Effects of internal radiation on heat flow and facet formation in Bridgman growth of YAG crystals

Internal radiation, in the crystal and the melt, is investigated using the P1-approximation for the Bridgman growth of YAG crystals. Its effects on the interface shape and facet formation are illustrated through threedimensional simulation. The P1-approximation is first validated by a one-dimensional solution. Further comparison for axisymmetric cases with the rigorous calculations by Brandon and Derby [J. Crystal Growth 121 (1992) 473] is performed for opaque melt, and reasonable agreement is obtained for optical distance being <1 cm. The no-slip Rosseland model also gives a reasonable prediction in the interface shape; however, interface position and facet size are over predicted due to the poor approximation in the thermal gradients at the interface. Furthermore, melt transparency introduces radiation heating from the hot zone to the interface. Accordingly, the interface concavity is reduced with the increasing optical distance of the melt.