Relaxation of the Bernal model

Abstract

RANDOM packings of spheres serve as models for a variety of noncrystalline particulate and molecular aggregates, some of which, for example the amorphous phases of metals and alloys, offer abundant possibilities for the comparison of theory and experiment^1–4. Nevertheless there remain significant discrepancies between the measured structural characteristics of real systems and the geometrical models considered by Bernal⁵, Cohen and Turnbull⁶ and others to be prototypes for the simple vitreous state. The most enduring of these is perhaps the difference in position and intensity between the two components of the split second peak in the radial distribution function observed in actual and artificial systems^2–4. Attempts to remove this disagreement by variation of the algorithm used in computer-simulated packings have only been partially successful. In particular Sadoc et al.² have noted that it is relatively easy to build in strong local density inhomogeneities associated with icosahedral arrangements^7,8 and Connell has experimented with the packing of compressible spheres, showing that significant shifts in the radial distribution function result from the softening of the interatomic potential⁹.