Effects of Concentration, Crystal Structure, Magnetism, and Electronic Structure Method on First-Principles Oxygen Vacancy Formation Energy Trends in Perovskites
Matthew T. Curnan and John R. Kitchin, “Effects of Concentration, Crystal Structure, Magnetism, and Electronic Structure Method on First-Principles Oxygen Vacancy Formation Energy Trends in Perovskites”, The Journal of Physical Chemistry C 118(49), 28776-28790 (2014). https://doi.org/10.1021/jp507957n
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Question
Perovskite oxides are candidate oxygen carriers for chemical looping and cathodes for solid oxide fuel cells, and selecting among them requires a consistent set of oxygen vacancy formation energies across many compositions, including ones with no experimental data. Earlier DFT screens of these energies relied on several shortcuts: a single, very high vacancy concentration (one vacancy in a five-atom cubic cell), the idealized cubic structure, no magnetism, and either plain GGA or Hubbard U values fitted to experiment. This paper asks which of those simplifications change the ordering of vacancy formation energies across a series of perovskites that share an A cation, and which only shift the values (Curnan 2014).
Approach
Bulk vacancy energies (per O, referenced to half of a gas-phase O2 molecule with a 1.36 eV/O2 overbinding correction) were computed with VASP, PBE and PAW potentials (550 eV cutoff, 6 x 6 x 6 k points per unit cell, Birch-Murnaghan fits for ground-state volumes). The baseline survey covered cubic ABO3 with A = La, Sr, Ba, K (Na also appears in one figure) and B = Sc to Cu. Concentration was probed with single vacancies in cubic 1 x 1 x 1, 1 x 1 x 2, 2 x 2 x 1 and 2 x 2 x 2 cells (delta = 1, 0.5, 0.25, 0.125). Structure was probed with 10-atom rhombohedral (R-3c) and 20-atom orthorhombic (Pbnm) cells compared with cubic cells of the same size, including both inequivalent oxygen sites (4c and 8d) in Pbnm. Magnetism was probed with ferromagnetic (FM) states across all of these cells and with A-, C- and G-type antiferromagnetic (AFM) orderings in 2 x 2 x 2 cells. For the electronic structure method, constant Dudarev U values were swept on paramagnetic systems (0 to 12 eV on La 4f, 0 to 8 eV in 0.5 eV steps on B 3d), and linear response U values were then computed in Quantum ESPRESSO with ultrasoft pseudopotentials for the pairs where the ordering changed.
Key findings
In the simplest cubic GGA survey the vacancy energies were roughly monotonic with B-site d filling over an A-site-dependent range, and perovskites whose A cations share a valence gave very similar trends, implying the A cation matters mainly through its oxidation state. Diluting the vacancy changed magnitudes, most strongly from the 1 x 1 x 1 cell to larger cells and at end points such as Sc, but not the ordering; the authors attribute the large jumps to removal of vacancy self-interaction between periodic images, and SrBO3 values converged more uniformly than LaBO3. Rhombohedral and orthorhombic distortions raised vacancy energies nearly uniformly relative to same-size cubic cells while preserving ordering, and the 4c and 8d sites differed by at most 0.13 eV. The distorted stoichiometric phases were lower in energy than cubic ones, so the authors suggest that easier vacancy formation at high temperature largely reflects the loss of these distortions.
Magnetism was the first factor to change ordering. In FM cubic cells of 20 atoms or more, LaVO3 dropped abruptly and changed the ordering between LaTiO3 and LaCrO3, but the Pbnm cell retained the original order, so the authors judge this an artifact of the cubic model. In FM SrBO3, SrMnO3 fell gradually with dilution and crossed SrFeO3, a change reproduced in Pbnm, though FM SrMnO3 is said to be stable only under large epitaxial strain. AFM states preserved ordering; the 2 x 2 x 2 cells found C-type LaVO3 and G-type LaCrO3 favored as in experiment, and C-type rather than the experimental A-type LaMnO3, with a 0.4 eV difference between the two that is small relative to gaps between neighbors in the trend.
Adding U to La 4f had no significant effect. Adding U to B 3d produced ordering swaps for LaVO3/LaCrO3 and LaMnO3/LaFeO3 between U = 3.5 and 4.0 eV, LaCoO3/LaNiO3 between 4.0 and 4.5 eV, SrCrO3/SrMnO3 between 4.0 and 4.5 eV, and SrCoO3/SrNiO3 near 6.0 eV; no swaps reversed at higher U. Linear response gave U = 6.2 (LaVO3), 10.7 (LaCrO3), 8.4 (LaMnO3), 7.0 (LaFeO3), 6.6 (SrCrO3) and 7.7 eV (SrMnO3), well above the thresholds. Because a 3.5% tensile change in lattice constant shifted computed U by up to 0.5 eV, and pseudopotential choice can change U by up to 1.0 eV, the authors conclude that the LaVO3/LaCrO3 and LaMnO3/LaFeO3 swaps occur, while the SrCrO3/SrMnO3 and (using literature U values of 7.0 and 5.7 eV) LaCoO3/LaNiO3 swaps likely occur.
Significance
The paper gives a practical hierarchy for perovskite vacancy screening: concentration and crystal structure mostly shift trends uniformly and can be simplified when only ordering matters, magnetism must be checked case by case with growing supercells, and the correction for 3d electron interaction can reorder materials and should be assessed by sweeping U and comparing with first-principles U values (Curnan 2014).