Dynamics and Instabilities of Defects in Two-Dimensional Crystals on Curved Backgrounds
arXiv:cond-mat/0610819 · doi:10.1103/PhysRevE.75.021404
Abstract
Point defects are ubiquitous in two dimensional crystals and play a fundamental role in determining their mechanical and thermodynamical properties. When crystals are formed on a curved background, finite length grain boundaries (scars) are generally needed to stabilize the crystal. We provide a continuum elasticity analysis of defect dynamics in curved crystals. By exploiting the fact that any point defect can be obtained as an appropriate combination of disclinations, we provide an analytical determination of the elastic spring constants of dislocations within scars and compare them with existing experimental measurements from optical microscopy. We further show that vacancies and interstitials, which are stable defects in flat crystals, are generally unstable in curved geometries. This observation explains why vacancies or interstitials are never found in equilibrium spherical crystals. We finish with some further implications for experiments and future theoretical work.
9 pages, 11 eps figures, REVTeX
References in corpus (15)
- Grain Boundary Scars and Spherical Crystallography
- Interacting Topological Defects on Frozen Topographies
- Crystalline Order on a Sphere and the Generalized Thomson Problem
- Direct Visualization of Dislocation Dynamics in Grain Boundary Scars
- Crystallography on Curved Surfaces
- Diffusion of Point Defects in Two-Dimensional Colloidal Crystals
- Equilibrium Configurations and Energetics of Point Defects in Two-Dimensional Colloidal Crystals
- Curvature-Induced Defect Unbinding in Toroidal Geometries
- Crystalline Particle Packings on a Sphere with Long Range Power Law Potentials
- Grain Boundary Scars on Spherical Crystals
- Influence of Dislocations in Thomson's Problem
- Point Defect Dynamics in Two-Dimensional Colloidal Crystals
- Defect generation and deconfinement on corrugated topographies
- Ground state of a large number of particles on a frozen topography
- Statistical Mechanics of Vacancy and Interstitial Strings in Hexagonal Columnar Crystals
Cited by in corpus (11)
- Fractionalization of Interstitials in Curved Colloidal Crystals
- Particles on curved surfaces - a dynamic approach by a phase field crystal model
- Co-existence of the Meissner and vortex-state on a superconducting spherical shell
- Structure and dynamics of topological defects in a glassy liquid on a negatively curved manifold
- Interstitial Fractionalization and Spherical Crystallography
- Crystalline Particle Packings on Constant Mean Curvature (Delaunay) Surfaces
- Glassy dynamics of dense particle assemblies on a spherical substrate
- Topological vacancies in spherical crystal clusters
- Mode-coupling approach for the slow dynamics of a liquid on a spherical substrate
- Geometric frustration of hard-disk packings on cones
- Relaxation of interstitials in spherical colloidal crystals