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

Abstract 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 order-disorder transitions, 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 La1−xSrxMnO3 (LSM) and LaxSr1-xCoyFe1-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.