Modeling of plasticity coupled to diffusion and chemical reaction in high-capacity electrodes for Li-ion batteries

Rechargeable Li-ion batteries operate by cyclically inserting lithium into, and extracting lithium from, solid electrodes. The diffusion of lithium into a solid host induces significant volume change, which in turn generates stresses when the expansion is constrained. Diffusion-induced stresses often lead to mechanical degradation of the electrode, and also have a major impact on the diffusion process and the electrochemistry of the battery. Predicting the stress generated during lithiation and delithiation is crucial for designing batteries with enhanced cycle life and electrochemical performance. We focus on silicon, a promising anode material with high specific capacity: each silicon atom can host up to 4.4 lithium atoms. Lithiation of silicon is accompanied by huge swelling (up to 300%), which can be accommodated by plastic deformations. However, the micro-mechanisms inducing the macroscopically observed plastic deformations in amorphous silicon are not well understood, raising fundamental questions regarding the coupling between inelastic deformation, diffusion and bulk chemical reactions. We propose a continuum model that couples mass transport to large, inelastic deformations within the framework of the thermodynamics of irreversible processes. In particular, the model introduces a coupling between the kinetics of plastic flow and that of insertion reaction. The model formulation and parameter identification is supported by ab-initio calculations, as well as experimental measurements on thin film electrodes. The model was implemented into a FE software, allowing us to predict the stress and electric potential in silicon electrodes subjected to cycles of lithiation and delithiation. The influence of several parameters (electrode dimensions, charging rate, yield strength) are discussed. The numerical tool is useful for optimizing electrode geometry and loading conditions.