Lithium intercalation into TiO2(B): A comparison of LDA, GGA, and GGA+U density functional calculations

Density functional theory has been used to study lithium intercalation into TiO2(B) at low to moderate concentrations (0 < x(Li) ≤ 0.25) with a range of density functionals: LDA, GGA (PW91, PBE, PBEsol), and GGA+U (PBE+U, PBEsol+U), with the GGA+U calculations employing a Hubbard +U correction to the Ti d states. LDA and GGA functionals give the same general behaviour, whereas qualitatively different behaviour is predicted by GGA+U for electronic structure and the order of stability of occupied intercalation sites. LDA/GGA functionals predict LixTiO2(B) to be metallic, with the excess charge distributed over all the Ti sites. In contrast, GGA+U predicts defect states in the band gap corresponding to charge strongly localised at specific Ti sites. All the considered functionals predict A1 and/or A2 site occupation at x(Li)=0.25, which challenges the interpretation of previous neutron data that at this composition the C site is preferentially occupied.

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Analysis of Intrinsic Defects in CeO2 Using a Koopmans-Like GGA+U Approach

Spin-density for a Ce vacancy, with U applied to O and Ti states, to give a defect state localised as four oxygen holes.We have investigated the formation of intrinsic defects in CeO2 using density functional theory with the generalized gradient approximation (GGA) corrected for on-site Coulombic interactions (GGA+U). We employed an ab initio fitting procedure to determine a U {O2p} value that satisfies a Koopmans-like condition and obtained a value of U {O2p} = 5.5 eV. We subsequently demonstrated that by applying GGA+U to the O2p states, in addition to the Ce 4f states, we were able to model localized holes in addition to localized electrons, thus improving the description of p-type defects in CeO2. Our results show that under oxygen-poor conditions the defects with the lowest formation energy are oxygen vacancies, while oxygen interstitials, which form peroxide ions, will be more favorable under oxygen-rich conditions. We carried out temperature and pressure dependence analyses to determine the relative abundance of intrinsic defects under real-world conditions and determined that oxygen vacancies will always be the dominant defect. Furthermore, we determined that at the dilute limit none of the defects studied can account for the intrinsic ferromagnetism that has been observed in nanosized CeO2.

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Chemical Bonding in Copper-Based Transparent Conducting Oxides: CuMO2 (M = In, Ga, Sc)

The geometry and electronic structure of copper-based p-type delafossite transparent conducting oxides, CuMO2 (M = In, Ga, Sc), are studied using the generalized gradient approximation (GGA) corrected for on-site Coulomb interactions (GGA + U). The bonding and valence band compositions of these materials are investigated, and the origins of changes in the valence band features between group 3 and group 13 cations are discussed. Analysis of the effective masses at the valence and conduction band edge explains the experimentally reported conductivity trends.

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The Role of Lithium Ordering in the LixTiO2 Anatase → Titanate Phase Transition

The mechanism of the tetragonal to orthorhombic phase separation of Li-intercalated anatase TiO2 has previously been proposed to be a cooperative Jahn-Teller distortion due to occupation of low-lying Ti 3dxz,yz orbitals. 1 Using density functional calculations we show that the orthorhombic distortion of Li0.5TiO2 is not a purely electronic phenomenon, and that intercalated Li plays a critical role. For a 2×1×1 expanded supercell for 0 ≤ x(Li) ≤ 1, the intercalation voltage is minimized for x(Li) = 0.5. The low energy structures display a common structural motif of edge-sharing pairs of LiO6 octahedra, that allows all Li to adopt favourable oxygen coordination. Long-ranged disorder of these sub-units explains the apparent random Li distribution seen in experimental diffraction data.

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The Origin of the Enhanced Oxygen Storage Capacity of Ce1-x(Pd/Pt)xO2

Doping CeO2 with Pd or Pt increases the oxygen storage capacity (OSC) and catalytic activity of this environmentally important material. To date, however, an understanding of the mechanism underlying this improvement has been lacking. We present a density functional theory analysis of Pd- and Pt-doped CeO2, and demonstrate that the increased OSC is due to a large displacement of the dopant ions from the Ce lattice site. Pd(II)/Pt(II) (in a d8 configuration) moves by ~1.2 Å to adopt a square-planar coordination due to crystal field effects. This leaves three three-coordinate oxygen atoms that are easier to remove, and which are the source of the increased OSC. These results highlight the importance of rationalising the preferred coordination environments of both dopants and host cations when choosing suitable dopants for next generation catalysts.

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GGA+U Description of Lithium Intercalation into Anatase TiO2

We have used density-functional theory [generalized gradient approximation (GGA)] to study lithium intercalation at low concentration into anatase TiO2. To describe the defect states produced by Li doping a Hubbard “+U” correction is applied to the Ti d states (GGA+U). Uncorrected GGA calculations predict LixTiO2 to be metallic with the excess charge distributed over all Ti sites, whereas GGA+U predicts a defect state 0.96 eV below the conduction band, in agreement with experimental photoelectron spectra. This occupied defect state corresponds to charge strongly localized at a single Ti 3d site neighboring the intercalated lithium with a magnetization of 1 μB. This polaronic state produces a redshifted optical absorption spectrum, which is compared to those for the native O-vacancy and Ti-interstitial defects. The strong localization of charge at a single Ti center lowers the symmetry of the interstitial geometry relative to that predicted by GGA. The intercalated lithium sits close to the center of the octahedral site, occupying a single potential energy minimum with respect to displacement along the [001] direction. This challenges the previous interpretation of neutron diffraction data that there exist two potential energy minima separated by 1.6 Å along the [001] direction within each octahedron. Nudged elastic band calculations give barriers to interoctahedral diffusion of ~0.6 eV, in good agreement with experimental data. These barrier heights are found to depend only weakly on the position of the donated electron. The intercalation energy is 2.14 eV with GGA and 1.88 eV with GGA+U, compared to the experimental value of ~1.9 eV. Li-electron binding energies have also been calculated. The [Lii-Ti′Ti] complex has a binding energy of 56 meV, and a second electron is predicted to be bound to give [Lii-2Ti′Ti] with a stabilization energy of 30 meV, indicating that intercalated lithium will weakly trap excess electrons produced during photoillumination or introduced by additional n-type doping.

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A First-Principles Study of Epitaxial Strain as a Method of B4 to BCT Stabilisation in ZnO, ZnS, and CdS

Density-functional-theory calculations have been used to examine stabilization of the low density BCT polymorph by epitaxial strain. The relative energies of B4 and BCT polymorphs were calculated for ZnO, ZnS, and CdS, as a function of epitaxial strain, for a B4[0001]||BCT[010]/B4[1-210]||BCT[001] correspondence. The phase stability is mapped in \({u,v}\) parameter space and the challenge of identifying a suitable epitaxial support to direct growth of the BCT phase is discussed. For ZnS, ZnSe, ZnTe, CdS, and CdSe, the optimized “BCT” geometry is orthorhombically distorted, in contrast to the tetragonal lattices of ZnO, CdO, and InN. This orthorhombic distortion is associated with a rotation of the four-membered rings in the BCT structure, and is enhanced in ZnO, ZnS, and CdS under epitaxial strain.

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Intrinsic n-type Defect Formation in TiO2: A Comparison of Rutile and Anatase from GGA+U Calculations

The formations of intrinsic n-type defects, that is, oxygen vacancies and titanium interstitials, in rutile and anatase TiO2 have been compared using GGA+U calculations. In both crystal structures, these defects give rise to states in the band gap, corresponding to electrons localized at Ti3+centers. O vacancy formation in rutile results in two excess electrons occupying 3d orbitals on Ti atoms neighboring the vacancy. Similarly, for anatase, two Ti 3d orbitals are occupied by the excess electrons, with one of these Ti sites neighboring the vacancy, and the second at a next-nearest Ti position. This localization is accompanied by one oxygen moving toward the vacancy site to give a “split vacancy” geometry. A second fully localized solution is also found for anatase, with both occupied Ti sites neighboring the vacancy site. This minimum is 0.05 eV less stable than the split vacancy and is thus expected to be present in experimental samples. A partially delocalized solution corresponding to the split vacancy geometry, with one electron occupying the bottom of the conduction band, is also identified as 0.28 eV less stable. Formation of titanium interstitials donates four electrons to the Ti lattice. In anatase, one of these electrons is located at the interstitial Ti site, and three occupied defect states are hybridized between three nearest neighbor Ti sites. In rutile, these excess electrons are mostly localized at four nearest neighbor Ti sites, with only a small amount of excess charge found on the interstitial Ti atom. This difference in the charge on the interstitial atom is a consequence of the differing interstitial geometries in the two polymorphs. Calculated optical absorption spectra for all defects show significant decreases of the optical band gap, with a larger red shift predicted for titanium interstitials in anatase than in rutile. Defect formation energies have been calculated under oxygen-rich and oxygen-poor conditions for both polymorphs. Under all conditions, O vacancy formation is slightly more favorable in anatase than in rutile, while Ti interstitials form more easily in rutile than anatase. Under O-rich conditions, O vacancies are the favored defect type, but both defect types have high formation energies. Under O-poor conditions, both defect types are stabilized, with Ti interstitials predicted to become the favored defect in rutile samples, particularly at elevated temperatures.

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Understanding Conductivity Anomalies in CuI-Based Delafossite Transparent Conducting Oxides: Theoretical Insights

The CuI-based delafossite structure, CuIMIIIO2, can accommodate a wide range of rare earth and transition metal cations on the MIII site. Substitutional doping of divalent ions for these trivalent metals is known to produce higher p-type conductivity than that occurring in the undoped materials. However, an explanation of the conductivity anomalies observed in these p-type materials, as the trivalent metal is varied, is still lacking. In this article, we examine the electronic structure of CuIMIIIO2 (MIII = Al, Cr, Sc, Y) using density functional theory corrected for on-site Coulomb interactions in strongly correlated systems (GGA+U) and discuss the unusual experimental trends. The importance of covalent interactions between the MIII cation and oxygen for improving conductivity in the delafossite structure is highlighted, with the covalency trends found to perfectly match the conductivity trends. We also show that calculating the natural band offsets and the effective masses of the valence band maxima is not an ideal method to classify the conduction properties of these ternary materials.

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Understanding Conductivity in SrCu2O2: Stability, Geometry, and Electronic Structure of Intrinsic Defects from First Principles

Density functional theory calculations have been performed on stoichiometric and intrinsically defective p-type transparent conducting oxide SrCu2O2, using GGA corrected for on-site Coulombic interactions (GGA+U). Analysis of the absorption spectrum of SrCu2O2 indicates that the fundamental direct band gap could be as much as 0.5 eV smaller than the optical band gap. Our results indicate that the defects that cause p-type conductivity are favoured under all conditions, with defects that cause n-type conductivity having significantly higher formation energies. We show conclusively that the most stable defects are copper and strontium vacancies. Copper vacancies introduce a distinct acceptor single particle level above the valence band maximum, consistent with the experimentally known activated hopping mechanism.

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