Preface ...................................................... xiii
Author ......................................................... xv
Chapter 1 Sintering of Ceramics: Fundamentals ................... 1
1.1 Introduction ............................................... 1
1.2 The Sintering Process ...................................... 1
1.2.1 Characterization of Sintering ....................... 3
1.2.2 Approach to Sintering ............................... 3
1.3 Driving Force for Sintering ................................. 4
1.3.1 Surface Curvature ................................... 5
1.3.2 Applied Pressure .................................... 6
1.3.3 Chemical Reaction ................................... 6
1.4 Defects in Crystalline Solids ............................... 6
1.4.1 Point Defects and Defect Chemistry .................. 7
1.4.2 Kroger-Vink Notation ................................ 8
1.4.3 Defect Reactions .................................... 8
1.4.4 Defect Concentration ................................ 9
1.4.5 Intrinsic Defects .................................. 11
1.4.5.1 Schottky Defect ........................... 11
1.4.5.2 Frenkel Defect ............................ 12
1.4.6 Extrinsic Defects .................................. 13
1.4.6.1 Nonstoichiometry .......................... 14
1.4.6.2 Influence of Solutes ...................... 15
1.4.6.3 Brouwer Diagram ........................... 16
1.4.7 Defect Chemistry and Sintering ..................... 18
1.5 Diffusion in Crystalline Solids ........................... 19
1.5.1 Diffusion Equations ................................ 19
1.5.1.1 Solutions of the Diffusion Equation ....... 21
1.5.2 Atomistic Diffusion Processes ...................... 22
1.5.3 Mechanisms of Diffusion ............................ 26
1.5.3.1 Lattice Diffusion ......................... 26
1.5.3.2 Grain Boundary Diffusion .................. 27
1.5.3.3 Surface Diffusion ......................... 28
1.5.3.4 Trends in Diffusion Coefficients .......... 28
1.5.4 Types of Diffusion Coefficients .................... 28
1.6 The Chemical Potential .................................... 29
1.6.1 Chemical Potential of a Mixture of Gases ........... 30
1.6.2 Chemical Potential of Solids and Liquids ........... 31
1.6.3 Chemical Potential of Atoms and Vacancies in a
Crystal ............................................ 31
1.6.4 Chemical Potential of Atoms and Vacancies beneath
a Curved Surface ................................... 32
1.6.5 Equilibrium Vacancy Concentration beneath a
Curved Surface ..................................... 34
1.6.6 Vapor Pressure over a Curved Surface ............... 35
1.7 Diffusional Flux Equations ................................ 36
1.7.1 Flux of Atoms ...................................... 36
1.7.2 Flux of Vacancies .................................. 37
1.8 Diffusion in Ionic Crystals: Ambipolar Diffusion .......... 37
1.9 Concluding Remarks ........................................ 41
Problems ....................................................... 41
References ..................................................... 43
Chapter 2 Solid-State and Viscous Sintering .................... 45
2.1 Introduction .............................................. 45
2.2 Mechanisms of Sintering ................................... 46
2.3 Effects of Grain Boundaries ............................... 48
2.4 Theoretical Analysis of Sintering ......................... 50
2.5 Herring's Scaling Law ..................................... 51
2.5.1 Derivation of the Scaling Law ...................... 51
2.5.1.1 Scaling Law for Lattice Diffusion ......... 52
2.5.2 Application and Limitation of the Scaling Law ...... 53
2.5.2.1 Relative Rates of Sintering Mechanisms .... 53
2.5.2.2 Limitation of the Scaling Law ............. 54
2.6 Analytical Models ......................................... 55
2.6.1 Stages of Sintering ................................ 55
2.6.1.1 Initial Stage ............................. 56
2.6.1.2 Intermediate Stage ........................ 56
2.6.1.3 Final Stage ............................... 56
2.6.2 Modeling the Sintering Process ..................... 57
2.6.3 Initial Stage Models ............................... 57
2.6.3.1 Geometrical Model ......................... 57
2.6.3.2 Kinetic Equations ......................... 58
2.6.3.3 Summary of the Initial Stage Sintering
Equations ................................. 61
2.6.3.4 Limitations of the Initial Stage
Sintering Equations ....................... 62
2.6.4 Intermediate Stage Models .......................... 63
2.6.4.1 Geometrical Model for Solid-State
Sintering ................................. 64
2.6.4.2 Mechanisms ................................ 64
2.6.4.3 Sintering Equations ....................... 64
2.6.4.4 Geometrical Model for Viscous Sintering ... 68
2.6.5 Final Stage Models ................................. 70
2.6.5.1 Geometrical Model for Solid-State
Sintering ................................. 70
2.6.5.2 Sintering Equations ....................... 71
2.6.5.3 Geometrical Model for Viscous Sintering ... 72
2.6.6 Limitations of the Analytical Models ............... 73
2.7 Numerical Simulation of Sintering ......................... 73
2.7.1 Numerical Simulation of Solid-State Sintering ...... 74
2.7.2 Numerical Simulation of Viscous Sintering .......... 76
2.8 Phenomenological Sintering Equations ...................... 78
2.9 Sintering Diagrams ........................................ 79
2.9.1 Construction of the Diagrams ....................... 80
2.9.2 Limitations of the Diagrams ........................ 81
2.10 Sintering with an Externally Applied Pressure ............. 81
2.10.1 Hot Pressing ....................................... 81
2.10.1.1 Hot Pressing Models ....................... 81
2.10.1.2 Densification Rate in Hot Pressing ........ 84
2.10.1.3 Hot Pressing Mechanisms ................... 85
2.10.2 Sinter Forging ..................................... 88
2.10.3 Hot Isostatic Pressing ............................. 88
2.11 Stress Intensification Factor and Sintering Stress ........ 89
2.11.1 Stress Intensification Factor ...................... 89
2.11.2 Sintering Stress ................................... 91
2.11.3 Measurement of the Sintering Stress and Stress
Intensification Factor ............................. 93
2.11.3.1 Zero-Creep Technique ...................... 93
2.11.3.2 Loading Dilatometry ....................... 93
2.11.3.3 Sinter Forging Technique .................. 96
2.12 Alternative Derivation of the Sintering Equations ......... 97
2.12.1 General Isothermal Sintering Equation ............. 100
2.12.2 General Isothermal Creep Equation for Porous
Solids ............................................ 100
2.13 Concluding Remarks ....................................... 101
Problems ...................................................... 101
References .................................................... 102
Chapter 3 Grain Growth and Microstructure Control ............. 105
3.1 Introduction ............................................. 105
3.2 General Features of Grain Growth ......................... 106
3.2.1 Grain Growth and Coarsening ....................... 106
3.2.2 Occurrence of Grain Growth ........................ 106
3.2.3 Driving Force for Grain Growth .................... 107
3.2.4 Normal and Abnormal Grain Growth .................. 107
3.2.5 Importance of Controlling Grain Growth ............ 108
3.2.5.1 Effect of Grain Size on Properties ....... 108
3.2.5.2 Attainment of High Density ............... 110
3.3 Ostwald Ripening ......................................... 110
3.3.1 The LSW Theory .................................... 112
3.3.1.1 Ostwald Ripening Controlled by the
Interface Reaction ....................... 112
3.3.1.2 Ostwald Ripening Controlled by
Diffusion ................................ 114
3.3.2 Modifications to the LSW Theory ................... 115
3.3.3 Time-Dependent Ostwald Ripening ................... 117
3.4 Topological and Interfacial Tension Requirements ......... 117
3.5 Normal Grain Growth in Dense Solids ...................... 119
3.5.1 The Model of Burke and Turnbull ................... 119
3.5.2 Mean Field Theories ............................... 121
3.5.3 Topological Analysis of Grain Growth .............. 123
3.5.4 Computer Simulation of Normal Grain Growth ........ 125
3.6 Abnormal Grain Growth in Dense Solids .................... 127
3.6.1 Causes of Abnormal Grain Growth ................... 128
3.6.2 Application of Controlled Abnormal Grain Growth ... 131
3.7 Grain Growth in Thin Films ............................... 133
3.8 Mechanisms Controlling the Boundary Mobility ............. 135
3.8.1 Pinning by Fine Second-Phase Particles ............ 135
3.8.1.1 The Zener Model .......................... 137
3.8.1.2 Computer Simulations of
Particle-Inhibited Grain Growth .......... 138
3.8.1.3 Comparison with Experimental Results ..... 140
3.8.2 Solute Drag ....................................... 141
3.9 Grain Growth and Pore Evolution in Porous Solids ......... 144
3.9.1 Pore Evolution during Sintering ................... 146
3.9.2 Thermodynamic Analysis of Pore Shrinkage .......... 148
3.9.1 Kinetics and Mechanisms of Grain Growth in
Porous Solids ..................................... 152
3.9.4 Grain Growth in Very Porous Solids ................ 152
3.9.5 Grain Growth in Less Porous Solids ................ 156
3.9.5.1 Pore Mobility ............................ 156
3.9.5.2 Kinetics of Pore-Boundary Interactions ... 159
3.9.5.3 Grain Growth Kinetics .................... 160
3.10 Simultaneous Densification and Grain Growth .............. 160
3.10.1 Microstructural Maps .............................. 162
3.10.1.1 Brook Model .............................. 162
3.10.1.2 Yan, Cannon, and Chowdhry Model .......... 165
3.10.2 Computer Simulations of Microstructural
Evolution ......................................... 168
3.11 Fabrication Principles for Ceramics with Controlled
Microstructure ........................................... 168
3.12 Concluding Remarks ....................................... 171
Problems ...................................................... 171
References .................................................... 172
Chapter 4 Liquid-Phase Sintering .............................. 177
4.1 Introduction ............................................. 177
4.2 Elementary Features of Liquid-Phase Sintering ............ 178
4.2.1 Enhancement of Densification ...................... 178
4.2.2 Driving Force for Densification ................... 179
4.2.3 Formation of the Liquid Phase ..................... 179
4.2.4 Microstructures ................................... 179
4.3 Stages of Liquid-Phase Sintering ......................... 180
4.4 Thermodynamic and Kinetic Factors ........................ 182
4.4.1 Wetting and Spreading of the Liquid ............... 182
4.4.2 Dihedral Angle .................................... 184
4.4.2.1 Liquid Penetration of the Grain
Boundary ................................. 185
4.4.2.2 Shape of the Liquid and the Grains ....... 186
4.4.3 Effect of Solubility .............................. 187
4.4.4 Capillary Forces .................................. 187
4.4.5 Effect of Gravity ................................. 191
4.5 Grain Boundary Films ..................................... 192
4.6 The Basic Mechanisms of Liquid-Phase Sintering ........... 196
4.6.1 Stage 1: Rearrangement and Liquid
Redistribution ........................... 197
4.6.1.1 Liquid Redistribution .................... 197
4.6.1.2 Particle Rearrangement ................... 200
4.6.2 Stage 2: Solution-Precipitation ................... 202
4.6.2.1 Densification by Contact Flattening ...... 203
4.6.2.2 Densification Accompanied by Ostwald
Ripening ................................. 205
4.6.2.3 Assessment of the Densification Models ... 206
4.6.2.4 Grain Shape Accommodation ................ 206
4.6.2.5 Coalescence .............................. 208
4.6.3 Stage 3: Ostwald Ripening ......................... 209
4.6.3.1 Densification by Pore Filling ............ 209
4.6.3.2 Microstructural Coarsening ............... 211
4.7 Numerical Modeling of Liquid-Phase Sintering ............. 214
4.8 Hot Pressing with a Liquid Phase ......................... 215
4.9 Use of Phase Diagrams in Liquid-Phase Sintering .......... 215
4.9.1 Zinc Oxide ........................................ 216
4.9.2 Silicon Nitride ................................... 217
4.9.1 Activated Sintering ............................... 220
4.11 Vitrification ............................................ 221
4.11.1 The Controlling Parameters ........................ 222
4.11.2 Vitrification of Silicate Systems ................. 223
4.12 Concluding Remarks ....................................... 224
Problems ...................................................... 226
References .................................................... 227
Chapter 5 Special Topics in Sintering ......................... 231
5.1 Introduction ............................................. 231
5.2 Inhomogeneities and Their Effects on Sintering ........... 232
5.2.1 Differential Densification ........................ 232
5.2.2 Control of Inhomogeneities ........................ 234
5.2.3 Correction of Inhomogeneities ..................... 234
5.2.4 Shrinkage of Large Pores .......................... 236
5.3 Constrained Sintering I: Rigid Inclusions ................ 240
5.3.1 Volume Fraction of Inclusions ..................... 241
5.3.2 Densification Rate of the Composite and the
Matrix ............................................ 242
5.3.3 The Rule of Mixtures .............................. 242
5.3.4 Transient Stresses during Sintering ............... 244
5.3.4.1 Composite Sphere Model ................... 244
5.3.4.2 Stress Components ........................ 245
5.3.4.3 Effect of Transient Stresses on
Sintering ................................ 246
5.3.4.4 Calculation of Transient Stresses and
Strain Rates ............................. 247
5.3.5 Percolation and Network Formation ................. 251
5.3.5.1 The Concept of Percolation ............... 253
5.3.5.2 Effect of Percolation on Sintering ....... 254
5.3.5.3 Numerical Simulations .................... 254
5.3.6 Factors Influencing the Sintering of Ceramic
Composites ........................................ 255
5.4 Constrained Sintering II: Adherent Thin Films ............ 258
5.4.1 Models for Constrained Sintering of Thin Films .... 258
5.4.2 Experimental Observations of Sintering of Thin
Films ............................................. 260
5.4.3 Crack Growth and Damage in Constrained Sintering
of Films .......................................... 262
5.5 Constrained Sintering III: Multilayers ................... 264
5.6 Constitutive Models for Porous Sintering Materials ....... 265
5.7 Morphological Stability of Continuous Phases ............. 266
5.7.1 Rayleigh Instability and Microstructural
Evolution ......................................... 267
5.7.2 Morphological Stability of Thin Films ............. 269
5.8 Solid Solution Additives and the Sintering of Ceramics ... 272
5.8.1 Effect of Additives on Kinetic Factors ............ 273
5.8.2 Effect of Additives on Thermodynamic Factors ...... 274
5.8.3 Segregation of Additives .......................... 275
5.8.3.1 Elastic Strain Energy .................... 275
5.8.3.2 Electrostatic Interaction and the Space
Charge Concept ........................... 276
5.8.4 The Role of MgO in Al2O3 .......................... 280
5.9 Sintering with Chemical Reaction: Reaction Sintering ..... 282
5.9.1 Influence of Process Variables .................... 284
5.9.1.1 Particle Size of Reacting Powders ........ 284
5.9.1.2 Sintering Temperature .................... 284
5.9.1.3 Applied Pressure ......................... 285
5.9.1.4 Processing Trajectories in Reaction
Sintering ................................ 285
5.9.2 Experimental Observations of Reaction Sintering ... 286
5.10 Viscous Sintering with Crystallization ................... 289
5.10.1 Effect of Process Variables ....................... 290
5.10.1.1 Viscosity ................................ 290
5.10.1.2 Pore Size ................................ 290
5.10.1.3 Applied Pressure ......................... 291
5.10.1.4 Heating Rate ............................. 291
5.10.2 Analysis of Viscous Sintering with
Crystallization ................................... 291
5.10.2.1 TTT Diagrams ............................. 291
5.10.2.2 Analysis in Terms of Sintering with
Rigid Inclusions ......................... 294
5.10.3 Experimental Observations of Sintering with
Crystallization ................................... 296
5.11 Concluding Remarks ....................................... 297
Problems ...................................................... 297
References .................................................... 298
Chapter 6 Sintering Process Variables and Sintering
Practice ............................................ 305
6.1 Introduction ............................................. 305
6.2 Sintering Measurement Techniques ......................... 305
6.2.1 Furnaces .......................................... 306
6.2.2 Shrinkage and Density ............................. 307
6.2.3 Grain Size ........................................ 309
6.3 Conventional Sintering ................................... 309
6.3.1 Particle and Green Compact Effects ................ 310
6.3.1.1 Particle Size ............................ 310
6.3.1.2 Particle Size Distribution ............... 310
6.3.1.3 Particle Shape and Particle Structure .... 311
6.3.1.4 Particle Packing ......................... 312
6.3.1.5 Effect of Green Density .................. 314
6.3.2 Anisotropic Sintering Shrinkage ................... 315
6.3.2.1 Pore Shape Anisotropy .................... 315
6.3.2.2 Particle Alignment ....................... 318
6.3.3 Heating Schedule .................................. 320
6.3.3.1 Stage 1: Binder Burnout .................. 321
6.3.3.2 Stage 2: Low-Temperature Soak ............ 321
6.3.3.3 Stage 3: Heat-Up to the Sintering
Temperature .............................. 321
6.3.3.4 Stage 4: Isothermal Sintering ............ 321
6.3.3.5 Stage 5: Annealing ....................... 322
6.3.3.6 Stage 6: Cool-Down to Room Temperature ... 322
6.3.3.7 Isothermal Sintering ..................... 322
6.3.3.8 Constant Heating Rate Sintering .......... 323
6.3.3.9 Effect of Heating Rate on Sintering ...... 323
6.3.3.10 Master Sintering Curve ................... 329
6.3.3.11 Multistage Sintering ..................... 330
6.3.3.12 Fast Firing .............................. 332
6.3.3.13 Rate-Controlled Sintering ................ 333
6.3.4 Sintering Atmosphere .............................. 334
6.3.4.1 Gases in Pores ........................... 334
6.3.4.2 Vapor Transport .......................... 338
6.3.4.1 Water Vapor in the Sintering
Atmosphere ............................... 338
6.3.4.4 Volatilization and Decomposition ......... 340
6.3.4.5 Oxidation Number ......................... 342
6.3.4.6 Defect Chemistry and Stoichiometry ....... 346
6.3.5 Production of Controlled Sintering Atmospheres .... 346
6.4 Microwave Sintering ...................................... 348
6.4.1 Interaction of Microwaves with Matter ............. 349
6.4.2 Microwave Sintering Techniques .................... 352
6.4.3 Microwave Sintering of Ceramics ................... 353
6.4.4 Plasma Sintering .................................. 355
6.4.5 Plasma-Assisted Sintering ......................... 356
6.5 Pressure-Assisted Sintering .............................. 357
6.5.1 Hot Pressing ...................................... 357
6.5.1.1 Hot Pressing Process Variables ........... 359
6.5.1.2 Analysis of Hot Pressing Data ............ 359
6.5.1.3 Reactive Hot Pressing .................... 360
6.5.2 Sinter Forging .................................... 361
6.5.3 Hot Isostatic Pressing ............................ 361
6.5.3.1 Hot Isostatic Pressing: Process
Variables ................................ 363
6.6 Concluding Remarks ....................................... 364
Problems ...................................................... 365
References .................................................... 366
Appendix A
Physical Constants ............................................ 371
Appendix В
SI Units—Names and Symbols .................................... 373
Appendix С
Conversion of Units ........................................... 375
Appendix D
Ionic Crystal Radii (in units of 10-10 m) ...................... 377
Appendix E
Density and Melting Point of Some Elements and Ceramics ....... 379
Index ......................................................... 383
|
