Effects of the inert phase on solidification near a triple-phase line

Abstract

The local temperature solution near the triple-phase line of a solidifying front, its melt, and a surrounding inert phase was obtained analytically including all three phases and solidification kinetics. This analytical solution was validated using a three-phase numerical model of the horizontal ribbon growth of silicon and compared to a two-phase analysis that models the effect of the third phase (e.g. the gas) as an applied heat flux. Although the three-phase solutions have additional modes to represent the gas behavior, for many conditions the two-phase and three-phase models predicted consistent behaviors. However, introduction of a non-zero growth angle causes the gas phase heat fluxes to have strong gradients near the triple-phase line. Even with zero growth angle, there are conditions in which the two-phase and three-phase solutions are very different; one predicting infinite heat fluxes while the other predicts finite fluxes. This depended on the ratios of thermal conductivities, and the angle at which the solid-melt interface intersected the free surface. In particular, when the thermal conductivity of the inert phase was comparable to the melt or solid phases there were significant differences.