Czochralski crystal growth radiation

E.M. Nunes et al., A volume radiation heat transfer model for Czochralski crystal growth processes. J. Cryst. Growth 236(4), 596-608 (2002). 

The next most importtmt parameters in Czochralski growth of crystals are the heat flow and heat losses in the system. Actually, aU of the parameters (with the possible exception of 2 and 9) are strongly ciffected by the heat flow within the crystal-pulling system. A tj pical heat-flow pattern in a Czochralski sjretem involves both the crucible and the melt. The pattern of heat-flow is important but we will not expemd upon this topic here. Let it suffice to point out that heat-flow is set up in the melt by the direction of rotation of the cr5rstal being pulled. It is also ctffected by the upper surface of the melt and how well it is thermally insulated from its surroundings. The circular heat flow pattern causes the surface to radiate heat. The crystal also absorbs heat and re-radiates it... 

In considering the effect of internal radiation in Czochralski growth of oxides the crystal/melt interface is commonly assumed rounded. Yet, many oxide crystals... 

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