The free energy of the concerted exchange mechanism for self-diffusion was estimated by using the thermodynamic integration method and Monte Carlo simulations, with an interatomic potential that had been fitted to local density approximation calculations. Anharmonicity and relaxation were taken fully into account in the calculations, since the phase space was extensively covered by the Monte Carlo simulations. The results indicated that the concerted exchange mechanism could make a significant contribution to the self-diffusion coefficient in Si.

A.Antonelli, S.Ismail-Beigi, E.Kaxiras, K.C.Pandey: Physical Review B, 1996, 53[3], 1310-4