The most prominent features of crystals such as those in Figs. 1 and 2(a) are their well-defined facets. A crystal's facets are stable against thermal capillary waves only if the latent heat of freezing per particle exceeds
where is the coordination number of a particle at the surface and z is the bulk coordination number . For low-index facets such as that in Fig. 2(a), , so that the latent heat is at least per particle.
This lower limit already is a factor of eight larger than the largest latent heat anticipated for spheres with purely repulsive pair-wise interactions. Entropically stabilized hard sphere crystals with short range contact repulsions are predicted  to have a latent heat only as large as per particle. Longer-range repulsions lead to even smaller latent heats . The discrepancy with our observations is accounted for most easily by positing the existence of a long-range attractive interaction contributing to the crystal's cohesive energy in addition to the core electrostatic repulsion. The attraction cannot be attributed to van der Waals interaction since such fluctuation-induced forces are utterly negligible at the crystal's lattice spacing . To account for the facets' stability, each nearest neighbor ``bond'' would have to reduce the system's free energy by on the order or .