Lateral or radial segregation in solidification of binary alloy with a curved liquid-solid interface

Abstract

This paper deals with steady state lateral or radial segregation of solute in solidification of a binary alloy with a curved solid-liquid interface. It is an extension of the work of Coriell and Sekerka and of Coriell et al. for interface shapes that meet the crucible wall at an arbitrary angle, as is commonly found in experiments. This work is limited to the diffusion controlled growth regime in which the Péclet number Pe = Vl/ D is large, and where the interface deflection is small. In the definition of Péclet number V is the growth rate, l is a characteristic length, and D is the binary diffusion coefficient of the solute in the liquid. We present analytical expressions for lateral and radial segregation which can be readily evaluated, given the material properties, growth velocity, and an interface shape obtained from experiment.