Role of Three-Body Potentials in Disordered Alloys. I: Binary Alloys

Abstract

Noting the need for taking into account the effects of irreducible many-body potentials in condensed systems, a formulation of the statistical mechanics of disordered binary alloys with arbitrary composition and arbitrary range of static two- and three-body potentials is given. High temperature series expansions for the pair-wise and the triplet correlations are derived. It is noted that in the linear, mean-field like, approximation, all the effects of the irreducible three- and higher-body potentials on the two-site correlation (i. e., the short range order parameter) can be represented in terms of an effective, composition dependent, pair-wise potential. The inclusion of the second and higher order terms in the (kT)-1 expansion, however, changes this situation. For the triplet correlations, on the other hand, the presence of the three-body potentials is found to make a contribution in the leading order in (kT)-1, such that it cannot altogether be represented by an effective pair-wise potential. Consequently, it is noted that experimental measurement of the triplet correlations would, under certain conditions, provide direct information about the three-body potentials.