References for 2.2

First-Principles Computation of Transition-Metal Diffusion Mobility

“…As a result, the activation energy for self-diffusion is mostly comprised of the energy for vacancy formation. These findings are supported by experimental data [2,3,[11][12][13] that showed the energy for vacancy formation constitutes a major part of the activation energy for diffusion in these metals. The addition of Ni in Mo, Cr, Fe, and W results in relatively small changes in the energy for vacancy and the activation energy for diffusion.…”

“…The energy of vacancy formation in Mo is 3.298 eV/atom for the 8-atom supercell, but it is 2.527 eV/atom for the 27-atom supercell. The experimental value of the energy of vacancy formation for Mo ranges from 2.6 to 3.2 eV/atom [11], in agreement with those of the 8-atom and 27-atom supercells. The 27-atom supercell without relaxation was selected for all computations since previous work [10] indicated that the E v value changed by less than 0.02 eV when the supercell size increased from 27 atoms to 54 atoms.…”

“…Once determined, the E s value was then summed with E v to obtain the activation barrier energy, Q, for the diffusion of Ni in Mo. The theoretical results are compared against literature data [3,[11][12][13] in Table 1, which indicates that good agreement between theoretical results from this study and experimental data.…”

“…For both cases, the first-principles computations are in good agreement with experimental data with a maximum error less than 9%. The computed Q values are independent of temperatures, as observed experimentally [3,[11][12][13]. (10) which can be equated to Eq.…”

“…Among the bcc metals investigated, the agreement between first-principles computation and experimental data are best for Mo, while the worst agreement is observed in W. For all metals, the energy of vacancy, E v , constitutes a significant portion of the activation energy, Q, for self-diffusion because the energy barrier for solute migration, E s , is comparatively small. [11,12] 0.16-1.28 [11] 277.9 [12] Ni in Fe 1.551 -0.055 154.99 ---…”