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.  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.  The output of these calculations is the thermal equilibrium concentration of all the defects for a particular temperature and composition. 
THERM