Quantifying free energies through local composition fluctuations in binary solid solutions: A proof-of-concept study using atomistic embedded-atom simulations

Abstract

While thermodynamic fluctuation theory has been extensively utilized in liquids for decades to obtain direct thermodynamic information, such as Gibbs free energies, from local composition fluctuations, this study presents an extension of the theory for its application in solids. It is demonstrated that composition fluctuations in solids are influenced by an additional elastic work term, which is specific to solids and encompasses liquids as a special case. To verify the extended fluctuation model, atomistic simulations were conducted on an exemplary Cu–Ni embedded-atom system. Monte Carlo simulations were performed in the semi-grandcanonical ensemble at a fixed temperature, covering the entire composition range. Composition fluctuations within a subvolume were monitored over time and statistically analyzed in terms of the variance. The atomistic results exhibit perfect agreement with the predictions derived from the extended model. This methodology has primarily been developed for the analysis of experimental atom probe tomography data, which provides three-dimensional chemical information with sub-nanometer precision. This technique enables the direct measurement of local composition fluctuations, facilitating the extraction of thermodynamic information from any allowed temperature–composition pair in the phase diagram.