Random transfer integrals in disordered alloys

The Koster-Slater formula expressing the change in the density of states introduced by the presence of localized impurities in metals is generalized to the case of random transfer integrals. It is then shown that the single site approximation first introduced by Shiba (1971) to deal with off diagonal randomness in binary alloys is consistent with this generalization and gives correctly the density of states in the dilute limit. The theory is discussed in the locator formulation and possible extensions to the calculation of transport properties are suggested. Numerical examples are presented to discuss the nature of impurity states when both diagonal and nondiagonal disorder are present.