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Naoto Kitamura, Hikari Matsubara, Koji Kimura, Ippei Obayashi, [Yohei Onodera](https://orcid.org/0000-0002-3080-6991), Ken Nakashima, Hidetoshi Morita, [Motoki Shiga](https://orcid.org/0000-0003-2434-4716), Yasuhiro Harada, Chiaki Ishibashi, Yasushi Idemoto, Koichi Hayashi

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[Relationship between network topology and negative electrode properties in Wadsley–Roth phase TiNb2O7](https://mdr.nims.go.jp/datasets/7ee3b4e5-745d-40d0-8d54-8f68f4dd3392)

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Relationship between network topology and negative electrode properties in Wadsley–Roth phase TiNb2O7Kitamura et al. NPG Asia Materials           (2024) 16:62 https://doi.org/10.1038/s41427-024-00581-5 NPG Asia MaterialsART ICLE Open Ac ce s sRelationship between network topology andnegative electrode properties in Wadsley–Rothphase TiNb2O7Naoto Kitamura 1,2, Hikari Matsubara1, Koji Kimura3, Ippei Obayashi4, Yohei Onodera 2, Ken Nakashima5,Hidetoshi Morita6, Motoki Shiga 2,6,7,8, Yasuhiro Harada 9, Chiaki Ishibashi 1, Yasushi Idemoto1 and Koichi Hayashi3AbstractWadsley–Roth phase TiNb2O7, with an octahedral network consisting of TiO6 and NbO6, has attracted significantattention as a negative electrode material for lithium-ion batteries in recent years owing to its excellent safety andhigh discharge capacity. In this work, we investigated the effect of the network structure (intermediate-rangestructure), which is considered to form Li+ conduction pathways, on the electrode properties of TiNb2O7. To this end,we prepared TiNb2O7 samples with different charge/discharge properties and generated atomic configurations thatsimultaneously reproduce both total scattering and Bragg profile data. Topological analyses based on persistenthomology demonstrated that the network disorder hidden in the average structure (crystal structure) significantlydegrades the negative electrode properties. In conclusion, controlling the network topology is considered the key toimproving the negative electrode properties of TiNb2O7.IntroductionIn recent years, global warming has become more ser-ious than expected worldwide, and countermeasuresagainst it are among the most important issues we need toaddress. Greenhouse gases such as CO2 are considered tobe the main cause of global warming, making it imperativeto realize a low-carbon society via the effective use ofrenewable energy. The development of rechargeable bat-teries capable of storing renewable energy is essential toachieve this goal.Given this background, lithium-ion batteries (LIBs),which have been used as rechargeable power sources forsmall portable devices such as laptops since the 1990s, arenow widely considered for use as large batteries for sta-tionary applications, vehicles, etc.1,2. One of the seriousproblems associated with the use of large LIBs is the riskof ignition. To overcome this problem, the constituentmaterials of LIBs have been reviewed in recent years, andthe use of transition metal oxides as negative electrode(anode) materials has been aggressively pursued3–5. Manycommercially available LIBs have a carbon negative elec-trode with a low working potential (0.1–0.2 V vs. Li/Li+)to achieve a high energy density, but since the carbonoperates near the Li metal deposition potential, there is arisk of internal short circuits due to Li metal deposition,especially when the battery is quickly charged. Therefore,replacing conventional carbon materials with oxides thatoperate at slightly higher potentials should reduce the riskof internal short circuits. Furthermore, oxides haveexcellent thermal stability, and thus, a considerableimprovement in safety can be expected. Notably, the useof oxide-based negative electrodes, which are insulators inthe fully discharged state, has the significant advantage ofinsulating the battery in the event of an accident. Indeed,Li4Ti5O12 (LTO) with a spinel structure that operates ca.1.5 V vs. Li/Li+ has been commercialized, and LIBs withLTO-based materials as the negative electrodes are beingimplemented in society as rechargeable batteries forvehicles, considering their capability for high Li+ diffu-sion6–8. However, the theoretical capacity of LTO is© The Author(s) 2024OpenAccessThis article is licensedunder aCreativeCommonsAttribution 4.0 International License,whichpermits use, sharing, adaptation, distribution and reproductionin any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate ifchangesweremade. The images or other third partymaterial in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to thematerial. 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To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.Correspondence: Naoto Kitamura (naotok@rs.tus.ac.jp)1Department of Pure and Applied Chemistry, Faculty of Science andTechnology, Tokyo University of Science, 2641 Yamazaki, Noda, Chiba 278-8510, Japan2Center for Basic Research on Materials, National Institute for Materials Science,1-2-1 Sengen, Tsukuba, Ibaraki 305-0047, JapanFull list of author information is available at the end of the article1234567890():,;1234567890():,;1234567890():,;1234567890():,;http://orcid.org/0000-0002-1940-4609http://orcid.org/0000-0002-1940-4609http://orcid.org/0000-0002-1940-4609http://orcid.org/0000-0002-1940-4609http://orcid.org/0000-0002-1940-4609http://orcid.org/0000-0002-3080-6991http://orcid.org/0000-0002-3080-6991http://orcid.org/0000-0002-3080-6991http://orcid.org/0000-0002-3080-6991http://orcid.org/0000-0002-3080-6991http://orcid.org/0000-0003-2434-4716http://orcid.org/0000-0003-2434-4716http://orcid.org/0000-0003-2434-4716http://orcid.org/0000-0003-2434-4716http://orcid.org/0000-0003-2434-4716http://orcid.org/0000-0002-7553-9532http://orcid.org/0000-0002-7553-9532http://orcid.org/0000-0002-7553-9532http://orcid.org/0000-0002-7553-9532http://orcid.org/0000-0002-7553-9532http://orcid.org/0000-0003-2778-0978http://orcid.org/0000-0003-2778-0978http://orcid.org/0000-0003-2778-0978http://orcid.org/0000-0003-2778-0978http://orcid.org/0000-0003-2778-0978http://creativecommons.org/licenses/by/4.0/mailto:naotok@rs.tus.ac.jp175mA h g–1, which is very small compared with that ofcarbon, i.e., 372 mA h g–1.Thus, many studies have been devoted to the discoveryof novel oxide-based negative electrodes with capacitiesexceeding that of LTO, and materials based on a per-ovskite (ABO3-type) structure are the most promisingcandidates. For example, (Li, La)NbO3, which lacks someof the A-site cations in the perovskite structure, hasremarkable Li+ conductivity and has been widely studiedas a solid electrolyte9–11. In addition, this material canfunction as a negative electrode12,13. Recently,Wadsley–Roth phase oxides have attracted even greaterattention14–20. The basic framework of the Wadsley–Rothphases is a ReO3-type structure, in which A-site cationsare completely absent from the perovskite structure (i.e.,BO3-type structure), and in the phases, the corner-sharingBO6 octahedral blocks are sheared periodically (3 × 3, 3 ×4, and so on), forming edge-sharing regions or tetrahedralsites. In the case of TiNb2O7, which is a representativematerial of Wadsley–Roth phase electrodes21–25, TiO6and NbO6 octahedra form 3 × 3 blocks (corner-sharingnetworks) with edge-sharing interfaces, as shown in Fig. 1,and lithium ions are considered to diffuse easily throughthe large free spaces (cavities) of the network20,26. Inaddition, many lithium ions can be inserted and dein-serted by utilizing Ti and Nb redox reactions (Ti3+/Ti4+,Nb4+/Nb5+, and Nb3+/Nb4+); thus, its theoretical capa-city (387 mA h g–1) is comparable to that of a carbon-based negative electrode material.Although TiNb2O7 is considered a promising negativeelectrode material, much remains unknown about itsatomic configuration, which is generally closely related tothe negative electrode properties. For example, based oncrystallography, a TiNb2O7 crystal has five cation sitesoccupied randomly by both Ti and Nb. On the otherhand, a locally stable cation arrangement has been pro-posed via a computational method26. Therefore, a sys-tematic elucidation of the atomic arrangements via anexperimental technique would be highly beneficial. Fur-thermore, because the network of corner-sharing octa-hedra mainly forms the Li+ conduction pathway in thematerial20,26, the order/disorder of the network (the shapeof the network) is considered closely related to thenegative electrode properties. However, quantitativelyelucidating such a network structure, which can beregarded as an intermediate-range structure, via conven-tional analysis of crystal structures is difficult.Considering the above situation, to clarify the relation-ship between the negative electrode properties and theatomic configuration of Wadsley–Roth phase TiNb2O7,the material was prepared via different methods in thisstudy, and the negative electrode properties were eval-uated via galvanostatic charge/discharge cycle tests. Totalscattering (diffraction) data were also measured withquantum beams, and reverse Monte Carlo (RMC) mod-eling using the data27–29 was performed in addition toRietveld analysis using the Bragg peaks. Furthermore,topological analysis based on persistent homology(PH)30,31, which has recently attracted considerableattention in various fields, was carried out on the three-dimensional atomic configurations obtained via RMCmodeling. Through these analyses, the relationshipbetween the topology of the atomic configuration and thenegative electrode properties was examined in detail. As aresult, a guideline for material development with excellentelectrode properties was developed for the first time onthe basis of topology.Materials and methodsSynthesis and characterizationIn this study, three different TiNb2O7 samples wereprepared according to the prior literature25,26: TiO2(anatase) and Nb2O5 were mixed in an appropriate pro-portion, and the mixture was calcined in air at 1100 °C for12 h. The as-synthesized sample is hereafter referred to as“TNO (Pristine)”. A portion of the pristine powder wasplaced in a container with ethanol and ground by ballmilling at 600 rpm for 12 h (PL-7, FRITSCH). The powderobtained after drying at 100 °C is hereafter referred to as“TNO (Ball-milled)”. The ball-milled sample was thenheat-treated in air at 650 °C for 1 h. The resulting samplewas designated “TNO (Heat-treated)”.Phase identification of TNO (Pristine), TNO (Ball-mil-led), and TNO (Heat-treated) was performed via X-raydiffraction (XRD) measurements (Cu Kα; Empyrean,PANalytical). The metal composition was analyzed viainductively coupled plasma atomic emission spectroscopy(ICP‒AES; ICPE-9820, Shimadzu). In this work, the totalmetal composition was normalized to 3. X-ray absorptionfine structure (XAFS) spectra were also measured viatransmission at BL01B1 (SPring-8), and the electronicstructure was subsequently studied via the AthenaFig. 1 Crystal structure of TiNb2O7 (2 × 2 × 2 cell). The red squaresrepresent corner-sharing blocks, and the other parts are edge-sharingparts. The unit cells (monoclinic) are represented by white lines.Kitamura et al. NPG Asia Materials           (2024) 16:62 Page 2 of 13    62 program32. The particle morphologies of the sampleswere also evaluated by scanning electron microscopy(SEM; JSM-7600F, JEOL), and the particle size distribu-tions were investigated via a particle size analyzer (FPAR-1000, Otsuka Electronics).Charge/discharge cycle testFor the charge/discharge cycle tests, an HS cell (HohsenCorp.) was used. The prepared sample, Super C65, andpolytetrafluoroethylene (PTFE) were mixed at a weightratio of 5:5:1 and then pressed onto an Al mesh. Thepressed sample was used as the working electrode aftervacuum drying. Li metal was used as the counter elec-trode, and a polypropylene film was used as the separator.The electrolyte was a solution of 1 mol dm–3 LiPF6 inEC:DMC with a 1:2 volume ratio (Kishida Chemical Ltd.).The cell was assembled under an Ar atmosphere in aglove box.Galvanostatic charge/discharge cycle tests (HJ1001SD8,Hokuto Denko) were performed at room temperatureusing the assembled cell. The cutoff voltages for charging(Li+ insertion) and discharging (Li+ deinsertion) were setat 1 V vs. Li/Li+ and 3 V vs. Li/Li+, respectively. Thecurrent density was 38.7 mA g–1, corresponding to 0.1 C.Average and local structural analysesAs a first step, synchrotron X-ray diffraction (λ= 0.8 Å;BL02B2, SPring-8) measurements were performed, andthen the obtained diffraction pattern of TNO (Pristine)was analyzed via Rietveld refinement using the Rietan-FPprogram33 to determine the average structure (crystalstructure).To clarify the intermediate-range structures (disorder ofthe network) of the samples, neutron total scatteringmeasurements (NOVA, J-PARC MLF) and X-ray totalscattering measurements (BL04B2, SPring-8) were per-formed. Neutron total scattering data were collected withthe 45° bank and then normalized to obtain Faber–Zimanstructure factors, S(Q), using calibration data, i.e., scat-tering intensities of the background, a V-rod, and a V-Niempty can. The X-ray total scattering patterns weremeasured at an incident energy of 61.4 keV, and the S(Q)were derived from them in a standard manner34. Reducedpair distribution functions, G(r), and total correlationfunctions, T(r), were also obtained from S(Q) via a Fouriertransform relation35.By RMC modeling using the total scattering datasimultaneously, we constructed the atomic configurationsof the samples using the RMCProfile code28. To extractinformation on nonperiodic structures (the local cationdistributions and the disorder in the network structure),S(Q) was convolved by considering a simulation box size,and the convolved S(Q), denoted as Sbox(Q) hereafter, wasused in the modeling. The initial simulation box (2 × 6 ×7 supercell) with 5040 atoms, Ti504Nb1008O3528, was madefrom the unit cell refined by the Rietveld analysis, and thecation distribution was optimized by exchanging Ti andNb in the RMC modeling. Bond-valence-sum (BVS)constraints, in which the bond valence parameters were1.815 and 1.911 (B= 0.37) for Ti4+–O2− and Nb5+–O2−,respectively, were applied to maintain appropriate Ti–Oand Nb–O distances36,37. From the obtained atomicconfiguration snapshots, the octahedral distortions ofTiO6 and NbO6 were estimated. To gain a deeperunderstanding of the atomic configurations, ring andtopological analyses, described in the following subsec-tion, were carried out.Topological analysisTo quantitatively investigate the free spaces forming Li+conduction pathways, the atomic structures, especially thenetwork structure formed by the octahedra, were analyzedvia the methods described below.In this study, free spaces in the atomic configurationswere calculated using Structural Order Visualization andAnalysis (SOVA) tools developed by Shiga and a cow-orker38, and the Li+ conduction pathways were confirmedvia BVS mapping with the PyAbstantia code39 using abond valence parameter of 1.466 and B= 0.37 forLi+–O2−. The free spaces in TiNb2O7 were also char-acterized by ring size distributions, which were calculatedusing the R.I.N.G.S. code40. Although there are variouscriteria for ring detection, a primitive method was adop-ted in this work41.As the other method to elucidate the atomic config-urations of the materials, an analysis based on PH wasperformed using the HomCloud code30,42. The analysiscan extract topological features from three-dimensionalatomic configurations, which can be regarded as a pointset in three-dimensional space, and the features can beexpressed in a two-dimensional format called the persis-tence diagram (PD). A schematic illustration of the con-struction of the PD is shown in Fig. S1. A sphere is placedat each atomic position, and the radius is increased fromzero to a larger value. The radius that generates a new ringor void (cavity) is called “birth”, and the radius thatannihilates this ring or void (cavity) is called “death”. Pairsof birth and death for all pairs are plotted in a two-dimensional graph, i.e., PD. This PD provides informationon structural features such as the sizes and shapes of therings and voids (free spaces) and thus enables us to gain adeep understanding of the atomic configurations. There-fore, in the case of the negative electrode materials ofLIBs, the analysis enables us to determine the sizes andshapes (distortions) of possible Li+ conduction pathways.To distinguish rings formed by Ti–O or Nb–O pairs andthen visualize their contributions to rings formed by allthe atoms, connected PDs were also constructed43.Kitamura et al. NPG Asia Materials           (2024) 16:62 Page 3 of 13    62 Further details on the PH analysis are described in theliterature30,31.Results and discussionMaterialsFigure 2a shows the XRD patterns (Cu Kα) of the as-synthesized and ball-milled samples [TNO (Pristine) andTNO (Ball-milled), respectively]. All the peaks in TNO(Pristine) can be attributed to the monoclinicWadsley–Roth phase (space group, C2/m; Fig. 1)21–25,44,yielding a single phase without any impurities. AlthoughTNO (Ball-milled) can be assigned to the same phase, theBragg peaks of TNO (Ball-milled) are weaker and broaderthan those of the pristine sample; this suggests that thecrystal structure was disturbed by the ball-milling process.The metal composition ratio evaluated by ICP‒AES wasTi:Nb = 1.026(1):1.973(2), which is almost equal to thenominal composition, i.e., Ti:Nb = 1:2.For the preparation of samples with a different degree ofdisorder (order) in the crystal structure, TNO (Ball-mil-led) was heat-treated at an elevated temperature in thisstudy. To determine the heat-treatment temperature, inFig. 2 XRD patterns, SEM images, and particle size distributions of TNO prepared by different processes. a XRD patterns at room temperature(Cu Kα) and (b) those of TNO (Ball-milled) recorded by in situ high-temperature measurements (λ= 0.8 Å). SEM images of (c) TNO (Pristine) and (d)TNO (Ball-milled). e Particle size distributions of TNO (Ball-milled) and TNO (Heat-treated).Kitamura et al. NPG Asia Materials           (2024) 16:62 Page 4 of 13    62 situ XRD measurements at high temperatures were pre-liminarily carried out for TNO (Ball-milled), and theresults are shown in Fig. 2b. There is no significant changein the crystal structure regardless of temperature,although the Bragg peaks shift to lower angles withincreasing temperature owing to thermal expansion.Notably, a significant increase in the Bragg peak intensitycan be observed at approximately 900 K (627 °C), sug-gesting that the crystallinity of the TNO particles isimproved by heat treatment. Based on these results, inthis study, TNO (Ball-milled) was heat-treated at 650 °Cto investigate the effect of crystallinity on the charge/discharge properties. The structural disorder in the crystalis discussed in more detail later.The particle morphologies (SEM images) of TNO(Pristine) and TNO (Ball-milled) are shown in Fig. 2c andd, respectively. The particle size is markedly reduced bythe ball-milling process. The particle size distributions(Fig. 2e) also revealed that the particle size of TNO (Ball-milled) is approximately 280 nm and is unchanged evenafter heat treatment at 650 °C; this demonstrates that onlythe crystallinity (the degree of disorder in the crystalstructure) is different between the TNO (Ball-milled) andTNO (Heat-treated) samples.Figure S2 shows X-ray absorption near-edge structure(XANES) spectra at the Ti K-edge and Nb K-edge of thesamples. The Ti K-edge spectra show that the absorptionenergy of Ti in each sample is close to that of TiO2 and istherefore considered to be tetravalent. The Nb K-edgeXANES spectra also indicate that the Nb ion is pentava-lent in the samples because the absorption energy at theNb K-edge of each sample is almost the same as that ofNb2O5. These results suggest that preparation processes,such as ball milling and heat treatment, do not affect thevalences of Ti and Nb in the case of TiNb2O7.Charge/discharge propertiesThe charge/discharge profiles of TNO prepared by thedifferent processes are shown in Fig. 3a–c, and the cycleperformance of the capacity for Li+ deinsertion, which isdefined as the discharge capacity, is summarized in Fig. 3d.TNO (Pristine) has an initial discharge capacity ofapproximately 260mA h g–1, which is higher than that of atypical oxide-based electrode material, Li4Ti5O126–8. How-ever, as the number of cycles increases, the capacity sig-nificantly deteriorates. This deterioration in TNO (Pristine)may be due to the large particle size (long Li+ diffusionlength), which is not suitable for Li+ insertion andFig. 3 Electrode properties of TNO prepared by different processes. Charge/discharge profiles of (a) TNO (Pristine), b TNO (Ball-milled), and cTNO (Heat-treated). d Discharge capacities (capacities for Li+ deinsertion) as a function of the number of cycles.Kitamura et al. NPG Asia Materials           (2024) 16:62 Page 5 of 13    62 deinsertion. According to the literature23, a smaller particlesize tends to improve the electrode properties. However, theinitial discharge capacity of TNO (Ball-milled) with asmaller particle size is significantly lower than that of TNO(Pristine), although the capacity retention can be improvedby ball milling; this means that electrode properties areaffected by factors other than particle size. Notably, TNO(Heat-treated) results in the highest initial discharge capa-city of approximately 270mAh g–1 while maintaining goodcapacity retention, although the particle size of this sampleis essentially the same as that of the ball-milled sample.Therefore, the change in crystallinity (atomic configuration)indicated by the XRD patterns is considered to affectelectrode properties.These results indicate that the charge/discharge prop-erties of TiNb2O7 depend significantly on the preparationprocess and that the significantly disordered atomicconfiguration manifested in the Bragg peak broadeningdegrades the discharge capacity. The disordered atomicconfiguration is quantitatively elucidated based on theaverage and local structures in the following subsections.Average structure of the pristine materialThe average structure of TNO (Pristine) was investi-gated via a Rietveld refinement using the synchrotronXRD pattern. In the analysis, the space group wasassumed to be C2/m44, and constraints were imposed sothat the metal composition calculated from the siteoccupancies was equal to that estimated by ICP‒AES.Figure 4 shows the Rietveld refinement pattern, and TableS1 shows the refined structural parameters. As shown inFig. 4, the average structure was successfully refinedunder the assumption mentioned above.Figure 4b shows the refined average structure. Thisstructure consists of five different cation sites, and thecations form octahedra with six oxide anions, for example,(Ti,Nb)1–O6. As summarized in Table 1 and Fig. 1,(Ti,Nb)1–O6 exist at the center of the corner-sharingblock and share apex oxygens with other octahedra,whereas the others share some edges with the otheroctahedra. Notably, the site occupancy of Nb is thegreatest at the (Ti, Nb)1 site, and the occupancies at the(Ti,Nb)2 and (Ti,Nb)4 sites are greater than those at the(Ti,Nb)3 and (Ti,Nb)5 sites. Therefore, Nb tends tooccupy octahedral sites with fewer shared edges. This maybe due to the higher valence of Nb5+ than of Ti4+; i.e., thedistances between the cations of the octahedra sharingedges are shorter, and thus, the electrostatic repulsionbetween the cations is stronger. Table 1 also presentsdistortions of (Ti,Nb)–O6 octahedra in TNO (Pristine); aFig. 4 Average structure of TNO (Pristine). a Rietveld refinement pattern (synchrotron X-ray) and b refined structure: blue, Ti; green, Nb; red, O.Kitamura et al. NPG Asia Materials           (2024) 16:62 Page 6 of 13    62 larger value of the quadratic elongation represents a largerdistribution of bond lengths, and a larger value of thebond angle variance represents a larger distribution ofbond angles45. As shown in this table, both the quadraticelongation and bond angle variance are the smallest in(Ti,Nb)1–O6, which exist at the center of the corner-sharing block. As lithium ions are considered to diffusethrough this block during charge/discharge processes, asdiscussed below, such a low distortion is considereddesirable for excellent negative electrode properties.Comparison of local structuresAs described above, the Bragg peaks of TiNb2O7markedly broadened when the sample underwent the ball-milling process, indicating that accurate information onthe relationship between the atomic configuration andnegative electrode properties cannot be derived only bythe average structure analysis using the Bragg peaks.Therefore, in this study, we focused on local structureanalysis (an analysis of structures without translationalsymmetry) using quantum beam total scattering data.Figure 5 shows the X-ray T(r) of TNO (Pristine), TNO(Ball-milled), and TNO (Heat-treated). For TNO (Pristine),the neutron T(r) is also presented in Fig. S3. In the X-ray T(r)of all the samples, the peak can be observed at approximately1.9 Å, which can be attributed to the Ti–O and Nb–O bondswithin the TiO6 and NbO6 octahedra. The peak intensitiesare almost identical, suggesting that the shape of the octa-hedra is not significantly changed by ball milling or heattreatment. Similarly, the peak intensity at approximately3.3 Å is not considerably affected by the treatments. Thepeak corresponds to the distance between the cations at theadjacent edge-sharing octahedra, indicating that the changein the edge-sharing part is not significant. Notably, this peakat 3.3 Å is negligible in neutron T(r), as shown in Fig. S3; thisis because Ti, with a negative coherent scattering length46(Table S2), exists predominantly in the edge-sharing region.This result is consistent with the site occupancies obtainedvia Rietveld refinement (Table 1).In contrast to these peaks, the peak intensity atapproximately 3.8 Å is markedly decreased by ball millingand increased again by the subsequent heat treatment at650 °C, as shown in Fig. 5a. Since this distance corre-sponds to the cation–cation correlation between thecenters of the adjacent corner-sharing octahedra, suchpeak behavior suggests that the structure of the corner-sharing blocks is significantly disturbed by the ball-millingtreatment. This result implies that the intermediate-rangestructure has a significant effect on the negative electrodeproperties, as in the case of another Wadsley–Roth phase,i.e., Ti2Nb10O2947. However, since the average structure ofTable 1 Number of shared edges, Nb occupancies, quadratic elongations, and bond angle variances of (Ti, Nb)–O6octahedra in TNO (Pristine).Site Number of shared edges Nb occupancy Quadratic elongation Bond angle variance / deg2.(Ti, Nb)1 0 0.864 1.002 0.9862(Ti, Nb)2 2 0.844 1.028 85.35(Ti, Nb)3 3 0.666 1.049 137.4(Ti, Nb)4 2 0.698 1.042 116.3(Ti, Nb)5 4 0.359 1.043 127.9Fig. 5 Analyses in real space. a X-ray T(r) of TNO and b the atomicconfiguration of TNO.Kitamura et al. NPG Asia Materials           (2024) 16:62 Page 7 of 13    62 TNO (Pristine) refined by the Rietveld method cannotreproduce an experimentally obtained neutron G(r), asshown in Fig. S4, the average structure does not provideaccurate information on the intermediate-range structure(network structure) forming Li+ conduction pathways.To gain a deeper understanding of the network struc-ture, three-dimensional atomic configurations of thesamples were constructed via RMC modeling based ontotal scattering data. Figure 6 shows neutron G(r), neu-tron and X-ray Sbox(Q), and the Bragg profile of TNO(Pristine). All the experimental data are well reproducedvia RMC modeling. The three-dimensional atomic con-figurations of TNO (Ball-milled) and TNO (Heat-treated)were also constructed via RMC modeling (Fig. S5).Snapshots of the simulated atomic configurationsincluding 5040 atoms are shown in Fig. 7a–c. Although allthe samples have 3 × 3 corner-sharing blocks terminatedby edge-sharing regions, the atomic positions areapparently disturbed in the ball-milled sample, as shownin Fig. 7b. This disordered atomic configuration isconsidered one of the reasons for the low dischargecapacity of TNO (Ball-milled). Thus, we analyzed theseatomic configurations quantitatively, with a particularfocus on the network structure.Effect of the preparation process on topologyIn Wadsley–Roth phase TiNb2O7, lithium ions areconsidered to diffuse through cavities formed by the ringstructures of the corner-sharing blocks. To confirm this,we performed cavity analysis with a cutoff distance of2.5 Å and estimated the possible Li+ positions via the BVSmapping technique. Figure 7d–i shows the results of theanalysis using the atomic configurations obtained viaRMC modeling. Large cavities are found in the corner-sharing blocks, and Li+ can exist at the cavities in all thesamples. Although the cavity volume is almost the sameamong the samples, the cavities for Li+ diffusion seem tobe disturbed considerably in TNO (Ball-milled), as shownby the BVS mappings. Such a cavity disturbance might beone of the reasons for the low discharge capacity of theball-milled sample (Fig. 3). Therefore, to study the Li+diffusion pathways in detail, we focused on the ringstructures in the samples. A conventional ring analysiswas performed on the RMC configurations with thedefinition of the primitive ring assuming a 1st coordina-tion distance of rM–O= 2.85 Å. Fig. S6 shows the ring sizedistributions and examples of the corresponding ringstructures. As shown in this figure, the ring size dis-tribution is hardly changed by ball milling and heattreatment, and all the samples have twofold rings (Fig.S6d) and threefold rings (Fig. S6e) in the edge-sharingregions, and flat fourfold rings (Fig. S6f) in the corner-sharing blocks. A small fraction of rings larger than thefourfold rings were also detected owing to the low sym-metry in the crystal structure: these rings are bent atalmost 90°, as shown in Fig. S6g. Considering the Li+Fig. 6 Comparison between experimental data and RMC model for TNO (pristine). a Neutron G(r), b neutron and c X-ray Sbox(Q), and d Braggprofile. The red plus marks and the blue line represent the experiment and RMC model, respectively.Kitamura et al. NPG Asia Materials           (2024) 16:62 Page 8 of 13    62 conduction pathways (for example, as presented in Fig. 7),only the flat fourfold rings shown in Fig. S6f may providespaces for Li+ diffusion. Accordingly, the shape, not thenumber of rings, is closely related to the insertion anddeinsertion of lithium ions during charging and dischar-ging, respectively.To quantitatively elucidate the shape of the networkstructure consisting of rings, we performed persistenthomology analysis. Figure 8 shows the one-dimensionalPD (PD1) of the three TNO samples. The PD1 of TNO(Heat-treated) with the best charge/discharge propertiesis similar to that of TNO (Pristine), whereas the PD1 ofTNO (Ball-milled) with low discharge capacity is appar-ently distributed. These results indicate that the atomicconfiguration is disturbed by the ball-milling process.The PD1s of the TNO samples can be divided into fourgroups, as shown in Fig. 8a, and the structural character-istics, from which each group originated, are extracted viainverse analysis. A small birth region close to the diagonalline (Group A) originates from small triangles consistingof a cation and two oxygen atoms. The triangle is formedby the central cation and two apex oxygens in TiO6 orNbO6. A relatively large birth region close to the diagonalline (Group B) could be assigned to triangles consisting ofthree oxygens within TiO6 or NbO6. Therefore, the pro-files in the vicinity of the diagonal line do not provide anyinformation on Li+ conduction pathways because theyhave a short lifetime and stem from short-range structuralunits such as TiO6 or NbO6.We also performed inverse analysis focusing on theother groups located away from the diagonal line. Theprofile observed at a birth value of approximately 1.1 Åand a death value of approximately 1.4 Å (Group C)mainly originates from twofold and threefold rings. Inother words, the profile is considered to reflect the ringshapes in the edge-sharing parts in the Wadsley–Rothphase; this means that the cavity represented by the smalldeath value of approximately 1.4 Å should be too narrowfor lithium ions to conduct. Thus, the profile of this groupis unlikely to account for the electrode properties of TNO.The profile observed at a birth value of approximately1 Å and a death value of approximately 1.8 Å (Group D)Fig. 7 Snapshots of the atomic configurations, surface-based cavities, and BVS mappings of TNO prepared by different processes.Snapshots of the atomic configurations of (a) TNO (Pristine), b TNO (Ball-milled), and c TNO (Heat-treated). Surface-based cavities of (d) TNO (Pristine),e TNO (Ball-milled), and f TNO (Heat-treated). BVS mappings with BVS= 0.7− 1.3 of (g) TNO (Pristine), h TNO (Ball-milled), and i TNO (Heat-treated).The mappings were visualized via the VESTA program48. The red square in (g) represents one of the corner-sharing blocks.Kitamura et al. NPG Asia Materials           (2024) 16:62 Page 9 of 13    62 originates from rings of fourfold or larger sizes. In addi-tion, there is no correlation between the ring size and thebirth/death ratio, indicating that rings larger than fourfoldare in a folded form, as mentioned above (Fig. S6g).Therefore, only the flat fourfold ring with a large free areais considered to be closely related to the Li+ conductionpathway. To investigate the cation species contributingthe fourfold rings, Ti- and O-centric PD1s and Nb- andO-centric PD1s were investigated and compared withPD1s composed of all atoms; the results are shown inFig. S7 as connected PD1s. In this figure, the upper left ofthe diagonal line represents PD1 considering all theatoms, which is essentially the same as that in Fig. 8a–c.The bottom right of the diagonal line is the Ti- andO-centric PD1 or Nb- and O-centric PD1. For the reader’sconvenience, these PD1s are plotted inverted against thediagonal line. The yellow lines in the connected PD1represent the correlations. In the case of the Nb- andO-centric PD1s that are inverted about the diagonal line(Fig. S7d–f), their profiles are similar to those of the PD1consisting of all the atoms, suggesting that the ringsconsisting of Nb and O contribute almost equally to therings consisting of all the atoms in TiNb2O7. However, thedistribution of the Ti- and O-centric PD1s is differentfrom that of the PD1s considering all the atoms (Fig.S7a–c). As emphasized in Fig. S7a, the rings consistingonly of Ti and O can hardly form the rings belonging toGroup D. In other words, most of the rings in Group Dcontain Nb, and the rings in Group D have changed torings with larger birth values when only Ti and O areconsidered, as indicated in Fig. S7g. These resultsdemonstrate that it is difficult for fourfold rings, whichconstitute a conduction pathway for Li+, to be formedonly by Ti and O. This corresponds to the high Nboccupancy in the (Ti,Nb)1 site belonging to the fourfoldrings (Table 1).To elucidate the effects of ball milling and heat treat-ment on the shapes of the rings in Group D, theFig. 8 Analysis using persistent homology for a topological dimensionality of 1. Persistence diagrams (PDs) for (a) TNO (Pristine), b TNO (Ball-milled), and c TNO (Heat-treated). The profiles associated with the areas highlighted in orange, corresponding to Groups C and D, are plotted for (d)TNO (Pristine), e TNO (Ball-milled), and f TNO (Heat-treated).Kitamura et al. NPG Asia Materials           (2024) 16:62 Page 10 of 13    62 distributions of the birth and death values for the threeTNO samples were examined and are shown in Fig. 8d–f.These profiles were generated considering the plots ofareas with birth values of 0.95–1.25 Å and death values of1.0–2.1 Å, i.e., the peak at a smaller death value representsthe rings of Group C, and the peak at a larger death valuerepresents the rings of Group D. Clearly, the ball-millingprocess broadens these peaks, particularly the peak at alarger death value, considering the fitting results of theprofiles (Fig. S8 and Table S3). This tendency suggeststhat the rings in the ball-milled sample have a large dis-tribution in shape and/or size. The inverse analysis of theplots of the boundary region between Groups C and D(Fig. 8b) revealed that the broadening of the peaks afterthe ball-milling process was caused by considerable dis-tortion of the rings, especially the fourfold rings. However,the subsequent heat treatment reduces the distribution, asshown in Fig. 8f, indicating that the ring shape essentiallyreturns to the pristine state. As previously mentioned, oneof the factors contributing to the low discharge capacity ofTNO (Ball-milled) is the disordering of the crystalstructure manifested by the broadening of the Braggpeaks. The topological analysis demonstrats that thedisordering is caused mainly by the change in the shape ofthe fourfold rings in the corner-sharing blocks, whichform the Li+ conduction pathways.Figure 9 shows the two-dimensional PD (PD2), whichcaptures the shapes of the cavities (free spaces) in thethree TNO samples. In this figure, the profiles in a redrectangle represent cubic cavities without apex cations inthe corner-sharing blocks, and the cavities are sig-nificantly disturbed by the ball-milling process. Sincethese cavities form Li+ conduction pathways, PD2 andPD1 indicate disturbed conduction pathways in TNO(Ball-milled).From the analytical results described above, it can beconcluded that the Li+ conduction pathway with lessdistortion results in better negative electrode properties:The highest charge/discharge capacities can be achievednot by simply reducing the particle size via ball milling butby relaxing the distortion in the network consisting ofTiO6 and NbO6 with subsequent heat treatment whilekeeping the particle size small. The result also indicatesthat the topology can be controlled by optimizing thepreparation process. Since this finding cannot be obtainedonly by conventional average structure analysis based onFig. 9 Analysis using persistent homology for a topological dimensionality of 2. Persistence diagrams (PDs) for (a) TNO (Pristine), (b) TNO (Ball-milled), and (c) TNO (Heat-treated).Kitamura et al. NPG Asia Materials           (2024) 16:62 Page 11 of 13    62 Bragg peaks, it has been demonstrated for the first timethat the combination of intermediate-range structure andtopology analyses is a very promising way to developguidelines for improving electrode properties.AcknowledgementsThis research was financially supported by JSPS Grant-in-Aid for TransformativeResearch Areas (A) “Hyper-Ordered Structures Science” (Grant Nos. 20H05880,20H05881, and 20H05884) and JSPS KAKENHI (Grant No. 19KK0068). We aregrateful to Dr. K. Ohara and Dr. S. Kawaguchi (JASRI) for their support with theX-ray total scattering/diffraction measurements at SPring-8, Japan (ProposalNos. 2022A1458 and 2022A1024) and Dr. T. Ina (JASRI) for his support with theX-ray absorption measurements at SPring-8, Japan (Proposal No. 2021B1031).We thank Prof. K. Ikeda (KEK) for his support of the neutron total scatteringmeasurement at J-PARC, Japan (Proposal Nos. 2019S06 and 2022A0120).Author details1Department of Pure and Applied Chemistry, Faculty of Science andTechnology, Tokyo University of Science, 2641 Yamazaki, Noda, Chiba 278-8510, Japan. 2Center for Basic Research on Materials, National Institute forMaterials Science, 1-2-1 Sengen, Tsukuba, Ibaraki 305-0047, Japan.3Department of Physical Science and Engineering, Nagoya Institute ofTechnology, Gokiso, Showa, Nagoya 466-8555, Japan. 4Center for ArtificialIntelligence and Mathematical Data Science, Okayama University, Okayama700-8530, Japan. 5Faculty of Materials for Energy, Shimane University, 1060Nishikawatsu-cho, Matsue 690-0823, Japan. 6Unprecedented-scale DataAnalytics Center, Tohoku University, 468-1 Aoba, Aramaki-aza, Aoba-ku, Sendai980-8578, Japan. 7Graduate School of Information Science, Tohoku University,6-3-09 Aoba, Aramaki-aza Aoba-ku, Sendai 980-8579, Japan. 8Center forAdvanced Intelligence Project, RIKEN, 1-4-1 Nihonbashi, Chuo-ku, Tokyo 103-0027, Japan. 9Corporate Research and Development Center, ToshibaCorporation, 1 Komukai-Toshiba-cho, Saiwai-ku, Kawasaki 212-8582, JapanAuthor contributionsN.K. designed this research. 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NPG Asia Materials           (2024) 16:62 Page 13 of 13    62 https://www.shiga-lab.org/sovahttps://shinichinishimura.github.io/pyabst/https://homcloud.dev/index.en.html Relationship between network topology and negative electrode properties in Wadsley–Roth phase TiNb2O7 Introduction Materials and methods Synthesis and characterization Charge/discharge cycle test Average and local structural analyses Topological analysis Results and discussion Materials Charge/discharge properties Average structure of the pristine material Comparison of local structures Effect of the preparation process on topology Acknowledgements