Norris, S.A., Davis, S.H., Watson, S.J. and Voorhees, P.W. (2008) Faceted interfaces in directional solidification. Journal of Crystal Growth, 310(2), pp. 414-427. (doi: 10.1016/j.jcrysgro.2007.10.048)
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Abstract
We consider the directional solidification, in two dimensions, of a dilute binary alloy having a large anisotropy of surface energy, (i.e., orientations with negative surface stiffness), where the sample is pulled in the highest-energy direction. Linear stability analysis reveals that the planar state is thermodynamically prohibited, leading to a search for faceted solutions. Below the critical pulling speed associated with constitutional supercooling, a small-wavelength assumption allows the reduction of interface dynamics to a single PDE. Matched asymptotic analysis then reveals a family of faceted interface profiles, while variational arguments confirm a small optimal wavelength. Questions on dynamic behavior lead to the derivation of a gradient-descent dynamics and an associated facet-velocity law. This reveals that faceted steady solutions are stable in the absence of supercooling, while coarsening replaces cell formation as the instability mechanism when supercooling is reached.
Item Type: | Articles |
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Status: | Published |
Refereed: | Yes |
Glasgow Author(s) Enlighten ID: | Watson, Dr Stephen |
Authors: | Norris, S.A., Davis, S.H., Watson, S.J., and Voorhees, P.W. |
Subjects: | Q Science > QC Physics |
College/School: | College of Science and Engineering > School of Mathematics and Statistics > Mathematics |
Journal Name: | Journal of Crystal Growth |
ISSN: | 0022-0248 |
ISSN (Online): | 1873-5002 |
Published Online: | 25 October 2007 |
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