Constitutive equations for self-limiting lithiation of electrode nanoparticles in Li-ion batteries

• Constitutive equations are developed for stress-induced diffusion in viscoplastic media.
• The model accounts for basic phenomena observed in electrode particles under lithiation.
• Simulation confirms its ability to predict self-limiting lithiation quantitatively.

Constitutive equations are developed for the viscoplastic response of a host medium induced by diffusion of guest atoms. These relations are applied to analyze formation of stresses in spherical electrode particles under lithiation. Ability of the model to describe basic phenomena observed in experiments (formation of a sharp interphase between a Li-poor core and a Li-rich shell, growth of tensile hoop stresses at the outer surface of a particle leading to its fracture, and slowing down of the interphase motion) is revealed by numerical simulation. Good agreement is demonstrated between observations on interphase propagation in amorphous silicon nanoparticles and predictions of the model.