Non-advective rate of curved step advance on smooth crystal face under steady-state conditions

TL;DR

This paper investigates the steady-state, non-advective growth rate of steps on a crystal face, revealing a non-monotonous relationship with curvature due to competing diffusion and Gibbs-Thomson effects.

Contribution

It introduces a theoretical analysis of step advance rates considering curvature effects under diffusion-controlled, steady-state conditions without advection.

Findings

Step velocity tends to zero as curvature increases.

The rate of step advance exhibits non-monotonous dependence on curvature.

Counteracts the Gibbs-Thomson effect in specific conditions.

Abstract

For low to moderate supersaturations, crystals grow by lateral build-up of new layers. The edges of the layers are known as "steps". We consider the rate of step advance on a flat crystal face under the influence of bulk diffusion in the complete absence of advection, assuming a steady-state. In such circumstances, the step velocity tends asymptotically to zero as the radius of curvature increases. This counters the Gibbs-Thomson effect according to which the rate of step advance should asymptotically increase \textit{ceteris paribus} with increasing radius of curvature. Because of these competing effects, the rate of step advance is expected to be non-monotonous in the radius of curvature.