Nth-nearest neighbor statistics for three-dimensional equilibrium arrays of monodisperse spheres

Measures based on mean Nth-nearest neighbor distances efficiently characterize particle clustering and deviation from the equilibrium random state (ERS) in microstructures. Mean center-to-center distances to the Nth-nearest neighbor particle have been determined for three-dimensional equilibrium ensembles of monodisperse spheres for N ≤ 200. Hard sphere distributions represent inhibited point processes, and for small N the inhibition effect was significant for volume fractions ranging from 0.01 to 0.40. Caution should therefore be exercised in comparing hard sphere distributions with point processes, even at low volume fractions. For volume fractions ≥ 0.20, a significant ordering-related oscillation arises in the inhibition ratio; the effect is sufficiently strong that at a volume fraction of 0.40 it extends over the entire range of N ≤ 200, and the inhibition ratio falls below unity for certain values of N. To enable calculation of the inhibition ratio for N ≤ 200, functions were fit to the data for the volume fractions considered in this investigation.