Thermodynamics in materials science

Chapter 1. INTRODUCTION 1.1. The Power and Breadth of Thermodynamics 1.2 The Generic Question Addressed by Thermodynamics 1.3. Thermodynamics is Limited to Systems in Equilibrium 1.4. The Thermodynamic Basis for Equilibrium Maps 1.4.1. The Principles 1.4.2. The Strategies 1.4.3. Data Bases 1.4.4. Maps of Equilibrium States 1.5. Three Levels of the Thermodynamic Apparatus Chapter 2. THE STRUCTURE OF THERMODYNAMICS 2.1. A Classification of Thermodynamic Systems. 2.2. Classification of Thermodynamic Variables 2.2.1. State Functions 2.2.2. Process Variables 2.2.3. Extensive and Intensive Properties 2.3. Classification of Relationships 2.4. Criterion for Equilibrium 2.5 Summary of Chapter 2. Chapter 3. THE LAWS OF THERMODYNAMICS 3.1. The First Law of Thermodynamics 3.2. The Second Law of Thermodynamics 3.3. Intuitive Meaning of Entropy Production 3.4. Relation Between Entropy Transfer and Heat 3.5. Combined Statement of the First and Second Laws 3.6. The Third Law of Thermodynamics 3.7. Summary of Chapter 3. Chapter 4. THERMODYNAMIC VARIABLES AND RELATIONS 4.1. Classification of Thermodynamic Relationships 4.1.1. The Laws of Thermodynamics 4.1.2. Definitions in Thermodynamics 4.1.3. Coefficient Relations. 4.1.4. Maxwell Relations 4.2. General Strategy for Deriving Thermodynamic Relations 4.2.1. Entropy and Volume Relations to T and P 4.2.2. Energy Functions Expressed in Terms of T and P 4.2.3. The General Procedure 4.2.4. Application to an Ideal Gas 4.2.5. Applications to Solids and Liquids 4.3. Summary of Chapter 4 Chapter 5. EQUILIBRIUM IN THERMODYNAMIC SYSTEMS 5.1. Intuitive Notions of Equilibrium 5.2. Thermodynamic Formulation of a General Criterion for Equilibrium 5.3. Mathematical Formulation of the General Conditions for Equilibrium 5.4. Application of the General Strategy for Finding Thermodynamic Equilibrium: The Unary Two Phase System. 5.5. Alternate Formulations of the Criterion for Equilibrium 5.6. Summary of Chapter 5. Chapter 6. STATISTICAL THERMODYNAMICS 6.1. Microstates, Macrostates and Entropy 6.2. Conditions for Equilibrium in Statistical Thermodynamics 6.2.1. Evaluation of Entropy. 6.2.2. Evaluation of the Isolation Constraints. 6.2.3. The Constrained Maximum in the Entropy Function. 6.2.4. Calculation of the Macroscopic Properties from the Partition Function 6.3. Applications of the Algorithm. 6.3.1. A Model with Two Energy Levels. 6.3.2. Einstein's Model of a Crystal. 6.3.3. Monatomic Gas Model. 6.4. Alternate Statistical Formulations. 6.5. Summary of Chapter 6. Chapter 7. UNARY HETEROGENEOUS SYSTEMS 7.1. Structure of Unary Phase Diagrams in (P, T) Space 7.1.1. Chemical Potential and the Gibbs Free Energy 7.1.2. Chemical Potential Surfaces and the Structure of Unary Phase Diagrams 7.1.3. Calculation of Chemical Potential Surfaces 7.1.4. Competing Equilibria: Metastability 7.2. The Clausius-Clapeyron Equation 7.3. Integration of the Clausius-Clapeyron Equation 7.3.1. Vaporization and Sublimation Curves 7.3.2. Phase Boundaries Between Condensed Phases 7.4. Triple Points 7.5. Computer Calculations of (P, T) Unary Phase Diagrams 7.6. Alternate Representations of Unary Phase Diagrams 7.7. Summary of Chapter 7 Chapter 8. MULTICOMPONENT, HOMOGENEOUS NON-REACTING SYSTEMS: SOLUTIONS 8.1. Partial Molal Properties 8.1.1. Definition of Partial Molal Properties 8.1.2. Consequences of the Definition of Partial Molal Properties. 8.1.3. The Mixing Process 8.1.4. Molar Values of the Properties of Mixtures 8.2. Evaluation of Partial Molal Properties 8.2.1. Partial Molal Properties from Total Properties 8.2.2. Graphical Representation of Partial Molal Properties 8.2.3. Evaluation of the PMP's of One Component from Measured Values of PMP's of the Other 8.3. Relationships Among Partial Molal Properties 8.4. Chemical Potential in Multicomponent Systems 8.5. Fugacities, Activities and Activity Coefficients 8.5.1. Properties of Ideal Gas Mixtures 8.5.2. Mixtures of Real Gases: Fugacity 8.5.3. Activity and the Behavior of Real Solutions 8.5.4. Use of the Activity Coefficient to Describe the Behavior of Real Solutions 8.6. The Behavior of Dilute Solutions 8.7. Solution Models 8.7.1. The Regular Solution Model 8.7.2. Modeling Real Solutions 8.7.3. Atomistic Models for Solution Behavior 8.8. Summary of Chapter 8 Chapter 9. MULTICOMPONENT HETEROGENEOUS SYSTEMS 9.1. The Description of Multiphase, Multicomponent, Nonreacting Systems 9.2. Conditions for Equilibrium 9.3. The Gibbs Phase Rule 9.4. The Structure of Phase Diagrams 9.4.1. Phase Diagrams Plotted in Thermodynamic Potential Space 9.4.2. Unary Systems 9.4.3. Binary Phase Diagrams 9.4.4. Ternary Phase Diagrams 9.5. The Interpretation of Phase Diagrams 9.5.1. The Lever Rule for Tie Lines 9.5.2. The Lever Rule for Tie Triangles 9.6. Applications of Phase Diagrams in Materials Science 9.7. Summary of Chapter 9 Chapter 10. THERMODYNAMICS OF PHASE DIAGRAMS 10.1. Free Energy - Composition (G-X) Diagrams. 10.1.1. Reference States for G-X Curves 10.1.2. The Common Tangent Construction and Two Phase Equilibrium 10.1.3. Two Phase Fields on Binary Phase Diagrams 10.1.4. Three Phase Equilibria 10.1.5. Intermediate Phases 10.1.6. Metastable Phase Diagrams 10.2. Thermodynamic Models for Binary Phase Diagrams 10.2.1. Ideal Solution Models for Phase Diagrams 10.2.2. Regular Solution Model for Phase Diagrams 10.2.3 The Midrib Curve 10.2.4. Pattern of Regular Solution Phase Diagrams 10.2.5. Diagrams with Three or More Phases 10.2.6. Modeling Phase Diagrams with Line Compounds 10.3. Thermodynamic Models for Three Component Systems 10.4. Calculation of Phase Diagrams in Potential Space. 10.5. Computer Calculations of Phase Diagrams 10.6. Summary of Chapter 10 Chapter 11. MULTICOMPONENT, MULTIPHASE REACTING SYSTEMS 11.1. Reactions in the Gas Phase 11.1.1. Univariant Reactions in the Gas Phase 11.1.2. Multivariant Reactions in the Gas Phase 11.2. Reactions in Multiphase Systems 11.3. Patterns of Behavior in Common Reacting Systems 11.3.1. Richardson-Ellingham Charts for Oxidation 11.3.2. Oxidation in CO/CO2 and H2/H2O Mixtures 11.4. Predominance Diagrams and Multivariant Equilibria 11.4.1. Pourbaix High Temperature Oxidation Diagrams 11.4.2. Predominance Diagrams with Two Compositional Axes 11.4.3. Interpretation of Predominance Diagrams 11.5. Compounds as Components in Phase Diagrams 11.6. Summary of Chapter 11. Chapter 12. CAPILLARITY EFFECTS IN THERMODYNAMICS 12.1. The Geometry of Surfaces 12.2. Surface Excess Properties 12.3. Conditions for Equilibrium in Systems with Curved Interfaces 12.4. Surface Tension: the Mechanical Analogue of Surface Free Energy 12.5. Capillarity Effects on Phase Diagrams 12.5.1. Phase Boundary Shifts in Unary Systems 12.5.2. Vapor Pressure in Equilibrium with Curved Surfaces 12.5.3. Effect of Curvature upon the Melting Temperature 12.5.4. Effect of Curvature on Chemical Potential in Unary Systems 12.5.5. Phase Boundary Shifts in Binary Systems 12.5.6. Local Equilibrium and the Application of Capillarity Shifts 12.6. The Equilibrium Shape of Crystals: the Gibbs-Wulff Construction 12.7. Equilibrium at Triple Lines. 12.8. Adsorption at Surfaces 12.8.1. Measures of Adsorption 12.8.2. The Gibbs Adsorption Equation 12.9. Summary of Chapter 12 Chapter 13. DEFECTS IN CRYSTALS 13.1. Point Defects in Elemental Crystals 13.1.1. Conditions for Equilibrium in a Crystal with Vacant Lattice Sites 13.1.2.

The Concentration of Vacancies in a Crystal at Equilibrium 13.1.3. Interstitial Defects and Divacancies 13.2. Point Defects in Stoichiometric Compound Crystals 13.2.1. Frenkel Defects 13.2.2. Schottky Defects 13.2.3. Combined Defects in Binary Compounds 13.2.4. Multivariate Equilibrium Among Defects in a 13.3. Nonstoichiometric Compound Crystals 13.3.1. Equilibrium in Compound Crystals with a Variety of Defects 13.3.2. Illustration of the Conditions for Equilibrium for Alumina. 13.4. Impurities in Nonstoichiometric Compounds 13.5. Summary of Chapter 13. Chapter 14. EQUILIBRIUM IN CONTINUOUS SYSTEMS: THERMODYNAMIC EFFECTS OF EXTERNAL FIELDS 14.1. Thermodynamic Densities and the Description of Nonuniform Systems 14.2. Conditions for Equilibrium in the Absence of External Fields 14.3. Conditions for Equilibrium in the Presence of External Fields 14.3.1. Potential Energy of a Continuous System 14.3.2. Conditions for Equilibrium 14.3.3. Equilibrium in a Gravitational Field 14.3.4. Equilibrium in a Centrifugal Field 14.3.5. Equilibrium in an Electrostatic Field 14.4. The Gradient Energy in Nonuniform Systems. 14.5. Summary of Chapter 14. Chapter 15. ELECTROCHEMISTRY 15.1. Equilibrium Within an Electrolyte Solution 15.1.1. Equilibrium in Weak Electrolytes 15.1.2. Equilibrium in a Strong Electrolyte. 15.2. Equilibrium In Two Phase Systems Involving an Electrolyte 15.3. Equilibrium in an Electrochemical Cell 15.3.1. Condition for Equilibrium in a General Galvanic 15.3.2. Temperature Dependence of the Electromotive Force a Cell 15.3.3. The Standard Hydrogen Electrode 15.4. Pourbaix Diagrams 15.4.1. The Stability of Water 15.4.2. Pourbaix Diagram for Copper 15.5. Summary of Chapter 15. APPENDICES Appendix A. Fundamental Physical Constants and Conversion Factors Appendix B. Properties of Selected Elements Appendix C. Phase Transformations for the Elements Appendix D. Properties of Some Random Solutions Appendix E. Properties of Selected Compounds Appendix F. Interfacial Energies of Selected Elements Appendix G. Electrochemical Series Appendix H. The Carnot Cycle Appendix I. Answers to Homework Problems.