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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 interface limit of the diffuse interface or • the traveling wave solution of the propagating phase field. Under the example of solute trapping and disorder trapping effects, comparing theoretical results with molecular dynamics simulations, and with the analysis of experimental data, the concrete workability of the developed hodograph equation is demonstrated for widest range of driving force in phase transformations.

Materials science --- Condensed matter. --- Metals. --- Thermodynamics. --- Mathematical physics. --- Computational Materials Science. --- Structure of Condensed Matter. --- Metals and Alloys. --- Phase Transitions and Multiphase Systems. --- Mathematical Methods in Physics. --- Data processing.

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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 cooling rates, thermal gradients, supersaturations and supercoolings, including applications to the microstructural pattern formation occurring in intensive laser annealing and rapid quenching from the liquid state. The reader will find theoretical treatment in the first half, while the latter half discusses numerical models.--

Crystallography, Mathematical.