Kinetics of short- and long-range B2 ordering in the pair approximation

The kinetic master equation is developed in the pair approximation to study disorder→B2 order transformations in bcc binary alloys. Coupled sets of rate equations for the pair variables are obtained for atom movements by either the direct interchange mechanism or the vacancy mechanism. Numerical integrations provide the nonequilibrium relaxations of short- and long-range order (SRO and LRO), and the vacancy balances between the two sublattices. For binary alloys, disorder→order transformations were studied for all combinations of interatomic interaction strengths, activation barrier heights, and alloy stoichiometry variations. After a transient vacancy relaxation, all cases began with a quick relaxation of SRO, followed later and independently by the growth of LRO and additional SRO. There were some variations in kinetic path through SRO and LRO, moderate variations in overall kinetics, and large variations in vacancy balance. Some non-physical aspects of kinetics in the pair approximation are discussed