Spherical Gaussians: An intuitive method for creating complex anisotropies in interface energies for the phase field method

The Phase Field Method requires continuous functions to control interface energies between phases. We have developed a method for phase field modeling where interface energies are described by spherical gaussians, a set of continuous functions which can simulate a wide variety of complex anisotropies. We demonstrate the use of the technique to produce a wide array of crystal geometries, including rods, hexagonal rods, cubes, and cubic dendrites, using the native properties of spherical gaussians to create specific interface energies throughout the full solid angle of an energy surface. Parameters controlling the sharpness of minima are shown to have a significant effect on morphology.