Modeling of Semitransparent Bulk Crystal Growth

Vladimir Kalaev, Yuri Makarov, Valentin Yuferev and Alexander Zhmakin 

Internal radiation through the crystal depends largely on the absorption coefficient and the refraction index. The first parameter determines the radiative heat absorption and emission inside the crystal, while the second determines reflection and refraction of radiation at the crystal side surface. The absorption coefficient of a melt is generally much greater than that of a crystal. Therefore, radiation is crucial in heat removal from the melt through the crystal/melt interface RTH within the crystal can even lead to instability of the crystallization front [5]. The refraction 

Crystal Growth Technology. Edited by Hans J. Scheel and Peter Capper Copyright 20( WILEY-VCH Verlag GmbH Co. KGaA, Weinheim ISBN 978-3-527-31762-2 

Finally, semitransparent crystals frequently demonstrate the pronounced tendency toward faceting of the sohdification front, and, thus, the shape of the crystals can strongly deviate from a circular cyhnder and present an irregular polyhedron. The 

Simulation of multidimensional RHT in a participating medium remains so far difficult. Detailed comparison with experimental data [24] shows that the diffusion approximation of RHT via an additional radiative thermal conductivity (for example in Ref [25] to study Cap2 melt growth), does not describe the correct temperature distribution in the growth system. Thus, advanced models, such as the discreet exchange factor method [26] or the characteristics method [27, 28] are needed. 

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