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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, 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.

Full text not available from this repository.

More information

Published date: 1996
Organisations: Mathematical Sciences

Identifiers

Local EPrints ID: 380293
URI: https://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

Catalogue record

Date deposited: 11 Aug 2015 16:18
Last modified: 06 Jun 2018 12:33

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