Emergent parabolic scaling of nano-faceting crystal growth

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 1 / 2 for the growth in time t of the characteristic length L .