A Free Volume-Based Viscoplastic Model for Amorphous Silicon Electrode of Lithium-Ion Battery

The phase transition of Si from crystalline phase to amorphous phase with the formation of metastable amorphous structures of Li₁₂Si₇, Li₇Si₃, Li₁₃Si₄ and Li₂₂Si₅ after the first few cycles suggests that the Si in Si-based lithium-ion battery is mainly present in amorphous phase. In this work, we extend the free volume theory, which has been widely used in the deformation analysis of bulk metallic glass, to describe the cycling-induced visco-plastic deformation in amorphous Si-electrode during electrochemical cycling and establish a constitutive relationship with the flow unit of free volume for the plastic flow in lithiated Si. The plastic flow in lithiated Si is accompanied with the creation and annihilation of free volume. Using the constitutive relationship and incorporating the concentration-dependent mechanical properties of lithiated Si, we study the cycling-induced evolution of Cauchy stress and free volume in amorphous, thin-film Si-electrodes. The numerical results are in good accord with the experimental results reported in literature, which validates the approximation used in the analysis of the cycling-induced deformation of the amorphous, thin-film Si-electrodes.