An Experimental and First Principles Study of the Energetics of Lithium Insertion into Fe3O4 and γ-Fe2O3
Authors: Lininger Christianna N , Marschilok Amy C , Takeuchi Kenneth J , Takeuchi Esther S , Hybertsen Mark S , West Alan C 
Published: February 2020

Inverse spinel magnetite, Fe3O4, has been studied as an electrode material for lithium-ion batteries due to its low cost, high abundance, and low environmental impact.1 Experimental discharge profiles of Fe3O4 initially show a concentration dependent voltage profile. The lithium concentration range of that profile varies as a function of nanoparticle size, with smaller particles exhibiting a larger intercalation regime.2,3 Thackeray et al. proposed initial lithium intercalation into magnetite on 16c sites, where the lattice accommodates a critical concentration of lithium without significant structural rearrangements. Above a critical concentration of lithium, Thackeray et al. proposed that with further discharge, lithium insertion to 16c sites leads to Fe8a displacement to vacant 16c sites in the material.4 It is also known that magnetite is iron deficient, Fe3-δO4 in the bulk and in the nanoparticulate forms with vacancies on the octahedral 16d sites.5–7 The most drastic manifestation of this oxidation process is maghemite, with δ=1/3, the topotactic oxidative product written as (Fe1
3+)8a[Fe1.66
3+♦0.33]16dO4 with ♦ as a 16d iron defect, or γ-Fe2O3. Menard et al. showed that the defects in nanoparticulate magnetite increase with decreasing nanoparticle size, but a thorough investigation of how defects affect the electrochemistry is yet to be presented.2

Using DFT+U calculations, we have investigated lithium intercalation in Fe3O4 magnetite. Our results show that stoichiometric Fe3O4 is not an intercalation material, with no stable phases for the LixFe3O4 0<x<1 convex hull. Resultantly, a voltage plateau at approximately 2.0 V is predicted, corresponding to a continuous phase transformation from inverse spinel Fe3O4 to rock-salt LiFe3O4with Li and Fe occupying 16c sites. This rules out the original hypothesis for a critical concentration of lithium hosted on the 16c sites resulting in a concentration dependent voltage at low concentrations of lithium in magnetite.
We have performed DFT+U calculations on lithiated Fe3-δO4 with δ=0,1/8, and 1/3 to understand how 16d iron defects affect the open circuit potential of magnetite and therefore the discharge behaviour. In the presence of 16d iron defects, we have found that even at low concentrations of lithium, insertion on vacant 16c sites causes significant Fe8a rearrangements. When lithium is inserted on 16c positions, its proximity to Fe8a induces Coulombic repulsion between the Li16c and the Fe8a, and the resultant material is thermodynamically unstable against phase segregation. On the other hand, when lithium is inserted on vacant 16d sites available in the δ=1/8 and 1/3 cases, a structurally stable intercalated material results and DFT+U predicted voltages align with experimental observation.
We further hypothesize that the concentration of defects is a function of nanoparticle size. Then we are able to explain the experimentally observed size-dependent open circuit potential and the variation of discharge capacity with particle size in a natural way. Finally, with DFT+U calculations we are able to provide a mechanism for intercalation and phase-segregation that is consistent with the nanoparticle size dependence observed in the electrochemical experiments.

This work was supported as part of the Center for Mesoscale Transport Properties, an Energy Frontier Research Center supported by the U. S. Department of Energy, Office of Science, Basic Energy Sciences, under award #DE-SC0012673. This research used resources of the Center for Functional Nanomaterials, a U.S. DOE Office of Science User Facility, at Brookhaven National Laboratory, Contract No. DE-SC0012704. The Extreme Science and Engineering Discovery Environment (XSEDE) was used, supported by National Science Foundation grant number ACI-1548562. The Yeti Shared HPC Cluster at Columbia University was used, which includes support from Empire State Development's Division of Science, Technology, and Innovation, contract number C090171. C. N. L. acknowledges the support of the National Science Foundation Graduate Research Fellowship under Grant No. DGE-11-44155. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.
(1) Ito, S.; Nakaoka, K.; Kawamura, M.; Ui, K.; Fujimoto, K.; Koura, N. J. Power Sources
2005, 146, 319–322. (2) Menard, M. C.; Marschilok, A. C.; Takeuchi, K. J.; Takeuchi, E. S. Electrochim. Acta
2013, 94, 320–326. (3) Menard, M. C.; Takeuchi, K. J.; Marschilok, C.; Takeuchi, E. S. 2013, 15, 18539–18548. (4) Thackeray, M. M.; David, W. I. F.; Goodenough, J. B. Mater. Res. Bull.
1982, 17, 785–793. (5) Daniels, J. M.; Rosencwaig, a. J. Phys. Chem. Solids
1969, 30, 1561–1571. (6) Dieckmann, R. Berichte der Bunsen-Gesellschaft fur Phys. Chemie
1982, 86, 112–118. (7) Johnson, C. E.; Johnson, J. A.; Hah, H. Y.; Cole, M.; Gray, S.; Kolesnichenko, V.; Kucheryavy, P.; Goloverda, G. Hyperfine Interact.
2016, 237, 1–10.