Berechnung der Bandstrukturen nichtstöchiometrischer Vanadiumcarbide VC_x / Band Structure Calculations on Nonstoichiometric Vanadium Carbides VC_x

Abstract

Herrn Prof. Dr. H. Hartmann aus Anlaß der 60. Wiederkehr seines Geburtstages in Verehrung gewidmet. Band, Structure Calculations on Nonstoichiometric Vanadium Carbides VCxUsing the augmented-plane-wave (APW ) method the electronic structure of stoichiometric vana dium carbide has been computed previously *. Since only nonstoichiometric cubic phases of vana dium carbide are stable and all experiments are made with such samples, the energy bands have been determined for some nonstoichiometric VCj; phases {x = 0.87; 0.833; 0.79; 0.75) using the APW virtual crystal (VCA) approximation similar to Schoen's work on TiO 7, 10. Our approach differs from his in two aspects: First, the potential is constructed from the self consistent potential of Ref. 1 instead of using atomic data. Thus, the important self consistent procedure is taken into account at least in an approximated form. Second, a more realistic scheme for occupying the states is suggested. Furthermore, an attempt is made to normalize the wave functions in order to obtain the charge distribution in the crystal.The density of states and the partial densities of states corresponding to the quantum numbers n and I have been computed using an LCAO interpolation scheme. The different VC^ phases show a fairly "rigid band structure" . The Fermi energy and the density of states at the Fermi level increase with decreasing carbon content. The calculated APW-as well as the LCAO-charge distribu tion indicate -in accordance with ESCA measurements 32 -that the charge-transfer from vanadium to carbon and the ionicity of VC^ decrease with increasing vacancy concentration. The results of X-ray-emission and heat capacity measurements are discussed in terms of the APW-VCA results.Especially for the X-ray-emission data the agreement between theory and experiment is fair.Einleitung

Chemical binding and energy band structure of vanadium monocarbide

“…The comparison of these results with those obtained by the L4PW method (Table 3 ) indicates that there is a satisfactory quantitative agreement in the densities of states a t the Fernii level, and the widths of the conduction band and its filled portion. However, the lower band in our calculation is wider than that found in [a] and as a result, the gap between the lower and the conduction bands is less than that obtained in [ 2 ] . This difference is likely to be caused by insufficient accuracy in coniputing the matrix elements of 2-4s and 2p-4s types, which are mainly responsible for the relative position and the width of low-energy band.…”

Recent investigations on the electronic structure of the fourth and fifth group transition metal monocarbides, mononitrides, and monoxides

“…Their results for the stoichiometric As has been noted earlier [70,71], the Fermi level is shifted to higher energies with increasing vacancy concentration. However, the experimental A2, band is found to be located at smaller binding energies.…”

Band structure of transition metal compounds

“…Of the calculations listed in table 1 for vanadium carbide, Neckel and co-workers [25][26][27][28][29][30] and Zbasnik and Toth [31] have obtained very similar results in their SC-APW calculations as far as bandwidths and gaps are concerned. The ordering of the one-electron energies do, however, differ in several symmetry points, as can be seen from table 3, which also shows the ordering obtained by Zbasnik Definitions /~1-/L is a shorthand notation for E/~I-E/~ ~ L 1 -F 1 width of the 2s band.…”

“…The material available is based either on band calculations [7,26,28,31,33,36,37] or cluster models [18][19][20][21][22].…”