Thermodynamic and kinetic properties of the Li-graphite system from first-principles calculations

We present an ab initio study of the thermodynamics and kinetics of ${\text{Li}}_{\text{x}}{\text{C}}_{6}$, relevant for anode Li intercalation in rechargeable Li batteries. In graphite, the interlayer interactions are dominated by Van der Waals forces, which are not captured with standard density-functional theory (DFT). By calculating the voltage profile for Li intercalation into graphite and comparing it to experimental results, we find that only by correcting for vdW interactions between the graphene planes is it possible to reproduce the experimentally observed sequence of phases, as a function of Li content. At higher Li content the interlayer binding forces are increasingly due to Li-C interactions, which are well characterized by DFT. Using the calculated energies, corrected for the vdW interactions, we derive an ab initio lattice model, based on the cluster-expansion formalism, that accounts for interactions among Li ions in ${\text{Li}}_{\text{x}}{\text{C}}_{6}$ having a stage I and stage II structure. We find that the resulting cluster expansions are dominated by Li-Li repulsive interactions. The phase diagram, obtained from Monte Carlo simulations, agrees well with experiments except at low Li concentrations as we exclude stage III and stage IV compounds. Furthermore, we calculate Li migration barriers for stage I and stage II compounds and identify limiting factors for Li mobility in the in-plane dilute as well as in the high Li concentration range. The Li diffusivity, obtained through kinetic Monte Carlo simulations, slowly decreases as a function of Li content, consistent with increasing Li-Li repulsions. However, overall we find very fast Li diffusion in bulk graphite, which may have important implications for Li battery anode optimizations.