Discharge, Relaxation, and Charge Model for the Lithium Trivanadate Electrode: Reactions, Phase Change, and Transport

Abstract

The electrochemical behavior of lithium trivanadate (LiV 3 O 8 ) 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 LiV 3 O 8 is ∼10 −13 cm 2 s −1 and the equilibrium compositions in the two phase region (∼2.5 V) are Li 2.5 V 3 O 8 :Li 4 V 3 O 8 . 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). Large scale transportation and stationary applications of lithium ion batteries require inexpensive, reliable, and safe systems.1 Transition metal (cobalt, iron, nickel, manganese, vanadium, titanium, tungsten, and molybdenum) oxides are attractive lithium intercalation cathode materials for these applications because of their natural abundance and high redox potentials.2 Conventional anode materials, such as graphite, typically have higher specific capacities than cathode materials, such as LiCoO 2 and LiFePO 4 . This difference in capacity is because typical cathode materials can only accept one lithium per formula unit; therefore, there is a potential breakthrough in developing cathode materials that are able to host lithium-ions in excess of one per formula unit. For example, LiV 3 O 8 is an attractive material because of its high potential suitable for battery applications (∼3 V) and high theoretical specific energy (∼374 mAh g −1 ). [3][4][5] The high capacity comes from the ability of the matrix to host three additional (excess) lithium ions (Li 4 V 3 O 8 ). 6Because LiV 3 O 8 is a promising mid-voltage material with high capacity and good cycling ability, it has received research attention. However, despite this attention, important physical parameters such as the diffusion coefficient of lithium in the material are not known with precision, varying by at least two orders of magnitude. 7,8 In addition, the material undergoes a phase change at ∼2.5 V from Li 1+x V 3 O 8 to Li 4 V 3 O 8 , 6,9,10 but the equilibrium composition, specifically in the lithium-deficient phase is not known with precision 11 and, to the authors' knowledge, there are no studies on the kinetics of phase change in this material.Through the development of a continuum model, this paper seeks to quantif...

Operando Study of LiV3O8Cathode: Coupling EDXRD Measurements to Simulations

“…Concentration variations within the solid-state are not neglected and are described by Equation 4, based on the crystal scale model developed by Brady et al 6 This equation describes the Fickian transport of lithium through the crystal and assumes that phase change proceeds through a chemical reaction. Equation 5 in Table I describes phase change: the process of lithium transferring between the α-and β-phases, is assumed not to be electrochemically driven, but chemically driven, where the term (c α -c α,sat ) is the driving force for phase change and k β is the kinetic rate constant.…”

“…The exponent m describes the dimensionality of phase growth (planar, cylindrical, spherical) and nucleation (instantaneous, progressive), and the exponent p describes the degree of self-passivation. It is assumed that the new phase grows planarly and self-passivation is proportional to the volume fraction 6 Electrode Scale Equations…”

“…The crystal scale model development is detailed by Brady et al 6 The most significant information is that the crystal is composed of three components: the α-phase, β-phase, and grain boundaries, whose volume fractions, θ i , sum to 1:…”

“…The crystal-scale parameters remain the same as those published by Brady et al 6 (D , but the phase change reaction rate constant, k β , was allowed to vary along with the solid-state electrical conductivity, σ, and electrolyte effective diffusion coefficient, D 0,ef f . These parameters were fit to the experimental data using 1000 Sobol points with the bounds:…”

“…1,4 Phase transitions during battery operation are significant because they have implications for electrochemical performance, rate capability, as well as cycle life. Previous studies have interrogated phase change using a variety of methods, both experimental and theoretical: electrochemical, [5][6][7] in-situ 8,9 and ex-situ 10 characterization (SEM, 7,11 XRD 4,5,7,10,11 ), DFT, 9,12 and continuum modeling. 6 Electrochemical measurements are commonly used to investigate battery performance.…”