A key aspect of statistical physics is that the fluctuations of a system encode information about the response of the system to changing thermodynamic variables. However in most studies, structural and chemical fluctuations in materials characterization are seen as a hindrance, that complicates analysis. Here, we present a method to take advantage of atomic-scale observations of chemical and structural fluctuations and use them to build a generative model that can be used to predict the phase diagram of the system in a finite temperature and composition space. We show the example for understanding cationic segregation in a manganite thin film (La5/8Ca3/8MnO3), where a combination of in-situ atomic imaging via scanning tunneling microscopy as well as bulk measurements of composition as a function of layer (via angle-resolved x-ray photoemission spectroscopy) enables constraining the generative model. Through use of a recently developed statistical distance framework, the fluctuations in the system are inherently captured (as opposed to averaged out). The model leads to the prediction of weak segregation forces in bulk (attributable to elastic effects) and weak de-segregation forces in the surface (attributable to electrostatic interactions), which agree with recent quantum-chemical calculations (J. Am. Chem. Soc. 135, 7909 (2013)), but which are derived entirely from experiment. We further extend this approach to mapping atomic dynamics observed with scanning transmission electron microscope, providing insight into solid state chemistry on a single-defect level. This approach can be applied to a large array of systems, wherein the observed fluctuations can be exploited to understand the interactions between the constituent components of the system.
The work was supported by the U.S. Department of Energy, Office of Science, Materials Sciences and Engineering Division (R. K. V., S. V. K., L.V). Research was conducted at the Center for Nanophase Materials Sciences, which is a DOE Office of Science User Facility.