Sticky sphere packings on a cone

Inspired by experiments on the self-assembly of colloidal spheres on the surface of a cone, we use a greedy packing algorithm with extremely short-range attractive interactions to study how crystal growth is affected by both surface geometry and the nature of nucleation events. Since local crystal packings are unaware of the delta function of Gaussian curvature at the apex until they have encircled the cone, an initial seed composed of a ring of particles at a commensurate height leads to very different structures than a three-particle triangular seed, for example. We characterize the distribution of defects (sites with coordination number different from six) for a variety of initial seed types and locations, focusing on commensurate cone angles at which defect-free growth is possible and comparing crystallization on cones to the well-studied case of crystallization on spheres. We will discuss how our results can be used to guide experimental design and shed light on observed motifs such as disordered regions close to the cone apex and wedge-shaped voids far from the apex.