Unified continuum approach to crystal surface morphological relaxation

TL;DR

This paper develops a continuum model based on atomic step interactions to predict how crystal surface profiles decay over time, unifying various experimental observations of surface relaxation in two dimensions.

Contribution

It introduces a tensor mobility in the PDE for surface height, unifying different surface relaxation behaviors and deriving from atomic step dynamics.

Findings

Predicts scaling laws for surface relaxation in two dimensions.

Unifies observations of bidirectional surface decay.

Reduces to known equations for specific geometries.

Abstract

A continuum theory is used to predict scaling laws for the morphological relaxation of crystal surfaces in two independent space dimensions. The goal is to unify previously disconnected experimental observations of decaying surface profiles. The continuum description is derived from the motion of interacting atomic steps. For isotropic diffusion of adatoms across each terrace, induced adatom fluxes transverse and parallel to step edges obey different laws, yielding a tensor mobility for the continuum surface flux. The partial differential equation (PDE) for the height profile expresses an interplay of step energetics and kinetics, and aspect ratio of surface topography that plausibly unifies observations of decaying bidirectional surface corrugations. The PDE reduces to known evolution equations for axisymmetric mounds and one-dimensional periodic corrugations.