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 Li2.5V3O8: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)

Modeling the Mesoscale Transport of Lithium-Magnetite Electrodes Using Insight from Discharge and Voltage Recovery Experiments

A multi-scale mathematical model, which accounts for mass transport on the crystal and agglomerate length-scales, is used to investigate the electrochemical performance of lithium-magnetite electrochemical cells. Experimental discharge and voltage recovery data are compared to three sets of simulations, which incorporate crystal-only, agglomerate-only, or multi-scale transport effects. Mass transport diffusion coefficients are determined by fitting the simulated voltage recovery times to experimental data. In addition, a further extension of the multi-scale model is proposed which accounts for the impact of agglomerate size distributions on electrochemical performance. The results of the study indicate that, depending on the crystal size, the low utilization of the active material is caused by transport limitations on the agglomerate and/or crystal length-scales. For electrodes composed of small crystals (6 and 8 nm diameters), it is concluded that the transport limitations in the agglomerate are primarily responsible for the long voltage recovery times and low utilization of the active mass. In the electrodes composed of large crystals (32 nm diameter), the slow voltage recovery is attributed to transport limitations on both the agglomerate and crystal length-scales