  To study the electrochemical reaction on surfaces, phase interfaces, and
crack surfaces in the 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 isogeometric finite element methods in
order to treat the high order terms in a straightforward sense. 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. Results
show that the ratio between the timescale of reaction and the diffusion can
have a significant influence on phase segregation behavior, as well as the
anisotropy of diffusivity. In turn, the distribution of the lithium
concentration greatly 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, simulations demonstrate that the
segregation of a Li-rich and a Li-poor phase during delithiation can drive the
cracks to propagate. Results indicate that the model can capture the
electrochemical reaction on the freshly cracked surfaces.
