Coupled morphological and thin film instabilities generated by inclusions in crystal growth

Abstract

The interaction of a foreign particle that is suspended in the melt with a planar solidifying interface may induce the onset of morphological instabilities provided that its distance from the interface falls below a critical value. This distance, which is of the order of the particle’s radius, depends on the governing processing and physical parameters. When the particle is in nearcontact with the solid-liquid interface, the disjoining pressure in the melt film that separates the particle from the interface influences the interaction. We derive an expression for the film thickness at which rupture occurs. The critical film thickness, which depicts the competition between the stabilizing influence of surface tension and thermal gradients and the destabilizing influence of the intermolecular forces, varies as (Sh)1/4, where Sh is the Scheludko number that is modifed by the imposed thermal gradients. We note the existence of a critical value for the particle’s radius below which the stabilizing effects are primarily due to surface tension and above which they are due to the thermal gradients.