Probing the effect of surface parameters and particle size in the diffusion-induced stress of electrodes during lithium insertion

Experimental studies have shown that the active particles of electrodes undergo phase transformations during ion-insertion, which are accompanied by diffusion induced stresses that result in fracture at the particle surface. Only a few studies have considered the effect that the surface stress has on the diffusion-induced stress that occurs in electrode materials that undergo elastic deformations during ion-insertion, while no studies have accounted for the effect of surface stresses in the case when plastic deformation is also present. In addition, there are only few comprehensive studies on the competing effect between the surface stress and the strain gradient during ion diffusion. The present work sheds light on the effect that the particle size has on the stresses generated due to the phase transformations that take place during ion-insertion by accounting for the surface residual stress with strain gradient elasticity or strain gradient plasticity. Due to the presence of surface stresses, the stress on the particle outer surface can be significantly reduced. In particular, when the residual surface stress and the surface elastic modulus are both positive, the hoop stress at the outer surface remains compressive, whereas tensile stresses are required for crack formation. This work, therefore, indicates that surface modification could be an effective approach for improving the structural integrity of electrodes during the lithiation process. The additional consideration of strain gradients further reduces the value of the equivalent plastic strain for elasto-plastic electrode particles. These findings render prospective insights for designing next-generation mechanically stable phase transforming electrode materials.