Model Hamiltonian Description of Ag-Au Alloys in the Coherent-Potential Approximation

Abstract

A simple model Hamiltonian relevant to binary noble-metal alloys is introduced. The model, which is easily treated in the coherent-potential approximation (CPA), contains one $s$ band of finite width and one $d$ level of zero width which hybridizes with the $s$ band. The Hamiltonian is examined using the CPA in two ways: first, purely as a model whose properties can be simply investigated, and second, as a Hamiltonian which may be considered to approximate that appropriate to noble-metal alloys. In regard to the first aspect of the model, interest is centered on special limiting cases such as the dilute-alloy and split-$d$-band limits. It is shown as a result of $s-d$ hybridization that the criterion for the split-$d$-band limit in the two-band model is considerably more severe than in a one-band model investigated previously. In regard to the second aspect, interest is focused on some electronic properties of Au-Ag alloys. It is not expected that Wigner-Seitz cells within these alloys will be neutral. In order to explain the observed concentration dependence of the optical-absorption edge, it is necessary to assume that electrons are transferred from Au to Ag sites, rather than from Ag to Au as has been commonly supposed. The concentration dependence of the $d$-level positions is obtained from a "renormalized atom" theory and the charge transfer, which is assumed to arise from $s$ electrons. The optical-absorption edge as a function of concentration is estimated from parameters appropriate to Ag-Au. Good qualitative agreement with experiment is obtained when the transfer of $s$ electrons from Au to Ag atoms is taken into account. By contrast, the predicted behavior is qualitatively incorrect if charge-transfer effects are neglected or assumed to go in the opposite direction.