Analysis of effective-medium approximation for a tight-binding model of a liquid metal

The perturbation expansion for the electronic structure of a tight-binding model of a liquid metal is studied by means of a diagram analysis. The previously developed effective-medium approximation is shown to correspond to the summation of the same terms as occur in Soven's coherent-potential approximation for alloys, within the validity of a generalized Kirkwood superposition approximation for ionic distribution functions. The terms omitted are shown to be of higher order in 1z̄, with z̄ an effective neighbor number. The results are extended to cover liquid alloys and solid alloys with short-range order and off-diagonal disorder, the latter results agreeing with work of Blackman et al. The conclusions apply also to a general model of a liquid metal.