Role of internal radiation at the different growth stages of sapphire by Kyropoulos method

Internal radiation is investigated using discrete ordinates (DO) model for the Kyropoulos growth of large-size LED-grade sapphire crystals. Its effects on the solid/liquid interface shape, melt convection, temperature and thermal stress are presented for the different growth stages characterized by the crystal length. The results are validated by observing cracked locations and remelting regions of the grown ingot. Internal radiation makes temperature distribution uniform by increasing heat transfer ability of the material, weakens natural and Marangoni convections in the melt, and reduces stress level in the crystal. It is also found that a slightly distorted interface is predicted affected by internal radiation, which is consistent with experimental observation. More reasonable flow patterns in the melt can be achieved taking into account the internal radiation. Natural convection at the early growth stage and Marangoni convection at the late growth stage are responsible for the interface and surface remelting. By analyzing thermal stresses, it is further concluded that the excessive stress is not the major cause of crystal cracking during Ky-sapphire growth. The maximum von Mises stress is always below the critical value predicted by other researchers. Consequently, the locally polycrystalline growth or the three-dimensionally non-uniform heating conditions are the most possible factors of crystal cracking.