Faceted interfaces in directional solidification

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)

Full text not currently available from Enlighten.

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
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

University Staff: Request a correction | Enlighten Editors: Update this record