The Mathematical Framework for the Interface Reaction Controlled the Two-Phase Lithiation of the Crystalline Silicon Nanowire

A modified chemo-mechanical model of crystalline silicon nanowire during the first lithiation is presented. Here, we incorporate the kinetics of the addition reaction, thereby mimicking the experimentally observed lithium-rich zone, lithium-poor zone, and the moving interface. Also, this model consists of a strongly two-way coupled diffusion of lithium through the lithium-rich zone. The total deformation gradient is expressed in terms of the elastic, plastic, and stress deformation using multiplicative decomposition. Interface reaction exponents are fitted by adjusting the same parameter so that it reproduces an interface velocity observed experimentally. Therefore, a comparative analysis with the result obtained for spherical crystalline silicon anode particles shows uniform distribution of lithium concentration and a non-hydrostatic state of stress in the lithium-poor zone.