A simple, general criterion for onset of disclination disorder on curved surfaces
arXiv:2003.07826 · doi:10.1103/PhysRevLett.125.078003
Abstract
Determining the positions of lattice defects on elastic surfaces with Gaussian curvature is a non-trivial task of mechanical energy optimization, particularly for surfaces with boundaries. We introduce a simple way to predict the onset of disclination disorder from the shape of bounded surfaces. The criterion fixes the value of a weighted integral Gaussian curvature to a universal constant and proves accurate across a great variety of shapes, even when previously suggested criteria fail. It is an easy avenue to improved understanding of the limitations to crystalline order in many materials.
References in corpus (20)
- Grain Boundary Scars and Spherical Crystallography
- Virus shapes and buckling transitions in spherical shells
- Mechanisms of virus assembly
- Two-Dimensional Matter: Order, Curvature and Defects
- Interacting Topological Defects on Frozen Topographies
- Crystalline Order on a Sphere and the Generalized Thomson Problem
- The Statistical Mechanics of Membranes
- Perspective: Geometrically-Frustrated Assemblies
- Crystallography on Curved Surfaces
- Recent advances in coarse-grained modeling of virus assembly
- Crystalline Particle Packings on a Sphere with Long Range Power Law Potentials
- Buckling transition in icosahedral shells subjected to volume conservation constraint and pressure: relations to virus maturation
- Influence of Dislocations in Thomson's Problem
- Crystalline Order On Riemannian Manifolds With Variable Gaussian Curvature And Boundary
- Defect generation and deconfinement on corrugated topographies
- Ground States of Crystalline Caps: Generalized Jellium on Curved Space
- Emergent structure of multi-dislocation ground states in curved crystals
- Neutral versus charged defect patterns in curved crystals
- Toroidal Crystals
- Elasticity in Curved Topographies: Exact Theories and Linear Approximations