PREFACE
1.1 What Is This Book About?
1.2 Who Is This Book For?
1.3 Historical Note
1.4 Nomenclature
References
PART I: Classical Theories of Phase Transformations
CHAPTER 1: Thermodynamic Equilibrium of Phases
1.1 Definition of a Phase and Phase Transition
1.2 Gibbs Phase Rule
1.3 Theory of Capillarity
Problems
References
CHAPTER 2: Ehrenfest Classification of Phase Transitions
Problems
References
CHAPTER 3: Isothermal Kinetics of Phase Transformations
3.1 JMAK Theory of Nucleation and Growth
3.2 Classical Nucleation Theories
3.2.1 Frenkel's Distribution
3.2.2 Becker-Döring Theory
3.2.3 Zeldovich Theory
Problems
References
CHAPTER 4: Stefan Problem
Problems
References
CHAPTER 5: Stability of States
5.3.1 Thermodynamic Stability
5.3.1 Dynamic Stability
5.3.3 Morphological Stability
Problems
References
CHAPTER 6: Dendritic Growth
Problems
References
CHAPTER 7: Coarsening of Second Phase Precipitates
Problems
References
CHAPTER 8: Magnetic Transitions
Problems
References
PART II: The Method
CHAPTER 1: Landau Theory of Phase Transitions
1.1 The Order Parameter: Phase Transition as a Symmetry Change
1.2 The Free Energy: Phase Transition as a Bifurcation
1.3 The Tangential Potential
1.4 Phase Diagrams and Measurable Quantities
1.4.1 First-Order Transitions
1.4.2 Second-Order Transitions
1.5 Effect of External Field on Phase Transition
Problems
References
CHAPTER 2: Heterogeneous Equilibrium Systems
2.1 The Free Energy
2.1.1 Gradient Energy Contributions
2.1.2 Gradients of Temperature and Pressure
2.1.3 Gradients of Conjugate Fields
2.2 Equilibrium States
2.3 One-Dimensional Solutions of Equilibrium Equation
2.3.1 Thermo-Mechanical Analogy
2.3.2 Classification of States
2.3.3 Type-e1 States: Bifurcation off the Transition State
2.3.4 Type-e3 States: Approach to Thermodynamic Limit
2.3.5 Type-e4 State: Plane Interface
2.3.6 Interfacial Properties: Gibbs Adsorption Equation
2.3.7 Type-n4 State: Critical Plate-Instanton
2.4 Free Energy Landscape
2.5 Multidimensional Equilibrium States
2.5.1 Multidimensional Close-to-Homogeneous Equilibrium States
2.5.2 Quasi One-Dimensional Equilibrium States: Sharp Interface (Drumhead) Approximation
2.5.3 Critical Droplet-3d Spherically-Symmetric Instanton
2.6 Thermodynamic Stability of States: Local versus Global
2.6.1 Type-e4 State: Plane Interface
2.6.2 General Type-e and Type-n States
2.6.3 3d Spherically Symmetric Instanton
Problems
References
CHAPTER 3: Dynamics of Homogeneous Systems
3.1 Evolution Equation: The Linear Ansatz
3.2 Solutions of the Linear-Ansatz Dynamic Equation
3.2.1 Evolution of Small Disturbances
3.2.2 More complicated types of OPs
3.2.3 Critical Slowing Down
3.2.4 Non-Linear Evolution
3.3 Beyond the Linear Ansatz
3.4 Relaxation with Memory
3.5 Other Forces
Problems
References
CHAPTER 4: Evolution of Heterogeneous Systems
4.1 Time-Dependent Ginzburg-Landau Evolution Equation
4.2 Dynamic Stability of Equilibrium States
4.2.1 Homogeneous Equilibrium States
4.2.2 Heterogeneous Equilibrium States
4.3 Motion of a Plane Interface
4.3.1 Thermo-Mechanical Analogy
4.3.2 Polynomial Solution
4.3.3 Morphological Stability
4.4 Motion of Curved Interfaces: Sharp Interface (Drumhead) Approximation
4.4.1 Non-Equilibrium Interface Energy
4.4.2 Evolution of a Spherical Droplet
4.5 Dynamics of Domain Growth
Problems
References
CHAPTER 5: Thermodynamic Fluctuations
5.1 Free Energy of Equilibrium System with Fluctuations
5.2 Levanyuk-Ginsburg Criterion
5.3 Dynamics of Fluctuating Systems: Langevin Force
5.4 Evolution of the Structure Factor
5.5 Drumhead Approximation of the Evolution Equation
5.5.1 Evolution of the Interfacial Structure Factor
5.5.2 Nucleation in the Drumhead Approximation
Problems
References
CHAPTER 6: Concluding Remarks
6.1 Parameters of the Method
6.2 Boundaries of Applicability of the Method
Problems
References
PART III: Applications
CHAPTER 1: More Complicated Systems
1.1 Conservative Order Parameter: Theory of Spinodal Decomposition
1.1.1 Thermodynamic Equilibrium in Binary Systems
1.1.2 Equilibrium in Inhomogeneous Systems
1.1.3 Dynamics of Decomposition in Binary Systems
1.1.4 Evolution of Small Disturbances
1.1.5 Role of fluctuations
1.2 Complex Order Parameter: Ginzburg-Landau's Theory of Superconductivity
1.2.1 Order Parameter and Free Energy
1.2.2 Equilibrium Equations
1.2.3 Surface Tension of the Superconducting/Normal Phase Interface
1.3 Multicomponent Order Parameter: Crystallographic Phase Transitions
1.3.1 Invariance to Symmetry Group
1.3.2 Inhomogeneous Variations
1.3.3 Equilibrium States
1.4 Memory Effects: Non-Markovian Systems
1.5 "Mechanical" Order Parameter
Problems
References
CHAPTER 2: Multi-Physics Coupling: Thermal Effects of Phase Transformations
2.1 Equilibrium States of a Closed (Adiabatic) System
2.1.1 Type-E1 States
2.1.2 Type-E2 States
2.2 Generalized Heat Equation
2.3 Emergence of a New Phase
2.4 Motion of Interfaces: Drumhead (Sharp Interface) Approximation
2.4.1 Generalized Stefan Heat-Balance Equation
2.4.2 Generalized Kinetic Equation
2.4.3 Gibbs-Duhem Force 2.4.4 Inter-Phase Boundary Motion: Heat Trapping 2.4.5 APB Motion: Thermal Drag
2.5 Length and Energy Scales
2.6 Pattern Formation
2.6.1 One-Dimensional Transformation
2.6.2 Two-Dimensional Transformation
2.7 Thermo-Mechanical Analogy
Problems
References
CHAPTER 3: Extensions of the Method
3.1 Cellular Automata Method: "Poor Man's Phase Field"
3.2 Phase-Field Models of Grain Growth
3.2.1 Multiphase Field Models
3.2.1 Orientational Order-Parameter Field Models
3.3 Phase-Field Models of Dislocations and Voids
3.4 Phase-Field Crystal
Problems
References
EPILOGUE
Challenges and Future Prospects
APPENDIX A: Coarse-Graining Procedure
APPENDIX B: Calculus of Variations and Functional Derivative
APPENDIX C: Orthogonal Curvilinear Coordinates
APPENDIX D: Classical Mechanics and Lagrangian Field Theory
APPENDIX E: Eigenfunctions and Eigenvalues of The Schrödinger Equation and Sturm's Comparison Theorem
APPENDIX F: Fourier and Legendre Transforms
APPENDIX G: Stochastic Processes
The Master and Fokker-Plank Equations
Decomposition of Unstable States
Diffusion in Bistable Potential
Autocorrelation Function
The Langevin Approach
APPENDIX H: Two-phase equilibrium in a closed binary system
APPENDIX I: The Stefan Problem
APPENDIX J: "On the Theory of Adsorption of Sound in Liquids"
By L. I. Mandelshtam and M. A. Leontovich
APPENDIX K: Thermodynamically Consistent Heat Equation
SUBJECT INDEX
