Characteristics of superlattice formation in alloys of face centered cubic structure

Abstract

The order-disorder transition in the face centered cubic (f.c.c.) lattice and that in the body centered cubic (b.c.c.) lattice, both calculated based on the tetrahedron approximation of the cluster-variation method, are compared. Although in the b.c.c. lattice the mathematics for the Ising model ferromagnets and for the AB-type alloys are completely equivalent, the transition point T c of superlattice formation in the f.c.c. lattice is of the first order and is much lower than T c of the Ising model ferromagnetism. Reflecting this characteristic, an appreciable degree of short-range order is extended over a wide temperature range above T c in f.c.c. alloys, while the short-range order is appreciable only near T c in b.c.c. alloys and decreases rapidly as the temperature rises. If only the nearest neighbor interaction is taken into account, both the A 3 B- and the AB-type superlattices are not deterministic with respect to the one-dimensional disorder created by the antiphase boundaries of the first kind. The degeneracy is removed by the inclusion of long-distance interactions. The relation of this charactersitic to the longperiod superlattice is discussed. It is shown that the stability of the long-period superlattice at higher temperatures than the normal superlattice cannot simply be derived from the entropy effect within a single antiphase boundary using the nearest-neighbor interaction, as it was sometimes suggested. All the results on the stoichiometric AB-type ordered structure can readily be applicable to Ising model antiferromagnets. Conclusions drawn for the f.c.c. structure are also applicable to any type of ideal, close-packed structure.