Modeling Phase Transition in Battery Electrodes Using the Coupled Cahn-Hilliard – Phase Field Crystal Methods

Phase transitions in electrode materials are typically accompanied by lattice distortions and defect formations. These microscopic configurations affect an electrochemical cycle and influence the physical properties of electrode materials. Here, we develop a 2D theoretical framework that couples a Cahn-Hilliard (CH) model describing Li-concentration evolution, with a phase-field crystal (PFC) model describing the underlying lattice symmetry of the electrode material. We apply this CH-PFC model to describe three representative examples of microstructures in a LiFePO₄ electrode. First, we model lattice arrangements in a uniformly lithiated (LFP) or delithiated (FP) electrode. Next, we model a partially lithiated electrode and describe the lattice distortions across a diffuse phase boundary. Finally, we model a Cahn-Hilliard type of diffusion for the Li-concentration field and compute the accompanying structural evolution of atomic arrangements. In this numerical study, we report the formation of grains in a single FP/LFP phase, and identify the position/orientation of grain boundaries. Furthermore, the simulations track the migration of grain boundaries and demonstrate the motion of lattice defects during an electrochemical cycle.