Packing fraction and measures of disorder of ultradense irregular packings of equal spheres. II. Transition from dense random packing

Abstract

Close packings of equal spheres with densities, ϕ, from 0.65 to 0.7405 were obtained from perturbed hexagonal close packing (h.c.p.) using the force-biased algorithm (FBA). Similarly, densities from 0.65 to 0.72 were obtained from face-centered cubic (f.c.c.) packing, completing our earlier study (0.70-0.7405). The disorder of these packings was measured using several transportation metrics, μ and the average local angular disorder, θ For slight or moderate perturbations of either lattice, both μ and θ were approximately constant for almost the whole range of ϕ, but order was re-established much more easily from slightly perturbed h.c.p. Densities from 0.62 to 0.71 were obtained from sets of random points. The disorder, ϕ for these packings decreased steadily with ϕ. The transition from random to ordered packing is frustrated by the occurrence of both f.c.c. and (preferentially) h.c.p. fragments and by the varied orientation of these fragments. Transportation metrics have limited utility as measures of disorder, but θ is versatile and useful.