Simple model for the static structure and the mean coordination of amorphous solids

TL;DR

This paper introduces a simple model to evaluate the static structure and average coordination of amorphous solids with spherical particles, based on a hyperquenching process from liquid to jammed states, useful for assessing structural homogeneity.

Contribution

The model provides a quantitative method to determine average coordination and structural inhomogeneity in amorphous solids without heterogeneities, based on the hard-core repulsion framework.

Findings

Model predicts average coordination from 55% to 64% volume fraction.

Characteristic length of structural distortion is about 3% of particle diameter.

Applicable for evaluating macroscopic properties in dense, homogeneous amorphous solids.

Abstract

We propose a simple route to evaluate the static structure, in terms of average coordination, of completely disordered solids with spherical constituents, from ca. 55% volume fraction up to random close packing, in the absence of structural heterogeneities. Based on the current understanding, according to which the structure-determining interaction in amorphous solids is the hard-core repulsion while weaker, longer-range interactions are mere perturbations, the model yields the average coordination in the solid as a result of a hyperquenching process where the instantaneous structure of the precursor liquid snapshot is distorted to the same degree required to quench the hard-sphere liquid into the isostatic jammed state at 64% volume fraction. The characteristic length of distortion turns out to be about 3% of the particle diameter. Extrapolating to lower volume fractions, this is thus the quenching route leading to the most spatially homogeneous states. Thus the model can be usefully employed to quantitatively assess the degree of structural inhomogeneity in amorphous solids. When spatial inhomogeneity is small, as for very dense systems, the model can be used to evaluate coordination-dependent macroscopic properties (e.g. the elastic moduli) as shown in parallel works.