  Motivated by the concept of partial ergodicity, we present an alternative
description of covalent and ionic glassy solids as statistical ensembles of
crystalline local minima on the potential energy surface. We show analytically
that the radial distribution function (RDF) and powder X-ray diffraction (XRD)
intensity of ergodic systems can be rigorously formulated as statistical
ensemble averages, which we evaluate for amorphous silicon and glassy silica
through the first-principles random structure sampling. We show that using
structures with unit cells as small as 24 atoms, we are able to accurately
replicate the experimental RDF and XRD pattern for amorphous silicon as well as
the key structural features for glassy silica, thus supporting the ensemble
nature of the glasses and opening the door to fully predictive description
without the need for experimental inputs.
