One of the processes limiting the rate of charging of lithium ion batteries is the possibility that lithium will plate onto the graphite anode at high charging currents, leading to safety hazards. Lithium can plate when the filling fraction of lithium within the graphite approaches unity near the particle surface, which occurs when transport into the particles is not fast enough compared to the intercalation current. Thus, models must correctly describe the transport of lithium within the graphite, a phenomenon complicated by the fact that graphite particles tend to phase separate, both by forming staged structures in which lithium is only located between every n'th layer of graphene, and also by forming high and low concentration domains within individual layers. The different stages correspond to plateaus in the open circuit voltage and are characterized by a distinct visual color change, allowing optical characterization of local state of charge of graphite electrodes and particles. We propose here a simple free energy model to explain the intralayer phase separation as well as the high filling fraction staging structures. Then, we apply this free energy to a phase field transport model which allows us to capture single-crystal experimental intercalation results and makes distinct predictions from Fickian diffusion models, which we describe here.