A vertex based approach to crystal facet modelling in phase field

This paper seeks a vertex based approach to faceted anisotropy in phase field modelling of crystal growth. We examine Wulff shapes and the connection they have with phase field formulations. On inspecting current approaches to modelling facets within phase field we observe that there are two distinct approaches: one implements the faceting purely in the kinetic parameter thus avoiding the complications of taking gradients of discontinuous functions; while the second is based upon regularisation of the anisotropy function within the free energy function. Armed with our new insight into the operation of anisotropy within phase field we refine the second of these and advocate a vertex based approach to facet anisotropy modelling. Results include regular and irregular morphologies and hill-valley growth. We also present high undercooling effects on faceting, which can cause breaks in facets and, in the case of irregular shapes, distortion of the underlying Wulff shape.