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This book deals with the use of the hodograph equation in phase transformations in condensed matter, especially, for crystallization and solidification processes. The main focus of the book is the interpretation of the phase-field equations for isotropic and anisotropic interfaces based on the advanced Gibbs–Thomson and Herring conditions, respectively. Beginning with the basic ideas behind the extended irreversible thermodynamics, the kinetic phase-field model for slow and arbitrarily fast phase transformations is derived where the unified hodograph equation follows from: • the sharp...

This volume presents the growth of macrostructures in first-order nonequilibrium phase transition in physical, chemical and biological multicomponent systems. Nonequilibrium thermodynamics and modern problems of crystallization synergetics are discussed. An introduction to the computer physics of dendrites is also given. Variety in growth structures appears to be the consequence of different nonequilibrium alloy crystallization conditions and concerns problems of crystallization synergetics. This book has computer simulation results of the origin and development of the observed variety of...

The Phase Field Crystal (PFC) model incorporates microscopic structural details into a mesoscopic continuum theory. Methods for fast propagation of PFC interfaces are discussed in this book. They can handle a wide range of thermal gradients, supersaturations and supercoolings, including applications such as selective laser melting. The reader will find theoretical treatment in the first half, while the latter half discusses numerical models.