Phase-field study of electrochemical reactions at exterior and interior interfaces in Li-ion battery electrode particles

To study the electrochemical reaction on surfaces, phase interfaces, and crack surfaces in lithium ion battery electrode particles, a phase-field model is developed which describes fracture in large strains and anisotropic Cahn-Hilliard-Reaction. Thereby the concentration-dependency of the elastic properties and the anisotropy of diffusivity are also considered. The implementation in 3D is carried out by the isogeometric finite element method in order to treat the higher order terms in a straightforward manner. The electrochemical reaction is modeled through a modified Butler-Volmer equation to account for the influence of the phase change on the reaction on exterior surfaces. The reaction on the crack surfaces is considered through a volume source term weighted by a term related to the fracture order parameter. Based on the model, three characteristic examples are considered to reveal the electrochemical reactions on particle surfaces, phase interfaces, and crack surfaces, as well as their influence on the particle material behavior. The results show that both the anisotropy and the ratio between the timescales of reaction and diffusion can have a significant influence on the phase segregation behavior. In turn, the distribution of the lithium concentration strongly influences the reaction on the surface, especially when the phase interfaces appear on exterior surfaces or crack surfaces. The reaction rate increases considerably at phase interfaces due to the large lithium concentration gradient. Moreover, the simulations demonstrate that the segregation of a Li-rich and a Li-poor phase during delithiation can drive the cracks to propagate. The results indicate that the model can capture the electrochemical reaction on the freshly cracked surfaces.