Emergent Parabolic Scaling of Nano-Faceting Crystal Growth
- Stephen Watson (University of Glasgow)
Abstract
The dynamics of slightly undercooled crystal-melt interfaces possessing strongly anisotropic and curvature-dependent surface energy and evolving under attachment-detachment limited kinetics finds expression through a certain singularly perturbed, hyperbolic-parabolic, geometric partial differential equation.
Among its solutions, we discover a remarkable family of 1D convex- and concave- translating fronts whose fixed asymptotic angles deviate from the thermodynamically expected Wulff angles in direct proportion to the degree of undercooling: a non equilibrium (thermokinetic) effect.
We also present a novel geometric matched-asymptotic analysis that demonstrates that the slow evolution of the large-scale features of 1D solutions
Related Article: Stephen J. Watson, "Emergent Parabolic Scaling of Nano-Faceting Crystal Growth", Proceedings of the Royal Society A, Vol. 471 (Issue 2174) , DOI: 10.1098/rspa.2014.0560