## Introduction

The vast majority of electrode materials operate via insertion chemistry1. Their performance is restricted by the homogeneity range of their crystal structures to (usually) 1e transfer (per formula unit) upon cycling, which limits their capacity. The search for next-generation materials with higher capacities is therefore essential to improve battery performance. As an alternative to insertion materials, conversion materials experience a complete reduction of the metal component upon discharge: $$(z \cdot n){\mathrm{Li}} + {\mathrm{M}}_y{{X}}_z \leftrightarrow y{\mathrm{M}} + z{\mathrm{Li}}_n{{X}}$$ (X = O, S, P, F, etc.). Such a reaction involves multiple-e transfer yielding high theoretical capacities (e.g., 1007 mAh/g for α-Fe2O3 c.f. 372 mAh/g for graphite)2 and, thus, these systems have consequently attracted considerable interest. However, the crystal structures of these materials are believed to undergo a complete de- and re-construction upon cycling—accompanied by significant volume changes that may impair the electrode’s mechanical integrity—leading to large voltage hysteresis, limited cycle life, poor rate performance and mediocre capacity retention1,2.

With the aim of enhancing their performance, much of the relevant research effort has focussed on material nanostructuring to promote efficient reaction with Li. In this respect, first-row transition-metal oxides (MxOy)—and particularly the Fe and Mn series (M = Fe, Mn)—have become the most studied conversion compounds due to their low cost and straightforward syntheses3. As a consequence, we now have a library of MxOy systems with diverse nanomorphologies4. Although these engineered oxides have proven effective in improving rate capability and cyclability, critical issues such as low power and energy efficiency remain key obstacles to commercial application1. The development of viable strategies to overcome these issues therefore demands a much-improved understanding of the underlying reaction mechanisms.

Regardless of the particular MxOy starting phase, these oxides undergo an electrochemical pulverisation during the conversion processes that leads to the formation of near-amorphous M and Li2O at the end of the first discharge5,6,7,8 (Fig. 1a). This M-Li2O mixture subsequently reconverts to an amorphous and/or disordered metal oxide phase (hereafter referred to as MxOy) upon charge. Despite lacking long-range order, this MxOy was found to locally resemble a rocksalt (rs) type MO structure5,7,9 in both Fe and Mn systems, in turn suggesting their delithiation might follow related pathways. More importantly, the following discharge step seems to mirror the charging process, implying the actual reversible reaction might be independent on the starting MxOy material. While earlier studies of these systems focussed predominantly on their initial insertion and conversion chemistry, it is critical to understand the reconversion mechanism and subsequent cycling steps, considering that these are the key processes that define the reversible capacity. Given the heterogeneous and nanoscopic nature of the (re)conversion process5,10, the characterisation used in previous studies primarily relied on conventional techniques such as X-ray diffraction (XRD)5,8, transmission electron microscopy (TEM)9,11,12 and X-ray absorption spectroscopy (XAS)7,8,11. Even with many in operando/in situ measurements undertaken, the inability of XRD to determine the short-range structure and the insensitivity of EXAFS to structure beyond the first few coordination shells13 means that the structural changes upon charging MxOy materials remain unestablished.

In this work, we seek to address these main challenges using in operando and in situ (hereafter simplified as in situ) pair distribution function (PDF) via X-ray total scattering, a powerful tool for studying various types of conversion materials14,15,16. For a systematic and robust investigation, we have selected a series of FexOy and MnxOy compounds and employed an analytical approach including Metropolis Monte Carlo (MMC) simulation17 and non-negative matrix factorisation (NMF)18. Our results show that these MxOy systems follow an analogous cycling behaviour within a given M family, but the pathways differ significantly between the Fe and Mn series despite their similar electrochemical profiles during reversible cycles. Surprisingly and importantly, although a one-step conversion process from M to rs-MO upon charge was widely accepted in the field, we show that both FexOy and MnxOy undergo two steps via diffusion-controlled displacement-like reactions, with O2− and Mn2+ as displaced species, respectively, for the Fe and Mn systems forming unexpected body-centred cubic (bcc) FeO and zincblende (zb) MnO. The mechanistic transition from a conversion process to an unexpected topotactic reaction elucidates the fundamental origins of the hysteretic behaviour, offering critical insight into effective material design in the future; on the other hand, it suggests the viability of deriving new MO polymorphs using an electrochemically assisted approach based on battery chemistry. In addition, our study also demonstrates the value of our methodology to investigate battery material systems with complex structures.

## Results

We selected candidate FexOy and MnxOy materials so as to include the most frequently studied compositional and crystallographic variants. The chosen Fe species were FeO19 (structure type: rocksalt/space group: Fm$$\bar 3$$m), α-Fe2O310 (corundum/R$$\bar 3$$c) and Fe3O420 (inverse spinel/Fd$$\bar 3$$m), while the MnxOy series consists of MnO21 (rocksalt/Fm$$\bar 3$$m), Mn3O422 (distorted spinel/I41/amd) and β-MnO223 (rutile/P42/mnm); the purity of these phases was confirmed by PDF refinement (Supplementary Fig. 1a). Note that these crystal structures are based on classic oxygen-packing frameworks, i.e., cubic-close packing (ccp) in rs-/spinel-related structure, hexagonal-close packing (hcp) in hexagonal corundum and tetragonal-close packing (tcp)24 in rutile. We thus expect any mechanistic similarity shared within or between the Fe and Mn families to reflect a general trend for a wider range of Fe- and Mn-oxide materials.

### Electrochemistry

Lithiation of MxOy begins with an insertion step (in some materials) at a higher voltage than the conversion process (c. 0.8 and 0.3 V for Fe and Mn, respectively) and is normally accompanied by electrolyte decomposition and other side reactions15, which collectively give rise to the extra capacity seen in the first discharge. The following delithiation (charge) process—which corresponds to the reconversion of M to form the MxOy phase—exhibits a maximum capacity of about 2 Li (per M) associated with 2e transfer (per M) regardless of the number of e involved in the initial discharge (Fig. 1a and Supplementary Fig. 1b). Discounting any side reactions after the first discharge, the removal of 2e per metal centre would result in a full oxidation from M to M2+O species. Based on a nearly identical capacity between the second discharge and the first charge, we can also infer the reconverted MO is the active and reversible oxide component in the following conversion–reconversion cycles. For a clearer comparison between different MxOy species, the electrochemistry profiles (Fig. 1a) are plotted against the normalised “relative Li content (per M centre)” and will be simplified as “Li content” hereafter unless otherwise stated. It is also worth noting that although most of the MxOy only exhibit one charge (pseudo-) plateau, two peaks can be resolved in their derivative curves (Fig. 1b) or cyclic voltammograms (CV)19,23,25,26,27,28. The two maxima are well separated in MnxOy, but are less easily distinguished in FexOy. Nevertheless, their presence suggests a two-step phase transition from M to MO, deviating from the commonly-assumed single-step reaction M + Li2O ↔ rs-MO + 2Li.

### Characterisation (X-ray total scattering and TEM)

Comparing the scattering patterns and PDFs (Fig. 2 and Supplementary Figs. 2–4) for different species within the same FexOy or MnxOy series, we find that the peak evolution—i.e., peak shifts, appearance and disappearance of Bragg reflections/atom pairs—shows a single common trend. This implies comparable structure changes between different FexOy or MnxOy systems despite their significant compositional and crystallographic differences at the beginning of first discharge. In addition, the structural change during the second discharge mirrors that during the first charge in both real and reciprocal space (Fig. 2) and the phase changes in the second charge are identical to that in the first charge (Supplementary Fig. 4b, c). This is consistent with a reversible phase behaviour. Based on the observed mechanistic resemblance within the same MxOy series, we chose α-Fe2O3 and Mn3O4 as model compounds for subsequent studies considering that they are the most explored oxide member within each MxOy family.

To obtain better knowledge of the starting phase for the 1st charge (“Li 0.0”), quantitative analysis was performed on the scattering data collected at the corresponding state of charge. As confirmed by PDF refinement (Supplementary Fig. 5) and supported by XRD simulation (Supplementary Figs. 6 and 7), the average particle size for M and Li2O phases was 2 and 3 nm, respectively. TEM analysis of the Fe sample (Fig. 3a–c) shows sphere-like Fe nanoparticles each a few nanometres in size. There is clear evidence of a well-ordered bcc lattice within nanoparticles, which can be discerned despite severe agglomeration. Upon charging, the scattering pattern evolves differently for the two systems (Fig. 2). While α-Fe2O3 only shows variations in peak intensities with very subtle changes in peak positions, Mn3O4 exhibits a distinct ‘waxing and waning’ effect. This contrast implies substantial mechanistic differences in the reconversion processes between the FexOy and MnxOy series despite their similar electrochemical profiles.

### α-Fe2O3 (model compound for FexOy)

An earlier study of α-Fe2O3 using in situ TEM9,11 reported a phase transition from α-Fe (Im$$\bar 3$$m) to FeO (Fm$$\bar 3$$m) during the charging process. Should this reaction take place, the Fe lattice will undergo a significant rearrangement from bcc to fcc resulting in a pronounced change of the local ordering (Supplementary Fig. 8). Surprisingly, our in situ PDF data (Fig. 4a) only show subtle peak shifts with slight peak broadening and intensity reduction upon charge, implying the α-Fe lattice is largely retained without transformation to the rs-FeO. TEM measurements (Fig. 3) of the sample at the end of charge (“Li −2.0”) further confirm the retention of bcc Fe order in the reconverted FeO structure (hereafter denoted as bcc-FeO). In addition, it is also possible to discern atomic displacements (Fig. 3d and Supplementary Fig. 9) that likely account for the increased peak widths in the XRD pattern (Supplementary Fig. 6a). Remarkably, while most of the PDF atom-pair intensities progressively decrease upon charge, a peak at 1.9 Å continues to grow (Fig. 4a). Atomic distances of ~2 Å are characteristic of the first coordination sphere in LinMxOy, and hence correspond to Li- or M-centred polyhedral environments. The peak cannot be ascribed to the tetrahedral Li–O in the antifluorite (af) Li2O because the concentration of this phase decreases during delithiation. Hence, we assign this peak to a Fe–O atom pair, which must correspond to O inclusion within the bcc-FeO phase.

The most commonly occupied interstitial site in bcc-Fe is the distorted octahedral site, such as is occupied by X = C or N in the Fe–X martensite alloys29,30,31. These sites are located at the centres of the faces and edges of the bcc unit cell (Fig. 4b). There are also 4-coordinated interstitial positions present at the 12d site. Both geometries are distorted compared to their fcc-counterparts32. An earlier computational study on oxygen diffusivity in bcc-Fe showed that the octahedrally coordinated oxygen is energetically more favourable than the tetrahedral one (hereafter denoted as oct- and tet-O, respectively)33. In the absence of any local structural relaxation due to the occupation of interstitial atoms, the six Fe–O pairs affiliated with the oct-O should contain four equatorial pairs and two short axial pairs with atomic distances of about 2.0 and 1.4 Å respectively, giving rise to an average distance of about 1.8 Å. For the tet-O, the four Fe–O pairs share equal distances of about 1.6 Å. Hence our experimental data, related precedent and energetic considerations all point to O inclusion within bcc-Fe on the octahedral interstitial site.

We developed a series of atomistic models for this bcc-FeOx phase for compositions 0 ≤ x ≤ 1. Here the oxygen stoichiometry x reflects the charging capacity based on a nominal Li content “Li −2x”, i.e., a formula of “FeO0.5” corresponds to the Li content of “Li −1.0”. For selected x values, we introduced local structure relaxation in our models by using an MMC algorithm to incorporate simple O–O interactions. In the dilute solid solution (FeO0.1), the MMC-derived oct-O distribution appears to be disordered (Supplementary Fig. 10). However, at the high-concentration limit (FeO1.0), the driving force to minimise O–O repulsion energies resulted in locally ordered domains (Fig. 4c). These domains all share the same short-range structure represented by a bcc-FeO unit cell (Fig. 4d) that contains a face and an edge O2‒, isostructural to the tetragonal FeO (I4/mmm)34. The phase encrypts a superstructure that mirrors the tetragonally distorted rs-FeO where the Fe sublattice retains the bcc order, hinting at an underlying link between the bcc- and rs-FeO.

An important test of the physical sense of these models comes from their ability to account for the experimental PDF data. Consequently, our model PDFs were calculated using additional physical parameters, e.g., scale factor and linear correlation factor (Supplementary Fig. 11a), which were predefined via initial refinement against the Fe structure. The resulting PDFs (Fig. 4e) indeed exhibit the Fe–O peak at around 2.0 Å with growing intensity as oxygen content increases. Nearly all other variations observed experimentally as a function of composition are also well represented by our calculated PDFs. The overall agreement between simulation and experiment appears surprisingly good.

### Mn3O4 (model compound for MnxOy)

In contrast to α-Fe2O3, the scattering patterns of Mn3O4 reflect the occurrence of a phase transition accompanied by significant Mn atomic rearrangement during charge. The broad width of the Bragg peaks (Supplementary Fig. 7) and the short coherence lengths (< 20 Å) of the PDF patterns (Fig. 5a) indicate that the average grain sizes of Mn-containing species remain small during delithiation. Despite a two-step electrochemical process, which suggests the involvement of an intermediate, preliminary PDF refinements were attempted using a two-phase model consisting of α-Mn (I$$\bar 4$$ 3 m) and rs-MnO (Fm$$\bar 3$$m). As anticipated, such refinements were unable to account satisfactorily for the data, demonstrating instead the necessity of including a third phase in the model. Given the analytic uncertainties concerning the intermediate, we implemented our recently developed method18 based on NMF35, a robust computational approach to study complex mixtures without a priori knowledge of the number and nature of each component. In the analysis, we employed three members each representing the starting, intermediate and end phases. The component representing the starting state was defined by the experimental pattern at the beginning of charge (“Li 0.0”), while the other two were both set as variable components to be determined by the NMF analysis. The resulting PDFs of the two unknown members (Supplementary Movie 1) both show well-resolved patterns (Fig. 5b) with their respective weightings (Fig. 5c) following systematic evolutions that resonate with the two-step mechanism. The reconstructed PDF using the NMF-derived output delivers a striking agreement with the experimental data (Rw < 1.6%), confirming the credibility of the approach (Supplementary Fig. 12).

PDF refinement was then performed to rationalise the two newly extracted components. For the reconverted phase at the end of charge, its local ordering can be well modelled using a (zb) MnO (F$$\bar 43$$m)36, whose (111) reflection contributes to the very intense Bragg peak at 2.3 Å−1 in the XRD pattern (Fig. 2). Modern computational studies36,37,38,39 on the polymorphic landscape of MnO highlight the relative stability of the zb phase36,37,38 compared to the rs ground-state structure; we also note the experimental discovery of a related wurtzitic polymorph40. Our refined lattice constant of the zb-MnO, 4.687 (± 0.006) Å, agrees excellently with the ab initio value 4.73 (± 0.004) Å38. For the intermediate component, its PDF fingerprint insinuates the Mn-containing atom pairs in an rs-related MnO (Supplementary Fig. 13), a phase that could also account for the scattering feature observed in the reciprocal space (Supplementary Fig.  7c). However, peak positions in real-space show discernible discrepancies implying distortion of the MnO6-octahedra7. To model this distortion, a monoclinically distorted rs-MnO (C2/m) was employed in the refinement, noticeably improving the fit to the NMF-derived intermediate component. Note that as a phase experiencing a transition from α-Mn/Li2O to zb-MnO, this intermediate is likely to remain lithiated. However, given the challenge in compositional determination, also considering the lack of structure periodicity and the likelihood of a heterogeneous cation distribution, it is difficult to reach a unique solution to fully model this intermediate. While our study concluded monoclinically distorted rs-MnO provides a good fit to its average short-range ordering, we cannot rule out other possible, related models.

## Discussion

Each of the phases af-Li2O, rs- and zb-MnO adopt an fcc-O lattice. As the MnxOy PDFs show little variation in the coherent length of the system—indicating comparable domain sizes of the hosting structure throughout the charge and subsequent discharge steps—we can infer the oxygen ordering likely remains essentially intact despite significant changes in the cation distribution. On the basis of this preserved oxygen framework, Mn intercalation accompanied by concurrent Li extraction (or vice versa) appears to follow a topotactic insertion-like transformation, mechanistically referred to as a displacement reaction41. Likewise, in the case of FexOy, the preservation of the bcc-Fe structure allows for its homogenous reaction with oxygen, implying the subsequent (dis)charge reactions of the Fe series are also diffusion-controlled, mechanistically similar to displacement, however, with O2− now the displaced species. In both systems, this mechanistic transition exerts a tremendous influence on the reaction thermodynamics and kinetics of the subsequent cycles.

For Fe oxides, upon initial Li+ withdrawal from Li2O (process I), the dissociated O2− migrates to the Li2O/Fe interface and diffuses within the Fe lattice (Fig. 6a). The inserted O2− occupies the bcc-octahedral site, dispersing throughout the phase to reduce anion–anion repulsion. The potential presence of the Fe vacancy defects could further increase the affinity for the oct-O in the bcc-Fe33. As the number of inserted O2− increases, the lattice expands continuously—hence a gradual shift of the Fe Bragg peaks to a lower scattering angle (Supplementary Fig.  6). In contrast, the Li2O reflections shift in the opposite sense due to a lattice contraction as a result of either a declining number of interstitial Li+ and/or reduced grain size42. When the oxygen content x reaches 0.5, the driving force to minimise the O–O interaction, hence the energy of FeOx (Supplementary Fig. 14), promotes a disorder–order transition (process II) during which oct-O2− rearranges to form an ordered sublattice. Upon further charging (x > 0.5), the structure becomes increasingly compact, which leads to progressively hindered O2− diffusion as is consistent with the significantly increased overpotentials (Supplementary Fig. 15); 43 this compact structure, on the other hand, results in an increasingly strained lattice. Without evident fracture of the FeOx nanoparticles, this strain instead manifests itself as local Fe displacements, which account for the increasingly broadened peak widths and reduced intensities observed in the PDF (Supplementary Fig. 11a). During subsequent discharge, physical parameters derived from the refinement (Supplementary Fig. 11b) exhibit a progression that echoes the evolution of the parameters obtained from the charge step. This implies a reversible two-step process occurring during the second discharge, and hence a symmetrical thermodynamic pathway between the reversible cycles.

In contrast to O2− insertion into the Fe-lattice, delithiation of Mn oxides takes place via the opposite route. This difference may arise in part due to the weaker metallic bond of Mn (3d54s2) that arises as a result of its half-filled d-orbitals. Upon charging, initial Li+ extraction partly vacates the tet-Li sites in af-Li2O while the oxidised Mn2+ dissociates from the metal nanoparticle and inserts into the octahedral vacancies in Li2O (Fig. 6b). This reaction (process I) results in an intermediate Litet2-2xMnoctxO phase whose cations may adopt an anisotropic distribution, rendering its average local structure similar to a distorted rs-MnO. Surprisingly, upon further removal of Li+, Mn2+ does not remain within the octahedral sites to form the naturally occurring rs-MnO; instead, it migrates to the tetrahedral positions (process II) where the cation ordering is as in zb-ZnO. During subsequent discharge cycles, based on our NMF analysis (Supplementary Figs. 16 and 17), Mn nanoparticles appear to extrude directly from the zb-MnO (and the remaining intermediate) without going through any traceable transition step, rendering the discharge pathway asymmetric to the charging process. For both Mn and Fe systems, based on the reaction reversibility, they should in principle exhibit identical or comparable (given the asymmetric reaction path for MnxOy) equilibrium voltages. Thus, very similar open-circuit voltages (OCVs) between the first charge and the second discharge steps would be expected in the galvanostatic intermittent titration (GITT) plot. However, a pronounced OCV gap within the reversible cycles is evident in the experimental data (Fig. 7, marked by green arrows), reflecting a deviation from the theoretical equilibrium. Such a deviation has a thermodynamic origin and could be largely due to the voltage modification as a result of inherent “zero-current” hystersis44. In addition, an earlier study observed that an increase in surface tension due to the particle size reduction could increase the OCV gap45. Given the inevitable electrochemical grinding of MxOy into ever smaller particles, their large surface energy might be another intrinsic factor contributing to this thermodynamic hysteresis.

Concerning kinetics, a displacement-like mechanism imparts a substantial dependence on the relative transport properties of different displaced species. As the discharge and charge overpotentials in both systems show an asymmetric response (Fig. 7 and Supplementary Fig. 15)—constituting a path hysteresis46 typical for displacement mechanism—we expect the mobilities of Mn and O in their respective host structures to be generally lower than Li diffusion in most cases. Hence, the discharge kinetics during the reversible cycles for both Mn and Fe systems is likely to be limited by Mn/O extraction from their hosts leading to a relatively small degree of variation in the discharge polarisation. By contrast, upon charge, the mobility difference between Li and Mn/O would result in more rapid Li removal than Mn/O insertion, which we observe as gradually increased overpotentials as lithium is removed. It is likely this asymmetric path hysteresis—in conjunction with other effects, such as passivation layers11 (hence sluggish interface mobilities)—plays a key role in modifying the voltage polarisation. The build-up of the hysteresis from both thermodynamic and kinetic origins eventually manifests itself as a voltage gap that looks unexpectedly large compared to that of conventional insertion materials. Having said that, MxOy’s hysteretic behaviour during the reversible cycles is notably reduced relative to that of the first cycle. It is also worth noting that the asymmetric properties in both thermodynamic (i.e., two-step charge vs one-step discharge) and kinetic pathways of the Mn system jointly give rise to its asymmetric (operating) voltage profile in which the discharge curve generally shows a prominent (pseudo-)plateau. By contrast, this effect is less pronounced in the Fe systems where both discharge and charge curves during reversible cycles appear more slope-like (Supplementary Fig. 1b).

Our results offer insights to guide the future improvement of metal oxides. Firstly, they imply that the key factors that influence the voltage polarisation are primarily mechanism-dependent—thus intrinsic to the materials. Hence, nanostructure engineering may have relatively little impact on the mitigation of the observed hysteretic behaviour43. That being said, MxOy with unique structure designs47—particularly when mechanically reinforced by carbon20,48—might have macro- and microscopic physical features such as structural hierarchy and mesoporosity that nonetheless survive the destructive pulverisation of the first discharge. The preserved structure integrity remains important in the subsequent cycling as it could ensure both effective spatial distribution between M and Li2O as well as adequate electrolyte permeability for Li reaction. As a result, structure-engineered47,48 MxOy is more likely to surpass non-structured11 materials (i.e., commercial materials) in rate performance and capacity retention (Supplementary Fig. 1b). To this end, effective morphology design remains important to harness the full potential of MxOy phases. Secondly, the 2e transfer pathway (per M centre) during reversible cycling and thus the obtainable capacity (i.e., excluding the contribution from side reactions) within the regular voltage window (0–3 V vs Li+/Li) appear insensitive to the MxOy composition. Therefore, although MxOy phases with high M oxidation states deliver a larger capacity in the first discharge, they also produce an excess of Li2O, which will remain inactive during subsequent cycles. Not only is this additional capacity inaccessible thereafter, but the excess Li2O also exacerbates volume expansion during the first discharge—in turn impairing the mechanical integrity of the electrode49. Moreover, the electronically insulating effect of Li2O and its accumulation during the following cycles may lead to further capacity fading11. Hence, to effectively minimise the inherent formation of excess Li2O, future material development should involve strategic selection of MxOy phases with lower metal oxidation states: i.e., FeO/MnO > Fe3O4/Mn3O4 > Fe2O3/Mn2O3 > MnO2. An alternative strategy to better control the M:Li2O ratio is to fabricate M/Li2O nano-mixtures as the pre-lithiated active material. This proof of concept has been proven viable in earlier studies where non-engineered M/Li2O nanocomposites were used as cathode additives50. It is worth exploring the application to anodes, with future effort directed towards carbon mixing and effective morphology engineering. Thirdly, from a broader perspective, the general interest in conversion metal oxides extends from binary to ternary phases51 and includes other 1st-row transition metals and beyond, e.g., Ni (fcc), Co (hcp), and Zn (hcp); we also noticed a change of MnxOy cycling behaviour in the literature due to an unintentional mixing with the Ni template52. In light of the mechanistic differences between the Mn and Fe systems observed here, we envisage that other binary metal oxides may exhibit quite unexpected electrochemical properties—given the distinct crystallographic and physicochemical properties of each metal. It will, therefore, be important to revisit these MxOy systems (possibly with supplementary XAS techniques to enhance the knowledge of their electronic structures), such that an improved and systematic understanding of (i) their generic reversible phase behaviours upon cycling and (ii) diffusion properties of different displaced species is gained. This will uncover synergies from different MxOy and hence enable the design of future materials with complex compositions that are doped with displaced species with fast mobilities, e.g., ternary systems.

As a final point we note that, while our focus has been on elucidating MxOy’s electrochemical transformation pathways, we do also report the first experimental observation of the non-equilibrium phases bcc-FeO and zb-MnO. In their ground states, both FeO and MnO are known to adopt the rs structure. Accessing other polymorphs normally requires high-temperature and/or high-pressure routes53,54. A recent attempt using hydrothermal methods successfully achieved nanostructured wurtzitic MnO40, demonstrating the viability to synthesise non-native MO polymorphs without extreme conditions. As a result of electrochemical pulverisation, the M/Li2O nanocomposites left after discharge possess a large surface energy. Under well-defined electrochemical conditions, this substantial surface energy can stabilise structure types that are otherwise kinetically or thermodynamically unstable, and hence allow the formation of new MO polymorphs. As MO with different structures exhibits interesting physicochemical properties, concerning the significance of MO in a wide range of fields, including but not limited to chemical engineering55, geoscience53,54, condensed matter physics36,56 and metallurgy33,57, the investigation of MO and its polymorphism has become one of the most active areas in modern solid-state chemistry. In this way, electrochemical devices may offer an alternative synthesis strategy to explore non-native metal monoxides with new functionalities—e.g., the unique formation pathway of bcc-FeO is based on diffusion of O2‒ in a close-packed Fe structure, indicating Fe nanoparticles could function as a metallic ionic conductor for O2‒, a rare property for Fe.

To summarise, we have used a combination of in operando/in situ PDF measurements, MMC simulations, and NMF analysis to elucidate the cycling mechanisms of FexOy and MnxOy phases following first discharge. The mechanism adopted depends on the choice of transition metal but is insensitive to the composition of the starting MxOy. Although a one-step conversion reaction from M to rs-MO has been widely accepted as the delithiation pathway upon charge given their similar voltage profiles, our study has shown that both Fe and Mn oxides exhibit a two-step mechanism via displacement-like reactions forming non-equilibrium bcc-FeO and zb-MnO phases. Importantly, while this topotactic behaviour in MnxOy manifests as intercalation of Mn2+ into the fcc-O sublattice, a different pathway based on O2‒ insertion into the bcc-Fe sublattice was observed in the Fe system. For both materials—based on their distorted voltage polarisations within the reversible cycles—we show that the path hysteresis originates from the mobility differences amongst displaced species. Given the reversible cycles (within the regular voltage window) only involve 2e transfer (per metal centre), future material design should be directed towards systems that can demonstrate better control over excess Li2O produced during the first discharge. In light of the new MO polymorphs reported in this work, electrochemical syntheses may offer exciting opportunities to the discovery of new MO materials. Finally, this work demonstrates the viability of using our newly developed analytical approach combining with in situ PDF experiments to investigate battery materials with highly heterogeneous or amorphous structures.

## Methods

### Materials

All FexOy and MnxOy materials were purchased from Sigma-Aldrich. The electrode pellets that contain 70 wt% MxOy active material, 10 wt% PTFE and 20 wt% Super P carbon (TIMCAL C65) were prepared in the atmosphere. Swagelok-type in situ cells were assembled in Ar-filled glovebox (MBraun) using the as-prepared electrode pellets with a glass fibre (Whatman) as the separator, an Li metal foil as the counter electrode, and l M LiPF6 in ethylene carbonate (EC)/dimethyl carbonate (DMC) solution (volume ratio 1:1) as the electrolyte. The fully discharged and charged α-Fe2O3 materials for ex situ TEM measurement were cycled in coin cells. The coin cells were made in the same way as the in situ cells apart from the fact that α-Fe2O3 powder was directly employed as electrode without additional carbon or PTFE. The cells were cycled at room temperature under a rate of C/15. They were stopped at 0 and 3 V, respectively, for the discharged and charged samples. To prepare the TEM samples, these cells were transported and disassembled inside the Ar-filled glovebox. After disassembling, the materials were rinsed with DMC twice before drying in the antechamber.

### Characterisation

The in situ X-ray total scattering data were collected at beamline I15-1 at the Diamond Light Source using an amorphous silicon area detector (Perkin Elmer, XRD4343CT) with an X-ray beam of energy 76.69 keV (λ = 0.1617 Å) and Qmax of 25 Å−1. Experiments were conducted in transmission geometry within perfluoroalkoxy alkane (PFA) Swagelok cells. Empty Swagelok cells were measured for the background of every in situ cell. The in situ electrochemistry was conducted using a rate of C/15 for every cell. Data reduction and normalisation were performed using DAWN58 and PDFgetX259, respectively. An additional LaB6 pattern was collected as a reference to obtain instrumental damping factor for PDF refinement. The PDF refinements were performed using the PDFgui60 software. For TEM measurements immediately following preparation of the ex situ samples, we used a JEOL 3000 F Field emission gun TEM with an air-tight TEM holder.

### MMC simulation

MMC simulations17 were performed on a supercell constructed using 7 × 7 × 7 α-Fe unit cell with the periodic boundary conditions applied. The dimensions of the box were determined based on the 2 nm size of the α-Fe particles suggested by PDF. The number of oxygen atoms was determined by the Fe:O ratio in FeOx and were first randomly distributed into the oct-sites of the bcc-Fe. The MMC energy was calculated on the basis of repulsion between oxygen considering the O–O interaction within the three nearest coordination shells of each oxygen. At each MMC step, a randomly selected oxygen atom was swapped with another randomly selected empty oct-site. The energy change (ΔE) due to the move was calculated. The move was automatically accepted if ΔE ≤ 0; for a positive energy change, the acceptance was subject to the Metropolis algorithm17 given by $${{P}} = {{e}}^{ - \Delta {\it{E}}/{\it{kT}}}$$, where k is the Boltzmann constant and T is the temperature. Moves were continuously proposed, and accepted or rejected until convergence was achieved.

### Non-negative matrix factorisation

The NMF approach followed closely the Metropolis Matrix Factorisation (MMF) method reported earlier18, which uses the MMC algorithm to carry out NMF35. The NMF analysis was performed on renormalised PDFs to satisfy the non-negative criterion of NMF. The renormalised $$g^{{\mathrm{exp}}}\left( r \right)$$ were derived from the experimental $$G^{{\mathrm{exp}}}\left( r \right)$$ using the equation $$G\left( r \right) = 4\pi r\rho _0({\mathrm{g}}\left( r \right) - 1)$$61, in which ρ0 refers to the number density of the structure model. Three fundamental components $${g \ast}_{{\hskip -6pt} i} \left( r \right)$$ (i = 3) were employed in the analysis. The goal of the analysis was to identify these $${g \ast}_{{\hskip -6pt} i} \left( r \right)$$ and associated weights wij (j corresponds to the number of experimental $$g_j^{{\mathrm{exp}}}\left( r \right)$$) to minimise $$|g_j^{{\mathrm{calc}}}\left( r \right) - g_j^{{\mathrm{exp}}}\left( r \right)|^2$$, where $$g_j^{{\mathrm{calc}}}\left( r \right) = {\sum}_{i{\mathrm{ = 1}}}^3 {w_{{\mathrm{ij}}}{g \ast}_{{\hskip -6pt} i} \left( r \right)}$$. Additional constraints were applied to ensure non-negative $${g \ast}_{{\hskip -6pt} i} \left( r \right)$$ for all i and r, and that $${\sum }_{i{\mathrm{ = 1}}}^3 w_{{\mathrm{ij}}}{\mathrm{ = 1}}$$ for all j. The initial $${g \ast}_{{\hskip -6pt} 1} \left( r \right)$$ representing the known component was fixed as the experimental function measured at the end of first discharge, whereas the two unknown components $${g \ast}_{{\hskip -6pt} 2} \left( r \right)$$ and $${g \ast}_{{\hskip -6pt} 3} \left( r \right)$$ and all wij were assigned randomly subject to the various constraints listed above. Each iteration involved a random variation of these parameters, followed by the calculation of the change in $$|g_j^{{\mathrm{calc}}}\left( r \right) - g_j^{{\mathrm{exp}}}\left( r \right)|^2$$. The acceptance or rejection of the variation follows MMC algorithm. The variation was repeated under increasingly stringent acceptance criteria using simulated annealing until convergence was achieved.