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 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 ϫ 10 −11 and 1 ϫ 10 −10 cm 2 / s, respectively.

Diffusion of alkali metals in the first stage graphite intercalation compounds by vdW-DFT calculations

“…Atomic jumping in a diffusion process may consist of several steps and the total jumping frequency is obtained from the individual jumps 25 .…”

“…Previous density functional theory (DFT) studies of alkali metal diffusion in graphite have primarily focused on Li-GICs, [25][26][27][28][29][30] while the diffusion of Na in Na-GICs and K in K-GICs has been comparatively less studied and a systematic comparison between Li, Na and K diffusion in GICs is lacking.…”

“…The energy barriers were calculated according to climbing image Nudged Elastic Band theory 32 and the diffusion coefficients were derived from transition state theory. 25 …”

Potential Energy Surface Mapping of Charge Carriers in Ionic Conductors Based on a Gaussian Process Model

“…The blue regions around the O ions are the most stable proton sites and are located ∼1 Å from the O ions. The OH distance is almost equivalent to that in water, indicating that OH bond formation stabilizes the protons in BaZrO 3 . There are four equivalent proton sites per O ion, which are connected by the low-PE points around the O ions.…”

“…ν 0 is typically a constant value in the range of 10 12 -10 13 s −1 associated with a lattice vibration [3][4][5][6][7][8]. Consequently, ΔE mig mainly determines the rate of an atomic jump in a solid.…”