Abstract
A numerical study was carried out to describe the flow field structure of an oxide melt under 1) the effect of internal radiation through the melt (and the crystal), and 2) the impact of surface tension-driven forces during Czochralski growth process. Throughout the present Finite Volume Method calculations, the melt is a Boussinnesq fluid of Prandtl number 4.69 and the flow is assumed to be in a steady, axisymmetric state. Particular attention is paid to an undulating structure of buoyancy-driven flow that appears in optically thick oxide melts and persists over against forced convection flow caused by the externally imposed rotation of the crystal. In a such wavy pattern of the flow, particularly for a relatively higher Rayleigh number , a small secondary vortex appears nearby the crucible bottom. The structure of the vortex which has been observed experimentally is studied in some details. The present model analysis discloses that, though both of the mechanisms 1) and 2) end up in smearing out the undulating structure of the flow, the effect of thermocapillary forces on the flow pattern is distinguishably different. It is shown that for a given dynamic Bond number, the behavior of the melt is largely modified. The transition corresponds to a jump discontinuity in the magnitude of the flow stream function.
Highlights
Refractory oxide crystals such as gadolinium gallium garnet (GGG) and yttrium aluminum garnet (YAG) are widely used as solid-state laser hosts and materials for epitaxial films in magneto-optical devices [1] [2]
Accounting for the internal radiation within the melt and crystal is of crucial importance in numerical modeling of Cz growth of oxides because they are often semitransparent to infrared radiation [7] [8]
We report the results of a numerical simulation of the Czochralski growth of a large-diameter GGG crystal
Summary
Refractory oxide crystals such as gadolinium gallium garnet (GGG) and yttrium aluminum garnet (YAG) are widely used as solid-state laser hosts and materials for epitaxial films in magneto-optical devices [1] [2]. Tsukada et al [10] have developed a global analysis of heat transfer in the Cz oxide growth system in which the influence of the optical properties of both the melt and the crystal on the interface morphology has been studied In their model, forced convection flow and thermocapillary effect was neglected. Jing et al [12] have numerically revealed that when the internal radiation was ignored, a spoke pattern was generated and the bulk melt flow was oscillatory; the pattern disappeared when the melt assumed to be semitransparent These computational efforts were generally based on three-dimensional modeling of Cz oxide melt in an open crucible and all effects attributed to the crystal, including its optical properties, were ignored. The transition of the flow pattern corresponds to a jump discontinuity in the magnitude of the flow stream function
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