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Phase-field theory of edges in an anisotropic crystal

Phase-field theory of edges in an anisotropic crystal
Phase-field theory of edges in an anisotropic crystal
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.
Phase-field, surface energy, anisotropy
1364-5021
3363-3384
Wheeler, A.A.
eb831100-6e51-4674-878a-a2936ad04d73
Wheeler, A.A.
eb831100-6e51-4674-878a-a2936ad04d73

Wheeler, A.A. (2006) Phase-field theory of edges in an anisotropic crystal. Proceedings of the Royal Society A, 462 (2075), 3363-3384. (doi:10.1098/rspa.2006.1721).

Record type: Article

Abstract

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.

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Published date: November 2006
Keywords: Phase-field, surface energy, anisotropy

Identifiers

Local EPrints ID: 19148
URI: http://eprints.soton.ac.uk/id/eprint/19148
ISSN: 1364-5021
PURE UUID: 5e8a9c12-1871-455f-84f0-eb4a80a8c759

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Date deposited: 09 Jan 2006
Last modified: 09 Jan 2022 07:22

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Author: A.A. Wheeler

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