Crystallography on Curved Surfaces

TL;DR

This paper investigates how curvature affects the behavior of two-dimensional crystals, revealing that geometric factors influence dislocation dynamics and defect energetics, with implications for understanding crystal stability on curved surfaces.

Contribution

It introduces a model explaining dislocation unbinding and defect energetics on curved surfaces, highlighting the role of geometry in crystal behavior.

Findings

Dislocation glide diffusion is suppressed by geometric binding potential.

Point defect energetics are governed by geometric potential.

Analytical treatment of dislocation unbinding on curved surfaces.

Abstract

We study static and dynamical properties that distinguish two dimensional crystals constrained to lie on a curved substrate from their flat space counterparts. A generic mechanism of dislocation unbinding in the presence of varying Gaussian curvature is presented in the context of a model surface amenable to full analytical treatment. We find that glide diffusion of isolated dislocations is suppressed by a binding potential of purely geometrical origin. Finally, the energetics and biased diffusion dynamics of point defects such as vacancies and interstitials is explained in terms of their geometric potential.