Heat transfer in vertical Bridgman growth of oxides: Effects of conduction, convection, and internal radiation

The vertical Bridgman growth of an oxide crystal with properties chosen to resemble those of yttrium aluminum garnet (YAG) is investigated. Internal radiation and heat conduction are accounted for in the crystalline phase, while transport through the melt (which is assumed opaque) is dominated by convection and conduction. Heat is also conducted through the ampoule walls, whose outer surface exchanges energy with the furnace via combined natural convection and enclosure radiation. A quasi-steady-state, axisymmetric Galerkin finite element method is employed for the calculation of thermal fields, melt flow patterns and melt/crystal interface shapes and positions for different parameter values. Results indicate that heat transfer through the system is strongly affected by the optical absorption coefficient of the crystal and that convective heat transfer through the melt is unimportant for this small-scale system. Coupling of internal radiation through the crystal with conduction through the ampoule walls promotes melt/crystal interface shapes which are highly deflected near the ampoule wall. This radiative interface effect is much more pronounced than that observed in the Bridgman growth of opaque crystals, where the interface deflection at the ampoule wall is attributed to the thermal conductivity mismatch between ampoule and charge. Calculations demonstrate that a flatter overall interface shape can be achieved through optimization of ampoule properties and furnace temperature profiles.