Effective cluster interactions from cluster-variation formalism. II

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Abstract
Using the recently developed direct-configurational-averaging method, we have considered the expansion of formation energies of the random and ordered states in terms of effective cluster interactions (ECI’s) for two model tight-binding binary-alloy systems. In particular, we have examined the rates of convergence of such expansions in two different averaging schemes. In the canonical scheme the ECI’s depend on the concentration (c) of the alloy explicitly, while for grand-canonical averaging they do not. For a model system in which the ordering energies are highly asymmetric about c=0.5, we find that an expansion in canonical ECI’s gives slightly better convergence. However, for the other system considered, both averaging schemes lead to similarly convergent expansions due to the symmetry of the system about c=0.5. We have also verified numerically formal relations between the ECI’s in the two averaging schemes. Such relations provide a useful convergence criterion of expansions in terms of ECT’s.