Preface to second edition .................................. xii
Preface to first edition .................................. xiii
1 Basic concepts of thermodynamics ............................. 1
1.1 External state variables ................................ 1
1.2 Internal state variables ................................ 3
1.3 The first law of thermodynamics ......................... 5
1.4 Freezing-in conditions .................................. 9
1.5 Reversible and irreversible processes .................. 10
1.6 Second law of thermodynamics ........................... 13
1.7 Condition of internal equilibrium ...................... 17
1.8 Driving force .......................................... 19
1.9 Combined first and second law .......................... 21
1.10 General conditions of equilibrium ...................... 23
1.11 Characteristic state functions ......................... 24
1.12 Entropy ................................................ 26
2 Manipulation of thermodynamic quantities .................... 30
2.1 Evaluation of one characteristic state function from
another ................................................ 30
2.2 Internal variables at equilibrium ...................... 31
2.3 Equations of state ..................................... 33
2.4 Experimental conditions ................................ 34
2.5 Notation for partial derivatives ....................... 37
2.6 Use of various derivatives ............................. 38
2.7 Comparison between Сv and Cp ........................... 40
2.8 Change of independent variables ........................ 41
2.9 Maxwell relations ...................................... 43
3 Systems with variable composition ........................... 45
3.1 Chemical potential ..................................... 45
3.2 Molar and integral quantities .......................... 46
3.3 More about characteristic state functions .............. 48
3.4 Additivity of extensive quantities. Free energy and
exergy ................................................. 51
3.5 Various forms of the combined law ...................... 52
3.6 Calculation of equilibrium ............................. 54
3.7 Evaluation of the driving force ........................ 56
3.8 Driving force for molecular reactions .................. 58
3.9 Evaluation of integrated driving force as function of
TorP ................................................... 59
3.10 Effective driving force ................................ 60
4 Practical handling of multicomponent systems ................ 63
4.1 Partial quantities ..................................... 63
4.2 Relations for partial quantities ....................... 65
4.3 Alternative variables for composition .................. 67
4.4 The lever rule ......................................... 70
4.5 The tie-line rule ...................................... 71
4.6 Different sets of components ........................... 74
4.7 Constitution and constituents .......................... 75
4.8 Chemical potentials in a phase with sublattices ........ 77
5 Thermodynamics of processes ................................. 80
5.1 Thermodynamic treatment of kinetics of internal
processes .............................................. 80
5.2 Transformation of the set of processes ................. 83
5.3 Alternative methods of transformation .................. 85
5.4 Basic thermodynamic considerations for processes ....... 89
5.5 Homogeneous chemical reactions ......................... 92
5.6 Transport processes in discontinuous systems ........... 95
5.7 Transport processes in continuous systems .............. 98
5.8 Substitutional diffusion .............................. 101
5.9 Onsager's extremum principle .......................... 104
6 Stability .................................................. 108
6.1 Introduction .......................................... 108
6.2 Some necessary conditions of stability ................ 110
6.3 Sufficient conditions of stability .................... 113
6.4 Summary of stability conditions ....................... 115
6.5 Limit of stability .................................... 116
6.6 Limit of stability against fluctuations in
composition ........................................... 117
6.7 Chemical capacitance .................................. 120
6.8 Limit of stability against fluctuations of internal
variables ............................................. 121
6.9 Le Chatelier's principle .............................. 123
7 Applications of molar Gibbs energy diagrams ................ 126
7.1 Molar Gibbs energy diagrams for binary systems ........ 126
7.2 Instability of binary solutions ....................... 131
7.3 Illustration of the Gibbs-Duhem relation .............. 132
7.4 Two-phase equilibria in binary systems ................ 135
7.5 Allotropic phase boundaries ........................... 137
7.6 Effect of a pressure difference on a two-phase
equilibrium ........................................... 138
7.7 Driving force for the formation of a new phase ........ 142
7.8 Partitionless transformation under local equilibrium .. 144
7.9 Activation energy for a fluctuation ................... 147
7.10 Ternary systems ....................................... 149
7.11 Solubility product .................................... 151
8 Phase equilibria and potential phase diagrams .............. 155
8.1 Gibbs'phase rule ...................................... 155
8.2 Fundamental property diagram .......................... 157
8.3 Topology of potential phase diagrams .................. 162
8.4 Potential phase diagrams in binary and multinary
systems ............................................... 166
8.5 Sections of potential phase diagrams .................. 168
8.6 Binary systems ........................................ 170
8.7 Ternary systems ....................................... 173
8.8 Direction of phase fields in potential phase
diagrams .............................................. 177
8.9 Extremum in temperature and pressure .................. 181
9 Molar phase diagrams ....................................... 185
9.1 Molar axes ............................................ 185
9.2 Sets of conjugate pairs containing molar variables .... 189
9.3 Phase boundaries ...................................... 193
9.4 Sections of molar phase diagrams ...................... 195
9.5 Schreinemakers' rule .................................. 197
9.6 Topology of sectioned molar diagrams .................. 201
10 Projected and mixed phase diagrams ......................... 205
10.1 Schreinemakers' projection of potential phase
diagrams .............................................. 205
10.2 The phase field rule and projected diagrams ........... 208
10.3 Relation between molar diagrams and Schreinemakers'
projected diagrams .................................... 212
10.4 Coincidence of projected surfaces ..................... 215
10.5 Projection of higher-order invariant equilibria ....... 217
10.6 The phase field rule and mixed diagrams ............... 220
10.7 Selection of axes in mixed diagrams ................... 223
10.8 Konovalov's rule ...................................... 226
10.9 General rule for singular equilibria .................. 229
11 Direction of phase boundaries .............................. 233
11.1 Use of distribution coefficient ....................... 233
11.2 Calculation of allotropic phase boundaries ............ 235
11.3 Variation of a chemical potential in a two-phase
field ................................................. 238
11.4 Direction of phase boundaries ......................... 240
11.5 Congruent melting points .............................. 244
11.6 Vertical phase boundaries ............................. 248
11.7 Slope of phase boundaries in isothermal sections ...... 249
11.8 The effect of a pressure difference between two
phases ................................................ 251
12 Sharp and gradual phase transformations .................... 253
12.1 Experimental conditions ............................... 253
12.2 Characterization of phase transformations ............. 255
12.3 Microstructural character ............................. 259
12.4 Phase transformations in alloys ....................... 261
12.5 Classification of sharp phase transformations ......... 262
12.6 Applications of Schreinemakers'projection ............. 266
12.7 Scheil's reaction diagram ............................. 270
12.8 Gradual phase transformations at fixed composition .... 272
12.9 Phase transformations controlled by a chemical
potential ............................................. 275
13 Transformations in closed systems .......................... 279
13.1 The phase field rule at constant composition .......... 279
13.2 Reaction coefficients in sharp transformations
for p = с + 1 ......................................... 280
13.3 Graphical evaluation of reaction coefficients ......... 283
13.4 Reaction coefficients in gradual transformations
for p = с ............................................. 285
13.5 Driving force for sharp phase transformations ......... 287
13.6 Driving force under constant chemical potential ....... 291
13.7 Reaction coefficients at constant chemical potential .. 294
13.8 Compositional degeneracies for p = с .................. 295
13.9 Effect of two compositional degeneracies for p =
с — 1 ................................................. 299
14 Partitionless transformations .............................. 302
14.1 Deviation from local equilibrium ...................... 302
14.2 Adiabatic phase transformation ........................ 303
14.3 Quasi-adiabatic phase transformation .................. 305
14.4 Partitionless transformations in binary system ........ 308
14.5 Partial chemical equilibrium .......................... 311
14.6 Transformations in steel under quasi-paraequilibrium .. 315
14.7 Transformations in steel under partitioning of
alloying elements ..................................... 319
15 Limit of stability and critical phenomena .................. 322
15.1 Transformations and transitions ....................... 322
15.2 Order-disorder transitions ............................ 325
15.3 Miscibility gaps ...................................... 330
15.4 Spinodal decomposition ................................ 334
15.5 Tri-critical points ................................... 338
16 Interfaces ................................................. 344
16.1 Surface energy and surface stress ..................... 344
16.2 Phase equilibrium at curved interfaces ................ 345
16.3 Phase equilibrium at fluid/fluid interfaces ........... 346
16.4 Size stability for spherical inclusions ............... 350
16.5 Nucleation ............................................ 351
16.6 Phase equilibrium at crystal/fluid interface .......... 353
16.7 Equilibrium at curved interfaces with regard to
composition ........................................... 356
16.8 Equilibrium for crystalline inclusions with regard
to composition ........................................ 359
16.9 Surface segregation ................................... 361
16.10 Coherency within a phase ............................. 363
16.11 Coherency between two phases ......................... 366
16.12 Solute drag .......................................... 371
17 Kinetics of transport processes ............................ 377
17.1 Thermal activation .................................... 377
17.2 Diffusion coefficients ................................ 381
17.3 Stationary states for transport processes ............. 384
17.4 Local volume change ................................... 388
17.5 Composition of material crossing an interface ......... 390
17.6 Mechanisms of interface migration ..................... 391
17.7 Balance of forces and dissipation ..................... 396
18 Methods of modelling ....................................... 400
18.1 General principles .................................... 400
18.2 Choice of characteristic state function ............... 401
18.3 Reference states ...................................... 402
18.4 Representation of Gibbs energy of formation ........... 405
18.5 Use of power series in T .............................. 407
18.6 Representation of pressure dependence ................. 408
18.7 Application of physical models ........................ 410
18.1 Ideal gas ............................................. 411
18.9 Real gases ............................................ 412
18.10 Mixtures of gas species .............................. 415
18.11 Black-body radiation ................................. 417
18.12 Electron gas ......................................... 418
19 Modelling of disorder ...................................... 420
19.1 Introduction .......................................... 420
19.2 Thermal vacancies in a crystal ........................ 420
19.3 Topological disorder .................................. 423
19.4 Heat capacity due to thermal vibrations ............... 425
19.5 Magnetic contribution to thermodynamic properties ..... 429
19.6 A simple physical model for the magnetic
contribution .......................................... 431
19.7 Random mixture of atoms ............................... 434
19.8 Restricted random mixture ............................. 436
19.9 Crystals with stoichiometric vacancies ................ 437
19.10 Interstitial solutions ............................... 439
20 Mathematical modelling of solution phases .................. 441
20.1 Ideal solution ........................................ 441
20.2 Mixing quantities ..................................... 443
20.3 Excess quantities ..................................... 444
20.4 Empirical approach to substitutional solutions ........ 445
20.5 Real solutions ........................................ 448
20.6 Applications of the Gibbs-Duhem relation .............. 452
20.7 Dilute solution approximations ........................ 454
20.8 Predictions for solutions in higher-order systems ..... 456
20.9 Numerical methods of predictions for higher-order
systems ............................................... 458
21 Solution phases with sublattices ........................... 460
21.1 Sublattice solution phases ............................ 460
21.-2 Interstitial solutions ............................... 462
21.3 Reciprocal solution phases ............................ 464
21.4 Combination of interstitial and substitutional
solution .............................................. 468
21.5 Phases with variable order ............................ 469
21.6 Ionic solid solutions ................................. 472
22 Physical solution models ................................... 476
22.1 Concept of nearest-neighbour bond energies ............ 476
22.2 Random mixing model for a substitutional solution ..... 478
22.3 Deviation from random distribution .................... 479
22.4 Short-range order ..................................... 482
22.5 Long-range order ...................................... 484
22.6 Long- and short-range order ........................... 486
22.7 The compound energy formalism with short-range order .. 488
22.8 Interstitial ordering ................................. 490
22.9 Composition dependence of physical effects ............ 493
References ................................................. 496
Index ...................................................... 499
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