A finite deformation stress-dependent chemical potential and its applications to lithium ion batteries

This paper reports the development of a new stress-dependent chemical potential for solid state diffusion under multiple driving forces including mechanical stresses. The new stress-dependent chemical potential accounts for nonlinear, inelastic, and finite deformation. By using this stress-dependent chemical potential, insertion and extraction of lithium ions into a silicon particle is investigated. The distribution and evolution of diffusion-induced stress during the insertion/extraction processes are numerically calculated. Critical particle size is obtained as a function of the charging/discharging rates. It is also found that when plastic deformation occurs, the hoop stresses on the particle surface, contrary to intuition, can become positive even during the charging process, which may explain some of the recent experimental observations.