Crystallography 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.

12 Pages, 8 Figures

References in corpus (3)

• Direct Visualization of Dislocation Dynamics in Grain Boundary Scars
• Ground state of a large number of particles on a frozen topography
• Solid domains in lipid vesicles and scars

Cited by in corpus (9)

• Two-Dimensional Matter: Order, Curvature and Defects
• Periodic boundary conditions on the pseudosphere
• Defects in nematic membranes can buckle into pseudospheres
• Crystalline Order On Riemannian Manifolds With Variable Gaussian Curvature And Boundary
• Toroidal Crystals
• Spontaneous chirality via long-range electrostatic forces
• Bubble Raft Model for a Paraboloidal Crystal
• Dynamics and Instabilities of Defects in Two-Dimensional Crystals on Curved Backgrounds
• Elastic Theory of Defects in Toroidal Crystals