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Emergent Parabolic Scaling of Nano-Faceting Crystal Growth

Presented by: 
Stephen Watson University of Glasgow
Friday 11th December 2015 - 16:15 to 17:00
INI Seminar Room 1
Nano-faceted crystals answer the call for self-assembled, physico-chemically tailored materials, with those arising from a kinetically mediated response to free-energy dis-equilibria (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 1D 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 characterised 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^{1/2} for the growth in time t of the characteristic length L .

Related Links
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons