Stress generation during lithiation of high-capacity electrode particles in lithium ion batteries

A model is developed to study the stress generation in a spherical particle subjected to lithium insertion. The model accounts for both the plastic deformation and the coexistence of lithium-poor and lithium-rich phases with a sharp and curved phase boundary. Such two-phase and inelastic deformation characteristics often arise during lithiation of crystalline particles with high capacity. A flexible sigmoid function is used to create the lithium profile with a step-like change in lithium concentration, mimicking a sharp phase boundary that separates a pristine core and a lithiated shell in the particle. The mechanics results, obtained by an analytic formulation and finite difference calculations, show the development of tensile hoop stress in the surface layer of the lithiated shell. This hoop tension provides the driving force of surface cracking, as observed by in situ transmission electron microscopy. The two-phase lithiation model is further compared with the single-phase one, which assumes a gradual and smooth variation in radial lithium distributions, and thus predicts only hoop compression in the surface layer of the particle. Furthermore, the effect of dilatational vs. unidirectional lithiation strains in the two-phase model is studied, thereby underscoring the critical role of anisotropy of lithiation strain in controlling stress generation in high-capacity electrodes for lithium ion batteries.