Kinetic paths of B2 and DO₃ order parameters: Theory

It is shown that a binary alloy with an AB₃ stoichiometry on a bcc lattice may develop various combinations of B2 and DO₃ order along its kinetic path toward equilibrium. The temporal evolution of these two order parameters is analyzed with an activated-state rate theory. Individual vacancy jumps are treated in a master equation formalism that involves first-nearest-neighbor (1nn) and second-nearest-neighbor (2nn) interactions. In our formulation, a set of coupled differential equations is obtained describing the time-dependence of six order parameters. These equations were integrated numerically for a variety of interatomic interactions and initial conditions. It was found that the relative rates of B2 and DO₃ ordering, and hence the path of the alloy through the space spanned by the B2 and DO₃ order parameters, depend on the relative strengths of the interatomic interaction potentials and on the temperature. For very strong 2nn interactions, a transient B32 structure was observed to develop at early times, although this phase disappeared as equilibrium was approached.