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Theory and application of microwave joining

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Theory and application of microwave joining
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Cozzi, Alex Douglas, 1963-
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English
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xx, 263 leaves : ill. ; 29 cm.

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Subjects / Keywords:
Ceramic materials ( jstor )
Dielectric materials ( jstor )
Electric fields ( jstor )
Gels ( jstor )
Heating ( jstor )
Iron oxides ( jstor )
Microwaves ( jstor )
Nickel oxides ( jstor )
Oxides ( jstor )
Silicon carbides ( jstor )
Dissertations, Academic -- Materials Science and Engineering -- UF
Materials Science and Engineering thesis, Ph. D
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bibliography ( marcgt )
government publication (state, provincial, terriorial, dependent) ( marcgt )
non-fiction ( marcgt )

Notes

Thesis:
Thesis (Ph. D.)--University of Florida, 1996.
Bibliography:
Includes bibliographical references (leaves 255-262).
General Note:
Typescript.
General Note:
Vita.
Statement of Responsibility:
by Alex Douglas Cozzi.

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University of Florida
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University of Florida
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Copyright [name of dissertation author]. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
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THEORY AND APPLICATION OF MICROWAVE JOINING


By

ALEX DOUGLAS COZZI





















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

UNIVERSITY OF FLORIDA

1996

UNIVERSITY OF r. -
































Copyright 1996

by

Alex Douglas Cozzi

































I would like to dedicate this dissertation to my father, Thomas. My only regret is that you
could not see me graduate.














ACKNOWLEDGEMENTS

The author would like to thank a number of people for their professional

suggestions and personal support towards this study. First I would like to thank Dr. David

Clark who not only showed me how to be a better scientist, but how to be a better person.

His guidance and constant reassurance allowed me to complete the graduate program. I

would like to express special thanks to Dr. Matt Ferber of Oak Ridge National Labs for

taking the time to provide assistance and guidance even though he is extremely busy with

many other projects.

I would like to also thank Drs. J.J. Mecholsky, B.V. Sankar, R.J. Singh, E. D.

Whitney and V.J. Tennery for their comments and suggestions that increased the technical

value of this study. I wish to thank Dr. Ron Hutcheon of the Atomic Energy of Canada

Ltd., Chalk River Laboratories for providing essential dielectric data and insight into the

meaning of that data.

The author appreciates the assistance of the administrative and technical staff of the

High Temperature Materials Laboratory at Oak Ridge National Labs, especially Arvid Pasto

and Billie Russell, the ringleaders of the HTML Fellowship program. I would like to thank

the members of Dr. Ferber's research group, Kristin Breder, Jason Canon, Dana Green,

Allen Haynes, Tim Kirkland, Edgar Lara-Curzio, Ron Ott, Laura Riester and Andy

Wereszczak. I would like to also thank Mark Janney and Jim Kiggans for providing me

with all the materials and assistance they could spare.

I would like to convey special thanks to Diane Folz and Rebecca Lynn Shulz for

both their professional help and friendship throughout my stay at the University of Florida.

I would like to also thank all of the past and present members in Dr. Clark's research








group, my peers in the Department of Materials Science and Engineering, Iftikhar

Ahmad,Salwan Al-Assafi, Attapon Boonyapiwat, Robert Dalton, Arindam Dd, Robert

DiFiore, Zak Fathi, Carl Jones, Don Jones, Michelle Lococo, Edmund Moore, Lorie

Stapler and Bruce Zoitos. I would like to convey special thanks to my friends, especially

Philip McCluskey, Andrew Duncan, Mark Weaver, Chris O'Gara, Lisa Demmy and

George Demmy.

I would like to express particular thanks to my family, my parent's Thomas and

Lillian, my sister Dianne, my brothers Tommy and Alan as well as their families for their

emotional and financial support through eight long years of graduate school. Finally, I

would like to acknowledge my wife, Sunday, who along with my family believed in me

when even I wasn't so sure. She watched me through the highs and lows of this study,

tried tirelessly to keep me focused on the goal and provided love and support without

which this study could not have been performed.

This research was sponsored by the Assistant Secretary for Energy Efficiency and

Renewable Energy, Office of Transportation Technologies, as part of the High

Temperature Materials Laboratory Fellowship Program, Oak Ridge National Laboratory,

managed by Lockheed Martin Energy Research Corp. for the U.S. Department of Energy

under contract number DE-AC05-960R22464.















TABLE OF CONTENTS


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

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

LIST OF FIGURES ............................................ xi

ABSTRACT ............................................... xix

CHAPTERS

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

2 SURVEY OF THE LITERATURE ........................ 7
M icrow aves .................................. 7
Background ............................. 7
Microwave Applicators ..................... 12
Microwave Processing of Materials ............. 16
Numerical Modeling of Microwave/Material
Interactions ........................ 17
Evidence of Microwave Enhancements ........... 26
Joining ..................................... 28
Joining M ethods .......................... 28
Joining processes .................... 32
Criteria for Joining ........................ 35
Effect of Process Variables on Joining ........... 38
Temperature ........................ 38
Pressure ......................... 41
Time ............................. 41
Reactions ......................... 44
Scales of Joining .......................... 44
Atom ic ........................... 44
N ano ............................ 46
M icro ............................ 49
Macro ............................ 50
M materials Joining .......................... 50
Metal/ceramic joining .................. 51
Ceramic/ceramic ..................... 52
Microwave Joining ........................ 53
Sum m ary ........... ........................ 60

3 MATERIALS AND METHODS .......................... 62
Phase O ne ................................... 63









Sol-G el ................................ 64
Basegel .......................... 64
Doped gel ......................... 65
Sol-Gel Characterization ..................... 68
Stand alone heating ................... 68
Differential scanning calorimetry .......... 70
X-ray diffraction analysis ............... 70
Dielectric properties ................... 71
Alum ina ............................... 71
Nickel Oxide ....................... 72
Surface roughness ................... 73
Phase Two ................................... 74
Microwave Joining Apparatus ................. 75
Microwave Susceptors ...................... 77
Specimen Preparation ...................... 86
Mechanical Testing ........................ 87
Phase Three .................................. 90
M microwave Joining ........................ 91
Conventional Joining ....................... 93
Optical Inspection ......................... 93
Statistical Analysis ........................ 94
Phase Four ................................... 95

4 NUMERICAL MODELING ............................ 96
Heat Transfer ................................. 97
Transient Heat Conduction ............... ........ 101
Boundary Conditions ........................... 103
The Physical M odel ............................ 105
Case Title ............................. 105
General Problem Parameters ................. 106
Region Data ............................ 106
M materials .............................. 107
Initial Temperature ....................... 109
Heat Generation ......................... 109
Boundary Conditions ...................... 110
G rids ... ... ... ... ... ... ... ... ... ... ... 112
Analytical Functions ........................... 113
Specific heat ............................ 114
Thermal conductivity ...................... 114
Power generation ........................ 114
Boundary condition ....................... 123
Tabular Functions ............................. 123
Thermal conductivity ...................... 126
Printout Tim es ............................... 127
Nodes M monitored ............................. 128
Transient Data ................................ 128

5 RESULTS ....................................... 137
M achined Surfaces ............................ 137
Sol-Gel Interlayers ............................ 137
Stand Alone Heating ...................... 137









Differential Scanning Calorimetry ............. 143
X-ray Diffraction Analysis .................. 145
Dielectric Measurements ................... 147
Microwave Susceptors .......................... 153
Joining .................................... 160
Joining Conditions ....................... 160
Visual Inspection ........................ 160
Flexure Testing .......................... 163
Statistical Analysis ....................... 184
Numerical Modeling ........................... 203

6 DISCUSSION .................................... 217
Phase O ne .................................. 217
Machined Surfaces ....................... 217
Sol-Gel Interlayers ....................... 218
Summary of Phase One .................... 221
Phase Two .................................. 223
Microwave Susceptors ..................... 223
Microwave Joining Apparatus ................ 224
Summary of Phase Two .................... 224
Phase Three ................................. 225
Experimental Design ...................... 225
Joining Experiments and Flexure
Tests ........................... 226
Statistical Analysis ....................... 229
Summary of Phase Three ................... 231
Phase Four .................................. 231
Computer Simulations ..................... 232
Summary of Phase Four .................... 234

7 SUMMARY AND CONCLUSIONS ..................... 235

8 FUTURE WORK .................................. 241

APPENDICES

A SAMPLE CALCULATIONS OF THE
PENETRATION DEPTH AND CRITICAL
THICKNESS FOR Al-66 CEMENT ................ 243

B SUMMARY OF INPUT DATA FOR HEATING 7.2
.. .. 245

C SAMPLE CALCULATIONS FOR STATISTICAL
ANALYSIS ................................. 251

REFERENCES .............................................. 255

BIOGRAPHICAL SKETCH ..................................... 263














LIST OF TABLES

Table 2-1. Error Associated with Simplified Equation for Penetration Depth for
Several e"eff/ E' Ratios. .............................. 11

Table 3-1. Manufacturer Reported Properties of Coors Alumina Used in Study.
7 2

Table 3-2. Levels of Varied Processing Conditions. ................... 91

Table 3-3. Experimental Design used to Aid in Determining the Effect of
Processing Conditions on the Strength of the Joint. ............. 92

Table 4-1. Summary of the Parameter Cards Used to Describe the Nine Model
Regions. ....................................... 108

Table 4-2. Input Parameters for the Four Materials Represented in the Model. .. 109

Table 4-3. Heat Generation Cards for the Four Materials in the Model. ...... 110

Table 4-4. Table of the Gross and Fine Grid Lines for Both the r and z Axes. 113

Table 4-5. Thermal Conductivity of Coors AD995 Alumina at Different
Temperatures ..................................... 126

Table 4-6. Thermal Conductivity of the Nickel Oxide Used in the Model at
Different Temperatures. ............................. 126

Table 4-7. Calculated Values for the Thermal Conductivity of a 30 wt.%
SiC/Cement Susceptor. .............................. 127

Table 4-8. Nodes of Interest and Their Placement in the Model. ........... 130

Table 5-1. Flexure Strength of AD995 Alumina Joined Under Various
Conditions Using Several Different Interlayer Materials. ......... 163

Table 5-2. Mean Strength and Standard Deviation of Bars Joined by either
Microwave or Conventional Heating. ................... .. 169

Table 5-3. Data Used to Perform ANOVA Analysis. ................... 192

Table 5-4. Output of Statistical Analysis of Data from Table 5-3. .......... 193








Table 5-5. Statistical Analysis of the Effect of Bar Position on the Flexure
Strength for both Microwave and Conventional Heating. ........ 199

Table 5-6. Effect of Position/Heating Method Interaction on the Flexure
Strength ........................................ 203














LIST OF FIGURES

Figure 1-1. Schematic depicting the intersection of two fields of modeling to
form a basis for research. ............................. 5

Figure 2-1. Representation of the lag in the current that determines the loss
tangent ......................................... 10

Figure 2-2. Ratio of transmitted to incident field for aperture diameter,
0.05< d/X
Figure 2-3. Radial temperature profiles in a cylindrical roast beef. ............ 20

Figure 2-4. Temperature of bread heated with two different field strengths. ..... 21

Figure 2-5. Effect of variable (-) versus constant (---) dielectric properties on
temperature in a raw beef sample. Depth in sample refers to fraction
of whole ......................................... 22

Figure 2-6. Measured and computed temperatures for the specimen and the
insulation during a microwave sintering run. ................. 24

Figure 2-7. The activation energy for 180 diffusion in sapphire measured using
both conventional and microwave heating. ................... 27

Figure 2-8. Diffusion of potassium in sodium aluminosilicate glass using
conventional heating and two different microwave power levels at a
temperature of4500C for 30 minutes. ..................... 29

Figure 2-9. Sketches of a) Typical setup used for joining ceramics in a hot press
and b) ceramic shapes commonly joined in a hot press. .......... 34

Figure 2-10. Schematic showing the six mechanisms of mass transfer that can
lead to joining; a) surface sources, b) bonding interface sources c)
bulk deformation after yield or during creep. ................. 36

Figure 2-11. Contact area of a) textured surface and b) smooth surface. Contact
area in a) is greater than in b) when the external dimension is the
same. ...................... .................... 37

Figure 2-12. Effect of surface roughness (as described in equation 3-1 and figure
3-4) on sample strength .............................. 39

Figure 2-13. Effect of joining temperature on the strength of a joint. ........... 40








Figure 2-14. The effect of pressure applied during joining on the strength of the
joint ................. ......................... 42

Figure 2-15. The effect of joining time on the strength of the joint. ............ 43

Figure 2-16. Graphic representation of the four scales of joining discussed in the
text ........................................... 45

Figure 2-17. Energy versus separation for two ions in proximity to each other. ... 47

Figure 2-18. Force versus separation for the two ions in figure 2-17. .......... 47

Figure 2-19. Computer derived, relaxed structure of the BaO/NiO interface. ..... 48

Figure 2-20. Effect of joining temperature on the strength of 92% alumina. ...... 55

Figure 2-21. The effect of joining time on bend strength of silicon nitride. ....... 56

Figure 2-22. Knoop hardness across joint for microwave joined alumina. ....... 57

Figure 2-23. Acoustic emission traces for a mullite joining experiment. ......... 58

Figure 3-1. Binary Cr203-Al203 phase diagram. ...................... 67

Figure 3-2. Binary Fe203-Al203 phase diagram. ...................... 67

Figure 3-3. Setup used to measure temperature of gel compositions heated solely
by microwaves (setup was placed in a microwave for heating). ..... 69

Figure 3-4. Simulated material profile depicting the arithmetic mean. .......... 73

Figure 3-5. Schematic of the microwave joining apparatus. ................ 78

Figure 3-6. Photograph of the microwave joining apparatus used in all of the
microwave joining experiments. ......................... 79

Figure 3-7. Flowchart used to produce susceptors for microwave joining. ...... 81

Figure 3-8. Cutaway view of the setup used to evaluate the heating ability of
susceptors ........................................ 82

Figure 3-9. Schematic of the specimen/susceptor setup used in the microwave
joining experiments .................................. 84

Figure 3-10. Photograph of susceptor set up inside the microwave cavity. ....... 85

Figure 3-11. Flow diagram of the microwave joining process and specimen
preparation ....................................... 88








Figure 3-12. Flexure fixture for room temperature testing of bars using four-point
bending, a) schematic of flexure rig and b) labels of relevant
dimensions. ....................................... 89

Figure 4-1. Grid structure surrounding node o, the node of interest. .......... 99

Figure 4-2. Two-dimensional grid structure using the r-z coordinate axes. ...... 99

Figure 4-3. Model used for the simulation of microwave hybrid heating. ...... 100

Figure 4-4. Time-temperature coordinates involved in the Crank-Nicolson
equation. The trapezoid connects the time-position values used to
calculate temperature values at the point indicated,0 ............ 102

Figure 4-5. Logarithmic fit to data for the specific heat of alumina. .......... 115

Figure 4-6. Linear fit for the specific heat of nickel oxide. ................ 116

Figure 4-7. Polynomial fit to thermal conductivity of insulating fiber board. .... 117

Figure 4-8. Temperature of water as a function of time. ................ 119

Figure 4-9. Power absorbed (calculated) as a function of temperature for AD995
alumina. ......................................... 121

Figure 4-10. Power absorbed (calculated) as a function of temperature for nickel
oxide. .......................................... 122

Figure 4-11. Power absorbed (calculated) as a function of temperature for the 30
vol. % SiC susceptor. ............................... 124

Figure 4-12. Curve fit for the emissivity of alumina as a function of temperature. 125

Figure 4-13. Sample input to calculate a heating profile of the model in figure 4-4.
..................... ..... ..................... 129

Figure 4-14. Map of node numbers for the input file in figure 4-13. Geometry
corresponds to the model in figure 4-3. The nodes that represent
thermocouple locations are 328 interlayerr) and 423 (bulk). The
pyrometer is represented by node 328. ................... 131

Figure 4-15. Temperature profiles for simulated microwave hybrid heating
generated using the input in figure 4-13. a) 10 minutes; b) 20
minutes; c) 30 minutes; d) 40 minutes; e) 50 minutes. .......... 132

Figure 5-1. Area of the surface of alumina end member used for roughness
analysis ........................................ 138








Figure 5-2. Profile of 5 mm x 5 mm area of alumina from figure 5-1 analyzed
using a laser profilometer. Light regions correspond to the area
above mean peak height and darker regions correspond to area
below mean peak height. ............................. 139

Figure 5-3. Area of the surface of nickel oxide interlayer used for roughness
analysis. ....................................... 140

Figure 5-4. Profile of 5 mm x 5 mm area of nickel oxide from figure 5-3
analyzed using a laser profilometer. Light regions correspond to the
area above mean peak height and darker regions correspond to area
below mean peak height. .............................. 141

Figure 5-5. Temperature of the potential interlayer materials heated using stand
alone microwave heating. .............................. 142

Figure 5-6. Differential Scanning Calorimetry (DSC) of the base gel, alone and
with additives. .................................... 144

Figure 5-7. X-ray Diffraction Analysis (XRD) of powders synthesized during
DSC analysis. Specimens containing iron compounds exhibited
spectra with reduced intensities. This is most likely due to the
fluorescence of iron from Cu k-alpha radiation. Fluorescence tends
to reduce peak/background ratios. ....................... 146

Figure 5-8. Dielectric constant versus temperature of potential interlayer
materials. Measured at 2.46 GHz ........................ 148

Figure 5-9. Dielectric constants, measured at 2.46 GHz, plotted without the iron
(11) oxide composition .............................. 149

Figure 5-10. Dielectric loss factor, measured at 2.46 GHz, versus temperature for
potential interlayer materials. .......................... 150

Figure 5-11. Dielectric loss factors plotted without the iron (III) oxide and nickel
oxide compositions. Measured at 2.46 GHz. ................ 151

Figure 5-12. Loss tangent, measured at 2.46 GHz, versus temperature for
potential interlayer materials. .......................... 152

Figure 5-13. Loss tangents plotted without iron (III) oxide and nickel oxide
compositions. Measured at 2.46 GHz. .................... 154

Figure 5-14. Temperature of alumina load in silicon carbide/alumina cement
susceptors heated using 3.2 KW with a 75% duty cycle (% time
on) ............................................. 155

Figure 5-15. Dielectric constant, measured at 2.46 GHz, versus temperature for
several compositions of susceptors. ..................... 156








Figure 5-16. Dielectric loss factor, measured at 2.46 GHz, versus temperature for
several compositions of susceptors. The minimum in the loss
factor, associated with some types of silicon carbide, has yet to be
explained. ....................................... 157

Figure 5-17. Loss tangent for several susceptor compositions at 2.46 GHz. ..... 158

Figure 5-18. Temperature of susceptors as a function of silicon carbide content. .. 159

Figure 5-19. Microwave processing conditions for trial #6 (14500C; 45 min; 3
MPa; nickel oxide interlayer). ......................... 161

Figure 5-20. Conventional processing conditions for trial #11 (1550C; 15 min; 1
MPa; nickel oxide interlayer). ......................... 162

Figure 5-21. Fracture surfaces of specimens from trial #4 (45 min; 1550'C; 1
MPa; nickel oxide interlayer; microwave heated). ............ 164

Figure 5-22. Fracture surfaces of specimens from trial #6 (45 min; 1450C; 3
MPa; nickel oxide interlayer; microwave heated). ............ 165

Figure 5-23. Fracture surfaces of a flexure bar joined using a gel-derived (4
mol% Cr203) interlayer .............................. 166

Figure 5-24. Mean flexure strength of bars for each of the trials in the
experimental design. Error bars correspond to one standard
deviation .............. .......................... 168

Figure 5-25. Fracture surface of specimen from trial #12, representative of all the
specimens joined using AD94 alumina as the interlayer material. ... 170

Figure 5-26. Joint line between AD94 alumina interlayer and AD995 alumina end
member (250x). Trial #14 (45 min/1450C/3 MPa/C/AD94). ..... 171

Figure 5-27. Micrograph of joint region in figure 5-26 showing porosity and
grain boundary material (20,000x). ..................... 172

Figure 5-28. Intact interlayer material in bar that fractured away from the joint
area. Trial #15 (15 min/15500C/3 MPa/C/AD94). ............. 173

Figure 5-29. Joint region of bar from trial #15, flexure strength 220 MPa (250x).
Trial #8 (45 min/1550C/3 MPa/M/AD94). .................. 175

Figure 5-30. Magnified micrograph of the joint line in figure 5-29 (20,000x). 176

Figure 5-31. Joint area of a bar microwave joined in trial #3 (15 min/15500C/l
MPa/M/AD94) (6,000x). a) micrograph and b) WDS x-ray map of
silicon ......................................... 177








Figure 5-32. Joint area of a bar conventionally joined in trial #15 (15
min/1550C/3 MPa/C/AD94) (6,000x). a) micrograph and b) WDS
x-ray map of silicon. ................................ 178

Figure 5-33. Joint area of a bar microwave joined in trial #2 (45 min/14500C/l
MPa/M/AD94) (6,000x). a) micrograph and b) WDS x-ray map of
silicon ......................................... 179

Figure 5-34. Joint area of a bar microwave joined in trial #8 (45 min/15500C/3
MPa/M/AD94) (6,000x). a) micrograph and b) WDS x-ray map of
silicon ......................................... 180

Figure 5-35. Matching fracture surface of bar joined with a nickel oxide interlayer
that failed before flexure testing. Compare to Figures 5-36 and 5-
37. Trial #11 (15 min/15500C/l MPa/C/NiO). ............... 181

Figure 5-36. Matching fracture surfaces of bar joined with a nickel oxide
interlayer with a flexure strength of 38 MPa. Trial #11 (15
min/1550OC/l MPa/C/NiO). ............................ 182

Figure 5-37. Matching fracture surfaces of bar joined with a nickel oxide
interlayer with a flexure strength of 45 MPa. Texture difference is
due to slow crack growth from controlled loading (slow rate). Trial
#11 (15 min/15500C/1 MPa/C/NiO). ..................... 183

Figure 5-38. Micrograph of joint region of bar from figure 5-35 joined with a
nickel oxide interlayer (2,000x). Flexure strength 0 MPa. ....... 185

Figure 5-39. Micrograph of joint region of bar from figure 5-35 joined with a
nickel oxide interlayer (5,000x). Flexure strength 0 MPa. ....... 186

Figure 5-40. Micrograph of joint region of bar from figure 5-37 joined with a
nickel oxide interlayer (1,000x). Flexure strength 45 MPa. ...... 187

Figure 5-41. Micrograph of joint region of bar from figure 5-37 joined with a
nickel oxide interlayer (5,000x). Flexure strength 45 MPa. ...... 188

Figure 5-42. Roughness of joined surface (trial #8) calculated from micrograph
taken at 500x. ..................................... 189

Figure 5-43. Roughness of joined surface (trial #12) calculated from micrograph
taken at 500x. ..................................... 190

Figure 5-44. Roughness of as-machined surface calculated from micrograph
taken at 500x. ..................................... 191

Figure 5-45. Effect of time on the flexure strength of joined bars. ........... 194

Figure 5-46. Effect of temperature on the flexure strength of joined bars. ...... 195

Figure 5-47. Effect of pressure on the flexure strength of joined bars. ......... 196








Figure 5-48. Effect of the heating method on the flexure strength of joined bars. .. 197

Figure 5-49. Effect of the interlayer material on the flexure strength of joined
bars. ......................................... 198

Figure 5-50. Effect of the heating method on the flexure strength of joined bars
plotted with error bars at the 90% confidence interval. .......... 200

Figure 5-51. Map of original bar positions in the joined cylinder before
machining ....................................... 201

Figure 5-52. Interaction chart showing the combined effect of the position of the
bar and the heating method on the flexure strength. ............ 202

Figure 5-53. Temperature of the workpiece measured using a thermocouple and
an optical pyrometer. ................................. 205

Figure 5-54. Variation in temperature of the workpiece between the thermocouple
and the optical pyrometer. ............................. 206

Figure 5-55. Temperature of the susceptor measured using both a thermocouple
and an optical pyrometer. .............................. 207

Figure 5-56. Variation in temperature of the susceptor between the thermocouple
and the optical pyrometer. ............................. 208

Figure 5-57. Temperature (calculated and measured) at the surface of the AD94
interlayer. ........................................ 209

Figure 5-58. Temperature (calculated and measured) at the surface of the NiO
interlayer. ........................................ 210

Figure 5-59. Temperature (calculated) at the surface of the joint region for various
heating conditions. .................................. 211

Figure 5-60. Temperature (calculated) at the surface of the end member for
various heating conditions. ........................... 213

Figure 5-61. Temperature (calculated) at the surface of the joint region (AD94)
and end member (AD995). ............................ 214

Figure 5-62. Temperature (calculated) at the surface of the joint region (NiO) and
end member (AD995). ................................ 215

Figure 5-63. Comparison of calculated temperatures for specimens heated with
nickel oxide interlayers of different thickness. ................ 216

Figure 6-1. Phase diagram of the FeO-A1203 system. ................... 220








Figure 6-2. Qualitative representation of the effect of temperature on the
dielectric loss factor of a typical dielectric material. Tc refers to the
critical temperature at which the efficiency of the absorption of
microwaves increases dramatically. ...................... 222














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


THEORY AND APPLICATION OF MICROWAVE JOINING

By

ALEX DOUGLAS COZZI

August 1996

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

Microwave processing of materials is advancing from a novel processing technique

into a viable method for processing industrial materials. It has been adopted by several

industries for the following reasons. Microwave processing can afford savings in energy

or space or, more importantly, it can provide a product with qualities that cannot be

achieved through conventional means. Even as the use of microwave processing increases

in industry, it is vigorously investigated by researchers attempting to better understand and

control the mechanisms that are responsible for microwave heating of materials. These

investigators are seeking evidence that can either demonstrate or disprove the concept of

enhanced microwave processing. Simultaneously, researchers also are looking for

innovative techniques that can provide other industrial applications for microwaves.

Joining has always been an integral component of the manufacturing industry. The

joint is often the weakest link of any manufactured item and researchers are continually

pursuing means of increasing the strength of the joint. Several ceramics have been joined

successfully using microwave energy. However, there are no processing guidelines

available so the data that have been generated cannot be easily compared. Furthermore,








much of the previous work reports the condition of the joint qualitatively, making

comparisons of joining procedures nearly impossible.

The research performed in this study attempts to address many of the issues

discussed above. The main goal of this research is to join alumina using microwave energy

and to develop an understanding of the microwave interactions with materials and its

relation to the joining process.

An apparatus for the microwave joining of materials was designed and pu into use.

A procedure for producing susceptors for microwave hybrid heating was developed.

Using the microwave joining apparatus and hybrid heating, high-purity alumina was joined

using several materials as the interlayer between the alumina end members. An

experimental design was used to provide data that then could be analyzed statistically to

determine the significance of the processing parameters varied during joining. A numerical

model simulated the microwave heating of the joining process. Simulated temperature

profiles were compared to experimentally measured temperatures to assess the usefulness

of the model.








CHAPTER 1

INTRODUCTION

Joining is an important step in the construction of engineering structures. This may

seem obvious when one thinks about the erection of a building or the assembly of an

automobile. However, joining is also a vital process in the formation of many of the

components that are later joined to produce these buildings and automobiles. The joining

process also extends beyond mechanical joints formed through the use of fasteners such as

bolts, nails and clamps. A remarkable number of products contain components that are

joined through chemical reactions.

While it is often preferable to fabricate the components that are used to assemble

products in one piece, it is not always possible or even the prescribed method for

manufacturing the desired shape. This is most apparent when the final product consists of

more than one material. Some of the newer types of cookware consist of a piece of

stainless steel sandwiched between two aluminum sheets. The stainless steel provides a

high heat capacity base needed for stove top cooking, while the aluminum contributes a

high thermal conductivity for even heating. Another example where joining is the preferred

method of manufacture is when the piece consists of a complex shape that would require

either a complicated mold or extensive machining. Joining can also be useful when a

compressive stress is added to increase the strength of the component. This effect is

observed when glaze is fired on a ceramic piece with a lower coefficient of thermal

expansion than the glaze. When the product cools, the glaze will contract more and be put

under a compressive stress.











All types of materials--ceramics, metals and polymers--have been joined to one

another for a multitude of applications. The applications that entail the joining of ceramics

are extensive. The most common joint involving ceramics is a ceramic to metal joint. These

types of joints are used in light bulbs to connect the metal base to the glass tube, and also in

spark plugs, to attach the metal core to the ceramic sheath. Ceramic/metal joints are created

in the enameling of household appliances such as washing machines and dishwashers. The

enamel coating on the steel housing not only increases the aesthetic value of the appliance,

but also serves as a rust-resistant coating on the steel. While the ceramic/ceramic joint is

somewhat less prevalent than the ceramic to metal joint, it plays an important role in the

traditional ceramic industries. Two of the most widely used examples of ceramic/ceramic

joints are joining bricks with mortar and attaching a handle to a ceramic mug. The use of

mortar to join bricks relies on the room temperature cementitious reaction. This reaction

causes the mortar to harden, thus joining the two bricks. The practice of joining a handle to

a ceramic mug is similar to joining bricks with mortar in that the interlayer material contains

an appreciable amount of water. When attaching handles to mugs, the interlayer material is

usually the same composition as the end members (cup and handle). The joint is formed

during the sintering of the interlayer material with the end members at elevated

temperatures. While these applications are less glamorous than the heat resistant coating on

space shuttle tiles, they make up a much greater share of the ceramic market. In the field of

structural ceramics, the greatest motivation to apply joining techniques is the size limitations

placed upon the part by the densification apparatus. Large parts such as heat exchanger

tubes can exceed fourteen feet in length. This requires the joining of smaller sections to

complete the part.

The formation of a ceramic to ceramic joint is not as straightforward as the typical

metallic joint. Most metallic joining operations include the formation of a liquid phase.

The liquid phase is usually made up of material from both end members and produces a











joint with properties that gradually change from those of one end member to those of the

other. The properties of ceramic joints made without liquid phase can change abruptly

from one end member to the other. Ceramic to ceramic joints are pursued because they

provide an opportunity to improve the final properties of the product. Ceramic to ceramic

joints can furnish an increased resistance to operating temperature over metallic alloys.

They also are more resistant to oxidation than most metal alloys. The enhanced resistance

to degradation and oxidation of ceramics over metals in high-temperature, corrosive

applications can be used to increase the efficiency of heat exchangers and turbine engines.

The joint area in this dissertation is considered to be the area that encompasses the

interlayer and the portion of the end members that has been altered during the joining

process. The joint can be described in three ways: according to its chemical,

microstructural or physical properties. In the first description, joining can be described

chemically by the mixing of the atoms of the components being joined. The mixing of the

atoms of the two components can result in the formation of a third component. When the

mixing of atoms is limited to materials that have mutual solubility, the concentration of

atoms gradually changes from 100% of the first material to 100% of the second material.

Secondly, the joint region may possess a microstructure similar to one or both of the pieces

being joined or it may be unique. A third classification would be to define the joint

physically. This is the manner in which the end members are macroscopically connected or

somehow attached. Although basic in description, this is the definition of "joined" that

matters most to consumers.

The definition of "joint" depends on the desired use of the end product. For the

ceramic to metal joint of the light bulb described above, hermeticity of the joint is the most

important feature with the strength of the joint only having to meet some minimum

requirement. For the purpose of this dissertation, "joint" will be referred to as the region

between two bulk materials that has a chemical composition or mechanical properties











different from either of the end members or the interlayers used in the joining process.

Materials are determined to be "joined" when they do not separate during normal handling.

Until recently, most of the work performed in the joining of materials has used

conventional heating. That is, the specimens to be joined were heated in either a resistance

or radio frequency (RF) heated furnace. Radio frequency heating is limited to materials that

are electrically conductive and capable of supporting an induced current. There has also

been some work done using lasers to heat the workpieces. Lately, microwaves have been

used to provide the energy necessary to heat the specimens to temperatures suitable for

joining. This has brought about a discussion of whether microwave heating can contribute

to the joining process in some way besides its use of an alternate heat source. There are

many reports of enhanced diffusion and lowered activation energies of transport that will be

discussed later. It is certain that if either of the above mentioned phenomena can be shown

to occur during the joining process in a microwave field, there could be a definite advantage

in the use of microwaves to join ceramics.

The goal of this research then, is to join alumina using microwave energy and to

develop an understanding of the joining process. In the literature, there are many models to

predict joining behavior between two materials of identical, similar or differing

compositions using conventional heating. There is also an abundance of experimental data

to support these models. Several models of microwave interactions with materials also can

be found in recent publications. These models and the experimental data to support them

are not as prevalent. In attaining the goal of this research, it is necessary to identify, and

begin to establish, the intersection of these two separate fields of study, figure 1-1.

























Models of Joining My Work Models of Microwave/
Materials Interactions

*equilibrium at interface *evaluate properties of -microwave most important
*surface texture ceramics joined using >communications
*mass transfer mechanisms microwave energy >probe
*residual stress elimination -material most important
>heating
>effect on properties

Figure 1-1. Schematic depicting the intersection of two fields of modeling to form a
basis for research.


While working toward the stated goal, the following objectives were identified and
achieved.

* Review the fundamentals of joining.
* Review the principles of microwave interactions with materials that are relevant to
Joining.
* Design and construct an apparatus for microwave joining.
* Prepare joined specimens that have strength approaching that of the original material.
* Evaluate the integrity and uniformity of joints based on strength.
* Demonstrate enhancements, if any, achieved during microwave joining.
* Use statistical tools to qualitatively assess the joining parameters used in this study.
* Employ numerical modeling to approximate heat flow during joining.
These objectives form the framework of the research performed. They also acted as

guidelines throughout the course of the study.









6

Several significant achievements have been realized during the course of this study.

These achievements either extend beyond the anticipated success of the associated objective

or, were accomplished in addition to the objectives. 1) A new generation of microwave

susceptors has been developed and characterized. 2) A microwave joining apparatus was

designed and constructed using closed loop control of the applied force and temperature.

3) An experimental design to provide the data for a statistical analysis of the effects of

joining parameters on flexure strength was constructed. 4) A heat transfer program was

manipulated to generate temperature profiles in a model that compares calculated

temperatures with experimentally measured temperatures. The calculated values provided

results comparable with other microwave heating models available in the current literature.














CHAPTER 2

SURVEY OF THE LITERATURE

Microwaves

Background

Like visible light, radio waves and x-rays, microwaves are a part of the electromagnetic

spectrum. Microwaves extend between the frequencies of 300 megahertz (MHz) and 300

gigahertz (GHz) This corresponds to wavelengths ranging from about one meter to less

than one millimeter in length.

In the past, microwaves were used almost exclusively in the field of communications2.

Any electromagnetic losses in the materials used were considered detrimental. The

relatively recent introduction of microwave ovens (1960s) to the general public was a result

of the realization that electromagnetic losses could be used for the purpose of cooking.

This was possible because the interactions of microwaves at 2.45 GHz with the water in

foods provided efficient and rapid heating. In 1985, Meek3 exploited the generation of heat

due to the electromagnetic losses in materials that do not contain water. He was able to heat

a ceramic material to a high enough temperature to induce melting. Shortly thereafter,

Meek4 proposed a model for the microwave sintering of powders of dielectric materials.

He describes the powder compact as a material/porosity (air) composite. Meek then

suggests that the higher electric field in the porosity induces densification in nearby grains.

Metaxas and Meredith5 furnish a thorough explanation of the theory behind the

microwave heating of materials. Heat generated due to losses in a material is related to the











electric permittivity (E*) and magnetic permeability (I*) of the material. Most ceramic

materials are not significantly influenced by the magnetic portion of the wave, therefore the

contribution to heating produced by the magnetic losses are generally ignored. Fathi6

provides an excellent review (from a materials science perspective) of the theory behind the

interactions of microwaves with materials. He discusses the different types of polarization

and the losses associated with them. Space charge polarization and orientation polarization

are the two active mechanisms in the microwave frequency range. Space charge

polarization refers to the charge build up at the interfaces of a non-homogeneous material in

an alternating electric field. Orientation polarization occurs in materials that are comprised

of permanent dipoles that have asymmetric charge distributions. The dipoles tend to

reorient in an alternating electric field. Fathi also describes the historical development of

the theory and equations pertaining to the dielectric heating of materials. The electrical

permittivity of a material is defined by the equation


E* = e' je" = e( E J"E) (2-1)
where
e' : dielectric constant (real)
e" : dielectric loss factor (imaginary)
E'r : relative dielectric constant (E'/Eo)
eeff: effective relative loss factor = E"r + o/Eo(0
"r : relative loss factor
S : electrical conductivity (ac + dc)
oE : permittivity of free space
S : angular frequency = 2cf,f in Hz.

The dielectric constant (real) and the dielectric loss factor (imaginary) of a material can be

measured experimentally. Using cavity perturbation theory, Hutcheon et al.7 were able to

measure the complex permittivity of several materials. They then were able to

mathematically isolate the real and imaginary portions of the complex permittivity. These











values describe the polarization and conductivity losses generated in a material. The loss

tangent, tan 8, relates the real and imaginary terms:


tan 8=- (2-2)


The value of tan 8 determines the amount of energy dissipated in a material exposed to an

alternating electric field. In an ideal dielectric, the induced current will lead the applied

voltage by an angle of 900 and 8 = 0. In a real material, the time required for polarization

causes a phase shift in the induced current in the dielectric, represented by the angle 8 in

figure 2-1. These losses are temperature dependent and can change rapidly over small

temperature regimes. Hutcheon et al.8 were able to measure the complex permittivity in a

material up to 1400'C. This made it possible to predict heating behavior of the material in a

microwave field. Another equation developed by Metaxas and Meredith5 that is necessary

to understand microwave heating identifies the average power absorbed in a unit volume,

Pay as

Pav= oEo EE.2 (W/m3) (2-3a)


in terms of tan 6


Pv = 27fee' tan E2 (W/m3) (2-3b)
where
o : angular frequency = 2nf
f : frequency of microwaves, in GHz
Erms :internal electric field (root mean square) (V/m).


The complexity of this equation arises in the determination of the internal electric field,

which can vary with position and temperature. The authors also derive and simplify other




















I, current in
ideal dielectric


,L -loss current in
dielectric material


'I induced current in
dielectric material


Vapp applied voltage


Figure 2-1. Representation of the lag in the current that determines the loss tangent. The
dielectric conductivity is a real number so the loss current is in phase with
the applied voltage,Vapp.










pertinent equations such as the penetration depth of the microwaves in the material, Dp.

The penetration depth is defined as the distance from the material's surface to the point at

which the power drops to e-1 of its surface value. This equation is also affected by

temperature due to the temperature dependence of "eff and E',

S" (2-4a)
Dp =---- [(1+( )
27c(2e')' E


For low loss dielectrics ("eff/ e'l 1) the equation is



'0(o') 2
Dp (2-4b)
27ce"


where 0'o is the wavelength of the electric field in free space. The errors associated with


the simplification of the penetration depth increase as the ratio E"eff/ approaches one.

Table 2-1 contains some representative values of ratios and errors calculated for a

frequency of 2.45 GHz.


Table 2-1. Error Associated with Simplified Equation for Penetration Depth for Several
e"eff/ E' Ratios.

eff/ e' % error
0.009 0.1
0.3 1

0.7 5

1 9











Microwave Applicators

The difference between the two most common types of microwave ovens is in the

microwave cavity where the material is processed. A multimode cavity is a metal box with

an opening in which microwaves are introduced. The microwaves, once introduced into

the cavity, reflect off the walls setting up a number of standing waves. The electric field in

multimode cavities is not very uniform and requires either a turntable or a mode stirrer

(rotating metal fan) to improve the uniformity of the electric field. A single mode cavity has

dimensions that are more precise than the multimode cavity. The length of the single mode

cavity is approximately the size of the wavelength of the microwave frequency being used.

One wall is adjustable so that the cavity can be tuned to the precise length to produce a

single standing wave. The advantage of multimode microwave ovens is that they can be

fabricated in almost any dimension and are relatively inexpensive. Single mode

microwaves have a calculable electric field that permit the identification of the position of

the high field strength. As opposed to single mode microwaves, multimode microwave

ovens are not capable of developing the power densities necessary to produce efficient

heating. Power densities of 107 kW/m3 can be achieved in a tuned single mode cavity5.

Typical power densities of 3 kW/m3 are produced in multimode microwave ovens for home

uses. In a tuned single mode cavity, incident and reflected waves are superimposed and the

position of maximum electric field can be determined. The specimen to be heated can be

positioned to provide the optimum transfer of energy. However, in a multimode cavity the

microwaves are constantly being perturbed and scattered, minimizing the chance that a

specimen is positioned at the point of maximum electric field for more than a few seconds.

In order to heat most ceramic materials in a multimode microwave oven, it is

beneficial, if not essential to use microwave hybrid heating (MHH). Microwave hybrid

heating incorporates a strong microwave absorbing material into a surrounding piece of









13

insulation. This material absorbs more microwaves than the material being processed.

Silicon carbide is the most common material of choice as the microwave absorbing material

in MHH. Silicon carbide is an excellent and inexpensive microwave absorber that can be

used in air at elevated temperatures. Above 9000C, the silicon carbide will oxidize to form

a protective silica layer. The weight gain associated with the oxidation increases as the

temperature increases9. The combination of the absorbing material and the insulation is

commonly called a microwave susceptor. The purpose of the susceptor is to assist the

material of interest in heating to the processing temperature. The development of

microwave susceptors has empowered researchers to investigate low loss materials such as

high-purity alumina using multimode microwave ovens.

One of the common modifications made to a microwave cavity is the addition of

holes to provide access for either a thermocouple, optical pyrometer or other probes. Holes

also may be necessary for the application of pressure to a workpiece in a microwave cavity.

The presence of holes in the cavity necessitates the use of some type of choking system to

prevent microwaves from escaping and presenting a potential health hazard. Holes of a

diameter less than one-quarter of the wavelength (3.06 cm for microwaves at 2.45 GHz)

theoretically emit no microwave energy. This originates from the equation


Z = Ztan(2ntd/X) (2-5)

where
Z = input impedance of hole
Zo = characteristic impedance of hole
d = diameter of hole

, = wavelength of microwaves in cavity.

If d = V/4, the input impedance goes to infinity and the hole acts as a open circuit. The

microwaves are reflected back into the cavity as if the hole did not exist. At aperture sizes











from 0 < d J1/2, there is a small impedance associated with the aperture than can lead to a

small emitted electric field. In reality, the wall material (usually aluminum or steel) has a

finite impedance and can emit a portion of the incident microwaves. Cathey to developed

two equations to calculate the ratio of the electric field scattered through an aperture to the

incident electric field,

E, d ] z d
Sx exp 1 I (2-6a)

and

it 2d n1 2d
E, 4 x 8 1 z d (2-6b)
Ei z 4A


where

Es = scattered electric field, V/m
Ei = incident electric field, V/m
d = aperture diameter, m
X = wavelength of microwave, m
z = distance from aperture, m.

This is the case for the viewing port for an optical pyrometer and the thermocouple

feedthrough. At an aperture diameter to wavelength ratio of 0.5, the intensity of

microwaves transmitted through the aperture becomes significant. Proximity to an aperture

greater than one-half the wavelength of the microwaves can pose a health hazard. Cathey

then calculated the ratio of transmitted to incident field for a range of aperture diameters,

figure 2-2. It can be ascertained from figure 2-2 that for an aperture of X/4 or less, the

fraction of transmitted power is small and attenuates quickly. As the aperture size is

increased, the intensity of the transmitted field increases greatly. In the situation where a

load is to be applied within the cavity, the hole, or aperture, is partially filled with a













































0 0.25 0.5 0.75 1.0 1.25 1.5 1.75


Figure 2-2. Ratio of transmitted to incident field for aperture diameter,
0.05 < d/< 110









16

dielectric material. This material, typically alumina, is used to transfer the load from the

external load cell to the workpiece. Here, the wavelength of the microwaves is decreased

by the square root of the dielectric constant of the filling material5. The decrease in

wavelength makes it possible for the incident microwaves to pass through a smaller

aperture than expected. This condition requires additional modifications to effectively

attenuate the microwaves. Metaxas and Meredith5 describe the use of a circular tube of

conducting material as a choke. If the diameter of the tube is less than one-half of the

incident wavelength, the microwaves are attenuated and the transmitted power decreases

rapidly. Under these conditions (d < 1/2), the attenuation of the power is proportional to

e-z, where X is the wavelength of microwaves in the dielectric material and z is the length of

the choke.

Microwave Processine of Materials

In the past fifteen years, numerous efforts to take advantage of the unique capabilities

of microwave processing have been undertaken. Suttonl outlines the potential advantages

of several characteristics of microwave processing over conventional heating processes.

These advantages include 1) uniform heating of large sections of material, 2) heating above

2000"C in air, vacuum or controlled atmospheres, 3) rapid processing with reduced grain

growth, 4) accelerated sintering and diffusion due to high electric fields, 5) selective

heating of particular materials or phases and 6) improvement of mechanical properties.

Katz and Blakell demonstrated that uniformity could be achieved over a large area by

simultaneously sintering twenty alumina cylinders. They reported that dimensional

tolerances were maintained from experiment to experiment as well as among specimens

within each experiment. Holcombel2 reported attaining a temperature of 2150"C when

sintering boron carbide and Tian et al.13 reached a temperature of 2200'C when sintering










silicon carbide in a positive pressure argon atmosphere. Other non-oxides have been

processed under flowing argon with the resulting x-ray diffraction pattern primarily

indicating peaks of the desired phase 14. Using microwave hybrid heating, D615 rapidly

sintered high-purity alumina to a nearly fully dense state. In D6's experiments, specimens

were held at the sintering temperature for thirty-five minutes. The lack of significant grain

growth reported was analogous to that exhibited in conventional rapid sintering. The

author also reported uniform hardness measured across a 25 mm diameter specimen.

Moore et al. 16 used the concept of selective coupling to demonstrate the effectiveness of

microwave heating. The authors used a lossy binder in the forming step of alumina

compacts. When heated using microwaves, the binder burned out cleanly leaving the

alumina unaffected. In an attempt to organize their approach to microwave processing,

Janney et al. 17 constructed guidelines for microwave processing at the Oak Ridge National

Laboratory. They describe the specimen/insulation configurations used and the temperature

measurement methods that provided consistent results. The progress demonstrated by

researchers worldwide in the microwave processing of materials gained the attention of the

U.S. government. Stein et al. 18 summarized a report commissioned by the Department of

Defense (DoD) and the National Aeronautics and Space Administration (NASA). This

report assessed the current status of the technology, ascertained which applications of the

technology show promise to provide energy or space savings and recommended future

activities in the field of microwave processing. Two industries in which microwave

processing has progressed from an emerging technology to a mature process are the rubber

industryl9 and the food industry20.

Numerical Modeling of Microwave/Material Interactions

Until now, all of the discussion concerning microwave/materials interactions has

been phenomenological. That is, only the behavior of materials after exposure to









18

microwaves has been considered. Due to the complexity and multiple interactions of the

components in equation 2-3, many researchers do not consider the theoretical aspects of

microwave heating. Another more practical reason that theoretical approaches are avoided

is the difficulty in measuring the conditions within the microwave during processing. More

specifically, it is very difficult to determine the electric field in a material inside a

microwave oven. Properties such as the dielectric constant and the loss tangent are

temperature dependent. The interaction of the electric field with the dielectric material in the

cavity alters the field through absorption or reflection of the waves.

To calculate the electric field in a microwave cavity, it is necessary to solve

Maxwell's equations simultaneously. Yee21 was the first to develop a numerical solution

for these equations in an isotropic medium by replacing them with a set of finite difference

equations. Previous to Yee's work, scattering of the electric field was calculated by a

laborious integration method that required numerous subdivisions of the material being

evaluated22. Taflove and Brodwin23 extended Yee's findings to determine the field within

a dielectric cylinder.

One of the early applications of the finite difference modeling techniques was used in

response to cataracts that developed in the eyes of microwave generator operators24. The

model was implemented to predict the electromagnetic fields and temperature induced in a

microwave irradiated human eye25. Recently, a similar model was used to determine the

specific absorption rate of various body components26. The authors suggest that it is

possible to take advantage of the potential for selective heating of various types of tissue in

surgical procedures.

The bulk of the research in microwave/material interactions has been performed in the

food industry. Datta27 judged the determination of the fields within a loaded microwave

environment to be too complex to predict accurately. The author concentrated on predicting









19

the heat and mass transfer associated with microwave processing of foods. Figure 2-3

compares the experimentally and predicted temperatures in a cylindrical roast beef heated

using microwaves. In a rigorous evaluation of microwave induced heat and mass transfer

in baked dough products, Tong and Lund 28 considered the temperature dependence of the

dielectric properties of the materials. The authors were able to measure the field strength

near the subject's surface and use these values for the model. Figure 2-4 compares their

model to experimental results obtained in two different microwave ovens. Pangrle et al.29

introduced the use of finite element analysis to model the microwave thawing of pure water

cylinders. Subsequently, Pangrle et al.30 extended the model to multilayer beef/water

composites. Many authors choose to neglect the temperature dependent properties of the

materials being heated. Ayappa et al.31 used the finite element method to determine the

effect of the temperature dependent properties on the temperature of various materials.

Ayappa et al.32 then extended their finite element model to a 2-dimensional situation.

Figure 2-5 is the temperature distribution of microwave heated raw beef using both

temperature dependent and constant dielectric properties.

In ceramics, Watters et al.33 used difference equations to calculate transient

temperature profiles in a ceramic using a simplified geometry to represent the ceramic

specimen. Gupta and Evans34 developed a 1-dimensional numerical model for chemical

vapor infiltration (CVI) using microwave heating. Using an integral method35 for

microwave material interactions, Gupta and Evans36 calculated the temperature in a

microwave heated 2-dimensional body. In the complicated system of hydrated porous

concrete with variable dielectric properties, Li et al.37 developed a numerical 1-dimensional

model to determine the temperature and steam pressure developed during microwave

heating. Ferber et al.38 were able to calculate stress and temperature distributions for a

simplified geometrical model of a ceramic window subjected to microwave heating.




























80



70
o 70

S Iexperimental

E 60 computed
t-

50
6 5 4 3 2 1 0 1 2 3 4 5 6
Radial Distance at Mid Height (cm)


Figure 2-3. Radial temperature profiles in a cylindrical roast beef26.










































Time (s)


Figure 2-4. Temperature of bread heated with two different field strengths28.






















147
15 min




10 min


107-


a)
E 5 min
I 67




1 min

27
0 0.2 0.4 0.6 0.8

Depth in Sample
Figure 2-5. Effect of variable (-) versus constant (---) dielectric properties on
temperature in a raw beef sample. Depth in sample refers to fraction of
whole32.









23

The joining of ceramics using microwave energy has been considered

theoretically39. It was suggested that the joint area be positioned in the area of a hot spot to

facilitate joining. However, no experimental data is presented in conjunction with the

numerical model. Dibben et al.40 presented a finite element and a finite difference method

for the modeling of the sintering of ceramics in a multi-mode microwave cavity. Their

effort included solving Maxwell's equations and producing 3-dimensional plots of electric

field and power density as a function of position. The finite difference method was used to

calculate temperatures in a 3-dimensional specimen41. To calibrate their model with the

microwave used for the experiments, water loads were heated and the electric field was

calculated from the rate of rise in temperature of the water. In a 1-dimensional model,

Skamser and Johnson42 developed a system to simulate microwave hybrid heating. The

microwave field was assumed to be uniform throughout the microwave. Temperature

dependent dielectric properties of the alumina fiber specimens were varied; those of the

susceptor were kept constant. Microwave hybrid heating experiments were carried out by

Thomas et al.43 using zirconia as the suscepting material. Measured temperatures of the

workpiece and the insulation were compared to those calculated using a 2-dimensional

numerical model. Differences between the measured and calculated temperatures of the

workpiece were as much as 120C during heating. In the insulation these temperature

differences exceeded 200C. When the temperature of the workpiece reached the sintering

temperature, the calculated and measured temperatures converged. Figure 2-6 is the

computed and measured temperatures of the workpiece and the insulation.

Kriegsmann44 proposed a 1-dimensional model to explain the phenomenon of

thermal runaway that is occasionally experienced during the heating of ceramics using

microwave energy. The author later expanded the model to encompass ceramic fibers and

proposed that there exist stable temperatures for given power levels in systems with highly
























1600 -
experiment
O --- --- Sample
1400 -
model

1200
model
S1000 r -- etA----:-A Insulation
' experiment
S800

600

400 I
10 15 20 25 30 35 40 45 50

Time (min)


Figure 2-6. Measured and computed temperatures for the specimen and the insulation
during a microwave sintering run43.











specified boundary conditions45. Spotz et al.46 use the principles put forth by Kriegsmann

to compare experimentally determined thermal stability conditions. They concluded that

microwave hybrid heating is an effective procedure for limiting the formation of hot spots

that can lead to thermal runaway. Beale and Arteaga47 proposed the use of a closed loop

control system to use feedback from a thermocouple to prevent thermal runaway during the

microwave joining of ceramics. Numerical simulations by the authors indicate that this

system demonstrates potential for experimental applications.

One element of the modeling that has been a constant source of difficulty is resolving

the electric field strengths through Maxwell's equations. Ayappa et al.48 investigated the

applicability of using Lambert's law to predict electric field strengths. Lambert's law

describes the exponential decay of the power flux from an initial intensity and is expressed

as

I(z) = Ie-2Z (2-7)

where

Io = transmitted power flux (W/m2),

B = penetration depth (cm) and

z = distance from the sample surface (cm).

The authors have determined a critical slab thickness (Lerit) above which Lambert's law is

valid. The critical thickness is dependent upon the penetration depth, equation 2-4a as

L, ,=2.7P 0.08 (2-8)

The validity of Lambert's law can be quickly determined for any materials system by

calculating the critical thickness at the lowest temperature of interest. That is, the

temperature with the largest penetration depth. This will ensure that Lambert's law will be

valid over the entire temperature range examined. The critical thickness for several ceramic










materials at a microwave frequency of 2.45 GHz are listed in Table 2-2. A sample

calculation of the penetration depth and critical thickness is in Appendix A. When the

critical thickness exceeds the sample thickness, it becomes necessary to solve Maxwell's

equations to determine the power within a material.


Table 2-2. Critical Thickness and Penetration Depth at Different Temperatures for Several
Ceramic Materials at a Frequency of 2.45 GHz.

Material Temperature Penetration Depth Critical Thickness
(C) (cm) (cm)
25 9553 25,793
1000 205 553.4

Al-66 cement 25 127 342.8
1000 28 75.5

nickel aluminate 12 148 4989
1000 5.4 14.5


Evidence of Microwave Enhancements

In the first reported evidence of enhanced diffusion, Janney and Kimrey49 used 180

tracer in a single crystal sapphire substrate in side by side annealing experiments using

microwave and conventional heating. Oxygen was selected instead of a more easily traced

species to avoid differential microwave coupling during the test. Figure 2-7 compares the

activation energies of diffusion for the two processes over a range of temperatures. A

single crystalline sample was used to eliminate microwave interactions with the grain

boundary phase. These interactions contribute to the decrease in activation energy. The

authors do not offer any explanation for the perceived effect. Fathi et al.50 performed ion

exchange in sodium aluminosilicate glasses. The authors exchanged potassium ions from a

salt with the sodium of the glass. The diffusion constants then were calculated from ion

concentrations that were measured using electron microprobe analysis. A variation in the

soda/alumina ratio resulted in differing penetration depths of the potassium ions. These




























-18



^-19

0

-20



-21


4.7 4.9 5.1 5.3 5.5 5.7 x 10-4
1/T (1/K)
Figure 2-7. The activation energy for 180 diffusion in sapphire measured using both
conventional and microwave heating49.


Microwave
409 kJ/mol



O









28

results were compared to identical ion exchange experiments carried out using conventional

heating. At soda/alumina ratios near 1:1, the measured diffusion distance of the potassium

ions is much greater in the microwave processed glasses than in the conventionally

processed specimens. As the ratio is varied from 1:1 in either direction, the differences in

the diffusion distance of the potassium ions were less discernible. In another variation of

the experiment, a smaller susceptor was used and more microwave power was utilized to

attain the required temperature. Figure 2-8 compares the use of two different microwave

powers with conventional heating for the ion exchange of K+<=>Na+ at 4500C.

To examine the effect of defect concentrations on diffusion in a microwave field,

Ahmad5s diffused zinc oxide into single crystals of sapphire with differing amounts of

lattice defects. He correlated the concentration of defects with the rate of formation of zinc

aluminate spinel. Similar experiments were executed by Fathi et al.52 using chromium

oxide as the diffusing species. No microwave effect was reported, but the authors

considered this evidence that thermometry was an acceptable measurement technique in a

microwave field. Tiegs et al.53 employed the premise of selective coupling described

earlier to couple microwave energy with the grain boundary phase of a low loss silicon

nitride. A post sintering anneal of the sintered specimens was carried out using both

microwave and conventional heating54. It was reported that in the specimens with a

significant volume of grain boundary phase, there was an improved resistance to creep

deformation.

Joining

Joining Methods

The term "joined" has several meanings in the materials world. It refers to

components that are held together by one of several methods. The two main types of

joining are mechanical joining and chemical joining. Mechanical joining uses fasteners or




















0.10 I i


K MICROWAVE
0.08 8 K (800 W)
o K CONVENTIONAL
t *m K K MICROWAVE
S"0. (1600 W)
0 0.06 "*



0.04 -


%
0.02 -

U

0.00 10 i !!"" I I *Ell.u.
0 10 20 30 40 50 60 70 80 90

PENETRATION DEPTH IN MICRONS

Figure 2-8. Diffusion of potassium in sodium aluminosilicate glass using conventional
heating and two different microwave power levels at a temperature of 450C
for 30 minutes50.









30

clamps to join two or more distinct pieces together. It is probably the most preferred

method of joining because the parts can often be easily separated at a later time for

repositioning or for re-use. Another type of mechanical joining involves the use of

interlocking pieces, such as a tongue-in-groove floor or a dovetail joint on a birdhouse

roof.

The other type of joining -- chemical joining -- can be further subdivided into direct

joining and indirect joining. Direct joining is the adherence of two components directly to

each other. These components can be either identical or different. The case in which the

two materials are identical is an attractive process because it minimizes the number of

components involved. It also eliminates the chance of mismatches in the thermal expansion

of the materials, which can lead to a weak joint. Direct joining of similar materials can be

accomplished by heating the area near the joint to a temperature at which a liquid will form.

However, there are not many materials that can be effectively joined in this manner55. In

ceramics, low thermal conductivity can result in material failure due to stresses that develop

during heating. When the two materials to be joined directly are different, the presence of a

compositional gradient provides a driving force for joining. Here also, care must be taken

to minimize the thermal stresses that can be induced during the joining process. Thermal

stresses can lead to low joint strengthss6. These stresses are induced by a mismatch in the

thermomechanical properties of the dissimilar materials.

Indirect joining employs a third component between the end members that facilitates

the bonding of the two parts. This is an excellent alternative to the direct bonding method.

Here, the end members can be either identical or dissimilar in composition. When the

materials are identical, the interlayer provides a compositional gradient to assist in the

joining process. In the case of dissimilar materials, the interlayer material is often chosen

to have thermomechanical properties between those of the end members so that thermal









31

stresses are minimized57. These interlayers are more commonly referred to as functionally

graded interfaces and will be discussed later in this chapter.

In addition to the various methods of joining, there are many ways to determine

whether components are joined. The final application of the joined materials is instrumental

in defining what is considered to be an acceptable joint. To say that pieces are joined may

mean welding two parts together so there is a gradient of chemical composition or

mechanical properties from one material to the next. It can also indicate the joining of a

film to a substrate where the purpose of joining the pieces is for physical support of the

film. Little or no chemical reaction is desired between the two materials. This joint may be

mechanically weak but still acceptable because it met the minimum requirements for use.

An example of this type of joint would be superconducting films on an alumina substrate.

The superconducting films form a Josephson junction and can detect small magnetic fields.

There is also the case of the ceramic/metal joint in a light bulb where the hermeticity of the

joint is the determining criterion for suitability. In this case it is not so much the strength or

the amount of reaction between the end members that's important, but the ability of the joint

to maintain a vacuum at elevated temperatures.

For the purpose of this work, a joined specimen will be defined as two or more

components that are physically and chemically attached after exposure to a high temperature

and an applied load. Additionally, the components may not be easily separated during

normal handling.

Currently, there are many processes in which the previously described methods of

joining can be accomplished. Joining by mechanical means requires not only knowledge of

the materials being joined, but also requires extensive design skill55. In chemical joining,

some processes involve only the heating of the area to be joined, whereas others require the

entire workpiece to be heated to the joining temperature. The application of pressure on the

joint area is usually required during the joining process to form a suitable bond.











Joining processes

Bolting. Bolting materials together is a popular method of joining metals. With

ceramic/metal joints care must be taken to avoid stress concentrations. This can be done

with the use of a soft washer (either lead or copper) between the metal bolt and the ceramic

piece.

Clamping. As with bolting, clamping requires the spreading of the load placed on

the ceramic material. Similarly, bending loads should be avoided and gaskets should be

used at all ceramic/metal interfaces55.

Welding. Oxide ceramics can be joined by welding. A laser or an electron beam is

used to heat the edges of the end members above their liquidus temperature. The liquid fills

the gap between the materials. This can produce intense local stresses as described

previously that can produce cracking during processing or cooling58. There is also the

possibility of the formation of an undesirable microstructure during the recrystallization of

the molten material55.

Brazing. Brazing entails the use of a low melting filler between the end members.

This is very common in the joining of metals because of the ease of the procedure. When

working with advanced ceramics, the use of a low temperature braze material decreases the

usefulness of the joined pieces by lowering their maximum use temperature. Other

undesirable aspects of brazing are a possible mismatch of thermal expansion coefficients or

a chemical reaction between the brazing material and the end member55. In the joining

process called active metal brazing, these phenomena are controllable and therefore

desirable.

Adhesive bonding. This process incorporates the use of an organic adhesive

between the ceramic and metal pieces. The organic adhesive is typically flexible compared

to the end members. The relative flexibility of the adhesive material can accommodate










stresses that develop between materials with differing thermomechanical properties. Joints

made with organic adhesives are usually limited by the strength of the adhesive and the

temperature at which the adhesive loses its mechanical integrity. An exceptional example of

adhesive bonding is the application of the ceramic insulating tiles to the aluminum skin of

the space shuttle.

Hot pressing. Hot pressing is used for both direct and indirect joining. Hot

pressing consists of heating the entire assembly to be joined and applying a load at some

time during the heating cycle. Direct and indirect joints are both possible using this

process. Pressure can be applied either uniaxially, where the end members are usually

cylinders, plates or blocks or the pressure can be applied isostatically where any shape can

be accommodated. The main limitation of uniaxial hot pressing is the simplicity of the

shapes that may be joined. Figure 2-9 represents a typical uniaxial hot pressing setup and

the shapes that are most often used. Hot pressing lends itself to the application of diffusion

bonding. Diffusion bonding is the formation of a joint through the interdiffusion of two

materials with a minimal amount of material deformation. The key requirements to

diffusion bonding are 1) intimate contact between the surfaces to be joined and 2) sufficient

interdiffusion between the materials being joined to produce a joint in a reasonable time

frame. The application of pressure aids in fulfilling both requirements for diffusion

bonding. It is a relatively simple matter to hold an assembly as shown in figure 2-9 at the

desired temperature and pressure for the extended periods of time that are sometimes

necessary for significant diffusion bonding to occur. The isostatic application of pressure

is a special case of hot pressing called hot isostatic pressing (HIPing). HIPing allows for

application of large pressures and high temperatures. The capital and operational cost of

HIPing limits its use to necessary applications.







34








P


parallelepipeds cylinders



HEAT HEAT
-- -




a) b)

P


Figure 2-9. Sketches of a) Typical setup used for joining ceramics in a hot press and b)
ceramic shapes commonly joined in a hot press.










Criteria for Joining

The joining method of interest in this study is indirect joining through the formation

of a diffusion bond. It is now accepted that the mechanisms of mass transfer responsible

for joining are the same as those that lead to pressure sintering59,60,61,62. Diffusion and

creep mechanisms are responsible for the pore closure that makes up the joining process.

These can be grouped most easily by sources and sinks and are illustrated in Figure 2-10.

Derby and Wallach62, describe the driving forces for each of the mechanisms in Figure 2-

10. The driving force for 1 (lattice diffusion) and 2 (vapor transport) is surface curvature

and is halted when uniform curvature is achieved. Mechanisms 3 (boundary diffusion) and

4 (surface diffusion) are driven by the chemical potential gradient; 5 (viscous creep) and 6

(dislocation motion) are driven by the applied pressure. The relative importance of each of

these mechanisms is determined by the material properties and the time interval required by

the joining process of interest.

In diffusion bonding, there are two distinct factors that must be considered for the

formation of a good joint. The first factor is the preparation of the surfaces to be joined.

For a diffusion bond, it seems reasonable to assume that a mirror smooth surface would be

desirable to provide intimate contact between the two surfaces63. Conversely, it also

makes sense that a larger contact area provided by a heavily textured surface, figure 2-11,

would be conducive to the joining process. The amount of surface texture can be described

quantitatively in terms of the ratio of the contact area to the unit area of the surface. The

smooth surface in figure 2-1 lb would have a ratio of one, whereas the textured surface in

figure 2-11a would have a ratio greater than one. Villagio64 contends that increasing the

area of the surfaces to be joined by enlarging the surface profile from a mirror flat finish

will increase the contact area and yield the strongest joint. He suggested that sinusoidal

shaped surfaces matched together would yield the optimum conditions. The final result is













material a











material



a) 2
line



4
invoid
b) jint


5 and 6

c) int


S- material source
Figure 2-10. Schematic showing the six mechanisms of mass transfer that can lead to
joining; a) surface sources, b) bonding interface sources c) bulk deformation
after yield or during creep.


























a) textured surface



textured surface


b) smooth surface

smooth surface

external dimension



Figure 2-11. Contact area of a) textured surface and b) smooth surface. Contact area in a)
is greater than in b) when the external dimension is the same.









38

a compromise between the two theories that includes a textured surface but not enough to

introduce notch stresses at the asperities caused by a reduced area supporting the applied

load. The amplitude of the curve suggested by Villagio is small relative to the period of the

surface. The ratio of contact area to unit area for the ideal surface discussed by Villagio is

only slightly greater than one. In figure 2-12, Suganama et al.65. show that an increase in

surface roughness of the ceramic decreased the strength of a Si3N4-Al brazed joint. In a

review paper, Akselson66 suggests that improved joint strengths could have been attained

using a higher pressure during processing.

The second factor that must be considered in joint formation is the driving forces

responsible for the processes that hold the two pieces together. The impetus for joining can

be in the form of van der Waals forces or with an electronic structure across the interface55.

The goal of all of these mechanisms working together is to reduce the free energy of the

system by eliminating the free surface.

Effect of Process Variables on Joining

Temperature

The mechanisms that control joining involve either diffusion or plastic deformation.

For the mechanisms that are diffusional, temperature is the most influential variable in the

joining process. This is explained by the presence of temperature in the exponent of the

diffusion equation. However, the maximum temperature for diffusion bonding is limited to

a fraction of the melting temperature of the material to be joined. Akselson66 reports the

temperature range for sufficient joining to be 0.5-0.8 of the lowest melting point of the

materials to be joined. Higher temperatures would lead to excessive creep deformation of

the specimen. Crispin and Nicholas67 calculated the bond strength of a steel/alumina joint

with an aluminum interlayer as a function of temperature. Figure 2-13 plots these values

and compares them with values measured between 0.75-0.95 of the melting temperature of



























600 3
base material
500 -........ ...........................................--

400


c 300
Cn
m 200
E
Ln 100


0 0.1 0.2 0.3 0.4

Surface Roughness (pm)


Figure 2-12. Effect of surface roughness (as described in equation 3-1 and figure 3-4) on
sample strength65.





























0 60

50

S40

S30 calculated values

L5. 2 0
- 20

O9 10[
0 -----
400 450 500 550 600 650 700

Bonding Temperature (oC)



Figure 2-13. Effect of joining temperature on the strength of a joint67.











aluminum. Derby and Wallach62 review the role of temperature in each of the mechanisms

in figure 2-10.

Pressure

The application of pressure during diffusion bonding has the effect of increasing the

intimate contact between the surfaces to be joined. When the joining temperature has been

attained, the application of pressure assists in deformation near the joint surface that results

in the closure of voids at the interface62. As reported by Allen and Borbidge68 in figure

2-14, at low applied pressures an increase in pressure greatly increases the bond strength.

This effect is diminished as the applied pressure is increased. This indicates that there may

be, for each joint, an optimum pressure where the greatest benefit of increased bond

strength can be realized without significant deleterious deformation of the original

materials69.

Time

The solid-state joining process of interest is diffusion controlled. The effect of time

on the strength of a joint is similar to that of time on atomic diffusion66. The well-known

equation for diffusion as a function of time is


X = k(Dt)n (2-9)

where X is the distance traveled by the diffusing species, k is a constant, D is the diffusion

coefficient and the exponent, n, is usually 0.5. The analogous expression

(2-10)
BS=Bot2


where BS is the bond strength, and Bo is a constant was developed by Crispin and

Nicholas67. The equation relates the joining time to the bond strength. Figure 2-15 shows

the effect of bonding time on the strength of an A1203-Al joint. This equation and plot



























-250
a-
'200
-c
S150


loo

50


0 2 4 6 8 10 12
Bonding Pressure (MPa)



Figure 2-14. The effect of pressure applied during joining on the strength of the joint68.





























70 -11

60
a_
50 50

4T 40

I-
30



m 10
" 20



0
0 20 40 60 80 100 120 140

Bonding Time (min)


Figure 2-15. The effect of joining time on the strength of the joint67.









44

assume that there is no chemical reaction in the form of a phase change associated with the

joining process.

Reactions

While not strictly process variables, reactions in and between the end members and

the interlayer may have a significant effect on the quality of the joint and the bond

strength. In metal/ceramic joining, there is the possibility of controlling the interfacial

reactions. Loehman and Tomsia60 compared results from two different investigations of

the strength of Nb-A1203 joined in a vacuum. They discovered that the formation of a

reaction layer reported by one set of authors agreed with theoretical prediction based on

thermodynamics, while reports by other researches yielded contradictory results. Loehman

and Tomsia suggest60 that these contradictions can be attributed to a difference in the

oxygen partial pressure during processing.

Scales of Joining

Joining can be described on a variety of scales. When two materials are joined

chemically, the interactions are typically discussed considering only the scale of interest.

That is, when the matching of crystal lattices is the topic, it would be discussed on a nano

or atomic scale and the macro and micro scales would not be considered. Figure 2-16

illustrates the four scales of joining that are referred to most often.

Atomic

On the atomic scale, joining can be thought of as interatomic bonding. This can be

illustrated by looking at adjoining atoms from the two surfaces. In the case of most metal

oxides, the interatomic bond is largely ionic. Kingery et al.70 state that as two oppositely

charged ions approach one another, the molecule becomes more stable. The energy of

attraction is due to the coulombic forces that arise between the oppositely charged ions.

















interatomic forces interdiffusion



0000 O 0



atomic / nano


Figure 2-16. Graphic representation of the four scales of joining discussed in the text.











The increase in stability continues until the electron shells associated with the two ions

overlap.

As described in the Pauli exclusion principle, only one electron is allowed for each

quantum state. As two ions approach each other, a strong repulsive force arises to work

against the coulombic attractive force. The combination of these two forces leads to an

energy minimum in an energy versus separation diagram, Figure 2-17. Ferrante et al.71

identify this energy minimum as the binding energy. The authors also state that the

derivative of figure 2-17 is the force versus separation curve, figure 2-18, and that the

maximum can be considered in simplest terms as the tensile stress (Fma/Asuface) necessary

to separate the two ions.

Nano

In the next largest scale examined, the first few atomic planes of each surface are

considered. Ferrante et al.71 discuss the difficulties in increasing the scale in the theoretical

evaluations. They note deviations from symmetry that muddles the theoretical approach.

Some of these deviations are caused by the use of two different planes of the same material

or the existence of two different materials in proximity. To simplify this problem, Clarke

and Wolf72 reduce the interface to a Van der Waals pair potential and sum the potentials

over the interface. This can be used for ceramics when the bonding is localized. Metals

require another approach that is more complicated and will not be discussed in this

dissertation. Stoneham and Tasker73 employed computer codes to model the interfaces

between materials. In the evaluation of the BaO/NiO interface, the authors matched

surfaces by rotating the 100 planes by 45. The resulting relaxed structure, figure 2-19,

placed the Ni3+ ion and vacancies from the disordered NiO lattice near the BaO surface.

This is depicted as the lowest energy structure. Unfortunately, the authors do not consider

any interdiffusion of the cations in their model.


























Inflection point


Figure 2-17. Energy versus separation for two ions in proximity to each other71.




FA !


Figure 2-18. Force versus separation for the two ions in figure 2-1771.



























axis












en
s




)) axis
liO


0) axis


Bulk NiO below
this plane


Figure 2-19. Computer derived, relaxed structure of the BaO/NiO interface73.











Micro

Joining on a micro scale can be reviewed in two ways. The most common way to

consider joining is by bringing together two distinct pieces of material. If the pieces are

determined to be joined, at some position in both materials there will be a deviation in

composition and/or structure. If the joining is done properly, the joint may be

indistinguishable from the bulk to the naked eye. Optical or electron microscopes may be

required to locate the position of the joint. Usually, the area where the initial surfaces

contact can be easily identified. Binner et al.74 recently reported grain growth across the

initial interface, making it difficult to recognize. Al-Assafi75 joined alumina of two

different purities using an alumina gel as an interlayer. The original interface was

indistinguishable from either end member. Backscatter electron microscopy was used to

determine the original interface by identifying the silica impurities in the two types of

alumina. Another feature associated with the micro scale of joining is the possible

observation of porosity. When joining fully dense end members, porosity can appear at the

original interface. This usually has a negative effect on the strength of the joint. The micro

scale is also where interdiffusion across the interface can be detected and measured. This

can be done with backscatter electron spectroscopy (BES), Secondary Ion Mass

Spectroscopy (SIMS)51 or with electron microprobe analysis (EMPA)76.

A second way to envision joining on a micro scale is to consider sintering.

Sintering is the joining of many smaller particles to each other to form a large mass. Solid

state sintering is analogous to joining via diffusion bonding. As discussed earlier, the

mechanisms for joining are based upon those developed for sintering. The end members

could be considered as grains and the joint line would represent a grain boundary.











Macro

In this paper, the macro scale is considered to encompass those aspects of the joint

that can be seen with the unaided eye. The features of a joint that can be discussed on a

macro scale include poorly formed joints, interlayers, reaction products and abrupt

discontinuities when materials of differing colors are used. When a joint is not fully

developed, the original interface is apparent because the edges of the end members still

contain porosity. Interlayers are almost always a different material from the end members.

Even when the joint is well made, the presence of an interlayer makes joint identification

fairly routine. In the situation where there is a reaction product, such as the joining of

alumina and nickel oxide to form a spinel, the color change provides a good indication of

the extent of the reaction.

Materials Joining

The joining of materials has attracted the interest of a growing number of

researchers. There is vast potential in the joining industry to improve the properties of

joined components. However, there are many theoretical and experimental issues

regarding the joining process that must be addressed if the industry is to fulfill its potential.

Some of the theoretical aspects of the joining process have been discussed previously in

this dissertation. A recent focal point has been the effect of the use of an interlayer on the

stresses developed in the final piece during joining77. Experimental work is being

performed on several elements of the joining process. This includes the development of

new methods for evaluating joint strength and new ways of joining materials. The joining

field includes laminar composites that consist of polymer/metal or ceramic/metal bonding,

and the more common butt joints of metal/metal, metal/ceramic, ceramic/metal/ceramic and

ceramic/ceramic. The most recent addition to the joining field is the functionally graded

interface (FGI). The functionally graded interface can be applied to any of the above

mentioned methods of joining. The joint consists of a gradual compositional variation from









51

one surface to the other (e.g.concentration and/or porosity). These changes result in

property gradients (e.g. strength, mechanical toughness or thermal expansion coefficients),

which can be adjusted by controlling the composition and/or the microstructure of the

interlayer.

Metal/ceramic joining

The metal/ceramic joint is present in two different situations. In one instance, it is

an element of the design of the component. This enables the exploitation of the properties

of both metals and ceramics. One example, mentioned earlier, is the case of a light bulb.

The metal base is electrically conductive and permits current flow to the filament with a

minimum of resistance. The ceramic component, a glass envelope, is transparent to the

visible light emitted by the filament. Joined together to form a vacuum seal, they provide a

package that would be difficult to imitate using only a metal or a ceramic. The other

instance of metal/ceramic joining occurs when it is necessary to join two ceramic pieces

using a metal interlayer. A common example of this is in high-temperature structural

applications. Under these circumstances, the high-temperature strength and refractory

properties of ceramics are desired. High melting point metals such as titanium are used as

interlayers when brazing ceramics for high-temperature applications. The brazing process

is used because it requires a minimum amount of metal. Increased metal content may

detract from the desired behavior of the ceramics.

Alumina is the most common ceramic material to be studied in metal/ceramic

joining. Perhaps this can be attributed to its popularity as a structural material, as well as

the wealth of information available on its thermodynamic and mechanical properties.

Routine polishing of the surface is the only treatment the ceramic piece receives prior to

joining. Conversely, the metals are carefully prepared from high purity materials and

meticulously cleaned and polished before these are used. When the joint is to be formed

via diffusion bonding, several different metals of varying thickness are used78,79. Usually









52

the added metallic layers are very thin and have a low melting temperature and elastic

modulus compared to either the ceramic or the primary metal. This correlates with several

thermal stress reduction methods in metal/ceramic joining discussed by Suga et also. Ishida

et al.81 relieved thermal stresses via the introduction of structural defects. This was

accomplished by orienting the lattice when joining single crystals of niobium and alumina.

Serier and Treheux82 increased the strength of a silver/alumina joint by work hardening the

silver. They offer several hypotheses for the increase in strength, including the inducement

of structural defects. Frequently, the methods described above are not practical for service

operations, and the formation of a liquid phase at the joining temperature is necessary to

form a good joint.

Ceramic/ceramic

In 1979, Hauth83 noted that several emerging technologies have high-temperature

use specifications for materials that will require ceramic/ceramic joining without the aid of a

metal interlayer. The example referred to was a high purity alumina pumpout port for a

thermonuclear fusion containment system. The pumpout port is a complex shape that is

comprised of several regular shapes (cylinders and plates) fitted together. The joining

method consisted of making a slurry of the unsintered material and buttering (as with toast)

the surfaces to be joined. This is the same procedure for attaching cup handles and other

extremities in the clay based ceramic industry. In the years since, numerous advances have

been made in ceramic/ceramic joining but there are still many hurdles to be overcome.

In the direct joining of similar ceramic materials, some chemical or physical

variation must be present to assist the driving forces that make up the joining process.

Scott and Brewer84 diffusion bonded alumina at 1500'C and 69 MPa. The joined pieces

were then heated to 1875'C to promote grain growth across the joint. They reported a

maximum joining strength of 59% of the starting material. This was achieved with an axial











deformation of 18% during joining. In similar experiments85, small amounts of MgO were

added as a sintering aid to the alumina cylinders to be joined. The joining temperatures

ranged between 1300"C and 1500'C with a pressure of 69 MPa. Deformation increased to

over 20% and no mechanical testing results were reported. Zdaniewski and Kirchner86

inserted thin polystyrene sheets between 96% alumina plates. The decomposition of the

polystyrene during heating created reducing conditions that enhanced interfacial bonding

and diffusion. In specimens joined at 1350'C and 17.5 MPa, the authors reported flexural

strengths of 194+94 MPa. Direct joining has also been investigated for SiC and Si3N4

with modest success87.88.

When the need for an indistinguishable joint is not imperative, there are more

straightforward ways of joining ceramics for high temperature use. Zimmer89 describes

the development of several ceramic cements that can withstand high temperatures

(>1450'C). Glass or glass-ceramics are also popular choices as interlayer materials.

Whereas some authorso9,91 chose glasses for their mechanical properties and crystallization

abilities, other researchers92.93 chose an interlayer glass composition that approximated the

composition of the grain boundary phase of the crystalline end members. When the glass

was chosen for its crystallization ability, joints of modest flexural strength and fracture

toughness were produced. Both groups of investigators who joined Si3N4 with a glass

similar to the grain boundary phase reported room temperature strengths of 450 MPa.

Microwave Joinine

Microwave joining of materials appears to be one of the most promising among the

areas of materials processing that have been included in microwave processing research.

Researchers have successfully joined alumina, silicon carbide, silicon nitride and mullite94-

100. With the exception of a few studies, most of the work has been performed using

single mode microwave applicators. The first report of joining ceramics using microwaves











was by Meek and Blake3. They successfully joined two alumina plates with a glass

interlayer in a home model microwave oven. Palaith et al.94 provide an overview of the

fundamentals of microwave heating and how it applies to joining. Using a tunable, single

mode microwave oven modified to allow for an application of pressure, Fukishima et al.95

joined several different purities of alumina and silicon nitride. Specimens consisted of

cylindrical rods measuring three millimeters in diameter. The alumina purities varied from

92% to 99%. Joining experiments were conducted at temperatures ranging from 1400'C to

1850'C and pressures up to 2.4 MPa. The authors were able to produce direct joints using

92% and 96% alumina that approached the original strength of the material. Figure 2-20 is

the effect of joining temperature on the bending strength of the 92% alumina. The 99%

alumina was successfully joined indirectly using both the 92% and the 96% alumina as

interlayers. Bending strengths of 90% of the original material were reported. No

information was provided regarding creep deformation. However, even at the low joining

pressures used, the temperature was high enough for creep to occur in high-purity

alumina. The same authors joined silicon nitride in a flowing nitrogen atmosphere using

silicon nitride with a greater dielectric loss than the end member material. The effect of

joining time on the bending strength of the joined silicon nitride is shown in figure 2-21.

Al-Assafi and Clark96 successfully joined 94% alumina to 99.5% alumina using a sol-gel-

derived alumina as the interlayer. The researchers used a multimode cavity and microwave

hybrid heating. Figure 2-22 is the Knoop hardness across the joint area for joints made

with and without the gel interlayer. The purpose of the gel interlayer is to provide a high-

purity powder with a large surface area to join the two surfaces. In an effort to evaluate

the joint non-destructively during processing, Palaith and Silberglitt97 introduced an

apparatus that provides an acoustic pulse echo axially through the sample during joining.

This provides information as to the extent of the joint formation. Figure 2-23 is the result

















600


Before joining
a-
400

S S *
I /1



200
I /
r-


Joining time: 3 min
Pressure: 0.6 MPa


1400 1600 1800 2000
Joining Temperature (C)
Figure 2-20. Effect of joining temperature on the strength of 92% alumina95.




















Si3N4


Base: SN220
Adhesive: SN501


a. 500 Base

0)
C Adhesive


.__

m 300





(1720C; 6.2 MPa; 0.6 mm)

100 1
0 5 10
Joining Time (min)
Figure 2-21. The effect of joining time on bend strength of silicon nitride95.



















2000

1800 99.5% Alumina 94% A

1600

1400 -

1200

1000

800 mr

600 -

400 -

200 -

0
-300 -150 0 150

Distance from Joint (lim)


Figure 2-22. Knoop hardness across joint for microwave joined alumina96.


300
































1400 700

1200) -600

1_000 500


800 400 "




400
0- 600 -300




200 100


0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
Time (min)

Figure 2-23. Acoustic emission traces for a mullite joining experiment97.









59

of an experiment involving the joining of mullite. Yu et al.98 employed this method in the

simultaneous sintering and joining of alumina powders. At a temperature of 1400'C and a

pressure of 0.238 MPa, they achieved a density of 99% theoretical.

Silicon carbide is an excellent microwave absorber and a ceramic material that has

many potential uses. Therefore, it has attracted the bulk of attention for microwave joining.

The processing of the silicon carbide, whether it is reaction bonded silicon carbide or hot

pressed silicon carbide, can significantly affect its ability to absorb microwaves. Reaction

bonded silicon carbide contains residual silicon metal throughout the microstructure.

Ahmad et al.99 direct joined hot pressed silicon carbide to hot pressed silicon carbide and to

reaction bonded silicon carbide. They accomplished this using both a single mode

microwave and a multimode microwave oven. Yin et al.loo joined the high dielectric loss

siliconized silicon carbide using a thin aluminum foil as an interlayer. The authors achieved

fracture strengths comparable to the original material. Other attempts to join silicon carbide

include the use of combustion synthesis. It has been demonstrated that microwaves are an

excellent source of energy for initiating and controlling the combustion synthesis

reaction0io. Silberglitt et al. 102 made successful SiC/SiC joints by initiating a combustion

reaction between titanium, silicon and carbon at the interface.

In an overview paper discussing the problems and opportunities in microwave

joining, Loehman 103 states that there are applications that hold promise but much work

needs to be done to prove the value of microwave joining. He discusses potential

advantages that could be realized by applying microwave processing to the joining of

ceramics. The author also identifies problems that may be encountered and offers solutions

through rigid process control.











Summary

Several authors 104,105 have discussed the potential for energy savings through the

use of microwave processing. It still is not clear if there is a significant energy

conservation to be realized. Katz 106, regardless of his involvement as a researcher in the

field of microwaves, displayed a skepticism towards many of the positive results being

published regarding microwave processing. Despite a wary community of researchers,

exploration of microwave processing has continued with success in specific areas. One

promising niche involves the recovery of common and precious metals from electronic

circuit boards107. Microwaves also have proved successful in several industrial

applicationso0. They are currently being used in some areas of food processing, rubber

vulcanization and wood curing.

Research in the microwave joining of ceramics is developing into a field that will

have viable approaches to engineering problems. Microwave joining has proved feasible

for several oxide and non-oxide ceramics. These materials can be joined with strengths at

or above those attained on conventional joining processes. Some of the advantages that

have been demonstrated by researchers include the ability to join materials with unfinished

surfaces (large surface roughness) as well as non-destructive evaluation of the joint during

the joining process. The in-situ joint evaluation can be performed because it is possible for

the end members to extend out of the heating zone. This provides access to the end

members for the acoustical equipment. In the brief period of time that microwave joining

has been investigated, many discoveries have been made that have led to further research.

Much of the work reported has been presented in one of two formats. In the first method,

the strength of a joint formed under specific conditions is presented with reference to the

strength of the original material. The second method is somewhat more informative in that

the results are compared to conventional joining of similar materials under comparable









61

conditions. The consequences of changing the processing parameters have not yet been

investigated. Results need to be evaluated in a more scientific manner than plotting strength

versus the processing parameter (temperature, pressure, etc.). These parameters need to be

evaluated to determine their relative importance in microwave joining. The intent of this

research was to provide reproducible, microwave joining data based upon

an experimental design coupled with numerical modeling of the experiment.

The data generated will contribute to the advancement of microwave joining

of materials by assisting in clarifying the effects of some of the processing

parameters on the joined materials.














CHAPTER 3

MATERIALS AND METHODS

There are several objectives encompassed by the experimental procedure. The first

objective was to choose a system of materials, consisting of end members and an

interlayer, that was of technical interest and could be joined successfully using microwave

energy. The second objective was to develop a device and procedure that could fabricate

joined specimens with reproducible properties. The first two objectives were incorporated

into the third objective to manufacture joined specimens that were tested for flexure

strength. These results then were analyzed to evaluate the relative importance of the

processing parameters on the strength of the joined specimens. A fourth objective of this

chapter was to monitor the temperature of the specimen and the susceptor during joining so

comparisons could be made to the numerically derived temperature profiles discussed in the

next chapter. The experimental work performed in this study can be separated into four

phases.

The first phase of the work was the preliminary testing of potential interlayer

materials. Various properties of several materials were tested to determine which materials

possess the characteristics required to produce a strong joint. The material properties of

greatest interest were the mechanical strength, refractoriness and microwave absorbing

capabilities. The results reported by Al-Assafi75 indicate that an alumina based sol-gel was

an excellent candidate to provide the desired characteristics.

The second phase consisted of designing and implementing a microwave joining

device to control and record the processing parameters. A microwave susceptor was









63

developed to heat the end members to a temperature at which they become more efficient

microwave absorbers. Using the materials that were classified as tenable interlayers,

experiments to join two viable end member materials were initiated. Flexure bars were

machined from the joined specimens and tested using four-point bending to evaluate the

interlayer and end member materials based on strength.

Phase three was the development of an experimental design that would use the

chosen materials system to evaluate the significance of each of the processing parameters

on the flexure strength of the joined material. Two values were selected for each

processing parameter and an analysis of variances was performed on the results of the

flexure tests.

In phase four, a heat transfer program was used to simulate microwave hybrid

heating. The results were compared to measured values collected in experiments run to

measure the temperature of the specimen and of the susceptor. Two methods of

temperature measurement were used to test the validity of the measuring process.

Phase One
The materials that were identified as potential interlayers were a series of alumina

based gels, 96% pure alumina and nickel oxide. The alumina gel used by Al-Assafi was

investigated as an interlayer material. It also served as a base gel that was combined with

other materials. The other materials were introduced to the base gel either by substituting

for the aluminum salt in the gel during formation or by admixing them to the stable sol

before gelation. All of the materials added to the base gel were considered to be strong

microwave absorbers. The intent of this approach was to increase the absorption of

microwave energy in the joint area. All of the joining experiments in this study were

performed in a constantly changing microwave field. Therefore, unlike the single mode

applicator used by Fukishima et al.95, there were no fixed positions where a high electric









64

field was present. Due to these processing conditions, there was no technique available to

determine the position of a stable hot spot as described by Booty and Kriegsmann39.

Five materials (chromium oxide, iron (II) oxide, iron (III) oxide, nickel oxide and

silicon carbide) were used in conjunction with the base gel to make ceramic powders for

subsequent evaluation. These materials were selected from a myriad of strong microwave

absorbers because of the way they combine with alumina. Chromium oxide is mutually

soluble in alumina for an entire range of compositions. Iron (III) oxide also forms a solid

solution with alumina, but each material is capable of dissolving around 10% of the other.

Iron (I) oxide and nickel oxide both form a spinel when combined with alumina. Silicon

carbide does not form any intermediate compounds with alumina.

Thin monolithic disks of 96% pure alumina and of nickel oxide also were examined

as potential interlayer materials. Alumina was considered because it is very similar to the

materials being used as end members: 99.5% and 96% alumina. Using a similar material

as the interlayer reduces the risk of stresses from differential expansion and maintains a

high strength material throughout the joint region. However, the similarity in composition

presents a challenge to joining because it reduces the presence of a compositional gradient

to act as a driving force. Nickel oxide was chosen over iron (II) oxide as the second solid

material because it is less sensitive than iron (II) oxide to oxygen partial pressures.

Sol-Gel

Base gel

The alumina based sol-gel interlayer was produced in accordance with a patent by

Clark et al. 109 for the creation of boehmite sols. The materials used to produce the base

gel are water*, aluminum sec-butoxide*, and aluminum nitrate nonahydrate***. The


* Deionized water resistance > 10 Mohms
* Alpha Chemicals # 11140 Al(OC4H9)3 F.W. 246.33
** Fisher Chemicals # A586-500 AI(NO3)3-9H20 F.W. 375.14









65

purpose of the aluminum sec-butoxide is to provide the solution with metal ions. The

water hydrolyzes the aluminum sec-butoxide. Aluminum nitrate nonahydrate is a peptizing

agent that breaks up the precursor, permitting the hydrolysis to occur. This facilitates the

formation of colloidal aluminum hydroxide particles. Throughout the remainder of this

thesis, aluminum sec-butoxide will be referred to as ASB, and aluminum nitrate

nonahydrate will be referred to as aluminum nitrate. Working within the parameters

established by the patent, Dalzelllo reported a ratio of ASB:aluminum nitrate of 25:1 as

providing a stable sol. The ratio of 25:1 ASB:peptizer was used throughout the course of

this study. The ratios of the three components for the initial sol were 100:1:0.04

corresponding to water:ASB:aluminum nitrate.

Under reflux conditions, 675 milliliters of deionized water was heated to 880C in a

1000 milliliter Pyrex flask that had been washed in a 6M nitric acid/0.2M hydrofluoric acid

solution and rinsed in deionized water. During heating the water was stirred continuously

by a Teflon coated magnet. Meanwhile, six grams of aluminum nitrate was dissolved in 45

milliliters of water. Rapidly, 104 milliliters of ASB was measured to minimize hydrolysis

of the ASB from the air. The ASB then was added to the water using two syringes*. The

aluminum nitrate solution then was immediately added to the flask. The result was a

cloudy, milky-white solution. This was stirred continuously until it became translucent.

The clearing process took several hours. After the sol cleared, it was cooled to room

temperature and stored in a polypropylene container until used.

Doped gel

According to the patent by Clark et al.109. several other metal nitrate salts may be

substituted for aluminum nitrate during the sol-gel process. Both chromium nitrate** and


*Fisher Chemicals # 14-823-2D 60 ml syringes
**Fisher Chemicals # C331-500 Cr(N03)3-9H20 F.W. 400.15











iron (1II) nitrate* can replace aluminum nitrate in the sol. Chromium oxide forms a solid

solution with alumina at every composition. Figure 3-1 is the binary A1203-Cr203 phase

diagram at elevated temperatures. The A1203-Fe203 phase diagram, figure 3-2, is more

complex. Below 1300C, there is a mixture of the Fe203 (hematite) phase solid solution

with A1203 and A1203 corundumm) phase solid solution with Fe203. Near 1400C,the

presence of FeO becomes significant as the spinel, FeAI204, is formed. McGill et al. mI

reported that both chromium oxide and iron (II) oxide are excellent microwave absorbers

in the temperature range investigated at the frequency of 2.45 GHz. The other additives,

silicon carbide**, nickel oxide*** and iron (II) oxide****, were admixed as powders into an

alumina sol and reduced to a solid. The yield of the sol was determined in two ways. In

the direct method, 200 milliliters of sol was dried and then heated to 12000C. This

temperature was above the crystallization temperature of the stable a-alumina phase. X-ray

diffraction analysis confirmed that the alpha phase was the only phase present in detectable

amounts. The resulting powder was weighed and had a mass of 5.08 grams. The yield of

the sols was also determined mathematically. Using the ratios of materials stated earlier,

calculations were made based on using 100 moles of water, one mol of ASB and 0.04

moles of aluminum nitrate. This would provide 1.04 moles of aluminum available for

oxide formation. This, in turn, would produce 0.52 moles of alumina which represents a

mass of 53 grams of alumina. By calculating the volume of the resulting sol, a yield of

0.026 grams of alumina per milliliter of sol was determined. For a 200 milliliter




*Fisher Chemicals # 1110-500 Fe(N03)3-9H20 F.W.
**Norton Company SiC E-85 Crystolon 220 grit F.W. 40.1
***Fisher Chemicals # N69-500 NiO F.W. 74.71
****Fisher Chemicals # 1119-500 FeO F.W. 231.54











Z'UU



S2200



s 2100
E
h 2045W5
2000 -


0 20 40 60 80 100
A1203 mol% Cr203 Cr203

Figure 3-1. Binary Cr203-A1203 phase diagram 12.
1600
Spinel ss Spinel s s
+
Hemotite ss Corundum s s
SpineSpine s

Fe20/ AI203
1400 -
0 ( Fe203-AI,20
Corundum s s
a) ff/ Fe2O03A1203

E Hematite ss + Fe20zA1203z ss
1200-

Hematite s s + Corundum s s




Fe203 20 Fez03-A2g03 60 80 AI203
wt.% A1203
Figure 3-2. Binary Fe203-A1203 phase diagram']3.











sol, this renders 5.12 grams of alumina -- a difference of less than one percent from the

experimentally determined value.

The powders were added to sols in a 1:1 molar ratio with the expected yield of

alumina. The mixture then was ultrasonicated for ten minutes to break up agglomerates.

The sol/powder mixture then was gently heated on a hot plate while stirring until much of

the liquid was removed. The resulting gel was heated overnight at 150 oC to remove most

of the remaining liquid. The end result was a solid mass of opaque material. This was

crushed in a mortar and pestle and sieved through a 325 mesh (44gm) screen. Using a 1.2

centimeter diameter steel die, 1.5 grams of each powder were pressed into pellets using a

13.3 kN force.

Sol-Gel Characterization

The gels produced were characterized using several diverse methods. The different

compositions of pellets were heated using microwave energy at 2.45 GHz to evaluate each

as a microwave absorber. Differential scanning calorimetry (DSC) was performed on the

various compositions with x-ray diffraction analysis conducted on the resulting material.

Dielectric properties of the different compositions were measured at 2.45 GHz as a function

of temperature.

Stand alone heating

A home-style microwave oven* was fitted with an on/off temperature controller.

An inconel-shielded, Type-K thermocouple was placed in contact with the specimen for

temperature measurement within the microwave. Refractory brick** was sculpted to

accommodate a specimen and a thermocouple feedthrough. The brick provides insulation

to reduce heat loss from the specimen during heating. The setup in Figure 3-3 has a



*General Electric 750 Watt Dual Wave II Microwave System
**Thermal Ceramics K-3000 3000F refractory brick






























sheath


Figure 3-3. Setup used to measure temperature of gel compositions heated solely by
microwaves (setup was placed in a microwave for heating).









70

maximum test temperature of 1175 C. Specimens were heated at full power (800 W)

using the setup in Figure 3-3. Temperature readings were taken periodically. Initial results

may have been influenced by arcing between the thermocouple and the specimen. Arcing is

the release of a charge build up between two points which can cause localized heating and

even melting of the thermocouple and the specimen. Another problem associated with

arcing is inaccurate, widely varied temperature readings. One way in which arcing was

reduced was by increasing the surface area of the tip of the thermocouple. In this case, a

thin nickel disk was placed between the thermocouple tip and the specimen. This

significantly reduced the amount of arcing encountered during the study.

Differential scanning calorimetry

Differential scanning calorimetry was performed on a Stanton Redcroft DSC

1500S. The gels were heated from room temperature to 14000C at ten degrees per minute

in flowing air. A second experiment was conducted on the sample containing FeO. This

time, the maximum temperature was 12500C in order to avoid any reactions that occur

above 12500C. A piece of sapphire, similar in mass to the sample powder, was used as a

reference material to maintain a level baseline.

X-ray diffraction analysis

The ceramic powders that resulted from heating in the DSC were subsequently

analyzed using a Scintag X-Ray Diffraction Analyzer. The x-rays were copper k-alpha at

45 kilovolts and 40 milliamps at a wavelength of 1.54060 angstroms. The powders were

scanned at one degree 20 per minute from twenty to sixty degrees 20. This 20 range was

sufficient to identify any of the compounds formed during heating that involved any of the

materials used.











Dielectric properties

The relative dielectric constant and loss factor, e', and e"eff, were measured for

several compositions of the dried powder at 2.45 GHz as a function of temperature.

Before analysis, the powders were heated to 4500C to remove all of the bound and

structural water. This was done to provide the instrument with a relatively constant mass

of material. The dielectric properties were measured from room temperature up to 14000C.

These measurements were performed at Chalk River Laboratories/Atomic Energy of

Canada, Ltd. using the cavity perturbation method*.

Alumina

The two purities of alumina used as an interlayer material were Coors AD94, 94%

alumina and Coors AD96, 96% alumina. The major impurities in all of the Coors alumina

products are silica, magnesia and calcia. These impurities act as fluxes for densification

and as grain-growth inhibitors. The manufacturer reports a room temperature flexure

strength for the AD94 of 350 MPa. The grain size ranges from 2-25 microns with an

average grain size of 12 microns. Other relevant properties of the alumina are in Table 3-1.

The interlayers were produced by cutting disks approximately 2 millimeters thick from a

cylindrical rod 2.54 0.0025 centimeters in diameter and 20.32 0.0025 centimeters long.

The disks were mounted on a glass plate and the surfaces were machined using a high

speed diamond grinding wheel*. The machining procedure used a downfeed of five

microns per pass and a crossfeed of 2.5 millimeters. The disks had a final thickness of 1.5

0.15 millimeters.






*R. Hutcheon AECL Chalk River Laboratories, Chalk River, Ontario, CA
**Norton ASD320-R75B99-1/4 320 grit wheel











Table 3-1. Manufacturer Reported Properties of Coors Alumina Used in Study.


+Coors Alumina and Beryllia Properties Handbook, Bulletin 952, Coors Ceramics, (1969)
Nickel Oxide

High-purity nickel oxide disks, hot pressed to >80% dense, were obtained from

Super Conductor Materials, Inc. The as-received disks were 2.5 centimeters in diameter

and 1.2 centimeters thick. The surface of the disks were impregnated with a graphite


Property Units AD-94+ AD-96+ AD-995+

Specific Gravity 3.62 3.72 3.84
Crystal range crowns 2-25 2-20 10-50
microns
Size average 12 11 20
Flexural 250C 350 359 310
MPa
Strength 10000C 140 172 230
Modulus of Elasticity GPa 282 303 358
Shear Modulus GPa 117 124 152
Bulk Modulus GPa 166 173 207
Poisson's Ratio 0.21 0.21 0.21
Maximum Use (no load)
TC 1700 1700 1,750
Temperature
Thermal 25C 18.0 18.0 31.4
Conductivity 100C 14.6 14.6 27.2
W/mK
4000C 7.1 7.1 11.7
8000C 4.2 4.2 7.1
Specific Heat 100C J/K(kg) 880 880 880

250C 8.9 8.9 9.4
Dielectric Constant 500C ratio 10.4
1 GHz 800C -- 11.0

250C 0.0008 0.0001 0.0001
Dielectric Loss 500C ratio 0.0002
Factor 1 GHz 8000C 0.0003

250C 0.007 0.001 0.001
Loss Tangent 5000C g"/g 0.002
(tan 8) 1 GHz 800C 0.003











residue from the manufacturing process. A low speed watering saw was used to section

the disks into thinner pieces. As with the alumina interlayer specimens, the nickel oxide

disks were mounted on a glass plate and machined to a thickness of 0.33 0.02

millimeters. All of the graphite was removed during the grinding step.

Surface roughness

The machined surfaces were characterized using a laser profilometer*. A 3-

dimensional scan was performed on a five millimeter by five millimeter square section of

the surface. A total of 250 line scans were performed on each material. The table speed

was 10 mm/minute. The average surface roughness was calculated from a single scan

using the same distance and table speed as the 3-dimensional scans. The roughness

reported is the deviation from the arithmetic mean and was calculated automatically from the

profiles using the equation


R, = l(x)dx. (3-1)


Figure 3-4 illustrates the arithmetic mean in a simulated profile and identifies the

components of equation 3-1 that are used to compute the surface roughness.

mean line





x
Ay m / a i R-






Figure 3-4. Simulated material profile depicting the arithmetic mean.


*Rodenstock RM-600 Laser Profilometer











Phase Two

Currently, there are no commercially available systems to perform the microwave

joining of ceramics. Therefore, an apparatus had to be designed and constructed to

accomplish this task. The modification of a microwave oven to accommodate the

application of pressure has many challenges associated with it. Turntables or fans used to

stir the microwave field may interfere with the application of pressure and must be removed

or repositioned. The external holes needed to apply a load on a specimen in the microwave

cavity are a breach of the microwave containment system and present a potential health

problem (see equation 2-5). Extreme care must be taken in the design and fabrication of the

joining apparatus to address these challenges and prevent them from hindering the joining

experiments.

There are several reasons why alumina was chosen as the material of interest for

this study. Alumina is one of the most widely used technical ceramics. It is prominent as a

substrate for electronic materials, as a refractory material, and as a structural ceramic.

Although alumina is not always the ideal material for the intended use, it is often chosen

because of its low cost. The thermal or mechanical properties of alumina are also

considered acceptable for many applications when the ideal material is either unavailable or

too costly. Alumina can be obtained in a multitude of purities, grades and sizes designed to

meet most of the needs of the technical community. Another predominant reason for

selecting alumina for this study is that it is a common material for testing and analysis.

There is an abundance of documentation available detailing its properties and performance

under widespread conditions. This includes the thermal, electrical, optical and mechanical

behavior upon exposure to elevated temperatures.

The end members considered for the joining experiments, 99.5% and 96% pure

alumina, are both poor microwave absorbers compared with the materials being surveyed









75

as potential interlayers. Without assistance, the end members are unable to heat to the

temperature required for joining using the microwave oven designated for this study.

Microwave hybrid heating, discussed in Chapter 2, is a logical approach to provide the

thermal energy for joining these end members. A microwave susceptor was used to

generate the radiant heat necessary to raise the temperature of the end members being joined

to a temperature where they could then more efficiently absorb microwaves. The susceptor

can be made from a number of materials, including those being examined as potential

interlayers. Design parameters that should be considered include the shape of the

workpiece being heated, the air gap desired between the workpiece and the susceptor, the

method in which the temperature of the workpiece will be measured, and most importantly,

the ability of the workpiece to absorb microwaves. This last factor will determine the

amount of microwave absorber needed in the susceptor to attain the desired temperature.

There are at least two methods of making susceptors. The first consists of fixing a

microwave absorbing material to a piece of low density insulation that has been shaped into

the desired configuration. This was simple to construct and works well for low

temperature applications. The second method involves casting a susceptor using a

refractory cement with granules of microwave absorbing material dispersed in it. This

method works very well at high temperatures. These susceptors tend to be more massive

than the first type and can shield very small specimens from the microwave field.

Microwave Joining Apparatus

The joining apparatus consisted of several components, each with a specific

function. To physically support the remaining components, a load frame, capable of

sustaining the maximum applied load, was machined from an aluminum alloy. A home

model microwave oven* was modified to facilitate the application of pressure and the


*Goldstar MA-1172M 1000 Watt microwave oven











monitoring and control of temperature. An air cylinder* capable of supplying a load of 2.2

kN was mounted on the top of the load frame. A load cell**, mounted in line with the air

cylinder, measured the load being applied. The feedback provided by the load cell in the

form of a voltage, was used to control the load applied by the air cylinder. An 18

millimeter diameter high-purity alumina rod was used to transfer the load into the

microwave cavity. A 20 millimeter feedthrough was machined in the top of the microwave

to provide the ram access to the cavity. The diameter of the hole was less than one-sixth

the wavelength of the microwaves used in this study. In Chapter 2, the critical hole

diameter for significant transmittal of microwaves was found to be one-half the wavelength

of the microwave. However, in this setup, there was a dielectric material (alumina push

rod, 'r = 9) partially filling the aperture in the wall of the microwave cavity. In this setup,

the dielectric material acts as an antenna for microwave propagation and the ability to

contain the microwaves was brought into question. To ensure a minimum transmittal of

microwave energy via the feedthrough, a 7.5 centimeter long copper tube of the same

diameter as the aperture was inserted into the feedthrough. The placement of an electrical

conductor tube prevents microwave leakage. Metallic tape was used to cover any other

gaps where microwaves might leak. The microwave's turntable was discarded and the

turntable motor was relocated to the side of the microwave opposite the wave guide. An

aluminum mode stirrer was attached to the motor to improve the uniformity of the field

within the microwave. Most of the operations performed during the joining process were

controlled by a computer program*** running on a Macintosh IIC. This included storing

the values of applied pressure and using this information to adjust the air cylinder. The


*Bellofram model # 900-009 500# air cylinder
**Revere Transducers model # 63HC-D3-500-10pl 500# load cell
**National Instruments Labview Version 2.0









77

computer was also used to store the temperature readings from two Type-R

thermocouples*. The two thermocouples were fed through an eight millimeter hole in the

back wall of the microwave cavity. A setpoint controller** was used to regulate the

maximum temperature during the process. The temperature controller was spliced into the

magnetron power supply so that the temperature could be regulated by turning the

magnetron on and off as necessary. Figure 3-5 is a schematic and figure 3-6 is a

photograph of the microwave joining setup.

Microwave Susceptors

In preliminary microwave hybrid heating experiments, D6114 heated alumina in a

microwave furnace using a commercially available susceptor***. These microwave

furnaces were simply a silicon carbide coating on a low density alumino-silicate refractory.

At temperatures near 15000C, both the silicon carbide coating and the refractory lining

experienced significant degradation. This led to a reduction in the furnace's ability to

absorb microwaves. Al-Assafi75 produced susceptors using a refractory with a lower

dielectric loss factor than the commercially available furnace. This enabled the maintenance

of temperatures of 15000C for one hour without destruction of the susceptor. These

susceptors proved sufficient for one experiment, but assembling a susceptor with a uniform

coating that maintained its microwave absorbing ability throughout a course of high-

temperature experiments was not feasible. It became necessary to seek an alternative

approach to microwave hybrid heating to provide a high-temperature, extended-use

susceptor. For this research, a mold of the desired susceptor was formed out of concentric




*ARi Inc. model # HIT-99N-4DR9AA-36 Type-R thermocouple
**Omega model # CN9000A Miniature Autotune Temperature Controller
**National Superconductor Microwave Glass Melter











air cylinder


HKtl I


temperature controller
Figure 3-5. Schematic of the microwave joining apparatus.


airresuM
boosterj






















































Figure 3-6. Photograph of the microwave joining apparatus used in all of the microwave
joining experiments.











polypropylene cylinders. High alumina content cement* was mixed with silicon carbide

granules and enough water to make a slurry. This was cast into the mold and allowed to

set. The process for forming the susceptor is outlined in figure 3-7. The polypropylene

rings were removed and the cement/SiC cylinder was cured by slowly heating it in a

conventional furnace to 1000 'C for one hour. After cooling, the susceptor was ready to

use.

The amount of cement and silicon carbide was varied to determine the amount of

silicon carbide that would absorb the appropriate amount of microwaves to provide the

desired thermal environment for the joining process. This was done systematically by

mixing the cement and silicon carbide in different ratios. Silicon carbide granules were

added in amounts of 5, 10, 20, and 30 volume percent of the cement. The volumes were

determined using the density of alumina to approximate the density of the cement (96%

alumina) and the density of silicon carbide. Enough water was added to make the mixture

castable. The cylinders were all approximately 300 grams. All of the cylinders were cured

as described earlier.

To determine the ability of the cylinders to heat, they were insulated as shown in

figure 3-8, placed in a microwave oven and heated using 3200 watts of power. The

temperature was measured in both the center of the suscepting cylinder and outside of the

refractory wall using Type-K thermocouples shielded from the microwaves by a inconel

sheath. The dielectric properties of the cylinders as a function of temperature were

measured at AECL using the cavity perturbation method.

The susceptor used for the joining process was similar to those used in the

susceptor evaluation experiments. A 36 volume percent loading of silicon carbide was

used in the susceptor. Two 4 millimeter in diameter hollow alumina tubes were fixed in


*Alcoa Al-66 97% A1203 3% CaO




Full Text

PAGE 1

THEORY AND APPLICATION OF MICROWAVE JOINING By ALEX DOUGLAS COZZI A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS F OR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 1996 UNIVERTY or FLORIO~ \J\311 RIES

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Copyright 1996 by Alex Douglas Cozzi

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I would like to d e dicate thi s dissertation to my father Thomas. My only regret is that you could not s ee me graduate.

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ACKNOWLEDGEMENTS The author would like to thank a number of people for their professional suggestions and personal support towards this study. First I would like to thank Dr. David Clark who not only showed me how to be a better scientist, but how to be a better person. His guidance and constant reassurance allowed me to complete the graduate program. I would like to express special thanks to Dr. Matt Ferber of Oak Ridge National Labs for taking the time to provide assistance and guidance even though he is extremely busy with many other projects. I would like to also thank Drs. J.J. Mecholsky, B.V. Sankar, R.J. Singh, E. D. Whitney and V.J. Tennery for their comments and suggestions that increased the technical value of this study I wish to thank Dr. Ron Hutcheon of the Atomic Energy of Canada Ltd., Chalk River Laboratories for providing essential dielectric data and insight into the meaning of that data. The author appreciates the assistance of the administrative and technical staff of the High Temperature Materials Laboratory at Oak Ridge National Labs, especially Arvid Pasto and Billie Russell, the ringleaders of the HTML Fellowship program. I would like to thank the members of Dr. Ferber's research group, Kristin Breder, Jason Canon, Dana Green, Allen Haynes, Tim Kirkland, Edgar Lara-Curzio, Ron Ott, Laura Riester and Andy W ereszczak. I would like to also thank Mark Janney and Jim Kiggans for providing me with all the materials and assistance they could spare. I would like to convey special thanks to Diane Folz and Rebecca Lynn Shulz for both their professional help and friendship throughout my stay at the University of Florida. I would like to also thank all of the past and present members in Dr. Clark's research lV

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group, my peers in the Department of Materials Science and Engineering, Iftikhar Ahmad,Salwan Al-Assafi, Attapon Boonyapiwat, Robert Dalton, Arindam De, Robert DiFiore, Zak Fathi Carl Jones, Don Jones, Michelle Lococo, Edmund Moore, Lorie Stapler and Bruce Zoitos. I would like to convey special thanks to my friends, especially Philip McCluskey, Andrew Duncan, Mark Weaver, Chris O'Gara, Lisa Demmy and George Demmy. I would like to express particular thanks to my family, my parent's Thomas and Lillian, my sister Dianne, my brothers Tommy and Alan as well as their families for their emotional and financial support through eight long years of graduate school. Finally, I would like to acknowledge my wife, Sunday, who a l ong with my family believed in me when even I wasn't so sure. She watched me through the highs and lows of this study, tried tirelessly to keep me focused on the goal and provided love and support without which this study could not have been performed. This research was sponsored by the Assistant Secretary for Energy Efficiency and Renewable Energy, Office of Transportation Technologies, as part of the High Temperature Materials Laboratory Fellowship Program, Oak Ridge National Laboratory, managed by Lockheed Martin Energy Research Corp. for the U.S. Department of Energy under contract number DE-AC05-960R22464. V

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TABLE OF CONTENTS ACKNOWLEDGEMENTS . ...... . ... . .. .. ... .. . .......... . lV LIST OFT ABLES . . . . . . . . . . . . . . . . . . . . . . . ix LIST OF FIGURES .................................... .. ..... X1 ABSTRACT CHAPTERS XlX 1 INTRODUCTION . . . . . . . . . . . . . . . . . 1 2 SUR VEY OF THE LI I'ERA TURE . . . . . . . . . . . . 7 Microwave s . . . . . . . . . . . . . . . . . 7 Background . . . . . . . . . . . . . . 7 Microwave Applicator s . . . . . . . . . . 12 Microwave Proce ss ing of Material s . . . . . . 16 Numerical Modeling of Microwave / Mat e rial Int erac tions . . . . . . . . . . . . 17 Evidence of Microwave Enhancements . . . . . 26 Joinin g . . . . . . . . . . . . . . . . . . 28 Joinin g Methods . . . . . . . . . . . . . 28 Joining proce sses . . . . . . . . . . 3 2 Criteria for Joining . . . . . . . . . . . . 3 5 Effect of Pro cess Variable s on Joining . . . . . 38 Temperature . . . . . . . . . . . . 3 8 Pressure . . . . . . . . . . . . 41 Time .... . ....................... 41 Reaction s . . . . . . . . . . . . 44 S c al es of Joining . . . . . . . . . . . . . 44 AtoID.i.c . . . . . . . . . . . . . 44 Nano . . . . . . . . . . . . . . 46 Micro . . . . . . . . . . . . . . 4 9 Ma c ro . . . . . . . . . . . . . . 50 Materi a l s Joining . . . . . . . . . . . . . 50 Metal/ceramic joining . . . . . . . . . 51 CeraID.i.c/ceraID.i.c . . . . . . . . . . 52 .Mi.crow ave Joining . . . . . . . . . . . . 5 3 SummaTy" . . . . . . . . . . . . . . . . . . 60 3 MATERIALS AND METHODS . . . . . . . . . . . . . 62 Ph ase One . . . . . . . . . . . . . . . . . 63 V l

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Sol-Gel . . . . . . . . . . . . . . . . 64 Ba se gel . . . . . . . . . . . . . 64 Doped gel . . . . . . . . . . . . 65 Sol-Gel Characterizat i on . . . . . . . . . . 68 Stand alone heating . . . . . . . . . 68 D ifferential sc anning calo 1im etry . . . . . 7 0 X ray diffraction analysi s . . . . . . . 7 0 Diele c tric prop e rties . . . . . . . . . 71 AlUini.na . . . . . . . . . . . . . . . 7 1 Ni c kel Oxide . . . . . . . . . . . 72 Surf ace roughne ss . . . . . . . . . 73 Pha se Two . . . . . . . . . . . . . . . . . 7 4 Microwave Joining Apparatus . . . . . . . . 75 Microwave Susceptor s . . . . . . . . . . . 77 Specimen Pr eparation . . . . . . . . . . . 86 Mechanical Te s ting . . . . . . . . . . . . 87 Pha se Three . . . . . . . . . . . . . . . . . 90 Micr o wave J oining . . . . . . . . . . . . 91 Conventional Joinin g . . . . . . . . . . . 93 Optical In spec tion . . . . . . . . . . . . 93 Stati stic al Analysi s . . . . . . . . . . . . 94 Ph ase Four . . . . . . . . . . . . . . . . . 95 4 NUME RI CAL MODELING . . . . . . . . . . . . . . 96 Heat Tran sf er . . . . . . . . . . . . . . . . 97 Transi e nt Heat Conduction . . . . . . . . . . . 101 Boundary Condition s . . . . . . . . . . . . . 103 Th e Phy sic al Mod e l . . . . . . . . . . . . . . 105 Case Title . . . . . . . . . . . . . . 105 General Problem Parameters . . . . . . . . 106 R egion Data . . . . . . . . . . . . . . 106 Material s . . . . . . . . . . . . . . . 10 7 Initial Temp e ratur e . . . . . . . . . . . 109 Heat Generation . . . . . . . . . . . . 109 Boundary Condition s . . . . . . . . . . . 110 Grids . . . . . . . . . . . . . . . . . . 112 Analytical Functions . . . . . . . . . . . . . 113 Specific heat . . . . . . . . . . . . . . 114 Ther1nal conductivity . . . . . . . . . . . 114 Power generation . . . . . . . . . . . . 114 Boundary condition . . . . . . . . . . . 123 Tabular Fun c tion s . . . . . . . . . . . . . . 123 Thermal conductivity . . . . . . . . . . . 1 26 Printout Time s . . . . . . . . . . . . . . . 12 7 Nodes Monitored . . . . . . . . . . . . . . 128 Tran sie nt Data . . . . . . . . . . . . . . . . 128 5 RESULTS . . . . . . . . . . . . . . . . . . . 13 7 Ma c hined Surf aces . . . . . . . . . . . . . . 1 37 Sol -Ge l Interlayer s . . . . . . . . . . . . . . 137 Stand Alone Heating . . . . . . . . . . . 137 vu

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Diff e rential Scanning Calorimetry . . . . . . X ray Diffraction Analy s i s . . . . . . . . . Diel ec tric Me as ur e ment s . . . . . . . . . . Mi c row ave Susceptors . . . . . . . . . . . . . J oini n g . . . . . . . . . . . . . . . . . . Joinin g Conditions .. ........ .... ..... Vi s ual In s pection ................. .... . Flexure Te s tin g .. . ... .. ...... ....... Stati s tical Analysis . . . . . . . . . . . Num erical M o d e ling . . . . . . . . . . . .... 143 145 147 153 160 160 160 163 184 203 6 DISCUSSION . . . . . . . . . . . . . . . . . . 217 7 8 APPENDICES s Ph ase One . . . . . . . . . . . . . . . . . 2 17 Machined Surf aces . . . . . . . . . . . 217 S o l-G e llnterlayer s . ........ .. .. .. .... 218 Summary of Pha se One . . . . . . . . . . 221 Pha se Two . . . . . . . . . . . . . . . . . 223 Microwave Su sce ptor s . . . . . . . . . . 223 Microwave Joining Apparatus . . . . . . . . 224 Summary of Pha se Two . . . . . . . . . . 224 Pha se Three . . . . . . . . . . . . . . . . 225 Experimental Design . . . . . . . . . . . 225 Joining Experiments and Flexure Tests . . . . . . . . . . . . . 226 Sta ti s ti cal Analy s i s . . . . . . . . . . . 229 Summary of Phase Three . . . . . . . . . 231 Pha se Four . . . . . . . . . . . . . . . . . 231 Computer Simulation s . . . . . . . . . . 232 Summary of Pha se Four . . . . . . . . . . 234 Y AND CONCLUSIONS . . . . . . . . . . 23 5 FUTURE WORK 241 A SAMPLE CALCULATIONS OF THE PENETRATION DEPTH AND CRITICAL TIDCKNESS FOR Al-66 CEMENT . . . . . . . . 243 B s Y OF INPUT DATA FOR HEATING 7.2 24 5 C SAMPLE CALCULATIONS FOR STATISTICAL ANALYSIS . . . . . . . . . . . . . . . . 251 REFERENCES . . . . . . . . . . . . . . . . . . . . . . . 25 5 BIOGRAPHICAL SKETCH . . . . . . . . . . . . . . . . . . 263 Vlll

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Table 2-1. Table 3-1. Table 3-2. Table 3-3. Table 4-1. Table 4-2 Table 4 -3. Table 4-4. Table 4-5. Table 4-6. Table 4-7. Table 4-8 Table 5-1. Table 5-2. Table 5-3 Table 5-4. LIST OF TABLES Error A ss ociated with Simplified Equation for Penetration Depth for Several 11 eff/ 1 Ratios. . . . . . . . . . . . . . . . 11 Manufacturer Reported Properties of Coors Alumina Used in Study. . . . . . . . 72 Level s of Varied Proce ss ing Conditions. . . . . . . . . . . 91 Experimental Design u se d to Aid in Determining the Effect of Proce ss ing Conditions on the Strength of the Joint. . . . . . . 92 Summary of the Parameter Cards Used to Describe the Nine Model Regions . . . . . . . . . . . . . . . . . . . . 108 Input Parameters for the Four Materials Represented in the Model. . 109 Heat Generation Card s for the Four Materials in the Model. 110 Table of the Gro ss and Fine Grid Lines for Both the r and z Axe s. . 113 Thermal Conductivity of Coors AD995 Alumina at Different Temperature s. . . . . . . . . . . . . . . . . . . 126 Thermal Conductivity of the Nickel Oxide Used in the Model at Different Temperatures . . . . . . . . . . . . . . . 126 Calculated Values for the Thermal Conductivity of a 30 wt. % SiC/Cement Su s ceptor . . . . . . . . . . . . . . . . 127 Node s of Intere s t and Their Placement in the Model. . . . . . 130 Flexure Strength of AD995 Alumina Joined Under Variou s Conditions Using Several Different Interlayer Materials . . . . . 163 Mean Strength and Standard Deviation of Bars Joined by either Microwave or Conventional Heating. . . . . . . . . . . 169 Data Used to Perform ANOV A Analysis. . . . . . . . . . 192 Output of Statistical Analy s is of Data from Table 5-3 193 IX

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Table 5-5. Table 5 6 Statistical Analy s i s of the Effect of Bar Po s ition on the Flexure Strength for both Microwave and Conventional Heating . . . . 199 Effect of Po s ition/Heating Method Interaction on the Flexure Strength. . . . . . . . . . . . . . . . . . . . . 203 X

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LIST OF FIGURES Figure 1-1. Schematic depicting the inter s ection of two fields of modeling to form a basis for research. . . . . . . . . . . . . . . . 5 Figure 2-1. Representation of the lag in the current that determines the loss tangent . . . . . . . . . . . . . . . . . . . . . 10 Figure 2-2. R a tio of tran s mitted to incident field for aperture diameter, o. 05 < d/'A < 1 . . . . . . . . . . . . . . . . . . . 15 Figure 2-3. Radial temperature proftle s in a cylindrical roast beef. . . . . . 2 0 Figure 2-4. Temperature of br ea d heated with two different field strengths. . . 21 Figure 2-5. Effect of variable (-) ver s us constant(---) dielectric propertie s on temperature in a raw beef s ample. Depth in sample refers to fraction of who l e. . . . . . . . . . . . . . . . . . . . . 22 Figure 2-6. Mea s ured and computed temperatures for the specimen and the in s ulation durin g a microwave s intering run . . . . . . . . . 24 Figure 27. The ac tivation e nergy for 180 diffusion in s apphire meastrred using b o th conventional and mi c rowave heating. . . . . . . . . . 27 Figure 2-8. Diffu s ion of potas s ium in sodi um aluminosilicate glass u s ing conventional heating and two different microwave power levels at a temperature of 450 C for 30 minutes . . . . . . . . . . . 29 Figure 2-9. Sketche s of a ) Typical setup used for joining ceramics in a hot press and b ) ceramic shapes commonly joined in a hot press. . . . . . 34 Figure 2-10. Schematic s howin g the s ix mechanisms of mass transfer that can lead to joinin g; a ) sur face sources, b ) bonding interface so urce s c) bulk deformation after yield or during creep. . . . . . . . . 36 Figure 2-11. Contact area of a) textured surface and b) smooth surface. Contact area in a ) i s greater than in b ) when the ex ternal dimension is the sa me . . . . . . . . . . . . . . . . . . . . . . 37 Figure 2-12. Effect of s urface rou g hne ss (as described in equation 3-1 and figure 3-4) on sa mple strength. . . . . . . . . . . . . . . . 39 Figure 2-13. Effect of joining temperature on the s trength of a joint . . . . . . 40 X1

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Figure 2-14 The effect of pres s ure applied during joining on the s trength of the jo i nt . . . . . . . . . . . . . . . . . . . . . . 42 Figure 2-15 The effect of joinin g time on the strength of the joint . . . . . . 43 Figure 2-16. Graphic repre se ntation of the four s cales of joining di s cussed in the te xt. . . . . . . . . . . . . . . . . . . . . . . 45 Figure 2-17. Energy versus se par a tion for two ion s in proximity to each other. . 47 Figure 2-18. Force ver s u s se paration for the two ions in figure 2-17. . . . . . 47 Figure 2-19. Computer derived relaxed sttucture of the BaO/NiO interface . . . 48 Figure 2-20. Effect of joining temperature on the s trength of 92 % alumina. . . . 55 Figure 2-21. Th e effect of joinin g time on bend s trength of silicon nitride . . . . 56 Figure 2-22. Knoop hardn ess across joint for microwave joined alumina. . . . 57 Figure 2-23 A co u s tic emission trace s for a mullite joining experiment. . . . . 58 Figure 3-1. Binary Cr 2 0 3Al 2 0 3 phase diagram. . . . . . . . . . . . 67 Figure 3-2. Binary Fe 2 0 3Al 2 0 3 phase diagram . . . . . . . . . . . . 67 Figure 3-3. S e tup u se d to measure temperature of gel compo s itions heated so lely by microwave s (s etup was placed in a microwave for heating). . . 69 Figure 3-4. Simulated material profi l e depicting the arithmetic mean . . . . . 73 Figure 3-5. S c h e mati c of the microwave joining apparatus. . . . . . . . . 7 8 Figure 3-6. Ph otog raph of the mi c rowave joining apparatu s used in all of th e microwave joining experiments . . . . . . . . . . . . . 79 Figure 37. Flowchart u se d to produce s usceptors for microwave joining . . . 81 Figur e 3-8. Cutaway view of the s etup u s ed to evaluate the heating ability of susceptors. . . . . . . . . . . . . . . . . . . . . 8 2 Figure 3-9. Schematic of the s pecimen/ s u sc eptor se tup used in the microwave joining experiments. . . . . . . . . . . . . . . . . . 84 Figure 3-10. Photograph of s usceptor set up inside the microwave cavity. . . . 85 Figure 3-11. Flow diagram of the microwave joining process and s pecimen preparation. . . . . . . . . . . . . . . . . . . . 88 X1l

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Figure 3-12. Flexure fixture for room temperature testing of bars using four-point bending. a ) schemat ic of flexure rig and b) label s of relevant dimensions. . . . . . . . . . . . . . . . . . . . 89 Figure 4-1. Grid structure s urrounding node o, the node of interest . . . . . 99 Figure 4-2. Two dimensional grid structure using the r-z coordinate axes. . . . 99 Figure 4-3. Model u s ed for the sim ulation of microwave hybrid heating . . . 100 Figure 4-4. Time-temperature coordi nates involved in the Crank-Nicolson equation The trapezoid connects the time-position values used to calculate temperature values at the point indicated, 0 . . . . . . 102 Figure 4-5. Logarithmic fit to data for the specific beat of alumina . . . . . 115 Figure 4-6 Linear fit for the specific heat of nickel oxide. . . . . . . . . 116 Figure 47 Polynomial fit to thermal conductivity of insulating fiber board. . . 117 Figure 4-8 Temperature of water as a function of time. 119 Figure 4-9 Power absorbed ( calculated) as a function of temperature for AD995 alumina . . . . . . . . . . . . . . . . . . . . . 121 Figu1 e 4-10 Power absorbed (c alculated) as a function of temperature for nickel oxide. . . . . . . . . . . . . . . . . . . . . . 122 Figure 4-11. Power ab s orbed ( calcu lated ) as a function of temperature for the 30 vol. o/o SiC susceptor. . . . . . . . . . . . . . . . 124 Figure 4-12. Curve fit for the emi ss ivity of alumina as a function of temperature. 125 Figure 4-13. Sample input to calculate a beating proftle of the model in figure 4-4. 129 Figure 4-14. Map of node numbers for the input file in figure 4-13. Geometry corresponds to the model in figure 4-3 The nodes that represent thermocouple locations are 328 (inter l ayer) and 423 (bulk). The pyrometer is represented by node 328. . . . . . . . . . . 131 Figure 4-15. Temperature profiles for simulated microwave hybrid heating generated using the input in figure 4-13. a) 10 minutes; b ) 20 minutes; c ) 30 minutes; d ) 40 minutes; e) 50 minutes. . . . . . 132 Figure 5-1. Area of the s urf ace of alumina end member used for roughne s s analysis. . . . . . . . . . . . . . . .. . . . . . 138 Xlll

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Figure 5 -2. Profile of 5 mm x 5 mm area of alumina from figure 5 1 analyzed u s ing a laser profilometer Light region s correspond to the area above mean peak height and darker regions correspond to area below mean peak h e ight . . . . . . . . . . . . . . . 139 Figure 5-3 Area of the su1iace of nickel oxide interlayer used for roughne ss analysis. . . . . . . . . . . . . . . . . . . . . 140 Figure 5-4 Profile of 5 mm x 5 mm area of nick e l oxide from figur e 5 -3 analyzed u s in g a la ser profilometer. Light regions correspond to the area above m ea n peak height and darker region s correspond to area b e low m ea n p eak height . . . . . . . . . . . . . . . 141 Figure 5 5 T em per a ture of the potential interlayer material s heated using s tand alone mi c rowave he a ting . . . . . . . . . . . . . . . 142 Figur e 5-6 Differential Scannin g Calorimetry ( DSC ) of the base gel, alone and with additives. . . . . . . . . . . . . . . . . . . 144 Figur e 5 -7. X-ray Diffraction Analysi s ( XRD ) of powders s ynthe s ized during DSC analy s i s Spe c imen s containing iron compounds exhibited spect ra with r e duced inten s itie s. This i s mo s t likely due to the fluore s cence of iron from Cu k-alpha radiation. Fluore s cence tend s to r e duce peak/background ratio s. . . . . . . . . . . . . 146 Figure 5 8 Dielectric constant versu s temperature of potential interlayer material s. Me as ured at 2.46 GHz. . . . . . . . . . . . 148 Figure 5-9. Di e lectric con s tants measured at 2 46 GHz plotted without the iron (III) oxide composition. . . . . . . . . . . . . . . . 149 Figur e 5 10. Di e l ec tri c l oss factor, mea sured at 2.46 GHz versus temperature for potential interlay e r m a terial s. . . . . . . . . . . . . . 150 Figure 5 11. Di e lectri c lo ss factors plotted without the iron ( III ) oxide and nickel oxide compo s ition s. Mea s ured at 2.46 GHz . . . . . . . . 151 Figure 5-12 Lo ss tangent, mea s ured at 2.46 GHz versus temperature for p ote ntial interlayer material s. . . . . . . . . . . . . . 15 2 Figure 5-13. Lo ss tangent s plotted without iron ( ID) oxide and nickel oxide compositions. Mea s ured at 2.46 GHz. . . . . . . . . . . 154 Figme 5 14 T e mperature of alumina load in s ilicon carbide/alumina cement s u sce ptor s heat ed u s ing 3 .2 KW with a 75o/o duty cycle (% time on). . . . . . . . . . . . . . . . . . . . . . . 155 Figur e 5-15 Dielectri c constant, measured at 2.46 GHz versus temperature for seve ral compo s ition s of s usceptor s. . . . . . . . . . . . 156 XlV

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Figure 5-16. Dielectric loss factor, measured at 2.46 GHz, versus temperature for several compositions of susceptors. The minimum in the loss factor, associated with some types of silicon carbide, has yet to be explained. . . . . . . . . . . . . . . . . . . . 157 Figure 5-17. Los s tangent for sever al susceptor compositions at 2 46 GHz. . . 158 Figure 5-18 Temperature of s u sce ptor s as a function of silicon carbide content. . 159 Figure 5-19. Microwave processing conditions for trial #6 ( 1450 C; 45 min; 3 MP a; nickel oxide interlayer). . . . . . . . . . . . . . 161 Figure 5-20. Conventional processing conditions for trial #11 (1550C; 15 min; 1 MPa; nickel oxide interlayer). . . . . . . . . . . . . . 162 Figure 5-21. Fracture s urfa ces of specimens from trial #4 ( 45 min; 1550 C; 1 MPa; nickel oxide interlayer; microwave heated). . . . . . . 164 Figure 5-22. Fracture surfaces of specimens from trial #6 (45 min ; 1450 C; 3 MPa ; nickel oxide interlayer; microwave heated). . . . . . . 165 Figure 5-23. Fractl1re surfaces of a flexure bar joined using a gel-derived (4 mol o/o Cr203) interlayer. . . . . . . . . . . . . . . . 166 Figure 5-24. Mean flexure s trength of bars for each of the trials in the experimental de s ign. Error bars correspond to one standard deviation. . . . . . . . . . . . . . . . . . . ... 168 Figure 5-25 Fracture surface of specimen from trial #12, representative of all the specimens joined using AD94 alumina as the interlayer material. . 170 Figure 5-26. Joint line between AD94 alumina interlayer and AD995 alumina end member (250x). Trial #14 (45 min/1450 C/3 MPa/C/AD94). . . 171 Figure 5-27. Micrograph of joint region in figure 5-26 showing porosity and grain boundary material (20,000x). . . . . . . . . . . . 172 Figure 5-28. Intact interlayer material in bar that fractured away from the joint area. Trial #15 ( 15 min/1550C/3 MPa/C/AD94). . . . . . . 173 Figu1e 5-29 Joint region of bar from trial #15, flexure s trength 220 MPa (250x). Trial #8 ( 45 min/1550 C/3 MPa/M/AD94). . . . . . . . . . 175 Figure 5-30. Magnified micrograph of the joint line in figure 5-29 (20,000x). . 176 Figure 5-31. Joint area of a bar microwave joined in trial #3 (15 min/1550 C/ 1 MPa/M/AD94) ( 6,000x ) a) micrograph and b) WDS x-ray map of silicon. . . . . . . . . . . . . . . . . . . . . 177 xv

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Figure 5-32. Joint area of a bar conventionally joined in trial #15 (15 min/1550 C/3 MPa/C/AD94) (6,0 00x ) a) micrograph and b) WDS x-ray map of silicon. . . . . . . . . . . . . . . . . 178 Figure 5-33 Joint area of a bar microwave joined in trial #2 (45 min/1450 C/l MPa/M/AD94) (6,000x). a ) micrograph and b) WDS x-ray map of s ilicon. . . . . . . . . . . . . . . . . . . . . 179 Figure 5-34. Joint area of a bar microwave joined in trial #8 ( 45 min/1550 C/3 MPa/M/AD94 ) (6, 000x ) a ) micrograph and b) WDS x-ray map of silicon. . . . . . . . . . . . . . . . . . . . . 180 Figure 53 5 Matching fractlrre surface of bar joined with a nickel oxide interlayer th a t failed before flexure testing. Compare to Figures 5-36 and 537. Trial #11 ( 15 min/1550 C/1 MPa/C/NiO). . . . . . . . 181 Figure 5-36. Matching fracture surfaces of bar joined with a nickel oxide interlayer with a flexure strength of 38 MPa Trial #11 (15 min/1550C/1 MPa/C/NiO ). . . . . . . . . . . . . . . 182 Figure 5-37. Matching fracture s urfaces of bar joined with a nickel oxide interlayer with a flexure s trength of 45 MPa. Texture difference is due to slow crack growt h from controlled loading (slow rate) Trial #11 (15 min/1550 C / 1 MPa/C/NiO). . . . . . . . . . . . 183 Figure 5-38 Micrograph of joint region of bar from figure 5 -3 5 joined with a nickel oxide interlayer (2,000x). Flexure s trength O MPa. . . . 185 Figure 5 39 Micrograph of joint region of bar from figure 5-35 joined with a nickel oxide interlayer ( 5,000x) Flexure strength O MPa. . . . 186 Figure 5-40 Micrograph of joint region of bar from figure 5-37 joined with a nickel oxide interlayer ( l ,OOOx). Flexure strength 45 MPa. . . . 187 Figure 5-41. Mi c rograph of joint region of bar from figure 5-37 joined with a nickel oxide interl aye r ( 5 000x ) Flexure strength 45 MPa. . . . 188 Figure 5-42. Roughne ss of joined surface ( trial #8 ) calculated from micrograph taken at 500x. . . . . . . . . . . . . . . . . . . 189 Figure 5 43. Roughnes s of joined surface (trial #12) calculated from micrograph taken at 5 OOx . . . . . . . . . . . . . . . . . . . 190 Figure 5-44. Roughnes s of as-machined surface calculated from micrograph taken at 500x. . . . . . . . . . . . . . . . . . . 191 Figure 5-45 Effect of time on the flexure strength of joined bars. Figure 5-46. Effect of temperature on the flexure strength of joined bar s Figure 5-47. Effect of pre ss ure on the flexure strength of joined bars XVI 194 195 196

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Figure 5 48 Effect of the heating method on the flexure strength of joined bar s. . 197 Figur e 5 49 Effect of the interlayer material on the flexure strength of joined bar s . . . . . . . . . . . . . . . . . . . . . . 19 8 Figure 5 50. Effect of the heating method on the flexure s trength of joined bar s plotted with error bar s at the 90o/o confidence interval . . . . . 200 Figure 5-51. Map of original bar po s ition s in the joined cylinder before hi m ac n1ng. ..................... .. ... ... .. ..... 201 Figure 5-52 Interaction chart s howing the combined effect of the po si tion of the bar and the heating method on the flexure strength. . . . . . . 202 Figure 5-53. Temperature of th e workpiece mea s ured u s ing a th e rmo c ouple and an optical pyrometer . . . . . . . . . . . . . . . . 205 Figure 5 54. Variation in temperature of the workpiece between the ther1nocouple and th e optical pyromet e r . . . . . . . . . . . . . . . 2 06 Figure 5-55 Temperature of the s u sc eptor mea s ured using both a thermocouple and an optical pyrometer . . . . . . . . . . . . . . . 207 Figure 5-56. Variation in temperature of the susceptor between the the11nocouple and the optical pyrometer. . . . . . . . . . . . . . . 208 Figure 5-5 7. Temperature (c alcul ate d and m eas ured ) at the s urfa c e of the AD94 interlayer . . . . . . . . . . . . . . . . . . . . 209 Figur e 5 58 Temperature (c alculated and measured ) at the surface of the NiO interlayer . . . . . . . . . . . . . . . . . . . . 210 Figure 5-59. T e mperature ( calculated) at the s urface of the joint region for variou s heating conditions. . . . . . . . . . . . . . . . . . 211 Figu1 e 5-60 Temperature ( calculated) at the surface of the end member for various heating conditions . . . . . . . . . . . . . . 213 Figu1e 5 61 T empe rature ( ca l culated) at th e s urface of the joint region ( AD94 ) and end member ( AD99 5 ) . . . . . . . . . . . . . . 214 Figure 5-6 2. Temperature (c alculat e d ) at the surface of the joint region (NiO ) and end member ( AD995 ). . . . . . . . . . . . . . . . 215 Figure 5-6 3. Comparison of calculated temperature s for s pecimen s heated with nickel oxide interlayers of different thickness. . . . . . . . . 216 Figure 6-1. Pha se diagram of the FeO Al 2 0 3 system. . . . . . . . . . 220 XVll

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Figure 6-2 Qualitative repre s entation of the effect of temperature on the dielectric loss factor of a typical dielectric material Tc refer s to the critical temperature at which the efficiency of the absorption of microwaves increa s e s dramatically . . . . . . . . . . . . 222 XVlll

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Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy THEORY AND APPLICATION OF MICROWAVE JOINING By ALEX DOUGLAS COZZI August 1996 Chairperson: Dr. David E. Clark Major Department: Materials Science and Engineering Microwave processing of materials is advancing from a novel processing technique into a viable method for processing industrial materials It has been adopted by several industries for the following reason s Microwave processing can afford savings in energy or space or, more importantly, it can provide a product with qualities that cannot be achieved through conventional means. Even as the use of microwave processing increases in industry it is vigorously investigated by researchers attempting to better understand and control the mechanisms that are re s ponsible for microwave heating of materials These investigators are see king evidence that can either demonstrate or disprove the concept of enhanced microwave processing. Simultaneously, researchers also are looking for innovative techniques that can provide other industrial applications for microwaves Joining ha s always been an integral component of the manufacturing industry. The joint is often the weakest link of any manufactured item and researchers are continually pursuing means of increasing the strength of the joint. Several ceramics have been joined successfully using microwave energy. However, there are no proce ss ing guidelines available so the data that have been generated cannot be easily compared. Furthermore, X1X

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much of the previous work reports the condition of the joint qualitatively, making comparisons of joining procedures nearly impossible. The research performed in this study attempts to address many of the issues discussed above. The main goal of this research is to join alumina using microwave energy and to develop an understanding of the microwave interactions with materials and its relation to the joining process. An apparatus for the microwave joining of materials was designed and pu into use. A procedure for producing susceptors for microwave hybrid heating was developed. Using the microwave joining apparatus and hybrid heating, high-purity alumina was joined using several materials as the interlayer between the alumina end members. An experimental design was used to provide data that then could be analyzed statistically to deter 1nine the significance of the processing parameters varied during joining. A numerical model simulated the microwave heating of the joining process. Simulated temperature profiles were compared to experimentally measured temperatures to assess the usefulness of the model. xx

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CHAPTERI INTRODUCTION Joining is an important s tep in the construction of engineering structures. This may seem obvious when one thinks about the erection of a building or the assembly of an automobile. However, joining is also a vital process in the formation of many of the components that are later joined to produce these buildings and automobiles. The joining process also extends beyond mechanical joint s formed through the use of fasteners such as bolts, nails and clamps. A remarkable number of products contain components that are joined through chemical reaction s. While it is often preferable to fabricate the components that are used to assemble products in one piece, it is not always possible or even the prescribed method for manufacturing the desired shape. This is most apparent when the final product consists of more than one material. Some of the newer types of cookware consist of a piece of stainless steel sandwiched between two aluminum sheets. The stainless steel provides a high heat capacity base needed for stove top cooking, while the aluminum contributes a high thermal conductivity for even heating Another example where joining is the preferred method of manufacture is when the piece consists of a complex shape that would require either a complicated mold or extensive machining. Joining can also be useful when a comp1essive s tre ss i s added to increase the s trength of the component. This effect is observed when glaze is fired on a ceramic piece with a lower coefficient of thermal expansion than the glaze. When the product cools, the glaze will contract more and be put under a compressive stress. 1

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2 All type s of materials--ceramics, metals and polymers--have been joined to one another for a multitude of application s. The applications that entail the joining of ceramics are extensive. Th e mo s t common joint involving ceramics i s a ceramic to metal joint. The se types of joint s ar e used in light bulb s to connect the metal base to the glass tube and also in s park plug s, to attach the metal core to the ceramic sheath. Ceramic/metal joint s are created in the enameling of hou se hold appliances such as washing machine s and dishwashers The enamel coating on the steel housing not only increases the aesthetic value of the appliance, but also serves as a ru s t-re s i s tant coating on the steel. While the ceramic/ceramic joint i s somewhat le ss pr eva lent than th e ceramic to metal joint it plays an important role in the traditional cerami c indu s trie s. Two of the most widely u s ed example s of ceramic/ceramic joints are joinin g bricks with mortar and attaching a handle to a ceramic mug The u s e of mo1 tar to join bricks relies on the room temperature cementitious reaction. This reaction causes the mortar to harden thus joinin g the two bricks. The practice of joining a handle to a ceramic mug i s s imilar to joining bricks with mortar in that the interlayer material contains an appreciable amount of water When attaching handles to mug s, the interlayer material i s u s ually the same co mpo s ition as th e end member s (c up and handle ). The joint i s formed during the s intering of the interlayer material with the end members at elevated temperatures While the s e application s are les s glamorou s than the heat resi s tant coating on space s huttle til es, they make up a much greater s hare of the ceramic market In the field of structural ceramics, the greatest motivation to apply joining technique s is the size limitation s placed upon th e part by th e den s ifi c ation apparatu s. Large part s s uch as heat exchanger tube s c an exceed fourteen feet in length. Thi s requires the joining of s maller sec tions to com plete the part The fo1rr1ation of a ceramic to ceramic joint is not as straightforward as the typical metallic joint Mo s t metallic joining operations include the formation of a liquid pha se. The liquid ph ase is usually made up of material from both end members and produce s a

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3 joint with properties that gradually change from those of one end member to those of the other. The properties of ceramic joints made without liquid pha s e can change abruptly from one end member to the other Ceramic to ceramic joints are pursued becau se they provide an opportunity to improve the final properties of the product. Ceramic to ceramic joints can furni s h an increased re s i s tance to operating temperature over metallic alloys. They also are more resi s tant to oxidation than most metal alloys. The enhanced resistance to degradation and oxidation of ceramics over metals in high-temperature, corrosive applications can be u se d to increase the efficiency of heat exchangers and turbine engines. The joint area in this dissertation is considered to be the area that encompasses the interlayer and the portion of the end members that has been altered during the joining process. The joint can be described in three ways: according to its chemical microst1 uctural or phy s ical propertie s In the first description, joining can be described chemically by the mixing of the atoms of the components being joined. The mixing of the atoms of the two components can re s ult in the formation of a third component. When the mixing of atoms i s limited to materials that have mutual solubility, the concentration of atoms gradually changes from 100 % of the first material to 100 % of the second material. Secondly, the joint region may posse ss a microstructure similar to one or both of the pieces being joined or it may be unique. A third classification would be to define the joint physically. Thi s is the manner in which the end members are macroscopically connected or somehow attached Although basic in description, this is the definition of ''joined'' that matters most to consumers. The definition of "joint depend s on the desired use of the end product For the ceramic to metal joint of the light bulb described above, hermeticity of the joint is the most important feature with the s trength of the joint only having to meet some minimum requiJ.-ement For the purpo se of thi s dissertation, "joint" will be referred to as the region between two bulk material s that ha s a chemical composition or mechanical properties

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4 different from either of the end members or the interlayers used in the joining process. Materials are dete1mined to be "joined" when they do not separate during normal handling. Until recently, most of the work performed in the joining of materials has used conventional heating. That is, the specimens to be joined were heated in either a resistance or radio frequency (RF) heated furnace. Radio frequency heating is limited to materials that are electrically conductive and capable of supporting an induced current. There has also been some work done t1sing lasers to heat the workpieces. Lately, microwaves have been used to provide the energy necessary to heat the specimens to temperatures suitable for joining. This has brought about a discussion of whether microwave heating can contribute to the joining process in some way besides its use of an alternate heat source. There are many reports of enhanced diffusion and lowered activation energies of transport that will be discussed later. It is certain that if either of the above mentioned phenomena can be shown to occur during the joining process in a microwave field, there could be a definite advantage in the use of microwaves to join ceramics. The goal of this research then is to join alumina using microwave energy and to develop an understanding of the joining process. In the literature, there are many models to predict joining behavior between two materials of identical, similar or differing compositions using conventional heating. There is also an abundance of experimental data to support these models. Several models of microwave interactions with materials also can be found in recent publications. These models and the experimental data to support them are not as prevalent. In attaining the goal of this research, it is necessary to identify, and begin to establish, the intersection of these two separate fields of study, figure 1-1.

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Models of Joining equilibrium at interface surface texture Models of Joining My Work My Wor Models of Microwave / Materials Interactions Models of Microwave/ Materials Interactions evaluate properties of cera m ics joined using mas s transfer mechanisms esidual stress elimination microwave ene rg y microwave most important >Communications >probe a t erial most impor tant >heating >ef f ect on properties 5 Figure 1-1. Schematic depicting the intersection of two fields of modeling to form a ba s is for research. While working toward the stated goal, the following objectives were identified and achieved. Review the fundamentals of joining. Review the principles of microwave interactions with materials that are relevant to JOlfllng. Design and construct an apparatus for microwave joining. Prepare joined s pecimens that have strength approaching that of the original material. Evaluate the integrity and uniformity of joints based on strength Demonstrate enhancements, if any, achieved during microwave joining Use statistical tools to qualitatively assess the joining parameters used in this study. Employ numerical modeling to approximate heat flow during joining. These objectives form the framework of the research performed. They also acted as guidelines throughout the coUI s e of the study.

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6 Several significant achievements have been realized during the course of this study. These achievements either extend beyond the anticipated success of the associated objective or, were accomplished i11 addition to the objectives. 1) A new generation of microwave susceptors has been developed and characterized. 2) A microwave joining apparatus was designed and constructed u s ing closed loop control of the applied force and temperature. 3) An experimental design to provide the data for a statistical analysis of the effects of joining parameters on flexure strength was constructed. 4) A heat transfer program was manipulated to generate temperature profiles in a model that compares calculated temperatures with experimentally measured temperatures. The calculated values provided results comparable with other microwave heating models available in the current literature.

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CHAPTER2 SURVEY OF THE LITERATURE Microwaves Background Like visible light, radio wave s and x-rays, microwaves are a part of the electromagnetic spectrum. Microwaves extend between the frequencies of 300 megahertz (MHz) and 300 gigahertz (GHz) I. This corresponds to wavelengths ranging from about one meter to less than one millimeter in length. In the past, microwaves were used almost exclusively in the field of communications2. Any electromagnetic losses in the materials used were considered detrimental The relatively recent introduction of microwave ovens (1960s) to the general public was a result of the realization that electromagnetic l osses could be used for the purpose of cooking. This was possible because the interactions of microwaves at 2 45 GHz with the water in foods provided efficient and rapid heating. In 1985, Meek3 exploited the generation of heat due to the electromagnetic losses in materials that do not contain water. He was able to heat a ceramic material to a high enough temperature to induce melting. Shortly thereafter, Meek4 proposed a model for the microwave sintering of powders of dielectric materials. He describes the powder compact as a material/porosity (air) composite. Meek then suggests that the higher electric field in the porosity induces densification in nearby grains. Metaxas and Meredith 5 furnish a thorough explanation of the theory behind the microwave heating of materials. Heat generated due to losses in a material is related to the 7

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8 electric permittivity ( *) and magnetic permeability ( *) of the material. Most ceramic materials are not s ignificantly influenced by the magnetic portion of the wave therefore the contribution to heating produced by the magnetic los s e s are generally ignored Fathi 6 provide s an excellent review ( from a materials sc ience perspective ) of the theory behind the interactions of microwaves with materials. He discusses the different types of polarization and the losse s associated with them. Space charge polarization and orientation polarization are the two active mechani s m s in the microwave frequency range. Space charge polarization refer s to the charge build up at the interface s of a non homogeneous material in an alternating electric field. Orientation polarization occurs in materials that are comprised of permanent dipoles that have a sy mmetric charge distributions. The dipoles tend to reorient in an alternating electric field Fathi also de sc ribes the historical development of the theory and equations pertainin g to the dielectric heating of material s The electrical permittivity of a material i s defined by the equation where e = e jE = 0 ( e r jE eff ) e' : diele c tric con s tant ( r eal) 11 : dielectric los s factor ( imaginary) E r : relative dielectric constant ( 1 IEo) 11 eff: effective relative lo ss factor= e''r + cr/ 0 0) E''r : r e lative lo ss fa c tor cr : electrical conductivity ( ac + de ) 0 : pertnittivity of free space ro : angular frequen cy = 21tf, fin Hz. (21 ) The dielectri c co n s tant ( real ) and th e dielectric lo ss factor ( imaginary ) of a material can be mea s ured experimentally. Using cav ity perturbation theory, Hutcheon et al. 7 were able to mea s ure the co mplex permittivity of s everal materials They then were able to mathematically i so late the real and imaginary portion s of the complex perrnittivity The s e

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9 values describe the polarization and conductivity losses generated in a material. The loss tangent, tan
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I c current in ideal dielectric I L -los s current in dielectric material I induced current in dielectric material V a p p applied volt a ge 1 0 Figure 21 Repre s en t atio n of the lag in the curre nt th at de t erm in e s the l oss tangent The dielectric co ndu ctivity i s a r eal n u m b er so t h e l oss c urr e nt i s in ph ase with the a p p li e d voltage V a p p

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11 pertinent equations such as the penetration depth of the microwaves in the material, DP. The penetration depth i s defined as the distance from the material's surf ace to the point at which the power drops to e 1 of its surface value. This equation is also affected by temperature due to the temperature dependence of e'' eff and e', 'A e I _1 __ o_l ((1 + ( eff )2) 2 -1 ] 2 I 27t(2t /) 2 t ( 2-4a ) For low loss dielectrics ( e" effl 1 << l) the equation is 1 D="'o (e ) 2 p 27tt II eff (2-4b) where 'A' 0 is the wavelength of the electric field in free space. The errors associated with the simplification of the penetration depth increase as the ratio c''etfl 1 approaches one. Table 2-1 contains s ome representative values of ratios and errors calculated for a frequency of 2 .45 GHz Table 2-1 Error As s ociated with Simplified Equation for Penetration Depth for Several 11 effl 1 R atios E 11 etf l E' I % error I I 0.009 0.1 I I 0 3 1 I I 0 7 5 I 1 9 I

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12 Microwave Applicators The difference between the two most common types of microwave ovens is in the microwave cavity where the material is processed. A multimode cavity is a metal box with an opening in which microwaves are introduced. The microwaves, once introduced into the cavity, reflect off the walls setting up a number of standing waves. The electric field in multimode cavities is not very uniform and requires either a turntable or a mode stirrer (rotating metal fan) to improve the uniforrnity of the electric field. A single mode cavity has dimensions that are more precise than the multimode cavity. The length of the single mode cavity is approximately the size of the wavelength of the microwave frequency being used. One wall is adjustable so that the cavity can be tuned to the precise length to produce a single standing wave. The advantage of multimode microwave ovens is that they can be fabricated in almost any dimension and are relatively inexpensive. Single mode microwaves have a calculable electric field that permit the identification of the position of the high field strength. As opposed to single mode microwaves, multimode microwave ovens are not capable of developing the power densities necessary to produce efficient heating. Power densities of 107 kW/m 3 can be achieved in a tuned single mode cavity5. Typical power densities of 3 kW/m 3 are produced in multimode microwave ovens for home uses. In a tuned single mode cavity, incident and reflected waves are superimposed and the position of maximum electric field can be determined. The specimen to be heated can be positioned to provide the optimum transfer of energy. However, in a multimode cavity the microwaves are constantly being perturbed and scattered, minimizing the chance that a specimen is positioned at the point of maximum electric field for more than a few seconds. In order to heat most ceramic materials in a multimode microwave oven, it is beneficial, if not essential to use microwave hybrid heating (MHH). Microwave hybrid heating incorporates a strong microwave absorbing material into a surrounding piece of

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13 insulation. This material absorbs more microwaves than the material being processed. Silicon carbide is the most common material of choice as the microwave absorbing material in MHH. Silicon carbide is an excellent and inexpensive microwave absorber that can be used in air at elevated temperatures. Above 900C, the silicon carbide will oxidize to form a protective silica layer The weight gain associated with the oxidation increases as the temperature increa ses 9. The combination of the absorbing material and the insulation is commonly called a microwave susceptor. The purpose of the susceptor is to assist the material of interest in heating to the processing temperature. The development of microwave susceptors has empowered researchers to investigate low loss materials such as high-purity alumina using multimode microwave ovens. One of the common modifications made to a microwave cavity is the addition of holes to provide access for either a ther1nocouple, optical pyrometer or other probes Holes also may be nece ssary for the application of pressure to a workpiece in a microwave cavity. The presence of holes in the cavity necessitates the use of some type of choking system to prevent microwave s from escaping and presenting a potential health hazard. Holes of a diameter less than one-quarter of the wavelength (3.06 cm for microwaves at 2.45 GHz ) theoretically emit no microwave energy. This originates from the equation where z Z o d input impedance of hole characteristic impedance of hole diameter of hole wavelength of microwaves in cavity. (2-5) If d = 'A,/4 the input impedance goes to infinity and the hole acts as a open circuit. The microwaves are reflected back into the cavity as if the hole did not exist. At aperture sizes

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14 from O < d t.J2, there is a sm all impedance associated with the aperture than can lead to a small emitted electric field In reality, the wall material (usually aluminum or steel) has a finite impedance and can emit a portion of the incident microwave s. Cathey 10 developed two equations to calculate the ratio of the electric field scattered through an aperture to the incident electric field and 7t d 2 exp 4 E s A E I z 'A where E s s cattered electric field, V /m Ei incident electric field, V /m d aperture diameter m 'A wavelength of mi c rowave m z di s tance from aperture, m. 'A z 2d 1 'A 1t I 2d 18 'A z d ~ 'A 4A z d -~ 'A 4'A (2-6a) (2-6b) This is the case for the viewing port for an optical pyrometer and the thermocouple feedthrough At an aperture diameter to wavelength ratio of 0.5, the intensity of mic1owaves transmitted through the ape1ture becomes significant. Proximity to an aperture greater than one-half the wavelength of the microwaves can pose a health hazard. Cathey then calculated the ratio of transmitted to incident field for a range of aperture diameters, figure 2-2. It ca n be ascertained from figure 2-2 that for an aperture of 'A/4 or les s, the fraction of transmitted power i s small and attenuates quickly As the aperture size is increased, the inten s ity of the transmitted field increases greatly. In the situation where a load i s to be applied within the cavity, the hole or aperture, is partially filled with a

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-LLJ "" VI w Cl) C) 0 N 15 3.9 to---T---......... 0 d /'A, = 1 0 1 0 d /'A, = 0 5 2 0 d /'A, = 0.2 3 0 d /'A, = 0.1 4 0 d /'A, = 0.05 0 0 25 0 5 0 75 1 0 1.25 1 5 1 75 2 0 Z I A Figur e 22 Rati o o f tr a n s mitt e d to incident field for aperture diameter 0 05 < d/A < 11 0.

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16 dielectric material. This material, typically alumina, is used to transfer the load from the external load cell to the workpiece. Here, the wavelength of the microwaves is decreased by the square root of the dielectric constant of the filling material5. The decrease in wavelength makes it possible for the incident microwaves to pass through a smaller aperture than expected. Thi s condition requires additional modifications to effectively attenuate the microwaves. Metaxas and Meredith5 describe the use of a circular tube of conducting material as a choke. If the diameter of the tube is less than one-half of the incident wavelength, the microwaves are attenuated and the transmitted power decreases rapidly. Under these conditions (d < ')J2), the attenuation of the power is proportional to e -z, where A is the wavelength of microwaves in the dielectric material and z is the length of the choke. Microwave Processing of Materials In the past fifteen years, numerous efforts to take advantage of the unique capabilities of microwave processing have been undertaken. Sutton 1 outlines the potential advantages of several characteristics of microwave processing over conventional heating processes. These advantages include 1) uniform heating of large sections of material, 2) heating above 2000 C in air, vacuum or controlled atmospheres, 3) rapid processing with reduced grain growth, 4) accelerated sintering and diffusion due to high electric fields, 5) selective heating of particular materials or phases and 6) improvement of mechanical properties. Katz and Blakel 1 demonstrated that uniformity could be achieved over a large area by simultaneously sintering twenty alumina cylinders. They reported that dimensional tolerances were maintained from experiment to experiment as well as among specimens within each experiment Holcombe1 2 reported attaining a temperature of 2150 C when sintering boron carbide and Tian et al.1 3 reached a temperature of 2200 C when sintering

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17 silicon ca1bide in a positive pre ss ure argon atmosphere. Other non-oxides have been proces se d under flowing argon with the resulting x-ray diffraction pattern primarily indicating peaks of the desi1ed phase 14 Using microwave hybrid heating, Del5 rapidly sintered high-purity alumina to a nearly fully dense state. In De's experiments, specimens were held at the sintering temperature for thirty-five minutes. The lack of significant grain growth reported was analogous to that exhibited in conventional rapid sintering. The author also reported uniform hardness measured across a 25 mm diameter specimen. Moore et al.16 used the concept of se lective coupling to demonstrate the effectiveness of microwave heating. The authors used a lossy binder in the forming step of alumina compacts. When heated using microwaves, the binder burned out cleanly leaving the alumina unaffected In an attempt to organize their approach to microwave processing, Janney et al.1 7 con s tructed guidelines for microwave processing at the Oak Ridge National Laboratory. They describe the specimen/insulation configurations used and the temperature measurement method s that provided consistent results. The progress demonstrated by researchers worldwide in the microwave processing of materials gained the attention of the U.S. government. Stein et al.1 8 summarized a report commissioned by the Department of Defense (DoD) and the National Aeronautics and Space Administration (NASA). This report assessed the current status of the technology, ascertained which applications of the technology show promise to provide energy or space savings and recommended future activities in the field of microwave processing. Two industries in which microwave processing has progressed from an emerging technology to a mature process are the rubber industry19 and the food industry 20. Numerical Modeling of Microwave/Material Interactions Until now, all of the discussion concerning microwave/materials interaction s has been phenomenological. That i s, only the behavior of materials after exposure to

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18 microwave s has been considered. Due to the complexity and multiple interactions of the components in equation 2-3, many researchers do not consider the theoretical aspects of microwave heatin g Another more pract i cal reason that theoretical approaches are avoided is the difficulty in m eas tlring th e conditions within the microwave during proce ssi ng. More s pecifically it is very difficult to determine the electric field in a material inside a microwave oven. Prop er tie s suc h as the dielectric constant and the los s tangent are temperature dependent. The interaction of the electric field with the dielectric material in the cavity alters the field through absorption or reflection of the wave s. To calculate the electric field in a microwave cavity, it i s neces sary to solve Maxwell' s equations simultaneously. Yee 21 was the first to develop a numerical solution for the se equations in an i so tropic medium by replacing them with a set of finite difference equations. Previous to Yee' s work, scattering of the electric field was calculated by a laborious integration method that required numerous subdivisions of the material being evaluated22. Taflove and Brodwin 23 extended Yee' s fmdings to determine the field within a diele ctr ic cylinder. One of the ear ly applications of the finit e difference modeling technique s was used in response to cataracts that developed in the eyes of microwave generator operators 24. The model was implemented to predict the electromagnetic fields and temperature induced in a microwave irradiated human eye25. Recently, a similar model was used to deterrnine the specific absorption rate of various body components 26. The authors s ugge s t that it is possible to take advantage of th e potential for se lective heating of various types of tissue in surgical procedure s. The bulk of the re s earch in microwave/material interactions has been performed in the food industry. Datta 27 judged the determination of the fields within a loaded microwave environment to be too complex to predict accurately The author concentrated on predicting

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19 the heat and mass transfer associated with microwave processing of foods Figure 2-3 compares the experimentally and predicted temperatures in a cylindrical roast beef heated using microwaves In a rigorous evaluation of microwave induced heat and mass transfer in baked dough products, Tong and Lund28 considered the temperature dependence of the dielectric properties of the materials. The authors were able to measure the field strength near the subject's surface and use these values for the model Figure 2-4 compares their model to experimental results obtained in two different microwave ovens Pangrle et al. 29 introduced the use of finite element analysis to model the microwave thawing of pure water cylinders. Subsequently, Pangrle et al. 30 extended the model to multilayer beef/water composites. Many authors choose to neglect the temperature dependent properties of the materials being heated. Ayappa et al 31 used the finite element method to determine the effect of the temperature dependent properties on the temperature of various materials Ayappa et al. 32 then extended their finite element model to a 2-dimensional situation. Figure 2-5 is the temperature distribution of microwave heated raw beef using both temperature dependent and constant dielectric properties. In ceramic s, Watters et al. 33 used difference equations to calculate transient temperature profiles in a ceramic using a simplified geometry to represent the ceramic specimen. Gupta and Evan s 34 developed a I -dimensional numerical model for chemical vapor infiltration (CVI) using microwave heating. Using an integral method 35 for microwave material interactions, Gupta and Evans 36 calculated the temperature in a microwave heated 2-dimensional body. In the complicated system of hydrated porous concrete with variable dielectric properties Li et al. 37 developed a numerical I-dimensional model to determine the temperature and steam pressure developed during microwave heating. Ferber et al. 38 were able to calculate stress and temperature distributions for a simplified geometrical model of a ceramic window subjected to microwave heating

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80 --() 0
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21 11 0 100 0 A A 4 A 90 () 80 0 Q) 70 "::::::, +J co D E = 42.5 V / cm "60 Q) Q. b.. E = 28 3 V / cm E 50 Q) model r40 30 20 -+----------,---...---,.-...----,.-----.--.--...---1 0 4 8 1 2 1 6 20 24 28 Time (s) Figure 2 4 T e mperatur e of bread heated with two different field s trengths 28.

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(.) 0 (1) ,._ :::, +-' al ,._ (1) 0. E (1) r147 107 67 0 . -. 0 2 15 min .. .. .. .. 10 5 min min 1 min .. 0 4 0.6 .. Depth in Sample .. . .. .. . -----0.8 1 Figure 2-5. Effect of variable (-) ve r s u s constant (---) dielectri c properties on temperature in a raw b eef sa mple. Depth in sam ple refer s to fraction of wbole 32. 22

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23 The joining of ceramics using microwave energy has been considered theoretically 3 9. It was suggested that the joint area be positioned in the area of a hot spot to facilitate joining However no experimental data is presented in conjunction with the numerical model Dibben et al .40 presented a finite element and a finite difference method for the modeling of the sintering of ceramic s in a multi-mode microwave cavity. Their effort included s olving Maxw e ll 's equations and producing 3-dimen s ional plot s of electric field and power density as a function of position. The fmite difference method was used to calculate temperatures in a 3 dimen s ional specimen41 To calibrate their model with the microwave used for the experiments water loads were heated and the electric field was calculated from the rate of ri s e in temperature of the water In a I-dimensional model, Skamser and John s on 4 2 developed a system to simulate microwave hybrid heating. The microwave field was assumed to be uniform throughout the microwave. Temperature dependent dielectric propertie s of the alumina fiber s pecimens were varied; those of the susceptor were kept con s tant. Microwave hybrid heating experiments were carried out by Thoma s et al 4 3 u s ing zirconia a s the suscepting material Mea s ured temperatures of the workpiece and th e insulation were compared to tho s e calculated u s ing a 2-dimen s ional numerical model Difference s between the measured and calculated temperature s of the workpiece w e re a s much a s 1 2 0 C during heating. In the in s ulation the s e temperature differences exceeded 200 C. When the temperature of the workpiece reached the sintering temperature the calculated and mea s ured temperatures converged. Figure 2-6 is the computed and mea s ured temperature s of the workpiece and the insulation. K1:iegsmann4 4 proposed a I-dimensional model to explain the phenomenon of ther1nal runaway that i s occa s ionally experienced during the heating of ceramic s using microwave energy The author later expanded the model to encompass ceramic fiber s and proposed that there exist s table temperatures for given power level s in system s with highly

PAGE 44

(.) -.., Q) '::, +J
PAGE 45

25 specified boundary conditions45. Spotz et al. 46 use the principles put forth by Kriegsmann to compare experimentally determined thermal stability conditions. They concluded that microwave hybrid heating i s an effective procedure for limiting the formation of hot spots that can lead to thermal runaway. Beale and Arteaga 47 proposed the use of a closed loop control system to use feedback from a thermocouple to prevent thermal runaway during the microwave joining of ceramics. Numerical simulations by the authors indicate that this system demon s trates potential for experimental applications One element of the modeling that has been a constant source of difficulty is resolving the electric field strengths through Maxwell's equations. Ayappa et al. 48 investigated the applicability of using Lambert 's law to predict electric field strengths. Lambert's law describes the exponential decay of the power flux from an initial intensity and is expressed as (2-7) where lo transmitted power flux (W /m2), B = penetration depth ( cm) and z = di s tance from the sample surface ( cm). The authors have determined a critical slab thickness CL crit) above which Lambert's law i s valid. The critical thickne ss is dependent upon the penetration depth, equation 2-4a as L 0 0 t = 2. 7~ 0. 08 (2 -8) The validity of Lambert' s law can be quickly detern1ined for any materials system by calculating the c ritical thickne ss at the lowe s t temperature of intere s t That is the temperature with the largest penetration depth Thi s will ensure that Lambert' s law will be valid over the entire temperature rang e ex amined The critical thickness for several ceramic

PAGE 46

26 materials at a microwave frequency of 2.45 GHz are listed in Table 2-2 A sample calculation of the penetration depth and critical thickness is in Appendix A. When the critical thickness exceeds the sample thickness, it becomes necessary to solve Maxwell's equations to detertnine the power within a material. Table 2-2. Critical Thickness and Penetration Depth at Different Temperatures for Several C M t al t F f 2 45 GH erarmc a er1 s a a requency o z. Material Temperature Penetration Depth Critical Thickness ( O C) (cm) (cm) 99 5% alumina 25 9553 25,793 1000 205 553.4 Al-66 cement 25 127 342.8 1000 28 75.5 nickel aluminate 25 1848 4989 1000 5.4 14.5 Evidence of Microwave Enhancements In the first reported evidence of enhanced diffusion, Janney and Kimrey49 used 180 tracer in a single crystal sapphire substrate in side by side annealing experiments using microwave and conventional heating. Oxygen was selected instead of a more easily traced species to avoid differential microwave coupling during the test. Figure 27 compares the activation energies of diffusion for the two processes over a range of temperatures. A single crystalline sample was t1sed to eliminate microwave interactions with the grain boundary phase. These interactions contribute to the decrease in activation energy. The authors do not offer any explanation for the perceived effect. Fathi et al. so performed ion exchange in sodium aluminosilicate glasses. The authors exchanged potassium ions from a salt with the sodium of the glass. The diffusion constants then were calculated from ion concentrations that were measured using electron microprobe analysis. A variation in the soda/alumina ratio resulted in differing penetration depths of the potassium ions. These

PAGE 47

-17---------------en ..._ 1 8 -1 9 0 0) 0 2 0 4.7 Conventional 710 kJ / mol 4.9 Microwave 409 kJ/mol 5.1 5.3 1 /T (1 /K) 5.5 5. 7 X 10 4 27 Figure 2 7 The activation energy for 1 8 0 diffusion in sapphire measured u s ing both c on v entional and microwav e heating 49

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28 results were compared to identical ion exchange experiments carried out using conventional heating. At soda/alumina ratios near 1: 1, the measured diffusion distance of the potassium ions is much greater in the microwave processed glasses than in the conventionally processed specimens As the ratio is varied from 1: 1 in either direction, the differences in the diffusion distance of the pota s sium ion s were less discernible. In another variation of the experiment, a s maller susceptor was used and more microwave power was utilized to attain the required temperature Figure 2-8 compares the use of two different microwave powers with conventional heating for the ion exchange of K+:::>Na+ at 450 C. To examine the effect of defect concentrations on diffusion in a microwave field Ahmad 5 1 diffu s ed zinc oxide into s ingle c rystals of s apphire with differing amounts of lattice defects. He correlated the concentration of defects with the rate of formation of zinc aluminate s pinel Similar experiments were executed by Fathi et aJ.52 using chromium oxide as the diffusing species No microwave effect was reported but the authors considered this evidence that thermometry was an acceptab l e measurement technique in a microwave field Tiegs et al. 53 employed the premise of selective coupling de s cribed earlier to couple microwave energy with the grain boundary phase of a low loss silicon nitride A post s intering annea l of the sintered specimen s was carried out using both microwave and c onventional heating 5 4. It was reported that in the specimens with a s ignificant volume of grain boundary pha s e, there was an i1nproved re s istance to creep deformation. Joining Joining Methods The term joined ha s s everal meaning s in the materials world It refers to component s that are held together by one of several methods. The two main type s of joining are mechani c al joining and chemical joining. Mechanical joining uses fastener s or

PAGE 49

0 < a:::: I 0.10 0.08 0.06 0.04 0.02 0.00 ~' \ \ 0 10 .. \ 'e ~ '. \ II. 20 .. 30 40 + K + K + K ... MICROWAVE (800 W) CONVENTIONAL MICROWAVE (1600 W) 50 60 70 80 90 PENETRATION DEPTH IN MICRONS 29 Figure 2-8. Diffusion of potassium in sodium aluminosilicate glass using conventional heating and two different microwave power levels at a temperature of 450 C for 30 minutes50

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30 clamps to join two or more distinct pieces together. It is probably the most preferred method of joining because the parts can often be easily separated at a later time for repositioning or for re use. Another type of mechanical joining involves the use of interlocking pieces such as a tongue-in-groove floor or a dovetail joint on a birdhouse roof. The other type of joining chemical joining -can be further subdivided into direct joining and indirect joining. Direct joining is the adherence of two components directly to each other. These components can be either identical or different. The case in which the two materials are identical is an attractive process because it minimizes the number of components involved. It also eliminates the chance of mismatches in the thermal expansion of the materials, which can lead to a weak joint Direct joining of similar materials can be accomplished by heating the area near the joint to a temperature at which a liquid will form. However, there are not many materials that can be effectively joined in this manner55. In ceramics, low thermal conductivity can result in material failure due to stresses that develop during heating. When the two materials to be joined directly are different, the presence of a compositional gradient provides a driving force for joining. Here also, care must be taken to minimize the ther1nal stresses that can be induced during the joining process. Ther111al stresses can lead to low joint strengths56. These stresses are induced by a mismatch in the thennomechanical properties of the dissimilar materials. Indirect joining employs a third component between the end members that facilitates the bonding of the two parts. This is an excellent alternative to the direct bonding method Here, the end members can be either identical or dissimilar in composition. When the materials are identical, the interlayer provides a compositional gradient to assist in the joining process. In the case of dissimilar materials, the interlayer material is often chosen to have thermomechanical properties between those of the end members so that thermal

PAGE 51

31 stresses are minimized5 7. These interlayers are more commonly referred to as functionally graded interfaces and will be discussed later in this chapter. In addition to the various methods of joining, there are many ways to determine whether components are joined. The final application of the joined materials is instrumental in defining what is considered to be an acceptable joint. To say that pieces are joined may mean welding two part s together so there is a gradient of chemical composition or mechanical propertie s from one material to the next. It can also indicate the joining of a film to a substrate where the purpose of joining the pieces is for physical support of the furn. Little or no chemical reaction is desired between the two materials This joint may be mechanically weak but still acceptable because it met the minimum requirements for use. An example of this type of joint would be superconducting films on an alumina substrate. The superconducting films form a Josephson junction and can detect small magnetic fields. There is also the case of the ceramic/metal joint in a light bulb where the hermeticity of the joint i s the determining criterion for suitability. In thi s case it is not so much the strength or the amount of reaction between the end members that 's important, but the ability of the joint to maintain a vacuum at elevated temperatures. For the purpose of this work, a joined specimen will be defined as two or more components that are physically and chemically attached after exposure to a high temperature and an applied load Additionally, the components may not be easily separated during normal handling. Currently, there are many processes in which the previously described methods of joining can be accomplished. Joining by mechanical means requires not only knowledge of the materials being joined, but also requires extensive design skill55. In chemical joining, so me processes involve only the heating of the area to be joined whereas others require the entire workpiece to be heated to the joining temperature. The application of pressure on the joint area is usually required during the joining process to form a suitable bond

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32 Joining processes Bolting. Bolting materials together is a popular method of joining metals With ceramic/metal joints care must be taken to avoid stress concentrations55. This can be done with the use of a soft washer (either lead or copper) between the metal bolt and the ceramic piece. Clamping. As with bolting, clamping requires the spreading of the load placed on the ceramic material Similarly, bending loads should be avoided and gaskets should be used at all ceramic/metal interfaces55. Welding Oxide ceramics can be joined by welding. A laser or an electron beam is used to heat the edges of the end members above their liquidus temperature. The liquid fills the gap between the materials. This can produce intense local stresses as described previously that can produce cracking during processing or cooling58. There is also the possibility of the formation of an undesirable microstructure during the recrystallization of the molten material55. Brazing. Brazing entails the use of a low melting filler between the end members. This is very common in the joining of metals because of the ease of the procedure. When working with advanced ceramics, the use of a low temperature braze material decreases the usefulness of the joined pieces by lowering their maximum use temperature. Other undesirable aspects of brazing are a possible mismatch of thermal expansion coefficients or a chemical reaction between the brazing material and the end member55. In the joining process called active metal brazing, these phenomena are controllable and therefore desirable. Adhesive bonding. This process incorporates the use of an organic adhesive between the ceramic and metal pieces. The organic adhesive is typically flexible compared to the end members. The relative flexibility of the adhesive material can accommodate

PAGE 53

33 stresses that develop between materials with differing thermomechanical properties. Joints made with organic adhesives are usually limited by the strength of the adhesive and the temperature at which the adhesive loses its mechanical integrity. An exceptional example of adhesive bonding is the application of the ceramic insulating tiles to the aluminum skin of the space shuttle. Hot pressing. Hot pressing is used for both direct and indirect joining. Hot pressing consists of heating the entire assembly to be joined and applying a load at some time during the heating cycle. Direct and indirect joints are both possible using this process. Pressure can be applied either uniaxially, where the end members are usually cylinders, plates or blocks or the pressure can be applied isostatically where any shape can be accommodated. The main limitation of uniaxial hot pressing is the simplicity of the shapes that may be joined. Figure 2-9 represents a typical uniaxial hot pressing setup and the shapes that are most often used. Hot pressing lends itself to the application of diffusion bonding. Diffusion bonding is the formation of a joint through the interdiffusion of two materials with a minimal amount of material deformation. The key requirements to diffusion bonding are 1) intimate contact between the surfaces to be joined and 2) sufficient interdiffusion between the materials being joined to produce a joint in a reasonable time frame The application of p1essure aids in fulfilling both requirements for diffusion bonding. It is a relatively simple matter to hold an assembly as shown in figure 2-9 at the desired temperature and pressure for the extended periods of time that are sometimes necessary for significant diffusion bonding to occur. The isostatic application of pressure is a special case of hot pressing called hot isostatic pressing (HIPing). HIPing allows for application of large pressures and high temperatures. The capital and operational cost of HIPing limits its use to necessary applications.

PAGE 54

34 p parallelepipeds cylinders ., .J'1 r HEAT HEAT I.I / .n ,_ a) b) p Figure 2-9. Sketches of a) Typical setup used for joining ceramics in a hot press and b ) ceramic shapes commonly joined in a h ot pre ss.

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35 Criteria for Joining The joining method of interest in this study is indirect joining through the formation of a diffusion bond. It is now accepted that the mechanisms of mass transfer responsible for joining are the same as those that lead to pressure sintering59 60,61 62. Diffusion and creep mechanisms are responsible for the pore closure that makes up the joining process. These can be grouped most easily by sources and sinks and are illustrated in Figure 2-10. Derby and Wallach62, describe the driving forces for each of the mechanisms in Figure 210. The driving force for 1 (lattice diffusion) and 2 (vapor transport) is surface curvature and is halted when uniform curvature is achieved. Mechanisms 3 (boundary diffusion) and 4 (surface diffusion) are driven by the chemical potential gradient; 5 (viscous creep) and 6 (dislocation motion) are driven by the applied pressure. The relative importance of each of these mechanisms is determined by the material properties and the time interval required by the joining process of interest. In diffusion bonding, there are two distinct factors that must be considered for the formation of a good joint. The first factor is the preparation of the surfaces to be joined For a diffusion bond, it seems reasonable to assume that a mirror smooth surface would be desirable to provide intimate contact between the two surfaces6 3 Conversely it also makes sense that a larger contact area provided by a heavily textured surface, figure 2-11 would be conducive to the joining process. The amount of surface texture can be described quantitatively in terms of the ratio of the contact area to the unit area of the surface. The smooth surface in figure 2-11 b would have a ratio of one, whereas the textured surface in figure 2-1 la would have a ratio greater than one. Villagio64 contends that increasing the area of the surface s to be joined by enlarging the surface profile from a mirror flat finish will increase the contact area and yield the strongest joint. He suggested that sinusoidal shaped surfaces matched together would yield the optimum conditions The fmal result is

PAGE 56

material a ----2 a ) jo i nt line __ __, 1 void void 5 and 6 c ) vo i d ~ mate r ial source 36 ________ j 9in t line Figure 2-10. Schematic s howing the s ix mechanism s of mass transfer that can lead to joining; a) s urface sources, b) bonding interface sources c) bulk deformation after yield or during creep

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37 a) textured surface ,__.--...., textured surface b) smooth surface smooth surface external dimension Figure 211. Contact area of a) textured surface and b) s mooth surface. Contact area in a) is greate r than in b ) when th e external dimension i s the same.

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38 a compromise between the two theories that includes a textured surface but not enough to introduce notch stresses at the asperities caused by a reduced area supporting the applied load The amplitude of the curve suggested by Villagio is small relative to the period of the surface. The ratio of contact area to unit area for the ideal surface discussed by Villagio is only slightly greater than one. In figure 2-12, Suganama et al. 65. show that an increase in surface roughness of the ceramic decreased the strength of a Si3N4-Al brazed joint. In a review paper, Akselson 66 suggests that improved joint strengths could have been attained using a higher pressure during processing. The second factor that must be considered in joint formation is the driving forces responsible for the processes that hold the two pieces together. The impetus for joining can be in the form of van der Waals forces or with an electronic structure across the interface55. The goal of all of these mechanisms working together is to reduce the free energy of the system by eliminating the free surface. Effect of Process Variables on Joining Temperature The mechanisms that control joining involve either diffusion or plastic deformation. For the mechanisms that are diffusional, temperature is the most influential variable in the joining process. This is explained by the presence of temperature in the exponent of the diffusion equation. However, the maximum temperature for diffusion bonding is limited to a fraction of the melting temperature of the material to be joined. Akselson66 reports the temperature range for sufficient joining to be 0.5-0.8 of the lowest melting point of the materials to be joined. Higher temperatwes would lead to excessive creep deformation of the specimen. Crispin and Nicholas67 calculated the bond strength of a steel/alumina joint with an aluminum interlayer as a function of temperature. Figwe 2-13 plots these values and compares them with values measured between 0.75-0.95 of the melting temperature of

PAGE 59

39 600-------------,------.---------ba se material -----~-----------------------------------------------500 a:, 0... I: ..._ 400 ..c ...... 0) 300 E -+,,..,I CJ) (D 200 .J co 100 (j) 0 0 0 1 0.2 0 3 0 .4 Surface Roughness (m) Figure 2-12. Effect of s urfa ce rou g hne ss (as described in eq u ation 3-1 and figure 3-4 ) on samp l e strength65 ,.

PAGE 60

ctS a.. ..c +J 0) C: 0) +J Cl) 0) 0. E ctS Cl) 70,-.---,.------------------60 50 40 30 20 1 0 0 400 450 calculated values 500 550 600 650 700 Bonding Temperature ( C) Figure 2 13 Effect of joining temp e rature on the strength of a joint6 7. 40

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41 aluminum. Derby and W allach62 review the role of temperature in each of the mechanisms in figure 2-10. Pressure The application of pressure during diffusion bonding has the effect of increasing the intimate contact between the surfaces to be joined .......... When the joining temperature has been attained, the application of pressure assists in deformation near the joint surface that results in the closure of voids at the interface62. As reported by Allen and Borbidge68 in figure 2-14, at low applied pressures an increase in pressure greatly increases the bond strength. This effect is diminished as the applied pressure is increased. This indicates that there may be, for each joint, an optimum pressure where the greatest benefit of increased bond strength can be realized without significant deleterious deformation of the original materials69. Time The solid-state joining process of interest is diffusion controlled The effect of time on the strength of a joint is similar to that of time on atomic diffusion66. The well-known equation for diffusion as a fimction of time is X= k(Dt:) 0 (2-9) where X is the distance traveled by the diffusing species, k is a constant, D is the diffusion coefficient and the exponent, n, is usually 0.5. The analogous expression (2-10) where BS is the bond strength, and Bo is a constant was developed by Crispin and Nicholas67. The equation relates the joining time to the bond strength Figure 2-15 shows the effect of bonding time on the strength of an Al203-Aljoint. This equation and plot

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42 300 .-250 ccs a. I --200 I I ..c +.J CJ) C Q.) 150 +.J Cl) -0 100 C Q.) co 50 2 4 6 8 1 0 12 Bonding Pressure (MPa) Figure 2 14 The e ffect of pre ss ure applied during joining on the strength of the joint 68.

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-... (0 Q_ :I:: ..c: ......, 0) C Q) !..... __, U1 Q) ,-0. E (0 c.n 1 0----------------,-----,---, ---..--. 60 50 40 30 20 1 0 0 0 20 40 60 B o nding 8 0 100 Time ( min ) 1 20 Figure 2-15. The effect of joining time on the strength of the joint67. 140 43

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44 assume that there is no chemical reaction in the form of a phase change associated with the JO tnmg process. Reactions While not strictly process variables, reactions in and between the end members and t he interlayer may have a significant effect on the quality of the joint and the bond strength. In metal/ceramic joining, there is the possibility of controlling the interfacial reac tions Loehman and Tomsia60 compared results from two different investigations of t he strength of Nb-Al20 3 joined in a vacuum. They discovered that the formation of a reac tion layer reported by one set of authors agreed with theoretical prediction based on t hermodynamics, while reports by other researches yielded contradictory results. Loehman and Tomsia suggest60 that these contradictions can be attributed to a difference in the oxygen partial pressu re during processing. Scales of Joining Joining can be described on a variety of scales. When two materials are joined chemically, the interactions are typically discussed considering only the scale of interest. That is, when the matching of crystal lattices is the topic, it would be discussed on a nano or atomic scale and the macro and micro scales would not be considered. Figure 2-16 illustrates the four scales of joining that are referred to most often. Atomic On the atomic scale, joining can be thought of as interatomic bonding This can be illustrated by looking at adjoining atoms from the two surfaces. In the case of most metal oxides, the interatomic bond is largely ionic Kingery et al. 70 state that as two oppositely charged ions approach one another the molecule becomes more stable. The energy of attraction is due to the coulombic forces that arise between the oppositely charged ions

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interatomic forces 0000 0000 0000 0000 atomic micro interdiffusion 000 0 000 0 000 0 000 0 nano macro Figure 2-16. Graphic representation of the four scales of joining discussed in the text. 45

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46 The increase in stability continues until the electron shells associated with the two ions overlap. As described in the Pauli exclusion principle, only one electron is allowed for each quantum state. As two ions approach each other, a strong repulsive force arises to work against the coulombic attractive force. The combination of these two forces leads to an energy minimum in an energy versus separation diagram, Figure 2-17. Ferrante et al. 71 identify this energy minimum as the binding energy. The authors also state that the derivative of figure 2-17 is the force versus separation curve, figure 2-18, and that the maximum can be considered in simplest terms as the tensile stress (F maxi A surface) necessary to separate the two ions. Nano In the next largest scale examined, the first few atomic planes of each surface are considered. Ferrante et al. 71 discuss the difficulties in increasing the scale in the theoretical evaluations. They note deviations from symmetry that muddles the theoretical approach. Some of these deviations are caused by the use of two different planes of the same material or the existence of two different materials in proximity. To simplify this problem, Clarke and Wolf72 reduce the interface to a Van der Waals pair potential and sum the potentials over the interface. This can be used for ceramics when the bonding is localized. Metals require another approach that is more complicated and will not be discussed in this dissertation Stoneham and Tasker 73 employed computer codes to model the interfaces between materials. In the evaluation of the BaO/NiO interface, the authors matched su1faces by rotating the 100 planes by 45 The resulting relaxed structure, figure 2-19, placed the Ni 3+ ion and vacancies from the disordered NiO lattice near the Bao surface. This is depicted as the lowest energy structure. Unfortunately, the authors do not consider any interdiffusion of the cations in their model.

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E re I I I I ~E I I I I I 1 'infle c tion I I I r point Figure 2-17. Energy versus separation for two ions in proximity to each other 71. F re \ I I I Fmax r Figure 2-18. Force versus separation for the two ions in figure 2-1771 47

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Bulk Bao above this plane _,. 0 -----t 2+ ..----1 0 ...... ___ ( 1 00) axis Ba of Bao 2+ 0 -------~---1 Ba t-----( ------1 Two intermediate planes 3 + 1----(0.,_---.Ni .___ 3+ ----10----Ni ----o----oxygen ___" ions --1 Vac--N i 3 + .,.._..___. Vac ,___._ 0 0 3 + ---Vac----Ni ____. oxy gen ion s ( 110 ) axis -""""0 ------. Q --0 .,_ ____ of NiO .,,,,-...v --------r--4 0 t------10 ,__ __ ___,. 0 ...._ __.. Bulk NiO below this plan e (100) axis of NiO Figure 2 19. Computer derived relaxed structure of the BaO/NiO interface 73. 48

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49 Micro Joining on a micro scale can be reviewed in two ways. The most common way to consider joining is by b1inging together two distinct pieces of material. If the pieces are determined to be joined, at some position in both materials there will be a deviation in composition and/or structure. If the joining is done properly, the joint may be indistinguishable from the bulk to the naked eye. Optical or electron microscopes may be required to locate the position of the joint. Usually, the area where the initial surfaces contact can be easily identified. Binner et al.74 recently reported grain growth across the initial interface, making it difficult to recognize. Al-Assafi75 joined alumina of two different purities using an alumina gel as an interlayer. The original interface was indistinguishable from either end member. Backscatter electron microscopy was used to determine the original interface by identifying the silica impurities in the two types of alumina. Another feature associated with the micro scale of joining is the possible observation of porosity. When joining fully dense end members, porosity can appear at the original interface. This usually has a negative effect on the strength of the joint. The micro scale is also where interdiffusion across the interface can be detected and measured. This can be done with backscatter electron spectroscopy (BES), Secondary Ion Mass Spectroscopy (SIMS)51 or with electron microprobe analysis (EMPA)76. A second way to envision joining on a micro scale is to consider sintering. Sintering is the joining of many smaller paiticles to each other to for1n a large mass. Solid state sintering is analogous to joining via diffusion bonding. As discussed earlier, the mechanisms for joining are based upon those developed for sintering. The end members could be considered as grains and the joint line would represent a grain boundary.

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50 Macro In this paper, the macro scale is considered to encompass those aspects of the joint that can be seen with the unaided eye The features of a joint that can be discussed on a macro scale include poorly formed joints, interlayers, reaction products and abrupt discontinuities when materials of differing colors are used. When a joint is not fully developed, the original interface is apparent because the edges of the end members still contain porosity. Interlayers are almost always a different material from the end members. Even when the joint is well made, the presence of an interlayer makes joint identification fairly routine. In the sit u ation where there is a reaction product, such as the joining of alumina and nickel oxide to form a spinel, the color change provides a good indication of the extent of the reaction. Materials Joining The joining of materials has attracted the interest of a growing number of researchers. There is vast potential in the joining industry to improve the properties of joined components. However, there are many theoretical and experimental issues regarding the joining process that must be addressed if the industry is to fulfill its potential. Some of the theoretical aspects of the joining process have been discussed previously in this dissertation. A recent focal point has been the effect of the use of an interlayer on the stresses developed in the final piece during joining77. Experimental work is being performed on several elements of the joining process. This includes the development of new methods for evaluating joint strength and new ways of joining materials. The joining field includes laminar composites that consist of polymer/metal or ceramic/metal bonding, and the more common butt joints of metal/metal, metal/ceramic, ceramic/metal/ceramic and ceramic/ceramic. The most recent addit i on to the joining field is the functionally graded interface (FGI). The functionally graded interface can be applied to any of the above mentioned methods of joining. The joint consists of a gradual compositional variation from

PAGE 71

51 one surface to the other (e.g.concentration and/or porosity) These changes result in property gradients (e g. strength, mechanical toughness or thermal expansion coefficients), which can be adjusted by controlling the composition and/or the microstructure of the interlayer. Metal/ceramic joining The metal/ceramic joint is present in two different situations. In one instance, it is an element of the design of the component. This enables the exploitation of the properties of both metals and ceramics. One example, mentioned earlier, is the case of a light bulb. The metal base is electrically conductive and pe1mits current flow to the filament with a minimum of resistance. The ceramic component, a glass envelope, is transparent to the visible light emitted by the filament. Joined together to for1r1 a vacuum seal, they provide a package that would be difficult to imitate using only a metal or a ceramic. The other instance of metal/ceramic joining occurs when it is necessary to join two ceramic pieces using a metal interlayer. A common example of this is in high-temperature structural applications. Under these circumstances, the high-temperature strength and refractory properties of ceramics are desired. High melting point metals such as titanium are used as interlayers when brazing ceramics for high-temperature applications. The brazing process is used because it requires a minimum amount of metal. Increased metal content may detract from the desired behavior of the ceramics. Alumina is the most common ceramic material to be studied in metal/ceramic joining. Perhaps this can be attributed to its popularity as a structural material, as well as the wealth of information available on its thermodynamic and mechanical properties. Routine polishing of the surface is the only treatment the ceramic piece receives prior to joining. Conversely, the metals are carefully prepared from high purity materials and meticulously cleaned and polished before these are used When the joint is to be formed via diffusion bonding, several different metals of varying thickness are used 78 79. Usually

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52 the added metallic layers are very thin and have a low melting temperature and elastic modulus compared to either the ceramic or the primary metal. This correlates with several thermal stress reduction methods in metal/ceramic joining discussed by Suga et al80. Ishida et al.81 relieved thermal stresses via the introduction of structural defects. This was accomplished by orienting the lattice when joining single crystals of niobium and alumina. Serier and Treheux82 increased the strength of a silver/alumina joint by work hardening the silver. They offer several hypotheses for the increase in strength, including the inducement of structural defects Frequently, the methods described above are not practical for service operations, and the formation of a liquid phase at the joining temperature is necessary to for1n a good joint. Ceramic/ceramic In 1979, Hauth8 3 noted that several emerging technologies have high-temperature use specifications for materials that will require ceramic/ceramic joining without the aid of a metal interlayer. The example referred to was a high purity alumina pumpout port for a thermonuclear fusion containment system. The pumpout port is a complex shape that is comprised of several regular shapes (cylinders and plates) fitted together. The joining method consisted of making a slmry of the unsintered material and buttering (as with toast) the surfaces to be joined. This is the same procedure for attaching cup handles and other extremities in the clay based ceramic industry. In the years since, numerous advances have been made in ceramic/ceramic joining but there are still many hurdles to be overcome. In the direct joining of similar ceramic materials, some chemical or physical variation must be present to assist the driving forces that make up the joining process. Scott and Brewer 84 diffusion bonded alumina at 1500 C and 69 MPa. The joined pieces were then heated to 1875 C to promote grain growth across the joint. They reported a maximum joining strength of 59o/o of the starting material. This was achieved with an axial

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53 defo1mation of 18 % during joining. In s imilar experiments 85, small amounts of MgO were added as a sintering aid to the alumina cylinders to be joined. The joining temperatures ranged between 1300 C and 1500 C with a pressure of 69 MPa Defo1mation increased to over 20% and no mechanical te st ing re s ult s were reported Zdaniewski and Kirchner 86 inserted thin poly styre ne sheets between 96% alumina plates. The decomposition of the polystyrene during heating created reducing conditions that enhanced interfacial bonding and diffusion. In spec imen s joined at 1350 C and 17.5 MPa, the authors reported flexural strengths of 194 MPa Direct joining has also been investigated for SiC and Si 3N 4 with modest success87 88. When the need for an indi s tinguishable joint is not imperative, there are more stra ightforward ways of joining ceramics for high temperature use. Zimmer 89 describes the development of several ceramic cements that can withstand high temperature s (> 1450 C). Glass or glass-ceramics are also popular choices as interlayer materials. Wherea s some authors90 9I chose glasses for their mechanical properties and crystallization abilities, other researchers 92,93 chose an interlayer glass composition that approximated the composition of the grain boundary phase of the crystalline end member s. When the glass was chosen for its crystallization ability, joints of modest flexural strength and fracture toughne ss were produced. Both groups of investigators who joined Si 3 N 4 with a glass similar to the grain boundary phase reported room temperature strengths of 450 MPa. Microwave Joining Microwave joining of materials appears to be one of the most promising among the areas of materials processing that have been included in microwave processing re search. Researchers have s uccessfully joined alumina, silicon carbide, silicon nitride and mullite94100. With the exception of a few studies, most of the work has been performed using single mode microwave applicators. The first report of joining ceramics using microwaves

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54 was by Meek and Blake 3 They successfully joined two alumina plate s with a glass interlayer in a home model microwave oven. Palaith et al 94 provide an overview of the fundamentals of microwave heating and how it applies to joining Using a tunable, single mode microwave oven modified to allow for an application of pressure Fukishima et al. 9 5 joined several di f ferent purities of alumina and silicon nitride. Specimens consisted of cylindrical rods mea s uring three millimeters in diameter. The alumina purities varied from 92 % to 99 % Joining experiment s were conducted at temperatures ranging from 1400 C to 1850 C and pres s ures up to 2 4 MPa The authors were able to produce direct joints using 92 % and 96 % alumina that approached the original s trength of the material. Figure 2 20 is the effect of joinin g temperature on the bending strength of the 92 o/o alumina. The 99 o/o alumina wa s s ucc es sfully join e d indirectly using both the 92 % and the 96 % alumina as interlayers. Bending s trength s of 90 % of the original material were reported No information was provided regarding creep deformation. However, even at the low joining pressures u s ed the temperature wa s high enough for creep to occur in high purity alumina. The s ame authors joined s ilicon nitride in a flowing nitrogen atmosphere using silicon nitride with a greater dielectric loss than the end member material. The effect of joining time on th e bending strength of the joined s ilicon nitride is s hown in figure 2 21. Al-Assafi and Clark 9 6 successfully joined 94 % alumina to 99.5 % alumina using a s ol gel derived alumina a s the interlayer. The researchers used a multimode cavity and microwave hybrid heating. Figure 2-22 is the Knoop hardnes s acros s the joint area for joints made with and without the gel interlayer The purpose of the gel interlayer is to provide a high purity powder with a large surface area to j oin the two surfaces In an effort to evaluate the joint non-de s tructively during processing Palaith and Silberglitt97 introduced an apparatus that provides an acou s tic pulse echo axially through the sample during joining Thi s provides information a s to the extent of the joint formation. Figure 2 23 is the result

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600 ccs a.. ._. 400 ..c: +,J 0) C (1) :i..... +,J Cl) 0) C -a C (1) co 200 1400 Before Jo1n1ng 1600 .~ I I ,..,, .. ,. Joining time: 3 min Pressure: 0 6 MPa 1800 Joining Temperature ( C) 2000 Fig ur e 2-20. Effect of joining temperature o n th e strengt h of 92 % alumina95 55

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ro a. 0) C (]) Cl) 0) C "'C C (]) co 500 300 100 0 "-sase dhesive Si s N4 Base: SN220 Adhesive: SN501 (1720 C; 6.2 MPa; 0.6 mm) 5 1 0 Joining Time (min) Figure 2-21 The effect of joining time on bend strength of silicon nitride9 5. 56

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z 2 2000 1800 1600 1400 1200 1000 800 600 400 200 0 99.5/o Alumina 94o/o Alumina ' ' ' . . no gel . . . -300 -150 0 150 300 Distance from Joint (m) Figure 2-22 Knoop hardne ss across jo int for microwave joined alumina 96. 57

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58 1400 700 1 2 00 .. 600 _1000 500 () 0 Q) 400 i... 800 .::, "Q) Cl) 300 :: a. 600 E 0 a.. 400 200 200 100 0 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Time (min) Figure 2-23. Acoustic emission traces for a mullite joining experiment97.

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59 o f an experiment involving the joinin g of mullite. Yu et al .98 employed thi s method in the s imultaneous sintering and joining of alumina powder s. At a temperature of 1400 C and a pre ss ure of 0.238 MPa, they achieved a den s ity of 99 % theoretical Silicon carbide i s an e x c ellent microwave ab s orber and a ceramic material that ha s many potential u ses. Therefore it ha s attra c ted the bulk of attention for microw a ve joining. The proce s sing of th e s ilicon carbide whether it i s reaction bonded s ilicon c arbid e or hot pre ss ed silicon carbide, c an s i g nificantly affect it s ability to absorb microwave s. Rea c tion bonded s ilicon carbide contain s r es idual s ili c on metal throughout the micro s tructure Ahmad et al. 99 dir e ct joined hot pre ss ed s ilicon carbide to hot pres s ed silicon carbide and to reaction bonded s ilicon cai bide They accomplished thi s using both a s in g le mode microwave and a multimode mi c rowave oven Yin et al. l oo joined the high dielectric lo ss s iliconized silicon c arbide u s ing a thin aluminum foil as an interlayer The authors achieved fracture s trengths c omparable to th e original material Other attempt s to join sili c on carbid e includ e th e u se of c ombu s tion s ynthe s i s. It ha s been d e monstrated that microw a ve s are an e x c ellent s ource o f e nergy for initiating and controlling the combu s tion s ynthe s i s reaction 1 0 1 Silber g litt e t a1.1 02 made s uc c e s sful SiC / SiC joints by initiating a c ombu s tion reaction between titanium s ilicon and carbon at the interface In an over v i e w paper di s cu ss ing the problem s and opportunitie s in microwave joining Loehman 10 3 s tate s that th e re are application s that hold promise but much work needs to be don e t o prov e th e value of mi c rowave joining He di s cu ss e s potential advantage s that c ould be realized by applyin g microwave proce ss ing to the joining of c eramics The author also identifie s problems that may be encountered and offer s s olutions through rigid pro c e ss c ontrol.

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60 Summary Several authors 104 105 have discussed the potential for energy savings through the use of microwave processing. It still is not clear if there is a significant energy conservation to be realized. Katz 106, regardless of his involvement as a researcher in the f ield of microwaves, displayed a skepticism towards many of the positive results being published regarding microwave processing. Despite a wary community of researchers, exploration of microwave processing has continued with success in specific areas. One promising niche involves the recovery of common and precious metals from electronic circuit boards 107. Microwaves also have proved successful in several industrial applications108 They are currently being used in some areas of food processing, rubber vulcanization and wood curing. Research in the microwave joining of ceramics is developing into a field that will have viable approaches to engineering problems. Microwave joining has proved feasible for several oxide and non-oxide ceramics. These materials can be joined with strengths at or above those attained on conventional joining processes. Some of the advantages that have been demonstrated by researchers include the ability to join materials with unfinished surfaces (large surface roughness) as well as non-destructive evaluation of the joint during the joining process The in-situ joint evaluation can be performed because it is possible for the end members to extend out of the heating zone. This provides access to the end members for the acoustical equipment. In the brief period of time that microwave joining has been investigated, many discoveries have been made that have led to further research. Much of the work reported has been presented in one of two formats. In the first method, the strength of a joint formed under specific conditions is presented with reference to the strength of the original material. The second method is somewhat more infonr1ative in that the results are compared to conventional joining of similar materials under comparable

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61 conditions. The conseq uen ces of chang in g the processing parameters have not yet been investigated. R esults need to be evaluated in a more scie ntific manner than plotting strength ve r s u s the processing parameter (temperature, pressure, etc.) The se parameters need to be eva luat ed to determine their relative importance in microwave joining. The intent of this research was to provide reproducible, microwave joining data based upon an experimental design coupled with numerical modeling of the experiment. The data generated will contribute to the advancement of microwave joining of materials by assisting in clarifying the effects of some of the processing parameters on the joined materials.

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CHAPTER3 MATERIALS AND :rvffiTHODS There are several objectives encompassed by the experimental procedure. The frrst objective was to choose a system of materials, consisting of end members and an i nterlayer, that was of technical interest and could be joined successfully using microwave energy. The second objective was to develop a device and procedure that could fabricate j oined specimens with reproducible properties. The first two objectives were incorporated i nto the third objective to manufacture joined specimens that were tested for flexure strength. These results then were analyzed to evaluate the relative importance of the processing parameters on the strength of the joined specimens. A fourth objective of this chapter was to monitor the temperature of the specimen and the susceptor during joining so comparisons could be made to the numerically derived temperature proftles discussed in the next chapter. The experimental work performed in this study can be separated into four phases. The first phase of the wo1k was the preliminary testing of potential interlayer materials Various properties of several materials were tested to deter1nine which materials possess the characteristics required to produce a strong joint. The material properties of greatest interest were the mechanical strength, refractoriness and microwave absorbing capabilities. The results reported by Al-Assafi75 indicate that an alumina based sol-gel was an excellent candidate to provide the desired characteristics. The second phase consisted of designing and implementing a microwave joining device to control and record the processing parameters. A microwave susceptor was 62

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63 developed to heat the end members to a temperature at which they become more efficient microwave absorbers. Using the materials that were classified as tenable interlayers, experiments to join two viable end member materials were initiated. Flexure bars were machined from the joined specimens and tested using four-point bending to evaluate the interlayer and end member materials based on strength. Phase three was the development of an experimental design that would use the chosen materials system to evaluate the significance of each of the processing parameters on the flexure strength of the joined material. Two values were selected for each processing parameter and an analysis of variances was performed on the results of the flexure tests. In phase four, a heat transfer program was used to simulate microwave hybrid heating. The results were compared to measured values collected in experiments run to measure the temperature of the specimen and of the susceptor. Two methods of temperature measurement were used to test the validity of the measuring process. Phase One The materials that were identified as potential interlayers were a series of alumina based gels, 96% pure alumina and nickel oxide. The alumina gel used by Al-Assafi was investigated as an interlayer material. It also served as a base gel that was combined with other materials. The other materials were introduced to the base gel either by substituting for the aluminum salt in the gel during forrnation or by admixing them to the stable sol before gelation. All of the materials added to the base gel were considered to be strong microwave absorbers. The intent of this approach was to increase the absorption of microwave energy in the joint area. All of the joining experiments in this study were performed in a constantly changing microwave field. Therefore, unlike the single mode applicator used by Fukishima et al. 95, there were no fixed positions where a high electric

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64 field was present Due to these processing conditions, there was no technique available to deter1nine the position of a stable hot s pot as described by Booty and Kriegsmann 39. Five materials (c hromium oxide, iron (Il) oxide, iron ( ill) oxide, nickel oxide and silicon carbide) were used in conjunction with the base gel to make ceramic powders for subsequent evaluation. These materials were selected from a myriad of strong microwave absorbers because of the way they combine with alumina. Chromium oxide is mutually soluble in alumina for an entire range of compositions. Iron (III) oxide also forms a solid so lution with alumina, but each material is capable of dis so lving around 10 % of the other. Iron (II) oxide and nickel oxide both form a spinel when combined with alumina. Silicon carbide does not form any intermediate compounds with alumina. Thin monolithic disks of 96% pure alumina and of nickel oxide also were examined as potential interlayer materials. Alumina was considered because it is very similar to the materials being used as end members: 99.5% and 96% alumina Using a similar material as the interlayer reduce s the risk of stresses from differential expansion and maintains a high s trength material throughout the joint region However, the similarity in composition presents a challenge to joining because it reduces the pre se nce of a compositional gradient to act as a driving force. Nickel oxide wa s chosen over iron (II) oxide as the second so lid material becau se it is less se nsitive than iron (II) oxide to oxygen partial pre ss ures. Sol-Gel Base gel The alumina based sol-gel interlayer was produced in accordance with a patent by Clark et al.109 for the creation of boehmite sols The mate1ials used to produce the base gel are water *, aluminum sec-butoxide **, and aluminum nitrate nonahydrate ***. The Deionized water resi s tance > 10 Mohm s ** Alpha Chemicals# 11140 Al ( OC~9 )3 F W. 246.33 *** Fisher Chemical s# A586 -5 00 Al ( N0 3 ) 3 -9H20 F.W 375.14

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65 purpose of the aluminum sec-butoxide is to provide the solution with metal ions. The water hydrolyzes the aluminum sec-butoxide. Aluminum nitrate nonahydrate is a peptizing agent that breaks up the precursor, permitting the hydrolysis to occur. This facilitates the formation of colloidal aluminum hydroxide particles. Throughout the remainder of this thesis, aluminum sec-butoxide will be referred to as ASB, and aluminum nitrate nonahydrate will be referred to as aluminum nitrate. W or.king within the parameters established by the patent, Dalzell I to reported a ratio of ASB:aluminum nitrate of 25 : I as providing a stable sol The ratio of 25: 1 ASB:peptizer was used throughout the course of this study. The ratios of the three components for the initial sol were 100: 1 : 0.04 corresponding to water:ASB :aluminum nitrate. Under reflux conditions, 675 milliliters of deionized water was heated to 88 C in a 1000 milliliter Pyrex flask that had been washed in a 6M nitric acid/0 2M hydrofluoric acid solution and rinsed in deionized water. During heating the water was stirred continuously by a Teflon coated magnet. Meanwhile, six grams of aluminum nitrate was dissolved in 45 milliliter s of water Rapidly, 104 milliliters of ASB was measured to minimize hydrolysis of the ASB from the air The ASB then was added to the water using two syringes *. The aluminum nitrate solution then was immediately added to the flask. The result was a cloudy, milky-white s olution This was stirred continuously until it became translucent. The clearing process took several hours. After the sol cleared, it was cooled to room temperature and stored in a polypropylene container until used. Doped gel According to the patent by Clark et al.109 several other metal nitrate salts may be substituted for aluminum nitrate during the sol-gel process Both chromium nitrate ** and Fisher Chemicals # 14-823-2D 60 ml syringes ** Fisher Chemicals # C33 l-500 Cr(N0 3 ) 3 -9H20 F. W. 400.15

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66 iron (Ill) nitrate* can replace aluminum nitrate in the sol. Chromium oxide f or1ns a solid solution with alumina at every composition Figure 3-1 is the binary Al20 3 -Cr 2 0 3 phase diagram at elevated temperatures The Al 2 0 3 -Fe 2 0 3 phase diagram, figure 3-2 is more complex. Below 1300 C, there i s a mixture of the Fe 2 0 3 (hematite) phase solid solution with Al 2 0 3 and Al 2 0 3 (corundum ) phase s olid solution with Fe 2 0 3_ Near 1400 C the presence of FeO b e comes significant as the s pinel, FeA1 2 0 4 is formed. McGill et al 111 reported that both c hromium oxide and iron ( III) oxide are excellent microwave absorbers in the temperature ran g e investigated at the frequency of 2.45 GHz The other additive s, silicon carbide **, nickel oxide *** and iron ( II) oxide ****, were admixed as powders into an alumina s ol and reduced to a s olid. The yield of the sol was determined in two ways In the direct method 200 milliliters of sol was dried and then heated to 1200 C. Thi s temperature was above the cry s tallization temperature of the stable a-alumina pha s e X ray diffraction analysi s confirmed that the alpha phase was the only phase present in detectable amounts The re s ultin g powder was weighed and had a mass of 5 08 grams. The yield of the sols was al s o d e te11nined mathematically. Using the ratio s of materials stated earlier calculations were made based on u s ing 100 moles of water one mol of ASB and 0 04 mole s of aluminum nitrate This would provide 1 04 moles of aluminum availabl e for oxide formation Thi s, in turn would produce 0.52 moles of alumina which represent s a mass of 53 grams of alumina By c alculating the volume of the resulting s ol a yield of 0 026 gram s of alumina per milliliter of sol wa s determined. For a 200 milliliter Fisher Chemical s # ll 10-500 Fe(N0 3)3 -9H 2 0 F W ** Norton Company SiC E-85 Cry s tolon 220 grit F.W. 40.1 *** Fi s her Chemical s # N69-500 NiO F W. 74.71 **** Fisher Chemi c al s # ll 19 500 FeO F.W. 231.54

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2300,--------------------.. _, _, ; _,, .,,., 2275:t25 -------2200 ,"" ,, ,,,, ,,,, ,,, ,,,, (].) I,... ::J ..... cc I,... 2100 E (].) J2000 20 40 60 80 Figure 31 Binar y C r 2 0 3Al20 3 phase diagram112 1600----------------Spinel s s Hematite s s + Spine I s s Spine! s s + Corundum s s Spinal s s r+ Fe 2 0 3 Al 2 0 3 V, V, 0 1400 V) V) Fe 2 0 3 Al 2 0 3 + Corundum s s E :l 't:J 0 (].) I,... ::J ..... cc I,... (].) c.. E (].) J1200 Q) 0 E Q) :i: Hematite s s + Corundum s s '0 u I \ I \ \ I 000 ...__J _____ --o __ ____. _____ .._ __, Fe 2 0 3 20 Fe203. Al203 60 wt 0 /o Al 2 Q 3 80 Figure 3-2. Binary Fe 2 0 3 -AI 2 0 3 phase diagram ll3. 67

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68 sol, this renders 5 .12 grams of alumina -a difference of less than one percent from the experimentally dete1n1ined value. The powders were added to s ols in a 1 : 1 molar ratio with the expected yield of alumina. The mixture then wa s ultra s onicated for ten minutes to break up agglomerate s The sol/powder mixture then wa s gently heated on a hot plate while stirring until much of the liquid wa s removed. The resulting gel was heated overnight at 150 C to remove most of the remaining liquid. The end result was a solid mass of opaque material. This was crushed in a mortar and pe s tle and sieved through a 325 mesh ( 44m ) screen. Using a 1 2 centimeter diameter steel die 1.5 grams of each powder were pressed into pellets using a 1 3 3 kN force Sol-Gel Characterization The gels produced were characterized u s ing several diverse method s The different composition s of p e llet s were heated using microwave energy at 2.45 GHz to evaluate each a s a microwave ab s orber. Differential s canning calorimetry ( DSC) was performed on the variou s compo s itions with x-ray diffraction analysis conducted on the resulting material. Dielectric properties of the different compositions were measured at 2.45 GHz a s a function of temperature. Stand alone heating A homes tyle microwave oven was fitted with an on/off temperature controller An inconel-shielded Type K thermocouple wa s placed in contact with the s pecimen for temperature mea s urement within th e microwave Refractory brick ** wa s s culpted to accommodate a s p ec imen and a thermocouple feedthrough The brick provides in s ulation to reduce heat los s from the s pecimen during heating. The setup in Figure 3 3 has a General Electric 7 50 Watt Dual Wave Il Microwave System ** Thermal Cerami cs K-3000 3000 F refractory brick

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refractory brick refracto ry brick 69 thermocouple Type-K ; inconel shea th Figure 3-3 Setup used to measure temperature of gel compositions heated solely by microwaves (setup wa s placed in a microwave for heating).

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70 maximum test temperature of 1175 C. Specimens were heated at full power (800 W) using the setup in Figure 3-3. Temperature readings were taken periodically. Initial results may have been influenced by arcing between the thermocouple and the specimen Arcing is the release of a charge build up between two points which can cause localized heating and even melting of the thermocouple and the s pecimen Another problem associated with arcing is inaccurate, widely varied temperature readings. One way in which arcing was red11ced was by increasing the surface area of the tip of the thermocouple. In this case, a thin nickel di s k was placed between the thermocouple tip and the specimen. This significantly reduced the amount of arcing encountered during the study. Differential scanning calorimetry Differential scanning calorimetry was performed on a Stanton Redcroft DSC 1500S. The gels were heated from room temperature to 1400 C at ten degrees per minute in flowing air. A second experiment was conducted on the sample containing FeO. This time, the maximum temperature was 1250 C in order to avoid any reactions that occur above 1250 C. A piece of sapphire similar in mass to the sample powder, was used as a reference material to maintain a level baseline X-ray diffraction analysis The ceramic powders that resulted from heating in the DSC were subsequently analyzed using a Scintag X-Ray Diffraction Analyzer. The x-rays were copper k-alpha at 45 kilovolts and 40 milliamps at a wavelength of 1.54060 angstroms. The powders were scanned at one degree 2 0 per minute from twenty to sixty degrees 2 0. This 20 range wa s sufficient to identify any of the compounds formed during heating that involved any of the materials used

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71 Dielectric properties The relative dielectric constant and loss factor, E'r and e''eff, were measured for several compositions of the dried powder at 2.45 GHz as a function of temperature. Before analysis, the powders were heated to 450 C to remove all of the bound and structural water. This was done to provide the instrument with a relatively constant mass of material. The dielectric properties were measured from room temperature up to 1400 C These measurement s were performed at Chalk River Laboratories/ Atomic Energy of Canada, Ltd. using the cavity perturbation method*. Alumina The two purities of alumina used as an interlayer material were Coors AD94, 94% alumina and Coors AD96, 96 % alumina. The major impurities in all of the Coors alumina products are silica, magnesia and calcia. These impurities act as fluxes for densification and as grain-growth inhibitors. The manufacturer reports a room temperature flexure strength for the AD94 of 350 MPa. The grain size range s from 2-25 microns with an average grain size of 12 microns. Other relevant properties of the alumina are in Table 3-1. The interlayers were produced by cutting disks approximately 2 millimeters thick from a cylindrical rod 2.54 0.0025 centimeters in diameter and 20.32 0.0025 centimeters long. The disks were mounted on a glass plate and the surfaces were machined using a high speed diamond grinding wheel **. The machining procedure used a downfeed of five microns per pass and a crossfeed of 2.5 millimeters. The disk s had a final thickness of 1.5 0.15 millimeters R. Hutcheon AECL Chalk River Laboratories, Chalk River, Ontario, CA ** Norton ASD320 R75B99-1/4 320 grit wheel

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72 Tab l e 3-1. Manufacturer R eported Properties of Coors Al u mina Used in Study. :.: Property Units AD-94 + AD-96 + AD-995+ Specific Gravity 3.62 3.72 3.84 Crystal range 2-25 2-20 10-50 rmcrons Size 12 11 20 average Flexural 2s 0 c MPa 350 359 310 Strength 1000 c 140 172 230 Modulus of Elasticity GPa 282 303 358 Shear Modulus GPa 117 124 152 Bulle Modulus GPa 1 66 173 207 Poisson's Ratio 0.21 0.2 1 0.21 Maximum Use (no load) cc 1700 1700 1,750 Temperature The11nal 25 c 18.0 18.0 31.4 Conductivity 100 c W/m K 14.6 14 6 27 2 400 C 7 .1 7 .1 11.7 800 C 4 2 4.2 7.1 S pecific Heat 100 c J/K(kg) 880 880 880 25 c 8.9 8 9 9.4 Die l ectric Constant 500 C ratio 10.4 1 GHz 800 C 11 0 25 c 0 0008 0.0001 0.0001 Die l ectric Loss 500 C ratio 0.0002 Factor 1 GHz 800 C 0.0003 25 c 0.007 0.001 0.001 Loss Tangent 500 C e" e' 0.002 (tan o) 1 GHz 800 C 0.003 +Coors Alumina and Beryllia Properties Handbook, B u l letin 952, Coors Ceramics, (1969 ) Nickel Oxide High-purity nickel oxide disks, hot pressed to >80 % dense, were obtained from Super Conductor Materials, Inc. The as-received disks were 2.5 centimeters in diameter and 1.2 centimeters thick. The surf ace of the disks were impregnated with a graphite

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73 residue from the manufacturing process. A low speed wafering saw was used to section the disks into thinner pieces. As with the alumina interlayer specimens, the nickel oxide disks were mounted on a glass plate and machined to a thickness of 0.33 0 02 m111imeters. All of the graphite was removed during the grinding step. Surface roughness The machined surf aces were characterized using a laser profilometer*. A 3dimensional scan was performed on a five millimeter by five millimeter square section of the surface. A total of 250 line scans were performed on each material. The table speed was 10 mm/minute. The average surface roughness was calculated from a single scan using the same distance and table speed as the 3-dimensional scans. The roughness reported is the deviation from the arithmetic mean and was calculated automatically from the profiles using the equation R = a 1 I T f IY ( x ) ldx C (3-1) Figure 3-4 illustrates the arithmetic mean in a simulated profile and identifies the components of equation 3-1 that are used to compute the surface roughness. m e an l ine y 0 X Figure 3-4 Simulated material profile depicting the arithmetic mean. *Rodenstock RM-600 Laser Profilometer

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74 Phase Two Currently, there are no commercially available systems to perform the microwave joining of ceramics. Therefore, an apparatus had to be designed and constructed to accomplish this task. The modification of a microwave oven to accommodate the application of pressure has many challenges associated with it. Turntables or fans used to stir the microwave field may interfere with the application of pressure and must be removed or repositioned. The external holes needed to apply a load on a specimen in the microwave cavity are a breach of the microwave containment system and present a potential health problem (see equation 2-5). Extreme care must be taken in the design and fabrication of the joining apparatus to address these challenges and prevent them from hindering the joining experiments. There are several reasons why alumina was chosen as the material of interest for this study. Alumina is one of the most widely used technical ceramics. It is prominent as a substrate for electronic materials, as a refractory mate1ial, and as a structural ceramic. Although alumina is not always the ideal material for the intended use, it is often chosen because of its low cost The thermal or mechanical properties of alumina are also considered acceptable for many applications when the ideal material is either unavailable or too costly. Alumina can be obtained in a multitude of purities, grades and sizes designed to meet most of the needs of the technical community Another predominant reason for selecting alumina for this study is that it is a common material for testing and analysis There is an abundance of documentation available detailing its properties and performance under widespread conditions. This includes the thermal, electrical, optical and mechanical behavior upon expo s ure to elevated temperatures. The end members considered for the joining experiments, 99 .5% and 96o/o pure alumina, are both poor microwave absorbers compared with the materials being surveyed

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75 as potential interlayers. Without assistance, the end members are unable to heat to the temperature required for joining u s ing the microwave oven designated for this study. Microwave hybrid heating, discussed in Chapter 2, is a logical approach to provide the thermal energy for joining these end members A microwave susceptor was used to generate the radiant heat necessary to raise the temperature of the end members being joined to a temperature where they could then more efficiently absorb microwaves The susceptor can be made from a number of materials, including those being examined as potential interlayers. Design parameter s that should be considered include the shape of the workpiece being heated, the air gap desired between the workpiece and the susceptor, the method in which the temperature of the workpiece will be measured, and most importantly, the ability of the workpiece to absorb microwaves. This last factor will determine the amount of microwave absorber needed in the susceptor to attain the desired temperature. There are at least two methods of making susceptors. The first consists of fixing a microwave absorbing material to a piece of low density insulation that has been shaped into the desired configuration. This was simple to construct and works well for low temperature applications. The second method involves casting a susceptor using a refractory cement with granules of microwave absorbing material dispersed in it. This method works very well at high temperatures. These susceptors tend to be more mas s ive than the fust type and can shield very small specimens from the microwave field Microwave Joining Apparatus The joining apparatu s consisted of several components, each with a specific function. To physically support the remaining components, a load frame, capable of sustaining the maximum applied load, wa s machined from an aluminum alloy A home model microwave oven* wa s modified to facilitate the application of pres s ure and the Goldstar MA-1172M 1000 Watt microwave oven

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76 monitoring and control of temperature. An air cylinder* capable of supplying a load of 2.2 kN was mounted on the top of the load frame. A load cell**, mounted in line with the air cylinder, measured the load being applied. The feedback provided by the load cell in the form of a voltage was used to control the load applied by the air cylinder. An 18 millimeter diameter high-purity alumina rod was used to transfer the load into the microwave cavity. A 20 millimeter feedthrough was machined in the top of the microwave t o provide the ram access to the cavity. The diameter of the hole was less than one -s ixth t he wavelength of the microwave s u se d in this study. In Chapter 2, the critical hole diameter for significant transmittal of microwaves was found to be one-half the wavelength of the microwave However in thi s setup, there was a dielectric material (alumina push r od, E'r z 9 ) partially filling the aperture in the wall of the microwave cavity In this setup, t he dielectric material acts a s an antenna for microwave propagation and the ability to contain the microwave s was brought into question. To ensure a minimum transmittal of microwave energy via the feedthrough a 7 5 centimeter long copper tube of the same diameter a s the aperture was inserted into the feedthrough. The placement of an electrical conductor tube prevents microwave leakage Metallic tape was used to cover any other gaps where microwave s might leak. The microwave's turntable was discarded and the turntable motor was relocated to the side of the microwave opposite the wave guide. An aluminum mode s tiner was attached to the motor to improve the unifor1nity of the field within the microwave Mo s t of the operations performed during the joining process were controlled by a computer program *** tunning on a Macinto s h IIC. This included storing the values of applied pressure and using thi s information to adjust the air cylinder. The Bellofram model # 900-009 500# air cylinder ** Revere Transdu ce rs model# 63HC-D3-500-10pl 500# load cell *** National Instruments Labview Version 2.0

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77 computer was also u s ed to store the temperature readings from two Type-R thermocouple s* The two thermocouple s were fed through an eight millimeter hole in the back wall of the microwave cavity A s etpoint controller ** was used to regulate the maximum temperature during the process. The temperature controller was spliced into the magnetron power s upply s o that the temperature could be regulated by turning the magnetron on and off a s nec ess ary. Fi g ure 3-5 i s a schematic and figure 3 6 is a photograph of the microwave joinin g s etup Microwave Susceptor s In preliminary microwave hybrid heating experiments Del 14 heated alumina in a microwave furnace using a commercially available su s ceptor ***. The s e microwave furnaces were s imply a silicon carbide coating on a low density alumino-silicate refractory. At temperatures near 1500 C both the s ilicon carbide coating and the refractory lining experienced significant degradation This led to a reduction in the furnace' s ability to ab s orb microwave s. Al-Assafi 75 produced s usceptors using a refractory with a lower dielectric lo s s factor than the commercially available furnace This enabled the maintenance of temperatures of 1500 C for one hour without destruction of the s usceptor. These su s ceptor s proved s uffi c ient for on e experiment, but a ss embling a susceptor with a uniform coating that maintained it s microwave absorbing ability throughout a course of high temperature experiment s was not fea s ible It became necessary to seek an alternative approach to microwave hybrid heating to provide a high-temperature, extended-use susceptor. For thi s research, a mold of the desired susceptor was formed out of concentric *ARi Inc. model# IIlT-99N-4DR9AA-36 Type-R the1mocouple ** Omega model # CN9000A Miniature Autotune Temperature Controller *** National Superconductor Microwave Gla s s Melter

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air cylinder thermocouple temperature controller Figure 3-5. Schematic of the microwave joining apparatus. DOD DOD aaa as [lD 78

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79 ..,., ... .'f. ... \ ... . l 1 .. 1 J "; . Figure 3-6. Photograph of the microwave joining apparatus used in all of the microwave joining experiments

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80 polypropylene cylinders. High alumina content cement* was mixed with silicon carbide granules and enough water to make a slurry. This was cast into the mold and allowed to set. The process for for1oing the susceptor is outlined in figure 37. The polypropylene rings were removed and the cement/SiC cylinder was cured by slowly heating it in a conventional ftnnace to 1000 C for one hour. After cooling, the susceptor was ready to use. The amount of cement and s ilicon carbide was varied to dete11nine the amount of silicon carbide that would absorb the appropriate amount of microwaves to provide the desired thermal environment for the joining process. This was done systematically by mixing the cement and silicon carbide in different ratios. Silicon carbide granules were added in amounts of 5 10, 20, and 30 volume percent of the cement. The volumes were determined t1sing the density of alumina to approximate the density of the cement (96 % alumina) and the density of silicon carbide. Enough water was added to make the mixture castable. The cylinders were all approximately 300 grams. All of the cylinders were cured as described earlier. To determine the ability of the cylinders to heat, they were insulated as shown in figure 3-8, placed in a microwave oven and heated using 3200 watts of power The temperature was measured in both the center of the suscepting cylinder and outside of the refractory wall using Type-K thermocouples shielded from the microwaves by a inconel sheath. The dielectric properties of the cylinders as a function of temperature were measured at AECL using the cavity perturbation method. The susceptor used for the joining process was similar to those used in the susceptor evaluation experiments. A 36 volume percent loading of silicon carbide was u s ed in the susceptor. Two 4 millimeter in diameter hollow alumina tubes were fixed in Alcoa Al 66 97 % Al 2 0 3 3 o/o CaO

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weigh SiC determine weight percent of SiC measure 20 ml water admix ceme nt t o water adm i x SiC to ce men t/ water YES pour into mold /cov er c ure at 1 000 C/1 hr weigh cement NO ----1 add water dropwise Figure 37. Flowchart used to produce suscepto r s for microwave joining. 81

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82 thermocouple ( TypeK) thermocouple (TypeK ) alumina load D AL 66 cement ~$~5 cement/Sic susceptor Figure 3 8 Cutaway view of the s etup u s ed to evaluate the heating ability of susceptor s.

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83 the side wall of the susceptor mold. The tubes allowed the thermocouples access to the specimen being joined. The alumina tubes were maintained as part of the susceptor to act a a barrier between the silicon carbide in the susceptor and the platinum sheath of the thermocouple. To insulate the susceptor, low density fiber board* was cut into pieces that formed a close fitting box around the susceptor A hole was machined in the top of the fiber board to accommodate the ram used to apply the load Two smaller holes were machined in the side for the thermocouples and a third hole provided a viewing port for the optical pyrometer. An additional hole was placed in the bottom piece so that another short rod of alumina could support the specimen from the bottom. Figure 3-9 is a schematic and figure 3-10 is a photograph of the susceptor used in the joining experiments. The first group of experiments involved the joining of assorted end members of AD995 and AD96 alumina using an alumina based gel or AD96 alumina as the interlayer material. The two sols used for these experiments were the sol made with 4 mol % chromia and the sol loaded with 50 mol % nickel aluminate spinel. These gels were chosen because they both heat better than the base gel in a microwave field and they both react predictably under the heating conditions used. Further discussion of the selection of these compositions will be presented in Chapter 5. The surfaces of the end members to be joined were thoroughly cleaned with acetone. A drop of ethanol was placed on the machined surface of one end member to promote the wetting of the alumina by the sol. The sol was added to the surface dropwise until it was covered completely -about two milliliters of sol total. The sol was dried in ambient air and formed a solid, glossy layer. The two end members were placed in contact and held together with cellophane tape. The specimen was positioned in a 36 volume percent silicon carbide susceptor and a 50 N load was applied to secure the specimen in *Rath Perfortnance Fiber Inc, Altra KVS 17 /400 high temperature insulating board

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Aluminosilicate refractory Alumina pushrods Type R shielde thermocouples Alumina cement/SiC granule susceptor Type R shielded --thermocouple Coors AD995 alumina specimen 84 side view top view Figure 3-9. Schematic of the specimen/susceptor setup used in the microwave joining experiments

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85 Figure 3-10. Photograph of susceptor set up inside the microwave cavity.

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86 place. The specimen was heated at full power to the setpoint of 1500C. Approximately 50 minutes were required to attain the setpoint temperature. The specimen temperature was measured with a single Type-R thertnocouple described previously, placed in proximity to the joint. From then on, the setpoint controller maintained the temperature at 7 C. A pressure of 2.5 MPa then was applied for a duration of 30 minutes. The power to the microwave was turned off and the pressure reduced. The specimen was allowed to furnace cool to room temperature. Specimen Preparation The joined specimens from the microwave joining experiments were characterized using a several step process. After joining, the specimen was visually inspected to determine if it was joined on a macro scale. This inspection was also to look for any indications of problems that may have occurred during the experiment. This included end members that are not parallel due to uneven loading or scorch marks left from extensive arcing between the specimen and the thermocouple. The joined specimens then were mounted upright onto a glass plate so they could be machined into bars for strength testing. The same machine used to prepare the specimens for joining was used for the machining of the flexure bars. A feed rate of five microns per pass was used to cut the joined cylinders into slabs approximately 4.5 millimeters thick. The position of each slab in the starting specimen was noted. The cut slabs then were remounted flat on the glass plate. The surfaces were marked with an indelible marker to ensure that material had been removed from the entire surface of each slab. The exposed surface of the slabs was machined using the diamond wheel described earlier. A downfeed of five microns per pass and a crossfeed of 2.5 millimeters per pass was used to limit the machining stresses experienced by the joined material. When the slabs were machined to a uniform size, the thickness was measured and remounted with the as-cut side exposed. For this side, the downfeed and crossfeed remained the same. However, the amount of material to be removed was

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87 calculated so that the finished slab would be 4.0 0.05 millimeters thick. After the desired thickness was achieved, the diamond slicing wheel was again used to cut the slabs into bar s approximately 3.5 millimeters thick The machined bars were cleaned using acetone in an ultrasonic bath to remove any remaining adhesive used to fix the specimens to the glass plate Each bar was motmted in a vise to expose the cut surf ace. In the same manner as the slabs, the bars were machined to a thickness of 3.0 0.05 millimeters. To limit the possibility of the bars fracturing at the edges during testing, a special vise was used to chamfer the edges of each bar Approximately 75 microns of material was removed from the edge of each bar using the grinding wheel and machining parameters described previously. During the machining of the test bars, the joined specimens were put under grinding stresses that were typically 5 MPa and above. Several of the joined specimens failed during various stages of the machining process In some instances, specimens that were considered joined after visual inspection, did not yield any intact bars after the machining process Figure 3-11 is a schematic of the joining process and the flexure bar preparation. Mechanical Testing The bars were tested in a screw-driven test machine*. Four-point bending was used to break the bars. A crosshead speed of 0.5 mm/min was used in all the experiments. Figure 3-12 is a schematic of the test fixture used for all the room temperature flexure tests. After each bar was fractured the fracture load was noted and the remnants of the test piece were collected for optical inspection of the fracture surface. Flexure tests were performed at 1000 C on some of the joined specimens. It was necessary to use a different load frame for the high-temperature tests. On this load frame, the load was applied pneumatically so the applied load was controlled as opposed to the ATS series 1605 computer controlled universal test machine

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end members hot pressed (joined) in microwave using various times, temperatures and pressures. machined into 3 mm x 4 mm x 50 mm flexure bars. Figure 3-11. Flow diagram of the microwave joining process and specimen preparation. 88

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h L FLEXURE BAR JOI NT a) p Lo LOAD TRAIN ADAPTER BUSHING R EGION OF MAXIMUM TENSILE S TRE SS GUIDE ROD ALIGNMENT FIXTURE BALL BEARING FOR ARTICULATION b h The maximum tensile stress occurs in this region b) Smax = 1.5 P (Lo Li) / (b h 2 ) 89 Figure 3-12. Flexure fixture for room temperature te s ting of bar s u s ing four-point b e nding a) sc h e matic of flexure ri g and b ) label s of relevant dimension s.

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90 screw driven machines where the crosshead speed was controlled. Bars from some of the experiments were loaded in an alumina fixture and heated to 1000 C in approximately 30 minutes. When the temperature stabilized, the bars were put under an increasing force of 7 N/s until fracture. Phase Three In phase three, the development of an experimental design was used to evaluate the significance of each of the processing parameters on the flexure strength of the joined material Five of the processing parameters were varied. Two values were selected for each processing parameter and an array of joining experiments were devised. Flexure tests of bars machined from the joined specimens provided the strength data to perform an analysis of variances comparing the two levels of each processing parameter. A separate study was done to evaluate the effect of the original position of the bar within the joined workpiece on the flexure strength. The effect of the bar's position on flexure strength was explored separately for specimens joined using microwave energy and those joined using conventional heating methods. Various analytical methods were employed to characterize the joint region in terms of microstructure, composition and reactivity. An experimental design was constructed in an effort to determine the relative importance of several of the variables in the joining process Along with time, temperature and pressure, the interlayer material and the method of heating were investigated. In order to assess the influence of each of the five variables, it was determined that the flexure strength of the joined materials would provide an accurate reflection of the integrity of the joint. Each of these processing parameters were considered at two levels, "high" and "low". For the linear parameters of time, temperature and pressure, the two levels were chosen from the typical range for these parameters for the joining of alumina. The "high'' and "low" levels of the non-linear parameters of interlayer material and heating method are

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91 fixed as shown in Table 3 2. Monolithic inter l ayer materials were used for this portion of the study instead of the gel-derived materials to provide more substantial contact between the end member s and the interlayer. To evaluate all of the possible effects of the processing parameters would require an exce s sive number of experiments Using the half factorial experimental de s ign laid out by Dav i es l 1 5 permitted the evaluation of the main effect of each of the proce ss ing paramter s on the flexure s trength of the joined specimens. The u s e of the half factorial design s acrifices the acquisition of information regarding s econd and higher order effects An example of a second order effect would be the influence of time on the way pre s sure effects the flexure strength of the joined mater i al. The number of experiments to fill out this design wa s calculated from the equation #ex.= 1 ( 3 2) wher e # ex is the number of experiments necessary and n i s the number of processing variables (five in this case). Table 3 2 Level s of Varied Processing Conditions. Time Temperature Pressure Heating method Interlayer (min ) (C C) (MPa ) material High ( + ) 45 1550 3 AD94 nucrowave Low() 15 1450 1 conventional NiO The sixteen experiment s needed to provide enough information to sufficiently evaluate each of the proce s sing parameter s are identified by this design Table 3-3 lists the required experiments along with the proce s sing parameters. Note that not e very combination of the two level s of each parameter wa s pre s ent Thi s was the advantage of the half factorial where there were no second order interactions. Microwave Joining The eight microwave joining experiments were carried out in the microwave apparatus described previou s ly u s ing the s u s ceptor produced with 36 volume percent

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92 silicon carbide. A nominal load of 50 N was used to secure the specimen in place Specimens were heated as rapidly a s possible to the joining temperature. At that time the temperature controller turned the microwaves on and off as necessary to maintain the setpoint temperature. Simultaneously, the load wa s increased to the predetermined value. After the prescribed soak at temperature, the load was reduced to the original level The initial 20 minute s of cooling was carried out by generating microwaves 40o/ o of the time. The second 20 minutes of cooling was facilitated by the generation of microwaves for 20 % of the time After the forty minute s of controlled cooling, the joined specimen was allowed to cool naturally This procedure paralleled the cooling profile in the conventional furnace more close ly than if the microwaves were just turned off. Table 3 3. Experimental Design used to Aid in Determining the Effect of Processing C d ti th Str th f th J t on 1 ons on e eng1 0 e 01n Trial time temperature pres s ure heating interlayer (min) ( Q C) (MPa) method material 1 15 1450 1 Microwave NiO 2 45 1450 1 Microwave Al 2 0 3 (94%) 3 15 1550 1 Microwave Al 2 0 3 (94%) 4 45 1550 1 Microwave NiO 5 15 1450 3 Microwave Al 2 0 3 ( 94 %) 6 45 1450 3 Microwave NiO 7 15 1550 3 Microwave NiO 8 45 1550 3 Microwave Al20 3 ( 94 %) 9 15 1450 1 Conventional Al20 3 (94%) 10 45 1450 1 Conventional NiO 11 15 1550 1 Conventional NiO 12 45 1550 1 Conventional Al 2 0 3 (94%) 13 15 1450 3 Conventional NiO 14 45 1450 3 Conventional Al 2 0 3 (94%) 15 15 1550 3 Conventional Al20 3 (94%) 16 45 1550 3 Conventional NiO ~,

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93 Conventional Joining The conventional joining experiments described in the experimental matrix were carried out in a furnace designed for high-temperature compression testing. Resistively heated molybdenum disilicide elements were used to heat the specimens. The specimen to be joined was placed between two 25 millimeter diameter silicon carbide rods extending through both the top and the bottom of the furnace. A load was applied to the upper rod by an air cy tinder capable of generating 2000 N of force. A load cell, connected to the lower silicon carbide rod, measured the applied load. As with the microwave joining experiments, a nominal load was used to secure the specimens in place. The temperature of the specimen was measured by a Type-S thermocouple placed within one centimeter of the bottom end member. The furnace was heated at full power up to the joining temperature at which the joining load was applied. When the duration of the joining portion of the experiment had concluded, the load was removed and the furnace was shut off and allowed to cool. A data collection program* was used to apply the load at the setpoint and record the applied load and specimen temperature during the experiment. Optical Inspection Specimens that appeared joined after visual inspection were viewed with a stereo microscope to evaluate the quality of the joint. Specimens that were initially considered to be joined but subsequently failed during handling were also inspected using the stereo rrucroscope. The fracture surf aces of all of the bars tested were inspected using the stereo microscope. Some of the bars were mounted in epoxy so that the joint region was exposed. The bars then were polished to a mirror finish with 0.25 micron diamond paste. The joint region of these specimens were examined in an optical microscope. Several of the *Keithley 500 data acquisition software; modified by M.K. Ferber, Metals and Ceramics Division, Oak Ridge National Labs

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94 specimens were coated with a carbon film and observed using a scanning electron microscope*. The roughness of the end member at the joint line was compared to the roughness of the end member prior to joining. This was accomplished by digitizing the joint line from micrographs taken of the profiles of the joint line and of the initial surface. The digitized images were plotted graphically and roughness values were calculated using equation 3-1. Wavelength dispersive spectroscopy (WDS) was performed using a JEOL Superprobe 733 electron microprobe. X-ray maps generated by this analytical method provide qualitative data with respect to the amount of each of the elements present. The ray maps are generated by first calibrating the detector using a standard that contains a known amount of the element to be measured. Then a photograph was taken of the area in question for reference purposes. Finally, the detector perforrr1s a sweep across the desired area, measuring the intensity of the x-rays corresponding to the standard. Silica was the main impurity in both AD995 and AD94 alumina. A silicon calibration standard was used to confirm the presence of silica near the joint area of several of the specimens joined using AD94 as the interlayer material. Statistical Analysis An analysis of variances (ANOVA) was performed using statistical software** to deterrnine the extent of the effect of the processing conditions on the strength of the bend bars. The program is capable of performing analysis on the half-factorial experimental design devised earlier. There are also provisions that can account for the specimens that were joined on a macro scale, but did not yield any flexure bars after the machining process. The ANOV A compares the mean strengths of the bars at the two levels of each *Hitachi S-800 Scanning Electron Microscope ** Abacus Concepts SuperANOV A version 1.11

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95 processing parameter. The program then determines if there is a significant difference between the strengths measured with the two levels at a 5% level of confidence. A separate ANOV A was performed only on the specimens joined using AD94 as the interlayer material. The effect of the position of the bar in the original material (i.e. center; middle; inside; outside) upon the flexure strength was investigated for both the microwave and conventionally joined specimens. A comparison of the results for the two heating methods provides insight into the contribution of vo l umetric heating towards the uniforrr1 heating of large pieces. Phase Four Phase four consisted of both the measurement of microwave heating profiles and the generation of these profiles using a heat transfer program. The measured profiles were collected for the workpiece and the outer wall of the susceptor The temperatures at these two positions were measured using both a shielded thermocouple and an optical pyrometer. In the simulated microwave hybrid heating portion of the experiment, the temperature was tracked at positions corresponding to those monitored in the laboratory experiments. Heating profiles were generated for different interlayer materials and thicknesses. The profiles were compared to the measured temperatures to determine the validity of the model. The development of the model for simulating microwave hybrid heating is discussed in detail in Chapter 4.

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CHAPTER4 NUMERICAL MODELING While the experimental joining work was being performed, a simultaneous effort was put forth to model the transient temperature profiles of the workpiece being joined and of the microwave susceptor The purpose of this endeavor was to evaluate the possibility of enhanced heating of the workpiece under microwave hybrid heating conditions. A conduction heat transfer program* was used to develop a model to simulate the heating profiles measured in a microwave oven. Heating 7 .2 is a multifaceted program that allows the user to choose from a variety of coordinate axes in onetwoor three dimensions to describe the physical model. Many of the material properties necessary for the heat transfer calculations can be input as a constant, or as a function of either time, temperature or position. Heating 7 .2 is capable of solving both steady-state and transient heat conduction problems. Transient heating profiles are calculated using one of several finite difference schemes available to the user. An explicit or implicit transient solution technique can be specified for solving the problem. The required input is read from a file resembling a set of Fortran punch cards, relying on keywords to identify the input data. The program output can be readily formatted as an ASCII file which then can be read by many available plotting programs. Heating 7.2 implements the computational method of finite time difference to solve the partjal differential equation used to describe heat transfer in materials. Due to the versatility of Heating 7 .2, the discussion of the elements of the program will be limited to those pertaining to the intended calculations. *Heating 7.2 K.W. Childs, Computing Applications Division, Oak Ridge National Labs 96

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97 Heat Transfer The fir s t s tep in cal c ulating heat transfer is to define a grid superimposed on a coordinate axi s. Grid inter se ction s are called node s and each node i s s urrounded ( in 3-d ) by eight element s and i s in contact with s ix other node s The temperature of each node i s c al c ulat e d from a c o mbination of th e prop e rtie s de sc ribing that node the temperature s of the s ix node s in co ntact a nd t o a l ess er e xtent, nod es that are nearby but not co nn ec ted t o the node in que s t i on The finite volum e heat balance i s based on the partial differential equation repre se ntin g heat tran s port in a material e quation 4-1 ( 4 1 ) where C p heat c apacity J/kgK p den s ity kg / m 3 K ther111al c ondu c tivity, W / mK and Pv ab s orbed power p e r unit volume W /m 3. When thi s p a rti a l differ e ntial equati o n i s c onverted into a finite-volume h e at balanc e e quation for nod e o it i s e xpr ess ed a s where T D m o Km C o Llt 6 = P 0 + L 0 K m( T : -T :) m = I temperature of the mth node adjacent to node o at time t n thermal condu c tivity between nodes o and m ( 4 2 ) h ea t c apacitance of node o, d e t e rmined from the material s a ss o c iated with th a t nod e, heat g enerati o n rate and time s t e p ( t n+l tn ).

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98 Node o and the six neighboring nodes are shown in figure 4-1. In a two-dimensional view, this simplifies to the grid structure in figure 4-2. The coordinate system chosen for this research was the r-z-0 s ystem. In the physical model, figure 4-3 there is a symmetry about the z-axis This symmetry permits the use of a two-dimensional r-z coordinate system instead of the more complicated r-z-0 system For the two-dimensional model that will be considered here, there will be one C, one P and four K's associated with each node. One K is for each quadrant in contact with the node. For node o, these parameters can be expressed by where Cpl P L V t Q1 Lm krn y 4 c o = I c p, P l v [ l = I 4 p o = L Q l V [ l = I 1 2 L k 111 y A 111; y 11 1 y = I specific heat of material in the lth quadrant, density of material in the /th quadrant, volume of the lth quadrant of node o, heat generation rate per unit volume in the lth quadrant, distance between node o and adjacent node m, (4-3) thermal conductivity of material in the yth of the two possible heat flow paths between nodes o and m, cross-sectional area of theyth heat flow path between nodes o and m For surf ace node s the general heat balance equation for node i having M i neighbors is T ~ + l_T ~ c I I = p ~ + 1 Llt I M i l, jK am (T ~m -T~ ) m = l (4-4 ) where am is the mth neighbor of the ith node and T is the temperature at node i at the nth time level.

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z Figure 4-1. Figure 4-2. , I , I I I I 6 y I I , I I I -----r----, I I , I I I I I I , I I I Jt '.,,,_ I 3 I , , I , I , I I I I I I I I I I I -----r---, I , I I , 2.,, , I I I I I ----,----I I Grid structure surrounding node o, the node of interest. z 0 r X Two-dimensional grid structure using the r-z coordina te axes. 99

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...._. AD995 alumina air ......... ,l',l',1',I' ................. ,I'. ,l',1',I'. ,l',I' ..................... ,I'. ,l',l',I' ,I' ,I' .......................... SiC / cement susceptor 1 "'11..:::..,l'~,1'~,1',l',l',1',I' .................... ,1',I' ,I'. ,I'. ,I' ................ ,I'. ,I'. ,I' ,I' ,I' ............... ,I' ,I' ,I' ,I' ,I' .............. D insulation t8J interlayer 0 region boundary condition z (mm) -,.. ... ..... ~:t. ; . ,,. . -' ,.t-1 ,I' ,I' ,I'. ,I' ............. ,I' ,I'. ,I'. ,I' ............ ,I' ,l',I' ., ............ ,I' ,l',I' ,I' ............ J',l',I' O 12 .7 20.7 27.7 53.1 r (mm) 114.8 .,_ ________ ____ 76.7 51.3 50.8 25.4 @) o,__ ______________ 100 Figure 4-3. 0 12.7---20.7 27 .7 53.1 r ( mm ) Model used for the simulation of microwave hybrid heating. ( 0 region s and Ll boundarie s refer to materials and conditions used in the model. )

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101 Transient Heat Conduction The heat transfer model that will be described later in the chapter is a transient heat flow problem and employs an implicit procedure known as the Crank-Nicolson technique to solve it. This is the technique recommended by the authors of Heating 7 .2 and i s alway s stable regardless of the s ize of the time step. The Crank-Nicolson technique generates a system of e quation s that are solved by a point-succe ss ive-overrelaxation iteration. The Heating 7 .2 program include s a provi s ion for automatically approximating the optimum acceleration parameter Using the Crank-Nicolson method, equation 4-2 becomes T 0 + 1 T 0 c ~+o s i i I ~t = p n+0 5 + 0.5 I M M I I K n+0 .5 ( T n+ I T ~+I ) + K n+0.5 ( T T ~) L., 1a a 1 L., 1a a 1 m=I m m m=l m m ( 4-5 ) For thi s equ a tion all of the finite difference s are taken about the point Xi, tn+ 112, halfway between the known and unknown time level s. Figure 4-4 is a graphical representation of the Crank Ni c olson point in a one-dimensional problem. For a problem with N nodes, thi s equation yield s N equations and N unknown s To so lve the se equations iterati ve ly se parate the temperature s so that temperatures at tn+ 1 are on the other s ide of the equation from temperature s at t 0 The equation then become s H -0 5 I where M i \' K o+0 5 T o+0 5 i..J i a a m=I U\ 01 + c ~+o s J Llt M i M I + o.5 L m = l i K :+0 .5 T~+l m H I c ~ +o.s I T ~ Lit I + p ~+0.5 + 0 5 I L j K :m+O.S ( T ~m T ~) m = I ( 4-6 ) ( 4-7 )

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102 t n+3 n+2 n+1 n X i-1 I i+ 1 i+2 Figure 4-4. Time-temperature coordinates involved in the Crank-Nicolson equation. The trapezoid connects the time-position values u s ed to calculate temperature values at the point indicated, 0 By defining D = I c ~+o.s I ~t M l + o.5 I: m= I K n +0.5 i a m ( 4-8 ) and omitting the superscript (n+ 1 ) on the temperature Ti the temperature of node i at the new time level can be written as M i 0 5 I: K n+o.s T +H i a a I ( 4-9 ) m=l m m T D I I However values of T a are unknown so thi s equation cannot be solved directly. The m existence of an estimate of the temperature distribution at the next time step can be used in equation 4-8 to calculate a new temperature distribution This process can be iterated until

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103 the approximation of the new temperature distribution converges at the new time level. For the first time step, the initial temperature distribution is input by the user. When there are temperature dependent thermal properties such as density, thermal conductivity or specific beat, they are recalculated after the new temperature distribution has been determined. The temperature dependent properties of the material between nodes are calculated by evaluating the property of the material at the average temperature of the two adjacent nodes. Boundary Conditions Heating 7 .2 can accommodate several types of boundary conditions. The boundary conditions are used to manage the discontinuities associated with a surface node. A surface node is a node on the face of a mate1ial that is not surrounded by other material nodes. The su1face node is connected to a boundary node. A boundary node is a dummy node that represents the temperature of the environment in contact with the surface node. Depending on the type of boundary condition that is specified, the temperature of the environment ( dummy node) can be determined in various ways. It can be a constant, a function of time or position, 01 it can be specified indirectly by defming the heat transfer mechanisms of the surface node. Convection (forced or natural) and radiation are the heat flux mechanisms that must be specified to describe heat flow from a surface node to a boundary node. Temperatures of the surface nodes that have specified boundary conditions are not calculated from equation 4-3. The heat flux is calculated from the specified mechanisms and multiplied by the nodes surface area. The result is added to the heat generation te1m in equation 4-3. Uncovered regions that are modeled without an assigned boundary condition are modeled as an adiabatic surface. Surface-to-environment and surface-to-surface are the two types of boundary conditions used in the modeling work in this dissertation. Surface-to-environment boundary conditions are used to describe beat transfer between a surface node and a

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104 boundary node. The surface-to-surface boundary conditions describe heat transfer directly between two corresponding nodes on opposing surfaces. This is an accurate approximation for narrow gaps that do not contain any material. For both of the boundary conditions disct1ssed, the heat flow term in equation 4-4 is calculated from where Tn b (4-10) effective conductivity from surface node i to either boundary node b or opposing surface node b. temperature of either boundary node b or opposing surf ace node b at time tn. The effective conductivity for the surface node is (4-11) where h is the effective heat transfer coefficient, and A is the surface area of node i associated with the boundary condition. The effective heat transfer coefficient is made up of the heat flux mechanisms discussed earlier and is calculated as where forced convection heat transfer coefficient, radiative heat transfer coefficient, coefficient for natural convection, exponent for natural convection. (4-12) These parameters must be specified by the user and can be represented as a constant, a function of time or a function of temperature. As with the other temperature dependent properties mentioned previously, the value of each of the parameters for the material between nodes is calculated using the average temperature of the nodes in question.

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105 The Physical Model Heating 7 .2 is an extremely versatile program that can provide a solution for a multitude of heat tran sfer problem s. Thi s versatility requires that a large number of parameters be specified. A complete table of all the possible input parameters is located in Appendix B. The phy sical model used is s hown in figure 4-3 as a sec tion of the microwave setup being modeled. This figure s hows nickel oxide as the interlayer material. In other problems, the nickel oxide is replaced by AD94 alumina For each problem, the material and thickne ss of the interlayer will be identified in the problem's input data As the input parameters are specified, the terms appearing in the model and the rea so nin g used in the development of the input parameter s will b e discus se d The data is input in an ASCII file that re se mble s Fortran punch cards. Each line in the input file is described as a ''card''. The parameter cards will be identified and discussed in the order that they appear in the input file. Occasionally, a parameter card will refer to another card that has not yet been introduced At thi s point, the discontinuity will be noted and the cards will continue to be addressed in the order that they will appear. Some cards will offer choices of input to choose from. The choices that are available ru:e identified in Appendix B The mks system of weights and measures is u sed for all of the data input into the sample problem discussed below. Input parameters for each card are identified below in the same manner that they are identified in Appendix B. Case Title Thi s parameter card i s available to the user to provide a description of the problem It associates the input data with the programs output. JOBDES Tbe case title ca rd may be left blank The different problems investigated in thi s s tudy are identified by the type and thickness of the interlayer material used in the physical model.

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106 General Problem Parameters The general parameters are specified in this card. These are required to initialize the Heating 7.2 program. MXCPU. This term sets a limit on the computer processor time, in seconds, that the problem may use. If the problem is not solved in the allotted time, the calculations are terminated For the current study, a large limit of 28,800 seconds (eight hours) was set to ensure the problem would run to completion. NGEOM. The cylindrical r-z coordinate system was chosen because it most closely resembled the actual problem. This is represented by the input value of 3 from the table in Appendix B. TIM. The initial problem time was set at zero. There is the potential to restart a previous problem, but this option was never pursued. IDEGRE. The Celsius temperature scale is used for all of the problems. This is indicated by a 1 on the parameter card, taken from the choices presented in Appendix B. Region Data This is actually a set of cards that describe the physical model using the coordinate axes chosen earlier. Each region is represented by two input cards. Card one is used to identify the regions by number, identify the material occupying the region and provide physical dimensions for the region. NOREG. For the example problem being set up here, the regions are identified in figure 4-3. In this model, there are nine regions that must be specified. MA TS. This term identifies the material occupying the region by a number that points to a card that contains the material's properties. REGDIM. The dimensional boundaries of each region are input in meters. The region boundaries are labeled in figUIe 4-3 as millimeters.

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107 The second card in the set specifies the initial temperature of each region, the heat generation of the region and the boundary condition associated with each physical dimension specified in the frrst card. ITS. The initial temperature can be varied from region to region. This card designates the card that will describe the initial temperature for a given region. NG ENS. This term inputs the identification number of the heat generation card associated with each region. The values for the different heat generations are specified later in the text. NREGBC The boundary conditions, specified later, are associated with each of the regions physical boundaries The values for all of the input data that describe the nine regions are summarized in Table 4-1. Materials The materials card specifies the various properties of the material that are necessary for the calculations. The four materials represented in the model are AD995 alumina, a silicon carbide/ AL-66 alumina cement, Rath fiber insulation and nickel oxide. MAT. This is the card identification number that is pointed to in the region material number card. MA TNAM. This space contains an allotment of eight characters for the name of the material. DENS TY This entry is for the density of the material in kilograms per cubic meter. The density values used for the AD995 alumina and the insulation was the density reported by the manufacturer The density of the susceptor was measured at AECL during the evaluation of the susceptors dielectric properties. A sintered density of approximately 80o/o of theoretical was reported by the manufacturer of the nickel oxide.

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108 SPHEA T This contains the specific heat if it is a constant. The manufacturer reports the specific heat of the insulation material to be 920 J /Kg C. T b l 4 1 S a e u, 111 1 ;, y O e arame er ar s se 0 escn e e me o e egions. fth p t C d U d t D 'b t h N M d 1 R card 1 material smaller r larger r smaller z larger z region card 2 initial heat smaller r larger r smaller z larger z temperature generation b o u ndary bou n dary bo u ndary boundary 1 1 1 0 0 0 1 27 0.0254 0 0508 2 1 1 0 1 0 0 1 2 2 0.0207 0 0277 0.0254 0 0894 2 1 2 1 0 0 0 1 3 3 0 0.0531 0 0.0254 2 1 3 0 1 1 0 1 4 3 0.0277 0.0 5 31 0 0254 0 0894 2 1 3 0 1 0 0 1 5 3 0 0.053 1 0 0894 0.1148 2 1 3 0 1 0 1 1 6 1 0.0127 0.0207 0.0254 0.0894 2 1 1 2 2 2 2 1 7 4 0 0 0 1 27 0.0767 0.0894 2 1 0 0 1 0 0 1 8 1 0 0.0127 0 0513 0.0767 2 1 1 0 1 0 0 1 9 5 0 0.0127 0.0508 0.0513 2 1 4 0 1 0 0 NCONTP. Thi s points t o a function card that represents the thermal conductivity of the material as a function of temperature. NSPHTP This point s to a function card that represents the specific heat of the material as a function of temperature. T h e materials cards for the four materials in the model are shown in Tab l e 4-2.

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109 Table 4-2. Input Parameters for the Four Materials Represented in the Model. material number material name density (kg/m3) 1 AD995 3810 2 susceptor 2060 3 insulation 400 4 nickel oxide 5336 temperature dependent the1mal conductivity function -1 -2 2 -3 temperature dependent specific heat function 1 1 1 3 A positive integer references an analytical function and a negative integer a tabular function. Initial Temperature This is the car d that was specified earlier in the region definition cards to describe the initial temperature of a paiticular region. INT This is the identification number of the initial temperature card for the problem. TEMPIN. An initial temperature of 45 C was u se d for all of the experiments. It wa s not nece ssary to start at a lower temperature because the thermocouples u se d in the actual experiments are not accurate at low temperatures Heat Generation This card was specified in the region definitions card. It represents a unique heat generation term for each material. NGN. This i s the heat generation identification number referred to previously. NGNFCN. Thi s term points to a function card that describes a temperature dependent heat generation function. The origin of the se functions will be addressed in the sec tion detailing the function car ds.

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110 Table 4-3 represents the heat generation cards for the four materials. A fifth material, air, has material properties accessible from the materials library contained in Heating 7 .2. Table 4-3. Heat Generation Cards for the Four Materials in the Model. material heat generation number temperature dependent function AD995 1 4 susceptor 2 5 insulation 3 6 nickel oxide 4 7 Boundary Conditions A boundary condition is defined for each unique boundary condition identification number. Each boundary condition consists of several cards that describe the characteristics of that boundary as well as the coefficients, exponents and functions that help define the boundary. The first card defines the type of the boundary condition present The second card specifies the coefficients and exponents associated with the heat transfer characteristics of the boundary condition. The third card points to equation cards that describe the dependent behavior of the heat transfer characteristics of the boundary condition NBDTB. This term identifies the boundary condition with a unique number that corresponds with a regions dimension Card 1. NBYTYP. Designates the type of the boundary condition that is associated with the boundary condition number. The type of boundary condition is chosen from the table in Appendix B. Card 1 B YTEMP. Specifies the boundary temperature in degrees Celsius. This is not applicable to surface-to-surface type boundaries. Card 1.

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111 BCDEF(2). This specifies the radiation coefficient term, hr, for the deter1nination of the effective heat transfer coefficient Since alumina is the predominant material in all of the boundary conditions, the radiation coefficient term for alumina will be used in the boundary condition description. To determine this, the material at the boundary condition is assumed to be a gray body. This leads to the equation where E hr (J T E = hr T4 energy emitted from a radiating gray body, radiation coefficient term, fraction emitted x cr, Stephan-Boltzman constant, 5 6697 x 10 8 W/m2K4 and temperature ( K ) ( 4-13) The fraction emitted refers to the percent of the energy that the gray body emits relative to a blackbody emitter. The emissivity for alumina is about 98% at room temperature, decreases to 80 % at 400 C and drops off steadily from therel 16. The radiation coefficient term is then calculated to be hr= 0.98 ( cr) = 5.5563 x 10 8 W/m 2 K4 ( 4-14 ) and was placed in card 2. Thi s i s the emissivity at room temperature. To calculate the emissivity at higher temperatures hr is multiplied by an analytical function deter1nined later in this chapter. BCDEF{3). This specifies the natural convection multiplier term, h 0 For natural convection, the coefficient is determined by the geometry of the boundary For a cylindrical configw.ation the empirical co1Telation is where L k C GrL = characteristic length of the configuration m thermal conductivity of air, W/mK correlation for geometry, Grashof number ( 4-15 )

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Pr a Prandtl number, typically 0.7 for air, natural convection exponent te1m. 112 The characteristic length, L, i s defined in a table for various geometries. For this model it is the height of the boundary 0 064 m. The thermal conductivity of air changes over the temperature range in question However, it is not a significant change so the thermal conductivity of air was taken to be that at 650 C, 0 0626 W/mK The correlation, C, is taken from the s ame table a s the characteri s ti c length and is determined to be 0.59 for this geometry. The natural convection exponent term a, was deterrnined from the same table to be 0.25. The Gra s hof number for an enclosed s pace i s calculated from the equation where g T s T b V 00 2 V acceleration due to gravity, 9 .81 m/s 2 coefficient of volume expansion= 1/T, surface temperature C, temperature of the environment, C distance between surfaces, m, velocity ( flux) of air m 2 /s. ( 4-16) To maintain con s istency in the calculations the Grashof number was calculated at 650 C and determined to be 15,032. Thi s wa s used to the calculate the natural convection multiplier term 5 85 W/m K Card 2. BCDEF(3). Thi s i s the exponent term a, that was determined in the previous calculations and i s now identified a s h e Card 2 NBCTEM This card refers to the temperature dependent function for radiation that is multiplied by the radiation coefficient specified earlier. The function will be determined later using the emissivity of alumina as a function of temperature Grids A set of two card s ru:e used to defme the grid for each axi s. The first card is the gross grid line s for the r and z axes. These are determined from the dimensional

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113 boundaries of the region s de s cribed previou s ly. The s econd card is the fine grid line s to be included between each set of gros s grid lines Fine grid lines are used to subdivide the material region s for more accurate calculations. There will be one less entry on thi s card than the frrst Table 4-4 i s both the gross and fine grid lines for each axis. Table 4-4. Table of the Gross and Fine Grid Lines for Both the r and z Axes. card 1 s malle st next lar ger next lar ger next lar g er next larger next larger next larger gr oss grid gross grid g ro ss grid gross grid gr oss grid gro ss grid gro ss grid divi s i o n s cLivi s i o n s divi s i o n s divi sio n s divi s ion s divi s ion s divi s ion s betwe e n } s t between between b e tw ee n between b e tween between c ard 2 and 2nd 2nd and 3 rd 3 rd and 4th 4th and 5th 5th and 6th 6th and 7th 7th and 8th gross grid gross grid gro ss grid gross g rid g r oss grid gross grid gross grid lin es line s line s lin es line s lin es line s 0.0 0.0127 0.0207 0.0277 0.0531 r -ax.is 4 3 3 8 r-axis 0.0 0 0254 0 0508 0.0513 0.0767 0.0894 0.1148 Zaxl S 8 8 1 8 4 8 z-axis Analytical Functions The analytical functions developed in this section describe either the time or temperature dependent propertie s that were addressed previously. When fitting data with an analytical function, care must be taken so that there is no aberrant behavior in the function outside of the data that ha s been fitted. An example of this would be fitting a set of decreasing thermal conductivities over a relatively s hort temperature range This provides a monotonic curve with a negative s lope. Over mo st of the temperature regime this does not represent a problem However, at very high temperature s the thermal conductivity become s negative, causing the heat to flow from the cooler to the hotter nodes within the material To avoid the se s ituations some of the data has been input as tabular functions which will be discussed later. For the input the frrst card identifies the analytical function. The second card is a s eries of pairs of values The first number in each pair refers to the coefficient index A i, for the general analytical equation

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114 F(V)=A 1 + A2V + A 3 V 2 + ~cos ( AsV ) + A6exp(A7V) + Agsin(A9V) + A1oln(A11V) (4-17) and the second number is the user specified value of the coefficient. Specific heat. The first analytical function represents the temperature dependent specific heat of the predominantly alumina materials, AD995 and the susceptor. Furukawa et al 117 measured the specific heat of alumina as a function of temperature. Figure 4-5 is a fitted plot of their reported data. The coefficients from the logarithmic fit are used in the analytical cards to describe the temperature dependent behavior of the specific heat of the AD995 alumina and the su s ceptor. Miyayama et al.11 8 reported the specific heat of nickel oxide at several temperatures. Figure 4-6 is a plot of analytical function fitting their data. Thermal conductivity. Unlike the less porous materials, the slope of the thermal conductivity for the insulation board is positive. Values for the thermal conductivity of the fiber board were taken from the manufacturer's information sheet* and plotted as a function of temperature in figure 47 along with an analytical fit of the data. Power generation. The determination of the power generation terrns for each of the materials in a microwave field was a several step process. The first piece of information needed was the magnitude of the electric field in the microwave. Typically, the electric field in a microwave oven varies with position throughout the microwave cavity Microwave oven manufacturer s attempt to obtain a uniform electric field by optimizing the dimensions of the microwave cavity. In addition, a metal fan to stir the microwaves or a turntable to move the load through the field is added to increase the uniformity of the electric field. For the purpose of these calculations, the electric field is assumed to be uniform throughout the microwave cavity Rath Performance Fibers Inc gm : ww\data\kvs\17-40.pri

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1300 --y = 195.96 + 359 541og (x) R = 0 99 7 93 1 2 50 0 ,,-... 1200 u 0 0) 1150 .......... -, .....__,, ...., 1100 ro Q.) I u 1050 u Q.) Q. V) 1000 950 0 900 0 2 00 400 600 800 1000 Temper a ture ( C ) Figure 4 5 Logarithmic fit to data f o r the s pecific heat of alumina

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,,-.... u 0 0) --...... --, ........... ...., C'O Q) :c u 4u Q) c.. (/) 770 760 750 740 730 720 710 700 690 300 --y = 657.47 + 0.11324x R= 1 400 500 600 700 800 900 1000 Temperature (C) Figure 4-6 Linear fit for the specific heat of nickel oxide

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+-J > +-J u ::J 0.35 0.3 0.25 "'C C 0.2 0 u C'O E
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118 Calorimetry wa s used to calculate the inten s ity of the electric field Thi s consisted of placing an insulated beaker of water in the microwave oven. A thermocouple was immersed in the water to a point approximately at the center of the beaker. The water then was heated using full power and the temperature was measured. Figure 4-8 is a plot of the temperatwe of the water as a function of time. The rate of rise of the water temperature is the slope of the graph. The electric field in the water can be calculated from the rate of rise in water temperature using the equation where p Cp T T 0 t f ( T T ) pe p l o V 10 0.556x 10 'fE etr m electric field, density of water ( Kg/m 3 ), specific heat of water (J/KgK) temperatwe rate of rise ( C/s ), frequency of microwave s (sec 1 ), effective dielectric loss (4-18 ) At a temperature of 50 C the electric field in the water is calculated to be 2.34 kV/m. The electric field in the microwave cavity ( external field) can be calculated u s ing the dielectric constant of water at 50 C, EH O = 80, from the equation 2 where E e x t = t ex t = external electric field (V /m), external dielectric constant ( air, E = 1 ) 4 2 (4-19)

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,,--.... u 0 "'--" Q) I,... =s +-' ro I,... Q) a. E Q) 110 100 90 80 70 60 50 40 30 0 0 10 y = 33.699 + 0.89971 X R= 0.99585 20 30 40 Time (s) so 60 Figure 4-8 Temperature of water a s a function of time 70 80

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120 The external electric field is calculated to be 187 .2 kV/m Since the field in the microwave is assumed to be unif or1r1 this will be the value used to calculate the absorbed power in each of the material s. The next bits of information needed were the dielectric properties of each of the materials as a function of temperature. The dielectric constant and dielectric loss were mea s ured on sa mple s of the AD995 the s usceptor and the nickel oxide by Ron Hutcheon at the AECL using the cavity perturbation method referred to previously. From these data as well as from the calculated electric field the power in the alumina, the nickel oxide and the susceptor was calculated at several temperature s using the equation p a = 21tf Ed tan8 I E iat 1 2 (4 -20 ) where Pa power absorbed by the material, W /m3, f frequency of microwaves s-1, Eo per111ittivity of free space, dielectric constant of material tan8 loss tangent of material, Eint internal electric field of material, W/m 2. The value for Eint in all three materials was calculated as a function of temperature using equation 4-19 and the dielectric data measured at AECL. These values then were plotted and fitted to a curve. Figure 4-9 is a power fit to the power absorbed versus temperature data for AD995 alumina. The coefficients were used to represent the temperature dependent power generation term as an analytical function. There was no dielectric data available for the insulation boru:d The insulation had a porosity of 90% (10% dense). Therefore, since the in s ulation board was predominantly alumina, the power generation was assumed to be 1 Oo/o of that of the AD995 alumina. For the nickel oxide, a similar set of calculations were perforn1ed using equation 4 -2 0 Figure 4-10 i s a second order

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,.......,, ('() E 3: .......... L. Q) 0 0.. 7 1 a s 6 1 a s 5 1 a s 4 1 a s 3 1 as 2 1 as 1 1 a s 0 y = 2622.8 e"(0.0037397x) R= 0.987 o 0 500 1000 1500 Temperature (C) Figure 4-9. Power absorbed ( ca lculated ) as a function of temperature for AD995 alumina.

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5 10 8 4 10 8 I... 2 10 8 0 a.. 1 10 8 0 0 0 200 0 0 0 Y = MO + M 1 *x + ... M8*x 8 + M9*x 9 MO -4.5389e+07 M1 1. 1 531 e+06 M2 -785.19 R 0.95037 ::. 400 600 800 1000 Temperature (C) Figure 4-10. Power absorbed (calculated) as a function of temperature for nickel oxide.

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123 polynomial fit to the power absorbed versus temperature data for nickel oxide. The susceptor is actually a composite material made from the relatively microwave transparent cement and th e strong ly absorbing si licon carbide. There are two possible approaches to determine the dielectric properties of the susceptor. The first is to treat it as a composite and use a weighted proportion of the dielectric properties for each material. The sec ond approach is to use the dielectric data measured from a specimen cast with the same composition as the susceptor. The second approach was chosen for use in the model using the data obtained for the susceptor in the experiments de sc ribed in Chapter 3 Figure 4-11 is the power curve fit to the data for the s usceptor similar to the one used in the laboratory experiments. The data in the curve is valid over only a limited temperature range. This is due to the increa s ing inaccuracy of the cavity perturbation method for dielectric measurements on strong microwave ab s orbers. As the dielectric losses increase, the penetration depth decrea ses and the material begins to act as a microwave reflector. This affects the ability to measure the dielectric properties accurately by increasing the error associated with the measurement. Boundary condition. As mentioned previou s ly the emissivity of alumina decrea ses with increasing temperature. The coefficient was calculated in equation 4-14 to be approximately 5 .56 x 10 -8 W/m 2 K 4. The function that accompanies the coefficient to describe the decreasing emissivity with temperature is shown in figure 4-12 Tabular Functions Tabular functions were u sed to repre se nt the thermal conductivities of the three materials that exhibited a decrease in thermal conductivity as a function of temperature. This was done to eliminate the possibility of the analytical equation resulting in erroneous values At temperature s below the temperature li s ted for the first tabular entry, Heating 7 .2 uses the lowe s t value. While within the temperature range of the table the function s values are interpolated. At temperatures above the highe s t tabular value, the last value is used.

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,--.... (V") E ......__., "'C Q) .0 I,... 0 V, .0 <{ I,... Q) 0 0... 4 10 7 3.8 10 7 3.6 10 7 3.4 10 7 3.2 10 7 3 10 7 2.8 10 7 2.6 10 7 2.4 10 7 0 --y = 5.5478e+07 + -1.233e+071og(x) R= 0.99651 so 100 150 200 Temperature 250 (OC) 300 350 400 Figure 4-11. Power absorbed ( calculated) as a function of temperature for the 30 vol. o/o SiC susceptor.

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> (/) (/) 1 0 0.8 0.6 0.4 0.2 0 0 0 300 Y = MO + M 1 *x + ... M8*x 8 + M9*x 9 0 600 900 Temperature MO M1 M2 R 1200 (OC) 1.0398 -0.00088092 2.0?e-07 0.98599 1500 1800 Figure 4-12. Curve fit for the emissivity of alumina as a function of temperature.

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126 The tabular functi o n option u s e s two cards to describe each function. The fir s t card is the function number that wa s referred to earlier in the inp u t The second card i s a se rie s of paired table value s The first number i s the independent value and the second number i s the co rre s ponding dep e ndent value. Thermal conductiv i ty. Th e thermal c onductivity at several temperature s for the AD995 alumina was obtained from th e s ame so urce as the emissivity for alurnina 1 1 6. Table 4 5 is the thermal conductivity data availab l e for the AD995 alumina T bl 4 5 Th al C d ti ty f C a e erm on UC Vl 0 oors um1na a eren em ::>era es. AD995 Al t Diffi t T tur Temp e rature ( C ) Thermal Conductivity ( W / m C ) 25 33 47 700 7 53 For nickel oxide the thermal conductivity values were obtained from the s ame source as the specific heat 11 s. Since the nickel oxide u s ed in thi s s tudy had a den s ity of 80% the theoretical value, the report e d values were adjusted for poro s ity u s ing the rule of mixture s where P = value of the material property of composite, P 1 = value of the material property of the first component, V 1 = volume fra c tion of frr s t co mp o nent, VP = volume fraction of poro s i ty. The se values for nickel oxide are li s ted in Table 4-6. ( 4-21 ) Table 4-6. Thermal Conductivity of the Ni c ke l Oxide Used in the Model at Different T tur em per a es. Temperature ( C ) Thermal Conductivity (W /m C ) 200 17 05 800 5.0 The susce ptor is a co mpo s ite of alumina cement, s ilicon carbide and poro s ity. The thermal conductivity of th e s u sce ptor was ca lculated using the rule of mixture s for the three

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127 materials. The volume percent of porosity can be calculated using the measured density, the density of alumina and silicon cru:bide and the proportions of cement and silicon carbide used in the susceptor. The thermal conductivity of the porosity was assumed to be zero. The thermal conductivity of the cement was taken from the information sheet provided by the manufacturer Select values of the thermal conductivity of silicon carbide were reported in a compilation of properties of materials 11 9 The volume weighted values of the cement and silicon carbide then were added to obtain the thermal conductivity of the composite. The calculated values for the thermal conductivity of the susceptor used in thi s model are listed in Table 47 Table 4-7. Calculated Values for the Thermal Conductivity of a 30 wt. % SiC/Cement s t usce P or Temperature C) Ther1nal Conductivity (W/mC) 200 2.07 700 1 35 Printout Times This card specifies the times at which a solution summary of the transient solution is written to the main output file. The times are consistent with the models units so for this study the times were in second s PRTIME. This is the value of the printout times listed s equentially An interval of 300 seconds was chosen for the printout times for all of the calculations in this study. The printout times are then at 300 s 600 s, 900 s, 1200 s, 1500 s 1800 s, 2100 s, 2400 s, 2700 s, and 3000 s. *The Carborundum Company Alfrax No 66 Aluminum Oxide Castable For111 A-2043.

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128 Nodes Monitored Heating 7 .2 has a provision for the monitoring of specified nodes during the calculations. The program has the ability to write the temperatures at these nodes to a separate file during calculations. NT S. This specifies the number of time steps between the writing of the temperature of the nodes to an output file. NDS. This entry contains the identity of the nodes by number that the user wishes to monitor. Transient Data This set of three cards is used to specify the parameters that are desired to govern the transient calculation technique. NTYPE. The transient solution technique to be used is specified from Appendix B. For all of the calculations, an implicit solution is used. Card 1. FTIME. This input specifies the final time for the calcu l ations, indicating when the program should terrninate. Card 1. THETA The input here deterrnines the differencing technique used. This value corresponds to several of the coefficients and exponents in equations 4-5 through 4-8. To specify the Crank-Nicolson technique, this value was set at 0.5. Card 2. DELTAT. This value is the initial time step for the implicit solution. A value of 0.5 seconds was chosen because it is near the value determined by Heating 7 .2 and provides a more organized output than the time step calculated by the program. The last card is the data termination card that sends a flag to the program that the input is complete. This card consists only of a percentage symbol,%. Figure 4-13 is the resulting input file for the situation that has been described here. The input directs Heating 7 2 to calculate the heating profile for the physical model in figure 4-3 heated in a microwave at full power for fifty minutes. The temperature at select nodes

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suscep t or 0 5mm nio 28800 3 0 1 regions 1 1 0 0 0 0127 0 0 0 0254 0.0508 1 1 0 1 2 2 0 0207 0 0277 0 0 0 0254 0 0894 1 2 1 3 3 0 0 0 0531 0 0 0 0 0 0254 1 3 0 1 0 0 1 4 3 0 0277 0 0531 0 0 0 0254 0 0894 1 3 0 1 5 3 0 0 0 0531 0 0 0 0894 0 1148 1 3 0 1 0 0 0 1 6 5 0 0127 0 0207 0 0 0 0254 0 0894 1 0 2 2 2 7 1 0 0 0 0127 0 0 0.0767 0 0894 1 1 0 1 8 1 0 0 0 0127 0 0 0 0513 1 1 0 1 9 4 0 0 0.0127 0 0 0 0508 1 4 0 1 Materials 1 AD995 2 SUS 3 insul 4 nio 0 3810 0 -1 0 1 0 2060 0 -2 0 1 0 400 0 2 0 1 0 5336 0 3 0 3 5 1 I nitial temperatures 1 45 .0 heat generations 1 0 0 4 2 0 0 5 3 0 0 6 4 0 0 7 boundary conditions 1 1 45 0 O 4 556e-8 5 85 0 25 O 2 0 8 2 3 O 4 556e-8 5 85 0 25 O 2 0 8 rgrid 0 0767 0 0513 0 0 0 0127 0 0207 0 0277 0 0531 4 3 3 8 zgrid 2 0 0 0 0254 0 0508 0 0513 0 0767 0 0894 0 1148 8 8 1 8 4 8 analytical functions 1 1 195 96 10 359 54 11 1 2 10.15238 2 -6 8073e-5 3 1 228 4e -7 3 1 657 47 2 0 11324 4 6 24917 7 3 7397e-3 5 1 5 5678e 7 10 -1.233e 7 11 1 6 6 2491 7 7 3 73978 3 7 1-4 53898721 153186 3 785 19 tabular functions 1 25 33 47 700 7 53 2 25 2.07 700 1 35 3 2 00 17 05 800 5 0 printout 300 600 900 1200 1500 18 00 2100 2400 2700 3000 nodes monitored 600 328 333 334 423 transient 2 3001 0 5 0 5 % Figure 4-13. Sample input to calculate a heating profile of the model in figure 4-4 129 title p r1 r2 r1 r2 r1 r2 r1 r2 r1 r2 r1 r2 r1 r2 r1 r2 r1 r2 m m m m ml I g g g g b1 b2 b4 b1 b2 b4 11 n1 12 n2 a1 a2 a1 a2 a1 a2 a1 a2 a1 a2 a1 a2 a1 a2 t1 t2 t1 t2 t1 12 0 s tr tr2 tr3 s

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130 corresponding to the several points of interest will be output for every five minutes of simulated heating. Figure 4-14 is a map of the node numbers with the material regions outlined. Table 4-8 lists the nodes of interest and where they are on figure 4 14 These nodes were chosen so that the calculated temperature could be compared to the temperatures that were mea s ured for the workpiece, s usceptor and interlayer in the preceding chapter. Table 4-8. Nodes of Interest and Their Placement in the Model. node number pos1t1on 326 interior of interlayer 328 exterior of interlayer, facing susceptor 334 interior of susceptor 335 exterior of susceptor, bounded by insulation 421 interior of end member 423 exterior of end member facing susceptor The input file in figure 4-13 was run u s in g Heating 7.2. The temperature at each of the nodes was written to a separate output ftle. The temperatures appear as a block of numbers for each of the output time s requested on the printout card, PRTIME. Figure 4-15 is a sequence of temperature proftles generated from the example using 10 minute increments of time. Similar input files, altered to reflect interlayers of varying materials and size, were also processed. Comparisons of the temperatures of the nodes that were monitored were made with the experiments performed in Chapter 3. These will be discussed in Chapter 5.

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2 692 693 691 698 699 700 701 702 7 3 673 674 678 679 680 681 682 683 ---659 660 661 662 663 664 insulation 640 2 843 64.t 645 621 623 624 625 626 607 588 538 539 546 547 5 5 5 1 9 520 28 529 531 510 12 air gap 90 491 4 93 .. 4 443 444 449 450 451 452 424 425 430 431 432 ,433 434 435 436 end 405 406 411 2 413 insulation 6 417 386 387 392 393 394 f7 398 member 373 374 375 376 377 878 379 interlayer 354 355 356 357 358 359 360 335 336 337 338 339 340 341 316 317 318 319 320 321 322 292 297 298 299 300 301 302 303 2 73 278 279 280 281 282 283 28-4 254 259 60 1 262 263 28-4 265 2 6 end 234 235 2 24 242 243 244 2 46 215 221 223 2 7 member 196 202 203 204 206 2 7 208 177 1 184 8 1 188 147 149 insulation 128 130 109 111 90 92 71 7 52 54 33 S5 Figure 4-14. Map of node numbers for the input file in figure 4-13. Geometry corresponds to the model in figure 4-3. The nodes that represent ther111ocouple locations are 328 (interlayer) and 423 (bulk). The pyrometer is represented by node 328.

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spacer end member end member 132 Figure 4-15 Temperature profiles for simulated microwave hybrid heating generated using the input in figure 4-13. a) 10 minutes; b) 20 minutes; c) 30 minutes ; d) 40 minutes; e) 50 minutes. Temperatures indicated represent thermoco u ple positions.

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spacer end member end member Figure 4 15 -continued 133

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134 Figure 4-15 -continued

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135 Figure 4-15 -continued

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136 Figure 4-15 -continued

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CHAPTERS RESULTS Machined Surf aces The machined s urfaces of all the sample alumina pieces used were similar. The finish of a typical machined surface finish i s shown in figure 5-1. The surface appears flat and featureless at the magnification used. The same machined surface was characterized with a laser profilometer using the conditions outlined in Chapter 3. A three-dimensional plot corresponding to the s urface in figure 5-1 i s displayed in figure 5-2. Using equation 3-1, the roughne ss (a rithmetic mean ) of a single surface scan was calculated to be 2.47 microns Figwe 5-3 is a photograph of the surface of a machined nickel oxide interlayer. The nickel oxide had a porosity of 20% and wa s much more delicate than the alumina During the machining process, special care was taken to avoid damaging the nickel oxide di s ks. After machining the cleaning of the s urface removed s ome of the surface texture imparted by the grinding wheel. Figure 5-4 is a laser profilometer profile generated for the machined nickel oxide s urface. The roughness (arithmetic mean) for the nickel oxide su1face was calculated to be 1.40 microns. Sol Gel Interlayers Stand Alone Heating All of the interlayer material s investigated that contained a sol-gel-derived powder were heated at full power (7 50 W *) in the microwave u s ing the setup in figure 3-4. Figure 5-5 is a plot of the temperature of the pellets made from the potential interlayer materials as *Microwave output reported by manufacturer 137

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138 Figure 5-1. Area of the surface of alumina end member u se d for roughness analy s i s

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Figure 5-2. Jl a n = S p e -= Sea = P o i .:: Di s p J a~: P ro f J l e 3 0 10 25 0 2 0 00 O tt t O ) fl V O I A C AO CJ
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140 Figure 5-3. Area of the surface of nickel oxide interlayer ttsed for roughness analysis.

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P r og r a "' 3 D Ran = Spe = Sea = Poi = Displ a y : Prof i le 3 0 10. 250 2000 Auto level ACNI03D [JIM ] 25 8 12.5 8.88 5.88 . . . '. _,,4' .. . 3.75 X [111,,.. 1 ~ ~ -. .,, . ... . .. ~ ;. .. .... ,., , r. .. . '. ~.,..,,... ,. .. .. -, .. t -._. ,-Ir .__ .:, 1 ., .. _., __ . , r \,. ... . ,, ., ,,, ,, r ,,.,.. 1tl .-, ... .. ,,.~ ...... ,. ... ., .... ... ,.. ,,, . . ,_ ~ ... ,,. ---. ._/.;.. .:. ,i, .. ;,:,,, ...,,,-,. .r.,l'i~-:, .. ,t .,.,. r, ., -1 J ~.,..,, I_. / ,, ~ _, r .. .,,._ . ;.,,.. ~ , .. ,. t i,; .~ I,: ',.~ . ; 'J .. ... .,. .... _.. . ., -, '/, .,, . . . .I ':,, .... , . . ,,. .. I , ,111~ ., . ,, Jl, __ fi I ,,.,.,. ., , #' -J-: _. ._ .. '1 ,., .... . ,. ~ ~,., ' t .. .# ,. I .....,r . . .. '- . ,. .... ~. ' 1,'I ... ... . .. ' . . ""., .. . ,. -. '' ~ . ,. . . ~ 1. . -.,, ___ .. . {. ..',, ,. ' :.!.' ,. , ,_ ,-, ,,;, I r ' i "' I ,. .. ~ ' .:JI' .. . .,,. .,. ~_ ,, ,,,,, . r .,. ' ,I':, '.J .. ,.. r .. ;;' . --, ., I ,, r,,. Ii' ., , .,~ .. ,.__ ,, ,,. .. .. "1 J., ,~ -, .: ,,,..,, , .. ,. .., ... ..;. .. ,. r .. ._ ;/,-,,J~ ... ,;_.t , ~,I. # ""' .. ,IJ, -, ,..,..,... ,.-. ,. r/ ... < ,., ~ .,, ,., .. ., .. :. ..; ,__ ,., ,.r , .. .,,.~ . ,,:,. :.,- , ,. .. . , ~ . ~ .. ,, .. ,. , ... .. . ,-, .,., ,. ... . ,.,, ,,, .. ,, J ., : . .. r: I I "" I ,. . . . .. '.. I ,. ., .. ,. .. ,,, .. ,. I' .. ,.. .. .. .,;.,,1 ~ ,, f~ .. /,~I .. "!'. ,._ ,~ -" 1 1 ,. 2.58 1.25 'I " _,,. r . r ;1, I Ill ,,,; .-. .. ',,., .j ':' 'j,.._. ~... ,.-:;, ,,,.I / .. 1 -. ... ; . ,~. ,,,~ ,-. .. .. ,, .. , . . ., ,:;. t 111 111 I ,,, ,", ,, ,,. .. / .. .. ,, I .. .. ,, ,. ,.. ,.. 2.58 1.25 5.00 3.75 8.88 8.88 8 DEGR Rod11nalocll Figure 5-4. Profile of 5 mm x 5 mm area of nickel oxide from figure 5-3 analyzed using a laser proftlometer. Light regions correspond to the area above mean peak height and darker regions correspond to area below mean peak height.

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1000 800 ,......._ u 0 ....._,,, Q) 600 L.. ::s ...., ctS L.. Q) C. 400 E Q) t200 0 + 10% Fe 3 + ; as Fe(NO ) salt 3 3 o+50% Fe o ; as powder 2 3 no additives; alumina gel --o- +50% SiC; as powder .----.---.------r------.--------.-.---------.------,------.~__,.--.---.---r----.--.--1 0 + 4 % C r 3 + ; as Cr( NO ) sa It 3 3 0 2 4 6 Time (min) 8 + 10% Cr o as powder 2 3' -6 +50% NiO; as powder EB + 1 0% FeO; as powder 10 12 Figure 5-5. Temperature of the potential interlayer materials heated using stand alone microwave heating.

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143 a function of time. All of the material s rapidly heated to 400 C in the microwave oven At t his point, the rate of the rise in temperature decreased in all but one of the materials. The pellet containing 10 mol % iron ( II) oxide continued to heat to a maximum temperature of 841 C. After the maximum was reached the temperature decreased to approximately 750 C where the experiment ended The pellet s made with either an iron or chromium salt substituted for the aluminum s alt heated at a slightly faster rate than the base gel. The pellets containing 4 mol % chromia and 10 mol o/o iron (III) oxide reached temperatures of 40 C and 100 C above that of the base gel, respectively. The pellet containing 50 mol % SiC reached a maximum temperature of 532 C, 75 C above that of the base gel. Differential Scanning Calorimetry The base gel and four of the more promising materials (nickel oxide, silicon carbide iron ( II ) oxide and 4 mol o/o chromia) were chosen for continued study Figure 5-6 shows the DSC traces for the five materials. The temperature regimes shaded on the figure are labeled with the reactions most likely responsible for peak formation. All of the gel derived powders exhibited an endotherm between 100 C and 200 C The next reaction observed appeared at a temperature slightly above 200 C The endother1n was observed in all of the material s and was most pronounced in the gel made with 4 mol % chromia. An endotherm was detected in all of the materials beginning at 400 C and ending near 450 C The specimen containing 50 mol o/o silicon carbide featured an exothermic peak between 525550 C. This was the only specimen to exhibit this behavior. All of the powders displayed an exotherm between 1150 C and 1210 C. The exotherrnic peaks for specimens with 50 mol % nickel oxide and s ilicon carbide closely resembled that of the base gel. However the peak s for both compositions were less intense than that of the ba s e gel. For the specimen made with 4 mol o/o chromia, the exotherrnic peak in this region was similar in size to the base gel endotherm. However it appeared at a temperature 50 C above that of the base gel. The s pecimen made with 50 mol % iron (II) oxide contained two exotherms in

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AIOOH AIOOH + SO mol% NiO C CJ) .,.> +-' C ro => AIOOH / 4 mo I% Cr o N 0 'ro +-' AIOOH + SO mol% FeO 'Cl) .,.> ..c '<( AIOOH + 5 0 mo I% SiC 0 200 400 600 800 1000 1200 1400 Temperature ( C) Figure 5-6. Differential Scanning Calorimetry (DSC ) of the base gel, alone and with additives.

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145 this temperature range. The two peaks were diffuse and overlaped each other but were still distinguishable a s two separate peaks An endothermic peak unique to the 50 mol % iron ( II) oxide specimen appeared near 1350 C. X-ray Diffraction Analysi s Powder x-ray diffraction analysi s was performed on the specimen s retrieved from the DSC. An additional sample of the 50 mol % iron (II) oxide was run in the DSC to a temperature of 1200 C to provide inforn1ation about the specimen prior to the last endotherm observed in the DSC trace The x ray analysis was carried out in the manner described in Chapter 3. Figure 5-7 show s the x-ray scans for the ceramic powders made f1om gel precursor s heated in the DSC The powder made s olely of the ba s e gel had x-ray peaks that correspond well to tho s e of high-purity alumina *. All of the peaks present had a corresponding peak on the ICDD card. The powder loaded with nickel oxide displayed peak s that could be attributed to alumina nickel oxide and a nickel aluminate spinel. The production of the gel with 4 mol % chromia rendered a specimen with x ray peaks that resemb l ed the alumina ICDD card. All of the peaks in thi s s pecimen were shifted slightly to lower 2 0 values. The s pecimen containing 50 mol % silicon carbide produced x-ray peaks corresponding to silicon carbide and alumina When the specimen loaded with 50 mol % iron ( II) oxide wa s heated to 1400 C alumina and iron (III ) oxide were the predominant phases pre s ent When a similar sp e cimen wa s heated to only 1200 C, there was evidence of a third phase in addition to alumina and iron ( III ) oxide with peaks that corre s pond to the iron ( II ) aluminate s pinel FeO Al 2 0 3 All of the s pecimen s were heated in flowing air and a change in the oxidation s tate of the some of the iron (II) oxide was expected. International Centre for Diffr a ction Data ; card 10-0173 aluminum oxide / corundum

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Cl) C: Q) +-' C: 20 F A F ,. A A ., A A A I 25 F F S i C s I I 30 A F A F A F A ~ F A A A F A I OO H +SO mol % Fe 0( 14 00 C) A F A A F A F .. .. A AJ OO H+S O mo l % Fe O( 1 200 C) SiC A A A SiC . A A A AI OO H+S O m o l % S iC (1 4 00 C) A A A s A AI OOH/ 4 mol % Cr 2 0 3 ( 14 00 C) s A A A s V s .. A A I OO H+ SO m o l % Ni O( 1 4 00 C) A A A A AI OO H ( 1 4 0 0 C) I I I I I I I I I 35 40 45 50 55 6 0 D egrees 2 T he t a Figure 5 -7 X Ray Diffra c tion Analysi s ( XRD ) of powder s s ynthe s ized during DSC analy s i s Specimen s containing iron compound s exhibited s pectra with reduced inten s itie s This i s mo s t likely due to the fluore s cence of iron from Cu k-alpha rad i ation. Fluore s cence tend s to reduce peak/background ratio s. A-al um i n a S-n i cke l al u minate spine! Ni0Al 2 0 4 SiC-silicon carbide F-iron ( Il l) oxide

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147 Dielectric Measurements The relative dielectric constant e' r, and the lo s s factor, e'' e tf, of several of the compositions investigated above were measured at AECL using the cavity perturbation method mentioned previously. Figure 5-8 is the relative dielectric constant as a function of temperature for s ix of the compositions being investigated as a potential interlayer material. The specimen containing iron (ill ) oxide had the largest dielectric constant over the temperature range investigated. Figure 5-9 is the same data plotted without the iron (III) oxide so the feature s of the other curves could be distinguished For the remaining materials, the curves display similar trends with temperature. In all cases, the dielectric constant decreased until 500 C, then increased steadily up to 1000 C, where it decreased slightly before rising dramatically at temperatures above 1200 C The dielectric loss factor was measured at the same time a s the dielectric constant. Figure 5 10 i s the loss factor measured as a function of temperature for the potential interlayer materials. As with the dielectric consta nt the loss factor of the specimen containing iron (ill) oxide was much greater than the other compositions at temperatures above 600 C. The specimen containing nickel oxide diverged from the range of values measured for the other materials. This effect was not as marked as in the iron (III) oxide specimen. The dielectric loss factor of these two specimens increased steadily with temperature. Figure 5-11 represents the loss factors of the remaining compositions. The trends followed by these compositions varied with temperature in the same 1nanner as the dielectric constants. The loss tangent, tan 0, for these material s was calculated using equation 2-2. These values are plotted in figure 512 as a function of temperature for the potential interlayer materials The appearance of

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14 +50% SiC; as powder 1 2 +50% NiO; as powder +4% Cr 3 + ; as Cr(NO ) salt ...--.. w 3 3 ........... D no additives; alumina gel 10 C 0 + 1 0% Cr o ; as powder ro 2 3 +50% iron (Ill) oxide; as powder V) C 0 8 u u "6 u (1) (1) 0 4 2 0 500 1000 1500 Temperature (C) Figure 5-8. Dielectric constant versu s temperature of potential interlayer materials. Measured at 2.46 GHz.

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4.5 +50% SiC; as powder +50% NiO; as powder 4 +4% Cr 3 + ; as Cr(N0 3 ) 3 salt -w ........... D no additives; alumina gel ,f,J C: + 1 0% Cr o ; as powder ro 3.5 2 3 ,f,J (/) C: 0 u u 3 I,,_ ,f,J u (1) (1) 0 2.5 2 0 500 1000 1500 Temperature (C) Figure 5-9 Dielectric constants measured at 2 46 GHz plotted without the iron (III) oxide composition.

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20 +50% SiC; as powder +50% NiO; as powder +4% Cr 3 + ; as Cr(NO ) salt w 3 3 ..._.., 1 5 no additives; alumina gel 0 0 + 1 0% Cr o ; as powder +J u 2 3 ro +50% Fe o ; as powder LL 2 3 V) 10 V) 0 ....J u +J u (l) 5 (l) 0 0 0 500 1000 1500 Temperature (C) Figure 5 10 Dielectric lo ss factor, measured at 2.46 GHz versus temperature for potential interlayer materials

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0.2 +50% SiC; as powder -. +4% Cr 3 + ; as Cr(N0 3 ) 3 salt no additives; alumina gel w ...._,, 0.15 + 1 0% Cr o ; as powder D 2 3 0 u ro LL en en 0.1 0 ...J u u (1) 0.05 0 0 0 500 1000 1500 Temperature (C) Figure 5-11 Dielectric loss factors plotted without the iron (III) oxide and nickel oxide compositions. Measured at 2 46 GHz

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1.4 +50% SiC; as powder 1.2 +50% NiO; as powder +4% Cr 3 + ; as Cr(NO ) salt ,--.. 1 3 3 D no additives; alumina gel C: ctS + 1 0% Cr o ; as powder -1-J 2 3 ........., 0.8 +50% Fe 2 o 3 ; as powder -1-J C: (]) C') C: 0.6 ctS ..... V, V, 0.4 0 _J 0.2 0 0 500 1000 1500 Temperature (C) Figure 5-12. Loss tangent measured at 2.46 GHz, versus temperature for potential interlayer materials.

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153 this set of curves is very similru: to that of the curves of the loss factors. The specimens containing iron (III) oxide and nickel oxide display a large increase in the loss tangent with increasing temperature The plots of the remaining materials, figure 5-13, resemble the curves in figure 5-11. Microwave Susceptors The su s ceptor s made with varying amounts of silicon carbide were heated using the setup shown in figure 3-4. Figure 5-14 is the temperature of a 50 gram 96% pure alumina l oad placed in the center of the susceptor during heating. The susceptor with no silicon carbide heated to a temperature slightly less than 600 C. As the volume percent of silicon carbide in the susceptor increased, the maximum temperature attained in the 50 minutes of heating time increased. The susceptor with 30 volume percent silicon carbide reached a temperature of 996 C in the same 50 minute period. As with the gel-derived ceramic powders dielectric properties were measured as a function of temperature at 2 46 GHz for specimens made from of each the susceptor compositions The dielectJ:ic constant for each of the susceptors is plotted as a function of temperature in figure 5-15. For all of the compositions investigated, the dielectric constant increased monotonically with temperat11re. As the amount of silicon carbide increased, the dielectric constant of the material increased for every composition investigated. Figure 516 shows the dielectric loss factors of the s usceptors measured at the same time as the dielectric constants The loss factor of the susceptor made without silicon carbide increased monotonically with temperature. In all of the susceptors containing silicon carbide, there was an initial decrease in the lo ss factor as the temperature increased. As the temperature rose above 400 C, the loss factor increased with increasing temperature. Similar trends were observed in the lo ss tangents of the susceptor s figure 5-17. Figure 5-18 are the temperatures of the susceptors at various times plotted as a function of silicon carbide content

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..c,o C: ro +..J 0.05 0.04 '::' 0.03 C: (l.) O') C: ro r 0.02 (/) (/) 0 _J 0.01 0 0 +50% SiC; as powder --o--+4% Cr 3 +; as Cr(NO ) salt 3 3 no additives; alumina gel + 1 0% Cr o ; as powder 2 3 500 1000 Temperature (C) 1500 Figure 5-13. Lo ss tangents plotted without iron (III) oxide and nickel oxide compositions. Measured at 2.46 GHz.

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,,--... u 0 ..._,,,, CJ) It... :J ,1-,,1 ro It... CJ) 0. E CJ) I1000 800 600 400 200 0 0 10 20 30 Time (min) 0% SiC 5% SiC 10% SiC 0 20% SiC 0 30% SiC 40 so Figure 5-14. Temperature of alumina load in silicon carbide/alumina cement susceptors heated using 3.2 KW with a 75% duty cycle(% time on). 60

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-w ,.__., """ C: ro """ Cl) C: 0 u u """ u (l) (l) 0 9 8 7 6 5 4 0 0% S i C --< O >-5% S i C 1t-1 0% SiC ~ o ~20% SiC ----< O >-3 0 % S i C -----------------e 200 ~--------........ ------... --.. --. 400 600 ... -------Temperature 800 (O C ) 1000 1200 Figure 5-15. Dielectric constant, measured at 2.46 GHz, versus temperature for several compositions of susceptors.

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-. L 0 +-' u ro LL CJ) CJ) 0 _J 1 0.8 0.6 u 0.4 L +-' u (l) (l) o 0.2 0 ----0 0 ------0% SiC 0 5% SiC ... 10% SiC D 20% SiC 0 30% SiC 0 --=-no----------200 400 600 800 1000 1200 Temperature (OC) Figure 5-16. Dielectric loss factor, measured at 2.46 GHz, versus temperature for several compositions of s usceptors. The minimum in the los s factor, associated with some types of s ilicon carbide has yet to be explained.

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.,J C 0.12 0.1 0.06 C ro t0.04 0 _J 0.02 0 -...... -. 0 -----0 % SiC ----< o ,__5 % Si C -10 % SiC ----1 0 ..... 2 0 % SiC ----c o ....3 0 % Si C 0 0 ___ .. 0 0 a'C".: =I---.. I-~ ... ...d. 0 __ ..,._.,-u.--. ..... .. .... ..... 200 .400 600 Temperature 800 (O C ) 1000 1200 Figure 5-17. Loss tangent for severa l susceptor compositions at 2.46 GHz.

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1 min 1000 5 min 20 min D 10 min 0 30 min 800 40 min ,---.. u 0 .._. 600 (l) \,... ::J +J ro \,... (l) 400 a. E (l) r200 0 0 5 10 1 5 20 25 30 35 Percent Silicon Carbide Figure 5-18 Temperature of susceptors as a function of silicon car bid e content

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160 Joining Joining Conditions All of the joining experiments were performed using the same protocol Although processing parameters (time, temperature and pressure) were varied, they were varied in a consistent fashion throughout the study Figure 5-19 is a typical joining curve used in microwave joining trial #6 (45 min/1450 C/3 MPa/M/NiO). The temperature of the end member closely matched that of the interlayer throughout the entire experiment The joining temperature of 1450 C was reached in 48 minutes using full power ( 1000 W *) The joining pressure of 3 MPa was achieved during a 75 s econd time span. The s pecimen was unloaded after the 45 minute soak at the processing temperature. Figure 5 20 i s the joining curve generated during trial #11 (15 min/1550 C/1 MPa/C/NiO ). In the conventional joining operation data collection of the force and temperature does not begin until the loading procedure has been initiated. In this experiment approximately 75 minutes were required to reach the proces s ing temperature of l 550 C This is in contrast to the 56 minutes needed in trial #8 (45 min/1550 C/3 MPa/M/AD94) to reach 1550 C u s ing microwave hybrid beating. Visual Inspection After the joining procedure wa s concluded, the s pecimens were visually inspected The specimens that separated easily after the joining process were designated unjoined. This occurred in two instances trials #1 ( 15 min/1450 C/1 MPa/M/NiO ) and #13 ( 15 min/1450 C/3 MPa/C/NiO) In both trials the interlayer material wa s nickel oxide. When the specimens were removed from the microwave, they were easily separated into three parts consisting of the two end members and the interlayer material. The blue color of the joint surfaces was the only sign of any interaction between the end members and the Microwave output reported by manufacturer

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1500 ........... t: 1000 Q.) L. ::::, ,+,J ro L. Q.) a. E Q.) 500 f0 0 --------Interlayer (NiO) -End Member Applied Force 20 { I I I I } 40 60 80 Time (min) 40% time-on 20% time-on 1000 800 ........... (/) ..0 600 Q.) u L. 0 LL "'O 400 -~ a. a. <( I I I I power off 2 OO L 100 120 0 140 Figure 5-19. Microwave processing condition s for trial #6 (1450 C ; 45 min; 3 MPa; nickel oxide interlayer ).

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,,.-.... u 0 '--""' (l) Ii... ::::s +-' co Ii... (l) 0.. E (l) I1 600 ----~ ---.__,___.. b ~. ~---. -------~ ---& llll-R -- 1400 1200 1000 800 600 400 200 0 0 Applied Force (N) Temperature (C) 5 10 1 5 Time (min) 20 1600 1400 1200 ,,.-.... z 1000:; 800 600 400 200 0 25 u Ii... 0 LL "U (l) 0.. 0.. <( Figure 5-20. Conventional proce s sing condition s for trial #11 ( 1550 C ; 15 min ; 1 MPa ; nickel oxide interlayer )

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163 i nterlayer. These two joining experiments were assigned a strength value of zero. Two of t he trials joined using a nickel oxide interlayer, trials #4 (45 min/1550 C/l MPa/M/NiO) and #6, were deemed joined after visual inspection. However, both of the specimens later fa iled during handling. Figures 5 21 and 5-22 are photographs of the fracture surfaces of the specimens from trials #4 and #6. F lexure Testing All of the s pecimens joined were machined into flexure bars. Bars that did not fail during the machining process were tested using 4-point bending The first set of bars tested were those joined using various sol-gel compositions as the interlayer material Table 5-1 presents the joining conditions and the result s of these experiments Table 5-1 Flexure Strength of AD995 Alumina Joined Under Various Conditions u S ID ffi tlnt 1 Mt al smg evera 1 eren er ayer a en s Temperature Pressure Heating Interlayer Flexure Standard Strength Deviation ( C) (MPa) Method Material (MPa) (MPa ) 1500 2 45 4 mol % Cr-sol 90 8 39.5 rrucrowave 1500 0 as-received 298.9 34 9 microwave 1400 1 85 AD96 184.5 11 2 rrucrowave 1500 2.45 conventional NiO/ A1 2 0 3 sol 108.4 28.2 1500 2 45 conventional 4 mol % Cr-sol 51.4 20 3 none 0 none as-received 303.0 19 7 *In all ca s es the time s pent at temperature was 30 minutes Both the as-received alumina and the as-received alumina that was heat treated in the microwave had flexure strengths that were s imilar to the flexure strength reported by the manufacturer All of the joined specimens had flexure strengths significantly lower than the as-received alumina Figure 5-23 is a typical fracture surface of a flexure bar joined using a gel derived interlayer. During the heating process, the gel shrinks considerably. Consequently, the interlayer material does not cover the entire surface of the end members.

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... ,. .. :, . .... If ;t 'I .. ; .. ' ,, ., .. \, . ,. .. . ,, ; .. (~ .. I .~ ,, ... . ,, . . ,, .. . . I . \ I q < . .,,. .f \ : ~t t .. .. .. Al O Figure 5 -2 1 Fracture surfaces of specimens from trial #4 ( 45 min; 1550 C; 1 MPa; nickel oxide interlayer; microwave heated)

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( ,l__r;. ' ,. ...... ~. . .. .to ~"' ,. .. .. < .. .... .. ' .. . .. I; r, I _. .. ... ,. ' ,. . ' .. . I I I ' t ... I -~ . !'c __ \ .. . ~, --4~~,. ,. r ' '. Figure 5 22. Fracture surfaces of specimen from trial #6 (45 min; 1450 C; 3 MPa; nickel oxide interlayer; microwave heated).

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166 Figur e 5-23. Fracture surfaces of a flexure bar joined u s in g a ge l-derived ( 4 mol % Cr 20 3 ) interlayer

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167 The specimen joined using a solid piece of AD96 alumina had a flexure strength of 184 5 MPa, more than 60% of the strength measured in the as-received material. The next se t of experiments considered either AD94 or nickel oxide as the interlayer. AD94 is an alumina material with a dielectric loss greater than the AD96. The other interlayer material, nickel oxide, reacts with alumina to form a nickel aluminate spine!, NiA1 2 0 4 As described in Chapter 3, an experimental design was developed to evaluate the joining parameters statistically, t1sing the flexure strength as the dependent variable. All of the joints made with AD94 alumina as the interlayer were intact at the conclusion of the experiments. However, trials #2 (45 min/1450 C/l MPa/M/AD94) and #9 (15 min/1450C/l MPa/C/AD94) both separated during the fabrication of the test bars. Other test specimens provided between five and eleven bars for strength testing. For the specimens joined with nickel oxide as the interlayer material only two specimens, #11 and #15 (15 min/1550 C/3 MPa/C/AD94 ), were joined sufficiently enough to provide bars for flext1re testing. Trials #1 and #13 were unjoined after visual inspection, trials #4 and #6 failed during handling and trials #7 (15 min/1550 C/3 MPa/M/NiO) and #10 (45 min/1450C/l MPa/C/NiO) failed during the machining of the bars Table 5-2 shows the results of the four-point bend testing of the joined bars compared to the as-received material. With the exception of a few bars from trial #15 which broke at the support pins all the bars failed at the interface between the interlayer and the end member. The highest strength recorded was 273 MPa for a bar from trial #15. The lowest measured strength was 19.2 MPa recorded from a bar in trial #16 (45 min/1550 C/3 MPa/C/NiO). Figure 524 is a plot of the str engths with the error bars at one standard deviation Trial #15 had the highest mean flexural strength at 252 MPa. Trial #11 had the lowest standard deviation ( 5.0 MPa ) and trial #8 had the highe s t standard deviation ( 57 3 MPa).

PAGE 188

300 250 J 0... I: 200 ..._ ..c +J CJ) C Q) 150 L +J (f) Q) L 100 :::s X Q) -LL so 0 ,/' ,/' .... ,/' ,/' ..... ........ ,/'. ,/' ........ ,/' ,/' ........ ,/' ,/' ........ rl'. ,/' ........ rl'. ,/' ........ ,/'. ,/' ........ ,/',/' ........ rl' ,/' ........ ,/' rl' ........ ,/' ,/' ........ ,/'. ,/' ........ -~--....... ,.,.,. ,/',/' ,,, ........ G) Trial#2 (ill Tria1#3 Trial#8 Trial#11 D Trial#12 Trial#14 Trial#1 5 [;l Trial#l 6 ,/' ,/' '---.a... '' ..L .............. u_ _J_ _.L _L __ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Trial Figure 5 -2 4. Mean flexure strength of bars for each of the trial s in the experimental de s ign. Error bar s correspond to one standard deviation. 0\ 00

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169 Table 5-2. Mean Strength and Standard Deviation of Bars Joined by either Microwave or C ti I H t onven ona earn Joining Conditions* Standard Trial time/temperature/pressure/ Strength (MPa) Deviation (MPa) heating method/interlayer 1 15/1450/1/M/NiO 0 2 45/1450/1/M/ AD94 3 15/1550/l/M/AD94 197 48.8 4 45/1550/1/M/NiO 5 15/1450/3/M/AD94 166 26.0 6 45/1450/3/M/NiO 7 15/1550/3/M/NiO 8 45/1550/3/C/ AD94 229 57.3 9 15/1450/1/C/AD94 10 45/1450/1/C/NiO 11 15/1550/1/C/NiO 41.6 5.0 12 45/1550/1/C/ AD94 172 37.7 13 15/1450/3/C/NiO 0 14 45/1450/3/C/ AD94 219 19.4 15 15/1550/3/C/ AD94 252 17.8 16 45/1550/3/C/NiO 19.2 9.4 AR 303 19.7 time (min); temperature (C); pressure (MPa); heating method (M-microwave, C-conventional) Figure 5-25 is a typical fracture surface for a specimen joined with an AD94 alumina interlayer. The interlayer and the end member separated leaving a fracture surface t hat was very smooth with little in the way of fracture markings on the surface. Figure 526 shows the joint line between the interlayer (AD94) and the end member (AD995) in a bar that had a strength of 142 MPa. The joint appears well formed along the majority of the joint line. A closer examination, figure 5-27, reveals a representative portion of the joint area exhibiting porosity, grains for the two surfaces in contact, and grains connected by a grain boundary 0.5 m thick. Figure 5-28 shows the intact joint in a bar from trial #15 that

PAGE 190

170 Figure 5-25 Fracture s urface of specimen from trial #12, representative of all the specimen s joined using AD94 alumina as the interlayer material

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171 t ~# .. ... I AD995 6'!?91 T' .. f 0 v 0 ~ ... f,I :s ~,. .. Qi e f. ,,, ,. # t ... 0 .;, . t,.,. '.... ...... --. joi!)t .... lfne J .. 9 .. l C1' ..... I r .. D 40m i > ' Figure 5-26. Joint line between AD94 alumina interlay ~ r and AD995 alumina end member (250x). Trial #14 (45 min/1450 C/3 ~1Pa/C/AD94).

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172 Figure 5-27 Micrograph of joint region in figure 5-26 s howing porosity and grain boundary material (2 0 000x ).

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173 AD995 AD995 Figure 5-28. .. .. :.. . :..,; . . ... .... . 1 ... .. Intact interlayer material in bar that fract1ired a'-' ay from the joint area. Trial #8 (45 min/1550 C/3 MPa/M/AD94) (6,000x )

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174 failed at a distance away from the interface and had a strength of 220 MPa The joint region in figure 5-29 seems to have less porosity than that in figure 5-26. Closer examination of the joint regions, figu1e 5-30, exhibits many of the same features as the specimen in figure 5-27 However there is evidence of increased contact between the grains of the interlayer and the end member At this magnificat i on, 20,000x, the joint line is hard to discern because interparticle contact interrupts the continuity of the grain boundary phase that forms the joint line. The wavelength dispersive spectroscopy feature of the electron microprobe was used to map the pre s ence of silicon near the joint area. It was assumed that all of the silicon present was in the form of silica. An area encompassing the joint, approximately 14 m by 14 m, was examined for specimens from trials #2 #3, #8, #12, #14, and #15 Trials #3 and #15 were joined at the same temperature with a force applied for the same duration of time. Trial #3 was joined using microwave energy while trial #15 was joined by conventional heating Figure 5 -3 1 and 5 -32 are micrographs and the accompanying silicon x-ray maps for the area surveyed for both trials In both instances there appears to be a greater concentration of silica in the joint area than in either the interlayer (AD94) or the end member (AD995). There does not appear to be a noticeable variation between the two specimens in the amount of silica at the joint interface. Trials #2 and #8 were both joined u s ing microwave energy for the same time duration However, trial #2 was joined at 1450 C whereas trial #8 was joined at a temperature of 1550 C Figure 5-33 and 5-34 are micrographs and the accompanying silicon x-ray maps for the areas surveyed in the two trials. In the specimen joined at the higher temperature, there is less contact between the grains of the interlayer material and the end member The x-ray maps also indicate a greater concentration of silica at the joint interface of the specimen joined at 1550 C Fracture surfaces of the specimens joined with nickel oxide as the interlayer material varied with the flexure strength of the bars. Figures 5-35 through 5-37 are fracture

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" AD94 .. I 4 l joint line !' .. 175 ; Ab995 .. 9 -, '? 40m I f't Figure 5-29 Joint region of bar from trial #15, flexure s trength 220 MPa ( 250x ). Trial #8 ( 45 min/1550 C/3 MPa/M/AD94 ) ( 6,000x ).

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i joint line Figure 5-30. Magnified micrograph of the joint line in figu r e 5-29 ( 20,000x ) 176

PAGE 197

joint 1ne int 1ne . .. .. ( ,. :, ~ : ,. .. .~11. r : , ~ . .. .. t; .., :. ..... : ._l .. .... .,. .,..., . ... "(. .. -~ .. .. . ... .... .. ,...~ _. I _. #. :. .. ~ .. ... ..... -. .... --.. ... .. ,-~-c . ,",-. ... ,. ... ... . I t f,('" : .I;. .. '.. .. 177 .. ., t-\ ..... . .. . ..... 4 s _., ~-4. -. .,. . .:,' I ..,. I ,. . .. t ": J ... .. .. I . .. .. . t .. .. . :.,, . .. . 11-. :. ... '' '":. ~ .,. . ~ r 1 . .. . ~~,~:i_, .. ~ . .,,, .. .. .. .. .. I . :, -. Figure 5-31. Joint area of a bar microwave joined in trial #3 (15 min/1550 C/l MPa/M/AD94 ) (6.000x). a) micrograph and b ) WDS x-ray map of silicon

PAGE 198

joint 1ne 1n e ... ... .. ~, . .:._. . . .. ....... .. .. "" .. """ t .. .. ,1 ,, '..J .., -: :-, : . . . .. ", : . . . ~ .. . .;:;-. ~ # : : < -.. .. ~ ~~--J ... .!411' .. ,..-, l , . 1' . c..,. '-" . l,. . . .. _. .-... 1-Z .(,.:., t . .. 178 \ .. 11 1 '"1 ,, '' "' .. Figure 5-32. Joint area of a bar conventionally joined in trial #15 (15 min/1550 C/3 MPa/C/AD94 ) (6,0 00x ). a) micrograph and b) WDS x-ray map of s ilicon

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int 1ne 1ne ,,. "' . ,.. . ... 1." ~ "... .. .. ' ..... . ,: .. J. .. . ... 179 Figure 5-33. Joint area of a bar microwave joined in trial #2 (45 min / 1450 C/l MPa/M/AD94 ) (6 .000x ) a) micrograph a nd b) WDS x-ray map of s ilicon

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JOln 1ne 01n .. .. > . .,.. > .. .. . ... .. . ~ .. .. .... ..,. ...... ~a, ' \ .. .. . 180 , .. .. "' . : : \. f 4 ~ , ., . . ~ .. ,. .. I Figure 5-34. Joint area of a bar microw ave joined in trial #8 ( 45 min / 1550 C/3 MPa/M/AD 94) (6. 000x ). a) micrograph and b) WDS x-ray map of sil i con

PAGE 201

. I I \ ' ,. .. ~... :,: . .. ,, . 'i ., . ' .. t < I .. ,, f' , ... I : ; ; .. t ,. , .. ' . .. . ', a ' ' \ .. .. Ao , . ' . ,,.; I ( "t . ( l > ... , "' -~ ,, I I : ' t ,"' . I l ' ,: l ... . }"". .. ~ ~ l ".'\ ( .. # .' . ,, ... ,, .. ... : ... 1 . . ... ~ .1 ... "~ -;. .. .. ,.. ,. it .... ...... .. .. t I : }, \. -~.-,~,t --,,. ~-'.: ,: ~{ -~ 'v l (~ ... 1 -. -. ... ~ ,. : ... .. .i .. ... 4 41', 41 ~ ' . "'"' I : ._ { ... ..i \. :!... i. : ......_ .; 4 ),_. .. .. 'I ~ \ --~ '." .. Ill ._ .. .""'\ .. .. '\ <. ... '' ) \ i .... . -..-'. -: .. .. ,-: ..... .. .~, '" ~ .. ,. i ,. 1../ a r~ --1 .. \ .. ; ., '.: I .''.~.... ... ', 'Y'l.,J r i';, ..... :, .. :it ~ .. ~~: i" . ,. -, .., ., ) .. .. "' . . ,' -; : ~ .... .. ~ .'D ~ ii:" ' -~::. ,,. :.. 't ~I# ;' -: ... . t. ' .... J .. 4 .i, 1,, J1 .' )~ "' "., ... ..... It'~ > ,. : .. : .... ,J ) i'9 I' '# ' I j;, i .... / "' 'A .,,. .,, ., . . } '\ '" . 1-.' _, : ; : , . . .. ' ,t l ,c -,:' -,1 r;-,. # ......... ,,. ... -~ I ''. 't ~... (" ... "" I 1 "\ ...... .;,_-: )''' ~,; . \ ... -~ J .... ... -, .. ., .. ,l_ ,, .. . \ I: ' ,.. ... t' -.., ' ... .I '-. '. .... l ., .... l ... ~ l t ., ,r 181 Figure 5-35. Matching fracture s urface of bar joined with a nickel oxide interlayer that failed before flexure testing. Compare to Figures 5-36 and 5-37. Trial #11 ( 15 min/ 1550 C/1 MPa/C/NiO )

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182 J Figure 5-36. Matching fracture surfaces of bar joined with a nickel oxide interlayer with a flexure strength of 38 MPa Trial #11 ( 15 min/l550 C/l MPa/C/NiO). I

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183 Figure 5-37. Matching fracture surfaces of bar joined with a nickel oxide interlayer with a flexure stre ngth of 45 MPa Textur e difference i s due to slow crack growth from contro ll ed loading (slow rate). Trial #11 (15 min /1550C/1 MPa/C~iO).

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184 surfaces of bars from trial #11 (15 min/1550 C/1 MPa/C/NiO) that had s trengths of 0 38 and 45 MPa, respectively Figure 5-38 is a micrograph of the joint region in the specimen with no flexure strength. The presence of a reaction layer between the alumina and the nickel oxide is noted along the entire length of the joint line. The reaction layer is approximately ten microns thick and does not have as much porosity as the nickel oxide. Figure 5-39 is a higher magnification photograph of the same area The joint area of the bar with a flexure strength of 45 MPa had a reaction layer of a thickness similar to the weaker specimen figure 5-40 A c l oser examination of the same area, figure 5-41 indicates that the nickel oxide in contact with the reaction layer is more sound than the nickel oxide in figure 5-39 The digitized surface profiles of microwave and conventionally joined end members were plotted for a 180 m length of the joint line, figures 5-42 and 5-43. A similar plot was made for a micrograph of the profile of an as-machined surface, figure 5 44. The roughness of the surface, calculated using equation 3-1, was 0.884 m for the microwave joined specimen (trial #8) and 1 115 for the conventionally joined specimen ( trial #12 ) The profile roughness calculated for the as-machined surface was 0 535 m. Statistical Analysis To perfor1n an analysis of variances (ANOVA) of the experimental design, the average strength of each of the trials was calculated from the strength of the individual flexure bars. The two trials that did not join at all, trial #1 and #13, were assigned a flexure strength of zero Six of the specimens that were determined to be joined during visual examination, failed during the machin i ng process. The values of the strengths for these trials were left vacant. There is a provision in the statistical software for uncollectible data that can evaluate the infor1nation with missing data Table 5-3 is the data as input into the analysis program The program performs a Type ill Sum of Squares on the data. This removes the influence of all of the other variables prior to testing the variable in question.

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185 Figure 5-38. Micrograph of joint region of bar from figu1e 5-35 joined with a nickel oxide interlayer (2,000x). Flexure strength O J\. 1Pa f

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186 Figure 5-39. Micrograph of joint region of bar from figure 5-35 joined with a nickel oxide interlayer ( 5,000x ). Flexure strength O MPa.

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187 Figure 5-40 Micrograph of joint region of bar from figure 5-37 joined with a nickel oxide interlayer ( 1 000x). Flexure s trength 45 MPa.

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188 Figure 5-41. Micrograph of joint region of bar from figure 5-37 joined with a nickel oxide interlayer ( 5,000x ). Flexure strength 45 MPa.

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Q) u C ro 3 2 1 0 1 0 2 3 ---profil e roughness R a --mean line ---R = 0.884 m a 4 ~_.__~-----_._~_._____.__._~_._~~~_.__._~~~ 0 so 100 Distance (m) 150 2 00 Figure 5-42. Rou gh ne ss of joined s urface (trial #8) ca lculated from micrograph taken at 500x.

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Q) u C ro .+-,J U) 0 6 ---profile 4 roughness R a --mean line 2 R = 1.115 m a --0 2 _4 ._~_.__-J--~_._~_.__----L--~-L-_._-L---L--'--L~ -A-L~ 0 so 100 Distance (m) 150 200 Figure 5-43. Roughne ss of joined s urface ( trial #12) calculated from micrograph taken at 500x.

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,,-.... E :::J. 2 1.5 1 -..0.5 (1) u C 0 (/) 0 -0.5 1 1 5 -tot 0 so 100 Distance (m) ---profile roughness R a --mean line R = 0.535 m a 150 200 Figure 5-44. Rou ghness of as-machined surface calculated from micrograph taken at 500x.

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192 Tab l e 5 -3. Data Used to Perform ANOV A Analy s i s. Name Time Temperature Pres s ure Heating Interlayer Flexure Method Strength Type Integer Integer Integer Integer String Real Mean 129.58 Std. Dev. 102.2 Std. Error 32.3 Minimum 15 1450 1 C Al20 3 0 Maximum 45 1550 3 M NiO 252 Range 3 0 100 2 1 1 252 Sum 1295 8 Sum of 261954 2 Squares 1 15 1450 1 C NiO 0 2 45 1450 1 C Al 2 0 3 3 15 1550 1 C Al20 3 197 4 45 1550 1 C NiO 5 15 1450 3 C Al 2 0 3 166 6 45 1450 3 C N o J 7 15 1550 3 C NiO 8 45 1550 3 C Al20 3 229 9 15 1450 1 M Al 2 0 3 10 45 1450 1 M NiO 11 15 1550 1 M NiO 41 .6 12 45 1550 1 M Al 2 0 3 172 13 15 1 450 3 M NiO 0 14 45 1450 3 M Al 2 0 3 219 15 15 1550 3 M Al 2 0 3 252 16 45 1550 3 M NiO 19.2 C conventional; M mic r owav e

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193 The full analysis of the data is in Table 5-4. The flexural strength is the dependent variable Table 5-4. Output of Statistical Analysis of Data from Table 5-3. Type 111 Sums of Sq uares Source Time Temperature Pressure Heating Method Interlayer Residual Dependent: Flexur e Strength df Sum of Squares Mean Square F-Value P-Value 1 294.648 294.648 .297 .6147 1 1839.608 1839 .608 1 .85 4 .2449 1 979.448 979.448 .987 .3766 1 190 .82 1 190.821 .192 .6836 1 64719.362 64719.362 65.241 .0013 4 3968.020 992.005 and the joining parameters (time, temperature, pressure, heating method and interlayer material) are the independent variables. The null hypothesis is a statement asserting that there are no difference s between the values of the dependent variable, flexure strength, caused by the differences in the independent variables. The model assumes a null hypothesis for each of the processing parameter s at a significance level of 0.05. This means that in 5% of the analyses, a valid hypothe sis will be rejected. The values of interest in Table 5-4 are in the column entitled ''F-values''. The F-value i s a ratio of the mean square of the processing parameter in question to the mean square of the residual. The value is compared to the theoretical value generated by the model assuming the null hypothesis is true. If the calculated F-value is larger than the theoretical value, it is assumed the null hypothesis was false; there is a significant influence of the processing parameter in question on the flexure strength The two F-values are compared to produce a p-value that then can be compared to the level of significance that has been stated earlier in the analysis. Appendix C is a set of sam ple calculations for a hypothetical series of experiments. According to the results in Table 5-3, the interlayer material is the only proces sing parameter that exhibited a significant difference on the flexure strength at a 95% confidence interval. Figures 5-45 through 5-49 are comparisons of the means of the flexure stre ngth at the two levels of each independent variable. The graphs are plotted with

PAGE 214

300 --ro a.. 250 ,.__, ..c ..... C) 200 C: Q) ..... (/) Q) 1 50 :, X Q) LL '+1 00 0 (/) C: ro 50 Q) Q) 0 u -50 M ea n s Tab l e E f fec t : T i m e De p e n de nt : Flexu r e St r en g t h Bar Count Mean Std. Dev Std Error 15 45 6 4 Interaction Bar Chart Effect: Time 109.433 109.312 159.800 96.972 Dependent: Flexure Strength With Standard Deviation error bars. I .. I 15 T i me ( min ) 44.626 48.486 I I 4 5 Fig ur e 5-45. Effect of t ime o n th e flexu r e s tr e n g th of jo in ed b ars. 19 4 .. ..

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300 --('13 0.. 250 ........ .c .-' C) 200 C Q) '.-' U) Q) 150 '::, X Q) 1 00 LL. 0 V) C so ('13 Q) Q) 0 u -so M ea n s Tab l e Effect : Tempe r at u re De p e n de n t: Flexure S treng t h Bar Count M e a n St d D ev St d Erro r 1 4 50 1550 4 6 96.250 15 1 .800 Interaction Bar Chart Effect: Temperature Dependent: Flexure Strength 11 3.227 98.161 W i th Standard Deviation error bars. I I 1450 T emperature ( C) 56.6 1 3 4 0.07 4 I I 1550 ... t-.. t-.. Figure 5-46. Effect of tempera tur e on t h e flex ur e s tr e n gt h of joined bars 195

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300 ........ 8:. 250 ...__, b> 200 C Q.) ..... (/) 1 50 Q.) ::, X Q.) 100 LL ...... 0 (/) C 50 ro Q.) 0 Q.) u -50 Me ans Ta b le Effect: P r essure Dependent: F l exure S t re n gth Bar Count M ean St d Dev. Std. E rror 1 3 4 6 102 650 147.533 Interaction Bar Chart Effect: Pressure Dependent: Flexure Strength 96.567 11 0.665 With Standard Deviation error bars. I I 1 Pressu r e ( M Pa) 48.283 4 5.179 I I 3 Figu r e 5-47 Effect of pre ss ure o n t h e fl e xu r e stre n gt h of jo in e d bars. 196 ... .. ... .. lo

PAGE 217

300 ,,-... ro 0... 2 ...._,, 250 .c .., C) C 200 (I) \... .., (./) (I) 150 \... :::, X (I) LL 100 0 (/) C ro so (I) 2 (I) 0 u 50 Mean s Table E ffec t: Heat i ng Meth od Dependent: Flexure Strength Bar Count M ean Std. Dev Std. Error C M 6 4 Interaction Bar Chart 117.300 148.000 Effect: Heating Method Dependent: Flexure Strength 110 .0 84 101.964 With Standard Deviation error bars. I I Convent i o nal Heat i ng Meth od 44.94 2 50.982 I I Microwave 197 Figure 5-48. Effect of the heating method on the flexure strength of joined bars.

PAGE 218

250 .......... 225 co c.. 200 ...._,, ..c: 1 75 +-' 0) C: Q) 1 50 '+-' (/) Q) 125 ':::, >< 100 Q) LL. 475 0 (/) 50 C: co Q) 25 Q) u 0 -25 Mean s Table Effect: Interlayer Dependent: Flexure St rength Bar Count Mean Std. Dev. Std. Error Al203 N iO 6 205.833 4 Interaction Bar Chart Effect: Interlayer 15.200 Dependent: Flexure Strength 33 618 19.791 With Standard Deviation error bars. I ... I Al203 Interlayer 13. 724 9.895 I I NiO i.. .. Figure 5-49. Effect of the interlayer material on the flexure stre ngth of joined bars. 198

PAGE 219

199 error bars equal to one standard deviation of the mean. The graph comparing the means for the two interlayer materials, figure 5-49, is the lone figure where the error bars do not overlap. When the data is evaluated at 90% confidence interval the difference in heating method does have a sta tistical effect on the flexure s trength Figure 5-50 During the machining the original position in the cylinder of each of the te st bar s wa s noted. The po s ition s were de s ignated as either outside, in s ide, middle or center. Figure 5-51 shows where these designations correlate to their position in the cylinder. Recovery of all of the bars from every joined s pecimen was not possible Several of the bars failed during different stages of the machining process. For the joined specimens that were machined, anywhere from two to eleven bar s were available for testing. A statistical analysis of the influence of the position of the bar on the flexure strength was performed for each heating method. Table 5-5 shows the results including the effect of the interaction between the bar position and the heating method Figure 5-52 plots the interaction of the effect of the po s ition of the bar and the heating method on the flexure s trength. The table of means in Table 5-6 provides the data used to generate the graph including the number of Table 5 5. Statistical Analy s is of the Effect of Bar Position on the Flexure Strength for both Microwave and Conventional Heating. Type Il l Sums of Squares Sou r ce df Sum of Squares Mean Square F -Value P-Value Position 3 13881.092 4627 .0 31 2.172 1041 Heating Method 1 605. 707 605. 707 284 5964 Position Heating 3 3580.446 1193 482 560 .6 440 Residual 46 97991.830 2130 257 Dependent : Flexure Strength

PAGE 220

Means Table Effect: Heating Dependent: M OR (MPa) Conve nt io n al M icrowave BarCount Mean 36 1 50.222 30 210.000 Interaction Bar Chart Effect : Heating Dependent : MOR ( MPa) Std. Dev Std. Error 98.504 16.417 48 492 8 853 With 90% Confidence error bars. as a.. --er: 0 0 en C as Q) Q) (.) 250 225 200 175 150 125 100 75 50 25 0 -25 I ' ... ' I Conventional Heating 200 90% lower 90% upper 122.484 1 77.961 194 .957 225 .0 43 I ,. ii,. I Microwave Figure 5-50. Effect of the heating method on the flexure s trength of joined bars plotted with error bar s at the 90% confidence interval.

PAGE 221

. .,. .,. .,.. .. ......... ,I'. ,I' ,I'. center middle inside ! ll!!!l!!!l l o u ts i d e Figure 5-51 Map of original bar positions in the joined cylinder before machining. 201

PAGE 222

250 -5 0) 200 C: ... Cl) 150 :, X (I) u. 0 100 en C: s (I) 50 (I) () 0 Interaction Bar Chart Effect: Position Heating Method Dependent: Flexure Strength With Standard Deviation error bars. Conventional Heating Method Microwave Figure 5-51. Interaction chart showing the combined effect of the position of the bar and the heatin g method on the flexure streng th. center inside middle outside N 0 N

PAGE 223

Table 5-6. Effect of Position/Heating Method Interaction on the Flexure Strength. Means Table Effect : Pos ition Heating Method Dependent : Flexure Strength center, Conventional center Microwave inside Conventional inside, Mi c rowave middle C o nventional middle Microwave outside, Conventional outside, Microwave Count 2 3 9 8 9 1 1 5 7 Mean Std. Dev. Std. Error 159.500 70 004 49 500 210.333 47 353 27 339 226 667 20 857 6 952 220 625 50 737 17 938 223 556 30 818 10 273 219 091 45 110 13 601 193 200 71 .304 31.888 184 143 56.010 21 170 203 bars at each position. The Type ill Sum of Squares uses a weighted average of the number of specimens to account for the different number of bars for each position. The F-value s calculated for the position, heating method and the combined influence of the two variables were relatively low Numerical Modeling The procedures detailed in Chapter 4 can be used to generate numerous heating profiles for various heating conditions Simulations were run for a case in which there is no susceptor, no interlayer a 500 m nickel oxide interlayer and a 500 m AD94 alumina interlayer In a ll situations, the model was heated at full power ( 1000 W ) for fifty minutes the approximate time needed to reach 1550 C in the laboratory. The heating profiles generated i n the example in Chapter 4, figure 4-15, provide information as to where the heat i s generated and how it i s transferred throughout the model. Experimentally, the temperature was measured only at the surface of both the interlayer and the end member. Nodes in the model corresponding to the position s of the thermocouples were monitored for comparison purposes. The po si tions of these nodes are highlighted in figure 4-14.

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204 The temperature of the workpiece and the susceptor was monitored during microwave heating using thermocouples and an optical pyrometer. Figure 5-53 is the temperature of the workpiece measured simultaneously by the optical pyrometer and a thermocouple. Figure 5-54 is the variation in temperature between the optical pyrometer and the thermocouple. As the heating initially increased, the thermocouple led the pyrometer by as much as 80 C. As the temperature approached the joining temperature, the difference was reduced to less than 30 C. Figure 5 55 is the temperature of the susceptor measured using both a ther1nocouple and an optical pyrometer. Using the two temperature monitoring methods the differences measured in the susceptor varied less than in the workpiece, figure 5 56. The temperature of the interlayer at node 328 calculated for the AD94 alumina is plotted with the measured temperature of the AD94 alumina interlayer in trial #8, figure 557 At low temperatures, the measured value at the interlayer is greater than either of the calculated temperatures. As the temperature increases, the measured and calculated temperatures converge These results are similar to those reported by Thomas et al 4 3 Figure 5-58 is a similar plot for measured and calculated temperatures of a specimen made with a nickel oxide interlayer Figure 5-59 shows the calculated temperatures at the surface of the joint region node 328, for the four simulations mentioned earlier. The simulation run with a specimen and no susceptor reached a maximum temperature of 51 C after 50 minutes. The simulation with AD94 as the interlayer material had a temperature profile similar to the case with no interlayer. When nickel oxide was used as the interlayer, the behavior of the interlayer was different. At low temperatures ( 40 C to 450 C ) the temperature of the nickel oxide interlayer was 20 C to 50 C higher than that of the AD94 alumina interlayer As the temperature of the specimens increased from 450 C to 1200 C, the temperature difference between the materials reached 17 5 C. Above 1200 C the difference in temperature of the two interlayer materials gradually decreased until they

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-u 0 ..__.... Q) !.... ::s ....., ro !.... Q) c.. E Q) I1500 1000 500 0 0 -: -_ _, : --' ' I . ' ' ' . . . -. -. --. -. .. --....... .. ... ----...,. .. . ---. . -, . I -.. ., ... ...... -... : ......... .. I I I 10 ' ' ' ' ' ' ' ' ' --Workpiece -Workpiece ( measured/pyrometer ) ( measured / thermocouple ) 20 30 Time ( min) 40 ' ' ' ' ' ' so 60 Figure 5 53. Tem p erature of t he workpiece measured using a thermoco u p l e and an optical pyromete r.

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Q) Q) E 0 CL I Q) 0. ::, 0 u 0 E Q) .c .. u 0 ., 60 40 20 0 20 40 60 80 100 ............. ---------------J ----------------------------{----------------------------------!--------------------' .. .. ----.... -......... .. ......................... ................. . ' ' ...................................................... .. ........... i .... ......... ........................................................................................................... ........................................ ..... ..................................... ..... 600 800 1000 1200 1400 1600 Thermocouple Temperature (OC) Figure 5-54. Variation in temperature of the workpiece between the thermocouple and the optical pyrometer

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1500 ,-... u 1000 0 ..__., Q) :::l ...., C'O Q) Q.. E Q) 500 r0 Figu r e 5-55. . . e ............................... {------------------------~--------.. --................................ ... ......................... ; ............. -.... -----~-------------... -~ ............... .. .......... .... .... --. ---.. ................... -------. -...... ~ ~ j : .,,,,,,, . ' . '-' ............. ............................ .... .... .. .. --------------.. .. -----------------' .. .. ............................ .. . ' ' . ' ~ / i 1 Susceptor Susceptor ( measured / pyrometer ) (measured/thermocouple) ........... ............ .. ]' .. .. ........... . ...... .. .... ................ ................................. f ................... .... .. ..... ;I _. . . . ; ; : l ; . . 1 ..... .. .... ............... : .................... ............ : .. ............................. : .. ......... .... .............. ' . . . . . . . ' 7 .. ... 1 -t 1 ' . . ; i . ' 4 .. ... ................ ..... __ __ ... 0 10 20 30 40 so 60 Time ( min ) Tempe r ature of the susceptor measured using both a t h ermoco u ple and a n optical pyrometer

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.. Q) -+Q) E 0 CL I Q) Q_ :::, 0 u 0 E Q) ..c .. u 0 60 40 20 0 20 40 60 ' ' -----. -........... ----... -. ---...... ..,. ............ ... ------. -------------.. .. -.------------................ ........ ' . ' ... ---.. --~--------. -----------!--................. ... }. -. --. -------~-................ -... ~ ... ................ ..... . . . 700 800 900 1000 1100 1200 1300 1400 1500 Thermocouple Temperature ( O C) Figure 5 56. Variation in temperature of the s u s ceptor between the thennocouple and the optical pyrometer

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1600 ,,(i) Trial #8; interlayer AD94 1400 -ecalculated; interlayer AD94 ~, 1200 ,~ ,,-.. u 0 __, 1 000 ,
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0 1600 1400 1200 .._, 1000 Q.) Ii... ::::s ....., 800 co Ii... Q.) E 600 Q.) r 400 200 0 0 ---Trial #7; interlayer NiO e calculated: interlayer NiO , 10 iJ , , {j) 20 , wJ' 30 Time (min) 40 __ _'if so Figure 5 58 Temperature (c alculated and measured ) at the s utface of the NiO interlayer 60

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.......... u 0 ....__,, Q) :::::s ,+,-1 ro Q) a. E Q) 1600 1400 1200 1000 800 600 400 200 0 no susceptor Uoint) -G no interlayer Uoint) ... 0.5mm NiO Uoint) o 0.5mm AD94 Uoint) 0 10 20 30 time (min) 40 so 60 Figure 5-59. Temperature (calculated) at the surface of the joint region for various heating conditions

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212 converged at 1550 C. Figure 5-60 plots the calculated temperature of the surface of the end member, node 423 for the same simulations in figure 5-59. In all cases, the material at this node is AD995 alumina. As in figure 5-59, little temperature rise was calculated in the simulation using no susceptor. The temperature of the end member calculated for the case with a AD94 alumina interlayer was almost identical to the end member in the simulation that used no interlayer. The difference displayed in the simulation that used nickel oxide as the interlayer material in figure 5-59 is also present in figure 5-60 Although the variation i n temperature of the end member is not as pronounced as the interlayer, there is a noticeable spread between the simulations that used nickel oxide and AD94 alumina as the interlayer. The calculated temperatures are plotted in figrue 5 61 for both the interlayer and the end member in the simulation that used AD94 as the interlayer Node 328 is AD94 alumina and represents the interlayer and node 423 is AD995 alumina and represents the end member. The calculated temperatures at the two positions were similar for the entire heating period. A similar plot was done for the simulation that used nickel oxide as the interlayer, figure 5-62. In this plot, the material represented by node 328 is nickel oxide As the specimen was heated to 450 C, the temperature of the interlayer was similar to the end member. The temperature of the interlayer rises faster from 450 C to 1200 C than that of the end member As the simulation continues, the temperatures of the interlayer and the end member converge. Figure 5-63 is a plot comparing the calculated temperature of a nickel oxide interlayer 0.5 mm thick with one 5 mm thick. Initially, the thicker interlayer heats much faster. As the simulation progresses the temperature of the thinner interlayer eventually exceeds that of the thicker nickel oxide piece.

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,,,.-... u 0 ...._., (l) I,... ::J .,J ro I,... (l) Q. E (l) r1600 1400 1200 1000 800 600 400 200 0 0 _..,__ no susceptor ( end member) _. e no interlayer (end member) _. _,,,,, @ 0.5mm AD94 (end member) /, /y 10 20 ,,y ,4 30 time (min) 40 so 60 Figure 5-60. Temperature (calculated) at the s urface of the end member for various heating conditions.

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,......._ u 1600 1400 1200 0 1000 Q) I... 3 800 ro I... Q) E 600 Q) r 400 200 0 0 0.5mm AD94 Uoint) e 0.5mm AD94 (end member) 10 20 30 time (min) 40 so 60 Figure 5-61. Temperature (calculated) at the surface of the joint region (AD94) and end member (AD995).

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1600 1400 1200 0 1000 (1) I,... 3 800 ro I,... (1) E 600 (1) r400 200 0 0 0.5mm nio Uoint) e 0.5mm nio (end member) ff 10 20 , jJ , 30 time (min) 40 50 60 Figure 5 62. Temperature ( calculated ) at the surfa c e of the joint region (NiO ) and end member ( AD995 )

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,,......,_ u 0 1600 1400 12 00 '-' 1000 (1) I,.... ::::::s 800 I,.... (1) E 600 (1) 400 2 00 0 / / 0 10 I I 2 0 / 30 time ( min ) 40 0.5 m m N i O -5 m m N iO so 60 Figure 5 63 Comparison of calculated temperatures for specimens heated with nickel oxide interlayer s of different thickness.

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CHAPTER6 DISCUSSION In Chapter 2, a survey was performed using available literature pertaining to microwave processing of materials and materials joining. Chapters three and four specified a course of experiments based on the information gathered in Chapter 2. The intent of the experiments was to broaden the knowledge in the area of microwave joining of materials. In Chapter 5, the results of the experiments designed in Chapters 3 and 4 are presented. In t his chapter, the results are reviewed and explanations are presented that may account for t hese result s. The rationale presented is compared and contrasted to discussions presented i n the literature evaluated in Chapter 2. Pha se One Phase one of the experimental procedure involved the investigation of potential interlayer materials for the joining portion of the research. Several different compositions of gel-derived powders were produced and analyzed to determine their potential as an interlayer Machined Surfaces The roughness of the machined surfaces that were in contact for the joining procedures were in the range of 1.0 m to 3.0 These numbers are within the parameters set forth by Villagio64. The 3-dimensional surface plots in figures 5-2 and 5-4 indicated that there was a textured s urface that could promote the interlocking of asperities without inducing significant interfacial porosity during joining. 217

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218 Sol-Gel Interlayers The initial rapid heating to 400 C of all of the gel pellets during stand alone heating is related to the removal of the free water and structural water present in the gel. The rise in temperature slowed as first the free water, and then the bound water were eliminated. As described in equation 2-3, the power absorbed in a material is proportional to the dielectric loss factor of the material. The dielectric loss factor for all of the gels, figure 5-11, is relatively high at room temperature and decreases steadily to a temperature of 500 C. The continued rise in the temperature of the gels can be attributed to the consistent increase in the dielectric loss factor with temperature. After the maximum of 841 C was reached, the pellet containing 10 mol % iron (II) oxide experienced a decrease in temperature. This can be associated with the oxidation of iron (II) oxide to iron (11,III) oxide. The further oxidized iron is a less efficient microwave absorber than the iron (II) oxide. Visual inspection of the pellet after heating showed it to be red, supporting the speculation of additional oxidation All of the DSC traces exhibited endothermic peaks corresponding to the removal of bound water between 75 C and 150 C and to the removal of structural water between 425 C and 500 C. The exotherm between 525-550 C, present in the sample containing 50 mol% silicon carbide, is due to the oxidation of free carbon in the silicon carbide 9. The base gel, the gel with 50 mol % nickel oxide and the gel with 50 mol % silicon carbide all displayed exotherms near 1160 C. This exotherm results from the formation of alpha-alumina. In the gel containing chromia, the exotherm corresponding to the crystallization of alpha alumina occurred at 1207 C. The partial substitution of chromia for alumina distorts the crystal structure, causing the peak to appear at higher temperatures In the DSC trace of the gel containing 50 mol % iron (II) oxide, two overlapping peaks appeared in the temperature range where crystallization is expected. This specimen was the only one that revealed an endotherm near l 350 C. Examination of the iron (II) oxide/alumina phase diagram figure

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219 6-1, shows a eutectic between 1300-1350 C. The formation of a liquid phase is possible in an iron (II) oxide rich environment(> 10 wto/o alumina). The presence of a liquid phase and flowing air led to an increased oxidation of the iron to the 3+ state. X-ray diffraction analysis was perforrr1ed on the four compositions heated to 1400C in the DSC. A second sample of the gel containing 50 mol o/o iron (II) oxide was heated in the DSC to 1200 C, a temperature lower than that at which the endotherm occurred. The peak positions of the base gel's x-ray diffraction pattern corresponded well to the peak positions published for alumina. This was confirmation that the method for producing alumina was acceptable. The nickel oxide containing specimen had peaks corresponding to alumina, nickel oxide and nickel aluminate spine!. The presence of alumina and nickel oxide are a result of the incomplete reaction of the two materials. This is understandable since the specimens were heated at 40 C/min. In the specimen containing chromia, all of the peaks present coincided well with the reference peak for alumina but the peak positions were all shifted to a smaller angle. This is due to the chromia entering the alumina as a solid solution. Chromium has a larger ionic radius than aluminum. When chromium is substituted for aluminum in the crystal lattice, the spacing between the lattice planes increases. This produces an increase in the d-spacing of the lattice. Applying Bragg's Law, nA = 2 d sin(0) (6-1) it is apparent that the x-ray peaks are shifted to smaller 20 values. In the specimen made with iron (ID oxide heated to 1200 C, peaks matching iron (II) oxide/alumina spine!, alumina and iron (II) oxide were identified. As with the specimen containing nickel oxide, the rapid heating in the DSC did not provide sufficient time for a complete reaction to occur. Additional oxidation of the iron was predicted from the results of the stand alone heating experiments. The x-ray diffraction pattern of the iron ( II) oxide specimen heated to

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2000 1800 Q) +-' s m 1600 a. E Q) .,_ 1400 FeO FeO A l 2 0 3 s s + Liquid Liquid + FeO A1 2 0 3 L i qu i d + FeO s s 20 40 60 wt. o/o Al 2 Q 3 Al 2 0 3 s s + Liquid + 80 Figure 6-1 Pha se diagram of the FeO-Al 2 0 3 system120 220

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221 1400C exhibited only peaks indicating the presence of alumina and iron (III) oxide. This is a result of the complete oxidation of the iron (Il) oxide to iron (III) oxide. As a function of temperature, the dielectric constant and the dielectric loss factor display similar trends for all of the gels examined. The decrease in the dielectric loss from 25 C to 500 C is associated with the removal of free and structural water. The ensuing increase in the loss factor is due to the typical behavior of a dielectric material with increasing temperature. Figure 6-2 is a qualitative graph of the typical loss factor versus temperature for a dielectric material. The figure illustrates the effect of increasing temperature on the effective loss factor. During the microwave heating of dielectric materials an increase in the effective loss factor results in an increase in the materials ability to absorb energy. This leads to a rise in temperature and subsequently, an increase in the effective loss factor. These related increases in the effective loss factor and temperature often lead to a condition known as thermal runaway. Thermal runaway is defined by Metaxas and Meredith5 as the uncontrolled temperature rise in a material heated by high f requency energy due to a positive rate of change of the effective loss factor with temperature As the materials are heated further the loss factor experiences another decrease from 1000 C to 1200 C. Thi s is probably caused by the ordering that the materials undergo during crystallization. Key features of the loss factor figure 5 11 take place at temperatures similar to those seen in the DSC traces, figure 5-6. In the present investigation, thermal runaway wa s prevented by controlling the duty cycle of the microwave generator through the use of a s etpoint controller. Summary of Phase One The two gel-derived materials that were for use in the joining experiments were the gel containing 50 mol % nickel oxide and the gel made with 4 mol % chromium salt. The gel containing iron (Il) oxide heated well but was eliminated from consideration due to its

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222 I I Temperatu re Figure 6-2 Qualitative representation of the effect of temperature on the dielectric loss factor of a typical dielectric material T c refers to the critical temperature at which the efficiency of the absorption of microwaves increases dramatically 5

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223 unstable oxidation characteristics. Silicon carbide was discounted as a potential additive for two reasons. First of all, the silicon carbide addition did not provide a significant increase i n heating ability during stand alone heating. Secondly, silicon carbide did not form any intermediate phases with alumina that could contribute to the joining process. Phase Two In the second phase of the research, microwave susceptors were developed in order to provide the energy necessary to attain joining temperatures on a consistent basis. The design, construction and implementation of a microwave joining apparatus was also a major topic of phase two of the study. The gel containing 50 mol % nickel oxide and the gel made with 4 mol % chromium salt were the interlayer materials used in this portion of t he investigation. Microwave Susceptors The temperature of all of the susceptors increased monotonically for the entire h eating experiment. The susceptor made with 5 vol% silicon carbide maintained a higher te mperature than the susceptor made entirely of cement. The difference, however, was not p roportional to the temperature differences attained by the susceptors made with more silicon carbide. The dielectric constants for all of the susceptor compositions were almost li near with respect to temperature The dielectric loss factor for the 0, 5, and 10 vol% susceptors had values that were similar to each other. When the volume percent of silicon carbide was increased to 20%, the value of the dielectric loss factor increased two-fold. All f our of these compositions exhibited dielectric loss factors that were not significantly i nfluenced by changes in temperature. The dielectric properties of these susceptors are governed by the alumina cement. In the susceptor made with 30 vol% silicon carbide, there was a sufficient quantity of silicon carbide present to influence the dielectric loss f actor and the heating behavior. The increase in the dielectric loss factor above 600 C is reflected in a rapid increase in temperature of the susceptor near 800 C, figure 5-14 The

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224 plot of temperature as a function of silicon carbide for several times, figure 5-18, provided some unanticipated results that are more easily understood when viewed in conjunction with the dielectric properties of the susceptors. Small additions of silicon carbide, 5 vol%, did not significantly improve the ability of the susceptor to heat. The superimposed dielectric loss factor curves for the O vol% and 5 volo/o silicon carbide susceptors suggest that this behavior can be expected. Microwave Joining Apparatus The description and photograph of the microwave joining apparatus described in Chapter 3 is the current version of a piece of equipment that bas been evolving since this study began. Significant challenges were involved in the modification of the microwave oven. The greatest challenge was to provide as uniform a microwave field as possible so that consistent joining results could be obtained. The joining experiments performed in phase two of the research accomplished two t asks. First, they demonstrated the viability of producing specimens joined using microwave energy (one of the original objectives). The second accomplishment of the j oining experiments in phase two was to dismiss gel-derived materials as potential i nterlayers. This decision was made partly because the measured flexure strengths were not in the range of the as-received material. More importantly, as seen in figure 5-23, the shrinkage that occurs in the gel interlayer during heating markedly decreases the area available for joining. The temperatures and times used in these experiments did not induce sufficient creep to provide the contact necessary to develop a complete joint. Additionally, t he relative thinness of the gel interlayer does not take full advantage of the potential for volumetric heating in the microwave joining experiments. Summary of Phase Two The development and characterization of the silicon carbide/cement susceptors contribute to the resources available for researchers working with microwave hybrid

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225 heating. The microwave joining apparatus has proved to be a reliable piece of equipment capable of attaining temperatures upwards of 1550C and applying forces of 2 kN. The elimination of gel-derived materials led to the introduction of densified materials as potential interlayers. Nickel oxide was retained as an interlayer material for its reactivity with alumina. Near dense (80% theoretical) disks are used in phase three of the research effort. The second material used as an interlayer for phase three was 94% pure alumina. The significant amount of impurities present in this alumina should provide an increase in microwave absorption over the high-purity alumina used as a base gel. The increase in absorption is ascribed to the high dielectric loss factor of the glassy grain boundary phase by Binner74. Phase Three In phase three of the study, a statistical analysis was performed on the results gathered from a course of joining experiments designed to evaluate the influence of processing parameters on the flexure strength of alumina butt joints. The fracture surfaces and joint areas were evaluated using SEM, WDS and image analysis. Experimental Design The purpose of an experimental design is to provide an organized set of experiments that will aid in the interpretation of the results. The use of the experimental design requires advance consideration of the goal of the experiments and the steps needed to achieve that goal. The subsequent statistical analysis of the experimental observations affords an unbiased interpretation of the results. A factorial design allows for evaluation of several factors that are varied throughout the experiments. This design method also affords the use of a minimum number of experiments. This is desirable when the cost of the experiments becomes prohibitive. This can occur through expenses stemming from either materials, machining or equipment usage.

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226 In this research, a one-half factorial experimental design was used to determine the effect of the processing parameters in question on the flexure strength of the joined alumina. The five processing parameters considered to be the most influential on the flexure strength were identified. Two levels of each parameter were chosen based on conventions gleaned from the literature. Joining Experiments and Flexure Tests During the microwave joining experiments, the temperature of the specimen increased steadily until it reached the temperature used for joining. Based on the information in figure 6-2, there should be a temperature at which the efficiency of the workpiece to absorb microwaves increases drastically. At this point, the temperature of the workpiece should increase commensurately with the microwave absorption This was not the situation recorded in figure 5-20. The dielectric loss factor of the AD995 alumina remains low even up to the temperatures used for joining in this study. If this is the case, the majority of the heat in the microwave joining experiments was generated in the susceptor and transferred to the workpiece via radiation and convection The similarity in the temperature of the AD995 alumina end member and the interlayer materials that were supposedly more absorptive, is evidence that this is probably the circumstance. The only confirmation that a reaction occurred between the nickel oxide interlayer and the end members of the two specimens that did not join at all during the experiment was the coloration of the contact surfaces. The blue surfaces are indicative of the formation of nickel oxide/alumina spinel, NiA1204. In the specimens that failed during handling that were joined with nickel oxide, figures 5-21 and 5-22, the residual nickel oxide that was exposed suggests that in addition to a de bonding at the interlace, failure also occurred through the bulk of the interlayer. From an examination of the figures, it is evident that the relative roughness of the fracture surface increases with increasing fracture strength. The specimens joined with nickel oxide that were strong enough to tolerate the applied

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227 machining stresses then were tested in four-point bending. Figure 5-35, a bar that failed prior to testing, debonded at the nickel oxide-alumina interface. All of the bars joined with a nickel oxide interlayer failed through the bulk of the nickel oxide. Nickel oxide is not considered a structural ceramic and no strength data is available in the current literature. The difficulty in producing dense nickel oxide contributes to the likelihood that the specimen will fail through the interlayer. Figures 5-36 and 5-37 are typical fracture surfaces observed in specimens with nickel oxide interlayers. The fracture surfaces are highly textured but do not provide any insight into the fracture strength of the specimens. The reaction layer was consistently eight to ten microns thick for all of the flexure bars examined Any spinel formation requires the solid state diffusion of either nickel or aluminum through the spinel l ayer. As the reaction layer for1ns, the reactants (Al203 and NiO) are separated by an ever increasing distance in the forrr1 of the spinel. At some time, the formation of the spinel phase is essential ly halted. For experiments of the time durations evaluated in this research there exists a maximum spinel thickness that can be utilized for the range of processing conditions used in this study. Based on the reaction layer thickness at both end member-interlayer interfaces, this maximum usable thickness of nickel oxide is 15-20 m. Any more nickel oxide present will go unreacted and ultimately lead to the failure of the specimen. The strength of the flexure bars is determined by the nickel oxide-spine! interface. The micrographs in figures 5-39 and 5-41 illustrate this point well. In both figures, the alumina-spine! interface was continuous. The nickel oxide spinel interface was poorly formed on the other side of the reaction layer of the bar that failed before testing. The fracture surfaces for specimens joined with AD94 alumina as the interlayer material had few features for discussion In these specimens, an abrupt change in the microstructure and elongated porosity were characteristic features of the joint line. When the joint line was examined using higher magnification, grains from the end member and

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228 the interlayer were separated by a glassy phase that extended the entire length of the joint line, figures 5-27 and 5-29. Binner et al.74, joining low purity alumina under similar conditions, reported comparable findings and suggested that this is the grain boundary material that has been ''squeezed'' out of the lower purity alumina during processing. X-ray maps of the joint line, created using wavelength dispersive spectroscopy, indicated that silica is the predominant interface material. Silica is the major impurity in the AD94 interlayer material. This supports the statement by Binner et al74 that the interface material did indeed originate in the grain boundaries of the AD94 alumina. Some grain-to-grain contact between the end member and interface was observed, but the majority of the interface was filled with this silica rich phase. Failure along this interface seems likely and may be the reason there is no appreciable texture to the fracture surfaces. Another observation made by Binner et al.74 was the appearance of this glassy phase on the outside surface of the joint. This phenomenon was not observed in this study. There are two contributing factors that would lead to this contrast in results. The first factor is the joining temperatures used. Although the temperatures used by Binner et al.74 were in the same range as the temperatures used in this study, overall, those used by Binner were nominally higher, leading to a more fluid liquid phase. The second factor is the purity of the alumina used in the research. The alumina used by the authors in the experiments that provided contrary results was 85% pure alumina and contained more silica for liquid formation. This is in comparison to the 94% pure alumina used in this study. The roughness measured from profiles of joined surfaces was influenced by the presence of the silica rich phase at the interface. Where the as-machined profile varied consistently across the length investigated, the profiles of both joined specimens have regions of small variations and regions of large variations. This can alter the interpretation of the reported profile roughnesses. The large variations experienced in both the

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229 microwave and conventionally joined specimens were caused by reactions during processing and by artifacts introduced during sample preparation. The processing related variations are due to incursions of the silica rich phase around the surface grains of the end member. The sample preparation artifacts are caused by pullout of interface grains during polishing of the specimens for microscopic analysis Statistical Analysis The mean strength of the bars microwave joined in trial #8 was 83% of the value reported for the unjoined material. These strengths are comparable with those reported for alumina by other authors. Not all of the bars failed at the joint area. A small number of microwave joined bar s failed within an end member. This result suggests that some of the joints may have been as strong as the machined bulk material. This phenomenon may also have had an effect on the statistical analysis, leading to the assertion that there is no significant difference between the conventional and microwave heating methods. For the processing conditions of time, temperature and pressure, the significance of the two levels is determined by the values chosen for each level The heating method and the interlayer material cannot be influenced by the magnitude and difference between the two levels. This means that by adjusting the values of the levels of the experiment, the significance of a condition can be dictated. Joining experiments carried out with longer times, higher pressures or higher temperatures should eventually produce results that would be considered significant. This reasoning initially appears sound. However, when the effect of time and pressure on strength is examined, figures 2-14 and 2-15, the benefit of increasing the time and pressure decreases. The temperature range for joining is also limited. On the low end joining may not occur, and on the high end melting or creep can interfere with the joining process For this materials system it then becomes uncertain whether a statistical significance for any of these parameters can be introduced.

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230 The processing parameter that had a significant effect on the flexure strength of the bars was the interlayer material. The low strengths measured for the bars made with nickel oxide signified that further analysis should be done without the nickel oxide data. This treatment, called blocking, permits the removal of all data associated with one level of a processing parameter. In this case the nickel oxide level of the interlayer parameter was removed and the statistical analysis was performed only on the specimens joined using AD94 alumina as the interlayer material. In the blocked analysis, as in the complete one, no significance between the levels of any of the processing parameters was observed at a 95% convidence level. When the data were evaluated at a 90% confidence level, there was a significant difference in the mean flexure strength of specimens joined using different heating methods Overall, the specimens joined using microwave energy had a flexure strength higher than those joined by the conventional heating method. One of the touted benefits of microwave processing is volumetric heating. That is, unifor1r1 distribution of energy throughout the volume of the workpiece leading to relatively unifor1n temperature profiles. The statistical analysis, performed to determine the effect of position of the bar on flexure strength, divided the joined specimens into four sections. No significant differences in strength were observed when the heating method was compared for a certain position at the 95 % confidence level. This was true for all four of the positions evaluated. Flexure strength also was compared among positions within a heating method. Again, no significant differences in the strength were noticed. However, the bars from the center position of the microwave heated specimen were stronger the bars from the center position of conventionally joined specimens. These results suggest that there may be some volumetric heating occurring but in the case of the low dielectric loss AD995 alumina, not a st1fficient amount to provide a statistical difference at the 95% confidence level.

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231 Summary of Pha se Three The experimental design developed in phase three facilitated an organized approach to produce an unbiased evaluation of the effect of several processing parameters on the joining of high-purity alumina. The parameters investigated were those most commonly varied in joining experiments: time temperature and pressure. In addition, the effects of heating method and interlayer material were observed. Under certain conditions, adequate flexure strengths were achieved in specimens joined by both microwave and conventional heating. However, the only processing parameter that produced significant variation in flexure strength was the interlayer material. The small number of bars from each trial available for flexure testing limit the conclusiveness of the statistical analysis. There is little evidence provided to support the concept that volumetr i c heating by the direct coupling of microwaves to the workpiece contributes to the overall temperature in the notably low dielectric loss AD995 alumina. Phase Four Phase four of this study was dedicated to developing a model that could be used to predict the heating behavior of materials in a microwave field. Laboratory heating experiments were performed in support of the modeling work to provide a basis for comparison of the temperatmes calculated during the computer simulation. Experimental St1pport The experiments performed in support of the model development consisted of measuring the temperature of the workpiece and susceptor during the heating process. At temperatures near the point at which the optical pyrometer becomes functional ( >600 C), the pyrometer recorded higher temperatures than did the thermocouple. This is probably an artifact of the way temperature i s measured with an optical pyrometer Unlike thermocouples, which convert the energy of the material they are in contact with into a voltage, optical pyrometers convert the intensity of light emitted or reflected from a surface

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232 into a voltage. In the joining experiments, the thermocouple is always measuring the temperature of the surf ace of the workpiece. Due to the fact that the s11sceptor initially heats much faster than the workpiece, the pyrometer i s measuring the temperature of the reflection of the susceptor off the face of the workpiece. The temperature measured by the ther1nocouple eventually exceeds that measured by the pyrometer This is caused by the measuring technique s and properties of the materials. The thermocouple accesses the workpiece through a small hole in the insulation and the susceptor. The optical pyrometer needs a larger hole in both the exterior insulation and the susceptor to view the workpiece The absence of s usceptor material apparently produces less heat in the area near the workpiece where the pyrometer i s focused In addition, there is an opening in the insulation that provides uninterrupted access between the workpiece and the much cooler environment. As presented in figure 4-12, the emissivity of alumina decreases considerably with increasing temperature. Modem pyrometers are equipped to compensate for variations in the emissivity of the material. However, the low emissivities associated with a very smooth alumina surface cannot be fully compensated for by the pyrometer. In the experiments measuring the temperature of the susceptor, the rough surface of the cement and the imbedded silicon carbide granules provided an adequate surf ace for measuring the temperature accurately with the optical pyrometer. The differences here are attributed to the exposure of the outside of the susceptor to the environment. Computer Simulations The data input for the model used in the computer simulations wa s based on physical, thermodynamic and electromagnetic properties of the materials used Data pertaining to the above mentioned properties were unavailable for some materials. In these instances the properties of a material with a s imilar composition were substituted. In the situation where the compo s ition of the material contains a nominal amount of a second element, the properties of the pure material are used When the material contains porosity,

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233 properties such as heat capacity and absorbed power were adjusted to reflect the smaller mass of material. The heating profiles generated during the computer simulations have an S-shaped curve. This feature is more prominent in the simulations using nickel oxide as the interlayer material. This behavior can be related back to the shape of the power absorption curves corresponding to the materials in the model. These curves generally exhibit an increase in power absorption as a function of temperature. The effect of the power absorption on the heating behavior is counteracted in part by the heat transfer properties of the model. Energy is removed from the system in the form of heat in proportion to the fourth power of the temperature gradient between the surf ace of the model and the environment. This is the reason for the flattening out of the temperature profile as temperature is increased. This behavior also was present in the experimental heating curves. Only small differences in temperature were calculated between the interlayer material and the end member. Even though the interlayer material in the simulation, either AD94 alumina or nickel oxide, absorbed a great deal more power per unit volume than the AD995 end member material, there was not enough interlayer material to significantly affect the temperature of the workpiece. The heating behavior in the simulation conducted with a five millimeter nickel oxide interlayer suggests that this is the case. A five millimeter thick nickel oxide interlayer for joining may provide improved heating near the joint. However, the mechanical properties of such a joint would be poor. Characteristically poor mechanical properties were measured in joints made with nickel oxide interlayers 150 m thick. The greatest disparity between the calculated and measured temperatures occurs in the first few minutes of heating when the temperature of the workpiece increases rapidly. In this temperature range, the calculated temperature lags and requires several minutes to reach the same value as the measured temperature. This may be due to the platinum thermocouple sheath acting as an antenna, concentrating the microwave field near the tip.

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234 This is more likely to happen at lower temperatures where the efficiency of the absorption of microwaves by the workpiece, insulation and susceptor is at its lowest. As these material s begin to absorb more of the microwaves, there is less of a tendency for the thermocouple tip to interfere with the microwave field. Summary of Phase Four Temperature profiles calculated using the model assembled in Chapter 4 were compared to experimentally measured temperatures. Nodes where the temperatures were calculated in the model were carefully selected to correspond to the position where the experimental temperature measurements were made Simulations were performed to compare the effect of interlayers of differing composition and thickness on the heating of the workpiece. Interlayers 500 m thick of nickel oxide and AD94 alumina contributed l ittle to the overall calculated values. When the interlayer thickness of nickel oxide was i ncreased to five millimeters, a noticeable change was observed in the heating behavior of the interlayer. Comparisons made between calculated and measured temperatures indicated that the model used can provide qualitative information pertaining to the heating behavior of materials in a microwave field The ability to qualitatively predict the heating behavior in a system of material s in a microwave field can be applied to experimental designs. Simple experiments can be used to gage the temperature profiles that can be expected during the experiment. Such experiments would include estimations of the electric field in a microwave cavity the electromagnetic and thermophysical properties of the materials along with the geometric configuration of the a s sembled materials to be heated. The i mplementation of a microwave heating model can assist in eliminating the trial and error experimentation that has been associated with microwave processing of materials.

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CHAPTER 7 SU:MMARY AND CONCLUSIONS The goal of this study as introduced in Chapter 1 was to provide experimental data coupled with numerical models that serve to further the understanding of the interactions between microwave energy and alumina ceramics, as well as how these interactions influence the mechanical behavior of joined materials. The literature survey in Chapter 2 provided background information on microwave interactions with materials. Additional reviews of papers covered the fundamentals of materials joining and summaries of joining experiments performed using conventional or microwave heating were provided. Chapter 3 discussed the experimental work required to accomplish the goal of this study. The issues that were addressed ranged from equipment development to experimental organization. The chapter also included a description of the analytical methods used to evaluate the joined specimens. A numerical model for modeling beat flow was developed in Chapter 4 to simulate the heating profiles generated during the heating of ceramics using microwave energy. The use of models to simulate microwave beating can provide information regarding the probable heating behavior of ceramics prior to the actual experimentation. The temperature at nodes in the model corresponding to the position of the thermocouples in the laboratory experiments was monitored. These temperatures were later used to compare the simulated temperatures to the temperatures that were determined experimentally 235

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236 Chapter 5 provided the results of the experimental work described in Chapters 3 and 4. The outcome of the experimenta l work was presented in a series of graphs and tables. These were accompanied by a description of the data with an emphasis placed on the most significant issues In Chapter 6, a discussion of the results was presented. The materials system investigated consisted of materials that are generally considered microwave transparent. This is due to the low dielectric loss factor of alumina and the resulting large penetration depth If the penetration depth remain sizeable at high temperatu res insufficient amounts of microwave energy will be absorbed and heating will not occur. The introduction of a strong microwave absorber as an interlayer material did not provide a sufficient volume of microwave absorbing material to influence the low dielectric loss alumina end members. Although the objective of demonstrating induced enhancements due to microwave processing remains a challenge, it is clear that joining other materials systems that interact with microwaves more vigorously than the high-purity alumina used in this study is possible. Important points discussed in Chapter 3, 4 and 5 the study are listed below by chapter. Chapter 3 An apparatus for joining ceramics using microwave energy was designed and fabricated Susceptors for microwave hybrid heating were developed and tailored to work at temperatu1es up to 15 50 C. Processing temperatures in excess of 1500 C could be reached in less than 45 minutes (several minutes faster than a conventional furnace). Sample cooling can be controlled with ease to fit any temperature profile

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237 Laboratory experiments were performed to provide comparable heating conditions to evaluate the effectiveness of the numerical model used. Chapter 4 A geometric model was constructed incorporating the physical dimensions physical, electromagnetic and thermodynamic properties of the materials being investigated. Numerical modeling was employed to approximate heat flow during microwave hybrid heating. Chapter 5 X-ray diffraction analysis confirmed the validity of the gel preparation method and identified the reaction products formed with other materials during heating. Many features of the differential scanning calorimetry results of the gel-derived materials can be correlated to changes observed in the dielectric loss factors. Under all of the processing conditions investigated, the nickel aluminate spinel formed was eight to ten microns thick. When the nickel oxide/spinel interface was poorly formed, the specimen failed at the interface. Specimens failed through the bulk of the nickel oxide when the nickel oxide/ spinel interface was of better quality. A nickel oxide interlayer thickness of 15-20 mis necessary for complete reaction of the interlayer to occur under the conditions evaluated in this work. Specimens joined using AD94 alumina as the interface material separated at the interlayer/end member interface. Only a few of the fracture surfaces examined contained markings such as f1acture origin, mirror planes and hackle. In the specimens joined with an AD94 interlayer, the interface between the interlayer and the end member was composed of grain boundary material from the lower purity interlayer that had been forced out during joining.

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238 Some of the bars joined using AD94 as the interlayer failed in the bulk of the end member, away from the joint interface. This suggests that the joints had strengths comparable to the as-received material. The uniformity of joints within a specimen were evaluated by position based on flexure strength. Bar positions were monitored to determine if volumetric microwave heating contributed to the flexure strength of joined specimens. Statistical tools were used to qualitatively assess the joining parameters used in this study. For the five parameters investigated (time temperature, pressure, interlayer material and heating method) only varying the interlayer material provided a statistically significant difference at the 95% confidence level in the mean flexure strength. A significant difference was noted between heating methods at the 90% confidence level with the microwave processed specimens having the higher flexure strengths. Temperature profile simulations were generated for several different joining conditions Temperature profiles that were measured experimentally or generated numerically were analogous. Thicker interlayers of nickel oxide (five millimeters) generated higher temperatures nume1ically. However the strength of a specimen joined with such an interlayer would be insufficient for most structural ceramic applications. In conclusion, microwave joining can play an important role in the advancement of the use of microwave processing in industry. Even materials systems that do not demonstrate enhancements in measured properties due to interactions with a microwave field can benefit from microwave processing. The most significant findings are listed below: High-purity alumina specimen s were joined using microwave energy with flexure

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239 strengths approaching that of the original material (86% strength of as-received alumina in trial #8). The significance of this is that complex products can be manufactured from simple shapes without seriously compromising the strength of the original material A difference in the mean strength was observed between bars from the center of the specimen was observed. This difference did not prove to be statistically significant at the 95% confidence level. However, the number of bars sampled at this position are insufficient to support a statistical conclusion. The addition of a 500 m thick interlayer of a strong microwave absorber did not provide an increase in temperature in either the experimental or numerical temperature profiles. When the thickness of the interlayer was changed to 5 mm, however, a dramatic increase in the numerically generated temperature profile was observed. Microwave absorption by the interlayer material can result in higher temperatures in the joint region than in the end member material. This can reduce the temperature-related negative effects (such as secondary grain growth and creep) that can lead to unpredicted failure of the joined specimen. The majority of the heat in the end members was generated by the microwave susceptor and transferred to the specimens via radiation and convection. The low dielectric loss of the AD995 alumina precluded significant absorption of microwave energy in the end members. The minimal interaction of microwaves with high purity alumina facilitates the maintenance of sub-joining temperatures in the end members (a short distance from the interface). The temperatures necessary for joining then can be limited to joint area through the use of a strong microwave absorbing interlayer material. This is yet another method of reducing the negative effects of the high temperatures associated with joining. Satisfactory joints could be produced from as-machined surfaces with a roughness

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240 in the range of 1.0 m to 3.0 m. Thus, the mirror finish of the surface recommended in many joining experiments may not be necessary to achieve adequate results This ha s the potential to reduce machining costs of ceramic products that contain a joining step in their manufacture.

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CHAPTERS FUTURE WORK Although this study resulted in many important findings, the topic of microwave joining of ceramics has not been exhausted. The microwave joining apparatus developed in the course of this research has the potential to open the door to many applications for multimode microwave ovens. Some issues that could provide interesting topics of research for future investigations are: Use the numerical model developed in this study to investigate systems prior to laboratory experimentation Simulation results should not be used to eliminate potential materials systems but to assist the user in developing a heating configuration more conducive to microwave processing. The model also could be used to determine the minimum amount of suscepting material necessary to achieve the desired processing temperatures. Optimizing the susceptor will allow microwave interaction with the workpiece to be maximized. The numerical model also can be helpful in the identification of potential opportunities for microwave processing. By simulating the heating conditions to be used, there is the capability of avoiding potential experimental pitfalls such as thermal runaway or non-uniforrr1 temperature distributions. Employ the microwave joining apparatus to investigate a materials system that is significantly influenced by microwave radiation. In laboratory scale experiments, the penetration depth of extremely low dielectric loss factor materials is too large to contribute notable power generation in the material. In future microwave joiningexperiments, materials such as zirconia, silicon carbide and alumina (with at 241

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242 least 6% impurities) can provide a system that is more interactive with microwaves than 99.5 % pure alumina. Investigate both strong and weak microwave absorbers as die materials for the utilization of the equipment developed as a microwave hot press for the pressure sintering of powders. A strong microwave absorber and a strong material such as silicon carbide can provide a setting similar to the radio frequency induction furnaces that use graphite dies. In this situation, poor microwave absorbing materials could be pressure sintered. If, on the other hand the material to be pressure sintered has a high dielectric loss, a microwave transparent structural ceramic like the AD995 alumina in this study could be used as the die material. Use high strength, low dielectric loss, high-purity alumina as a die material for performing self propagating high temperature synthesis of materials under an applied pressure. The benefits of microwave ignited combustion synthesis has been demonstratedlOI. By performing the synthesis under an applied pressure, there is the potential for increasing the density of the combusted products

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APPENDIX A SAMPLE CALCULATIONS OF THE PENETRATION DEPTH AND CRITICAL TillCKNESS FOR Al-66 CEMENT Penetration depth at 25C for Al-66 ceme nt : From equation 2-4, I A. ~( ') 2 D = =-P ., 27t eff D. 1 tri P rti f Al 66 C t 1e ec C rope es o emen Temperature (C) dielectric constant ( 1 ) effective lo ss factor ( 1 ') 25 4.34 0.032 1000 4.82 0 151 the wavelength of free space, "A,' 0 i s assumed to be that of the incident microwave, 2.45 GHz where C f A, at 1000 c, C = A/ the speed of light 2. 998 x 10 Io cm/s frequency of microwave s, 2.45 x 109 s-1 wavelength = 12.24 cm. I D = p ( 12 24 cm )( 4 82) 2 (2)( 7t )( 0.151 ) 243 = 28.32 cm.

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244 Critical thickness at 1000 C for Al-66 cement To calculate the critical thickness, L e nt, recall equation 2-9, L c rit = 2.7p 1 0.08 where pis the penetration depth. L e nt= 2.7 x (28 32)-1 0 08 = 0.0153 cm

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APPENDIXB s Y OF INPUT DATA FOR HEATING 7.2

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JOBDES Title Card Job DEscription Up to 72 Alphanumeric Characters MAXCPU NGEOM TIM IDEGRE I QSUM CNVRG IMONTR p CPU time in Geometry Type Initial time Temperature un i ts Flag to calculate net Flag to output Flag to output seconds for problem Cylndrical 0 = F energy changes for convergence nto selected i n f ormaoon execution. Cartesian 1 = c transient. during calculation s. during calculations 1 r 8-z 6 X Y Z 2 = absolute 0 = do not calculate 0 = do not output 2 r-8 7 x-y 1 = calculate 1 = output 3 r z 8 X Z 4 r 9x 5z Spher ic al 10 r 11 12 r-8$ REGIONS NOREG R1 MATS REGDIM (1) REGDIM (2) REGDIM (3) REGDIM (4) REGDIM (5) REGDIM (6) Region number Region material Smaller x or r Larger x or r region Smaller y or 8 Larger y or 8 region Smaller z or Smaller z or $ number region dimension dimension region amension. dimension region dimension region dimension I TS NGENS NREGBC (1) NREGBC (2) NREGBC (3) NREGBC (4) NREGBC (5 ) NREGBC (6) R2 Region nllal Region heat Boundary condition Boundary condition Boundary condition Boundary condition Boundary condition Boundary condition temperature generation number on smaller x or r on larger x or r on smaller y or 6 on large r y or 6 on smaller z or~ on larger z or t number MATERIALS r. M AT MATNAM CONDUC DENSTY SPHEA T NCONTP NDENTP NSPHTP MCP M Material number Material name Material M a t erial density M aterial specific Conductivity Density Specific heal Phase change flag (8 characters max ) Conductivity heat. temperature temperature temperature 0 = no phase dependent function dependent function dependent function change 1 = phase change SLT M SI.HM SLT M SLHM PC First phase change Latent heat for f i rst Second phase Latent heat for or transition phase change change or transition second phase temperature temperature change M A T MATNA M MUNCH XD XC XK XT XTP MCP ML Ma terial number Material name Data units Unit conll8f"Sion Unit con118rslon Unk conll8rsion Unit conll8rSion Unit COll118rslon Phase change flag (Library material conwrsion flag factor for density factor for specific lactor for factor (multiplier) factor (additive) for proceeded by an heal conductivity for temperature temperature asterisk( )

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' INITIAL TEMPERATURES ... INT TEMPIN NITPOS (1) NITPOS (2) NITPOS (3) I Initial temperature Initial temperature. x or r dependent y or 8 dependent 2 or $ dependent number function number function number function number HEAT GENERATIONS NGN GENO NGNFCN (1) NGNFCN (2) NGNFCN (3) NGNFCN (4) NGNFCN (5) G Heat generation Volumetric heal Time dependent Temperalure x or r dependent y or 8 dependent 2 or lj) dependent number generation rate funct i on number dependent function function number function number function number number BOUNDARY CONDITIONS NBOTP NBYTYP BYTEMP NBTFN NBTPOS (1) NBTPOS (2) NBTPOS (3) B1 Boundary condition Boundary condition Boundary lime dependent x or r dependent y or 8 dependent 2 or $ dependent number type. temperature function number function number function number function number 1 = surface-to(not used for boundary NBYTYP=3) 2 = prescribed surface temperature 3 = surface-tosurface BCDEF (1) BCDEF (2) BCDEF (3) BCDEF (4) BCDEF (5) IBHFLP 82 Forced convection Radiation coefficient Natural convection Natural convection Prescribed heat flux. Parameter flag heat transfer hr multiplier term, h 0 exponent term, he hf O=no addaional cards coefficient he, 1 =B3 card only 2=84 card only 3=84 and B4 cards NBCTIM (1) NBCTIM (2) NBCTIM (3) NBCTIM (4) NBCTIM (5) B3 Forced convection Radiation time Natural convection Natural convection Heal flux time time dependent dependent function multiplier time exponent time dependent function function dependent !unction dependent funct i on NBCTEM (1) NBCTEM (2) NBCTEM (3) NBCTEM (4) NBCTEM (5) 84 Forced convection Radaticrl Natural convection Natural convection Heat flux temperature temperature multi>lier exponent temperature dependent function dependent function temperature temperature dependent function dependent function dependent function

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XGRID AG ( 1 ) AG (1) AG (1) AG ( N ) X1 Smallest x or r Ne xt larger x or r Next larger x or r Largest x or r gross gross grid line gross grid line gross grid line grid Une NORG ( 1 ) NORG (2) NORG (N-1) X2 Number of
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ANALYTICAL FUNCTIONS NANALT NOTE : Entries on A2. Card define an analytical funct ion of the following form Only those A1 Analytical function terms having non-zero values need to be entered number F(V) = Ai+ A 2 V + A3V2 + A,icos (AsV) + A6exp(A1V) + Assin(AgV) + A 1oln(A11V) NPRM A(MPRN ) NPRM A(MPAN ) A2. Coefficient inde x I. Coefficient vah.1e Coefficient index, l. Coefficient value A i. A ~, TABULAR FUNCTIONS J NTABL T1 Tabular function number. ARG (1) VAL(1) ARG (2) VAL (2) T2 F irst independent First dependent Second ndependent Second dependent value value value value PRINTOUT TIMES PATIME (1) PATIME (2) P RTIME (3) PATIME (4) 0 F irs t printout time Second printout Third prin t out time Fourth printout t i me time NODES MONITORED NTS NOS (1) NOS (2) s Number of iterations First node Second node or time steps monitored monitored between output.

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STEADY ST ATE NTYPE NOITX EPI BETA MCOUNT TIM ss Solution T echnlque Max imum number of Steady-state SOR overrelaxation Number of iterations Value to reset 1 = SOR steady-state conwrgence factor. between evaluations problem lime to 2 = Direct iterations criterion. 1 0S~<2 0 of temperature (Used only when 3 = Conjugate (Defaults : 500 for (Default = 1 9) dependent thermal following a transient gradient SOR, 20 for direct properties for SOR solution) and conjugate (Default = 1, gradient) Maximum= 10) TRANSIENT NTYPE FTIME NOTE : For NTYPE = 1 supply TA1 Card TR Solution Technique Final time For NTYPE = 2 supply TR2 and one or more TR3 Cards 1 = Explicit 2 = Implic it DELTAT KTMFCT NSTPEX TR1 Time step Factor by which Number of time stable time step is steps between increased wtth Levy's evaluation of method temperature dependent properties THETA RESDUL NITREZ RELDIF ABSDIF BETAT NUPBTA ITLRCO ITLR C I TR2 Parameter defining Convergence Number of iterations Relative convergence Absolute Initial value for SOR Number of time For BETAT = 0, Number of i terations differencing criterion for imp l icit fl rtnear loop between criterion for nonlinear convergence criterion acceleration steps between number of iterations criterion to term i nate technique solu1ion tests for (temperature fO( noolinear parameter attempted criterion to initiate acceleration 0.5 = Crank Nicolson (Default = 10-5) convergence dependent (temperature =O, optimize acceleration acceleration parameter updates 1 0 = Backwards (Default = 1) properties) loop dependent empirically parameter updates parameter updates (De fa ult = 2) Euleo' (Default =10) propertles) loop <0, Carre's Used whe n BETAT (Default = 5) (Delaull = 1) opeimization =0 <0 use constant (default = 1) For BETAT
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APPENDIX C SAMPLE CALCULATIONS FOR STATISTICAL ANALYSIS For a half factorial experimental design it is possible to evaluate five factors in s ixteen observati o n s. The letter s A B C D and E represent five variables than can be adjusted durin g s ome manufacturing proce s s or treatment s uch as temperatur e, amount of mixing purity o f material or som e other parameter Each of these variables can be inve s tigated at tw o different level s designated a s low (-) and high ( + ). After the trial s have been performed the re s ulting sixteen observations are tabulated. Trial/effect A B C D E observation 1 155 2 + + 184 3 + + 19 7 4 + + 201 5 + + 166 6 + + 156 7 + + 215 8 + + + + 229 9 + + 205 10 + + 184 11 + + 168 12 + + + + 1 72 13 + + 210 14 + + + + 219 15 + + + + 252 16 + + + + 200 251

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252 To begin the analysis the sum of the ob s ervations are taken two at a time and placed in a third co lumn. This fills one-half of the new column. The second half of the column is filled by the difference of the observations taken two at a time. This method, developed by Yates 1 2 I is a more organized approach to the bookkeeping involved in determining the mean effect and the s um of squares of the observations This method provide s the same re s ults as if the observations were added and s ubtracted in the standard order set out by the signs in the table above. The table then look s like trial observation (1) 1 155 155 + 184 = 339 2 184 197 + 201 = 398 3 197 166 + 156 = 322 4 201 215 + 229 = 444 5 166 205 + 184 = 389 6 156 168 + 172 = 340 7 215 210 + 219 = 429 8 229 252 + 200 = 452 9 205 184 155 = 29 10 184 201 197 = 4 11 168 156 166 = -10 12 172 229 215 = 14 13 210 184 205 = -21 14 2 19 172 168 = 4 15 252 219 210 = 9 16 200 200 252 = -52 This proce s s of addition and subtraction is repeated in three more instances with the

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253 finished table containing four columns of calculations in addition to the original ob s ervations The mean square for each variable is calculated by dividing the square of column ( 4) by s ixteen, the number of trial s in the experiment trial observation ( 1 ) ( 2 ) (3) ( 4 ) mean s quare ( 4)2/16 1 (-) 155 339 737 1503 3113 2A 184 398 766 1610 -3 0.56 3B 197 322 729 57 155 1501.56 4C 2 01 444 881 -60 -57 203.06 5D 166 389 33 181 181 2047.56 6E 156 340 24 -26 -35 76.56 7AB 215 429 -17 -21 135 1139 06 8CE 229 452 -43 -36 -57 203.06 9CD 205 29 59 29 107 715.56 lODE 184 4 122 152 -117 855.56 11 AC 168 10 -49 -9 -207 2678.06 12AD 172 14 23 -26 -15 14 06 13AE 2 10 -21 -25 63 123 945.56 14BC 219 4 4 72 -17 18.06 15BD 252 9 25 29 9 5.06 16BE 200 -52 -61 -86 -115 826 56 The confidence values for an F di s tribution for one degree of freedom are

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254 pro b a b i l ity point for one degree of freedom 0 1 39.9 0 05 161 0 01 4052 The re s ult s indicate that observation s A AD BC and BD have no significant effect on the proces s Ob s ervation Ei s significant in the 5 % < P < 10 % confidence level. All other observation s are significant in the 1 % < P < 5 % confidence interval. This in c ludes second order int e raction s betw e en two variables in the experimental design.

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REFERENCES 1 Sutton W H. Am Ceram. Soc. Bull. Vol. 68 [2] pp.376 386 ( 1989 ). 2. Bruce R W. in Microwa v e Proces s ing of Materials, edited by W.R. Sutton M.H. Brook s and I.J. Chabinsky ( Mater Res Soc. Proc. Vol. 124 Pittsburgh, PA), pp 315 (1988 ) 3 Meek T T and Blake R.D ., U.S. Patent No 4 529 857 July ( 1985 ). 4 M e ek T T ., J. Mat. Sci L e t ., Vol 6 pp 6 3 8-640 ( 1987 ) 5. Metaxa s, R.C and Meredith R.J. Industrial Microwave Heating pp. 7 0 102 Peter Per e grinu s Ltd ., London ( 1983 ) 6 Fathi, Z. Ph.D Di sse rtation Univer s ity of Florida, 59-110 ( 1993 ) 7 Hutcheon R M ., DeJong M.S ., Adams F.P., Hunt L ., Iglesias F. Wood, G W. and Parkinson G., Electromagnetic Energy Reviews Vol 2 [4] part 2 pp 46 50 ( 1989 ). 8. Hutcheon R M ., DeJong M.S. Adam s, F.P. Lucuta, P.G ., McGregor J. E and Bahen L ., in Microwave Processing of Materials ill (eds. R.L Beatty W R. Sutton a nd M.F Iskand e r ) Proceeding of the Materials Re s earch Society Sympo s ium Vol. 2 69 pp. 541 551 ( 1992 ). 9. Graziani T Baxter D. and Nannetti C A. in Corro s ion of Advanced Ceramic s, ( eds. R J Fordham, D.J Baxter and T Graziani ) Proceedings of a Special Session a s Part of the 4th European Ceramic s Society Conference Vol. l 13pp. 153-164 ( 1996 ) 10 Cathey Jr. W.T., IEEE Tran s on Blee. Comp ., Vol. EMC 25 [3] pp. 339-345 ( 1983 ) 11 Katz J D and Blake R.D. Am. Ceram Soc. Bull., Vol. 7 0 [8] pp. 1304 1308 ( 1991 ) 1 2. Holcomb e, C E ., Am Ceram. Soc. Bull Vol. 62 [12] pp 1388-1345 ( 1983 ) 1 3. Tian Y L ., Brodwin M E Dewan, H S. and John s on D L in Microwave Processing of Materials, ( ed s. W R. Sutton, M.H. Brooks and I.J. Chabin s ky ) Proceedin g of the Material s Re s earch Society Symposium, Vol 124 pp 21 3218 ( 1988 ). 14. Katz J D ., Blake R D. and Scherer C P ., Ceram. Eng S c i. Proc Vol. 10 [7 8] 255

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261 98. Yu, X D Varadan, V.V. and Varadan, V.K., in Microwaves: Theory and Application in Materials Processing, (eds. D.E. Clark, F.D. Gae and W.H. Sutton) Ceramic Transactions Vol. 21, pp. 497-505 ACerS, Westerville (1991). 99. Ahmad, I., Silberglitt, R ., Black, R.M. Sa'Adaldin, S. and Katz, J.D., in Microwave Processing of Materials III, (eds. R L. Beatty, W.H. Sutton, M.F. Iskander) Mat. Res. Symp Proc ., Vol 269 pp. 271-276 Materials Research Society, Pittsburgh (1992). 100. Yin, T Y ., Varadan, V V. Varadan V.K. and Conway, J.C., in Microwaves: Theory and Application in Materials Processing, (eds. D.E. Clark, F.D. Gae and W.H. Sutton ) Ceramic Tran sa ctions Vol 21 pp. 507-514 ACerS, Westerville (1991). 101. Dalton, R C. Ahmad I. and Clark, D E ., Ceram. Eng. Sci. Proc., Vol. 11 [9-10], pp. 1729 -174 2 (1990). 102. Silberglitt, R., Palaith, D., Black, R.M., Sa'Adaldin, H.S., Katz, J.D. and Blake, R.D., in Microwaves: Theory and Application in Materials Processing. (eds. D.E. Clark, F.D. Gae and W.H. Sutton) Ceramic Transactions Vol. 21, pp. 487-495 ACerS, Westerville (1991). 103. Loehman R.E., in Microwaves: Theory and Application in Materials Processing II (eds D.E. Clark, W.R. Tioga and J .R. Laia Jr.) Ceramic Transactions Vol. 36, pp. 417-430 ACerS, Westerville (1993). 104 Das S. and Curlee, T.R., Am. Ceram. Soc. Bull., Vol. 66 [7] pp. 1093-1094 ( 1987 ). 105 Sheppard L.M., Am Ceram. Soc Bull., Vol. 67 [10] pp. 16561661 (1987). 106. Katz, J.D., in Annu. Rev Mater. Sci., (eds. R.A. Huggins, J.A. Giordmaine and J.B. Watchman, JR. ) Vol 22 pp. 153 170 Annual Review Inc. Palo Alto (1992). 107. Schulz, R.L., Folz, D.C., Clark, D E., Schmidt, C J. And Wicks, G.G ., in Microwaves: Theory and Application in Materials Processing ill, (eds. D.E Clark, D.C Folz, S.J Oda and J.R. Laia Jr .) Ceramic Transactions Vol 59 pp 107-114 ACerS Westerville (1995). 108 Schiffmann R.F., in Microwaves: Theory and Application in Materials Processing, (eds. D.E Clark, D.C. Folz, S.J. Oda and R Silberglitt) Ceramic Transactions Vol. 59, pp. 7-16 ACerS Westerville, ( 1995). 109. Clark D .E Dalzell, W. J and Adams, B L., U.S. Patent Number 4,801 399, ( 1989) 110. Dalzell, W J., Masters Thesis University of Florida, (1988). 111. McGill S.L. Walkiewicz J. and Smyres G A., in Microwave Processing of Materials (eds. W.H. Sutton, M H Brooks and I.J. Chabinsky ) Mat Res. Symp Proc., Vol. 11 pp 247-252 Materials Research Society, Pittsburgh (1988)

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262 112. Bunting E.N., Bur. Standards J Re s earch, Vol 6 [6] p. 948 ( 1931 ). 113 Muan A ., Amer J. S c i ., Vol 256 p 420 ( 1958 ) 114 D e, A ., M as ter s The s i s Uni v er s ity of Florida ( 1990 ) 115. Davie s, O.L ., The Design and Analysis of Industrial Experiments pp 440-494 Longman In c ., New Tork ( 1978 ) 116. Gitzen W.H ., Alumina a s a Ceramic M a terial, pp. 6 397 Americ a n Cerami c Society Columbus ( 1970 ). 117 Furukawa, G.T Douglas T B. Mcco s key R.E and Ginnings D C ., Re s Natl Bur Std s Vol. 57 [2] pp. 67 82 ( 1956 ) 11 8. Miyayama M. Koumoto K. a nd Yanagida, H. in Engineered Material s Handbook Volume 4 Ceramics and Glasse s, pp. 748-749 ASM International USA ( 1991 ). 119 Batelle M e morial In s titute Engineering Properties of Selected Cerami c Material s 5.2 3 2 The American Cerami c Soci e ty Columbu s ( 1966 ) 120 Fi s cher W A and Hoffman A. Arch Eis e nhuttenw ., Vol 2 7 [5] p 344 ( 1956 ). 1 2 1 Yate s, F ., Design and Analy s i s of Factorial Experiments, Imperial Bureau of Soil Science London ( 19 3 7 ).

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BIOGRAPHICAL SKETCH Alex Cozzi was born May 22, 1963 in Nyack New York. He attended the New York State College of Ceramics at Alfred University in Alfred, New York In May of 1985 he received his bachelor 's degree in ceramic engineering In May of 1986 he accepted a position as a laboratory engineer a t American Marazzi Tile Inc. in Sunnyvale Texa s Cozzi enrolled in the graduate program in the Department of Materials Science and Engineering at the University of Florida in 1988 He earned his M.S degree in material s science and engineering in 1991. He is a student member of the American Ceramic Society and the National Institute of Ceramic Engineers. 263

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I certify that I have read this s tudy and that in my opinion it conforms to acceptable standards of scholar ly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy avid E. Clark, Chairman Professor of Materials Science and Engineering I ce1tify that I have read this study and that in my opinion it conforms to acceptable standards of scholar ly presentation and i s fully adequate, in scope an quality, as a dissertation for the degree of Doctor of Philo sophy. E.Dow tney Professor of Materials Scien.l:t:i--' and Engineering I certify that I have read this study and that in my opinion it conforms to acceptable standards of scho larly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philo sophy. Jpfui J. ~ L .. ...,lsky and gineering I certify that I have read this study and that in my opinion it conforms to acceptable standards of scho larly presentation and is fully adeq uate in scope and quality, as a dissertation for the degree of Doctor of Philosophy. Rajiv Singh Associate Professor of Materials Science and Engineering I certify that I ha ve read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. Bhavani V. Sankar Professor of Aerospace Engineering, Mechanics and Engineering Science

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I certify that I have read this s tudy and that in my opinion it conforms to acceptable standards of scho larly presentation and is fully adequate, in scope and quality as a dissertation for the degree of Doctor of Philo so phy Mattison K. Ferber High Temperature Material s Laboratory at Oak Ridge National Laboratory, Senior Research Staff This di sser tation was submitted to the Grad11ate Faculty of the College of Engineering and to the Graduate School and was accepted as partial fulfillment of the requirement s for the degree of Doctor of Philo so phy. August 1996 1-~ Winfred M. Phillips Dean College of Engineering Dean Graduate School

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SCIENCE LTBRA"Y UNIVERSITY OF FLORIDA II I II IIII II II Il l l ll ll l lll II I I II II II II II II I ll 11 1 11111 11 111111 1 3 1262 08554 9565


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