Spherical Crystallography: Virus Buckling and Grain Boundary Scars

Abstract

Ordered states on spheres require a minimum number of topological defects. For the case of crystalline order, triangular lattices must be interrupted by an array of at least 12 five-fold disclination defects, typically sitting at the vertices of an icosahedron. For R>>a, where R is the sphere radius and a the particle spacing, the energy associated with these defects is very large. This energy can be lowered, however, either by buckling, as appears to be the case for large viruses, or by introducing unusual finite length grain boundary scars. The latter have been observed recently for colloidal particles adsorbed onto water droplets in oil.