Configurational Continuum modelling of crystalline surface evolution

TL;DR

This paper introduces a new continuum model for crystal surface evolution that tracks an ensemble of step configurations, effectively handling singular structures and offering computational benefits over discrete models.

Contribution

It presents a novel continuum approach based on large ensembles of step configurations, differing from traditional methods that require many steps per feature.

Findings

Handles singular surface structures like corners and facets

Offers computational advantages over discrete models

Enables accurate modeling with fewer steps per feature

Abstract

We propose a novel approach to continuum modelling of dynamics of crystal surfaces. Our model follows the evolution of an ensemble of step configurations, which are consistent with the macroscopic surface profile. Contrary to the usual approach where the continuum limit is achieved when typical surface features consist of many steps, our continuum limit is approached when the number of step configurations of the ensemble is very large. The model is capable of handling singular surface structures such as corners and facets and has a clear computational advantage over discrete models.