Computer investigation of long-range correlations and local order in random packings of spheres

Abstract

Random packings containing 8192 hard spheres in three dimensions have been built with an efficient computer algorithm for various packing fractions up to $c=0.643\mathrm{}$, a value close to the upper limit $c_b\simeq 0.649$. Long-range correlations and local order have been investigated via the calculation of the two-point correlation function $g\left(r\right)\mathrm{}$ and the Voronoi tessellation, respectively. The $g\left(r\right)\mathrm{}$ curve exhibits large-$r$ damped oscillations characterized by a correlation length $\xi$ that increases with $c$ and whose extrapolation for $c>\mathrm{}{c}_b$ diverges at $c_0=0.754\mathrm{}$, which would be the volume fraction of an ideal icosahedral order. When they are extrapolated in the same manner, most of the geometrical characteristics of the Voronoi cells converge to their corresponding values for the perfect dodecahedron circumscribed around a sphere.