Due to their mixed ionic-electronic conduction (MIEC) properties, advanced functional materials like La_1-xSr_xFeO_3-δ (LSF) are being explored for a variety of fuel cell, catalyst, and other electrochemical applications.^1–3 The ionic conductivity of MIEC materials depends on their oxygen vacancy concentration and ionic mobility; quantities which both depend on the Fe charge state and hence vary with the LSF La/Sr ratio. Past modeling work has shown that a distribution in the Fe charge state, originated by the different d-orbital splitting in octahedral (Oh) and square pyramidal (SP) Fe-O polyhedra, exists in cubic SrFeO₃.⁴ Further, this d-orbital splitting ensures that the two electrons left behind when a charge-neutral oxygen vacancy forms do not transfer to the Fe atoms directly connected to the oxygen vacancy (as one might expect), but instead are transferred to the second nearest neighbors in cubic SrFeO₃.⁴ This new “long-range charge transfer” mechanism results in large oxygen vacancy polaron sizes that cause strong oxygen vacancy interactions and an increase in the oxygen vacancy formation energy with increasing oxygen vacancy site fraction. The objective of the present work was to examine the impact of lanthanum doping on 1) this oxygen vacancy formation behavior and 2) the oxygen vacancy migration behavior of a variety of LSF compositions.

Here, 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 Fe from 2+ to 4+ (U = 3 was selected, as done previously).⁴ The charge state of Fe in different LSF phases was then determined by interpreting the DFT-predicted Fe magnetic moment. The oxygen vacancy formation energy as a function of oxygen non-stoichiometry (δ) was then calculated at 0K in vacuum by varying the size of the supercell, with oxygen vacancy interactions being enabled by the periodic boundary conditions. The oxygen vacancy concentration (c) at elevated temperatures at an oxygen partial pressure of 0.21 atm was then determined using a previously developed thermodynamic model.⁴ Next, the oxygen migration barriers between all the possible oxygen vacancy sites in each material were calculated and compared at 0K. The oxygen vacancy diffusivity (D) at elevated temperature and an oxygen partial pressure of 0.21 atm was then determined by assuming Arrhenius behavior of the diffusion coefficient and a temperature and oxygen partial pressure independent migration energy. Lastly, the ionic conductivity was determined from the oxygen vacancy concentration and the diffusivity by applying Einstein’s relation and the definition of the ionic conductivity.

For all modeled LSF compositions (i.e. cubic SrFeO₃, rhombohedral La_0.5Sr_0.5FeO₃, cubic La_0.5Sr_0.5FeO₃, and orthorhombic LaFeO₃), the oxygen vacancies remained dilute (i.e. they did not interact) when the oxygen nonstoichiometry (δ) was < 0.1. When δ > 0.1, the oxygen vacancy formation energy was observed to increase for SrFeO₃ and La_0.5Sr_0.5FeO_3-δ with increasing δ. However, the oxygen vacancy formation energy in LaFeO₃ remained constant for δ = 0 to 0.25.

The calculated oxygen migration barriers for cubic SrFeO₃ were 0.58 and 0.62 eV at δ = 0.04 and 0.13, respectively. Due to the presence of multiple oxygen vacancy migration paths in tetragonal and orthorhombic strontium ferrite, the minimum energy path was considered (the migration paths in Figure 1 are designated by different Wyckoff positions traversed by the oxygen atoms). For tetragonal and orthorhombic strontium ferrites the migration barriers were 0.77 and 1.17 eV, respectively. In LaFeO_3, the calculated oxygen vacancy migration barrier was 0.88 eV which is comparable to the 0.77 eV observed in oxygen tracer diffusion experiments.⁵

Additional work aimed at calculating the oxygen vacancy formation energies, migration barriers, and ionic conductivities of other LSF compositions are in progress.

References

1. Hombo et al., J. Solid State Chem., 84, 138 (1990).

2. Maiya et al., Solid State Ion., 99, 1 (1997).

3. Yang et al., Solid State Ion., 249, 123 (2013).

4. Das et al., J Mater Chem A , In Press, http://dx.doi.org/10.1039/C6TA10357J  (2017).

5. Ishigaki et al., J. Solid State Chem., 73, 179 (1988).