Elastic instability of a crystal growing on a curved surface.

Although the effects of kinetics on crystal growth are well understood, the role of substrate curvature is not yet established. We studied rigid, two-dimensional colloidal crystals growing on spherical droplets to understand how the elastic stress induced by Gaussian curvature affects the growth pathway. In contrast to crystals grown on flat surfaces or compliant crystals on droplets, these crystals formed branched, ribbon-like domains with large voids and no topological defects. We show that this morphology minimizes the curvature-induced elastic energy. Our results illustrate the effects of curvature on the ubiquitous process of crystallization, with practical implications for nanoscale disorder-order transitions on curved manifolds, including the assembly of viral capsids, phase separation on vesicles, and crystallization of tetrahedra in three dimensions.