The increasing demand for high-energy-density lithium-ion batteries motivates a search for alternative electrode materials. Experimentally obtained graphene-based structures have been suggested to replace the state-of-the-art graphitic anode. For a thorough characterization of Li adsorption on graphene, we study the interaction of Li with graphene both at zero and finite temperatures. The zero-temperature study was carried out by means of density functional theory (DFT), accounting for van der Waals (vdW) interactions, whereas the finite temperature behavior was studied by Monte Carlo techniques with a DFT-derived Li-graphene interaction potential constructed via cluster expansion method. Our calculations reveal two distinct types of orderings of Li on graphene, Li-gas (dispersed Li-ion) and Li-cluster phases. The zero-temperature calculations show that, even when vdW is included, the Li-graphene interaction is mainly electrostatic and phase separation to pristine graphene and bulk Li is energetically most favorable. However, at nonzero temperatures, entropy contribution to free energy allows the lesser-ordered Li-gas and Li-cluster states to be more favorable at sufficiently low concentrations: at temperatures below 400 K and concentrations below 1Li:6C, Li-gas and Li-cluster phases coexist whereas at higher concentrations, only clusters remain stable. At temperatures above 400 K, Li-gas phase can be stabilized with respect to Li cluster or Li bulk at higher concentrations. Furthermore, small variations in chemical potential are shown to be enough to change that concentration threshold. Finally, we show that the Li-cluster phases can have Li-island or Li-stripe ordering; however, Li stripes appear due to the finite size of the simulation cell and therefore the Li-island phase is expected to dominate in the thermodynamic limit instead.
