Numerical simulation of the sapphire growth process using a self-regulating thermal boundary condition method

Sapphire is widely used in many industries, including the military, electronic, and astronautic industries. Therefore, its growth quality is very important for its application. Obtaining a good-quality sapphire crystal requires the investigation of its growth process with a proper thermal boundary condition. The growth process of sapphire crystals with different sizes was numerically studied in the present work. The temperature distribution in crucibles and the thermal boundary conditions of the crucibles, which could guarantee an accurate amount of energy for the sapphire crystal in each growth period, were also determined. The results showed that specific regulation techniques should be adopted at each sapphire growth stage to avoid high temperature gradient and thermal stress. On the other hand, the validity of the theoretical analysis that the solid-liquid interface angle of a high-quality sapphire is distributed among ∼90° in the shouldering and iso-diameter stages was proven. Accordingly, a new crystal growth method, called the self-regulating method, is proposed based on this study.