Kinetics of order–disorder transformations in alloys. II

Abstract

As a continuation of previously published work, isothermal ordering and disordering processes (of B2 type structure) in bcc binary alloys from initial states both near and far from equilibrium are investigated theoretically. The vacancy mechanism for atomic migration is assumed, interactions among nearest neighbors are taken into account, and the pair approximation of the path probability method of irreversible, cooperative phenomena is utilized. This leads to a set of nonlinear rate equations derived in a systematic, statistical fashion which describes the dynamical behavior of the system. The rate equations can be linearized near equilibrium and are shown to obey in this form the formalism of irreversible thermodynamics of Onsager. The driving forces are identified as the partial derivatives of the free energy function of the system with respect to state variables. Several relaxation times are obtained which characterize near equilibrium relaxation, and their meanings are discussed. Nonlinear coupling of relaxation modes occurs in relaxation processes from states far from equilibrium. Especially, a distinct three step relaxation of internal energy and a two step relaxation of the long range order are predicted when the alloy is quenched from states having zero or small long range order. The behavior is strikingly similar to the three step relaxation process of the internal energy observed in Ni3Fe near the order–disorder transition point. These relaxation effects are related to the geometry of the free energy surface.