Modeling intercalation in cathode materials with phase-field methods: Assumptions and implications using the example of [formula omitted

Abstract

The multiphase-field method has great potential to advance future research on battery materials. In this work, we discuss the modeling of phase-separating intercalation compounds based on the Cahn-Hilliard equation as well as a multi-phase, multi-component model operating in an Allen-Cahn framework. Modeling assumptions are introduced step-by-step to facilitate future developments and bridging the gap across scales. Dimensionality reduction reflecting the material anisotropies can be critical for combining the phase-field approach with Newman-type models. Furthermore, we discuss a nano-particle battery model starting from intercalation in a defect-free, single-crystalline platelet. The underlying modelling assumptions are reduced step-by-step, first, including in-plane diffusion as a result of crystal defects and finally accounting for a polycrystalline material section. We show how faster in-plane diffusion promotes phase separation while higher C-rates and coherency strain lead to the opposite effect. This work highlights the importance to consider pre-existing grain boundaries for nucleation at higher-order junctions, heterogeneity of the intercalation fluxes and grain-by-grain filling behaviour. Anisotropic elastic deformation leads to high stresses at the evolving phase boundaries, especially at high misorientations between neighbouring grains. The maximum principle stress is used as an estimate for degradation by fracture in polycrystals.