Introduction to Aspects of Thermodynamics and Kinetics Relevant to Materials Science (eBook)

Front Cover 1
An Introduction to Aspects of Thermodynamics and Kinetics Relevant to Materials Science, Third Edition 4
Copyright Page 5
Contents 6
Preface to Third Edition 16
Chapter I: Thermodynamics of Phases having Constant Composition 18
Introduction 18
1. Thermodynamic potentials 20
1.1. Energy 20
1.2. Entropy 23
2. Polymorphism 28
2.1. Phase transitions on varying the temperature 28
2.2. Phase transitions on varying the pressure 31
2.3. P–T phase diagram 32
2.4. Effect of magnetic entropy on polymorphic transitions 35
2.5. Melting transition in hard sphere system 36
2.6. Polymorphs of a 2D system 38
2.7. Disordered, short-ranged-ordered and long-range-ordered solid solutions of invariant composition 41
2.8. Polymorphism in oligomers and polymers 48
3. Summary 62
Appendix 1 63
Appendix 2 66
Appendix 3 69
Appendix 4 70
References 72
Bibliography 74
Problems 78
Chapter II: Thermodynamics of Solid Solutions 80
Introduction 80
1. Random solutions in binary systems 80
1.1. Free energy of a random binary solution 80
1.2. Free energy of a mixture of solutions 82
1.3. Phase boundary compositions corresponding to miscibility gap compositions of a random binary solution 84
1.4. Regular solutions 87
1.5. Equilibrium between terminal solutions of different crystal structure 88
2. Non-random binary solid solutions 90
2.1. Positional entropy or entropy of mixing 90
2.2. Other contributions to the entropy of solution 91
3. Concept of strain energy in solid solutions 91
3.1. Metallic alloys 91
3.2. Semiconductor alloys 94
4. Factors other than atomic size deviation that affect the enthalpy and entropy of solid solutions 95
5. Activity and activity coefficient of solutions 97
6. Polymer alloys 98
7. Equilibrium in a stressed solid 99
8. Remarks about liquid solutions 101
9. Hard sphere fluid in a cell model 101
10. Summary 104
Appendix 1 104
References 105
Bibliography 106
Problems 107
Chapter III: Free Energy and Phase Diagrams 108
Introduction 108
A. Free Energy and Phase Diagrams – Binary Systems 108
1. Solid–liquid equilibria 108
2. Origin of eutectic phase diagram in isomorphic systems 113
3. Solid–solid equilibria equivalent to the solid–liquid case 115
4. Intermediate phases 116
5. Metastability 119
6. Temperature dependence of free energy–composition curves and phase diagrams 120
7. Prediction of phase diagrams 122
8. Coherent equilibrium 126
9. Summary for Section A 127
B. Heterogeneous Chemical Equilibria and Phase Diagrams 127
1. Thermodynamics of heterogeneous chemical reactions 127
References 131
Bibliography 132
Problems 132
Chapter IV: Thermodynamics of Interfaces 134
Introduction 134
1. Concept of surface quantities 134
2. An approximate model for evaluating the surface energy 135
2.1. Wulff plot of surface energy 135
3. Surface reconstruction 137
4. Some particle size effects 138
4.1. Effect of particle size on difference in pressure between a small spherical isotropic solid and an external fluid in local equilibrium 138
4.2. Effect of particle size on difference in pressure between a crystal particle that develops surface facets and external fluid in local equilibrium 139
4.3. Dependence of equilibrium vapor pressure on particle size 139
4.4. Dependence of solvus composition on precipitate particle size 141
5. Adsorption 144
5.1. Gibbs' adsorption 144
5.2. Guggenheim's pseudo-thermodynamic model of an interface phase 146
5.3. Other adsorption isotherms 150
6. Surface stress 151
7. Surface energies or solid–gas and liquid–gas interface energies 152
8. Solid–liquid interfaces 154
9. Solid–solid interfaces 155
9.1. Grain boundaries 155
9.2. Interphase interfaces 159
9.3. Local equilibrium at grain boundary intersections 161
10. Diffuse interfaces 163
11. Methods of measuring interface energies 166
12. Pseudomorphic stabilization of metastable phases in thin films 167
13. Wetting transition 169
14. Soft matter interfaces 172
References 172
Bibliography 173
Problems 174
Chapter V: Heterophase and Homophase Fluctuations 176
Introduction 176
1. Heterophase fluctuations 176
1.1. Heterogeneous distributions of heterophase fluctuations 181
1.2. Effect of stress on fluctuation probability and embryo shape 184
2. Homophase fluctuations of composition in a metastable homogeneous phase 187
3. Spinodals and their relationship to mode of metastable phase decomposition 193
4. Easy embryo formers in stable host phases 193
Appendix 1 197
References 198
Bibliography 199
Problems 199
Chapter VI: Thermodynamics of Defects 202
Introduction 202
1. Monatomic solids 202
1.1. Point defects 202
1.2. Electronic defects 206
2. Compounds 211
2.1. Defects in stoichiometric compounds 211
2.2. Non-stoichiometric compounds 213
3. Comparison of defects in metals, semiconductors and ionic crystals 220
4. Average free energy of defects 220
References 221
Bibliography 221
Problems 221
Chapter VII: Concepts in Kinetics in Solids 224
Introduction 224
1. Activation energy 224
2. Computer assisted methods in kinetics 229
3. Competing processes 231
4. Thermodynamic theory of irreversible processes 232
5. Computer simulation methods 236
5.1. Monte Carlo 236
5.2. Molecular dynamics 238
5.3. Phase field 238
5.4. Level set 239
References 239
Bibliography 240
Problems 240
Chapter VIII: Diffusion 242
Introduction 242
1. Phenomenological basis 242
1.1. Intrinsic diffusivities 242
1.2. Chemical diffusivity 246
1.3. Darken's relations 249
1.4. Additional driving forces 250
1.5. Applications of phenomenological equations of irreversible thermodynamics to ionic crystals 251
2. Mechanisms of diffusion 251
2.1. Metals 252
2.2. Ionic crystals 259
2.3. Semiconductors 262
3. Nernst–Einstein relation 262
4. Empirical rules 264
5. Solutions to diffusion equations 264
6. High diffusivity regions in solids 265
6.1. Models for evaluating the grain boundary diffusivity 266
6.2. Mechanism of diffusion along grain boundaries 268
6.3. Empirical results 268
6.4. Electromigration along grain boundaries 269
7. Computer assistance in solving diffusion problems 269
8. Polymer diffusion 271
Appendix 1 274
References 276
Bibliography 277
Problems 278
Chapter IX: Nucleation and Growth Kinetics 280
Introduction 280
1. Rate of heterophase nucleation 280
1.1. Homogeneous nucleation theory and its experimental verification 280
1.2. Heterogeneous nucleation 287
2. Spinodal decomposition 288
3. Nucleation at high supersaturation but not beyond spinodal 291
3.1. DFT and nucleation 293
4. Growth from nucleation onwards 298
5. Summary 301
References 302
Bibliography 303
Problems 304
Chapter X: Solid–Solid Interface Migration Kinetics 306
Introduction 306
1. Driving forces for recrystallization and grain growth 306
2. Growth laws for pure materials 309
2.1. Primary recrystallization 309
2.2. Secondary recrystallization or abnormal grain growth 312
2.3. Grain growth 313
2.4. A/& #945
3. Effect of dispersed particles on grain boundary migration 315
4. Grain boundary mobility 316
5. Mechanisms of interface migration 320
5.1. Grain boundaries 320
5.2. Boundaries between different phases 324
5.3. Effect of interface roughness on migration mechanism 326
5.4. Effect of solute on boundary mobility 327
6. Summary 332
References 332
Bibliography 334
Problems 335
Chapter XI: Growth of Phases: Diffusion or Interface Reaction Control 336
Introduction 336
1. Diffusion couple (alpha/beta), no intermediate phase 336
1.1. Components have equal molar volumes 336
1.2. Components have unequal partial molar volumes 338
2. Diffusion couple (alpha/beta) with intermediate phase, incoherent interfaces and at constant molar volume 339
2.1. One intermediate phase 339
2.2. Many possible intermediate phases 347
2.3. Amorphous intermediate phase 350
3. Growth involving interface migration 350
3.1. Continuous precipitation 350
3.2. Diffusion-induced grain boundary migration 361
4. Solidification 363
4.1. Pure materials 363
4.2. Multicomponent systems 364
5. Physical vapor deposition 371
6. Chemical vapor deposition 375
7. Sintering 376
8. Summary 378
References 378
Bibliography 380
Chapter XII: Morphological Instability and Growth of Phases 382
Introduction 382
1. Morphological instability 382
1.1. Basis for morphological instability at a reaction front 382
1.2. Liquid–solid interface (solidification) 384
1.3. Vapor–solid interface 389
1.4. Solid–solid interface 393
2. Dendritic solidification 394
2.1. Pure materials 394
2.2. Multicomponent materials 401
3. Eutectic solidification 404
4. Summary 413
References 414
Bibliography 415
Chapter XIII: Thermodynamics, Kinetics and Patterns 416
1. Spatial periodic patterns having a thermodynamic origin 416
1.1. Dipole patterns 417
1.2. Modulated surface patterns 421
1.3. Short-range repulsion 422
1.4. Bulk matter 423
2. Spatial periodic patterns far from equilibrium 427
2.1. Dissipative crystals 427
Appendix 1 439
References 440
Chapter XIV: Thermodynamics of Micelles 442
1. Micelles 442
1.1. Nucleation of micelles 442
2. Characteristics of micelles 447
2.1. Total free energy per unit volume of system 447
2.2. Are micelles phases? 448
2.3. The critical micelle concentration 449
2.4. Contrasting nucleation of heterophases and micelles 452
2.5. What factor(s) control the shape of micelles? 452
2.6. Equilibrium size distribution of micelles and their coexistence 457
3. Vesicles 461
3.1. Bilayer disk to vesicle transition 461
4. Phase equilibria of micellar aggregates 466
References 470
Index 472
A 472
B 472
C 472
D 473
E 473
F 474
G 474
H 474
I 475
J 475
K 475
L 475
M 475
N 476
O 476
P 476
R 476
S 477
T 477
U 478
V 478
W 478
Z 478