The energy during the process of self-diffusion in body-centered cubic transition metals Fe, W, Mo, Cr, Ta, Nb and V was calculated by using modified analytic embedded-atom method. For each kind of 3 diffusion mechanisms nearest-neighbor, next-nearest-neighbor and third-nearest-neighbor, the energy curve was symmetric and the maximum value of the energy appeared at the middle point of the diffusion path. Determined mono-vacancy formation energy, migration energy and activation energy for self-diffusion agreed well with available experimental data of nearest-neighbor diffusion and were better than those obtained by the analytic embedded-atom method and Finnis–Sinclair models. Compared the energies corresponding to 3 diffusion mechanisms, the nearest-neighbor diffusion needs the lowest activation energy (and thus the lowest migration energy). So that, the nearest-neighbor mono-vacancy diffusion was favorable in body-centered cubic transition metals.

Self-Diffusion of BCC Transition Metals Calculated with MAEAM. J.M.Zhang, G.X.Chen, K.W.Xu: Physica B: Condensed Matter, 2007, 390[1-2], 320-4