Theory of binary alloys including short-range order properties

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Abstract
A new method for studying the electronic structure of binary alloys within the tight-binding framework is presented and developed in detail. The method involves treating part of the system exactly as a cluster of atoms and simulating the rest of the environment by connecting to each atom at the surface of the cluster a Bethe lattice of the same coordination number. The method includes from its inception the idea of short-range correlation effects of a nearest-neighbor order parameter. Clusters of different size have been studied and analyzed in detail. An illustrative example is presented to show the striking differences which appear in various concentration sequences. These sequences are selected to be (i) random, (ii) with a tendency to segregation, and (iii) with a tendency to form binary compounds. The results emphasize the need to include short-range correlation effects when dealing with alloys. The method also provides a clear identification of localized states. In addition, it gives very naturally the position of band edges and energy gaps. The method, when averaged over all alloys with equal concentration and all short-range order parameters, reproduces in a satisfactory way the results of the single-site coherent-potential approximation.