Pressure-Gradient Dependent Diffusion and Crack Propagation in Lithiated Silicon Nanowires

Silicon is a promising material for use in lithium-ion battery electrodes due to its extremely high theoretical capacity. The difficulty associated with using silicon in these applications is due to the fact that it undergoes large volumetric expansions of up to 400% during lithiation; such extreme expansions generate high stresses that can lead to fracture and capacity loss. Previous attempts at modeling cracking in lithiated materials have entirely ignored or simplified the effects of pressure-gradients on the diffusive flux, which leads to an overestimation of the stress-state within the material. We have developed a method of studying lithiation-induced crack propagation in silicon nanowires that accounts for the effects of pressure-gradients within the material on the flux. Our approach consists of finite element simulations in which the pressure-gradients are computed numerically and used to calculate the flux vector. This method allows us to capture the effect of the crack-tip on the localized diffusion, which plays an important role in arresting crack growth. We have used our method to study the effects of charging rate and particle size on crack propagation in silicon nanowires. Three crack growth regimes have been observed depending on the charging rate and nanowire diameter - no growth, arrested growth, and complete growth - and they have been tabulated in a failure diagram.