Effect of anisotropic thermal conductivity on the morphological stability of a binary alloy

Abstract

We perform a linear morphological stability analysis of a planar interface during unidirectional solidification of a binary alloy for the case of a crystal having an anisotropic thermal conductivity. We calculate a dispersion relation which shows that the onset of instability depends on the orientation of the growth direction with respect to principal crystallographic axes and on the orientation of the wavevector of the perturbation. The onset of instability can be either oscillatory (travelling waves) or non-oscillatory in time. For growth along a principal axis of the crystal there is an exchange of stabilities, and the onset of instability is non-oscillatory. For a uniaxial crystal, we explore the dispersion relation in detail, and give numerical results for the case of an alloy of 0.78 at % bismuth in tin. For low growth velocities the onset of instability is non-oscillatory and occurs for perturbations having a wavevector that lies along a principal crystallographic axis.