Electronic Structure of Metal Alloys

Abstract

The change in the density of states when a transition metal impurity is substituted into a copper, silver, or gold host is calculated using the Riedinger model, in which the host bandstructure is described using a combined interpolation hamiltonian and the change in the potential caused by the introduction of the impurity is fixed by the condition that the Friedel Sum Rule be satisfied. The impurities are assumed to be non-magnetic and non-interacting. The calculations involve the evaluation of density of states integrals over the Brillouin Zone. The advantages and disadvantages of a number of methods for computing these integrals are investigated both practically and theoretically leading to a new approach to estimating the error in a calculation of a density of states integral over the Brillouin Zone. The method finally used for the calculations of the alloy densities of states is the CLQ method which uses quadratic interpolation to find the eigenvalues and gradients required by the Gilat-Raubenheimer method. For most alloys it is found that the change in the density of states has a well-defined peak, which has, to a good approximation, a lorentzian shape. The peak becomes broader as it moves to higher energies with increasing host-impurity valence difference. In gold and silver based alloys the impurities with high host-impurity valence difference do not give rise to well-defined lorentzian peaks, the change in the density of states being almost structureless near the fermi level but showing some structure near the energy of the host Lul level, corresponding to an increase in the density of states immediately below this energy. The best agreement with experiment is found for impurities from the same row as the host and it is suggested that better agreement between the calculated and experimental results for a row could be obtained by using the experimental results for one impurity from the row to fix certain parameters of the change in the potential.