Oxygen vacancy formation energies in Sr-doped complex perovskites: ab initio thermodynamic study

La 1 − x Sr x Co 0.25 Fe 0.75 O 3 − δ is known as one of the best cathode materials for permeation membranes and solid oxide fuel cells. Optimization of its chemical composition is a challenging problem. One of the key properties is concentration of oxygen vacancies, which is controlled by their formation energies. Ab initio calculations were employed in order to study the formation of oxygen vacancies in La 1 − x Sr x Co 0.25 Fe 0.75 O 3 − δ perovskites by varying the Sr content from x = 12.5% to 50%. The formation energies were obtained for different stoichiometries as functions of temperature and oxygen partial pressure. For this purpose we calculated the phonon frequencies in the solid phase and the chemical potential of oxygen. We have shown that the phonon contribution to the free energy of formation becomes increasingly important in La 1 − x Sr x Co 0.25 Fe 0.75 O 3 − δ not only with rising temperature but also with rising Sr content. We find that the formation energies decrease significantly with increasing Sr content due to the phonon contribution. A simple explanation is proposed for the increasing role of phonons in the oxygen vacancy formation energies on the basis of phonon mode changes in comparison to defect-free materials. A careful analysis of the experimental results from the literature is also presented.