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A general approach to diffusion-limited crystal growth is proposed. It consists of a modified (nonequilibrium) Cahn-Hilliard representation of the interface coupled to a diffusion equation. Arguments are given as to its superiority over previous models. These are illlustrated in a one-dimensional solution which shows how the system selects a unique interface velocity. The selection can be interpreted as the requirement of consistency between the interfacial undercooling as determined by the (microscopic) kinetics and as determined by the (macroscopic) diffusion equation.
Collins et al. (Wed,) studied this question.