Stress and strain-energy distributions within diffusion-controlled insertion-electrode particles subjected to periodic potential excitations

We derive and implement analytic solutions for the description of insertion particles subject to cyclic surface concentration variations consistent with a periodic voltage excitation source applied to an insertion electrode wherein the overall resistance is dominated by that of solid-state diffusion within the electrode particles. The form of the analytic solution allows for a direct analogy to cyclic fatigue phenomena that have been examined in detail for structural materials over the past two centuries. We utilize the strain-energy density to assess the potential for crack nucleation, and we show that while the shear stress is independent of the surface tension and surface modulus, the strain-energy density, which drives particle fracture, is sensitive to the surface mechanics and therefore the particle radii. Specifically, the analysis implies that smaller particles are more stable relative to diffusion-induced decrepitation and cracking, consistent with experimental observations.