Polytetrahedral Nature of the Dense Disordered Packings of Hard Spheres

We study the structure of numerically simulated hard sphere packings at different densities by investigating local tetrahedral configurations of the spheres. Clusters of tetrahedra adjacent by faces present relatively dense aggregates of spheres atypical for crystals. The number of spheres participating in such polytetrahedral configurations increases with densification of the packing, and at the Bernal’s limiting density (the packing fraction around 0.64) all spheres of the packing become involved in such tetrahedra. Thus the polytetrahedral packing cannot provide further increase in the density, and alternative structural change (formation of crystalline nuclei) begins henceforth.

Figure 1

Volume fraction of a packing occupied by tetrahedral configurations as a function of packing density. Different curves correspond to different criteria for selection of the tetrahedra: $\delta =0.255$, 0.20, and 0.15, from top to bottom. Every symbol corresponds to one of the packings. Dashed horizontal line corresponds to value $1/3$.

Figure 2

Examples of polytetrahedral aggregates (clusters of face-adjacent tetrahedra). (a) three tetrahedra, (b) a ring of five tetrahedra, (c) a typical polytetrahedral cluster in dense disordered packing. The lower row shows motifs of the clusters: the points mark the centers of the tetrahedra, and the lines indicate that they are adjacent through a common face.

Figure 3

Volume fraction occupied by polytetrahedral aggregates (Fig. 2) as a function of packing density. Different curves correspond to different quality of the selected tetrahedra. Vertical lines correspond to a packing fraction of 0.646.

Figure 4

Fraction of hard spheres in the packing involved in tetrahedra as a function of packing density. The inset shows a blowup of the region in the vicinity of the limiting density.