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 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 18.8 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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