Modeling of Coupling Between Free Volume Evolution and Diffusion in Silicon Electrodes of Lithium-Ion Batteries

Silicon, a leading candidate for electrode material for lithium-ion batteries, has garnered significant attention. During the initial lithiation process, the alloying reaction between silicon and lithium transforms the pristine silicon microstructure from crystalline to amorphous, resulting in plastic deformation of the amorphous phase. This study proposes the free volume theory to develop a fully coupled Cahn-Hilliard phase-field model that integrates viscoplastic deformation, free volume evolution, and diffusion. This model investigates the chemophysical phenomenon of self-limiting behavior occurring during the initial lithiation of silicon anodes. Unlike most existing models, the proposed model considers free volume-dependent diffusion using a physically-based approach. The model's temporal variation in the lithiated phase thickness aligns well with experimental results, confirming the model's accuracy. Stress field calculations reveal the coexistence of compressive and tensile stresses within the lithiated phase, which may not cause the limiting effect under the frame of the stress-induced diffusion. Analyses indicate that high effective stress increases free volume, enhancing lithium diffusion and augmenting the diffusion coefficient. Reducing the diffusion coefficient in the lithiated phase due to free volume evolution is the primary cause of self-limiting lithiation.