Effect of the ratio of solid to liquid conductivity on the stability parameter of dendrites within a phase-field model of solidification.

Abstract

We use a phase-field model of dendritic growth in a pure undercooled melt to examine the effect of the ratio mu=kappa(s)/kappa(l) on the operating point of the needle crystal and hence the stability parameter sigma(*), where kappa(s) and kappa(l) are the thermal conductivities of the solid and liquid phases, respectively. These results are compared with the microscopic solvability calculations of Barbieri and Langer [Phys. Rev. A 39, 5314 (1989)]. We find that in our phase-field model sigma(*) varies much more rapidly with mu than is predicted from solvability theory.