Thermodynamic models of multicomponent nonstoichiometric solution phases using internal process order parameters

Many multi-component compounds are nonstoichiometric due to the competing energetic and entropic thermodynamic contributions at finite temperatures. In CALPHAD-type thermodynamic descriptions, their chemical potential or molar Gibbs free energy at a given temperature is often expressed as a function of site fractions or occupation probabilities of different atomic/ionic/defect species on different sublattices. However, these site fractions are generally not independent from each other due to internal processes involving atomic exchange reactions, redox reactions, and defect formation. Here, we propose a general, systematic thermodynamic description of nonstoichiometric compounds by introducing a set of order parameters describing the extent of these internal processes. The equilibrium state at a given temperature and an overall chemical composition is then obtained by minimizing the chemical potential of a compound with respect to these order parameters. We demonstrate the mutual relationships between site fractions and order parameters using two types of practically important multicomponent phases as examples: perovskite La_1−xSr_xMnO₃ (LSM) and La_xSr_1-xCo_yFe_1-yO₃ (LSCF) used as solid oxide fuel cell cathodes and the spinel Co-Fe-O system as a catalyst for CO oxidation. We demonstrate that this proposed thermodynamic model can be directly incorporated in kinetic modeling, e.g., phase-field simulation, of diffusion-reaction and phase transformation processes involving nonstoichiometric phases as well as the kinetics of the internal processes within the nonstoichiometric compound under non-equilibrium conditions. Thus, a general link can be established between thermodynamic databases in terms of site fractions and phase-field simulations of kinetic processes and microstructure evolution using order parameters.