P. Herzig

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

Abstract 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 3 d 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.

Characterization of the electronic properties of YB12, ZrB12, and LuB12 using 11B NMR and first-principles calculations

Three metallic dodecaborides, YB12, ZrB12 and LuB12, have been investigated by electric-field gradient (EFG) measurements at the boron sites using the 11B nuclear magnetic resonance (NMR) technique and by performing first-principles calculations. The NMR powder spectra reveal patterns typical for a completely asymmetric EFG tensor, i.e., an ? parameter close to unity. The absolute values of Vzz (the largest component of the EFG) are determined from the spectra and they range between 11 ? 1020?V?m?2 and 11.6 ? 1020?V?m?2 with an uncertainty of 0.8 ? 1020?V?m?2, being in very good agreement with the first-principles results. In addition the electronic structure and chemical bonding are analysed from partial densities of states and electron densities.

First-principles investigations of transition metal dihydrides, TH2: T = Sc, Ti, V, Y, Zr, Nb; energetics and chemical bonding

Self-consistent full-potential linearized augmented-plane-wave (LAPW) band-structure calculations are performed for the fluorite-type dihydrides ScH2, TiH2, VH2, YH2, ZrH2 and NbH2 as well as for the tetragonal low-temperature phases of TiH2 and ZrH2. For all compounds studied which show metallic behaviour, band structures, densities of states, electron densities and the total-energy minima with respect to the lattice parameters are computed. Additionally, the bulk moduli for the cubic phases are given. Good agreement with experimental data is found where they are available. The results obtained confirm previous interpretations of the tetragonal distortion of the cubic unit cell as a Jahn-Teller-type effect and show how the electron densities of the tetragonally distorted phases depend on the splitting of states near the Fermi level. The total-energy curves for TiH2 and ZrH2 as functions of the c/a ratios show two minima each, of which only the ones for c/a<1 have been observed experimentally.

The effect of vacancies on the electronic structure of Nbo

Abstract The crystal structure of NbO is considered as a NaCl structure with 25% ordered vacancies in each sublattice. Self-consistent energy band structure calculations using the augmented plane wave (APW) method have been carried out for a hypothetical NbO with the full NaCl structure and for the structure with the vacancies. We find that the introduction of the vacancies leads to (1) a lowering of the Nb- d like bands with respect to the O- p bands, (2) an almost completely filled “vacancy band”, and (3) a splitting and broadening of the O- p like band. These effects are shown to have a significant influence on both the theoretically calculated X-ray photoemission spectra (XPS) and the X-ray emission spectra (XES). All theoretical spectra obtained with the vacancy-structure are found to be in good agreement with experiments in contrast to those spectra calculated for hypothetical NbO in the NaCl structure.

Vacancy induced changes in the electronic structure of titanium nitride

Abstract A self-consistent APW band structure calculation has been performed for TiN0.75, assuming long-range ordered vacancies at the nonmetal lattice sites. Two different kinds of titanium atoms occur in this model: Ti[6] atoms that are octahedrally surrounded by six nitrogen atoms and Ti[4] atoms that have only four nitrogen neighbors and are adjacent to two vacancies. The model structure can be described as Ti[4]3Ti[6]N3□N, where □N denotes a nitrogen vacancy. In the densities of states, two sharp vacancy peaks have been found which are not present in stoichiometric TiN. The bonding situation is discussed by means of electron density plots. It is found that the chemical bonding is characteristically influenced by the introduction of vacancies. The calculated XPS and K XES are shown to be in good agreement with the experimental spectra.

Vacancy induced changes in the electronic structure of titanium carbide—II. Electron densities and chemical bonding

Abstract In a recent paper, we presented the band structure and the state densities for an ordered model structure for TiCn 0.75 and discussed the changes which occur in comparison with stoichiometric TiC. Starting from these results, we investigate in the present paper, on the basis of calculated electron densities, how the bonding situation is influenced by the vacancies on the carbon sublattice in TiC 0.75 . The results can be summarized as follows: The presence of empty lattice sites leads to the formation of new types of bonds not present in TiC; i.e., weak bonds between second nearest Ti neighbors across the vacancy sites and stronger Ti-Ti bonds in the Ti octahedra around the vacancies caused by the reduction of the number of C-Ti bonds. An analysis of the electron densities also shows a strengthening of the covalent Ti-Ti bonds involving Ti atoms not immediately adjacent to a vacancy as well as an increase of the ionic character of the C-Ti bonds.

A theoretical investigation of titanium aluminium nitrides, (Ti, Al)N: Electronic structure and chemical bonding

Titanium aluminium nitrides, Ti1-xAlxN, can be prepared as films by various sputtering methods. They form metastable phases in which the titanium and aluminium atoms are randomlydistributed over the metal sublattice. In the present work two ordered model structures, Ti3AlN4 and TiAlN2, have been chosen, for which LAPW band-structure calculations have been performed. The calculated densities of states (DOS) and the local partial DOS for both model structures are compared with the corresponding values for TiN. Characteristic changes in the DOS of the “p band” are observed which are caused by the nitrogenp orbitals that point towards the aluminium spheres. The bonding situation is investigated on the basis of electron density and difference electron density plots. The substitution of titanium atoms by aluminium atoms leads to stronger covalent Ti−Ti and N−Ti bonds and to additional ionic bonding contributions by the aluminium atoms whose ionicity increases from Ti0.50Al0.50N to Ti0.75Al0.25N.

Energetics, electric-field gradients and optical properties of YH3 (YD3) by first-principles calculations

Abstract The exact crystal structure of the switchable mirror material YD3 is still not fully understood. Presently, three structure models with P 3 c1 , P63cm, and P63 symmetry are under discussion. While the first two structures are supported by neutron powder diffraction experiments, the latter one was derived by ab-initio methods. In this paper the phase stability of these structures is established by geometry optimization and accurate total energy calculations from first-principles. The P63 structure is obtained with lowest energy followed by the P63cm structure and the latter followed by the P 3 c1 structure. However, these results are not decisive enough for definitive structure assignments because of the very small energy differences involved. Comparison of experimental and calculated electric-field gradients (EFGs) reveal best agreement for the P63cm structure. From band-structure calculations it is found that within standard density-functional theory the P 3 c1 and P63cm structures are obtained as metals whereas for the P63 structure a small fundamental gap of ca. 1 eV results. Calculations within the screened-exchange local-density approximation (sX-LDA) lead to fundamental band gaps of 1.8–2.1 eV for all three structures.

Titanium carbonitrides, Ti(C,N): electronic structure and chemical bonding

Abstract The structures of the titanium carbonitrides are derived from the sodium chloride structure and do not show long-range order at the non-metal sublattice. To investigate the bonding properties, band structure calculations for three ordered model structures with compositions TiC0.75N0.25, TiC0.5N0.5 and TiC0.25N0.75 using the linear augmented plane-wave (LAPW) method have been performed. For these structures densities of states (DOS), local partial DOS and electron densities have been calculated. The DOS are in fairly good agreement with those previously obtained by the Korringa-Kohn-Rostoker — coherent-potential approximation (KKR-CPA) method where the C and N atoms are assumed to be randomly distributed over the non-metal sublattice. The covalent CTi bonds are in general much stronger than the NTi bonds and therefore successive replacement of N atoms in TiN by C atoms leads to a strengthening of covalent non-metal-Ti bonds. This is accompanied by a weakening of TiTi bonds and by a decreasing ionicity of the non-metal-Ti bonds.

A KKR-CPA study of the electronic states in Ti0.75Al0.25N

The partial densities of states (DOS) and the X-ray emission spectra of the random alloy Ti0.75Al0.25N were calculated using the KKR-CPA method. While the Ti and N atoms behave much the same as in TiN, the Al bonding is found to be different from both A1N and metallic Al.