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This book describes a novel and popular method for the theoretical and computational study of phase transformations and materials processing in condensed and soft matter. The field theoretic method for the study of phase transformations in material systems, also known as the phase-field method, allows one to analyze different stages of transformations within a unified framework. It has received significant attention in the materials science community due to many recent successes in solving or illuminating important problems. In a single volume, this book addresses the fundamentals of the method starting from the basics of the field theoretic method along with its most important theoretical and computational results and some of the most advanced recent results and applications. Now in a revised and expanded second edition, the text is updated throughout and includes material on the classical theory of phase transformations. This book serves as both a primer in the area of phase transformations for those new to the field and as a guide for the more seasoned researcher. It is also of interest to historians of physics.
Classical Theories of Phase Equilibria and Transformations
Thermodynamic States and Their Stabilities
Thermodynamic Equilibrium of Phases
Examples of Phase Transitions
Isothermal Kinetics of Phase Nucleation and Growth
Coarsening of Second-Phase Precipitates
Spinodal Decomposition in Binary Systems
Thermal Effects in Kinetics of Phase Transformations
The Method
Landau Theory of Phase Transitions
Heterogeneous Equilibrium Systems
Dynamics of Homogeneous Systems
Evolution of Heterogeneous Systems
Thermodynamic Fluctuations
Multi-Physics Coupling: Thermal Effects of Phase Transformations
Validation of the Method
Applications
Conservative Order Parameter: Theory of Spinodal Decomposition in Binary Systems
Complex Order Parameter: Ginzburg-Landau’s Theory of Superconductivity
Multicomponent Order Parameter: Crystallographic Phase Transitions
“Mechanical” Order Parameter
Continuum Models of Grain Growth