The self-consistent mean field method was used to calculate the transport coefficients in a dilute body-centered cubic alloy with the dumb-bell diffusion mechanism. The first degree of approximation (first shell) of the self-consistent mean field formalism coincided with the formerly derived pair association method, and the second degree of approximation (second shell) led to a more accurate analytical formulation. The self-consistent mean field results were compared with other formalisms as well as existing and new Monte Carlo simulations, including the solute/dumb-bell binding energy. This theory showed a good balance between accuracy and complexity in the investigated systems, and a simple criterion was proposed for the preferential use of the first and second shell approximations.

Phenomenological Coefficients in a Dilute BCC Alloy for the Dumb-Bell Mechanism. V.Barbe, M.Nastar: Philosophical Magazine, 2007, 87[11], 1649-69