Energy Bands forV3XCompounds

Abstract

The augmented-plane-wave (APW) method has been used to calculate energy bands for a number of ${\mathrm{V}}_{3}X$ compounds having the $\beta$-wolfram structure, including hypothetical ${\mathrm{V}}_3$Al, ${\mathrm{V}}_3$Si, ${\mathrm{V}}_3$Co, ${\mathrm{V}}_3$Ga, ${\mathrm{V}}_3$Ge, and ${\mathrm{V}}_3$As. These calculations have been carried out at symmetry points in the Brillouin zone for all the above compounds and, in addition, along symmetry lines for ${\mathrm{V}}_3$Ga so that a rough density of states could be constructed for this compound. It has been found that: (a) the calculated density of states is in qualitative agreement with the schematic model proposed by Clogston and Jaccarino to explain the temperature dependence of the Knight shifts and the susceptibility for ${\mathrm{V}}_3$Ga; (b) the Fermi energy for ${\mathrm{V}}_3$Ga coincides with a peak in the density-of-states curve which is due primarily to the vanadium $3d$ bands; (c) the APW wave functions at the Fermi surface for ${\mathrm{V}}_3$Ga contain an admixture of gallium $4p$ character which is an order of magnitude smaller than that predicted by Clogston and Jaccarino to account for the negative Knight shift at the gallium site; (d) to a good approximation, a rigid-band model can be used to represent the variation in the density of states at the Fermi surface for the series of compounds ${\mathrm{V}}_3$Ga, ${\mathrm{V}}_3$Ge, and ${\mathrm{V}}_3$As; (e) the energy bands for hypothetical ${\mathrm{V}}_3$Al and ${\mathrm{V}}_3$Si are very similar to those obtained for ${\mathrm{V}}_3$Ga and ${\mathrm{V}}_3$Ge, respectively; (f) the gross features of the energy bands for these compounds are relatively insensitive to the potentials used in these calculations, though the width and position of the vanadium $3d$ bands relative to the other pertinent bands is potential-dependent; (g) the linear chain model for these ${\mathrm{V}}_{3}X$ compounds provides an inadequate description of their energy-band structure.