Large deformation analysis of diffusion-induced buckling of nanowires in lithium-ion batteries

Buckling due to diffusion-induced compressive stress has been observed during the lithiation of various nanowires, and can affect the mechanical and electrochemical performance of nanowire-based electrodes. This study is focused on the diffusion-induced buckling of nanowires. Two diffusion paths are analyzed; one with radial diffusion only, and the other with axial diffusion. For the diffusion-induced buckling of nanowires with radial diffusion, the theory of large deformation is used in the description of the coupling between mass transport and deformation in large deformed solids. Using the linear theory, analytical solution of the critical length of a nanowire, below which there is no buckling, is obtained, which is dependent on the constraint of the ends of the nanowire and the volumetric strain of the nanowire at the fully lithiated state. The comparison between the linear analytical solution of the critical length and the numerical solution from the theory of large deformation shows that the linear analytical solution is valid for the influx less than 1 mol · m⁻²· s⁻¹ and configurations considered in the work. Numerical analysis shows that the critical buckling time decreases with the increase of nanowire length and current density, and the nanowire with two fixed ends has a larger critical buckling time than that for the same nanowire with a fixed end and a pinned end. The nanowire length plays a bigger role in determining the critical state of charge for the onset of the buckling than that of the diffusion flux. The state of charge (SOC) at the state of critical buckling decreases with the increase of the nanowire length and increases with the increase of current density. For the diffusion-induced buckling of nanowires with axial diffusion, numerical analysis is performed. The numerical result reveals similar trend, i.e., the critical buckling time decreases with the increase of nanowire length and current density. The comparison of the critical buckling times for the conditions with axial diffusion, radial diffusion and diffusion from all sides, respectively, reveals that the contribution from axial diffusion is negligible even for small aspect ratio, and it does not change significantly with the increase of the aspect ratio.