Linear instability criteria for ordering and phase separation in tricritical systems

Instability criteria for identical systems of binary alloys with ordering and phase separation are derived from linearized coupled kinetic equations for local composition and local degree of order. The analysis clearly shows that deviation from stoichiometry leads to instability against heterogeneous ordering associated with compositional fluctuations, when the degree of order is around 1/√3 of the equilibrium value. Heterogeneous ordering or spinodal decomposition is expected to occur even in the single phase field of the order phase as well as within the miscibility gap between ordered and disordered phases. Transmission electron microscopy on an Fe-14.6 at.% Si alloy revealed that D0₃-type ordering is accompanied by heterogeneous fluctuations of the degree of order as predicted by the derived instability criteria.