Effect of Internal Radiation on Heat Transfer during Ti:sapphire Crystal Growth Process by Heat Exchanger Method

Abstract

In this study, the effect of internal radiation on the heat transfer during titanium-doped sapphire (Ti:sapphire) crystal growth process by heat exchanger method (HEM) was comprehensively investigated based on a global heat transfer model. Radiation absorption, emission and scattering in the semitransparent melt and crystal were modeled with the rigorous finite volume method. The numerical results show that internal radiation strongly enhances the heat transport in the melt and crystal, strengthens the melt convection and reduces the temperature gradient in the central body of the crystal. However, it renders the isotherms intensively concentrated in the narrow bottom region of the crystal, resulting in a significant increase in the temperature gradient in this region compared to the case without internal radiation. What's more, internal radiation makes the melt-crystal interface deeply convex towards the melt, which could be responsible for the radial non-uniformity of titanium concentration in the large Ti:sapphire crystal by HEM. The sensitivity of internal radiation to the optical properties was also parametrically studied. It was found that the heat transfer is strongly depended on the absorption coefficients of the crystal and melt. Particularly, the interaction between internal radiation and heat conduction in the crystal is strongest at the intermediate value of the absorption coefficient of the crystal, leading to the largest values of conduction heat transfer rate and maximum temperature gradient at the bottom of the crystal. The influence of scattering in the crystal becomes significant only after the scattering coefficient is larger than absorption coefficient. This study suggested that the effect of internal radiation on the heat transfer during HEM Ti:sapphire crystal growth process shows some difference from that during Kyropoulos and Czochralski oxide crystal growth processes.