The Free-Electron Network Model for Metals: II

The free-electron network model for metals originally introduced by the writer is extended in two ways. First an allowance is made for the strong electron attraction towards the nuclei by inserting δ-function potential wells at the positions of these nuclei. Secondly, the potential between the nuclei is not regarded as constant but may be of arbitrary shape. Provided that this potential does not fluctuate too fast along the `bonds', its influence on band shape is shown to be small, in agreement with the situation found without δ-functions by Raychaudhuri. Atoms of different kinds may be introduced into the lattice, and the particular cases of the diatomic cubic lattice AB and the planar hexagonal lattice of graphitic type (example, boron nitride) are studied in detail. A possible application to the problem of antiferromagnetism is pointed out, involving a splitting of one otherwise continuous energy band into two separated parts as a result of partial localization of electrons of similar spin on alternate atoms.