Long Range Charge Transfer and Oxygen Vacancy Interactions in Strontium Ferrite

Abstract

Introduction Mixed Ionic Electronic Conducting (MIEC) perovskite materials are used for high-performance gas separation membranes,1 gas sensing electrodes,2 solid oxide fuel cell (SOFC) catalysts,3 and photoelectrodes.4 SrFeO3-δ is a prototypical member of this perovskite family possessing large oxygen vacancy and electronic carrier concentrations due to the reaction:5 Oo x = Vo ** +2e/ +1/2O2(g) (1) Unfortunately, even though SrFeO3-δ shows a large variation in oxygen nonstoichiometry (0-0.5) over a broad temperature range (0 – 1400 oC) in air,6 vacancy-ordering-induced phase transitions (from cubic to tetragonal to orthorhombic to brownmillerite, with increasing temperature) decrease the oxygen ion conductivity through a reduction in the number of mobile oxygen sites.6 In this study, a combined density functional theory (DFT) + thermodynamics approach was used to reveal the relationship between oxygen vacancy formation and the charge states of Fe in various SrFeO3-δcrystal structures as the oxygen nonstoichiometry was varied from 0-0.5. Computational Methods Here a DFT based approach with the GGA+U method implemented in VASP was utilized for the energy calculations. A U parameter of 3 was selected based on computational agreement with the experimental magnetic moments and lattice parameters of perfect SrFeO3 and LaFeO3 (indicating that this U paramter could be used to describe both Fe4+ and Fe3+ in these structures). A total Bader charge analysis was not able to differentiate the charge states of Fe in these structures. Therefore, a linearly-interpolated magnetic moment interpreted iron oxidation state was determined by assigning the calculated magnetic moments of Fe in SrFeO3 (3.61 μB) and Fe in LaFeO3 (4.23 μB) to a Fe charge of 4+ and 3+ respectively. As shown in Figure 1, the Fe oxidation state change caused by the operation of Eqn. 1 was determined using a 4x4x4 supercell. After determining the oxygen vacancy formation site within each SrFeO3-δstructure (i.e. the site with the lowest oxygen vacancy formation energy), the supercell size was varied to calculate the vacancy formation energy at various oxygen vacancy site fractions. A thermodynamic method was then developed to predict the oxygen vacancy site fraction and oxygen nonstoichiometry at SOFC-relevant temperatures and oxygen partial pressures. Results and Discussion Perfect cubic SrFeO3 contains all its Fe in octahedral coordination with 4+ charge and no tilt exists between these octahedra. As shown in Figure 1, the formation of a single oxygen vacancy in cubic SrFeO3 creates two square pyramidal Fe-O coordination polyhedra adjacent to an oxygen vacancy. Further, the computational results show that within each SrFeO3-δ structure, oxygen vacancies are always formed at the site shared by the two highest charged Fe atoms. Figure 1 also illustrates a new long-range charge transfer phenomena whereby electrons left by the oxygen vacancy are transferred to the second nearest neighbor iron atoms (not those directly connected to the oxygen vacancies). This long-range charge transfer causes strong oxygen vacancy interactions that 1) lead to the oxygen formation energy increasing with oxygen nonstoichiometry and 2) contribute to oxygen vacancy induced phase transformations. To fully describe the interacting oxygen vacancies, a new numerical method treating both dilute and non-dilute point defect concentrations was developed. The good agreement between the predicted and experimentally-reported oxygen vacancy nonstoichiometry over the 300-1300oC range in air demonstrates the robustness of this approach. Conclusions These calculations resolve a long-standing debate in the literature on the mixed charge states of Fe in SrFeO3-δand explain the origin of the oxygen vacancy interactions in this material. Furthermore, the predicted oxygen vacancy concentration (not the total nonstoichiometry) decreases above 600˚C, causing a loss of oxygen conductivity.