Stress evolution with concentration-dependent compositional expansion in a silicon lithium-ion battery anode particle

Abstract

Silicon with the highest known theoretical capacity for lithium uptake may expand in volume by as much as 400%, leading to pulverization and capacity fading. This volume expansion is traditionally modelled using a constant value of the coefficient of compositional expansion (CCE) even though it has been already shown that the CCE may vary significantly with lithium concentration. In the present work, this variation is incorporated into a continuum model based on finite deformation theory, and the resulting framework is used to study two model cases: a solid Si particle and an annular Si particle undergoing lithiation. The mechanical behavior is investigated considering the two-way coupling between stress and diffusion of lithium in silicon both with and without plasticity. Striking quantitative and qualitative differences are observed when the mechanical stresses within the Si particle are compared for the cases of concentration-dependent CCE and constant CCE.