The internal radiative contribution on heat transfer will enhance the heat transport inside the crystalline phase during growth of the transparent sapphire crystal using a heat-exchanger-method (HEM). The artificially enhanced thermal conductivity of the solid to include the internal radiation effect was used in the present study. Numerical simulations using FIDAP were performed to investigate the effects of the thermal conductivity on the shape of the melt-crystal interface, the temperature distribution, and the velocity distribution. Heat transfer (including radiation) from the furnace to the crucible and heat extraction from the heat exchanger can be modeled by the convection boundary conditions. In the present study, we focus on the influence of the conductivity on the shape of the melt-crystal interface. Therefore, the effect of the other growth parameters during the HEM crystal growth was neglected. For the homogenous conductivity (km = kS = k), the maximum convexity decreases as k increases and the rate of maximum convexity increases for a higher conductivity is less abrupt than for a lower conductivity. For the inhomogenous conductivity (km ≠ kS), the higher solid's kS generates lower maximum convexity and the variation in maximum convexity was less abrupt for the different melt's km. The maximum convexity decreases slightly as the enhance conductivity of the sapphire crystal increases. The effects of the anisotropic conductivity of the sapphire crystal were also addressed. The maximum convexity of the melt-crystal interface decreases when the radial conductivity (ksr) of the crystal increases. The maximum convexity increases as the axial conductivity (ksz) of the crucible increases.
- Single crystal growth
- Thermal conductivity