Pair Effects in Substitutional Alloys. II. Multiple-Scattering Formulation

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Abstract
A single-band model Hamiltonian is used to study the effects of clustering on the electronic properties of disordered binary alloys. Alternate methods are used to calculate corrections to the coherent potential (CP) approximation due to two-atom clusters. The distinction between these methods is essentially one of self-consistency vs non-self-consistency. The non-self-consistent calculation isolates those terms in the multiple-scattering series that correspond to two-atom molecules embedded in the CP medium. These terms can be summed exactly, and the resulting expression for the electron propagator indicates that under certain conditions discrete states may exist outside the CP band edges. In the dilute split-bandlimit, for example, nearest-neighbor clusters are found to produce satellite levels on either side of the impurity subband. The second approach, which is identical to the method proposed by Cyrot-Lackmann and Ducastelle, is based on a reformulation of the multiple-scattering equations in terms of two-site scattering operators. The relationship between these results and the self-consistent pair equations derived by Schwartz and Siggia is discussed in detail. The latter equations have been shown to describe both the broadening of the satellite levels and the shifting of the CP-band edges.