Thermodynamic approach to the stability of multi-phase systems: Application to the Y₂O₃-Fe system

Oxide-metal systems are important in many practical applications, and they are undergoing extensive study using a wide range of techniques. The most accurate theoretical approaches are based on density functional theory (DFT), which is limited to ∼10² atoms. Multi-scale approaches, e.g. DFT + Monte Carlo, are often used to model oxide metal systems at the atomic level. These approaches can qualitatively describe the kinetics of some processes but not the overall stability of individual phases. In this article, we propose a thermodynamic approach to study equilibrium in multi-phase systems, which can be sequentially enhanced by considering different defects and microstructures. We estimate the thermodynamic equilibrium by minimization of the free energy of the whole multi-phase system using a limited set of defects and microstructural objects for which the properties are calculated by DFT. As an example, we consider Y₂O₃ + bcc Fe with vacancies in both the Y₂O₃ and bcc Fe phases, Y substitutions and O interstitials in Fe, Fe impurities, and antisite defects in Y₂O₃. The output of these calculations is the thermal equilibrium concentration of all the defects for a particular temperature and composition. The results obtained confirmed the high temperature stability of yttria in iron. Model development toward more accurate calculations is discussed.