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Smallest metastable clusters

As the initially large metastable crystallites melt, they create a population of smaller crystals. Eventually, these crystals shrink to the radius tex2html_wrap_inline513 at which their surface energy exceeds the binding energy holding them together and they dissociate. The critical radius for a face-centered cubic crystal with lattice constant d, latent heat per particle L, and surface tension tex2html_wrap_inline519 is

equation70

The smallest metastable crystals thus allow us to set a lower limit on the surface tension of the crystal-fluid interface.

Figure 3 shows four stages in the dissociation of a minute crystal whose radius is one lattice constant. Very shortly after one additional sphere separates from the surface, the remaining spheres go on their separate ways. While we regularly observe crystals such as that in Fig. 3(a), we do not find smaller long-lived ordered clusters. If we identify tex2html_wrap_inline521 and apply the above result for L, then we can estimate a lower limit for the surface tension: tex2html_wrap_inline525 . This value is about an order of magnitude larger than the largest surface tension anticipated for a system with purely repulsive pairwise interactions [25, 26, 27]. Once again, the discrepancy is naturally explained by assuming a long-range attractive component in the pairwise interaction.



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