Theory of Nonequilibrium Distribution Coefficients during Crystallization

Abstract

A phase transformation in a multicomponent system is described in terms of a set of coupled reactions of the transformation type and the redistribution type. The interface region is considered as an open thermodynamic system undergoing irreversible changes. The nonequilibrium partitioning of impurities is calculated for nonionic systems and the nonequilibrium partition coefficient is found to depend on the interface temperature $T_i$ and the growth velocity $V$ of the new phase. Whether the equilibrium partition coefficient $k^e$ is greater than, less than, or equal to 1, for an ideal solution the actual partition coefficient $k$ is greater than, less than, or equal to 1 dependening on $T_i$ and $V$ . Using a “large departure from equilibrium” approximation, it is shown that $\text{k\hspace{0.17em}→\hspace{0.17em}1}$ as $\mathrm{V\hspace{0.17em}\to \hspace{0.17em}\infty }$ independent of whether $k^e$ is less than or greater than 1, and a mathematical relationship is derived to give $k$ as a function of $V$ .