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Grain selection in faceted crystal growth using the phase field theory
A new application of the phase field theory is developed describing faceted crystal growth. The faceted growth is modeled by assuming the attachment kinetics of the liquid phase to the phase boundary to be dependent o the angle of the phase boundary to the normal of the individual facet. The model reproduces the competitive growth of different facets of an individual grain as well as the “non faceted” remelting behaviour of faceted crystals. The model is applied to the directional solidification of pure silicon. The selection of different grains is discussed with reference to its dependency on the crystallographic orientation of neighbouring grains. Therefore, each grain has its own individual phasefield. The selection behaviour is compared to geometrical considerations. It is shown to remain unchanged for directional growth in a temperature gradient, although the mesoscopic shape of the phase boundary is then determined by the temperature profile rather than the faceted crystallographic structure of the phase boundary.