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Exploration of structure-property relationships as a function of dopantconcentration is commonly based on mean field theories for solid solutions.However, such theories that work well for semiconductors tend to fail inmaterials with strong correlations, either in electronic behavior or chemicalsegregation. In these cases, the details of atomic arrangements are generallynot explored and analyzed. The knowledge of the generative physics andchemistry of the material can obviate this problem, since defect configurationlibraries as stochastic representation of atomic level structures can begenerated, or parameters of mesoscopic thermodynamic models can be derived. Toobtain such information for improved predictions, we use data from atomicallyresolved microscopic images that visualize complex structural correlationswithin the system and translate them into statistical mechanical models ofstructure formation. Given the significant uncertainties about the microscopicaspects of the material's processing history along with the limited number ofavailable images, we combine model optimization techniques with the principlesof statistical hypothesis testing. We demonstrate the approach on data from aseries of atomically-resolved scanning transmission electron microscopy imagesof Mo$_x$Re$_{1-x}$S$_2$ at varying ratios of Mo/Re stoichiometries, for whichwe propose an effective interaction model that is then used to generate atomicconfigurations and make testable predictions at a range of concentrations andformation temperatures.

Order and randomness in dopant distributions: exploring the thermodynamics of solid solutions from atomically resolved imaging