Emergent parabolic scaling of nano-faceting crystal growth

Watson, S. J. (2015) Emergent parabolic scaling of nano-faceting crystal growth. Proceedings of the Royal Society of London Series A: Mathematical, Physical and Engineering Sciences, 471(2174), p. 20140560. (doi: 10.1098/rspa.2014.0560)

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Publisher's URL: http://dx.doi.org/10.1098/rspa.2014.0560

Abstract

Nano-faceted crystals answer the call for self-assembled, physico-chemically tailored materials, with those arising from a kinetically mediated response to free-energy disequilibria (thermokinetics) holding the greatest promise. The dynamics of slightly undercooled crystal–melt interfaces possessing strongly anisotropic and curvature-dependent surface energy and evolving under attachment–detachment limited kinetics offer a model system for the study of thermokinetic effects. The fundamental non-equilibrium feature of this dynamics is explicated through our discovery of one-dimensional convex and concave translating fronts (solitons) whose constant asymptotic angles provably deviate from the thermodynamically expected Wulff angles in direct proportion to the degree of undercooling. These thermokinetic solitons induce a novel emergent facet dynamics, which is exactly characterized via an original geometric matched-asymptotic analysis. We thereby discover an emergent parabolic symmetry of its coarsening facet ensembles, which naturally implies the universal scaling law L∼t<sup>1/2</sup> for the growth in time t of the characteristic length L.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Watson, Dr Stephen
Authors: Watson, S. J.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Proceedings of the Royal Society of London Series A: Mathematical, Physical and Engineering Sciences
Publisher:Royal Society
ISSN:1364-5021
ISSN (Online):1471-2946

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