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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 SiO₂over 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 SiO₂) shows excellent agreement, thus supporting the ensemble picture of glasses and opening the door to fully predictive description without the need for experimental inputs.

We investigate electronic structure and dopability of an ultrawide bandgap (UWBG) AlScO3 perovskite, a known high-pressure and long-lived metastable oxide. From first-principles electronic structure calculations, HSE06(+G0W0), we find this material to exhibit an indirect bandgap of around 8.0 eV. Defect calculations point to cation and oxygen vacancies as the dominant intrinsic point defects limiting extrinsic doping. While acceptor behaving Al and Sc vacancies prevent n-type doping, oxygen vacancies permit the Fermi energy to reach ∼0.3 eV above the valence band maximum, rendering AlScO3 p-type dopable. Furthermore, we find that both Mg and Zn could serve as extrinsic p-type dopants. Specifically, Mg is predicted to have achievable net acceptor concentrations of ∼1017 cm−3 with ionization energy of bound small hole polarons of ∼0.49 eV and free ones below 0.1 eV. These values place AlScO3 among the UWBG oxides with lowest bound small hole polaron ionization energies, which, as we find, is likely due to large ionic dielectric constant that correlates well with low hole polaron ionization energies across various UWBG oxides.