Pattern selection with anisotropy during directional solidification

R. B. Hoyle*, G. B. Mcfadden, S. H. Davis

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

20 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)2915-2949
Number of pages35
JournalPhilosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
Issue number1721
StatePublished - Dec 15 1996

ASJC Scopus subject areas

  • Mathematics(all)
  • Engineering(all)
  • Physics and Astronomy(all)


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