Determining the positions of lattice defects on bounded elastic surfaces with Gaussian curvature is a nontrivial task of mechanical energy optimization. We introduce a simple way to predict the onset of disclination disorder from the shape of the surface. The criterion fixes the value of a weighted integral Gaussian curvature to a universal constant and proves accurate across a great variety of shapes. It provides improved understanding of the limitations to crystalline order in many natural and engineering contexts, such as the assembly of viral capsids.
ASJC Scopus subject areas
- Physics and Astronomy(all)