Solute redistribution during solidification with rapid solid state diffusion

Abstract

Unidimensional solute redistribution during freezing is modelled for the important case of complete diffusion in the liquid and incomplete back-diffusion in the solid by the Brody and Flemings analysis. The treatment, however, does not conserve solute and leads to predictions which are incorrect unless solid state diffusion is very limited. This paper outlines the origin of this effect and presents a modification to the model in which the predicted behavior is quantitatively correct in the important limits. Application of the modified analysis is shown to be simple and to lead to realistic descriptions of the solidification behavior in mushy freezing alloys. As an example, the model is applied to two steels solidifying over a range of cooling rates and the results indicate that such systems will in many cases be quite close to thermodynamic equilibrium with respect to carbon redistribution.