Rigid-band model of alloys

The electronic structure of normal alloys is considered. This structure is divided into two categories, geometric and density of states. The geometric structure is the shape of constant-energy surfaces in reciprocal space. Under three conditions, the geometric structure of the alloys is the same as that of the pure solvent, but the density of states is different. These conditions are that: (a) the excess charge of the solute localizes around it; (b) the mean free path of the electrons is many interatomic spacings; (c) the electron states of interest in the pure solvent are in one band and are greatly separated in energy from the other bands. Under these same conditions, even when the electronic specific heat of dilute alloys is found experimentally to depend on only the electron per atom ratio and the change in volume produced by alloying as predicted by the rigid-band model, the value of the specific heat in the alloy still differs from the value given by the rigid-band model because the density of states of the alloy is different from that of the pure solvent. As a sideline of this investigation, it is pointed out that an expansion of the electronic structure of the alloy in terms of the concentration of the solute is not valid for concentrated alloys and only has validity in the dilute limit.