Densest local sphere-packing diversity. II. Application to three dimensions

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