Fine structure in randomly packed, dense clusters of hard spheres

Abstract

Very dense, randomly-packed clusters of 500 equal spheres produced by computer using the algorithm described show significant differences from extended dense packings. The free boundary makes volume available to allow collective rearrangements which result in packing densities 4.5% higher than otherwise possible. The radial distribution functions of the dense clusters show a reversal in intensity of the split second peak as density is increased, and an additional small peak at about 1.4 diameters in the very high density packings can be correlated with the local arrangements found in the clusters. The topological statistics of the Voronoi polyhedra show differences from the extended random packing which can also be interpreted in terms of the extra freedom conferred by the free boundary. In contrast with soft sphere packings, the icosahedral arrangements are squeezed out at high densities in favour of more complex local regions. This supports previous suggestions that the detailed structure of a random packing depends upon both the softness and nature of the intermolecular potential function, the nature of the boundary, and the conditions of preparation, and warns that packing models of real amorphous solids must be used with care.