On the definition of an ideal amorphous solid of uniform hard spheres

Abstract

Perfection of structure is defined firstly by the definition of imperfections that may occur in that structure, and secondly by the strict requirement of absence of those imperfections. An ideal amorphous solid is a geometrical structure with perfectly random (as distinct from disordered) packing of spheres/atoms. This is achieved by requiring all spheres to be in fixed positions (no rattlers) and the packing to obey certain statistical rules (without exceptions). The random configurations of local clusters are described by the mathematics of self-avoiding random walks, and the distribution of mutual contacts (coordination numbers) is described by combinatorics developed in connection with an earlier work on the structure of liquids. Flaws in the structure are defined. An ideal amorphous solid, based on packing of identical spheres and without any flaws, appears to have packing density close to approximately 0.61. Flaws which form clusters with close packing configurations (fcc and hcp) have the effect of increasing the packing density, whereas other type of flaws, i.e., loose spheres or vacancies will inevitably decrease the packing density. This relationship is revealed by analysis of recently published experimental packings and computer simulations. In that sense, the ideal amorphous solid described here is entirely new and original.