INTERNAL RADIATIVE TRANSPORT IN THE VERTICAL BRIDGMAN GROWTH OF SEMITRANSPARENT CRYSTALS

A quasi-steady-state model for the vertical Bridgman growth of semitransparent (partially absorbing and emitting) crystals is developed. For the first time, internal radiative heat transfer through the crystal (considered to be a participating medium) is calculated rigorously, taking into account the full three-dimensional shape of the crystal, including curvature of the melt/crystal interface. The crystal is assumed to be grey, and the ampoule walls, as well as the crystal/melt interface, are assumed to be grey and diffuse. Heat transfer through the melt is considered to be dominated by conduction. A Galerkin finite element method is employed to determine the position and shape of the interface and the temperature field in the crystal and melt. Results for a model oxide growth system demonstrate the sensitivity of melt/crystal interface shape, position, and interfacial gradients to changes in optical properties. The total heat flow through the melt and crystal also depends strongly on the optical parameters of the system. The phenomenon of radiative supercooling is not observed for the system considered here.