Serially Deposited Amorphous Aggregates of Hard Spheres

Aggregates of several thousand equal hard spheres were constructed by depositing additional spheres, one at a time, at surface sites on a small seed cluster, placing each new sphere in contact with three already present and not moving it afterward. Always choosing the site closest to the center of the original seed results in an aggregate showing no evidence of crystallinity, with a pair correlation function quite similar to that of the dense random packings which have been prepared from ball bearings, and to the pair correlation functions calculated from x-ray diffraction work on amorphous alloys. The packing density ⅙πNσ3/V and the mean coordination number both decrease with distance from the center; the large-aggregate limits are, respectively, 0.61 (extrapolated, 4% lower than the ball-bearing value), and exactly 6.0 (in agreement with the ball-bearing value). The apparent difficulty of homogeneously nucleating crystallization in hard-sphere systems, even when simultaneous relaxation of many particle positions is allowed, is attributed to the fact that small hcp and fcc fragments are more bulky and have no more hard contacts than amorphous arragements of the same number of atoms.