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A general formulation of phase-field models for nonisothermal solidification in multicomponent and multiphase alloy systems is derived from an entropy functional in a thermodynamically consistent way. General expressions for the free energy densities, for multicomponent diffusion coefficients, and for both weak and faceted types of surface energy and kinetic anisotropy are possible. A three-dimensional simulator is developed to show the capability of the model to describe phase transitions, complex microstructure formation, and grain growth in polycrystalline textures.
Nestler et al. (Wed,) studied this question.