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Pattern selection with anisotropy during directional solidification

Pattern selection with anisotropy during directional solidification
Pattern selection with anisotropy during directional solidification
The effects of surface-tension anisotropy on interface morphology during the directional solidification of a binary alloy are studied. The long-wave evolution equation derived by Brattkus & Davis to describe growth near the absolute stability limit is generalized to include the effects of a surface tension with cubic anisotropy. The special cases of growth in the [001], [011] and [111] directions are considered. The resulting evolution equations are derived, and amplitude equations governing roll/rectangle and roll/hexagon competition are obtained. The coefficients of the amplitude equations depend on the surface-tension anisotropy, and determine how pattern selection is influenced by the presence of geometrically preferred directions. Anisotropy leads to changes in the existence and stability criteria for each pattern, to imperfect bifurcations, and to loss of degeneracy in bifurcations.
1364-503X
2915-2949
Hoyle, R. B.
e980d6a8-b750-491b-be13-84d695f8b8a1
McFadden, G. B.
c108bcae-5274-4839-b508-febd6ab3e546
Davis, S. H.
a0b6714e-4d2d-4731-bf4b-a1ebde5ff8bf
Hoyle, R. B.
e980d6a8-b750-491b-be13-84d695f8b8a1
McFadden, G. B.
c108bcae-5274-4839-b508-febd6ab3e546
Davis, S. H.
a0b6714e-4d2d-4731-bf4b-a1ebde5ff8bf

Hoyle, R. B., McFadden, G. B. and Davis, S. H. (1996) Pattern selection with anisotropy during directional solidification. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 354 (1721), 2915-2949. (doi:10.1098/rsta.1996.0135).

Record type: Article

Abstract

The effects of surface-tension anisotropy on interface morphology during the directional solidification of a binary alloy are studied. The long-wave evolution equation derived by Brattkus & Davis to describe growth near the absolute stability limit is generalized to include the effects of a surface tension with cubic anisotropy. The special cases of growth in the [001], [011] and [111] directions are considered. The resulting evolution equations are derived, and amplitude equations governing roll/rectangle and roll/hexagon competition are obtained. The coefficients of the amplitude equations depend on the surface-tension anisotropy, and determine how pattern selection is influenced by the presence of geometrically preferred directions. Anisotropy leads to changes in the existence and stability criteria for each pattern, to imperfect bifurcations, and to loss of degeneracy in bifurcations.

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Published date: 1996
Organisations: Mathematical Sciences

Identifiers

Local EPrints ID: 380293
URI: http://eprints.soton.ac.uk/id/eprint/380293
ISSN: 1364-503X
PURE UUID: 389daae1-0e0a-40b2-a40d-4b8eb368a870
ORCID for R. B. Hoyle: ORCID iD orcid.org/0000-0002-1645-1071

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Date deposited: 11 Aug 2015 16:18
Last modified: 15 Mar 2024 03:36

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Contributors

Author: R. B. Hoyle ORCID iD
Author: G. B. McFadden
Author: S. H. Davis

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