Fermi Level in Disordered Alloys

The Fermi level or electrochemical potential $\overline{\mu }$ is considered as a function of concentration in disordered alloys. In the case that the perturbation introduced by substituting one type of atom by another is localized around the site of substitution, $\overline{\mu }$ is a constant independent of concentration. Localization of the perturbation requires that there be no volume change in alloying and that the perturbation be shielded so that it decays in an exponential manner away from the site of substitution. When boundary conditions between the interior of the alloy and exterior to it are considered, nonlocalized perturbations are introduced which cause a variation of $\overline{\mu }$ with concentration. However, such nonlocalized perturbations do not change the microscopic properties of the interior of the alloy but cause simply a rigid shift in energy of the electronic structure.