An evaluation was made of mean frequencies, for atomic jumps in a crystal,

starting from first principles based upon transition-state theory. Lithium diffusion

in LiC6 via the interstitial and vacancy mechanisms was taken 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

within the harmonic approximation. The lattice vibrations were treated within

quantum statistics, not using the usual Vineyard treatment corresponding to the

classical limit, and the discrepancy between the two treatments was quantitatively

considered. The apparent activation energies and the vibrational pre-factors of the

mean jump frequencies depended essentially upon temperature; unlike the classical

approximation case. The discrepancies in the activation energies corresponded to

the changes in zero-point vibrational energy at 0K, and the effect persisted even at

1000K. With regard to the vibrational pre-factors, the classical approximation

wildly over-estimated the pre-factors at low temperatures while the discrepancies

rapidly decreased with increasing temperature: e.g., by 30% at room temperature

and by 5% at 1000K. The calculated chemical diffusion coefficients of lithium

atoms via the interstitial and vacancy mechanisms were 10−11 and 10−10cm2/s,

respectively.

First-Principles Approach to Chemical Diffusion of Lithium Atoms in a Graphite

Intercalation Compound. K.Toyoura, Y.Koyama, A.Kuwabara, F.Oba, I.Tanaka:

Physical Review B, 2008, 78[21], 214303