Learning from Imperfections: Predicting Structure and Thermodynamics from Atomic Imaging of Fluctuations.

In materials characterization, traditionally a single experimental sample is used to derive information about a single point in the composition space, while the imperfections, impurities, and stochastic details of material structure are deemed irrelevant or complicating factors in the analysis. Here we demonstrate that atomic-scale studies of a single nominal composition can provide information about microstructures and thermodynamic response over a finite area of chemical space. Using the principles of statistical inference, we develop a framework for incorporating structural fluctuations into statistical mechanical models and use it to solve the inverse problem of deriving effective interatomic interactions responsible for elemental segregation in a La