To study the electrochemical reaction on surfaces, phase interfaces, andcrack surfaces in the lithium ion battery electrode particles, a phase-fieldmodel is developed, which describes fracture in large strains and anisotropicCahn-Hilliard-Reaction. Thereby the concentration-dependency of the elasticproperties and the anisotropy of diffusivity are also considered. Theimplementation in 3D is carried out by isogeometric finite element methods inorder to treat the high order terms in a straightforward sense. Theelectrochemical reaction is modeled through a modified Butler-Volmer equationto account for the influence of the phase change on the reaction on exteriorsurfaces. The reaction on the crack surfaces is considered through a volumesource term weighted by a term related to the fracture order parameter. Basedon the model, three characteristic examples are considered to reveal theelectrochemical reactions on particle surfaces, phase interfaces, and cracksurfaces, as well as their influence on the particle material behavior. Resultsshow that the ratio between the timescale of reaction and the diffusion canhave a significant influence on phase segregation behavior, as well as theanisotropy of diffusivity. In turn, the distribution of the lithiumconcentration greatly influences the reaction on the surface, especially whenthe phase interfaces appear on exterior surfaces or crack surfaces. Thereaction rate increases considerably at phase interfaces, due to the largelithium concentration gradient. Moreover, simulations demonstrate that thesegregation of a Li-rich and a Li-poor phase during delithiation can drive thecracks to propagate. Results indicate that the model can capture theelectrochemical reaction on the freshly cracked surfaces.
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