Cellular interface morphologies in directional solidification. II. The effect of grain boundaries

Abstract

Grain boundaries along a planar melt/solid interface significantly affect the onset and small-amplitude development of morphological instabilities during the solidification of a binary alloy. A singular perturbation analysis valid for small grain-boundary slopes is used with the one-sided model for solidification to show that grain boundaries introduce imperfections into the symmetry of the developing cellular interfaces which rupture the junction between the family of planar shapes and the bifurcating cellular families. Undulating interfaces are shown to develop first near grain boundaries, in agreement with experiments, and to evolve with decreasing temperature gradient either by a smooth transition from the almost planar family or by a sudden jump to moderateamplitude cellular forms, depending on the growth rate. Finite-element calculations for the Pb-Sb system give interface shapes for the large grain-boundary slopes which are typically observed.