Spherical Crystallography: Virus Buckling and Grain Boundary Scars

TL;DR

This paper explores how crystalline order on spherical surfaces involves topological defects, which can be alleviated through buckling or grain boundary scars, reducing energy in large viruses and colloidal particles.

Contribution

It introduces the concept of grain boundary scars as a novel defect structure that reduces energy in spherical crystals, complementing buckling mechanisms.

Findings

Grain boundary scars observed in colloidal particles on droplets.

Buckling reduces defect energy in large viruses.

Topological defects are essential for ordered spherical structures.

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.