Solute redistribution in dendritic solidification with diffusion in the solid

Abstract

An investigation of solute redistribution during dendritic solidification with diffusion in the solid has been performed using numerical techniques. The extent of diffusion in the solid during solidification is characterized by two parameters, namely the instantaneous and average diffusion parameters, respectively. These parameters are functions of the diffusion Fourier number, the partition ratio and the fraction solid. The diffusion Fourier number is that originally defined by Brody and Flemings; it is D s t f / λ 2 with D s = solute diffusivity in the solid, t f = local solidification time and λ = one-half of the characteristic dendrite arm spacing. The numerical results are presented as an approximate model, which is used to predict the average diffusion parameter. In turn, the average diffusion parameter can be used to calculate the composition of the interdendritic liquid during solidification in a simple manner. Also, an approximate model is presented to predict the solute distribution at the end of solidification. This result is put in a convenient form and is useful to those who wish to consider homogenization kinetics of as cast alloys.