The charge excess functional theory and ordering properties of metallic alloys

Many current models of ordering phenomena in metallic alloys are based on the approximation that effective atomic interactions can be truncated by considering few-body terms only. As it has been recently shown, the charge excess functional theory (CEF) very accurately accounts for total energies and charge transfers in metallic alloys. The parameters required by the CEF theory can be easily obtained from ab initio electronic structure calculations. For binary alloys, only three CEF parameters are needed: two of them are related with the response of each atomic site to an external perturbing field, while the third is connected with the alloying species electronegativity difference. In this paper, I shall discuss the effective interatomic interactions that are implied by the CEF model. In particular, I will show that, once put in Hamiltonian form, in spite of its simplicity, the theory contains infinite body effective atomic interactions. Furthermore, in the special case in which the above responses have the same numerical values for all the alloying species, it is shown that the theory becomes equivalent to an Ising model with infinite range pair-wise interactions. The consequences for the ordering mechanisms in metallic alloys are discussed.