Theory of electrical conductivity in disordered binary alloys; discussion of the validity of CPA

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Abstract
Using the functional derivative techniques, the coherent potential approximation (CPA) is analysed for a two s-d band model relevant to the investigation of some concentration dependent properties of noble and transition metal based disordered alloys. The discussion reveals that when delta , the difference between site potentials may not be regarded as a small parameter, the natural small parameter of the theory is ( gamma 2/ delta wsZ) where gamma is the hybridization constant, ws the band width and Z the number of nearest neighbours. This quantity is the product of the one band small parameter (1/Z) and the small parameter relevant to discuss the two band model split band limit.