Lateral solute segregation during undirectional solidification of a binary alloy with a curved solid—Liquid interface

Abstract

The lateral solute segregation associated with a slightly curved solid-liquid interface during steady-state unidirectional solidification of a binary alloy is calculated under the assumption of no convection in the liquid. This is done to first order in the deviation of the interface from planarity by an adaptation of the perturbation methods of the theory of morphological stability. The calculation is based on an assumed knowledge of the solid-liquid interface shape; no attempt is made to relate this shape to the thermal field. The results are valid for the case where the solute boundary layer is thick compared to the deviation of the solid-liquid interface from planarity. In the limiting case of a very thick boundary layer, the lateral segregation in the solid is simply the product of the distribution coefficient, the deviation from planarity and the concentration gradient applicable to a planar interface. Numerical estimates of the relative lateral segregation are in reasonable agreement with experimental data of Witt et al. on crystals of gallium-doped germanium grown in space.