Kinetics of ordering and spinodal decomposition in the pair approximation

The kinetics of atomic ordering and phase separation in inhomogeneous systems were investigated employing microscopic master equations in the pair approximation. For a homogeneous system at completely thermodynamic equilibrium, the kinetic equations produce the same equilibrium states as the cluster variation method. We studied the kinetics of both short- and long-range order and spinodal decomposition kinetics, as well as the morphological pattern formation and evolution. It is shown that the development of long-range order and growth of concentration wave amplitudes are significantly delayed due to the decreases in driving forces as a result of short-range order relaxation in the pair approximation as compared to that obtained from the point approximation with the same initial condition. It is demonstrated that the kinetics obtained by assuming the pair distribution functions always at equilibrium is found to be a good approximation for the pair approximation. The effect of bond energies on the ordering kinetics will be discussed.