Electronic energy bands in model three dimensional lattices

Abstract

The paper presents a discussion of the energy bands in a three dimensional lattice in which the potential is assumed to have a constant nonvanishing value in a spherical region round each nucleus and vanishes in the interspace. Introducing some simplifying approximations, a relation between the electronic energy and the wave vector is obtained. The case of an ordered diatomic alloy is next considered and the splitting of the bands for such a lattice is clearly brought out. The significance of this result in the theory of antiferromagnetism is pointed out. Lastly it is noted that for our model alloy, the theorem enunciated by Saxon and Hutner is valid.