Oxygen Vacancies in Oxides
Oxygen vacancies are point defects that control ionic conductivity, reducibility and much of the chemistry of transition metal and rare earth oxides. In calculations, the vacancy formation energy is usually defined as the energy of the defective cell plus a reference oxygen energy (often half of gas-phase O2) minus the energy of the perfect cell. Because periodic images of the vacancy interact, the value depends on supercell size and vacancy concentration, and it also depends on the coordination of the oxygen site removed. Vacancy migration is characterized by minimum energy paths and barriers from the nudged elastic band method, or by effective activation energies from Arrhenius fits to diffusivities from molecular dynamics (see Transport properties from molecular dynamics).
Sputter reduction and surface resistivity of TiO2(001) (2003)
In an experimental study of rutile TiO2(001), Ar+ sputtering removed surface oxygen and lowered the O/Ti ratio measured by Auger spectroscopy from 2 to about 1.5 after 2500 s, while the surface resistivity measured by a four-point probe dropped in parallel. The authors connect this to the narrowing band gap of reduced titanium oxides (about 0.9 eV for TiO1.3 versus 3.1 eV for TiO2) and note that near-surface reduction during cleaning was hard to avoid, requiring extended annealing in about 10-5 Torr O2. Reoxidation by O2 at 300 K raised the resistivity irreversibly (McCormick et al. 2003). Summary: mccormick2003.
Surface vacancies on 3d perovskites and their link to O adsorption (2012)
Akhade and Kitchin computed the energy to remove an oxygen atom from BO2-terminated (001) surfaces of LaBO3 and SrBO3 (B = Sc to Cu) with GGA DFT in a small 1 x 1 cell. The vacancy formation energy was roughly linearly correlated with the dissociative O adsorption energy: as the B-site d filling decreases, adsorption strengthens and vacancies become more costly, so late transition metal perovskites are expected to form vacancies readily. Vacancies formed more easily on the SrBO3 surfaces than on LaBO3, compressive strain generally lowered the vacancy energy, and the vacancy energy also correlated with the B-site d-band center. Their PW91 trends for B = Mn, Fe, Co, Ni agreed with published DFT+U results at U = 0 but not with those using material-specific U values (Akhade 2012). Summary: akhade2012; see also Perovskite oxides.
Concentration, structure, magnetism and U in bulk perovskite vacancy trends (2014)
Curnan and Kitchin computed bulk oxygen vacancy formation energies of LaBO3 and SrBO3 (B = Sc to Cu) with PBE, referenced to O2 with a 1.36 eV/O2 overbinding correction. Diluting a single vacancy from 1 x 1 x 1 to 2 x 2 x 2 cubic cells (delta = 1 to 0.125) changed magnitudes, sometimes abruptly at end points such as Sc, which they attribute to removing vacancy self-interaction between periodic images, but it did not change the ordering across B. Rhombohedral and orthorhombic distortions raised vacancy energies nearly uniformly, and the two inequivalent Pbnm oxygen sites differed by at most 0.13 eV. Ferromagnetism could change ordering with concentration (SrMnO3 versus SrFeO3), while AFM orderings did not. A Hubbard U on the B 3d states reordered several neighboring pairs at U values of about 3.5 to 6 eV, below the linear response U values they computed, so the authors conclude that concentration and structure can be simplified when only ordering matters, but magnetism and U cannot (Curnan 2014). Summary: curnan2014; see also Perovskite oxides.
Vacancies in strained rutile and its polymorphs (2015)
Xu and Kitchin computed bulk vacancy formation energies at 6.25% vacancy concentration for strained rutile RuO2, RhO2, IrO2 and PtO2 and for their anatase, brookite, columbite and pyrite polymorphs. Both compressive and tensile strain of rutile made vacancy formation much more exothermic, attributed to the extra relaxation an unstable strained lattice can undergo around a vacancy. The polymorphs, relaxed at their own equilibrium volumes, generally had more endothermic vacancy energies than highly strained rutile, and unlike strained rutile they did not follow a single correlation between vacancy and O adsorption energies. The authors argue that this lets polymorphs vary adsorption strength without giving up stability in reactive environments (Xu 2015). Summary: xu2015a; see also Oxide polymorphs.
Vacancies in zirconia polymorphs from a neural network potential (2018)
For ZrO2, Wang, Tharval and Kitchin found PBE formation energies in the cubic phase that dropped from 5.89 to 5.64 eV as the supercell grew, consistent with repulsive vacancy interactions. Values for the other polymorphs were roughly 5.8 to 6.1 eV, depending on the phase and the oxygen site coordination. A neural network potential trained on these data matched the cubic, tetragonal and orthorhombic Pnma values within 0.07 eV but underestimated the monoclinic values by about 0.2 to 0.3 eV. The PBE barrier for a [100] hop in tetragonal zirconia was 2.13 eV, and MD with the network gave an effective vacancy diffusion activation energy of 0.272 eV for tetragonal zirconia between 1000 and 1800 K (Wang et al. 2018). Summary: wang2018.