Melting on a sphere

Melting in two-dimensional flat-space is typically two-step and via the hexatic phase. How melting proceeds on a curved surface, however, is not known. Topology mandates that crystalline particle assemblies on these surfaces harbor a finite density of defects, which itself can be ordered, like the icosahedral ordering of five-coordinated disclination defects on a sphere. Thus, melting even on a sphere, the simplest closed surface, involves the loss of both crystalline and defect order. Here, by tuning interparticle interactions in-situ, we report the observation of an intermediate hexatic phase during the melting of colloidal crystals on a sphere. Remarkably, the vanishing of the shear modulus in the hexatic phase resulted in a precipitous drop of icosahedral defect order. Furthermore, unlike in flat-space, where disorder can fundamentally alter the nature of the melting process, on the sphere, we observed the signature characteristics of ideal melting. Our findings have profound implications for understanding, for instance, the self-assembly and maturation dynamics of viral capsids and also phase transitions on curved surfaces.