Real-space tight-binding approach to electronic structure and stability in substitutional alloys

A real-space approach based on the tight-binding approximation is proposed for studying electronic structure properties, stability and order in substitutional multi-component chemically random alloy based on periodic as well as topological disordered lattices. We show that the coherent potential approximation (CPA) equations including Shibaʹs off-diagonal disorder can be solved self-consistently in real-space with the same accuracy currently achieved in reciprocal space. An effective one-electron Green function is given by a continued fraction expansion, and the associated effective medium is used to determine the effective cluster interactions which enter the expression of the configurationl part of the total energy for describing order-disorder phenomena in alloys. Some applications will be presented.