Phenomenological coefficients in a dilute BCC alloy for the dumbbell mechanism

The self-consistent mean field (SCMF) method is applied to calculate the transport coefficients in a dilute BCC alloy with the dumbbell diffusion mechanism. The first degree of approximation (first shell) of the SCMF formalism coincides with the formerly derived pair association method, and the second degree of approximation (second shell) leads to a more accurate analytical formulation. The SCMF results are compared with other formalisms as well as existing and new Monte Carlo simulations, including the solute-dumbbell binding energy. This theory shows a good balance between accuracy and complexity in the investigated systems, and a simple criterion is proposed for the preferential use of the first and second shell approximations.