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
3363-3384
Wheeler, A.A.
eb831100-6e51-4674-878a-a2936ad04d73
November 2006
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), .
(doi:10.1098/rspa.2006.1721).
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: 15 Mar 2024 06:11
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Author:
A.A. Wheeler
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