In the presence of sufficiently strong surface energy anisotropy the equilibrium shape of an isothermal crystal may include corners or edges. Models of edges have, to date, involved the regularisation of the corresponding free boundary problem resulting in equilibrium shapes with smoothed out edges. In this paper we take a new approach and consider how a phase-field model, which provides a diffuse description of an interface, can be extended to the consideration of edges by an appropriate regularisation of the underlying mathematical model. Using the method of matched asymptotic expansions we develop an approximate solution which corresponds to a smoothed out edge from which we are able to determine the associated edge energy
To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.