Elastic Theory of Defects in Toroidal Crystals

Abstract

We report a comprehensive analysis of the ground state properties of axisymmetric toroidal crystals based on the elastic theory of defects on curved substrates. The ground state is analyzed as a function of the aspect ratio of the torus, which provides a non-local measure of the underlying Gaussian curvature, and the ratio of the defect core-energy to the Young modulus. Several structural features are discussed,including a spectacular example of curvature-driven amorphization in the limit of the aspect ratio approaching one. The outcome of the elastic theory is then compared with the results of a numerical study of a system of point-like particles constrained on the surface of a torus and interacting via a short range potential.

24 pages, 24 figures

References in corpus (10)

• Global Optimization by Basin-Hopping and the Lowest Energy Structures of Lennard-Jones Clusters Containing up to 110 Atoms
• Grain Boundary Scars and Spherical Crystallography
• Interacting Topological Defects on Frozen Topographies
• Crystallography on Curved Surfaces
• Melting as a String-Mediated Phase Transition
• Dislocations and the critical endpoint of the melting line of vortex line lattices
• Curvature-Induced Defect Unbinding in Toroidal Geometries
• Grain Boundary Scars on Spherical Crystals
• Influence of Dislocations in Thomson's Problem
• Crystalline Order On Riemannian Manifolds With Variable Gaussian Curvature And Boundary

Cited by in corpus (13)

• Two-Dimensional Matter: Order, Curvature and Defects
• Active Flows on Curved Surfaces
• Kibble-Zurek mechanism in curved elastic surface crystals
• Crystalline Particle Packings on Constant Mean Curvature (Delaunay) Surfaces
• Crystalline Order on Catenoidal Capillary Bridges
• Plastic deformation of tubular crystals by dislocation glide
• Topological Phases and Curvature-Driven Pattern Formation in Cholesteric Shells
• Transitions between phyllotactic lattice states in curved geometries
• Shape multistability in flexible tubular crystals through interactions of mobile dislocations
• General Solution for Elastic Networks on Arbitrary Curved Surfaces in the Absence of Rotational Symmetry
• Dynamics of Vortex Clusters on a Torus
• On irreducible triangulations of punctured and pinched surfaces
• On the nature of the phase transitions in two-dimensional type II superconductors