Understanding the mechanism of stress mitigation in Selenium-doped Germanium electrodes via a reaction-diffusion phase-field model
Stone, Tonya W.
Recent experiments revealed micrometer (µm)-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. And, the high Li diffusivity of the amorphous Li-Ge-Se network provides an effective Li diffusion path for inter-particle diffusion, reducing stress difference between the surfaces of neighboring particles. Besides, the constraint between the adjacent particles induces a higher compressive stress at the reaction front impeding the mobile Li insertion during lithiation. Though small c-Ge nano-particle in the Ge0.9Se0.1 microparticle is lithiated faster than large one, the compressive stress is generated at the center of small one for stress equilibrium which causes more retardation effect. Meanwhile, the size difference between adjacent particles increases the principle and shear stresses in the inactive Li-Ge-Se network near adjacent surfaces, which could potentially lead to mechanical failure and debonding of the amorphous network. We believe that the results of this investigation can shed some light on the optimization design of electrodes.