Talk

Emergent Parabolic Scaling of Nano-Faceting Crystal Growth

  • Stephen Watson (University of Glasgow)
A3 01 (Sophus-Lie room)

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 I are captured by a Wulff-faceted interface A evolving under an intrinsic facet dynamics. This emergent dynamics possesses a Peclet length Lp below which a spatio-temporal symmetry of parabolic type appears. We thereby theoretically predict, and numerically verify, that within the sub-Peclet regime the universal scaling law Lt1/2 governs the time t evolution of the characteristic length L of the interface I.

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

Upcoming Events of this Seminar

  • Monday, 14.07.25 tba with Alexandra Holzinger
  • Tuesday, 15.07.25 tba with Anna Shalova
  • Tuesday, 12.08.25 tba with Sarah-Jean Meyer
  • Friday, 15.08.25 tba with Thomas Suchanek
  • Friday, 22.08.25 tba with Nikolay Barashkov
  • Friday, 29.08.25 tba with Andreas Koller