First-principles-based calculation of self- and solute diffusion in bcc-Fe

DFT calculations were performed in order to study self-diffusion as well as oxygen and titanium diffusion in bcc Fe. It is commonly accepted that self-diffusion proceeds via the exchange of a Fe atom with a vacancy. The octahedral interstitial site is the most stable position of oxygen in bcc Fe. Therefore, it is assumed that O diffuses via the interstitial mechanism, i.e. an O atom moves from one octahedral site to the other. As for other substitutional solutes in bcc Fe, in the case of Ti the vacancy mechanism is considered. The migration barriers occurring in all these processes were calculated using the Nudged Elastic Band method. The corresponding attempt frequencies were obtained from the difference between the vibrational contribution to the free energy of the related equilibrium and saddle point configurations. While in the case of self- and O-diffusion only one saddle point and one attempt frequency are relevant, several barriers and frequencies must be determined to consider Ti diffusion by the vacancy mechanism. Different models were used to obtain the diffusion coefficient of Ti: (i) the original nine-frequency model [1], (ii) a modified nine-frequency model [2], and (iii) the Self-Consistent Mean Field model [3]. The comparison between the calculated self-, O-, and Ti-diffusion coefficients with experimental data shows significant differences. This is mainly due to fact that electron and magnon excitations were neglected in the calculations, whereas the phonon excitations were taken into account via the vibrational free energy. Under the assumption that electron excitations are small different phenomenological models are applied to consider the magnon excitations, which decrease the spontaneous magnetization of bcc Fe with increasing temperature. Choosing suitable model parameters a good agreement with measurements is obtained for self- and Ti-diffusion. On the other hand, the agreement with the few existing experimental data on O diffusion is poor. Possible reasons for this are discussed.

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[2] L. Messina, M. Nastar, T. Garnier, C. Domain, P. Olsson, Phys. Rev. B 90, 104203 (2014)
[3] M. Nastar, Philos. Mag. 85, 3767 (2005).