First principles calculations of oxygen vacancy formation in barium-strontium-cobalt-ferrite

Abstract

Perovskite-type barium-strontium-cobalt-ferrite (BSCF) is a potentially significant material in the development of electrodes for solid oxide fuel cells and electrolysis cells, primarily because of its large oxygen vacancy concentration and mobility. Using density functional theory (DFT) with the DFT + U approach, we perform first principles calculations of oxygen vacancy formation in bulk BSCF with the composition Ba 0.5 Sr 0.5 Co 0.75 Fe 0.25 O 32d , in which a range of oxygen deficiencies (0.125 ¡ d ¡ 0.875) is investigated. Contrary to previous DFT studies for d = 0.125, DFT + U predicts that the non-stoichiometric structure is more stable than its stoichiometric counterpart with d = 0, and that this originates from a significantly different atomic and electronic structure following the introduction of the Hubbard U term in the calculations. As more vacancies are created there is no tendency for ordering and the total vacancy formation energy becomes positive and increases as the oxygen deficiency increases. Using ab initio thermodynamics, the heat of formation of BSCF as a function of oxygen partial pressure and temperature is determined and the results are in broad agreement with available stoichiometry measurements.

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“…30 For Hubbard's correction, 31,32 the U eff value was set to 4 eV and 3.32 eV for Fe and Co, respectively. 33 For all optimization calculations, the convergence criteria for energy and force were set to 10 -5 eV and 0.03 eV Å -1 , respectively. The cutoff energy was set to 520 eV, and a 4×4×4 K-point mesh gamma centred was chosen to describe the Brillouin zone.…”

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“… 52 Similarly, the structure of the Co d and Fe d states of BSCF with U = 0 ( Figure 8 B) agrees well with the DOS reported previously. 51 Figure S1 (Supporting Information) gives a complete overview of the DOS.…”

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“…The Brillouin zone integrations were approximated using the special 3 Â 3 Â 3 k-point sampling scheme of Monkhorst-Pack for the unit cell. 50 The valence electronic congurations were taken as O 2s 2 2p 4 , Fe 3d 6 4s 2 , Gd 4f 7 5s 2 5p 6 5d 1 6s 2 and Ba 5s 2 5p 6 6s 2 , for the ground state electronic structure calculations. The spin polarization calculation was adopted, and the formal spin was used as the initial one.…”