Discharge, relaxation, and charge model for the lithium trivanadate electrode: Reactions, phase change, and transport

The electrochemical behavior of lithium trivanadate (LiV₃O₈) during lithiation, delithiation, and voltage recovery experiments is simulated using a crystal-scale model that accounts for solid-state diffusion, charge-transfer kinetics, and phase transformations. The kinetic expression for phase change was modeled using an approach inspired by the Avrami formulation for nucleation and growth. Numerical results indicate that the solid-state diffusion coefficient of lithium in LiV₃O₈ is ∼10^-13 cm² s^-1 and the equilibrium compositions in the two phase region (∼2.5 V) are Li_2.5V₃O₈:Li₄V₃O₈. Agreement between the simulated and experimental results is excellent. Relative to the lithiation curves, the experimental delithiation curves show significantly less overpotential at low levels of lithiation (end of charge). Simulations are only able to capture this result by assuming that the solid-state mass-transfer resistance is less during delithiation. The proposed rationale for this difference is that the (100) face is inactive during lithiation, but active during delithiation. Finally, by assuming non-instantaneous phase-change kinetics, estimates are made for the overpotential due to imperfect phase change (supersaturation).