The determination of configurational energies in terms of effective cluster interactions in substitutionally disordered alloys from a knowledge of the alloy electronic structure is examined within the methods of concentration waves (CW) and the generalized perturbation method (GPM), and for the first time within the embedded-cluster method (ECM). It is shown that the ECM provides the exact summation to all orders of the effective cluster interaction expansions obtained in the partially renormalized GPM. The connection between the various methods (CW, GPM, and ECM) is discussed and illustrated by means of numerical calculations for model one-dimensional tight-binding (TB) systems and for TB Hamiltonians chosen to describe Pd-V alloys. These calculations, and the formal considerations presented in the body of the paper, show the complete equivalence of converged GPM summations within specific clusters and the ECM. In addition, it is shown that an exact expansion of the configurational energy can be obtained in terms of fully renormalized effective cluster interactions. In principle, these effective cluster interactions can be used in conjunction with statistical models to determine stable ordered structures at low temperatures and alloy phase diagrams.
ASJC Scopus subject areas
- Condensed Matter Physics