Ordered states in binary alloys with one magnetic component: A binomial description

A description of chemically and magnetically ordered states, based on the binomial formalism, is presented. By this method, one can analyze all possible configurations that depend on the crystalline structure and the size of the basic cluster used for the description of the system. The procedure is outlined for a cluster of n sites and its application is illustrated for a 4-point cluster in fcc and bcc lattices. This cluster size is big enough to describe ordered alloys with magnetic atoms forming decorated ferromagnetic, antiferromagnetic, superantiferromagnetic and other more complex arrangements.