Journal
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
Volume 462, Issue 2075, Pages 3363-3384Publisher
ROYAL SOC
DOI: 10.1098/rspa.2006.1721
Keywords
anisotropy; interface; phase-field; regularization; surface energy
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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 regularization 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 regularization 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.
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