Effect of Internal Radiation on Heat Transfer during Ti:sapphire Crystal Growth Process by Heat Exchanger Method. (May 2021)

• Record Type: Journal Article
• Authors: Qi, Xiaofang; Ma, Wencheng; Liu, Lijun
• Is Part Of: International journal of heat and mass transfer. Volume 170(2021)
• Publication Date: 2021-05
• Subjects: Internal radiation -- Absorption and scattering coefficients -- Ti:sapphire crystal -- Heat exchanger method -- Numerical simulation; Heat -- Transmission -- Periodicals; Mass transfer -- Periodicals; Chaleur -- Transmission -- Périodiques; Transfert de masse -- Périodiques; Electronic journals; 621.4022
• DOI: 10.1016/j.ijheatmasstransfer.2021.121000
• Languages: English
• ISSNs: 0017-9310

Abstract

Highlights: Internal radiation, including absoption, emission and scattering, was numerically investigated. The deeply convex interface due to internal radiation accounts for the radial variation of Ti dopants. Internal radiation is highly sensitive to the absoption and scattering coefficients. Scattering in the crystal is significant only after the scattering albedo is larger than 0.5. The effect of internal radiation shows some difference from that during KY and CZ processes. 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.