A phase-field model integrating reaction-diffusion kinetics and elasto-plastic deformation with application to lithiated selenium-doped germanium electrodes

Recent experiments revealed micrometer (m)-sized selenium (Se)-doped germanium (Ge) particles forming a network of inactive phase (Li-Ge-Se) bring superior performance in cycling stability and capacity over un-doped Ge particles. Therefore, based on two states of Li (one for diffusion and another for alloyed reaction), a phase-field model (PFM) is developed incorporating both chemical reaction and Li diffusion to investigate remaining elusive underpinning mechanism. The reaction-diffusion PFM enables us to directly determine the conditions under which the lithiation process is diffusion- and/or reaction-controlled. Moreover, coupling the elasto-plastic deformation, the model allows us to investigate the role of the inactive phase in morphology and stress variation of Se-doped Ge electrode upon lithiation. The numerical results reveal that the tensile hoop stress at the surface of the particles is significantly suppressed due to softness of the inactive Li Ge Se phase, in line with the experimental observation of surface fracture-free behavior. Further, we find that the soft Li Ge Se phase reduces a compressive mean stress at the reaction front, thus alleviating the stress retardation effect on the lithiation kinetics.