Mathematical Analysis of Solute Redistribution during Solidification Based on a Columnar Dendrite Model

Abstract

An exact solution and an approximate solution have been derived for the columnar dendrite model proposed by Ohnaka, ⁸⁾ in which a solidification rate, equilibrium distribution coefficient and diffusion coefficient in solid are assumed to be constant throughout the solidification. By comparing with the exact solution, it has been shown that the approximate solution has good accuracy. Further the model is extended on the basis of the derived approximate solution by incorporating a thermal model of solidification. The extended model includes multi-component alloy accompanying phase transformation in solid and temperature dependence of diffusion coefficients, and excludes the assumption of a given solidification rate. The calculated results of the extended columnar dendrite model agreed well both with the available experimental data and the calculated results of the extended planar dendrite model proposed previously. The assumption of the solidification geometry is unimportant for quantifying the microsegregation effects.