Three-dimensional equilibrium crystal shapes with corner energy regularization

Antonio Mastroberardino, Brian J. Spencer

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


The evolution equations of crystal growth often employ a regularization of the surface energy based on a corner energy term. Here, we consider the effect of this regularization on the equilibrium shape of a solid particle in three dimensions. We determine that a sufficient regularization involves only one of the two isotropic invariants related to curvature. Using a long-wave approximation, we derive a non-linear equation for the shape of a semi-infinite wedge in the case when the surface energy has cubic symmetry. An analytic description of the solution along an edge is given as well as an exact solution for a special case of anisotropy. Finally, this equation is solved numerically to demonstrate explicit solutions for which the regularization rounds the edges of the unregularized crystal shape.

Original languageEnglish (US)
Pages (from-to)190-205
Number of pages16
JournalIMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications)
Issue number2
StatePublished - Apr 2010

All Science Journal Classification (ASJC) codes

  • Applied Mathematics


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