Contents. Part I Basic Thermodynamics and Kinetics of Phase Transformations 1

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1 Contents Preface List of tables Notation page iii xiii xiv Part I Basic Thermodynamics and Kinetics of Phase Transformations 1 1 Introduction What Is a Phase Transition? Atoms and Materials Pure Elements Alloys Unmixing and Ordering Transitions and Transformations Brief Review of Thermodynamics and Kinetics 15 Problems 19 2 Essentials of T-c Phase Diagrams Overview of the Approach Intuition and Expectations about Alloy Thermodynamics Free Energy Curves, Solute Conservation, and the Lever Rule Common Tangent Construction Continuous Solid Solubility Phase Diagram Solid Solutions Unmixing Phase Diagrams Eutectic and Peritectic Phase Diagrams Ternary Phase Diagrams Long-Range Order in the Point Approximation Alloy Phase Diagrams 51 Problems 53 3 Diffusion The Diffusion Equation Gaussian and Error Function Solutions to the 1D Diffusion Equation Fourier Series Solutions to the Diffusion Equation 66 7

2 8 Contents 3.4 Bessel Functions and other Special Function Solutions to the Diffusion Equation Kinetic Master Equation and Equilibrium Linear Kinetic Response 76 Problems 77 4 Nucleation Terminology and Issues Critical Nucleus Heterogeneous Nucleation Free Energy Curves, Elastic Energy The Nucleation Rate Time-Dependent Nucleation 98 Problems Effects of Diffusion and Nucleation on Phase Transformations Non-Equilibrium Processing of Materials Alloy Solidification with Solute Partitioning Alloy Solidification Suppressed Diffusion in the Solid Phase Alloy Solidification Suppressed Diffusion in the Solid and Liquid Practical Issues for Alloy Solidification and Evaporation Heat Flow and Kinetics Nucleation Kinetics Glass Formation Solid-State Amorphization and Suppressed Diffusion in a Solid Phase Reactions at Surfaces The Glass Transition 129 Problems 131 Part II The Atomic Origins of Thermodynamics and Kinetics Energy Molecular Orbital Theory of Diatomic Molecules Electronic Energy Bands in Solids Elastic Constants and the Interatomic Potential Linear Elasticity Misfitting Particle Surface Energy 169 Problems 172

3 9 Contents 7 Entropy Static and Dynamic Sources of Entropy Short-Range Order and the Pair Approximation Local Atomic Structures Described by Clusters Thermodynamics with Cluster Approximations Concept of Vibrational Entropy Phonon Statistics Lattice Dynamics and Vibrational Entropy Bond Proportion Model Bond-Stiffness-versus-Bond-Length Model 201 Problems Pressure Materials under Pressure at Low Temperatures Thermal Pressure, a Step Beyond the Harmonic Model Free Energies and Phase Boundaries under Pressure Chemical Bonding and Antibonding under Pressure Two-Level System under Pressure Activation Volume 223 Problems Atom Movements with the Vacancy Mechanism Random Walk and Correlations Phenomena in Alloy Diffusion Diffusion in a Potential Gradient Non-Thermodynamic Equilibrium in Driven Systems Vineyard s Theory of Diffusion 252 Problems 258 Part III Types of Phase Transformations Melting Free Energy and Latent Heat Chemical Trends of Melting Free Energy of a Solid Entropy of a Liquid Thermodynamic Condition for T m Glass Transition Two Dimensions 281 Problems Transformations Involving Precipitates and Interfaces Guinier Preston Zones 285

4 10 Contents 11.2 Surface Structure and Thermodynamics Surface Structure and Kinetics Chemical Energy of a Precipitate Interface Elastic Energy and Shape of Growing Precipitates Precipitation at Grain Boundaries and Defects The Eutectoid Reaction and Ferrous Metallurgy The Kolmogorov-Johnson-Mehl-Avrami Growth Equation Coarsening 313 Problems Spinodal Decomposition Concentration Fluctuations and the Free Energy of Solution Adding a Square Gradient Term to the Free Energy F(c) Constrained Minimization of the Free Energy The Diffusion Equation Effects of Elastic Strain Energy 332 Problems Phase Field Theory Spatial Distribution of Phases and Interfaces Solidification Ginzburg Landau Equation and Order Parameters Interfaces Between Domains 344 Problems Method of Concentration Waves and Chemical Ordering Structure in Real Space and Reciprocal Space Symmetry and the Star The Free Energy in k-space with Concentration Waves Symmetry Invariance of Free Energy and Landau Lifshitz Rule for Second-Order Phase Transitions Thermodynamics of Ordering in the Mean Field Approximation with Long-Range Interactions 372 Problems Diffusionless Transformations Dislocations and Mechanisms Twinning Martensite The Crystallographic Theory of Martensite Landau Theory of Displacive Phase Transitions First-Order Landau Theory Phonons and Structural Collapse Soft Phonons in BCC Structures 404

5 11 Contents Problems Thermodynamics of Nanomaterials Grain Boundary Structure Grain Boundary Energy Gibbs Thomson Effect Energies of Free Electrons Confined to Nanostructures Configurational Entropy of Nanomaterials Vibrational Entropy Gas Adsorption Characteristics of Magnetic Nanoparticles Elastic Energy of Anisotropic Microstructures 429 Problems Magnetic and Electronic Phase Transitions Overview of Magnetic and Electronic Phase Transitions Exchange Interactions Correlated Electrons Thermodynamics of Ferromagnetism Spin Waves Thermodynamics of Antiferromagnetism Ferroelectric Transition Domains 458 Problems Phase Transitions in Quantum Materials Bose-Einstein Condensation Superfluidity Condensate Wavefunction Superconductivity Quantum Critical Behavior 480 Problems 483 Part IV Advanced Topics Low Temperature Analysis of Phase Boundaries Ground State Analysis for T= Richards, Allen, Cahn Ground State Maps Low, but Finite Temperatures Analysis of Equiatomic bcc Alloys High Temperature Expansion of the Partition Function 497 Problems 499

6 12 Contents 20 Cooperative Behavior Near a Critical Temperature Critical Exponents Critical Slowing Down The Rushbrooke Inequality Scaling Theory Scaling and Decimation Partition Function for One-Dimensional Chain Partition Function for Two-Dimensional Lattice 512 Problems Elastic Energy of Solid Precipitates Transformation Strains and Elastic Energy Real Space Approach k-space Approach 522 Problems Statistical Kinetics of Ordering Transformations Ordering Transformations with Vacancies B2 Ordering with Vacancies in the Point Approximation Vacancy Ordering Kinetic Paths 536 Problems Diffusion, Dissipation, and Inelastic Scattering Atomic Processes and Diffusion Dissipation and Fluctuations Inelastic Scattering Phonons and Quantum Mechanics 554 Problems Vibrational Thermodynamics of Materials at High Temperatures Lattice Dynamics Harmonic Thermodynamics Quasiharmonic Thermodynamics Thermal Effects Beyond Quasiharmonic Theory Anharmonicity and Phonon-Phonon Interactions Electron-Phonon Interactions and Temperature 575 Problems 577 Further Reading 579 References 583 Index 595