Energy Bands in the Body-Centered Lattice

Abstract

Slater's method of finding the structure of electronic energy bands in the body-centered lattices is extended so as to satisfy boundary conditions at fourteen points of the polyhedral cell surrounding an atom, instead of eight as in previous applications. Since this requires the use of all the "$d$" spherical harmonics, the method is now applicable to elements which have "$d$" electrons. Greater accuracy is also to be expected for other elements. The expansions of the determinants relating the energy $E$ to $k$, the wave number vector, are given for all symmetry axes, and points, and in part for the symmetry planes. From group theory the places where various bands will stick together, i.e. degeneracies required by symmetry, are also determined.