Ordering in fcc lattices with first- and second-neighbor interactions

A prototype phase diagram for the <1120> family of the ordered superstructures in fcc lattices is calculated in the tetrahedron-octahedron approximation of the cluster variation method. The tetrahedron-octahedron cluster combination allows for first- and second-neighbor interactions, both essential for the <1120> superstructures to be ground states. Calculations are carried out for positive (antiferromagnetic) nearest-neighbor pair interactions and for a ratio of second- to first-neighbor interaction energies of 0.25. Salient features of the resulting phase diagram are tricritical points in the fcc to A₂B₂ and the fcc to A₃B transitions, and the presence of a bicritical point at the junction of the A₂B₂ and A₃B critical lines with the A₂B₂ to A₃B first-order transition line. The A₂B phase of the <1120> family is found to be stable at relatively low temperatures and in a very narrow composition range. Stability of the disordered state is investigated in k space and the <1120> ordering spinodal is determined.