Sphere-in-contact model for the development of new graphite-based intercalated battery materials

We apply the sphere-in-contact model/theorem to the crystallographic analysis of graphite intercalation compounds (GICs), using a unit cell description based on the AαAα stacking of two graphene layers. Under ambient conditions, the model predicts that LiC₆ has the largest diffusion rate parameter based on geometric considerations and repulsive interactions between intercalated atoms and has a thermodynamically stable lithium GIC stoichiometry; furthermore, two crystallographically distinct forms of LiC₈ are attainable but have lower diffusion rate parameters. Notably, the only experimental input required to predict stoichiometric stability is the interlayer spacing, which is readily obtained from X-ray diffraction (XRD) data. Additional empirical formulae-MC₂, MC₃, and M₃C₈-are geometrically permissible but thermodynamically destabilised by repulsive interactions between intercalants. The density, packing fraction, and ion diffusivity during charge and discharge are derived analytically from the void space within the unit cell. The framework is broadly applicable to any intercalant and provides a simple, computationally and experimentally accessible basis for the rational design of graphite-based materials for next-generation ion-battery applications.