Three-dimensional phase field modeling of the faceted cellular growth

The new phase field model for strongly anisotropic systems proposed by Torabi et al. was employed to simulate the faceted cellular growth in three dimensions. Simulation reveals the whole formation process of the faceted cellular clearly. Simulation results also show that a linear relation of undercooling and growth velocity when the shape selection is completed at the late stage of the evolution, but a nonlinear relation holds during the shape selection stage. During the facet cellular formation, the crystal-melt interface is kept isothermal although the interface is sawtooth, and areas with negative temperature gradient appear in the melts, particularly at the ravine bottom of the sawtooth interface.