A Computational Comparative Study of the Lithium Diffusion in Amorphous Silicon Spheres, Rods, and Circular Disks

Abstract

We study through extensive finite element analysis the lithium diffusion in small elements of Si anodes under the forms of spheres, rods, and circular disks for Li-ion batteries. Elastoplastic properties of the amorphous silicon are assumed to be lithium concentration-dependent. Effects of the normalized flux of Li-ions on the lithium concentrations, stresses, and total equivalent plastic strains are considered. Effects of the disk's thickness are also included. At a given normalized flux, the heterogeneity of the lithiation, stresses, and plastic deformation increases in the order: disk, sphere, and rod. The thinner disk the better performance is. Below a critical value of the normalized flux of Li-ions, silicon spheres and disks exhibit linear elasticity and homogeneous distribution of Li-ions, whereas silicon rods undergo always plastic deformation after lithiation. When the radii of these three structures are smaller than several micrometers and the normalized flux is taken as 95% of their critical value, the charge time falls in the range from minutes to several hours. Our findings will help to optimize the charge and geometrical parameters for silicon anodes.