Electronic structure of a single oxygen vacancy in rutile TiO2

Summary I report calculations of the electronic structure of an ideal (undistorted) oxygen vacancy in rutile TiO₂ using the equation-of-motion method. I use a full phenomenological tight-binding Hamiltonian due to Vos to describe the electronic structure. The bulk band structure is also discussed in detail using the traditional Green’s-function method. I illustrate an efficient way to calculate the perfect-crystal Green’s-function matrix elements for any structure, including those that belong to non-symmorphic space groups. The results show that the oxygen vacancy in rutile TiO₂ results in deeply localized states in its vicinty.     

The defect structure of silver-doped CdS

High-temperature Hall effect measurements are carried out on CdS doped with 2·5 × 10¹⁷?2·3 × 10²⁰ Ag cm^?3 under various cadmium and sulfur pressures. At high p_cd and low silver concentrations, Ag acts as a donor. At higher concentrations self compensation occurs. An anomalous variation of the Hall coefficient with p_s2 indicates that the electron concentration increases with increasing p_s2. This is attributed to the formation of anti structure defects S_cd. A complete defect model is proposed, and published solubility and diffusion data for Ag in CdS in equilibrium with (Ag, Cd) alloys are reinterpreted on the basis of this model.     

Point,linear and extended defect structures in nonstoichiometric rutile

TiO_2-x crystals (0 < x ≤ 0.0035) prepared at 1323 K and given controlled thermomechanica treatment were examined by high-resolution electron microscopy (HREM). Crystallographic shear planes (CSP) were not present in non-deformed specimens quenched from 1323 K but appeared, mostly as closely-spaced pairs, in slowly-cooled or deformed and reduced specimens. Lateral and longitudinal disorder in the fine structure of the CSP, which was strongly dependent upon cooling rate was observed. Platelet defects, approximately parallel to {100}, formed at about 400–600°C. Defects intermediate in size between point defects and CSP were also discovered. In situ observations revealed some details of the mechanisms of formation and dissolution of CSP and platelets.

New interstitial cation structural models were derived using the above observations and electrostatic energy arguments. Linear defects, consisting of two face-shared pairs of octahedra containing trivalent cations are proposed. These have very much lower formation and migration energies than the traditional model. Diffusion mechanisms were derived which allow the linear defects to aggregate and readily form pairs of CSP or platelets without the necessity to nucleate dislocation loops.     

The defect structure of calcia stabilized zirconia

Theoretical techniques have been used to examine the two models proposed for the defect structure of stabilized zirconias. The first model is based on simple clusters of dopant ions and the charge compensating oxygen vacancies, while the second suggests that fluorite-related microdomains form within the host lattice.

We show that the energies of formation of the clusters and microdomains are almost equal, the microdomain being favoured by 0.09 eV per dopant ion. Thus the calculations suggest that both point defects and microdomains may be present, with point defects predominating at low dopant concentration and higher temperatures.     

Electron structure of “oxygen vacancy” defect in SiO2

Electron structure calculations of the bulk defects, connected with oxygen vacancies in SiO₂ have been performed by the non-empirical discrete variational method. Two models of E′₁-center are analyzed, the first considering the unpaired electron in the planar SiO₃ fragment and the second in the pyramidal one (“asymmetrically relaxed vacancy”). The comparison of calculation results with ESR and optical data gives evidence in favour of the asymmetrical relaxation model.     

The effects of plastic deformation on band gap, electronic defect states and lattice vibrations of rutile

The extensive polygonization of 200 nm rutile crystals in high-energy dry milling allowed to study the spectral properties of grain boundaries and adjacent microstrained crystalline matter. Changes in UV, VIS, NIR, IR and FIR spectra during milling were followed. For the UV absorption edge the value of unstrained rutile was retained while residual traces of anatase, intergrown with the rutile phase, continued to act as traps for photoinduced charges. The evolving broad absorption in VIS and NIR could be attributed to electrons weakly bound to defects in the packing of oxygen anions at the grain boundaries, which may relax to face-sharing Ti³⁺-O octahedra. Among the IR-active lattice vibrations, the narrow E_u⁽²⁾ band showed a shift to higher frequencies by 15 cm⁻¹ which is definitively not due to phonon confinement or Fröhlich surface modes but probably to coupling of the bulk phonon to a plasmon at the grain boundary. At the external surface of the polygonized primary particle, the regular atomic order is destroyed by milling so that hydroxylation is replaced by physisorption of H₂O, as shown by IR and TG.     

金红石相和锐钛矿相TiO2本征缺陷的第一性原理计算

采用第一性原理的计算方法, 分别研究了金红石相和锐钛矿相TiO₂各种缺陷态形成的类型, 以及几何结构、生长气氛和Fermi能级位置对缺陷形成能的影响, 从理论上预测产生点缺陷的实验条件. 重点是讨论带电点缺陷的形成能, 并对结果进行适当修正. 研究发现, 本征缺陷的类型和浓度对 TiO₂的性能有一定的影响: 在富O条件下, TiO₂容易形成V_Ti(Ti空位)缺陷; 在富Ti条件下, TiO₂的Ti_i⁴⁺和V_O(O空位)缺陷将大量出现, 形成Schottky缺陷.     

Optical properties of germanium dioxide in the rutile structure

We present first-principles calculations for the optical properties of germanium dioxide in the rutile structure. The electronic band structure has been calculated self-consistently within the local density approximation using the full-potential linearized augmented plane wave method. The electronic band structure shows that the fundamental energy gap is direct at the center of the Brillouin zone. The determinant role of a band structure computation with respect to the analysis of the optical properties is discussed.     

Phase stability and structure of alkali doped-beta-gallia rutile intergrowths

The incorporation of alkali cations into the tunneled structure of Ga₄TiO₈ was investigated and compared to predictions based on atomistic computer simulations. Samples were prepared as A_xGa_4−xTi_1−xO₈, A=Li, Na, and K, x ≤ 0.7, and as Na_xGa_4+xTi_2−xO₁₀ (x = 0.7, 0.85, and 1.0) using solid-state reactions at 1050–1350 °C. The sodium-containing tunneled structure, Na_xGa_4−xTi_1−xO₈, formed via solid-state reaction, but the potassium and lithium analogs did not. Instead, these systems formed mixed-phase assemblages, which are discussed in reference to compatibility triangles in the Li₂O–Ga₂O₃–TiO₂ and K₂O–Ga₂O₃–TiO₂ systems. Experimental results were compared to the results of energy minimization calculations using the General Utility Lattice Program (GULP). For the lithium-containing system, the computer simulations correctly predicted the formation of a mixed-phase assemblage containing LiGa₅O₈, Ga₂O₃, and TiO₂. For the sodium- and potassium-containing system, the computer simulations suggested that mixtures of the single-cation oxide components should be the stable phase assemblages, in contradiction with experimentally observed results. Energy minimization calculations conducted on structurally different Na_xGa_4+xTi_2−xO₁₀ and Na_xGa_4+xTi_3−xO₁₂ phases indicated that those based on the n = 6 and n = 7 β-gallia rutile intergrowth structures have lower lattice energies than the experimentally observed sodium titanogallate structures reported previously in literature.     

The anomalous thermal expansion of VO2 crystal with the rutile structure

The large coefficient of thermal expansion parallel to the c-axis in the rutile phase of VO₂ is explained using the phonon-softening model of the metal-insulator transition.     

Effects of oxygen vacancy location on the electronic structure and spin density of Co-doped rutile TiO2 dilute magnetic semiconductors

According to density functional theory （DFT） using the plane wave base and pseudo-potential, we investigate the effects of the specific location of oxygen vacancy （Vo） in a （Ti,Co）06 distorted octahedron on the spin density and magnetic properties of Co-doped rutile Ti02 dilute magnetic semiconductors. Our calculations suggest that the Vo location has a significant influence on the magnetic moment of individual Co cations. In the case where two Co atoms are separated far away from each other, when the Vo is located at the equatorial site of a Co-contained octahedron, the ground state of the two Co cations is d6（t3g↑, t23g ↓） without any magnetic moment. However, if the Vo is located at the apical site, these two Co sites have different ground states and magnetic moments. The spin densities are also observed to be modified by the exchange coupling between the Co cations and the location of Vo. Some positive spin polarization is induced around the adjacent O ions.     

A study of oxygen self-diffusion in the C-direction of rutile using a nuclear technique

Oxygen-18 has been used as a tracer to study diffusion in the c-direction of rutile single crystals in the temperature range 1173–1473K. The distribution of the tracer was determined by means of a nuclear technique. The diffusion coefficient can be represented in this temperature range by the equation $\text{D = 2.4 × 10}{}^{\mathrm{?6}}\text{exp}\text{?}\text{(2.826 ± 0.05) × 10}{}^5\text{RT}\text{m}{}^2\text{s}{}^{\mathrm{?1}}$. A diffusion coefficient obtained at 1673 K using a different technique agrees well with the value obtained by extrapolation from the other results. Consideration of the results from specimens with different impurity concentrations leads to the conclusion that the diffusion which has been studied is extrinsic.The results obtained in this investigation are in good agreement with those of Haul and Dümbgen[l] and (by extrapolation) Gruenwald and Gordon [2] but not with those of Doskocil and Pospisil[3] and Bagshaw and Hyde[4].