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.

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