The effect of compositionally-generated elastic stresses on morphological instability during directional solidification

We investigate the effect of compositionally-generated elastic stresses on the conditions for morphological instability during directional solidification. The Gibbs-Thomson conditions that incorporate the effects of compositionally-generated elastic stresses for a solid with negligible surface stress are derived for a solid-liquid system. These conditions are then used in a linear stability analysis of directional solidification for a dilute binary alloy. We find that the presence of these elastic stresses has a small stabilizing influence on the Mullins-and-Sekerka cellular interfacial instability. The stabilization is due to a stress-induced alteration of the interfacial concentration of the solid which, in turn, modifies the amount of solute rejected and inhibits the growth of perturbations to the interface. We also find that the presence of these stresses can generate a new oscillatory instability (standing or travelling interfacial waves). The oscillatory instability is driven by the nonlocal nature of the stresses, which induces a phase difference between the interface shape and the amount of solute rejected along the interface. The conditions for which the oscillatory instability is predicted are given in terms of experimentally relevant parameters. These conditions are shown to be experimentally attainable for some alloys, as illustrated by a comparison of the predictions of the theory with the results of experiments in the AgCu system.