Thermodynamics and kinetics of order-disorder processes derived from the cluster-activation method and microscopic diffusion theory

The thermodynamics and kinetics of order-disorder processes derived from the cluster-activation method (CAM) and microscopic diffusion theory (MDT) are examined. In the single-site approximation, the homogeneous long-range-order kinetic equations for the direct exchange mechanism (Kawasaki dynamics) in the CAM are derived by employing a kinetic theory of a Markovian nature whereas the kinetic equations in MDT are derived from the Onsager-type diffusion equations based on a microscopic mean-field free-energy functional. While the single-site approximation in MDT results in equilibrium states corresponding to the Bragg-Williams approximation, the same approximation in the CAM produces equilibrium states close to the Bethe (nearest-neighbor-pair) approximation. The physical origin underlying the partial inclusion of nearest-neighbor-pair correlation information in the single-site approximation of the CAM is discussed. It is shown that if the values of (ordering energy)/kBT and the time-dependent long-range parameter η are small (1), the kinetic equations in the CAM reduce to those in MDT. It is demonstrated that the disordering kinetics obtained from the linearized equations for both models agree, at least qualitatively, with those from nonlinear equations but not the ordering kinetics.