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

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