Stress distribution within spherical particles undergoing electrochemical insertion and extraction

We examine the effects of surface tension and surface modulus on diffusion-induced stress (DIS) within spherical nano-particles undergoing electrochemical insertion and extraction. By assuming small mechanical deformation characterized by isotropic linear elasticity and a dilute solution within the solid state for the diffusion problem, we are able to generate analytic solutions for the combined problem of mechanical deformation and diffusion of the insertion species. The results may be viewed as benchmark calculations that help one to understand how stress evolves within insertion electrodes. Both the magnitude and distribution of stress are affected by the surface mechanics if the particle diameter is sufficiently small; for example, during insertion, the tensile state at the center of spherical particles may be significantly reduced in magnitude or even converted from hydrostatic tension to compression with decreasing particle radius. This reduction in tensile stress motivates the examination of reducing particle size so as to improve the mechanical stability of electrode materials.