TY - JOUR

T1 - Three-dimensional equilibrium crystal shapes with corner energy regularization

AU - Mastroberardino, Antonio

AU - Spencer, Brian J.

PY - 2010/4

Y1 - 2010/4

N2 - 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.

AB - 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.

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U2 - 10.1093/imamat/hxq007

DO - 10.1093/imamat/hxq007

M3 - Article

AN - SCOPUS:77950360132

SN - 0272-4960

VL - 75

SP - 190

EP - 205

JO - IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications)

JF - IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications)

IS - 2

ER -