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

Abstract

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. Large increases in the use of distributed and intermittent energy sources (i.e., wind and solar) have increased the need for cost effective, reliable, and efficient energy storage technologies.1 To address these needs, significant research efforts have focused on the development of next generation materials for secondary batteries, which can provide inexpensive and long lasting energy storage solutions.2-4 In particular, considerable work has focused on the advancement of magnetite (Fe 3 O 4 ) as an electrode in lithium-ion batteries due to its high theoretical capacity (926 mAh g −1 ), low cost and safety (non-toxic). 5-14Despite these advantages, one of the major challenges limiting the advancement of magnetite electrodes is a considerable difference between the maximum, theoretical capacity and the observed, experimental capacity of the active material. This difference increases the anticipated cost of magnetite batteries because it requires the electrodes to be overdesigned with excess amounts of active material. The difference between the theoretical and experimental capacity is related to the close-packed inverse spinel structure of Fe 3 O 4 , which restricts the transport of lithium in the material. To address this issue, several authors have synthesized Fe 3 O 4 nano-crystallites in attempts to minimize the path length for ion transport.9-14 The smaller path length increases the utilization of the active material by making it possible for ions to penetrate to the center of the crystals, especially at high rates of discharge. Electrodes fabricated with nano-crystalline magnetite have shown significant improvement in capacity; however, the theoretical capacity has still proven difficult to obtain.11 Further improvements in capacity may requir...

Simulations of Lithium-Magnetite Electrodes Incorporating Phase Change

“…According to the schematic in Figure 1, the existence of the plateau from x = 1 to x = 3 suggests that, at equilibrium, the α phase has a solid state lithium concentration of x = 1 (α-LiFe 3 O 4 ) and the β phase has a concentration of x = 3. However, this result is only valid under the assumption that the voltage recovery experiments have reached equilibrium potentials after 11 and the voltage in Figure 3 roughly corresponds to the equilibrium potential [41,42]. For experiments lithiated to x > 3.0, the voltage of the electrodes is still changing significantly at 30 days.…”

“…The experimental data are obtained by exploiting the fact that the voltage recovery curves (see inset in Figure 3 for example) have two characteristic regions. During the first ~200 hours, there is a voltage recovery that can be attributed to the relaxation of concentration profiles in the agglomerate and crystal length-scales [42]. Afterwards, there is a slower, seemingly linear recovery at long times that can be attributed to phase change.…”

“…In this work, we seek to simulate the phase changes within magnetite during lithiation by incorporating the kinetics of nucleation and growth of new phases into a previously developed model [41][42][43]. The previously developed model, which did not include phase change, simulates the electrochemical performance of a Fe 3 O 4 electrode by coupling the lithium transport in the agglomerate and crystal length-scales to thermodynamic and kinetic expressions.…”

“…The previously developed model, which did not include phase change, simulates the electrochemical performance of a Fe 3 O 4 electrode by coupling the lithium transport in the agglomerate and crystal length-scales to thermodynamic and kinetic expressions. In previous work, the model without phase change was able to capture the electrochemical performance of an electrode at low levels of lithiation, where Fe 3 O 4 undergoes an intercalation process [42]. To expand our understanding to higher levels of lithiation, the formation of new phases are incorporated into the previously developed model using kinetic expressions inspired by the Avrami theory for nucleation and growth [44][45][46].…”

Operando Study of LiV3O8Cathode: Coupling EDXRD Measurements to Simulations

“…The LVO500 cell was discharged to 1.8 V vs. Li/Li + and charged to 3.8 V at a current rate of C/18 (20.2 mA/g) on a Maccor cycle life tester while the EDXRD patterns were continuously collected. During lithiation 9 scans were taken (scans 1-9), at average equivalences (x in Li x V 3 O 8 ): x = 1.1, 1.5, 1.8, 2.0, 2.3, 2.6, 2.9, 3.2, and 3.5; during delithiation 10 scans were taken (scans [11][12][13][14][15][16][17][18][19][20], at average equivalences x = 3.6, 3.3, 3.0, 2.7, 2.3, 2.1, 1.8, 1.5, 1.3, and 1.2. Figure 2 is a schematic of the set-up used for the operando EDXRD measurements.…”