Competitive ion diffusion within grain boundary and grain interiors in polycrystalline electrodes with the inclusion of stress field

Herein, we present a phase-field model (PFM) representing ions diffusion/intercalation into polycrystalline battery electrodes and its coupling to mechanics equations. Electrochemical free energy functions, considering ions diffusion within the grains and the grain boundary (GB), along with the elastic stress field associated with ions intercalation, are considered. The phase-field GB model is used to generate thin film grain structures and subsequently to study their evolution during the ions diffusion. The partial differential equations, representing ions concentration progress and the GB evolution, are solved computationally using the finite element method. In order to validate and to demonstrate capabilities of the model, we use examples of SnSb thin film sodiation. The results showed that the generated stress upon Na diffusion tends to slow down diffusion kinetics. In order to assess the effects of various model parameters on the sodium diffusion and the GB evolution, a sensitivity analysis was performed by calculating the sodiation rate. The present paper, in addition to the development of the coupled grain boundary to concentration field phase-field model, provides new insights concerning the influences of Na diffusion on the SnSb thin film performance.