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ОбложкаFultz B. Phase transitions in materials. - Cambridge: Cambridge university press, 2014. - xxiv, 563 p.: ill. - Bibliogr.: p.545-553. - Ind.: p.554-563. - ISBN 978-1-107-06724-0
Шифр: (И/Ж-F96) 02
 

Место хранения: 02 | Отделение ГПНТБ СО РАН | Новосибирск

Оглавление / Contents
 
Preface ...................................................... xiii
Acknowledgments .............................................. xvii
Notation ...................................................... xix

Part I  Basic thermodynamics and kinetics of phase 
transformations ................................................. 1

1  Introduction ................................................. 3
   1.1  What is a phase transition? ............................. 3
   1.2  Atoms and materials ..................................... 4
   1.3  Pure elements ........................................... 6
   1.4  Alloys: unmixing and ordering ........................... 9
   1.5  Transitions and transformations ........................ 11
   1.6  Brief review of thermodynamics and kinetics ............ 14
   Problems .................................................... 18
2  Essentials of T-c phase diagrams ............................ 20
   2.1  Overview of the approach ............................... 20
   2.2  Intuition and expectations about alloy thermodynamics .. 22
   2.3  Free energy curves, solute conservation, and the 
        lever rule ............................................. 26
   2.4  Common tangent construction ............................ 28
   2.5  Continuous solid solubility phase diagram .............. 30
   2.6  Solid solutions ........................................ 31
   2.7  Unmixing phase diagrams ................................ 37
   2.8  Eutectic and peritectic phase diagrams ................. 39
   2.9  Ternary phase diagrams ................................. 42
   2.10 Long-range order in the point approximation ............ 44
   2.11 Alloy phase diagrams ................................... 48
   Problems .................................................... 49
3  Diffusion ................................................... 52
   3.1  The diffusion equation ................................. 52
   3.2  Gaussian and error function solutions to the 
        ID diffusion equation .................................. 56
   3.3  Fourier series solutions to the diffusion equation ..... 61
   3.4  Bessel functions and other special function solutions 
        to the diffusion equation .............................. 66
   3.5  Kinetic master equation and equilibrium ................ 69
   3.6  Linear kinetic response ................................ 71
   Problems .................................................... 72
4  Nucleation .................................................. 74
   4.1  Terminology and issues ................................. 75
   4.2  Critical nucleus ....................................... 76
   4.3  Heterogeneous nucleation ............................... 79
   4.4  Free energy curves and elastic energy .................. 81
   4.5  The nucleation rate .................................... 85
   4.6  Time-dependent nucleation .............................. 92
   Problems .................................................... 94
5  Effects of diffusion and nucleation on phase 
   transformations ............................................. 96
   5.1  Nonequilibrium processing of materials ................. 96
   5.2  Alloy solidification with solute partitioning .......... 99
   5.3  Alloy solidification: suppressed diffusion in the 
        solid phase ........................................... 100
   5.4  Alloy solidification: suppressed diffusion in the 
        solid and liquid ...................................... 105
   5.5  Practical issues for alloy solidification and 
        evaporation ........................................... 106
   5.6  Heat flow and kinetics ................................ 109
   5.7  Nucleation kinetics ................................... 111
   5.8  Glass formation ....................................... 112
   5.9  Solid-state amorphization and suppressed diffusion 
        in a solid phase ...................................... 114
   5.10 Reactions at surfaces ................................. 115
   5.11 The glass transition .................................. 120
   Problems ................................................... 121
   
Part II The atomic origins of thermodynamics and kinetics ..... 125
   
6  Energy ..................................................... 127
   6.1  Molecular orbital theory of diatomic molecules ........ 127
   6.2  Electronic energy bands in solids ..................... 134
   6.3  Elastic constants and the interatomic potential ....... 145
   6.4  Linear elasticity ..................................... 149
   6.5  Misfitting particle ................................... 153
   6.6  Surface energy ........................................ 158
   Problems ................................................... 161
7  Entropy .................................................... 163
   7.1  Static and dynamic sources of entropy ................. 163
   7.2  Short-range order and the pair approximation .......... 165
   7.3  Local atomic structures described by clusters ......... 168
   7.4  Thermodynamics with cluster approximations ............ 170
   7.5  Concept of vibrational entropy ........................ 172
   7.6  Phonon statistics ..................................... 175
   7.7  Lattice dynamics and vibrational entropy .............. 176
   7.8  Bond proportion model ................................. 179
   7.9  Bond-stiffness-versus-bond-length model ............... 187
   Problems ................................................... 190
8  Pressure ................................................... 194
   8.1  Materials under pressure at low temperatures .......... 194
   8.2  Thermal pressure, a step beyond the harmonic model .... 199
   8.3  Free energies and phase boundaries under pressure ..... 200
   8.4  Chemical bonding and antibonding under pressure ....... 202
   8.5  Two-level system under pressure ....................... 205
   8.6  Activation volume ..................................... 208
   Problems ................................................... 209
9  Atom movements with the vacancy mechanism .................. 211
   9.1  Random walk and correlations .......................... 211
   9.2  Phenomena in alloy diffusion .......................... 220
   9.3  Diffusion in a potential gradient ..................... 227
   9.4  Nonthermodynamic equilibrium in driven systems ........ 232

   9.5  Vineyard's theory of diffusion ........................ 235
   Problems ................................................... 240
   
Part III Types of phase transformations ....................... 245
10 Melting .................................................... 247
   10.1 Free energy and latent heat ........................... 247
   10.2 Chemical trends of melting ............................ 248
   10.3 Free energy of a solid ................................ 250
   10.4 Entropy of a liquid ................................... 257
   10.5 Thermodynamic condition for Tm ........................ 259
   10.6 Glass transition ...................................... 261
   10.7 Two dimensions ........................................ 264
   Problems ................................................... 266
11 Transformations involving precipitates and interfaces ...... 268
   11.1 Guinier-Preston zones ................................. 268
   11.2 Surface structure and thermodynamics .................. 270
   11.3 Surface structure and kinetics ........................ 276
   11.4 Chemical energy of a precipitate interface ............ 278
   11.5 Elastic energy and shape of growing precipitates ...... 280
   11.6 Precipitation at grain boundaries and defects ......... 282
   11.7 The eutectoid reaction and ferrous metallurgy ......... 285
   11.8 The Kolmogorov-Johnson-Mehl-Avrami growth equation .... 291
   11.9 Coarsening ............................................ 293
   Problems ................................................... 296
12 Spinodal decomposition ..................................... 298
   12.1 Concentration fluctuations and the free energy of 
        solution .............................................. 298
   12.2 Adding a square gradient term to the free energy 
        F(c) .................................................. 300
   12.3 Constrained minimization of the free energy ........... 304
   12.4 The diffusion equation ................................ 309
   12.5 Effects of elastic energy ............................. 311
   Problems ................................................... 313
13 Phase field theory ......................................... 315
   13.1 Spatial distribution of phases and interfaces ......... 315
   13.2 Solidification ........................................ 318
   13.3 Ginzburg-Landau equation and order parameter .......... 319
   13.4 Interfaces between domains ............................ 322
   Problems ................................................... 330
14 Method of concentration waves and chemical ordering ........ 332
   14.1 Structure in real space and reciprocal space .......... 332
   14.2 Symmetry and the star ................................. 338
   14.3 The free energy in &-space with concentration waves ... 341
   14.4 Symmetry invariance of free energy and Landau-
        Lifshitz rule for second-order phase transitions ...... 344
   14.5 Thermodynamics of ordering in the mean field 
        approximation with long-range interactions ............ 349
   Problems ................................................... 353
15 Diffusionless transformations .............................. 355
   15.1 Dislocations and mechanisms ........................... 356
   15.2 Twinning .............................................. 360
   15.3 Martensite ............................................ 362
   15.4 The crystallographic theory of martensite ............. 368
   15.5 Landau theory of displacive phase transitions ......... 370
   15.6 First-order Landau theory ............................. 374
   15.7 Crystal instabilities and phonons ..................... 377
   Problems ................................................... 381
16 Thermodynamics of nanomaterials ............................ 383
   16.1 Grain boundary structure .............................. 384
   16.2 Grain boundary energy ................................. 386
   16.3 Gibbs-Thomson effect .................................. 387
   16.4 Energies of free electrons confined to 
        nanostructures ........................................ 390
   16.5 Configurational entropy of nanomaterials .............. 392
   16.6 Vibrational entropy ................................... 394
   16.7 Gas adsorption ........................................ 397
   16.8 Characteristics of magnetic nanoparticles ............. 399
   16.9 Elastic energy of anisotropic microstructures ......... 401
   Problems ................................................... 402
17 Magnetic and electronic phase transitions .................. 404
   17.1 Overview of magnetic and electronic phase 
        transitions ........................................... 405
   17.2 Exchange interactions ................................. 410
   17.3 Correlated electrons .................................. 414
   17.4 Thermodynamics of ferromagnetism ...................... 417
   17.5 Spin waves ............................................ 420
   17.6 Thermodynamics of antiferromagnetism .................. 423
   17.7 Ferroelectric transition .............................. 426
   17.8 Domains ............................................... 428
   Problems ................................................... 430
18 Phase transitions in quantum materials ..................... 432
   18.1 Bose-Einstein condensation ............................ 432
   18.2 Superfluidity ......................................... 435
   18.3 Condensate wavefunction ............................... 437
   18.4 Superconductivity ..................................... 440

   18.5 Quantum critical behavior ............................. 448
   Problems ................................................... 452
   
Part IV Advanced topics ....................................... 453
   
19 Low-temperature analysis of phase boundaries ............... 455
   19.1 Ground-state analysis for T = 0 ....................... 456
   19.2 Richards, Allen, Cahn ground-state maps ............... 457
   19.3 Low but finite temperatures ........................... 458
   19.4 Analysis of equiatomic bcc alloys ..................... 463
   19.5 High-temperature expansion of the partition function .. 465
   Problems ................................................... 466
20 Cooperative behavior near a critical temperature ........... 468
   20.1 Critical exponents .................................... 468
   20.2 Critical slowing down ................................. 469
   20.3 The Rushbrooke inequality ............................. 471
   20.4 Scaling theory ........................................ 472
   20.5 Scaling and decimation ................................ 474
   20.6 Partition function for one-dimensional chain .......... 475
   20.7 Partition function for two-dimensional lattice ........ 479
   Problems ................................................... 482
21 Elastic energy of solid precipitates ....................... 483
   21.1 Transformation strains and elastic energy ............. 483
   21.2 Real space approach ................................... 485
   21.3 k-space approach ...................................... 488
   Problems ................................................... 491
22 Statistical kinetics of ordering transformations ........... 492
   22.1 Ordering transformations with vacancies ............... 493
   22.2 B2 ordering with vacancies in the point 
        approximation ......................................... 495
   22.3 Vacancy ordering ...................................... 499
   22.4 Kinetic paths ......................................... 500
   Problems ................................................... 506
23 Diffusion, dissipation, and inelastic scattering ........... 508
   23.1 Atomic processes and diffusion ........................ 508
   23.2 Dissipation and fluctuations .......................... 512
   23.3 Inelastic scattering .................................. 515
   23.4 Phonons and quantum mechanics ......................... 518
   Problems ................................................... 521
24 Vibrational thermodynamics of materials at high
   temperatures ............................................... 522
   24.1 Lattice dynamics ...................................... 522
   24.2 Harmonic thermodynamics ............................... 527
   24.3 Quasiharmonic thermodynamics .......................... 528
   24.4 Thermal effects beyond quasiharmonic theory ........... 531
   24.5 Anharmonicity and phonon-phonon interactions .......... 532
   24.6 Electron-phonon interactions and temperature .......... 536
   Problems ................................................... 538
   Further reading ............................................ 540
   References ................................................. 545

Index ......................................................... 554

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