The suppression of volatilization via high pressure during melt crystal growth: Analysis via two models of the optical floating zone

Abstract

We investigate the role of ambient pressure on volatilization during melt crystal growth using the high-pressure optical floating zone (OFZ) as a prototypical model. Species transport is incorporated into a previously-developed, thermal-capillary model which includes the effects of energy and momentum transport while computing the shape of the zone meniscus, melting front, and solidification front. Results from this model show that pressure monotonically decreases volatilization from the melt zone into the ambient gas and that species transport is both inhibited via diffusion and enhanced via convection as pressure increases. A lumped-parameter model corroborates these findings and clarifies the interaction between diffusion and convection using boundary-layer theory. While increasing pressure always suppresses volatilization, the concurrent strengthening of gas-phase flows with pressure diminishes its effects. For the OFZ system studied here, the evaporative flux of volatile species from melt scales nonlinearly with pressure as $J_i\sim P^{-2/5}$, which is greater than the expected scaling of $J_i\sim P^{-1}$ when gas-phase convection is unimportant.