Vacancy induced changes in the electronic structure of titanium carbide—I. Band structure and density of states

Results of a self-consistent “Augmented Plane Wave” (APW) band-structure calculation are presented for substoichiometric titanium carbide with 25% vacancies on the carbon sublattice sites (TiC_{0 75}) assuming a model structure with ordered vacancies Comparison with an earlier APW study on stoichiometric TiC reveals that the carbon vacancies induce two pronounced peaks in the density of states (DOS), 0.4 eV below and 0.8 eV above the Fermi energy E_γ, thus forming electronic states in a region where the DOS for stoichiometric TiC exhibits a minimum So-called “vacancy states” with an important amount of charge on the vacancy site are found to be derived from Ti 3d states extending into the vacancy muffin tin sphere An angular momentum decomposition with respect to the center of the vacancy muffin tin sphere shows that the s character predominates for the occupied and the p character for the unoccupied “vacancy states” The theoretical findings explain features near E_γ, observed in recently published X-ray emission spectra Furthermore, we find a slight increase of electronic charge in the carbon muffin tin spheres as compared with stoichiometnc TiC.     

The influence of oxygen vacancies on the chemical bonding in titanium oxide

A self-consistent LAPW band structure calculation for TiO_0.75 has been performed, assuming long-range order of vacancies on the oxygen sublattice. The calculation is based on a hypothetical model structure which can be described as Ti ₃ ^[4] Ti^[6]O_3o, where _o denotes an oxygen vacancy. In the model structure two types of titanium atoms occur: Ti^[4] atoms which have two vacancies as neighbours and are quadratically surrounded by four oxygen atoms, and Ti^[6] atoms which are octahedrally surrounded by six oxygen atoms. The calculated density of states (DOS) and the local partial densities of states are compared with the respective values for stoichiometric TiO containing no vacancies. A characteristic difference is the appearance of two sharp peaks in the DOS curve below the Fermi energy which are caused by the vacancies. These vacancy states exhibit a considerable amount of charge in the vacancy muffin-tin sphere and are found to be derived from Ti 3d states extending into the vacancy sphere. The introduction of vacancies also leads to a lowering of the Fermi energy indicating a stabilizing effect. The bonding situation in TiO_0.75 as compared to TiO as well as the changes in chemical bonding in the series TiC_0.75–TiN_0.75–TiO_0.75 are discussed on the basis of electron density plots. The loss of Ti^[4]–O bonds (as compared to TiO) is compensated by the formation of Ti^[4]–_o–Ti^[4] bonds across the vacancy and by an increase of the bond strength of the Ti^[4]–O bonds. On the other hand, the Ti^[4]–Ti^[4] and particularly the Ti^[4]–Ti^[6] bonds are weakened by the introduction of vacancies.Dedicated to Professor F. Kohler on the occasion of his 65^th birthday     

Native defects and Pr impurities in orthorhombic CaTiO3 by first-principles calculations

Formation energies of native defects and Pr impurities in orthorhombic CaTiO₃ are explored using the first-principles calculations. The Ca vacancy (V_Ca), Ti vacancy (V_Ti) and Ca antisite (Ca_Ti) are found to be energetically preferable. The Ti antisite (Ti_Ca) and O vacancy (V_O) are not energetically favorable in the wide range of Fermi level. In Pr-doped CaTiO₃, Pr substituting for Ca (Pr_Ca) is likely to form under condition A in which CaTiO₃ is in equilibrium with CaO and O₂. Under condition B (TiO₂, CaTiO₃ and O₂ are in equilibrium), Pr_Ti defect is energetically preferable depending on the Fermi levels. Several native defects and the two sites of Pr impurities in CaTiO₃ are coincided with several different defects in Pr-doped CaTiO₃ reported in the literature. Based on the present calculations, we can elucidate that the Ca deficiency design of the traditional formula Ca_1−xV_Ca(x/2)Pr_xTiO₃ is not the best for efficient red photoluminescence, which is realized via the experimental measurements.     

Electronic properties of TiC(100) and polar TiC(111) surfaces

The energy bands of films of TiC have been calculated using the linear-combination-of-atomic-orbitals method with parameters obtained by a fit to the bulk band structure. The Madelung potentials and charge redistribution have been determined self-consistently. For the neutral TiC(100) surface, the density of states (DOS) is similar to that of the bulk. For the non-neutral Ti-covered TiC(111) surface, Ti 3d-derived surface states appear around the Fermi energy E_F. The long-range electric field produced by the polar surfaces is screened by the charge redistribution, and the polar surfaces are stabilized. Characteristic features of TiC(111) compared to other surfaces of TiC are attributed to the high surface DOS at E_F.     

Directionality of the metallic bonding in titanium carbide

The ionic-covalent bonding in TiC is studied within a CNDO parameterized cluster model. Distribution of charge density reveals a directionality of the Ti-Ti metal bond as observed in the Ti dimer. This directionality is particularly significant at the Fermi level because of hybridisation involving d_xy ,d_xy and d_yz types of states. However, in the presence of a carbon vacancy the directionality of the metal bond is not as clear with charge spilling over into the vacant lattice site. The directional nature of the Ti-Ti bond at the Fermi level remains fairly unchanged.     

The influence of oxygen vacancies on the electronic and magnetic properties of perovskite-like SrFeO3-x

The electronic, magnetic properties and lattice relaxations of oxygen-deficient cubic strontium ferrite, SrFeO_2.875, in ferromagnetic configuration are studied by means of the density functional theory using LCAO basis (SIESTA code) calculations. It is shown that Fe and Sr atoms are displaced from oxygen vacancies while oxygen anions are attracted to the vacancies. The DOS distributions, magnetic moments and atomic effective charges are analyzed in comparison with vacancy free SrFeO₃; these parameters are found to change weakly with appearance of oxygen vacancies, in contrast to conventional ionic picture. Some strengthening of Fe-O covalent bonds in the vicinity of the oxygen vacancy is found. The formation energy of oxygen vacancies and divacancies are evaluated.     

Electronic structures and optical properties of rutile TiO2 with different point defects from DFT + U calculations

The electronic states and formation energies of four types of lattice point defects in rutile TiO₂ are studied using the first-principles calculations. The existence of oxygen vacancy leads to a deep donor defect level in the forbidden band, while the Ti interstitial forms two local states. It is predicted that oxygen vacancy prefers to combine with Ti-interstitial to form V_O–Ti_i dimer by a partial 3d electron transfer from the Ti_i to its neighboring V_O. The charge distribution between a Ti interstitial and its neighboring Ti ions partially shields the Coulomb interactions. Lastly, optical properties of these defective lattices are discussed.     

Structure,ionic conduction,and phase transformations in lithium titanate Li<Subscript>4</Subscript>Ti<Subscript>5</Subscript>O<Subscript>12</Subscript>

The spinel structure of lithium titanate Li₄Ti₅O₁₂ is refined by the Rietveld full-profile analysis with the use of x-ray and neutron powder diffraction data. The distribution and coordinates of atoms are determined. The Li₄Ti₅O₁₂ compound is studied at high temperatures by differential scanning calorimetry and Raman spectroscopy. The electrical conductivity is measured in the high-temperature range. It is shown that the Li₄Ti₅O₁₂ compound with a spinel structure undergoes two successive order-disorder phase transitions due to different distributions of lithium atoms and cation vacancies (□, V) in a defect structure of the NaCl type: (Li)_8a[Li_0.33Ti_1.67]_16dO₄ → [Li□]_16c[Li_1.33Ti_1.67]_16dO₄ → [Li_1.33□_0.67]_16c[Ti_1.67□_0.33]_16dO₄. The low-temperature diffusion of lithium predominantly occurs either through the mechanism ... → Li(8a) → V(16c) → V(8a) → ... in the spinel phase or through the mechanism ... → Li(16c) → V(8a) → V(16c) → ... in an intermediate phase. In the high-temperature phase, the lithium cations also migrate over 48f vacancies: ... Li(16c) → V(8a, 48f) → V(16c) → ....     

Mechanical properties and electronic structure of TiC,Ti0.75W0.25C,Ti0.75W0.25C0.75N0.25, TiC0.75N0.25 and TiN

The first-principles calculations are performed to investigate the mechanical properties and electronic structure of TiC, Ti_0.75W_0.25C, Ti_0.75W_0.25C_0.75N_0.25, TiC_0.75N_0.25 and TiN. Density functional theory and ultrasoft pseudopotentials are used in this study. From the formation energy, it is found that nitrogen can increase the stability of TiC. The calculated elastic constants and elastic moduli of TiC compare favorably with other theoretical and experimental values. Tungsten and nitrogen are observed to significantly increase the bulk, shear and Young's modulus of TiC. Through the analysis of B/G and Cauchy pressure, tungsten can significantly improve the ductility of TiC. The electronic structure of TiC, TiN, Ti_0.75W_0.25C, Ti_0.75W_0.25C_0.75N_0.25, and TiC_0.75N_0.25 are used to describe nonmetal–metal and metal–metal bonds. Based on the Mulliken overlap population analysis, the hardness values of TiC, Ti_0.75W_0.25C, Ti_0.75W_0.25C_0.75N_0.25, TiC_0.75N_0.25 and TiN are estimated.     

Ab initio electronic structure,bonding and optical properties of two relatively new ceramics Hf2Al3C4 and Hf3Al3C5: A comparative study

The structural, electronic and optical properties of the ternary carbides Hf₂Al₃C₄ and Hf₃Al₃C₅ are studied via first principles orthogonalized linear combination of atomic orbitals (OLCAO) method. Results on crystal structure, interatomic bonding, band structure, total and partial density of states (DOS), localization index (LI), effective charge (Q*), bond order (BO), dielectric function (ε), optical conductivity (σ) and electron energy loss function are presented and discussed in detail. The band structure plots show the conducting nature of Hf₂Al₃C₄ and Hf₃Al₃C₅ carbides. DOS results disclose that the total number of states at Fermi level N(E_F) are 1.89 and 2.38 states/(eV unit cell) for Hf₂Al₃C₄ and Hf₃Al₃C₅ respectively. The Q* calculations show an average charge transfer of 0.723 and 0.711 electrons from Hf and 0.809 and 0.807 electrons from Al to C sites in Hf₂Al₃C₄ and Hf₃Al₃C₅ respectively. The BO results provide the dominating role of Al–C bonds with BO value of 6.62 (BO%?=?59%) and 6.66 (BO%?=?49%) for Hf₂Al₃C₄ and Hf₃Al₃C₅ respectively and are considered responsible for the crystals cohesion. The LI results reflect the presence of highly delocalized states in the vicinity of the Fermi level. The dielectric function plots of the real (?₁(?ω)) and imaginary (?₂(?ω)) parts show the anisotropic behavior of Hf₂Al₃C₄ and Hf₃Al₃C₅. The results on optical conductivity (σ) support the trends observed in dielectric functions. The electron energy loss functions reveal the presence of sharp peaks both in ab-plane and along c-axis around 20?eV in Hf₂Al₃C₄ and Hf₃Al₃C₅ ternary carbides.     

Vibrational and electronic spectra of alkali halides doped with CrO42− ions

The i.r. spectra of alkali halides doped with FrO₄^2? ions are very sensitive to the concentration of background divalent impurities. Highly pure crystals containing CrO₄^2? ions show a 5 line i.r. spectrum in the v₃ stretch frequency region. One of these lines is attributed to CrO₄^2? ions in perfect crystal surroundings having T_d symmetry and the other 4 lines are attributed to C_s symmetry produced by a charge compensating anion vacancy in the nearest neighbour position. If the crystal contains a concentration of divalent cation impurity which is equal to or more than that of CrO₄^2? ions, a different spectrum characteristic of C_2x symmetry as well as the line corresponding to T_d symmetry are obtained. The crystals of ordinary purity contain all the three (C_s, C_2x and T_d symmetry) species and show eight line spectra. The changes in force constants calculated from the observed splitting of the energy levels agree with those evaluated from the known polarizability of the chromate ions.At 600°C, the vibration spectra of the highly pure crystals doped with CrO₄^2? ions show an increase in intensity of the line characteristic of T_d symmetry and the other lines practically disappear, because the anion vacancies move away from the neighbourhood of the CrO₄^2? ions at high temperatures. The energy of association of the vacancy with CrO₄^2? ions and the energy of migration of the vacancy are derived from the spectra obtained at different temperatures and with different heat treatments.The electronic spectra of the crystals show 3 bands (at 345, 270 and 240 nm for KCI). The lowest energy band has a fine structure with a spacing of about 800 cm^?1 at LAT. Since the transition involved is from a non-bonding to an antibonding state, the Condon parabola is shifted in the excited state and therefore the fine structure is attributed to a vibrational progression involving a totally symmetric frequency 800 cm^?1 in the excited state.     

Effect of the long-range order in the vacancy distribution on the electronic structure of titanium monoxide TiO1.0

The effect of the long-range order in the vacancy distribution according to the type of monoclinic Ti₅O₅ superstructure on the electronic structure of titanium monoxide TiO _y with the stoichiometric composition has been studied by the supercell method within the DFT-GGA approximation with the use of pseudopotentials. It has been established that, in spite of an increase in the Fermi energy, the stability of the compound increases with increasing degree of the long-range order η. The ordering of the structural vacancies leads to the considerable increase in the depth of the pseudogap at the Fermi level. It has been shown that the effect of the long-range order on the electronic structure in the range of η from 0 to 1.0 is much weaker than the effect of the nonstoichiometry of TiO _y in the range of y from 0.75 to 1.33.     

Spintronic properties of the Ti2CoB Heusler compound by density functional theory

The electronic structure and magnetic properties of the Ti₂CoB Heusler compound with a high-ordered CuHg₂Ti structure were investigated using the self-consistent full potential linearized augmented plane wave (FPLAPW) method within the density functional theory (DFT). Spin-polarized calculations show that the Ti₂CoB compound is half-metallic ferromagnetic with a magnetic moment of 2 μ_B at the equilibrium lattice constant, a=5.74 Å. The Ti₂CoB Heusler compound is ferromagnetic below the equilibrium lattice constant and ferrimagnetic above the equilibrium lattice constant. A large peak in majority-spin DOS and an energy gap in minority-spin DOS are observed at the Fermi level, yielding a spin polarization of 100%. A spin polarization higher than 90% is achieved for a wide range of lattice constants between 5.6 and 6.0 Å.     

The first-principle calculation of structures and defect energies in tetragonal PbTiO3

The first-principle calculation had been adopted to investigate various neutral vacancies and vacancy pairs under seven thermodynamic conditions in bulk PbTiO₃. The electronic structures, atomic relaxations, and formation energies of vacancies were obtained. Depending on the thermodynamic condition, the main and stable defects are different. It was found that V_O is the main defect under the reducing condition, whereas V_Pb becomes dominating under the oxidizing condition. The Pb-O vacancy pair forms more easily than the isolated vacancies under certain thermodynamic condition. Due to the introducing of vacancies, the acceptorlike levels and donorlike levels appear in the cases of the cation and anion vacancies, respectively.     

Structure,electronic and magnetic properties of hexagonal boron nitride sheets doped by 5d transition metal atoms: First-principles calculations and molecular orbital analysis

A first-principles calculation based on density functional theory is carried out to reveal the geometry, electronic structures and magnetic properties of hexagonal boron nitride sheets (h-BNSs) doped by 5d transitional mental atoms (Lu, Hf, Ta, W, Re, Os, Ir, Pt, Au and Hg) at boron-site (B_5d) and nitrogen-site (N_5d). Results of pure h-BNS, h-BNS with B vacancy (V_B) and N vacancy (V_N) are also given for comparison. It is shown that all the h-BNSs doped with 5d atoms possess a C_3v local symmetry except for N_Lu and N_Hg which have a clear deviation. For the same 5d dopant, the binding energy of B_5d is larger than that of N_5d, which indicates the substitution of a 5d atom for B is preferred. The total densities of states are presented, where impurity energy levels exist. Besides, the total magnetic moments (TMMs) change regularly with the increment of the 5d atomic number. Theoretical analyses by molecular orbital under C_3v symmetry explain the impurity energy levels and TMMs.     

Role of structural vacancies in the stabilization of the basic B1 structure in nonstoichiometric titanium monoxide TiO y

The electron structures and formation enthalpies of vacancy-free cubic TiO, vacancy-ordered monoclinic Ti₅O₅, and vacancy-disordered cubic TiO _y have been investigated using DFT+GGA calculations. Ti₅O₅ was found to be the stablest phase and TiO was found to be the least stable. The reason for the stability of the titanium and oxygen vacancies in the basic B1 structures of Ti₅O₅ and TiO _y has been deduced. The titanium vacancies lead to a decrease in the Fermi energy. Oxygen vacancies cause strengthening in covalent Ti-Ti bonding.     

An investigation on the defect structures and spin Hamiltonian parameters for the two orthorhombic Ti3+ centers in ZnWO4

By employing the perturbation formulae of the spin Hamiltonian parameters (SHPs) (g factors g_xx, g_yy, g_zz, hyperfine structure constants A_xx, A_yy, A_zz and superhyperfine parameters A_xx׳, A_yy׳, A_zz׳) for a 3d¹ ion in orthorhombically elongated octahedra and tetrahedra, the defect structures and the experimental EPR spectra are theoretically and systematically investigated for the two orthorhombic Ti³⁺ centers C₁ and C₂ in ZnWO₄. Center C₁ is ascribed to the impurity Ti³⁺ at host W⁶⁺ site associated with two nearest neighbor oxygen vacancies due to charge compensation. The resultant tetrahedral [TiO₄]^5– cluster is determined to undergo the local orthorhombic elongation distortion, characterized by the axial distortion angle Δθ (=θ–θ₀≈–6.84°) of the local impurity-ligand bond angle θ related to θ₀ (≈54.74°) and the perpendicular distortion angle Δε (=ε–ε₀≈2.5°) related to ε₀ (≈45°) of an ideal tetrahedron because of the Jahn–Teller effect. Center C₂ is attributed to Ti³⁺ on Zn²⁺ site, and this octahedral [TiO₆]^9– cluster may experience the local axial elongation ΔZ (≈0.001 Ǻ) and the planar bond angle variation Δφ (≈9.1°) due to the Jahn–Teller effect, resulting in a more regular oxygen octahedron. All the calculated SHPs (i.e., g factors for both centers, the hyperfine structure constants for center C₂ and superhyperfine parameters of next nearest neighbor ligand W for center C₁) show good agreement with the observed values. However, the theoretical results based on the previous assignment of center C₁ as Ti³⁺ on W⁶⁺ site with only one nearest planar oxygen vacancy (i.e., five-fold coordinated octahedral [TiO₅]^7– cluster) show much worse agreement with the experimental data. The defect structures and the SHPs (especially the g anisotropies) are discussed for both centers. The present studies on the superhyperfine parameters of ligand W⁶⁺ for center C₁ would be helpful to further investigations on the superhyperfine interactions of cation ligands which were rather scarcely treated before.     

First-principles study on the electronic structure and optical properties of La0.75Sr0.25MnO3-σ materials with oxygen vacancies defects

The electronic structure and optical properties of La_0.75Sr_0.25MnO_3-σ (LSMO_3-σ) materials with 1 × 1 × 4 orthorhombic perovskite structure were performed by first-principles calculation. The structural changing of LSMO₃ (ideal structure, σ = 0) was not obvious under generalized gradient approximation (GGA) and GGA + U arithmetic. On the contrary, the structural changing of LSMO_3-σ (σ = 0.25, with oxygen vacancies defects in the z = 0, c/8, c/6, c/4, and c/2) with GGA + U were more obvious than the result of ideal. This structural distortion induced distinct changing in density of states (DOS) for LSMO_3-σ materials. Oxygen vacancy defects caused a shift of the total density of states (TDOS) features toward low binding energies and LSMO_3-σ keep half-metal properties as well as LSMO₃ ideal structure. In addition, the hybridization between the Mn-e_g and O-2p orbital was weakened and the partial density of states (PDOS) of Mn indicated a strong d-d orbital interaction. By the result of oxygen vacancy formation energy, oxygen vacancy defects can be more easily formed in La-O layers (z = 0 and c/6) to compare with other layers (z = c/8, c/4 and c/2). The calculation result of optical properties suggested that the ideal LSMO could be produced strong absorption in the range of ultraviolet and visible light, while the LSMO_3-σ with oxygen vacancies defects were presented weak absorption in the range of visible light.     

Effects of aluminum vacancies on electronic structure and optical properties of Ta4AlC3: A first principles study

We investigated the effect of aluminum vacancies (V_Al) on the structural, electronic and optical properties of Ta₄Al_1−xC₃ (x=0, 0.25, 0.5, 0.75) based on the first-principle calculation using density functional theory. We found that the lattice constant a remains almost unchanged with the variation of V_Al concentration, while c and c/a ratio decrease with increasing V_Al concentration. Moreover V_Al induced local distortions have significant influence on the electronic and optical properties of Ta₄AlC₃, especially beyond the critical V_Al concentration (x=0.5). On the other hand, the presence of V_Al can improve the dielectric properties of Ta₄AlC₃. From the optical properties analysis, we predicted that Ta₄Al_1−xC₃ is not suitable as a coating material to avoid solar heating.     

Electronic and magnetic properties of SmCrSb3 and GdCrSb3: A first principles study

The density of states (DOS) and the magnetic moments of SmCrSb₃ and GdCrSb₃ have been studied by first principles full-potential linearized augmented plane wave (FP-LAPW) method based on density functional theory (DFT). For the exchange-correlation potential, the local-spin density approximations with correlation energy (LSDA+U) method have been used. Total and partial DOS have been computed using the WIEN2k code. DOS result shows the exchange-splittings of Cr-3d and rare-earth (R) 4f states electrons, which are responsible for the ground state ferromagnetic (FM) behavior of the systems. The FM behavior of these systems is strongly influenced by the average number of Cr-3d and Sm (Gd) 4f-electrons. The effective moment of SmCrSb₃ is found to be 7.07 μ_B while for GdCrSb₃ it is 8.27 μ_B. The Cr atom plays a significant role on the magnetic properties due to the hybridization between Cr-3d and Sb-5p states.