Thermostatistical Theory of Long Period Superlattice Structure in Binary Alloy on FCC Lattice

Spatially modulated structures in the Ising model on the fcc lattice with anisotropic nearest-neighbour and next-nearest-neighbour interactions are investigated, to compare with the long period superlattice (LPS) structure of CuAuII appearing in Cu–Au alloy. The free energy is calculated as a function of the order parameter for each of relevant structures, by making use of the method of symmetry-breaking field. Thus, it is shown that commensurate and incommensurate phases as well as homogeneous or normal ordered phases are stabilized, depending on the temperature and the interaction coupling ratios. Effects of higher harmonics are also taken into account and found to be small, although they have not to be neglected. It is noted that the anisotropy in the couplings causes the LPS structure to be stabilized.