Some considerations regarding the application of a linear chain model to some compounds of the β-W structure

In A₃B compounds possessing the A15 (β-W) lattice, such as V₃Si, "A" atoms are arranged in families of interpenetrating linear chains. As a consequence, the electronic band structure may display one-dimensional properties. A model lattice is considered by the tight-binding approximation, and it is shown that sections of the constant energy surfaces are approximately planes, and the wave functions are concentrated on chains perpendicular to these planes, even for quite strong interchain coupling. The symmetries of 3d states localized on atoms of a single chain are investigated, for the cubic and strained states of the lattice. It is shown that for some bands, the interchain coupling vanishes for k = 0; for these bands, it is conceivable that the density of states displays a sharp maximum there. It is also shown that due to the special symmetry of the lattice, a uniform uniaxial strain can open up a gap at the center of several of the bands of the linear chains, and this effect may also lead to a lattice instability.