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...

The mass transport processes occurring within magnetite electrodes during discharge and voltage recovery are investigated using a combined experimental and modeling approach. Voltage recovery data are analyzed through a comparison of the mass transport time-constants associated with different length-scales within the electrode. The long voltage recovery times can be hypothesized to result from the relaxation of concentration profiles on the mesoscale, which consists of the agglomerate and crystallite length-scales. The hypothesis was tested through the development of a multi-scale mathematical model, which showed good agreement with experimental data.

At low concentrations of lithium insertion into inverse spinel magnetite Fe 3 O 4 , a phase change to rock-saltlike Li x Fe 3 O 4 has been observed. We used density-functionaltheory-based (DFT-based) calculations to study the structural origins of this phase change, the concentration at which it occurs, the role of iron vacancies, and the stability of the various motifs that form during the electrochemical reduction process in the Li−Fe−O ternary space up to x = 1.33. We compared our results to new experimental measurements of the open circuit voltage for 8−9 nm magnetite particles over a comparable range of lithium insertion. Of the vacant sites in magnetite (16c, 8b, and 48f) lithium insertion was found to be most stable on 16c. Coulomb interactions between the added lithium and iron at the 8a site in magnetite led to substantial displacement of the iron. As further lithium was added, the most energetically favored motif involved lithium clustering in 16c sites around the shifted 8a iron up to a total of three lithiums. In competition with the lithium clustering motif, lithium insertion could be accompanied by the full displacement of all 8a iron to 16c sites, to form the rock-salt-like Li x Fe 3 O 4 , saturating at x = 1. The defective rock-salt structure was found to be more stable than the lithium clustering motif for x ≥ 0.5. The rock-salt-like LiFe 3 O 4 was found to be stable in the Li−Fe−O ternary space for a continuous range of Li−Fe organization on the 16c sites, stabilized by Coulomb interactions. For x < 1, neither the lithium clustering motif, nor the defective rock-salt-like structure for Li x Fe 3 O 4 were stable against phase segregation to LiFe 3 O 4 and Fe 3 O 4 . This phase segregation (0 < x < 1) occurred at a predicted voltage of ∼2.0 V. However, when iron vacancies on the 16d site were introduced, lithium insertion to those vacant 16d sites in Fe 2.875 O 4 , and γ-Fe 2.67 O 4 (maghemite), resulted in stable intercalated materials at a predicted voltage of ∼3.0 V. Beyond the concentration of such iron vacancy sites, phase segregation was predicted to the rock-salt-like Li 1.125 Fe 2.875 O 4 and Li 1.33 Fe 2.67 O 4 , again at ∼2.0 V. These results were consistent with measured open circuit voltages. Finally, the relative stability for several lithium compositions along the FeO to LiFeO 2 tie line in the defective rock-salt structure suggested stable compound formation for a range of lithium−iron compositions, but without long-range order in the cation sublattice, consistent with what has been commonly observed in the literature.

Our direct DFT decomposition of CO frequency shifts updates the paradigm for metal carbonyl binding.