Colloidal Crystallization on Cones

We explore experimentally how a conical surface frustrates the growth of colloidal crystals. Whereas crystals on a cylinder can form perfect commensurate bands, crystals on a cone tend to form tilt grain boundaries with misorientation angles set by the conical geometry. However, at small cone angles, where the surface deviates only slightly from that of a cylinder, crystals can form commensurate bands, the widths limited by the emergence of dislocations. The dislocations allow the crystal to continue growing beyond the limiting width. We relate these effects to the gradient in circumference on a cone, a consequence of the Gaussian curvature localized at the apex.