Analytical solutions for composition and stress in spherical elastic–plastic lithium-ion electrode particles containing a propagating phase boundary

Analytical solutions are derived for the distribution of Li concentration, chemical potential, and stress in a spherical particle of an active Li insertion material containing a propagating phase boundary. Results are presented both for elastic and inelastic host materials. We focus in particular on understanding the coupling between the solution thermodynamics, transport, and mechanical forces in the particle. It is shown that solution chemistry can have a strong influence on the stress state; and conversely, the stress state may significantly alter the equilibrium conditions at the phase boundary and the driving forces for phase boundary migration.