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Stable Facets

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 tex2html_wrap_inline485 is the coordination number of a particle at the surface and z is the bulk coordination number [22]. For low-index facets such as that in Fig. 2(a), tex2html_wrap_inline489 , so that the latent heat is at least tex2html_wrap_inline491 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 [23] to have a latent heat only as large as tex2html_wrap_inline493 per particle. Longer-range repulsions lead to even smaller latent heats [24]. 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 [19]. To account for the facets' stability, each nearest neighbor ``bond'' would have to reduce the system's free energy by on the order or tex2html_wrap_inline495 .

David G. Grier
Mon Dec 2 14:09:59 CST 1996