Coarsening scenarios in unstable crystal growth

TL;DR

This paper analyzes the coarsening dynamics of crystal surface instabilities, identifying three possible scenarios and providing analytical results for the growth laws of mound sizes over time.

Contribution

It offers the first rigorous analytical characterization of coarsening scenarios in unstable crystal growth, including explicit growth exponents.

Findings

Three coarsening scenarios identified: perpetual, interrupted, and none.

Derived explicit growth laws for mound size over time.

Established conditions for faceting and non-faceting regimes.

Abstract

Crystal surfaces may undergo thermodynamical as well kinetic, out-of-equilibrium instabilities. We consider the case of mound and pyramid formation, a common phenomenon in crystal growth and a long-standing problem in the field of pattern formation and coarsening dynamics. We are finally able to attack the problem analytically and get rigorous results. Three dynamical scenarios are possible: perpetual coarsening, interrupted coarsening, and no coarsening. In the perpetual coarsening scenario, mound size increases in time as L=t^n, where the coasening exponent is n=1/3 when faceting occurs, otherwise n=1/4.