Mathematical analysis of solute redistribution during solidification with diffusion in solid phase.

Abstract

Solute redistribution during solidification has been analyzed by a profile method which has approximately considered the two-dimensional diffusion in solid phase. Derived equations have been compared with conventional equations, numerical analyses and experimental data. It was found that a newly derived simple equation can estimate the liquid concentration better than Brody-Flemings' equation but numerical calculation or further improvement of the analytical treatment is required for estimating the segregation ratio correctly. 7n addition, calculations showed that the dendrite shape, growth mode (parabolic and constant growth) and diffusion in the liquid phase did not affect so much the solute redistribution at least for fS<0.9. The diffusion path, which is thought to be a more important factor, has also been discussed and an equation is proposed for the case where diffusion path or the partition coefficient changes stepwise.