title: Densest local sphere-packing diversity. II. Application to three dimensions.
abstract: The densest local packings of N three-dimensional identical nonoverlapping spheres within a radius R(min)(N) of a fixed central sphere of the same size are obtained for selected values of N up to N=1054. In the predecessor to this paper [A. B. Hopkins, F. H. Stillinger, and S. Torquato, Phys. Rev. E 81, 041305 (2010)], we described our method for finding the putative densest packings of N spheres in d-dimensional Euclidean space R(d) and presented those packings in R(2) for values of N up to N=348. Here we analyze the properties and characteristics of the densest local packings in R(3) and employ knowledge of the R(min)(N), using methods applicable in any d, to construct both a realizability condition for pair correlation functions of sphere packings and an upper bound on the maximal density of infinite sphere packings. In R(3), we find wide variability in the densest local packings, including a multitude of packing symmetries such as perfect tetrahedral and imperfect icosahedral symmetry. We compare the densest local packings of N spheres near a central sphere to minimal-energy configurations of N+1 points interacting with short-range repulsive and long-range attractive pair potentials, e.g., 12-6 Lennard-Jones, and find that they are in general completely different, a result that has possible implications for nucleation theory. We also compare the densest local packings to finite subsets of stacking variants of the densest infinite packings in R(3) (the Barlow packings) and find that the densest local packings are almost always most similar as measured by a similarity metric, to the subsets of Barlow packings with the smallest number of coordination shells measured about a single central sphere, e.g., a subset of the fcc Barlow packing. Additionally, we observe that the densest local packings are dominated by the dense arrangement of spheres with centers at distance R(min)(N). In particular, we find two "maracas" packings at N=77 and N=93, each consisting of a few unjammed spheres free to rattle within a "husk" composed of the maximal number of spheres that can be packed with centers at respective R(min)(N).
authors.affiliation: Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA.
authors.forename: Adam B
authors.initials: AB
authors.lastname: Hopkins
authors.forename: Frank H
authors.initials: FH
authors.lastname: Stillinger
authors.forename: Salvatore
authors.initials: S
authors.lastname: Torquato