Numerical study on the effect of additional resistive heating and crystal rotation on sapphire single crystals (Al2O3) grown by the Kyropoulos method

In this paper, numerical simulations were performed to investigate the effects of additional heating and crystal rotation on Kyropoulos (Ky) sapphire crystal growth for different crucible corner shapes. The present model takes into account induction heating, resistive heating, heat transfer by conduction in all furnace parts, free convection in the melt, radiation exchange between inner furnace surfaces, thermo-capillary at the melt-free surface, internal radiation inside the sapphire crystal and phase change. The computational results show the advantage of using the additional heating and crystal rotation especially when a slipped crucible bottom corner is used. The crucible with slipped and curved corner shapes decreases both the convexity of the melt-crystal interface and the flow intensity of the molten sapphire more than the cylindrical crucible does. The convexity of the melt-crystal interface is reduced by 22%, 24% and 26% when additional heating is used and by 38%, 44% and 48% when this heating is used with crystal rotation for cylindrical, curved and slipped crucible bottom shapes, respectively. A less convex and more stable growth interface can be obtained when using the slipped crucible bottom shape and additional heating at the crucible bottom for a given crystal rotation rate.