Coherent-Potential Model of Substitutional Disordered Alloys

TLDR

The coherent potential is a complex, energy‑dependent quantity. The authors introduce a substitutional alloy model that uses an effective coherent potential placed on every lattice site to simulate the alloy’s electronic properties. They evaluate this model on a one‑dimensional δ‑function potential alloy and compare its spectrum to that obtained with Beeby’s average t‑matrix approximation. The comparison shows that the average t‑matrix approximation fails to describe transition‑metal alloys, whereas the coherent‑potential model yields a more realistic density of states.

Abstract

We introduce a model of a substitutional alloy based on the concept of an effective or coherent potential which, when placed on every site of the alloy lattice, will simulate the electronic properties of the actual alloy. The coherent potential is necessarily a complex, energy-dependent quantity. We evaluate the model for the simple case of a one-dimensional alloy of $\ensuremath{\delta}$-function potentials. In order to provide a basis for comparison, as well as to see if a simpler scheme will suffice, we also calculate the spectrum of the same alloy using the average $t$-matrix approximation introduced by Beeby. On the basis of these results, we conclude that the average $t$-matrix approximation is not adequate for the description of an actual transition-metal alloy, while the coherent-potential picture will provide a more reasonable facsimile of the density of states in such an alloy.