Charging and the Properties of Alloys

In contrast to pure metals, the electron states in alloys exhibit a charging effect, i.e., a different electronic charge is deposited on each constituent in the alloy for a given state. The criterion for perturbation theory to be valid for an alloy is that the charging effect be small, i.e., the amplitude of an electron state be about the same on each constituent. It is not sufficient that the alloy be dilute. In fact if perturbation theory applies for a dilute alloy, it applies for any concentration. The charging effect is expected to be small, and thus perturbation theory to be valid, when the difference in the valence of the two constitutents is a small fraction of the smaller valence. The charging effect causes the energy of a given electron state in a binary alloy to deviate from a linear interpolation between the values of the pure metals. Such a linear interpolation is what one expects if the band structure is determined only by the average potential. Perturbation theory predicts that the specific heat of a binary solid-solution alloy deviates from a linear interpolation as $K\alpha (1-\alpha )$, where $\alpha$ is the fractional amount of one of the constituents and $K$ depends, among other things, on the variation of the potential from the average and on the amount of short-range order in the alloy. Optical measurements at frequencies high compared with the relaxation time of the electrons measure the band structure determined by the average potential only. Experiments have shown that the properties of the Ag-Au alloy system near the Fermi surface can be treated by perturbation theory, and on this basis all of the experimental measurements of this alloy system can be understood, including recent specific-heat measurements. The $d$-band of the Ag-Au alloy system exhibits large charging effects and cannot be treated by perturbation theory.