Study of internal radiation with solute inclusions during Czochralski sapphire crystal growth

Internal radiation is investigated using discrete ordinates (DO) radiation model for Czochralski growth of sapphire single crystal. Its effects on the solid/liquid (S/L) interface, melt flow and temperature distribution are presented. Using the internal radiation model, the influences of melt inclusions on the S/L interface are further examined with special attention directed to optical properties of inclusions, opaque or transparent, and locations of inclusions in the crystal. The results show that the predicted convexity of the interface increases after taking into account internal radiation. A local surface with accumulation of opaque inclusions bends towards the crystal. On the contrary, transparent inclusions result in a more convex interface into the melt. These phenomena are both revealed in two- and three-dimensional calculations.