Emergent parabolic scaling of nano-faceting crystal growth

Abstract

Nano-faceted crystals answer the call for selfassembled, 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 nonequilibrium 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.

Nucleation of crystal surfaces with corner energy regularization

“…Here, we study the case of metastable surfaces, in which a nucleation event is necessary to reach the true equilibrium. Indeed, the effect of regularization on the equilibrium shape and on the dynamics of stable orientation formation in the spinodal regime as well as coarsening either by surface diffusion and motion by curvature or during reaction-limited crystal growth from a melt have been thoroughly studied, both in phase-field models and sharp-interface theories [13][14][15][16][17][18][19][20][21][22][23]. However, the effect of the corner energy on the nucleation regime remains unclear and even though the analogy with Cahn-Hilliard theory has already been shown in the context of spinodal decomposition of facets [19], it is difficult to anticipate, a priori, the shape of the nucleating surface and its dynamic evolution.…”

Lorentzian symmetry predicts universality beyond scaling laws

“…3. Here, A[t] is dinormal, with its two possible time-independent facet normals, say n + and n − , being mutually perpendicular (n + ⊥ n − ), while the (instantaneous) normal velocity ν of each facet is determined solely by the reciprocal of the facet's current length l [13], namely…”

Corners in phase-field theory

“…when crystal grows. Equation ( 8) is also the dimensionless equation for the sharp-interface velocity [28,[36][37][38][39]. Therefore, in the limit ε α 1, the sharp-interface result was recovered.…”