Coupled relaxation of concentration and order fields in the linear regime

The relaxation rates of concentration and long-range-order fields in substitutional alloys are known to be coupled not only by the driving forces, as they derive from a single free-energy functional, but also by kinetic coefficients, since the very same atomic jumps drive both relaxations. For the simplest kinetic lattice model (the kinetic counterpart of the Bragg-Williams model), the detailed expressions of the coefficients of the appropriate mobility matrix that had been derived previously [G. Martin, Phys. Rev. B 50, 12 362 (1994)] contain two errors, which are corrected in the present paper. Then, using these expressions, we discuss the conditions for the existence of coupling of the relaxation rates of composition and long-range order. In the most general case, where relaxation takes place around an equilibrium state that is inhomogeneous and ordered, the presence of this kinetic coupling is confirmed. In the case where relaxation takes place around a disordered state (homogeneous or inhomogeneous), we show that the mobility matrix reduces to a diagonal form, i.e., that there is no kinetic coupling. In the case of an ordered homogeneous equilibrium state, however, the mobility matrix is found to be symmetrical with off-diagonal terms which do not vanish, in general, although they may vanish for some specific crystallographic structures, or along specific crystallographic directions. It is shown that, near the homogeneous equilibrium state, even in the presence of kinetic coupling, the relaxation rates are such that the free energy of the system decreases monotonically with time, as expected from the second law of thermodynamics. The model is applied to a few ordered structures with cubic or tetragonal symmetry.