Site percolation in randomly packed spheres

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Abstract
Three-dimensional structures of equal-sized randomly packed hard spheres (RPHS) have been built on a computer, and the site-percolation threshold has been calculated. The mean coordination of RPHS is 6 and we find a site-percolation threshold of 0.310 (±0.005). This value of the percolation threshold is the same as the simple cubic lattice, which has an exact coordination of 6. Expressing the percolation threshold for randomly packed hard spheres, in terms of the volume of occupied space, gives a critical-volume fraction of 0.183 (±0.003).