Order-disorder phase transition of the Co_xFe_1-x system

The order-disorder phase transitions in binary alloys with magnetic interactions are studied. We introduced an electronic theory for magnetic binary alloys, which is an extension of the cluster-Bethe lattice method. In this approximation we incorporate electronic correlations, itinerant and localize nature of electrons 3d, and both long-range and short-range chemical correlations. The magnetism is described by means of a Hubbard Hamiltonian that in conjunction with Green's functions techniques is used to calculate local densities of electronic states. For it we take an atom in the real lattice and it is joined to a Bethe's lattice with the same coordination number. The diagram for order-disorder phase transition is obtained. It is achieved by coupling the electronic theory introduced here, to combinatorial theory developed by Kikuchi. The first is used for calculating the alloy internal energy so long as the second is used for obtain the configurational entropy. An application to order-disorder transition of Co_xFe_1-x is studied and good agreement with experiment is obtained.