Materials Thermodynamics

Y. Austin Chang is Wisconsin Distinguished Professor Emeritus in the Department of Materials Science and Engineering at the University of Wisconsin–Madison. He is a member of the National Academy of Engineering, Foreign Member of the Chinese Academy of Sciences, and the recipient of many honors and awards, including the J. Willard Gibbs Award, the Gold Medal, and A. E. White Distinguished Teacher Award of ASM International, and the W. Hume-Rothery Award, John Bardeen Award, and the Educator Award, all awarded by The Minerals, Metals and Materials Society (TMS). W. Alan Oates is a recipient of several awards, including the W. Hume-Rothery Award of TMS.¿Since 1992, Oates has held the position of Honorary Professor at the Science Research Institute, University of Salford, England.

• Preface xiiiQuantities, Units, and Nomenclature xix1 Review of Fundamentals 11.1 Systems, Surroundings, and Work 21.2 Thermodynamic Properties 41.3 The Laws of Thermodynamics 51.4 The Fundamental Equation 81.5 Other Thermodynamic Functions 91.5.1 Maxwell’s Equations 111.5.2 Defining Other Forms of Work 111.6 Equilibrium State 14Exercises 152 Thermodynamics of Unary Systems 192.1 Standard State Properties 192.2 The Effect of Pressure 272.2.1 Gases 282.2.2 Condensed Phases 292.3 The Gibbs–Duhem Equation 302.4 Experimental Methods 31Exercises 323 Calculation of Thermodynamic Properties of Unary Systems 353.1 Constant-Pressure/Constant-Volume Conversions 363.2 Excitations in Gases 373.2.1 Perfect Monatomic Gas 373.2.2 Molecular Gases 393.3 Excitations in Pure Solids 393.4 The Thermodynamic Properties of a Pure Solid 433.4.1 Inadequacies of the Model 46Exercises 464 Phase Equilibria in Unary Systems 494.1 The Thermodynamic Condition for Phase Equilibrium 524.2 Phase Changes 544.2.1 The Slopes of Boundaries in Phase Diagrams 544.2.2 Gibbs Energy Changes for Phase Transformations 574.3 Stability and Critical Phenomena 594.4 Gibbs’s Phase Rule 61Exercises 635 Thermodynamics of Binary Solutions I: Basic Theory and Application to Gas Mixtures 675.1 Expressing Composition 675.2 Total (Integral) and Partial Molar Quantities 685.2.1 Relations between Partial and Integral Quantities 705.2.2 Relation between Partial Quantities: the Gibbs–Duhem Equation 725.3 Application to Gas Mixtures 735.3.1 Partial Pressures 735.3.2 Chemical Potentials in Perfect Gas Mixtures 745.3.3 Real Gas Mixtures: Component Fugacities and Activities 75Exercises 756 Thermodynamics of Binary Solutions II: Theory and Experimental Methods 796.1 Ideal Solutions 796.1.1 Real Solutions 826.1.2 Dilute Solution Reference States 836.2 Experimental Methods 856.2.1 Chemical Potential Measurements 86Exercises 897 Thermodynamics of Binary Solutions III: Experimental Results and Their Analytical Representation 937.1 Some Experimental Results 937.1.1 Liquid Alloys 937.1.2 Solid Alloys 957.2 Analytical Representation of Results for Liquid or Solid Solutions 97Exercises 1028 Two-Phase Equilibrium I: Theory 1038.1 Introduction 1038.2 Criterion for Phase Equilibrium Between Two Specified Phases 1048.2.1 Equilibrium between Two Solution Phases 1048.2.2 Equilibrium between a Solution Phase and a Stoichiometric Compound Phase 1078.3 Gibbs’s Phase Rule 108Exercises 1109 Two-Phase Equilibrium II: Example Calculations 113Exercises 12110 Binary Phase Diagrams: Temperature–Composition Diagrams 12510.1 True Phase Diagrams 12610.2 T –xi Phase Diagrams for Strictly Regular Solutions 12810.2.1 Some General Observations 13110.2.2 More on Miscibility Gaps 13310.2.3 The Chemical Spinodal 13410.3 Polymorphism 135Exercises 13611 Binary Phase Diagrams: Temperature–Chemical Potential Diagrams 13911.1 Some General Points 140Exercises 14612 Phase Diagram Topology 14912.1 Gibbs’s Phase Rule 15112.2 Combinatorial Analysis 15112.3 Schreinemaker’s Rules 15312.4 The Gibbs–Konovalov Equations 15412.4.1 Slopes of T –μi Phase Boundaries 15512.4.2 Slopes of T –xi Phase Boundaries 15712.4.3 Some Applications of Gibbs–Konovalov Equations 159Exercises 16213 Solution Phase Models I: Configurational Entropies 16513.1 Substitutional Solutions 16813.2 Intermediate Phases 16913.3 Interstitial Solutions 172Exercises 17414 Solution Phase Models II: Configurational Energy 17714.1 Pair Interaction Model 17814.1.1 Ground-State Structures 17914.1.2 Nearest Neighbor Model 18014.2 Cluster Model 183Exercises 18815 Solution Models III: The Configurational Free Energy 18915.1 Helmholtz Energy Minimization 19015.2 Critical Temperature for Order/Disorder 193Exercises 19616 Solution Models IV: Total Gibbs Energy 19716.1 Atomic Size Mismatch Contributions 19916.2 Contributions from Thermal Excitations 20216.2.1 Coupling between Configurational and Thermal Excitations 20316.3 The Total Gibbs Energy in Empirical Model Calculations 204Exercises 20517 Chemical Equilibria I: Single Chemical Reaction Equations 20717.1 Introduction 20717.2 The Empirical Equilibrium Constant 20717.3 The Standard Equilibrium Constant 20817.3.1 Relation to Δr G◦ 20817.3.2 Measurement of Δr G◦ 21117.4 Calculating the Equilibrium Position 21317.5 Application of the Phase Rule 217Exercises 21818 Chemical Equilibria II: Complex Gas Equilibria 22118.1 The Importance of System Definition 22118.2 Calculation of Chemical Equilibrium 22418.2.1 Using the Extent of Reaction 22518.2.2 Using Lagrangian Multipliers 22718.3 Evaluation of Elemental Chemical Potentials in Complex Gas Mixtures 22918.4 Application of the Phase Rule 231Exercises 23219 Chemical Equilibria Between Gaseous and Condensed Phases I 23319.1 Graphical Presentation of Standard Thermochemical Data 23319.2 Ellingham Diagrams 23419.2.1 Chemical Potentials 238Exercises 24020 Chemical Equilibria Between Gaseous and Condensed Phases II 24320.1 Subsidiary Scales on Ellingham Diagrams 24420.2 System Definition 247Exercises 25221 Thermodynamics of Ternary Systems 25521.1 Analytical Representation of Thermodynamic Properties 25621.1.1 Substitutional Solution Phases 25621.1.2 Sublattice Phases 25921.2 Phase Equilibria 260Exercises 26422 Generalized Phase Diagrams for Ternary Systems 26722.1 System Definition 276Exercises 278Appendix A Some Linearized Standard Gibbs Energies of Formation 279Appendix B Some Useful Calculus 281Index 289