LAUSR

We present an alternative and, for the purpose of non-crystalline materials design, a more suitable description of covalent and ionic glassy solids as statistical ensembles of crystalline local minima on the potential energy surface. Motivated by the concept of partially broken ergodicity, we analytically formulate the set of approximations under which the structural features of ergodic systems such as the radial distribution function (RDF) and powder X-ray diffraction (XRD) intensity can be rigorously expressed as statistical ensemble averages over different local minima. Validation is carried out by evaluating these ensemble averages for elemental Si and SiO 2 over the local minima obtained through the first-principles random structure sampling that we performed using relatively small simulation cells, thereby restricting the sampling to a set of predominantly crystalline structures. The comparison with XRD and RDF from experiments (amorphous silicon) and molecular dynamics simulations (glassy SiO 2 ) shows excellent agreement, thus supporting the ensemble picture of glasses and opening the door to fully predictive description without the need for experimental inputs.