First principles study on formation and migration energies of sodium and lithium in graphite

Graphite is used as an anode material in conventional lithium-ion batteries owing to its ability to form stable Li-intercalated graphite intercalation compounds (Li GICs). Its application to sodium-ion batteries has long been of great interest, but the instability of Na GICs hampers its implementation. First-principles calculations were performed to gain physical insight into the intercalation process in alkali-metal (AM) GICs, where $\mathrm{AM}=\mathrm{Li}$, Na. In this study, the structure, stability, and diffusion properties of AM GICs with various in-plane AM concentrations were systematically investigated using a van der Waals density functional simulation, and the differences between Li and Na GICs were discussed. Li GICs were found to be quite stable over a wide range of in-plane Li concentrations, with a change in the favorable stacking sequence of graphite. In terms of diffusion, the migration energy for Li in graphite increases as the graphite stacking transition occurs, suggesting that hindering the stacking transition could realize fast and uniform Li diffusion. In contrast, Na GICs are less stable than Li GICs because of following two reasons: (1) interaction between Na and carbon is less stable than that between Li and carbon, and (2) a larger amount of deformation in the interlayer distance is necessary. The Na GICs tend to be stabilized by increasing the number of Na-carbon interactions. Namely, fasted Na diffusion is expected in the Na-rich phase. Our systematic simulations of the formation energy and migration energy of Na GICs with different structures and in-plane AM concentrations suggested that the expansion of graphite layers prior to Na intercalation could achieve graphite anodes for Na-ion batteries.