INTERFACE SHAPES AND THERMAL FIELDS DURING THE GRADIENT SOLIDIFICATION METHOD GROWTH OF SAPPHIRE SINGLE-CRYSTALS

We present a finite-element model describing the melt-growth of cylind rical sapphire single crystals via the gradient solidification method. The advantage of this model lies in its ability to accurately capture complex physical phenomena associated with heat transfer through the system, while remaining modest in its computational requirements. Inte rnal radiative heat transport through the transparent crystalline phas e is accounted for in our formulation, as are details of flow fields e volving in the melt during growth. Both buoyancy and surface-tension-g radient (Marangoni) driven convection effects are considered. Results show a strong dependence of the thermal field in the charge and of mel t/crystal interface shapes on operating parameters such as crystal gro wth rate and furnace temperature gradient. Specifically, the large lat ent heal value associated with this system, coupled with enhanced radi ative cooling through the crystalline phase, causes a dramatic reducti on in interface curvature and position for relatively high growth rate s and shallow furnace gradients. In addition, effects of fluid flow on the thermal field are shown to be unimportant in this system, even wh en considering growth in relatively large-diameter crucibles. Trends r eported here are in general agreement with experimental observations.