Mesoscale Transport in Magnetite Electrodes for Lithium-Ion Batteries

Cama

et al. 2015

J. Electrochem. Soc.

Self Cite

100

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...

Section: Methods Of Approachmentioning

confidence: 55%

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

Knehr

Cama

et al. 2015

J. Electrochem. Soc.

Self Cite

100

“…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.…”

Section: Resultsmentioning

confidence: 93%

“…The parameters used to model the phase change and mass transport are provided in Table III along with the mass transport parameters used in the model without phase change, for comparison [42]. Values for all other parameters can be found in [41].   sat c , , c β , and c α,max in Table III correspond 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 [50].…”

Section: Model Parameterizationmentioning

confidence: 99%

“…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.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Simulations of Lithium-Magnetite Electrodes Incorporating Phase Change

Knehr

Cama

et al. 2017

Electrochimica Acta

The phase changes occurring in magnetite (Fe 3 O 4 ) during lithiation and voltage recovery experiments are modeled using a model that simulates the electrochemical performance of a Fe 3 O 4 electrode by coupling the lithium transport in the agglomerate and nano-crystal lengthscales to thermodynamic and kinetic expressions. Phase changes are described using kinetic expressions based on the Avrami theory for nucleation and growth. Simulated results indicate that the slow, linear voltage change observed at long times during the voltage recovery experiments can be attributed to a slow phase change from α-Li x Fe 3 O 4 to β-Li 4 Fe 3 O 4 . In addition, the long voltage plateau at ~1.2 V observed during lithiation of electrodes is attributed to conversion from α-Li x Fe 3 O 4 to γ-(4 Li 2 O + 3 Fe). Simulations for the lithiation of 6 and 32 nm Fe 3 O 4 suggest the rate of conversion to γ-(4 Li 2 O + 3 Fe) decreases with decreasing crystal size.

“…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.…”

Section: Methodsmentioning

confidence: 99%

Operando Study of LiV₃O₈Cathode: Coupling EDXRD Measurements to Simulations

Zhang

Bruck

et al. 2018

J. Electrochem. Soc.

The electrochemical and phase-change behavior of lithium trivanadate during lithiation and delithiation is analyzed by comparing a coupled electrode/crystal-scale mathematical model to operando experiments. The model expands on a previously published crystalscale model by adding descriptions for electrode-scale resistances. Agreement between simulated and observed electrochemical measurements is compelling. Time and space-resolved operando EDXRD measurements on the cathode are compared with simulated concentration profiles. Both simulation and experiment reveal that during lithiation, phase transformations preferentially occur near the separator, while during delithiation the disappearance of the lithium-rich β-phase occurs uniformly across the electrode. Lithium trivanadate, LiV 3 O 8 , and transition metal oxides in general are attractive cathode materials for lithium-ion batteries due to their moderate redox potential, high theoretical capacity, and good rate capability.1,2 LiV 3 O 8 , as with many other transition metal oxides, undergoes phase change during lithiation. 1,3,4 Up to a composition of Li 2.5 V 3 O 8 , the material is in the parent layered α-phase; from Li 2.5 V 3 O 8 to Li 4 V 3 O 8 , the α-to β-phase transition process takes place where the layered phase transforms into the defected rock-salt β-phase; beyond Li 4 V 3 O 8 , lithiation occurs into the single β-phase. 1,4Phase 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, 5-7 in-situ 8,9 and ex-situ 10 characterization (SEM,7,11 XRD 4,5,7,10,11 ), DFT, 9,12 and continuum modeling. 6Electrochemical measurements are commonly used to investigate battery performance. While these measurements are useful, they are indirect measurements of the physical processes that govern performance. For this reason, direct measurements through characterization, such as SEM, XRD, and TEM are used in-situ and ex-situ to try to understand the internal processes. However, because battery systems are highly dynamic, if there are even short delays between operating the battery and interrogating it, the observed profiles may not be indicative of the profiles that exist during operation. This concept is illustrated in Figure 1. Using the parameters listed in Table II and discharging at C/18 until an equivalence of Li 2.4 V 3 O 8 , simulations show that even with a short gap between discharge and characterization (two hours) the spatial profiles change significantly. And if there is a 10-hour delay or more, the non-uniformities present during operation will be completely undetectable. operando studies are therefore very valuable because they allow for characterization in time and position and show how these profiles evolve during battery operation; insights about the physical process can be gained from this characterization information. Z...