First-principles studies on the oxygen vacancy formation in α-Na 2 FePO 4 F and (3-Na2FePO4F

The orthorhombic (3- Na 2 FePO 4 F has been extensively studied, however, a novel monoclinic alpha-Na2FePO4F 2 FePO 4 F has not been explored sufficiently. Oxygen vacancies (VO) V O ) can affect the physical and chemical properties of materials, and oxygen vacancy formation energy reflects the difficulty of V O formation. Using first-principles methods, we have calculated the formation energies of V O and their relevant charge states in both alpha-Na2FePO4F 2 FePO 4 F and (3- Na 2 FePO 4 F. Our results reveal that charged vacancies ( V O +1 or V O +2 ) are easier to form than neutral vacancies (VO0). V O 0 ). The reduction of the Fermi level, the decrease in the oxygen partial pressure, or the increase of the temperature are found to decrease the formation energy of V O . The formation energy of V O in alpha-Na2FePO4F 2 FePO 4 F is slightly lower than that in (3- Na 2 FePO 4 F. The electronic density of states of alpha-Na2FePO4F 2 FePO 4 F and (3- Na 2 FePO 4 F suggest that more defect states are introduced into the band gap as the charge states increase. These defect states are mainly the 3d orbitals of the Fe atoms. The introduction of oxygen vacancies distorts the [FeO4F2] 4 F 2 ] octahedra, which affect the charge density distribution and the defect states introduced in the band gap. Significantly, oxygen vacancies have a local impact on the charge density redistribution in both alpha-Na2FePO4F 2 FePO 4 F and (3- Na 2 FePO 4 F. These findings provide theoretical insights into the formation of oxygen vacancies and the control of oxygen release.