Free Energy Model for Lithium Intercalation in Graphite: Focusing on the Coupling with Graphene Stacking Sequence

During intercalation, some layered intercalation compounds undergo phase separation between several stable phases, known as stages. Of particular interest is the case of graphite, widely used in negative electrodes of batteries. Here, thermodynamics and kinetics of stage formation are studied using a multilayer free energy framework based on mean-field theory, accounting for both intralayer and interlayer interactions. More specifically, an order parameter is introduced to describe the local evolution of the stacking sequence of graphene sheets around lithium islands, enabling the distinction between the liquid-like stage 2L and the stage 2. In particular, we show that an interlayer interaction between the lithium ions and the host structure is necessary to counterbalance the enthalpic term of the lithium intralayer energy and allow the formation of islands with intermediate concentrations, characteristics of the liquid-like phases. Introducing the developed free energy model in Cahn–Hilliard's and Allen–Cahn's equations, we study the stages emergence during spinodal decompositions. Staggered domains of lithium surrounded by different graphene stacking arise naturally with characteristics typical of stages 1′, 3L, 2L, 2, and 1.