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We report a comprehensive first-principles study of the thermodynamics and transport of intrinsic point defects in layered oxide cathode materials LiMO$_2$ (M=Co, Ni), using density-functional theory and the Heyd-Scuseria-Ernzerhof screened hybrid functional. We find that LiCoO$_2$ has a complex defect chemistry; different electronic and ionic defects can exist under different synthesis conditions, and LiCoO$_2$ samples free of cobalt antisite defects can be made under Li-excess (Co-deficient) environments. A defect model for lithium over-stoichiometric LiCoO$_2$ is also proposed, which involves negatively charged lithium antisites and positively charged small (hole) polarons. In LiNiO$_2$, a certain amount of Ni$^{3+}$ ions undergo charge disproportionation and the concentration of nickel ions in the lithium layers is high. Tuning the synthesis conditions may reduce the nickel antisites but would not remove the charge disproportionation. In addition, we find that LiMO$_2$ cannot be doped $n$- or $p$-type; the electronic conduction occurs via hopping of small polarons and the ionic conduction occurs via migration of lithium vacancies, either through a monovacancy or divacancy mechanism, depending on the vacancy concentration.

The combination of density functional theory and single-site dynamical mean-field theory, using both Hartree and full continuous-time quantum Monte Carlo impurity solvers, is used to study the metal-insulator phase diagram of perovskite transition-metal oxides of the form $AB$O$_3$ with a rare-earth ion $A$=Sr, La, Y and transition metal $B$=Ti, V, Cr. The correlated subspace is constructed from atomiclike $d$ orbitals defined using maximally localized Wannier functions derived from the full $p$-$d$ manifold; for comparison, results obtained using a projector method are also given. Paramagnetic DFT+DMFT computations using full charge self-consistency along with the standard "fully localized limit" (FLL) double counting are shown to incorrectly predict that LaTiO$_3$, YTiO$_3$, LaVO$_3$ and SrMnO$_3$ are metals. A more general examination of the dependence of physical properties on the mean $p$-$d$ energy splitting, the occupancy of the correlated $d$ states, the double-counting correction, and the lattice structure demonstrates the importance of charge-transfer physics even in the early transition-metal oxides and elucidates the factors underlying the failure of the standard approximations. If the double counting is chosen to produce a $p$-$d$ splitting consistent with experimental spectra, single-site dynamical mean-field theory provides a reasonable account of the materials properties. The relation of the results to those obtained from "$d$-only" models in which the correlation problem is based on the frontier orbital $p$-$d$ antibonding bands is determined. It is found that if an effective interaction $U$ is properly chosen the $d$-only model provides a good account of the physics of the $d^1$ and $d^2$ materials.

We investigate the behavior of oxygen vacancies in three different metal-oxide semiconductors (rutile and anatase TiO2, monoclinic WO3, and tetragonal ZrO2) using a recently proposed hybrid density-functional method in which the fraction of exact exchange is material-dependent but obtained ab initio in a self-consistent scheme. In particular, we calculate charge-transition levels relative to the oxygen-vacancy defect and compare computed optical and thermal excitation/emission energies with the available experimental results, shedding light on the underlying excitation mechanisms and related materials properties. We find that this novel approach is able to reproduce not only ground-state properties and band structures of perfect bulk oxide materials, but also provides results consistent with the optical and electrical behavior observed in the corresponding substoichiometric defective systems.

Previous work on the physical content of exchange correlation functionals that depend on both charge and spin densities is extended to elemental transition metals and a wider range of perovskite transition metal oxides. A comparison of spectra and magnetic moments calculated using exchange correlation functionals depending on charge density only or on both charge and spin densities, as well as the $+U$ and $+J$ extensions of these methods confirms previous conclusions that the spin-dependent part of the exchange correlation functional provides an effective Hund's interaction acting on the transition metal $d$ orbitals. For the local spin density approximation and spin-dependent Perdew-Burke-Ernzerhof generalized gradient approximation, the effective Hund's exchange is found to be larger than 1 eV. The results indicate that at least as far as applications to transition metals and their oxides are concerned, $+U$, $+J$ and +dynamical mean field theory extensions of density functional theory should be based on exchange-correlation functionals of charge density only.