Model for solute redistribution during rapid solidification

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Abstract
A microscopic model for impurity uptake at a sharp crystal-liquid interface during alloy solidification is presented in terms of the bulk properties of the liquid and solid phases. The results for stepwise growth and continuous growth at the same interface velocity differ quantitatively but exhibit the same qualitative features. A transition from equilibrium segregation to complete solute trapping occurs as the velocity surpasses the diffusive speed of solute in the liquid. The location of the transition varies little with equilibrium segregation coefficient, and a kinetic limit to solute trapping is found to be quite unlikely. Comparison is made with other models; critical differences are pointed out. Coupled with a growth velocity equation and with macroscopic heat- and solute-diffusion equations, the model forms a complete description of one-dimensional crystal growth. The steady-state solution to this system is indicated for the case of a planar interface. The results are applied to describe regrowth from laser-induced melting. Preliminary comparison with experiment is made. The steady-state solution for thermal and impurity transport is suggested for use whenever detailed computer calculations are unavailable or are unnecessarily involved.