  We characterize the structure of maximally random jammed (MRJ) sphere
packings by computing the Minkowski functionals (volume, surface area, and
integrated mean curvature) of their associated Voronoi cells. The probability
distribution functions of these functionals of Voronoi cells in MRJ sphere
packings are qualitatively similar to those of an equilibrium hard-sphere
liquid and partly even to the uncorrelated Poisson point process, implying that
such local statistics are relatively structurally insensitive. This is not
surprising because the Minkowski functionals of a single Voronoi cell
incorporate only local information and are insensitive to global structural
information. To improve upon this, we introduce descriptors that incorporate
nonlocal information via the correlation functions of the Minkowski functionals
of two cells at a given distance as well as certain cell-cell probability
density functions. We evaluate these higher-order functions for our MRJ
packings as well as equilibrium hard spheres and the Poisson point process. We
find strong anticorrelations in the Voronoi volumes for the hyperuniform MRJ
packings, consistent with previous findings for other pair correlations [A.
Donev et al., Phys. Rev. Lett. 95, 090604 (2005)], indicating that large-scale
volume fluctuations are suppressed by accompanying large Voronoi cells with
small cells, and vice versa. In contrast to the aforementioned local Voronoi
statistics, the correlation functions of the Voronoi cells qualitatively
distinguish the structure of MRJ sphere packings (prototypical glasses) from
that of the correlated equilibrium hard-sphere liquids. Moreover, while we did
not find any perfect icosahedra (the locally densest possible structure in
which a central sphere contacts 12 neighbors) in the MRJ packings, a
preliminary Voronoi topology analysis indicates the presence of strongly
distorted icosahedra.
