Dynamics of impurity redistribution at solution interfaces: phase-field approach

A thermodynamically consistent phase-field model of locally nonequilibrium solidification of concentrated two-phase binary solutions is proposed. The model is based on the division of the impurity concentration field into independent concentration fields formally defined in the entire available space for each of the phases. The impurity dynamic equations follow from the division of the complete impurity conservation law into separate phases. The phase-field equation and flow expressions are derived from the general principles of nonequilibrium thermodynamics. A feature of the derived equations is the impurity capture by the growing phase when the interface moves. Diffusion flow is divided into processes and phases. The resulting model has been tested using numerical simulation of a one-dimensional problem of directional solidification of a Si–As solution.