Mean frequencies for atomic jumps in a crystal were evaluated from first principles based upon transition state theory, taking lithium diffusion by interstitial and vacancy mechanisms in LiC6 as a model case. The mean jump frequencies were quantitatively evaluated from the potential barriers and the phonon frequencies for both initial and saddle-point states of the jumps under the harmonic approximation. The lattice vibrations were treated within quantum statistics, not using the conventional treatment by Vineyard corresponding to the classical limit, and the discrepancy between the two treatments was quantitatively discussed. The apparent activation energies and the vibrational pre-factors of the mean jump frequencies essentially depended on temperature, unlike in the case of the classical approximation. The discrepancies of the activation energies correspond to the changes in zero-point vibrational energy at 0K, and there remains the effect even at 1000K. With regard to the vibrational pre-factors, the classical approximation extremely overestimates the pre-factors at low temperatures while the discrepancies rapidly decrease with increasing temperature, e.g., by 30% at room temperature and by 5% at 1000K. The calculated chemical diffusion coefficients of lithium atoms by the interstitial and vacancy mechanisms were 1 x 10-11 and 1 x 10-10cm2/s, respectively.

First-Principles Approach to Chemical Diffusion of Lithium Atoms in a Graphite Intercalation Compound. Toyoura, K., Koyama, Y., Kuwabara, A., Oba, F., Tanaka, I.: Physical Review B, 2008, 78[21], 214303