A simple anisotropic surface free energy function for three-dimensional phase field modeling of multi-crystalline crystal growth

Phase field modeling has emerged as a powerful tool in crystal growth simulation, but the description of the anisotropic function for three-dimensional (3D) interfacial free energy without miss-orientation remains quite difficult, especially for the multi-crystalline cases. In this paper, a simple function for keeping the convexity in the reciprocal surface free energy is proposed, and the simulated equilibrium shapes are in good agreement with the analytical ones. Some examples on the dendritic growth in a supercooled melt for mono- and multi-crystalline crystals are also illustrated.

► A new function with a single parameter n for the highly anisotropic interfacial energy without missing orientation. ► The value n varies with the anisotropic strength ε4 in two- and three-dimensions. ► Good agreement with the traditional model in the equilibrium shapes and dendritric growth. ► This new function makes the phase field simulation of multicrystalline growth with high anisotropy much easier.