Onset of initial planar instability with surface-tension anisotropy during directional solidification

A simple model is presented to describe the variation of the onset of the initial planar instability with surface tension anisotropy during directional solidification. The effect of surface-tension anisotropy on the incubation time and the initial average wavelength of planar instability are predicted by the simple model quantitatively, which are also verified by phase field simulation. Investigation results reveal that surface-tension anisotropy is one of important factors in the dynamic process of planar instability. The contribution of surface-tension anisotropy to the tilting modulation is also analyzed by comparing the results from the present simple model with those from phase field simulation.