A tracer representation of the rate coefficient involved in the relaxation of diffuse spherical phase–antiphase boundaries in symmetric B2 binary ordering alloys is presented. Adopting broadly accepted Allen–Cahn [Acta Metall. 27, 1085 (1979)] diffusion-reaction phenomenology, but incorporating vacancy kinetics together with a conventional Landau driving force based upon mean curvature K and the surface free energy σ following Lifshitz, we obtain a non-Arrhenius rate coefficient D = 2Mκ appearing within the Allen–Cahn [Acta Metall. 27, 1085 (1979)] velocity expression which pertains to the symmetric β-brass type coarsening kinetics: v/K = 2Mκ ≃ 2D∗(Tc−T)/(Tc)1/2, where M is a non-Einstein mobility coefficient, κ is the gradient energy coefficient, D∗ is a near-Arrhenius empirical mean tracer diffusion coefficient, and Tc is the critical temperature. This temperature dependency, together with Arrhenius D∗, offers satisfactory agreement with the experiments of Allen, Cahn, and Krzanowski. On the basis of an Allen–Cahn [Acta Metall. 27, 1085 (1979)] σ for a diffuse interface in the mean field approximation this translates to a velocity curvature relation of the form v ∼ D∗σ1/3K. This represents an element of conflict since Allen and Cahn [Acta Metall. 27, 1085 (1979)] have favored a velocity or mobility which is independent of σ. © 1998 American Institute of Physics.