Concurrent reaction and plasticity during initial lithiation of crystalline silicon in lithium-ion batteries

In an electrochemical cell, crystalline silicon and lithium react at room temperature, forming an amorphous phase of lithiated silicon.  The reaction front—the phase boundary between the crystalline silicon and the lithiated silicon—is atomically sharp.  Evidence has accumulated recently that the velocity of the reaction front is limited by the rate of the reaction at the front, rather than by the diffusion of lithium through the amorphous phase.  This paper presents a model of concurrent reaction and plasticity.  We identify the driving force for the movement of the reaction front, and accommodate the reaction-induced volumetric expansion by plastic deformation of the lithiated silicon.  The model is illustrated by an analytical solution of the co-evolving reaction and plasticity in a spherical particle.  We derive the conditions under which the lithiation-induced stress stalls the reaction.  We show that fracture is averted if the particle is small and the yield strength of lithiated silicon is low.  Furthermore, we show that the model accounts for recently observed lithiated silicon of anisotropic morphologies.