First-Principles Calculation of Self-Diffusion Coefficients

We demonstrate a first-principles method to compute all factors entering the vacancy-mediated self-diffusion coefficient. Using density functional theory calculations of fcc Al as an illustrative case, we determine the energetic and entropic contributions to vacancy formation and atomic migration. These results yield a quantitative description of the migration energy and vibrational prefactor via transition state theory. The calculated diffusion parameters and coefficients show remarkably good agreement with experiments. We provide a simple physical picture for the positive entropic contributions.

Figure 1

First-principles (GGA) calculated phonon DOS of defect-free fcc Al, Al with a single vacancy, and Al with the diffusing atom in the transition state. The negative frequencies in phonon DOS of TS are due to the unstable mode.

Figure 2

Equilibrium vacancy concentration from first-principles (LDA and GGA quasiharmonic calculations) plotted in comparison with experimental data [30, 43, 44]. The experimental results of Seeger [44] are from monovacancies only.

Figure 3

Complete first-principles calculation results of self-diffusion coefficients for Al. Results are shown for both the HA and QHA using both LDA and GGA. Calculated results are compared with experimental results [25, 26, 27, 28, 29].