Structuring of Hard Spheres

The computer study of this phase ttansition in the 1960s and 1970s led rapidly to a keen understanding of how hard, nonadhering spheres behaved as they were compacted towards the dense state. There were two outstanding problems what was the range of the transition between random and fully sUuctured packings and what was the ultimate stable form of the sUuctured material  

The second problem, that of the preferred geometry in the structured state, was much more difficult because there were three possible candidate structures, and all of them were rather similar in energy. The crux of the problem was finding the lowest energy structure because this should be the one most stable and eventually dominant. 

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The surfaces in Fig. 1 are obtained from arbitrarily selected computer-generated instantaneous configurations of an (oxide) BS and amorphous (liquid) carbon with the help of a probe hard sphere with a diameter close to that of an argon atom (0.33 nm). The upper of these surfaces is generated by the center of the probe sphere which rolls over the BS structure of hard spheres with diameter of a typical oxide ion (0.28 nm). In the case of amorphous carbon, a hard sphere with the van der Waals diameter of carbon (0.33 nm) is described around each carbon atom. These spheres overlap because the distances between carbon atoms are about 0.14 nm. The surface of amorphous carbon in Fig. 1 is generated by the center of the probe sphere that rolls over those overlapping hard spheres. 

Yu YX, WuJZ Structures of hard-sphere fluids from a modified fundamental-measure theory, J Chem Phys 117(22) 10156-10164, 2002. 

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