Previous calculations demonstrated that the Fe atom charge state distribution observed in strontium ferrite (SrFeO3-δ) is caused by differences in the d-orbital splitting of octahedral (Oh) versus square pyramidal (SP) Fe-O coordination (Figure 1).5 This d-orbital splitting ensures that the two electrons left behind when a charge-neutral oxygen vacancy forms in cubic SrFeO3-δ are transferred to the second nearest Fe neighbors,5 resulting in a large oxygen vacancy polaron size that produces strong oxygen vacancy interactions at high oxygen nonstoichiometry. As a result, the oxygen vacancy formation energy increases with oxygen nonstoichiometry in cubic SrFeO3-δ.5 Previous calculations also demonstrated that in orthorhombic lanthanum ferrite (LaFeO3-δ) the formation of a neutral oxygen vacancy produces a polaron that is localized to the oxygen-vacancy-adjacent Fe atoms. Hence, in orthorhombic LaFeO3-δ the oxygen vacancies do not interact with increasing oxygen nonstoichiometry.6
The objective of the present work was to examine whether d-orbital splitting could also explain the oxygen vacancy behavior of other MIEC perovskites. Hence, the impact of d-orbital splitting on oxygen vacancy polaron size and formation energies in lanthanum strontium manganite and lanthanum strontium cobaltite were modeled for the first time.
Here, the charge redistribution caused by oxygen vacancy formation was studied for six different compositions: LaFeO3-δ, SrFeO3-δ, LaMnO3-δ, SrMnO3-δ, LaCoO3-δ, and SrCoO3-δ. The GGA+U method with PAW potentials implemented in VASP was utilized for all the structural energy calculations. First, the Hubbard-U parameter was calibrated to describe the charge on the B-site atom (U = 3 was selected for Fe, as done previously).6 The oxygen vacancy formation energy as a function of oxygen non-stoichiometry (δ) was then calculated at 0 K in vacuum by varying the size of the supercell, with oxygen vacancy interactions being enabled by the periodic boundary conditions.
The calculated polaron size for neutral-oxygen-vacancy–containing ABO3 structures are summarized in Table 1.In LaMnO3-δ, Mn3+ has an [Ar] 3d4 electronic configuration in Oh coordination. After the formation of a neutral oxygen vacancy, the two Mn atoms adjacent to the oxygen vacancy go from Oh to SP coordination and the excess electrons left behind by the removed oxygen are pushed to the a1g level of the second nearest neighboring Oh-Mn (instead of remaining localized to the b1g level of the SP-Fe). This long range charge transfer results in large polaron size. This behavior is in contrast with that of LaFeO3-δ. However, LaMnO3-δ and SrFeO3-δ exhibit comparable polaron sizes since Fe4+ has an [Ar] 3d4 electronic- configuration. In SrMnO3-δ, Mn4+ has a [Ar] 3d3 electronic configuration in Oh coordination. Therefore, the formation of a neutral oxygen vacancy localizes the electrons to the oxygen vacancy adjacent Mn atoms, producing a small polaron, as explained by the d-orgbial splitting in Figure 1. This d-orbital splitting analysis indicates that the polaron size in LSM > LSF > LSC. Additional work aimed at calculating the oxygen vacancy formation energies of other ABO3 compositions are in progress.
1. C. H. Kim, G. Qi, K. Dahlberg, and W. Li, Science, 327, 1624–1627 (2010).
2. E. D. Wachsman and K. T. Lee, Science, 334, 935–939 (2011).
3. Jason D. Nicholas, Electrochem. Soc. Interface, 49 (2013).
4. J. Mizusaki, T. Sasamoto, W. R. Cannon, and H. K. Bowen, J. Am. Ceram. Soc., 66, 247–252 (1983).
5. T. Das, J. D. Nicholas, and Y. Qi, J. Mater. Chem. A, 5, 4493–4506 (2017).