A Microscopic Theory for Domain Wall Motion and Its Experimental Verification in Fe‐Al Alloy Domain Growth Kinetics

— A microscopic theory for curved antiphase domain wall motion in ordered structures leads to a prediction that velocity is proportional to mean curvature. Unlike previous models, the velocity is not proportional to domain wall free energy. Experimental results on domain growth in ordered FeAl alloys over a range of temperatures, times and compositions, are consistent with the theory. In the vicinity of the critical temperature where domain wall free energy tends to zero, domain growth is not slowed. Introduction. — Antiphase domain boundaries are a non-equilibrium feature of real ordered alloys. Since there is a positive excess surface free energy associated with these boundaries, they move by diffusion in such a way that the total area of the boundaries is reduced. A long-standing phenomenological theory of interface motion [1-3] states that interfacial velocity is proportional to the thermodynamic driving force, the proportionality constant being a positive quantity called a mobility. The thermodynamic driving force in this theory is the product of the local mean curvature of the boundary and the excess surface free energy per unit area of boundary. A feature of higher-order transitions in ordering alloys is that the antiphase boundary energy approaches zero as the critical temperature is approached [4, 5]. Thus, the phenomenological theory of interface motion would seem to indicate that as the critical temperature for ordering is approached, antiphase domain growth should become very sluggish. In this paper, a new expression for interfacial velocity will be derived using a microscopic model. The excess surface free energy per unit area does not appear in this new formulation, and hence, the behavior of systems near critical points is more clearly represented. Application of the new result to the problem of macroscopic antiphase domain growth leads to a simple experimental test of the theory. Microscopic theory. — The kinetic equations of continuous ordering reflect the fact that the order parameter r\ is not a conserved quantity. If the free energy is not at a minimum with respect to a local variation in r\ there is an immediate change in r\ given by dr\ SF 5 ? = K ^ (1) where dFjStj is the variational derivative of the free energy of the system with respect to a local change in r\, and a is a positive kinetic coefficient. In a non-uniform system [5] bF\br\ = dFjdri 2 K VTJ (2) where dF/drj is the rate of change in free energy for uniformly ordered systems and 2 K Vr\ is the gradient energy contribution in a system in which r\ is varying spatially. We obtain for the time dependent problem