket rapidly increases and decreases repeatedly. This

321

Table V-2-l. Geometry and composition of the zirconia/aluminosilicate caskets
employed in this study

 

 

 

Casket Casket 1 Casket 2 Casket 3 Casket 4

Outer Diameter (cm) 10.16 7.62 10.16 10.16

Inner Diameter (cm) 7.62 5.08 5.08 7.62

Thj°ckyrfi°§§§féi$°nia 1.27 1.27 2.54 1.27

“6553;322:223“: a s 3 5

Volume of zirconia (cm3) 106 76 182 177
Volume of SALI (orn3) 347 193 334 231
Total volume (cm3) 453 269 516 408
Outer surface area (cmz) 386 259 386 386
Inner surface area (cmz) 151 80 80 187

 

322

  

311': C ‘ ”Mrs: "J!

l 4— Short Position
Upper Limit Switch _ Adjusting Motor

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Finger Stock
fl?-
L s
h__ 1
Probe Position
Adjusting Motor

 

 

 

Figure V-2-1. Schematic of a cylindrical single-mode microwave cavity defining the
cavity height, Ls, (short position) and probe position, Lp.

323

rapid change of properties will make the uniform measurement of the reflected power
difficult as a function of cavity height to determine the resonance length of the cavity
modes available in the cavity. The cavity height was increased by 0.4 mm from 7.3 cm to
21.95 cm by using a computer-controlled stepper motor to displace the moveable top
plate of the microwave cavity.

A minimum reflected power reading corresponds to a maximum power absorption
by the cavity walls and (when it was present) the casket. The cavity heights
corresponding to reflected power minima were compared to theoretical resonance lengths
of the cylindrical single-mode cavity at 2.45 GHz.

For an ideal cylindrical cavity (no load and no wall losses) with cavity radius, or, and
cavity height, (1, the theoretical resonance frequencies, f0, can be calculated for various

modes using an equation expressed as [1, 2]

 

 

v PM, 2 In 2
(f ., ),,,,,; = a; a + 7 for TM,,,"; modes (1)
where v = speed of light in a medium

= 2.998 x 108 m/sec in fi'ee space
PM, = mm x value at which J..(x) = 0
J n = Bessel function of the First Kind of order n
n = number of periodicity in 4) direction (11 = 0,1,2,3...)
m = number of zero fields in radial direction (m =1,2,3...)
l = number of half-waves in axial direction (1 = 0,1,2,3...)

and

324

 

(f. )nmr = 3v; \K-Q'ai) + (17”) for mom] modes (2)

Qnm = mu, x value at which Jn'(x) = 0

n = number of periodicity in 4) direction (11 = 0,1,2,3...)

m = number of zero fields in radial direction (m = 1,2,3...)
1 = number of half-waves in axial direction (1 = 1,2,3,4...).

Using equations 1 and 2, one can construct a mode chart (Figure V-2-2) which gives
the theoretical cavity lengths for a range of frequencies, including 2.45 GHz. For an
empty (no caskets or other material loaded into the cavity) 7 inch single-mode cavity
operated at 2.45 GHz, there are eight or nine expected cavity modes, namely TE2; ; ,
TMlll (T5011), TE112, TMorz, TEsll, T5212, TE113, and TM013 (Table V'Z'Z and Figure V'
2-2). The TM; ;; mode and TEo;; mode have the same resonance frequency for a given
cavity size, which are called “degenerated modes.”

Reflected power measurements at high input power was done during microwave
heating. As the casket was heated, the short position, Ls, (i.e. cavity height) was adjusted
every 2-3 minutes during the entire heating cycle. In every case, the short position was

adjusted to give a minimum reflected power.

2. ELECTRIC FIELD PROBE MEASUREMENTS

An electric field probe was made by soldering a small SMA semi-rigid coaxial cable
about 8.5 cm long and 2 mm in diameter to a SMA connector with RG58C/U 500

coaxial cable (Pastemack Enterprises, Irvine, CA). The probe was used to determine the

325

fo, GHz (resonant freqency)

 

 

 

# L h

J

 

 

 

 

16
Lo, cm (resonant length)

20

24

Figure V-2-2. Mode diagram for ideal 7 inch cylindrical single-mode microwave cavity.

Table V-2-2. Summary for the cavity short position (i.e. cavity height), L5, as a function

of the electromagnetic resonance cavity mode, determined at a microwave input power of

 

 

50 Watts.
Ls (cm) for Ls (cm) 143(cm) Ls (cm) Ls (cm) Ls (cm)
Mode idea] 7” for empty for for for for
cylindrical cavity casket casket casket casket
_ empty cavity 1 2 3 4
TMorr 7.21 7.66 * "‘ "' *
TE2;; 8.24 8.43 7.72 8.15 7.47 7 .65
TMlll 11.29 11.62 9.77 10.32 9.45 9.50
TB; ;2 13.38 13.60 12.83 12.96 12.52 12.80
TM;;;2 14.41 15. 13 14.43 14.63 14.30 14.35
TE3;; 15.71 16.63 15.31 16.26 15.10 15.35
TE2;2 16.48 17.19 16.20 16.71 16.00 16.17
TE; ;3 20.07 20.46 19.79 19.92 19.49 19.70
kTMm 21.62 * 21.76 * 21.34 21.68

 

 

*

326

Could not determine, outside the range of the adjustable cavity height

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

- WAVEMAT
$1,311,135 1 mm 1 not.
\ assembly
\\ f /

Holes for field A» E
strength [1‘1
determination

Grip

Gait—LL] ;
Electric probe Coaxial cable / :11:

Power meter

 

 

 

Figure V-2-3. Schematic of single-mode microwave cavity and schematic of electric
probe for field strength determination.

327

radial component of relative electric field strength, E,, around the cavity wall for various
electromagnetic modes (Table V-2-2 and Figure V-2-3).

The empty microwave cavity or the cavity loaded with casket was tuned to a
microwave resonant condition with an input power of 50 Watts. The microwave power
then was measured using the electric probe as a function of azimuthial and axial positions
along the cavity using holes (hole dimensions) in the cavity wall that were provided by
the cavity vendor. During the measurements, the probe tip was positioned 1 mm inside

from the inner wall of the cavity (Figure V-2-3)

3. HEATING OF MICROWAVE CASKETS

The heating experiments were done in two stages. First, the minimum coupling
power was determined at various modes for each of the four caskets in Group 1 listed in
Table V-2-1. In this study, the minimum coupling power is defined as a microwave input
power required to heat the casket to 500°C within 30 minutes or less. A fixed microwave
input power of 50 Watts was fed into the cavity loaded with caskets l - 4 (Table V—2-1) in
the electromagnetic modes listed in Table V-2-2.

For the caskets in Group 1, the microwave cavity was initially tuned at a minimum
coupling power until the caskets began to heat above 500°C. Based on the minimum
coupling power determined for TM; ;; cavity mode for the four caskets in Group 1 (which
varied from 100 Watts to 130 Watts), for each of the caskets in Group 2 and 3 the cavity
was tuned to TM; ;; mode at 120 Watts for initial heating above 500°C (The input power
of 120 Watts was sufficient to couple the microwaves to the caskets in Group 2 and 3).

Then the microwave input power was increased by 30 Watts every three minutes up to a

328

maximum power of either 600 Watts or 1000 Watts. This rate of power increase resulted
in a relatively slow heating rate ranging fi'om 8°C/min. to 22°C/min. for the temperature
range from 500°C to the maximum temperatures depending on casket and operating mode

and helped to reduce the thermal gradients with the casket.

4. RESULTS AND DISCUSSION
4.1. Measurements of Reflected Power as a Function of Cavity Height, for Low and
High Power Levels

During the low power measurements, for each cavity mode, the short position (i.e.
cavity height) shifted as a function of the volume and the geometry of the refractory
caskets (Figure V-2-4). The cavity height (short position) corresponding to the minimum
reflected power for the apparent modes shifted by less than 1 cm fi'om the theoretical
cavity height for the various modes, except for the TM;;; mode (see Table V-2-2). For
the TM; ;; mode the cavity height shifted by up to about 2 cm.

For casket 1, the cavity height changed during microwave heating by up to about 3
cm (Figure V-2-5). The TE modes tend to transfer to TM modes during the tuning
process performed during microwave heating. This shift or hybridization of the

electromagnetic cavity modes resulted in similar maximum temperatures for adjacent TE

and TM modes (Figure V-2-5).

329

 

 

 

 

 

 

 

 

 

_ 1 I . 1 L.-. ; . 1 trams”, 1 3
40 . \1/ 1“ 1] 1 1f \31 f \V \/ ll-
. ‘ \‘v/l ‘ 7
20 — l -
. Casket 4 -
O P ,1 .. T ,I _\ 1 ' l ' 1 ' M; l I 3
L PM“ 17““ f V”\\ . ’
4O / \\ / 1 1/“\\ / \/_
r 1 1' l K, ‘
20 '- 1,; V \J _
r Casket 3 -
0 . .
A '1 1"""‘\T ."""F—H"‘1f~q~‘ ’ \ , //M flw‘x
g 40 111 1’ 11’ 11 V11“ V ‘
cc * 1/ ‘
3 20 e a
v 1 Casket 2 a
*“ 0
a...“ 40 All 1 /‘ l 1/ “UV fl/ 11‘
a; . 1, 1
o 20 h j
Qt - Casket l
B 0 .- .___a - a.
a 40 - 1‘11 V ""1 pm/T‘ 11":
0 .TMOll TE211 TMlll TE112 TM012 TE3ll TE113 .
‘11:) 20 _ r5212 _
M r Empty cavity .
O 1 l 1 L 1 4 1 r L r 1 r 1 1

 

8 10 12 14 16 18 20 22
Short position, Ls (cm)

Figure V-2-4. Measurements of reflected power as a function of cavity height.

330

 

 

 

 

 

 

I U l U I l I I I I I I I I I 1 T I I I I U I

22 " TM013 —
K * A». .1

A ‘1 I _. ‘M‘? ‘ ‘
20 _ «'I/ “4,91", H 1;- A4\ f"
1%; r,‘ "Hak‘wj:{: .; 2:2} ,; _‘_ _ __ ,— v—I— —
S ‘. TE113 “ ' ‘ ' .
18 - A —
J P TE2 1 2 ;,;H<:‘£~—A \ .r
" l6 AF—e—Aue ’7' 1. ‘3 —

EA_ lua- . 1
o " TMOIZ lite-{st $1.. \— if". \i g; -1
:E 14 IWWI Iii Hist; . _
m .. .;
8" lZin—B-("ZF‘1EF :1 fl
1: ~ \ n .
o 10 .. TM] 1 1 d
.c: 1, .
m 3 _ TE211 M _
tr—é—Q‘teee . ; _ g _ _
6 1 1 I g r 1 1 1 1 1 1 I L 4 I 1 L 1 1 1 I 1 n

 

0 15 30 45 60 75 90 105 120
Time (min.)

Figure V-2-5. Change of short position, Ls, (i.e. cavity height) as a fimction of time
during microwave heating of Casket 1 at various modes.

4.2. Determination of relative radial component of electric field strength, E,, agar-rag
the cavity wall in various modes

The field patterns of relative radial component of electric field strength, E,, was
determined by measuring the power around the cavity wall using an electric probe as a
function of positions in both circumferential direction and axial direction (Figure V-2-6).
The field patterns of various cavity modes for the cavity loaded with different caskets
were similar for the field patterns of the corresponding cavity modes determined for the
empty cavity (Figure V-2-6). The determined field patterns allowed us to identify each
cavity mode. In particular, the variations in the field pattern as a function of axial

direction exactly matches the theoretically expected field patterns. For example, for

331

 

0.08 . v 1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0.10

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

I T I ' ' I 7' r 7 ' ' I I ' I I— I I I 1- I fi— I— T
'I'MOll mode ti 4+ mama). mon mode L *9- urn-awn}
0.08 - .1
0.06 *- .,
t
4 006 ~ e
g 004. :4;+.1i¢—+3—{v——+§+<-€H34:R1¥_ «x *A_. 4: T Q 7:, E9". b
1 . 0.04 - ,1“ -
1- f " 71’ XI;
0.02 - - .10 ‘
0.02 " / “OX .1
1 _ d
\\
0‘00 1 1 1 1 1 1 1 1 1 . 1 1 1 1 1 1 0.00 1 1 1 1 1 1 1 .3 1 1
0 30 60 90 120 150 I80 0 l 2 3 4 5 6 7 8 9 10
Position in 0 direction (deg) Position in z direction (cm)
0- '0 I ' I ' ' I ' ' I r' ' I r ' I I 0 I0 I I I I I I I I I
L TE211 mode «9- mmm»- 1 112211 mode “d1 mwwo- 1
0.08 1. + run-urn:- _ 0 08 . + emu-1.12- _
+ )‘afiglrtlS- . 1 + rank-tu-
i
0.06,;.+--‘_ - 1392.1» 0.06 _ _
E ’ I. “ m0 ’H‘ "/9 ‘ E /\\\
0.0-““1 ‘. "ifllw/ ‘ 0.04 ~ / 1
\‘ ’F, ' \ / \\ ‘
-5"; 4/ . .p .1: ~ //‘/r-\ m\ \\
.4 [fa .. .. 1;! ‘1 \ 1; _ , /‘ \. ~ _
0.02 its”: (:11 3;,“ I. 0.02 i - \\ y
_ + P i + \l‘:\
O/ ‘30
0.00 1 1 1 1 1 1 1 1 4 1 1 1 0.00 1 1 #1 1 L 4 E 1 1
0 30 60 90 120 150 180 0 l 2 3 4 5 6 7 8 9 IO
Position in e direction (deg) Position in z direction (cm)
0.10 . . . . r 1 - . I 1 . . . . . 0.10 1 1 1 1 1 x u 1 1
W1 11 mode 429- 1......11...“ ~ mm mode 9- hem-wu-
0.08 - (T5011 mode) + '“H-"- 0.03 - ('I'EOll mode) + r-«wv-
+ rerun-no.1:- + J'mU-IOJIQ
0.06 - 4 0.06 ~ ‘
a“ < a; 1
0.044;;44tk1 +fl _' Effie/M “*9 «51,; ‘ 0-04 ” 1’7 x ‘
* fir;ti ‘ ‘+*%‘\—5 -4r*¥~ii //’ \l‘ 1
3-45" ‘11‘ ” ,. \
0.01:9)?” ‘t\_\\\\\ 1../""" - 0.02 - I/J’WKQ: \ I
‘4 L {/6 ‘ 1 4
0.00 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0.00 1 C7] 1 1 1 1 1 1 1 1"»:
0 30 60 90 120 150 180 0 l 2 3 4 5 6 7 8 9 10
Position in 0 direction (deg) Position in z direction (cm)
0- lo ' ' I ' T I I ' I I ' I ‘ r I 0 lo I I I I i I I I I
> 113112 mode —6— mmwm- T5112 mode ~e— human-nu-
0.08 r- + ""'1”- 0 08 +- + cat-urns:-
+ renal-11m- I L + “In-““1”-
0.06 e -+ 0.06 ~ .1
0.04 - - 0.04 - e
. - ,1; cxiww—figH?’ ” 1
‘ . -—3;7‘ jiiHj_—t.tfi°fi “A. ,7”, -
O-OZ‘Jij/j '4 0.02 " jig-{3N4 ,1” f“ .1
r i r 5'57 44 / t 4
000 . 1 l 1 1 l 1 1 l 1 1 l 1 l 4 0.00 J l l l I l l l l
0 30 60 90 l20 150 180 0 l 2 3 4 5 6 7 8 9 10

Position in 0 direction (deg)

Position in z direction (cm)

Figure V-2-6a. Relative radial component of electric field strength, E,, around the cavity
wall in various modes.

332

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0- lo I I I I I I I I I I—I I I I I # 0.10 ‘I r 1 I I I I I I
TMOIZ mode "6‘ M”v“'"-"" * TMOIZmodc '9- manna-15.1:-
0.08 __ + emu-11.n- 0.08 _ + numb-Ico-
. + ran-unw- + "“‘Hw-
0.06 _ - 0.06 >- ‘
g: ‘ [fa—11‘ ‘ E i I
0.044r/m". . '/’::-#—49-1’:‘~1. _ III 0'04 .- /"/‘d\\\. A
“M7fi1;fi*+#v-.f— 4/M;_¢_;_:; I? 1 /‘ x/’,Ifi:~%:‘ift X“ )I‘
‘ 11.437 ‘ ”Mfr-i //, 5f “*\\‘\0 /"/
0.02 - *1 ~ 0.02 ~ “ . 1 ,«r -
.M. g \\ E :‘;;P’./‘)
f _ \d“ ‘\.9J
0.m 1 1 l 1 1 L 1 1 l 1 1 l 1 1 l 1 1 01m I l L J l 1 I l I
0 30 60 90 120 150 180 0 I 2 3 4 5 6 7 8 9 10
Position in ¢ direction (deg) Position in z direction (cm)
0.10 I I I I I I fI I I I I I I— I I I 0-08 7 I I I I I I I I
* T8311 mode *3” 1.11.11.11.11.“ T1531 1 mode ‘9‘ ”“11”“-
008 L- + r“,|‘-|SJ|- i + faith-lul-
~+— run-unus- 0.06 *- + runny-1m-
0.06 - )t
E9. ’ A ' a 0.04 _ ..

1\\) ‘/ I i. \\ . 1 m I
0.025% ,4 , K, \\\"L-~~¢1~1..\..,J ‘ 0.02 .- /, 1.... - ..

 

 

 

 

 

 

 

 

 

 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

om 1 1 l 1 1 l 1 1 l 1 1 l 1 1 1 1 1 0m 1 l l l l l L L l
0 30 60 90 120 150 180 O l 2 3 4 5 6 7 8 9 10
Position in 4» direction (deg) Position in z direction (cm)
0.") v ' I Y T r ' ' r V Y r r ' 1 ' ' 0.10 r 1 1 1 1 _e‘
f mama-11.11-
TE212 mode : mm-Wi'm i 113212 mode + rmww_
0086-9 I‘ll-“m- 0-08 I + rut-1.114111-

1.41;. . + run-1111.1111-

1 Q r ' ‘21:?

1 k_ ~11... _ _ _

—. 0.06 r ‘21‘2; .r .\ —. 0.06 f 914$ \,
E]. L {)1 i ' \I‘x ‘ E b /‘ \\:\ C11“
0.04 " \fi‘r " 0.04 " ‘/ \\\K F1 "‘
i“ \,;:\:—‘1—N\‘ ’1’ x \

i . HP“: 5’" \ I
0-02 L 3‘ 0.02 » g" 1
0.“) A_ 1 L 1 1 l 1 1 l 1 1 1 1 1 l 1 L 0.00 l l l L l l l l l

0 30 60 90 120 150 180 0 l 2 3 4 5 6 7 8 9 IO

Position in o direction (deg) Position in z direction (cm)
0.10....Tr..,..,..,.. o,10....,..,.....,
1 T5113 mode —8— mama-nu- - TE113 mode -€9~ manna-na-
008 _ + fflalrllfl- 008 _ + f‘AU-l’.”-
¥+ reign-19.n- + rank-19.n-
0 06 - 1 0 O6 - -
1._fi_ 59".
0.04 1— Wfi/FR~\\& " 0.04 ’- «Neck '1
(Ye/12% ‘— Q‘Ekfi , fi/e/Qr’ ' &&€> I

‘1‘ 1 « ” —4 C ‘ 1 b 1,— _
0.021133%?” 144-:1: .. , ., 1, 0'02“:ng 1 .4: 1&1, , 1.1.

- 4 1. «1
01m 1 1 l 1 1 l 1 1 1 L 11 l 1 1 l 1|_A_ 000 1 1 l 1 1 l 1 1 J 1 1 l 1 1 l 1 1

0 30 60 90 120 150 ISO 0 30 60 90 120 150 180

Position in Q direction (deg) Position in I direction (deg)

Figure V-2-6b. Relative radial component of electric field strength, E,, around the cavig
wall in various modes.

333

TE112 mode, the third subscript, 2, of the mode notation (which indicates there should
exist two half cycles along the axial direction) can be determined for the cavity modes

with resonant length of about 13 cm.

4.3. Dependence of heating characteristics on microwave cavity modes

In this study, the cylindrical single-mode microwave cavity was able to heat the
caskets to relatively high temperatures in various cavity modes which were set up in the
cavity at different cavity height (resonance length) (Tables V-2-3 to V-2-6). Depending
on the cavity modes the temperature differed by up to about 23 0°C at 1000 Watts for
Casket 1. The relative percent standard deviation of the temperature for a casket was less
than 7% for Casket 3. The heating rate varied by up to about 6.6°C/min. from mode to
mode for Casket 4. The highest relative percent standard deviation was about 18% for

Casket 4.

5. CONCLUSIONS

For the caskets of various dimensions, the apparent TE modes showed lower
minimum coupling power than apparent TM modes. For example, the minimum
coupling power for TB modes ranged from 70 to 150 Watts, while for TM modes the
minimum coupling power ranged fi'om 100 to 300 Watts.

At high temperatures, the TB modes tend to hybridize into the TM modes as the

cavity is tuned.

334

Table V-2-3. Summary of the heating behavior of Casket 1 (Table V-2-2) for various
electromagnetic cavity modes.

 

 

Minimum Temp. afier Temp. at 1000 Average heating
input power coupling at Watts input power rate from 500°C to
Mode for coupling minimum (at 600 Watts) temp. at 1000
within 30 power Watts (temp. at 600
min. Watts)
TE2;] 80 Watts 658 °C 1248 °C (1055 °C) 8.0 °C/min. (10.7)
TM.” 130 Watts 764 °C 1392 °C (1133 °C) 9.8 °C/min. (12.2)
TE112 90 Watts 704 °C 1396 °C (1134 °C) 9.6 °C/min. (12.0)
mm 150 Watts 814 °C 1454 °C (1186 °C) 11.1 °C/min. (14.9)
TE2;2 90 Watts 762 °C 1455 °C (1172 °C) 10.3 °C/min. (12.7)
TEm 90 Watts 852 °C 1431 °C (1100 °C) 9.9 °C/min. (11.2)
TM013 170 Watts 870 °C 1478 °C (1134 °C) 11.4 °C/rnin. (14.2)

 

 

Table V-2-4. Summary of the heating behavior of Casket 2 (Table V—2-2) for various
electromagnetic cavity modes.

 

 

Minimum input Temperature Temperature at Average heating
Mode power for after coupling §_09_ Watts rate from 500°C

coupling within at minimum input power to temp. at 600

30 minutes power Watts

TE,“ 80 Watts 685 °C 1520 °C 18.7 °C/min.
mm 100 Watts 798 °C 1519 °C 19.8 °C/min.
TE112 70 Watts 774 °C 1519 °C 18.7 °C/min.
mm 220 Watts 1035 °C 1345 °C 21.4 °C/min.
TE2;2 150 Watts 732 °C 1368 °C 20.0 °C/min.
TE“; 80 Watts 882 °C 1406 °C 16.9 °C/min.
TM013 * Ill # *

 

 

335

Table V-2-5. Summary of the heating behavior of Casket 3 (Table V-2-2) for various
electromagnetic cavity modes.

 

 

Minimum input Temperature Temperature at Average heating
Mode power for after coupling @9 Watts rate from 500°C

coupling within at minimum input power to maximum

30 min. power temp.

TE211 80 Watts 668 °C 1454 °C 17.5 °C/min.
TMm 120 Watts 799 °C 1446 °C 18.9 0C/min.
TE112 70 Watts 762 °C 1255 °C 13.9 °C/min.
mm 160 Watts 859 °C 1253 °C 16.4 °C/min.
TE212 140 Watts 891 °C 1243 °C 15.5 °C/min.
TEm 80 Watts 858 °C 1334 °C 15.4 °C/min.
TM013 180 Watts 912 °C 1402 °C 20.5 °C/min.

 

 

Table V-2-6. Summary of the heating behavior of Casket 4 (Table V-2-2) for various
electromagnetic cavity modes.

 

 

Minimum Temp. afier Temperature at Average heating
input coupling at 1000 Watts input rate from 500°C to
Mode power for minimum power (at 600 temp. at 1000
coupling power Watts) Watts (temp. at 600
within 30 Watts)
min.
TEzn 100 Watts 728 °C 1302 °C (1120 °C) 8.8 °C/min. (11.9)
mm 130 Watts 807 0C 1309 °C (1112 °C) 8.9 oC/rnin. (12.1)
TE112 100 Watts 825 °C 1328 °C (1110 °C) 10.2 °C/min. (11.6)
mm 210 Watts 864 °C 1343 °C (1124 °C) 10.4 °C/min. (15.2)
TEm 110 Watts 826 °C 1361 °C (1122 °C) 9.6 °C/min. (12.6)
TB,” 110 Watts 808 °C 1308 °C (1084 °C) 8.9 °C/min. (11.2)
TM013 300 Watts 1020 °C 1303 °C (1062 0C) 11.2 oC/min. (17.8)

 

 

336

Table V-2-7. Temperatures and heating rates averaged for various cavity modes tuned to

 

 

 

 

heat each type of casket.
Casket Casket l Casket 2 Casket 3 Casket 4
Temp. at 600 Watts (°C) 1131 1446 1341 1105
Temp. at 1000 Watts (°C) 1408 "' * 1322
Heating rate from 500°C
to max. temp. (QC/min.) 10.0 19.3 16.9 9.7
REFERENCES

1. Y. Liao, Microwave Devices and Circuits, 3rd ed., p. 16-21, p. 133-141, Prentice
Hall, Englewood Cliffs, New Jersey (1990).

2. D.M. Pozar, Microwave Engineerig, p. 34-3 8, p. 330-354, Addison-Wesley
Publishing Company, Inc., Reading, Massachusetts (1990).

337

APPENDIX VI. THERMAL ETCHING

Figure VI-l. Surface profile for sintered AKP30 alumina, thermally etched via
microwave heating for one hour at 1858K. (a) The surface profile data as displayed on
the Digital Instruments AF M used in this study includes markers to analysis features such
as the groove depth, as shown here (part a). (b) Line L is the path along which the surface
profile data shown in (a) was collected. Triangular symbols in both (a) and (b) designate
the same points.

m1

 

250

 

 

 

 

0 2:5 5:0 7:5 1o'.o

 

338

Figure VI-2.
temperature for ADS- 995.

 

 

 

 

 

 

 

 

L2 . I - . . , , . , .
> -9— CV. 10°C/min _ -

1.0 + MF, 75°C/min ADS 995 -
A _ + MS. 10°C/min A A
E 0.8~
v i A
.5 0.6» -
32

0.4 - -
3 .

0.2 - -

0.0 m I A l A l l I L

1200 1250 I300 1350 1400 1450 1500
Temperature (°C)
(a)

(a) AF M-measured groove width and (b) groove depth as a fimction of

 

 

 

 

 

 

 

 

 

_ 4.2.— Ezv, Rafe/.11; ' ' '. '
0.25 L. + MF, 75‘C/min ADS 995 d

, —A—1MS,1£PC/nun. ,
0.20 - A .

. 4
0.15 r -
0.10 y- -
(105~ ~

'. 1
0. 00 fi‘ ‘ ‘

1200 1250 1300 1350 1400 1450 1500
Temperature (°C)
(b)

Figure VI-3. (a) AF M-measured groove width and (b) groove depth as a function of

temperature for AKP30.

2.5 ‘ I ' I V I

 

 

. —9— cv. 10°C/min
+ us. 10°C/min

 

 

 

2.0
1.5 ~

1.0

I

Width (m)

0.5 _

 

AKP30 ‘
‘d

4

 

1 A I

 

00 4 I . I n l
1300 1350 1400

I450 1500 l550

l 600

Temperature (°C)

(80

Depth (urn)

339

 

0.30
0.25
0.20
0.15
0.10
0.05

YfY Ifi I

I

 

 

. , . , .
—e— CV. 10°C/min
+ us. IO'C/min

 

 

I

' I

 

 

lLlLlll

 

 

0.00

1300 1350 1400 I450 1500

1550 1600

Temperature ( °C)

(b)

Figure VI-4. (a) AF M-determined groove profiles of ADS-995 specimens heated in a
microwave cavity and (b) - (e) the groove profiles determined by AF M and expected
from least-squares fitting by equation 12 in Chapter 6, Part I, obtained from Mullins’

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

theory.
0.2 r I fi' I ' I fl I f I f I I I ' I ' T
— 1469°C, 1 hour
. _ 1411-c. 1 hour ADS 995, MS .
01 —— 1353'C. 1 hour _
a ‘ 7 — 1295'C. 1 hour
v
.g 0.0 - ~
11' .
o
> J
-0.1
.
_02 1 1 1 1 g 1 1 . 1 1 1 1 1
-2.5 -2.0 -1.5 -l .0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5
Horizontal (pm)
(a)
0.4%.VTY,.V.Yfi+ 0.4'1-11 1-1,
— Rlsht hand side ADS-995, Ms. , — mam hand side ADS-995, ms.
0'3 ' : fixagfidlazlde 1295°C “ 0'3 : gxagxdlazide ”53°C 7
A 1 ""‘ Equation 12 1 A 1 ~---- Equation 12
a 0.2 F —4 i 02 -
a 0.1 L a a 0.1 _ a
.g y g
> 00 F " > 0.0 "‘ p/-—-"___ m :1
-o.1 ~ - -0.l » «
T
.02 - I 1 l - l 1 l A l L l _02 1 l - l A l . I A l A l .
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
Horizontal (um) Horizontal (pm)
(b) (C)
04 r ' J L ‘ 1 I ' T 0.4 . 4 . I . f v 1 . y Y r v
— Rieht hand side ADS-995, MS — Risht hand aide ADS-995, M8.
0.3 ~ : fig‘ggdfid, 1411°c 0.3 ~ : fifi‘fifjd‘fm [469°C
A --- Equation 12 A . --— Equation 12
i 0.2 F i 0.2 _ _
'5 0.1 . _ g 4
s -- ~ .._ 1:,
> > 1
_02 L . J #1 A 1 1 L _02 . l 1 .L . l 4 L A I l
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
Horizontal (um) Horizontal (11m)
(d) (e)

340

Figure VI-S. (3) AF M-determined groove profiles of AKP30 specimens heated in a
conventional furnace and (b), (c) the groove profiles determined by AF M and expected
from least-squares fitting by equation 12 in Chapter 6, Part I, obtained from Mullins’
theory.

 

 

t I v r v I . I 1 l , l , T T 1 ' I t
‘_ 1527'C. 1 hour
0.2-l — 1469'C. 1 hour AKP30, CV _
l — 1411-c. 1 hour

 

 

9

Vertical (11m)
55 s:
-- o

.—

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

-0.2 — -
l l l l l l l 4 l l
-5 -4 -3 -2 -1 O l 2 3 4 5
Horizontal (um)
(a)
0.3 _ ‘T ' ' I ' I I I I 0.3 f r I J I f I
1 —— Right hand side AKP30, cv , j — mam hand side AKP30, CV .
— lulllna‘ m o — x 11m ' m
0.2 i ..... Left ma :3: 1469 C ~ 0.2 g ..... 1:1: hznd :3: ”27°C
A , --- lumna' theory A l -—— Mullina' theory
5 0.1 . ~« g 0.1 - 4
3 0.0 fix- ~ 3 0.0 ~
0 ' 0
> -o.1 -- . > -o.1
.02 ~ « .02
0.0 0.5 1.0 1.5 2.0 2.5 0.0 0.5 1.0 1.5 2.0 2.5
Horizontal ( 11m) Horizontal ( pm)
0)) (C)

34]

Figure VI-6. The ratio of AFM-measured groove depth to width, d/w as a fimction of
reciprocal temperature. The curves represent a least-squares linear regression.

 

 

0.3 I I ‘ r I I

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

AKP30‘
0.2 ~ j
3 _ .
E N
0.1 b \ _
r G’OCV ‘ O .
HHS ‘
0.0 A A x 0.0 A . A A A . A . A
0.56 0.58 0.60 0.62 0.64 0.66 0.52 0.54 0.56 0.58 0.60 0.62
1000/T (l/K) 1000/T (UK)
(a) (b)

Figure VI-7. Linear thermal expansion coefficient as a function of temperature for
polycrystalline on alumina [Wachtman]. The curve in (a) represents data fitting to a fourth
order polynomial equation and the curve in (b) represents a linear fit of the data as a
function of temperature, T.

 

 

 

 

 

 

 

 

10 r 1 1 - I . I 9.0 I . 1

g . Polycrystalline . 5 Polycrystalline
"-9 9 _ a-Ale: _, g * a-Ale: ‘
a . c?
o A o A 8.5

v , ‘7 . .

O O
x _ 7 ,_ x _
0 x 0 ><
E 6* E
g 5 L 4 . 1 1 L 1 1 fi 7. 5 4 - 1 1 1 . 1

0 400 800 1200 I600 I400 1600 l 800 2000
Temperature ( C) Temperature (K)
(a) (b)

342

Table VI-l. Surface diffusion coefficients, Ds, calculated using equations 8 and 10
(Chapter 6, Part H) based on measurements of the groove depth & angle, the groove
width, and the measured groove depth & angle, calculated by equation 7 (Chapter 6, Part

II), respectively.

 

 

 

 

 

Material Process Temperature Ds(d,\y) Ds(w) Ds(d, cal.\p)
(K) (cmz/sec) (cmZ/sec) (cm2/sec)
1510 1.66x10"° 7.34x10'12 7.85x10‘12
1568 6.64x10'“ 9.49x10'12 1.21x10‘”
1626 3.57x10'll 2.71x10'” 2.69x10'“
CV 1656 1.65x10"° 4.63x10'” 3.99x10'“
10 K/min. 1684 1.01x10"° 1.06x10'lo 1.1ox10'lo
1714 8.91x10"° 3.41x10"° 4.05x10"°
1742 1.79x10'09 3.40x10"° 3.42x10"°
1510 9.07x10"° 3.44x10‘“ 3.13x10‘“
1568 5.97x10'“ 1.92x10'11 1.85x10‘“
Coors 1626 1.50x10"° 6.61x10'” 5.78x10'”
ADS-995 MF 1656 1.00x10'08 4.96x10'lo 5.00x10"°
75 K/min. 1684 2.97x10'09 7.67x10"° 6.91x10"°
1714 1.49x10'08 6.50x10'09 6.28x10'09
1742 1.43x10'08 4.17x10‘09 4.16x10'09
1510 2.4Ox10'09 1.04x10"° 1.11x10'10
1568 6.00x10'09 2.11x10“° 1.9ox1'0"°
1626 1.44x10'09 6.53x10"° 6.31x10"°
MS 1656 1.79x10'08 9.06x10"° 8.81x10“°
10 K/min. 1684 4.98x10'09 4.12x10'09 3.77x10'09
1714 4.13x10'08 1.53x10'08 1.7lx10'08
1742 1.43x10'08 1.36x10'08 1.35x10'08
1626 6.80x10"° 1.56x1o"° 1.47x10"°
CV 1684 4.89x10“° 2.43x10"° 2.02x10"°
1742 4.94x10"° 1.32x10"° 1.29x10"°
Sumitomo 1800 3.68x10’08 4.06x10'09 3.74x10'09
AKP30 1626 1.80x10'09 5.31x10'” 4.48x10'“
1684 5.38x10’m 1.12x10“° 1.07x10"°
MS 1742 4.44x10'09 3.01x10'09 2.84x10‘09
1800 7.91x10'09 6.87><10*’9 6.21x1om
1858 1.29x10'06 3.67x10’07 3.39x10'07

 

 

343