New approach to the study of binary alloys

Abstract

We have developed a method to study the electronic densities of states in disordered binary alloys where correlation and clustering effects can be large. In this method, we consider a large cluster of atoms surrounded by a Bethe lattice. Any strong clustering and correlation effects can be built into the cluster. Assuming a mean-field approximation in the Bethe lattice, we can treat the cluster exactly by solving a set of linear equations. In the present work we have studied the coherent-potential approximation and the Bethe-Peierls approximation for the mean-field Bethe lattice. Then we have studied the systematics of densities of states at a central site of various different clusters consisting of different numbers of atoms ranging from 5 to 29 and of various compositions. An averaged density of states per site has been calculated for a linear chain and compared with numerical and other calculations. We have outlined a procedure for obtaining an estimate of the optimum cluster sizes based on localization of wave functions. The present method is simple, fast, and free from any undesirable singularity in the self-energy which has marred all the previous attempts to go beyound single-site coherent-potential approximation.