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# Multi-electron transfer enabled by topotactic reaction in magnetite

## Abstract

A bottleneck for the large-scale application of today’s batteries is low lithium storage capacity, largely due to the use of intercalation-type electrodes that allow one or less electron transfer per redox center. An appealing alternative is multi-electron transfer electrodes, offering excess capacity, which, however, involves conversion reaction; according to conventional wisdom, the host would collapse during the process, causing cycling instability. Here, we report real-time observation of topotactic reaction throughout the multi-electron transfer process in magnetite, unveiled by in situ single-crystal crystallography with corroboration of first principles calculations. Contradicting the traditional belief of causing structural breakdown, conversion in magnetite resembles an intercalation process—proceeding via topotactic reaction with the cubic close packed oxygen-anion framework retained. The findings from this study, with unique insights into enabling  multi-electron transfer via topotactic reaction, and its implications to the cyclability and rate capability, shed light on designing viable multi-electron transfer electrodes for high energy batteries.

## Introduction

Intercalation-type electrode materials are commonly employed in commercial lithium-ion batteries (LIBs), as they accommodate Li via topotactic transformation, conducive to small structural change over cycling1. Unfortunately, their capacity is low, limited by one or less electron transfer per redox center, which has been a bottleneck for the large-scale applications2,3. In contrast, multi-electron transfer (MET) electrode materials, such as transition metal (TM) compounds (TMaXb, where TM: Fe, Co, Ni, …; X: O, F, S, …), hold great promise for use in next-generation LIBs due to their extremely high capacity4,5,6,7,8. Nonetheless, Li conversion is involved during MET reaction, and according to the traditional view, the lattice  structure of the host will break down upon lithiation, i.e., from the initial TMaXb into the nano-sized TM and LinX (where n is the formal oxidation state of X), and therefore degrades over cycling9,10,11,12.

One exception is inverse-spinel structured magnetite (Fe3O4;  space group: Fd$$\bar 3$$m)13,14, wherein high cyclability has been demonstrated20,21,22,23. And due to its high capacity, low cost, and natural abundance, Fe3O4 is of great interest for battery application12,15,16,17,18,19. The recent mechanistic studies on electrochemical reaction in Fe3O4 provided insights into the structure-determined ionic transport and high cyclability in this material12,16,24,25,26. Particularly, a combination of synchrotron X-ray and electron microscopy measurements revealed preferential orientation of the formed  Fe nanoparticles12. A similar phenomenon has also been observed in Co3O4 spinel27 and FeF210,11, suggesting a crystallographic correlation between the parent reactant and converted phases despite their abrupt structural difference. In addition, the formation of metallic nanoparticles has been shown to improve the electronic conductivity and reversibility of the electrodes9,10,28, but it is still unclear how those metallic nanoparticles initially nucleate and grow from the parent or intermediate phases, and consequently, impact the conversion process during lithiation. Since batteries generally operate under an overpotential, little is known about the dynamic process of structural evolution and the involved formation of metallic nanoparticles under non-equilibrium conditions.

Traditional X-ray diffraction based in situ techniques have been widely used for obtaining information on structural changes over large areas of the electrode materials, which, however, cannot catch the progression of the reaction front, namely, where and how the reaction is initialized and how the involved phases evolve and structurally correlate with each other throughout the reaction process29. In situ transmission electron microscopy (TEM) approaches, such as electron diffraction (ED), have been proven to be powerful in tracking the local structural evolution in the selected areas or individual particles29,30,31,32,33. In the particular systems that undergo MET reaction, multi-phase transformations occur within nano-sized domains, which have often been complicated by the  use of polycrystalline materials, since the random orientation of constituent crystallites obscures the crystallographic relationship between the involved intermediates as they develop30. Herein, single-crystal samples are employed for in situ ED studies of the MET reaction in Fe3O4, allowing us to track the associated crystallographic evolution during lithiation. The crystallographic correlation between all of the involved phases during intercalation and conversion processes are revealed, indicating co-operative migration of Li and Fe ions within the O-anion cubic close-packed (ccp) framework. Contradicting the conventional belief of causing structural breakdown, conversion in Fe3O4 resembles the intercalation process, going via topotactic reaction with the ccp oxygen-anion framework retained, thereby enabling multi-electron transfer in this material. The experimental observation is further coupled to first principles calculations, allowing identification of ionic transport pathway, and  making direct correlation to the cyclability and rate capability in Fe3O4.

## Results

### Real time observation of topotactic reaction in single-crystal Fe3O4

Figure 1a shows the experimental  setup that was used to perform time-resolved in situ ED and spatially-resolved atomic imaging at the reaction front. A thin slice sample was cut from one large single crystal along the zone axis [1$$\bar 1$$0], as shown in Fig. 1b (see also details in the Supplementary Methods and Supplementary Fig. 1 in the Supplementary Information). Compared to polycrystalline materials with random orientations, such type of sample is advantageous in interrogating the crystallographic correlation between the pristine and all of the lithiated phases by tracking changes in the highly relevant planes, such as {002}, {111} and {220}, from the corresponding diffraction spots (Fig. 1c). Complementary to in situ ED experiments on crystallographic evolution in the bulk, atomic imaging enabled by aberration-corrected high angle annular-dark-field (HAADF) and annular-bright-field (ABF) techniques, was also used for identifying atomic arrangements of anions and cations, locally at the pristine and partially lithiated states. Occupancies of Fe cations at the tetrahedral sites (8a) and octahedral sites (16d), and O anions at the 32e sites in Fe3O4, were unambiguously determined by HAADF and ABF imaging (Fig. 1d–f).

Figure 2 shows the main results from time-resolved ED measurements conducted on the Fe3O4 single-crystal during lithiation. Representative patterns recorded at the pristine, intermediate/final states (Fig. 2a), clearly show the crystallographic correlation between all of the involved phases. During initial lithiation, all the reflection spots of the Fe3O4 (Fig. 2a at 0′) turned into the spots of intermediate LixFe3O4 (Fig. 2a at 27′). Spots associated with Li2O and metallic Fe projected along the [100] direction (Case-I from hereafter), were also detected by 27′ although they are diffusive and weak (Fig. 2a), and importantly, they all appeared at certain positions adjacent to the reflection spots of LixFe3O4, indicating certain crystallographic correlation between those phases. By 48′, all of the spots associated with LixFe3O4 turned into the ones of FeO, and in the meanwhile those ones associated with Fe-I and Li2O phases became more intense (Fig. 2a). Additional spots associated with {101}Fe group were also identified, but they don’t belong to Fe-I, and have never been reported in previous work12,30, so-called Case-II from hereafter. Together with the spots belonging to the group of {020}Fe-II, the Fe-II phase was determined to project along the [$$10\bar 1$$] zone axis. At the fully lithiated state (54′), the diffraction spots associated with FeO were completely absent in the pattern, indicating the full conversion into Li2O and Fe phases (Fig. 2a).

Crystallographic evolution as a function of time is shown by the false-colored intensity map related to several specific planes, and the corresponding intensity profiles (Fig. 2b). Further quantitative analysis was also made to the evolution in the intensities of diffraction spots, and related lattice changes of all the involved phases (as given in Fig. 2c and d), which highlights two different sequences in the phase transformation. In Sequence 1, the phase evolution followed Fe3O4 → LixFe3O4 → Li2O and Fe-I. During this process, lithiation proceeded continuously until the 16th minute, during which all the peaks associated with pristine Fe3O4 shifted to lower angles, indicating an increase in the lattice constant and the related, gradual transformation from Fe3O4 to LixFe3O4 (Fig. 2d). By the 27th minute, some portion of LixFe3O4 started to be converted into Li2O and Fe-I, as shown by the appearance of (220)Li2O peak along the line scan 1, and (111)Li2O and (011)Fe-I peaks along the line scan 2 (Fig. 2a, b and Supplementary Fig. 2a). At this stage, the spots related to the FeO phase were not detected anymore (Fig. 2b).

A second sequence of phase evolution was also found (Sequence 2): Fe3O4 → LixFe3O4 → FeO →Li2O, Fe-I and Fe-II. Starting from the 48th minute, the LixFe3O4 phase was converted into FeO first, as shown by the evolution of diffraction peaks (Fig. 2b). Specifically, the peaks of (111)LixFe3O4 in the line scan 2 and (002)LixFe3O4 in the line scan 3 disappeared, whereas the peaks of (440)LixFe3O4, (222)LixFe3O4 and (004)LixFe3O4 further shifted to the left and became (220)FeO, (111)FeO and (002)FeO, respectively (Fig. 2b and Supplementary Fig. 2b). The FeO phase was further transformed to Li2O and Fe-I/Fe-II, as indicated by the substantial increase in the intensities of (220)Li2O, (011)Fe-I and (101)Fe-II (Fig. 2c). It should be noted the formation of Fe-II occurred at a stage much later than that of Fe-I, and that the intensities of peaks related to Fe-II were significantly weaker than those of Fe-I (Fig. 2c), suggesting that Fe-I is the dominant type of metallic Fe formed during the conversion reaction.

The direct transformation from LixFe3O4 to the final Fe phase in the Sequence 1 (i.e., without going through FeO) is basically the same as that observed by in situ ED measurements on agglomerate Fe3O4 particles30. However, in the present work, the use of single crystal enabled, for the first time, the identification of the second different sequence of phase transformation in local regions, by first forming the rocksalt-like phase LixFe3O4 (0 < x < 2), followed by the formation of the highly structurally-integrated FeO and Li2O domains as evidenced by a high-resolution TEM image in Supplementary Figure 3, and finally the Li2O and Fe phases12. Such local information may have been obfuscated by the agglomerate behavior and reaction inhomogeneity in a polycrystalline powder sample30.

All the above observations indicate a topotactic relationship between the pristine Fe3O4 and the intermediate/final phases, LixFe3O4, FeO, Li2O, Fe-I, and Fe-II, as explicitly given below:

$$\begin{array}{l}\left[ {1\bar 10} \right]_{{\mathrm{Fe3O4}}}//\left[ {1\bar 10} \right]_{{\mathrm{FeO}}}//\left[ {1\bar 10} \right]_{{\mathrm{Li2O}}},\left( {440} \right)_{{\mathrm{Fe3O4}}}//\left( {220} \right)_{{\mathrm{FeO}}}\\ //\left( {220} \right)_{{\mathrm{Li2O}}},\left( {004} \right)_{{\mathrm{Fe3O4}}}//\left( {002} \right)_{{\mathrm{FeO}}}//\left( {002} \right)_{{\mathrm{Li2O}}};\\ \left[ {1\bar 10} \right]_{{\mathrm{FeO}}} //\left[ {100} \right]_{{\mathrm{Fe}} {\hbox{-}} {\mathrm{I}}},\left( {220} \right)_{{\mathrm{FeO}}}//\left( {010} \right)_{{\mathrm{Fe}} {\hbox{-}} {\mathrm{I}}}\left( {002} \right)_{{\mathrm{FeO}}}//\left( {001} \right)_{{\mathrm{Fe}} {\hbox{-}} {\mathrm{I}}};\\ \left[ {1\bar 10} \right]_{{\mathrm{FeO}}}//\left[ {10\bar 1} \right]_{{\mathrm{Fe}} {\hbox{-}} {\mathrm{II}}},\left( {220} \right)_{{\mathrm{FeO}}}//\left( {010} \right)_{{\mathrm{Fe}} {\hbox{-}} {\mathrm{II}}}\left( {002} \right)_{{\mathrm{FeO}}}//\left( {101} \right)_{{\mathrm{Fe}} {\hbox{-}} {\mathrm{II}}}.\end{array}$$

The observation of the crystallographic correlation between Fe3O4, LixFe3O4, FeO, Li2O, and Fe-I is consistent with previous ex situ results obtained using coin cells12. But through in situ observation on the single crystal, the dynamic process of crystallographic transformation has been revealed in detail. Furthermore, by tracking the formation of Li2O and Fe-II phases (not reported previously) along with other involved phases (LixFe3O4, FeO), and their crystallographic orientation, we were able to unambiguously determine the topotactic pathway throughout the entire process, during which all of the involved phases share the same ccp O-anion framework (as further discussed below). Such a topotactic pathway has also been observed on additional single-crystal samples (see Supplementary Fig. 4 and Supplementary Note 1). The process of phase transformation, two sequences of phase evolution, the crystallographic correlation between different phases and the formation of Fe-II phase are all the same as that in Fig. 2. Therefore, in addition to offering more details about structural evolution than what was reported in previous work12, the in situ studies provided new insights into the crystallographic correlation between them, which can only be achievable using the newly developed methodology in the present work.

### Spatial correlation between intermediates

Complementary to in situ ED on crystallographic evolution in the bulk crystals, HAADF images were taken from a partially-lithiated Fe3O4 single-crystal (as given in Fig. 3). A series of atomic images were taken from local regions, showing different nucleation and growth states of the intermediate phases: from the initial spinel Fe3O4 (labeled as “S”) to rocksalt-like LixFe3O4 phase (labeled as “R”), and then to Fe (see also Supplementary Fig. 5). The Fe3O4, LixFe3O4, and Fe phases located at different regions, due to their different diffraction contrast (as shown in Fig. 3a), were well distinguished from each other and further identified by the fast Fourier transform (FFT) patterns of the HAADF images (shown in Supplementary Fig. 5). In some regions (e.g., b), small grains of LixFe3O4 were found within the matrix of the spinel phase (Fig. 3b). At the early lithiated state, the inserted Li ions first occupy the empty octahedral 16c sites in Fe3O4,  and so force the adjacent Fe ions at 8a to move to the neighboring 16c sites, leading to the formation of rocksalt-like LixFe3O4 structure34. Due to the projected view along the [$$1\bar 10$$] direction, Fe ions at the tetrahedral 8a sites of Fe3O4 and those at the octahedral 16c site of LixFe3O4 appear nearly overlapped in the HAADF images (Fig. 3b). In the deeper lithiated region (Fig. 3c), LixFe3O4 became populated, forming a sharp interface of {111} planes between Fe3O4 and LixFe3O4 (as marked by the dashed line). In region d (of an even deeper lithiated state), LixFe3O4 were partially converted to Fe-I, in the form of nanograins, giving rise to a different contrast in Fig. 3d (in purple). At regions of even deeper lithiation, the Fe-I nanograins were still embedded inside LixFe3O4, but grew out in the region (Fig. 3e). The Fe-I nanograins were projected along the [100] direction, exactly the same as the projection detected by ED (Fig. 2). In the region f at the full lithiated state, only multiple Fe-I nanograins, aligned along the same orientation, were observed (Fig. 3f). The interfaces between Fe-I nanograins and ccp framework were marked by white and black dashed lines in Fig. 3f, corresponding to {001}Fe-I // {001}ccp and {010}Fe-I // {110}ccp, respectively. Moreover, structural transformation from FeO to Fe-I, as given in Supplementary Fig. 6, shows the orientation relationship of [100]Fe-I // [1$$\bar 1$$0]FeO, which is the same as that in Fig. 2. The interface planes were determined to be {010}Fe-I and {110}FeO. Therefore, in addition to the topotactic transformation observed through in situ ED measurements, complimentary HAADF imaging enabled direct visualization of the atomic-scale sharp interfaces between the involved phases, and elucidation of their spatial correlation at the reaction front.

### Ionic transport during topotactic reaction

A combination of in situ ED (in the bulk) and HAADF imaging (local), provided details of the reaction process, regarding the phase transformation from Fe3O4 to LixFe3O4, to FeO and then to Li2O/Fe phases, as schematically illustrated in Fig. 4a–c and Supplementary Fig. 7. In combination with the insight provided by previous work12, Fig. 4 also shows how Li and Fe ions are relocated within the ccp framework. Briefly speaking, the process consists of three steps: (i) Relocation of Fe ions with initial lithiation, during which Fe ions move from tetrahedral 8a to octahedral 16c sites as Li ions insert into the 16c sites, leading to the formation of LixFe3O4 (Fig. 4a, b)12. (ii) Local Li/Fe migration with continuous lithiation, during which atomic rearrangement occurs within the ccp framework, leading to the formation of Li2O and FeO domains (Fig. 4c)12. Since all these phases share the same ccp framework, it only causes small changes in the host structure with small lattice mismatch, i.e., only ~2.5% mismatch along [100] direction between Fe3O4 and FeO, and ~6% between FeO and Li2O. (iii) Fe extrusion with further lithiation, during which Li2O grows at the expense of FeO, and concomitantly, nucleation of Fe clusters occurs preferably at the Li2O/FeO boundaries, facilitated by the strain-induced space at boundaries (Fig. 4c)12. Two types of Fe nanograins (Fe-I and Fe-II; shown in Fig. 2a) possess different orientation relationships with other phases, which should be determined by the different pathways of Fe migration within the ccp framework. As illustrated in Fig. 4d and e, there are two open channels for Fe migration, either along the [110] or [112] direction. When Fe ions move along the [110] direction, the interface plane should be perpendicular to the diffusion direction (Fig. 4d), i.e. (110)ccp or (010)Fe-I (as marked in pink), which is consistent with what was observed in the HAADF image (Fig. 3f). The lattice mismatch at the interface is about 5.3% along the [$$1\bar 10$$] direction of ccp framework, and about 34% along the [001] direction, using the experimental lattice constants for bulk FeO and Fe of 0.86 nm and 0.288 nm, respectively. When the Fe ions migrate along the [112] direction, Fe-II nanograin is formed, with the interface plane of (112)ccp parallel to the (111)Fe-II plane. The value of lattice mismatch at the interface is the same as that of case-I, about 5.3% along the [$$11\bar 1$$] direction of ccp framework, and about 34% along the [$$1\bar 10$$] direction. After establishing a unit cell of Fe phase, the orientation relationship between Fe-I/Fe-II and ccp framework turns out to be the same as that experimentally determined in Fig. 2. Such a large mismatch, of about 34%, might be relieved by forming dislocations on the interface between Fe and ccp framework (Supplementary Fig. 6), which were also commonly observed in other conversion or intercalation electrodes12,33,35.

Owing to the much higher energy barrier of Fe diffusion along the [112] direction (Fig. 4f), the Fe-II nanograins should be formed in the later stage of lithiation and less frequently than the Fe-I nanograins. The sluggish Fe diffusion along the [112] direction can be attributed to the fact that the Fe ion has to push its way through a channel formed by Fe ions with a width as small as 3.0 Å, as shown in Supplementary Fig. 8a. At the intermediate state, the Fe ions are pushed apart by the diffused Fe ion with a much greater separation of 4.6 Å. In contrast, Fe diffusion along the [110] direction allows the Fe ion to pass through a relatively wide channel with Fe-Fe distance of 5.2 Å (Supplementary Fig. 8d), which is only slightly enlarged at the intermediate state (5.5 Å). Therefore, the barrier for Fe migration is relatively low, below 1.4 eV (Fig. 4f), similar to the values obtained from experimental measurements36,37,38. Although the calculated barrier for Fe diffusion along the [112] direction is much higher, it should be noted that the existence of nearby Li ions, which was not considered in the calculations, would be a driving force large enough for the Fe ions to overcome the energy barrier and diffuse to the vacancy sites. In addition, the interfacial mismatch between FeO and Li2O domains (~6%) may further lower the diffusion barrier and facilitate the formation of Fe-II nanograins. Therefore, it is reasonable that the appearance of Fe-II nanograins was only detected after the formation of FeO domains.

## Discussion

Compared to the transport of Li+ ions with an energy barrier lower than 1 eV39, the higher energy barrier for Fe2+/3+ migration may be due to stronger coulombic interaction with surrounding anions/cations. As also demonstrated in Galvanostatic Intermittent Titration Technique (GITT) type measurements (Supplementary Fig. 9), the kinetics of initial Li intercalation is surprisingly lower than that during conversion in the later stage12, which contradicts the traditional view of the slow conversion reaction. The results suggest that the energy barrier for Fe migration, even from 8a to the neighboring 16c, is indeed high. Furthermore, the improved kinetics during conversion indicates that the energy barrier for Li/Fe migration is reduced once nano-sized FeO and Li2O domains are formed, as suggested from theoretical calculations40. Due to the sluggish movement of Fe ions, some intermediates of FexLi2−xO may also exist, similar to the observation of FexLi2−xF2 during conversion reaction in iron fluoride6.

From the view of structural changes, the topotactic transformation during conversion reaction in Fe3O4 resembles that of intercalation process, during which the host structure of the ccp framework is maintained despite abrupt phase transformations, going through intermediate phases of completely different structures, such as LixFe3O4, FeO and Li2O12. The delithiation process takes place through the reaction: Fe + Li2O → FeO + 2Li+, during which the ccp framework is still maintained due to the same framework in both of FeO and Li2O phases12. Therefore, during the MET reaction, the sustenance of the ccp framework during conversion and re-conversion processes, appears to be  cruical to the structural integrity and high reversibility in Fe3O4. On the other hand, the transformation from LixFe3O4 to FeO and Li2O is sluggish (Fig. 2b), likely due to the slow process of long-range re-ordering and segregation of Fe and Li ions, as suggested in the previous work12. It is not electronic transport, but ionic transport involving sluggish migration of Fe ions, that appears to be the main limiting step of the kinetics during MET reaction. Therefore, designing nano-sized Fe3O4 particles for shortening the path of ionic transport is important to enabling both high-rate capability and cyclability, as demonstrated in nano-sized Fe3O4 (Supplementary Fig. 10), and  previous observation in the nano-architectured Fe3O422.

The low energy efficiency of conversion electrodes, another major concern rooted in the large voltage hysteresis during cycling, has been demonstrated in Fe3O4 despite its high-rate capability in the nano-architectured electrodes22. A detailed theoretical study has demonstrated that the voltage hysteresis in conversion electrodes arises from two thermodynamic factors: (1) a large difference in the diffusivity between Li and TM ions and (2) an insufficient thermodynamic driving force for the TM ions to re-enter the structure during lithiation41, which should also be applicable to Fe3O4. Due to the sluggish migration of Fe ions with a larger energy barrier of ~1.4 eV than that of Li ions (below 1 eV), the Li-ion migration only occurs after Fe ions move out to make room for Li ions during lithiation. But Li ions can first move out of the structure through many open channels during delithiation, and thus are not limited by Fe insertion. Such different reaction pathways during lithiation and delithiation may be one origin of voltage hysteresis. But it may only cause a small degree of hysteresis, because we should note that Li2O and FeO phases have similar structure with the same ccp framework, similar as the situation in Li3Sb42. Therefore, we expect that the main part of hysteresis results from the driving force for Fe extrusion during lithiation and Fe insertion during delithiation42. Further studies on the evolution of Fe chemical potential during lithiation and delithiation are needed for elucidating and reducing the hysteresis in Fe3O4; but findings from studies on metal fluorides, particularly on the kinetic nature of the voltage hysteresis and its reduction via tuning ionic transport by cationic substitution may also be applied to Fe3O4, indicating the potential of making it a viable electrode in commercial batteries43,44.

### Conclusion

In summary, we investigated the dynamic MET reaction process in Fe3O4 through time-resolved in situ ED and spatially-resolved atomic imaging. The use of single crystal in this study enabled us to reveal the crystallographic correlation among all the involved phases, and the co-operative migration of Li and Fe ions within the ccp O-anion framework. In contrast to conventional view of dramatic collapse of the host structure during conversion, this study provided direct evidences of a topotactic transformation with the ccp oxygen framework retained, thereby enabling structural integrity and high cyclability in Fe3O4. Ionic transport involving sluggish Fe2+/3+ migration in Fe3O4 was elucidated through first-principles calculations, and enhancing rate capability and high cyclability by nanosizing was also demonstrated. The findings may help to pave the way for designing viable MET electrode materials for next-generation high energy LIBs.

The developed platform for in situ single-crystal electron diffraction may be applied broadly to studies of electrochemical reaction in various electrode materials, to reveal crystallographic correlation among the intermediates at the reaction front, which is typically obfuscated by random orientation of constituent crystallites in the commonly employed polycrystalline samples.

## Data availability

All data generated or analyzed during this study are included in this published article and its supplementary information files.

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## Acknowledgements

This work was supported as a part of the Center for Mesoscale Transport Properties, an Energy Frontier Research Center supported by the U.S. Department of Energy (DOE), Office of Science, Basic Energy Sciences, under award #DE-SC0012673. Lijun Wu and Yimei Zhu were supported by the U.S. Department of Energy, Office of Basic Energy Science, Division of Materials Science and Engineering, under Contract No. DE-SC0012704. TEM sample preparation and measurements carried out at the Center for Functional Nanomaterials, Brookhaven National Laboratory, were supported by the U.S. Department of Energy, Office of Basic Energy Sciences, under Contract No. DE-SC0012704.

## Author information

Authors

### Contributions

F.W. and E.S.T. initiated the project. F.W. and W. Z. conceived the experiments. W.Z. conducted the measurements and analyzed the data. L.W. and Y.Z. assisted with data analysis and developing structure model. Y. L. performed calculations. Y. D., K.K., C. C., and F. P. prepared the samples and assisted the interpretation. D.C. B., A.C.M., K.J.T., and E.S.T. performed the electrochemical measurements and assisted the interpretation. W.Z. and F.W. wrote the paper, and all authors contributed to revisions of the manuscript.

### Corresponding author

Correspondence to Feng Wang.

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The authors declare no competing interests.

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Zhang, W., Li, Y., Wu, L. et al. Multi-electron transfer enabled by topotactic reaction in magnetite. Nat Commun 10, 1972 (2019). https://doi.org/10.1038/s41467-019-09528-9

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