Faceting of the melt-crystal interface is an important phenomenon affecting crystal quality. It is related with generation of many defects. For example strained core of YAG is assumed to be produced by the faceting of the interface [1]. The localization of the core along the axis of the crystal correlates with facets arising on the peak of conical interface. Another example is a spot-like defect structure with symmetry by 120 degrees rotation around the crystal axis which is observed in garnets grown in <111>  direction. This 3-fold symmetry also can be explained by the faceting of the interface. Faceting affects the crystal quality by stress generation, by different segregation at the facets and at rough surface or by some other way. Anyway regardless to the mechanism of defect generation the control of facet formation allows to improve the crystal quality. To investigate possible ways of controlling crystal facets, computer modeling of Cz growth of YAG and GGG has been performed by CGSim software package [2]. This software allows to take into account heating, crystallization, convection and radiation inside the whole furnace in axisymmetric approximation. It should be noted that despite of the three-dimensional shape of faceted crystal the axisymmetric simulation is quite reasonable for the aim to avoid faceting (because of axysymmetric shape of non-faceted melt-crystal interface). Facet formation has been modeled by taking into account the anisotropy of interface undercooling. The interface of growing crystal is colder than the melting temperature. The value of undercooling affects the local crystallization rate in different extent for rough and faceted growth.  CGSim computes undercooling anisotropy using the model of Weinstein and Brandon [3, 4]. This model suggests the crystallization rate to be proportional to the undercooling on the rough part of interface. Crystallization rate on the faceted part is assumed to be depending not only on undercooling but also on the angle of misorientation between facet direction and normal to the interface. Obtained results are verified using available experimental data.

1. C.W. Lan,C.Y. Tu, J. Cryst. Growth 233, 523 (2001)
2. www.str-soft.com
3. O. Weinstein, S. Brandon, J. Cryst. Growth 268, 299 (2004) 
4. O. Weinstein, S. Brandon, J. Cryst. Growth 268, 232 (2004)

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1. Modeling of Dislocation Dynamics and Facet Formation in VGF of GaAs
2. Numerical study of dislocation formation during transient growth of multi-Si by the direct solidification technique