First-principles approach to chemical diffusion of lithium atoms in a graphite intercalation compound

Abstract

We evaluate mean frequencies for atomic jumps in a crystal from first principles based on transition state theory, taking lithium diffusion by the interstitial and vacancy mechanisms in ${\text{LiC}}_{6}$ as a model case. The mean jump frequencies are 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 are treated within quantum statistics, not using the conventional treatment by Vineyard corresponding to the classical limit, and the discrepancy between the two treatments is quantitatively discussed. The apparent activation energies and the vibrational prefactors of the mean jump frequencies essentially depend 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 0 K, and there remains the effect even at 1000 K. With regard to the vibrational prefactors, the classical approximation extremely overestimates the prefactors at low temperatures while the discrepancies rapidly decrease with increasing temperature, e.g., by 30% at room temperature and by 5% at 1000 K. The calculated chemical diffusion coefficients of lithium atoms by the interstitial and vacancy mechanisms are $1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}11}$ and $1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}\text{ }{\text{cm}}^{2}/\text{s}$, respectively.