M.G. Vasiliev

Variations of solid-liquid interface in the BGO low thermal gradients Cz growth for diffuse and specular crystal side surface

Abstract A global analysis of heat transfer in growing BGO (Bi4Ge3O12) crystals was carried out to explain the significant variation of the solid–liquid interface shape observed in practice during crystal growth. Special attention was given to the accurate treatment of radiative heat transfer in crystal and the gap between crystal and crucible wall. Crystal side surface was assumed to be transparent and diffuse or specular (Fresnel) reflective while melt was opaque. Spectral absorptivity of crystal was approximated by a three-band model. It is shown that rotationally driven vortex dominates under the solid–liquid interface during the whole growth process and no reconstruction of flow pattern, which could lead to interface inversion, takes place. As a result, in the case of diffuse crystal surfaces, the calculated deflection of the crystallization front does not exceed several millimeters and that completely disagrees with the observations. In contrast, for the specular crystal surface the solid–liquid interface turns out to be deeply convex toward the melt at the initial stage of the growth, and then, as the crystal is pulled, its convexity strongly diminishes. Such behavior is in good agreement with the experiment and mainly determined by specular reflection at the conical part of the crystal (its shoulder) while the effect of specular reflectivity of the cylindrical part and melt-free surface is significantly less. It is also shown that radiation transfer in the wavelength band of crystal opacity in conjunction with the specular reflection of radiation in the band of crystal transparency result in the appearance of “convex–concave” isotherms in the upper part of the crystal.

Global analysis of heat transfer in growing BGO crystals (Bi4Ge3O12) by low-gradient Czochralski method

A numerical analysis of heat transfer in a set-up for growing BGO crystals is undertaken. Consideration is given to the correct treatment of radiative heat transport inside and outside the crystal. Effect of internal radiation is demonstrated. Conjugate heat transfer in crystal, melt and crucible was studied for different crystal lengths. Violation of the fully faceted growth at the initial stage of pulling is discussed.

Investigation of the variations in the crystallization front shape during growth of gadolinium gallium and terbium gallium crystals by the Czochralski method

Numerical investigation of the variations in the crystallization front shape during growth of gadolinium gallium and terbium gallium garnet crystals in the same thermal zone and comparison of the obtained results with the experimental data have been performed. It is shown that the difference in the behavior of the crystallization front during growth of the crystals is related to their different transparency in the IR region. In gadolinium gallium garnet crystals, which are transparent to thermal radiation, a crystallization front, strongly convex toward the melt, is formed in the growth stage, which extremely rapidly melts under forced convection. Numerical analysis of this process has been performed within the quasistationary and nonstationary models. At the same time, in terbium gallium garnet crystals, which are characterized by strong absorption of thermal radiation, the phase boundary shape changes fairly smoothly and with a small amplitude. In this case, as the crystal is pulled, the crystallization front tends to become convex toward the crystal bulk.

Heat source optimization in a multisection heater for the growth of bismuth germanate crystals by the low-gradient Czochralski method

The growth of bismuth germanate crystals with uniform heater control has been simulated within the time-dependent approach. To optimize the multisection heater control, the global heat transfer optimization problem in a crystallization setup was considered. A new control algorithm, based on the solution of the optimization problem, is proposed.

Comparative analysis of the heat transfer processes during growth of Bi12GeO20 and Bi4Ge3O12 crystals by the low-thermal-gradient Czochralski technique

The heat transfer processes occurring in the solid and liquid phases during growth of Bi12GeO20 and Bi4Ge3O12 crystals by the low-thermal gradient Czochralski method are analyzed and compared. It is experimentally found that, under similar growth conditions, the deflection of the crystallization front for the Bi12GeO20 crystal is considerably smaller than the deflection of the crystallization front for the Bi4Ge3O12 crystal and the faceting of the former front is observed at the earlier stage of pulling. The results of the numerical simulation demonstrate that the different behavior of the crystallization fronts is associated with the difference between the coefficients of thermal absorption in the crystals.