The glassy solid as an ensemble of crystalline microstates

While theoretical modeling of the atomic scale structure of non-crystalline solids has become well developed, deriving functional properties from these models still faces challenges. In order to address this deficit, we analytically demonstrate a decomposition of the non-equilibrium glassy macrostate into a statistical ensemble of crystalline microstates with an effective temperature. Crystalline microstates are calculated as local potential energy minima using density functional theory. With the radial distribution function and powder diffraction intensity as signatures of short- and long-range order respectively, we show that the glassy states of both silicon and silica can be reproduced with remarkable fidelity using crystalline microstates with unit cells on the order of just a few dozen atoms. Our approach offers a complementary view to the conventional supercell-based continuous random network model, which typically singles out a single representative microstate for the purposes of modeling. By contrast, our model presents the glassy state as an effective liquid, which visits crystalline potential energy minima ergodically, opening the door to new predictive methods for property calculations based on ensemble averaging and to the rational design of glassy solids.