The engulfment of a precipitated particle in a saturated melt during solidification

A rigorous, finite-element model is employed to study the engulfment of a precipitated solid particle during solidification in a saturated melt, in which solute segregation, compositional effects on melting temperature, and reaction of the solute with the particle occur. The case of a silicon carbide (SiC) particle approaching a solid–liquid interface in a silicon melt supersaturated with carbon is specifically considered. Critical engulfment velocities are computed for particles with different surface reaction rates, as characterized by the Damköhler number, a dimensionless ratio of reaction to diffusion. Consistent with prior studies, an inert particle is predicted to be less likely to be engulfed when solute effects are present. However, a particle with fast surface reaction is more likely to be engulfed than in a system without solute effects, which is likely relevant for SiC particles during silicon crystal growth. Most interestingly, a particle for which the surface reaction is characterized by a Damköhler number of order unity is predicted to never be engulfed.