Role of internal radiation during Czochralski growth of YAG and Nd:YAG crystals

Crystals of YAG and Nd:YAG are grown from their molten state by the Czochralski technique. Oxide crystals are semi-transparent to infrared radiation. In many instances, radiation losses from the bulk of the crystal and melt are quite large. The scattering of radiation in doped melts can be significant during the growth process. The present study is a numerical simulation of flow and heat transfer during the growth of YAG and Nd:YAG crystals in a Czochralski process. The importance of radiation in the growth process has been examined. The heat flux in the melt comprises of contributions from conduction, advection and radiation. The radiative portion of heat transfer comprises of internal absorption, emission and scattering. It has been calculated in the present work by solving the radiative transfer equation (RTE) simultaneously with the conservation of energy equation. The Czochralski domain is considered to be an isotropically scattering gray medium. The radiative properties are assumed to be independent of wavelength and temperature. The boundaries are taken as diffusely emitting and reflecting opaque surfaces. The results obtained in the present study clearly show that the losses calculated by including internal radiation are higher, when compared to surface radiation alone. In addition, the temperature distribution develops skewness with respect to the crystal axis and thereby influences the shape of the melt–crystal interface. Calculations incorporating the bulk radiation model also show the importance of enclosure conditions for controlling the crystal growth process.