Real-space tight-binding approach to electronic structure and stability in substitutional alloys J.P. Julien a,c, * , P.E.A. Turchi b , D. Mayou c a CUPF, Universite Francaise du Paci®que, BP 6570, Faa'a-Aeroport, Tahiti, French Polynesia, France b Lawrence Livermore National Laboratory, L-268, P.O. Box 808, Livermore, CA 94551, USA c LEPES-CNRS, 25 Avenue des Martyrs, BP 166, F-38042, Grenoble Cedex 9, France Abstract 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 Shiba's o-diagonal disorder can be solved self-consistently in real-space with the same accuracy currently achieved in recip- rocal space. An eective one-electron Green function is given by a continued fraction expansion, and the associated eective medium is used to determine the eective cluster interactions which enter the expression of the con®gurationl part of the total energy for describing order-disorder phenomena in alloys. Some applications will be presented. Ó 2000 Published by Elsevier Science B.V. All rights reserved. 1. Introduction The coherent potential approximation (CPA) [1,2] and its later Shiba's multiplicative o-diago- nal disorder (ODD) [3] improvement is one of the most used mean ®eld theories of disordered sub- stitutional alloys. Even in partially ordered sys- tems, it is the basis for determining the interaction potentials that can lead to the prediction of phase stability [4]. This approximation leads to self- consistent equations for the Green's function (GF), which are usually solved for each energy z. Here, we present a completely dierent way of solving the CPA equations within the Shiba's ODD. An auxilary GF associated to an eective Hamiltonian, which is energy-independent but acts in greater space so that the recursion can be ap- plied, is calculated and from this GF, it is possible to obtain all physical quantities, like component- projected densities of states (DOS), the alloy av- erage GF and also quantities used to compute the eective interactions that enter the con®gurational (or ordering) energy for a binary alloy, within the embedded cluster method (ECM) and the orbital peeling technique. 2. Real-space solution of CPA equation with Shiba's ODD The tight-binding (TB) Hamiltonian H for a given con®guration of the alloy is written in a form that exhibits both diagonal and ODD H  X n  n jnihnj X n;m6n b nm jnihmj; 1 www.elsevier.com/locate/commatsci Computational Materials Science 17 (2000) 217±223 * Corresponding author. 0927-0256/00/$ - see front matter Ó 2000 Published by Elsevier Science B.V. All rights reserved. PII: S 0 9 2 7 - 0 2 5 6 ( 0 0 ) 0 0 0 2 7 - 6