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

The effect of compositionally-generated elastic stresses on the conditions for morphological instability during directional solidification of a dilute, ideal binary alloy is investigated using the Gibbs-Thomson equations for an elastically-stressed solid with zero surface stress in equilibrium with a liquid. It is found that these stresses lead to a small stabilization of the Mullins and Sekerka cellular mode of instability. The steady mode is stabilized by a stress-induced modification to the interfacial concentration of the solid, which in turn alters the amount of solute rejected to inhibit the growth of perturbations. The presence of elastic stresses could generate a new oscillatory instability which is most likely to be found in experiments near absolute stability for materials with segregation coefficients near unity and large solute expansion coefficients.