Preface to second edition page 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 CV 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
T or P 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 = c + 1 280
13.3 Graphical evaluation of reaction coefficients 283
13.4 Reaction coefficients in gradual transformations
for p = c 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 = c 295
13.9 Effect of two compositional degeneracies for p = c . 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 fluidfluid interfaces 346
16.4 Size stability for spherical inclusions 350
16.5 Nucleation 351
16.6 Phase equilibrium at crystalfluid 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
18.8 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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