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Naoto Kitamura, Yizhong Tang, Koji Kimura, Ippei Obayashi, [Yohei Onodera](https://orcid.org/0000-0002-3080-6991), Ken Nakashima, Chiaki Ishibashi, Yasushi Idemoto, Koichi Hayashi

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[Cation distribution and diffusion-path topologies of A-site-deficient perovskite Li<i><sub>x</sub></i>La<sub>(1−</sub><i><sub>x</sub></i><sub>)/3</sub>NbO<sub>3</sub>](https://mdr.nims.go.jp/datasets/f00b2269-0168-45ac-93aa-5ea883e90fbe)

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Cation distribution and diffusion-path topologies of A-site-deficient perovskite LixLa(1−x)/3NbO3FULL PAPERCation distribution and diffusion-path topologiesof A-site-deficient perovskite LixLa(1¹x)/3NbO3Naoto Kitamura1,2,³, Yizhong Tang1, Koji Kimura3, Ippei Obayashi4, Yohei Onodera2,Ken Nakashima5, Chiaki Ishibashi1, Yasushi Idemoto1 and Koichi Hayashi31Department of Pure and Applied Chemistry, Faculty of Science and Technology, 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, Japan3Department of Physical Science and Engineering, Nagoya Institute of Technology, Gokiso, Showa, Nagoya 466–8555, Japan4Center for Artificial Intelligence and Mathematical Data Science, Okayama University, Okayama 700–8530, Japan5Faculty of Materials for Energy, Shimane University, 1060 Nishikawatsu-cho, Matsue 690–0823, JapanLixLa(1¹x)/3NbO3 with an A-site-deficient perovskite structure was investigated with a focus on the relationshipbetween its atomic configuration and Li+ diffusion properties. To this end, total scattering (diffraction) measure-ments were performed, and then reverse Monte Carlo modeling using the data was employed to construct theatomic configuration. The results suggest that the partial occupancy of La in the La-poor layer facilitate Li+diffusion across the layer owing to the volume contraction. Furthermore, topological analyses conducted viapersistent homology using the constructed atomic configuration indicate that a large fourfold ring formed by Nband O is one of the reasons for superior Li+ diffusion in LixLa(1¹x)/3NbO3.Key-words : A-site-deficient perovskite, Li+ conduction, Total scattering, Local structure, Persistent homology[Received May 27, 2025; Accepted October 7, 2025; Published online November 12, 2025]1. IntroductionIn recent years, the realization of low-carbon societiesthrough a reduction in CO2 emissions has become anurgent need, and renewable energy resources such as solarenergy need to be effectively harnessed. Achieving thisgoal requires the widespread use of large rechargeablebatteries for storing renewable energy, and lithium-ionbatteries—which have been used as a power source forsmall portable devices—are expected to be applied even tolarger systems.1,2) However, serious safety issues exist inthe case of large lithium-ion batteries; thus, the develop-ment of batteries carrying minimized risks of ignition hasbeen promoted in the last few decades, such as all-solid-state lithium-ion batteries that use solid electrolytes in-stead of liquid ones. Oxides possessing a perovskite struc-ture (ABO3-type structure) are regarded as candidates forthe solid electrolyte; in this regard, LixLa(1¹x)/3NbO3 withA-site vacancies (LLNO) showing remarkable Li+ con-duction has been extensively studied.3–14) Moreover, thecapability of LLNO for allowing insertion and deinsertionof lithium ions at around 1.5V vs. Li/Li+ has recentlyattracted significant attention, and some studies havefocused on LLNO as a negative-electrode (anode) materialthat can replace carbon materials used in commercializedlithium-ion batteries.15,16) Given this background, one ofthe most important focus areas in the field of rechargeablebatteries is the elucidation of the ion diffusion mechanismin materials with an A-site-deficient perovskite structure.As is well known, ion diffusion in crystals is generallyclosely related to the atomic configurations. In the case ofperovskite-type oxides such as LLNO that partially lack A-site cations, lithium ions are thought to diffuse via vacan-cies at the A sites.6,14) Therefore, the distributions of Li+,La3+, and vacancies at the A sites in LLNO are thought tohave a considerable influence on the ease of Li+ diffusion.However, because these distributions often do not showtranslational symmetry, conventional analyses of Braggpeaks in powder X-ray diffraction (XRD) patterns, i.e.,Rietveld refinement, may neglect important structuralinformation. Indeed, some studies on LLNO have exam-ined the atomic configuration (La distribution) in a select-ed area via electron microscopy6,8,12,14) and also discussedthe relationship between the configuration and ionic con-duction properties using computational methods.8,11,13)However, the atomic configuration of the whole crystalhas not been sufficiently elucidated experimentally.As one of the experimental methods to fill this gap inliterature, our previous work focused on X-ray fluores-³ Corresponding author: N. Kitamura; E-mail: naotok@rs.tus.ac.jp‡ Preface for this article: DOI https://doi.org/10.2109/jcersj2.134.P4-1Journal of the Ceramic Society of Japan 134 [4] 225-231 2026DOI https://doi.org/10.2109/jcersj2.25074 JCS-Japan©2025 The Ceramic Society of Japan 225This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0/),which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.https://doi.org/10.2109/jcersj2.134.P4-1https://doi.org/10.2109/jcersj2.134.P4-1https://doi.org/10.2109/jcersj2.25074https://creativecommons.org/licenses/by/4.0/cence holography (XFH), which records the modulation ofthe fluorescent X-ray intensity emitted from a target atomby surrounding atoms.17,18) We applied XFH to a LLNOsingle crystal grown by the Czochralski method to investi-gate the distribution of La within the crystal.10,19) AlthoughLLNO has been believed to have essentially a layeredstructure with alternatively stacked La-occupied and La-deficient layers, as shown in Fig. 1,3) the XFH techniquesuccessfully demonstrated that a certain amount of La ex-isted in the La-deficient layer, at least in the single crys-tal, and it also indicated the presence of column-like Laarrangements locally.19) Moreover, the analyses also sug-gested that La migrating into the defective layer contrib-uted to the enhanced Li+ conduction across this layer.However, as discussing the atomic positions in detailbased solely on XFH is very difficult, the relationshipbetween the atomic configuration and Li+ diffusion is notwell understood.Therefore, this study involves construction of the three-dimensional atomic configuration of LLNO with an A-site-deficient perovskite structure and a discussion of its corre-lation with Li+ diffusion. To this end, we performed neu-tron total scattering measurement experiments on LLNOalong with reverse Monte Carlo (RMC) modeling usingthe obtained data20,21) to examine the distribution of Li, La,and vacancies in the A-site and local environments aroundthem. Furthermore, as it is known that insertion and de-insertion of Li+ is possible in TiNb2O7 in the Wadsley–Roth phase, the structure of which partially contains pe-rovskite blocks without cations at the A site (Fig. 1),22–26)we compared the shape of the perovskite blocks inTiNb2O7 with that of the blocks in LLNO. Based on theresults thereof, we discuss the influence of the perovskiteblock shape on Li+ diffusion.2. Experimental2.1 SynthesisLLNO with x = 0.20, i.e., Li0.2La0.8/3NbO3, was syn-thesized via a conventional solid-state reaction methodemploying LaNb3O9 and LiNbO3 as per previous liter-ature.7) To prepare LaNb3O9, a mixture of La2O3 andNb2O5 with a molar ratio of 1:3 was calcined at 1100 °Cfor 3 h and then sintered at 1200 °C for 12 h. LiNbO3 wasprepared by sintering a mixture of Li2CO3 and Nb2O5 at1000 °C for 5 h. The synthesized LaNb3O9 and LiNbO3were then mixed in an appropriate proportion and sinteredat 1200 °C for 12 h. As a reference material, LLNO withx = 0.10 was also prepared in the same manner.2.2 Average and local structure analysesA phase of the synthesized LLNO was identified via asynchrotron XRD pattern measured using BL19B2 in-stalled at SPring-8 (­ = 0.5¡), following which Rietveldrefinement employing the pattern was conducted using theRietan-FP program.27)To uncover the distributions of Li, La, and vacanciesat the A-sites and local environments around them, neu-tron total scattering measurements were performed usingNOVA installed at J-PARC. The scattering pattern was col-lected with a 45° bank, and then a Faber–Ziman structurefactor, S(Q), was obtained from the pattern using calibra-tion data (background, V-rod, and V-Ni alloy can). Thereduced pair distribution function, G(r), was also derivedfrom S(Q) using a Fourier transform relation.28)To construct a snapshot of the atomic configuration ofLLNO, RMC modeling simultaneously employing thetotal scattering data and Bragg profile was performed usingRMCProfile code.29) For the modeling, S(Q) was con-Fig. 1. Schematic illustrations of perovskite-related structures. (a) Perovskite structure (ABO3), (b) A-site-deficient perovskite structure [LixLa(1¹x)/3NbO3], (c) ReO3-type structure (BO3 with corner-sharing BO6 net-work), (d) structure of ReO3-type 3 © 3 © 3 super cell, and (e) Wadsley–Roth phase TiNb2O7 with 3 © 3 © 3corner-sharing networks (perovskite blocks) represented by red squares. Color code: A atom, green; B atom, blue;and O, red.Kitamura et al.: Cation distribution and diffusion-path topologies of A-site-deficient perovskite LixLa(1−x)/3NbO3JCS-Japan226volved by considering a simulation-box size to extractinformation on the local structures, and the convolvedS(Q) is referred to as Sbox(Q) hereafter. An initial simula-tion box with 964 atoms and 116 transparent atoms for thevacant positions was created from the unit cell refinedusing the aforementioned Rietveld analysis. For the RMCmodeling, the Li, La, and vacancies were swapped tooptimize the cation and vacancy distributions; moreover,bond-valence-sum (BVS) constraints, using bond valenceparameters of 1.466, 2.172, and 1.911 (B = 0.37) for Li+–O2¹, La3+–O2¹, and Nb5+–O2¹, respectively, were appliedto maintain appropriate nearest-neighbor distances.30,31)The polyhedral volumes of LiO12 and LaO12 were esti-mated from the obtained snapshot of the atomic configura-tion. For elucidation of the possible Li+ positions, whichare supposed to reflect the Li+ diffusion paths, distributionof BVS within the atomic configuration was also calcu-lated using PyAbstantia code.32) For obtaining a deeperunderstanding of the configuration, a topological analysiswas conducted, as described in the following subsection.2.3 Topological analysisAccording to existing literature on TiNb2O7 containingperovskite blocks in its crystal, the ring shape formed bya corner-sharing BO6 octahedral network has a significantinfluence on Li+ diffusion.26) Therefore, for evaluatingring size and shape, ring size distributions were calculatedusing the R.I.N.G.S. code33) and an analysis based on per-sistent homology (PH) was performed using HomCloudcode.34,35) The latter analysis returns topological features,such as information of rings and voids (cavities), fromthree-dimensional atomic configurations, and these fea-tures are presented in two-dimensional format, i.e., a per-sistence diagram (PD) (Fig. S1). In the analysis, a spherewas placed at each atomic position, and its radius wasincreased from 0 to a larger value. The “birth” representsthe radius at which a new ring or void is generated, and the“death” represents the radius at which this ring or void isannihilated. All pairs of birth (¡) and death (¡) are plottedin the PD. Therefore, the PD provides information on thesizes and shapes of the rings and voids. In other words, itenables us to investigate the sizes and shapes of possibleLi+ diffusion pathways in Li+-conducting materials. Inthis study, we developed the one-dimensional PD (PD1) toobtain information on the ring shape formed by the BO6octahedral network. Further details on the PH analysis aredescribed in existing literature.34,36)3. Results and discussion3.1 Average structurePrior to examining the local structure of LLNO withx = 0.20, we identified the phase of LLNO and performedRietveld analysis to refine the average structure. Figure 2shows the analytical pattern obtained using synchrotronXRD as well as the refined average structure, and Table S1shows the refined structural parameters. Additionally, anenlarged view of the diffraction pattern around d = 1.38¡is also presented in Fig. S2. In the XRD pattern, all Braggpeaks can be assigned to the perovskite structure with A-site defects. Typically, LLNO around x = 0.20 is consid-ered to be tetragonal, and the two prominent peaks ob-served in Fig. S2 are assigned to the (024) and (220)planes of the tetragonal structure.3) However, under thesynthesis conditions employed in this study, the lower-angle peak shown in Fig. S2 broadened, indicating a slightchange toward an orthorhombic structure. Therefore,Rietveld analysis was performed herein assuming anorthorhombic structure, and good fitting was resultantlyobtained, as shown in Fig. 2(a). Furthermore, while thereliability factor, RF, was 4.19% when we assumed that Ladid not exist at the 4h site in the La-deficient layer (thisresult is now shown), the RF was 4.05% when we assumedthat La could occupy this layer (Table S1). That is, the RFvalue decreased slightly under the latter assumption, andthe La occupancy was 0.038. This trend is consistent withthe results of previous studies employing XFH19) and scan-ning transmission electron microscopy (STEM).6,8) There-fore, hereafter, we refer to the layer as not “La-deficient”but “La-poor.”To gain further insight into the structural differencesbetween the La-rich and La-poor layers, we calculated thevolumes of the AO12 polyhedra formed at the two A-sites(4g and 4h sites shown in Table S1). The results demon-strate that the volume in the La-rich layer was 46.78¡3,while that in the La-poor layer was 54.47¡3. Previousstudies have reported that Li+ diffuses predominantlyFig. 2. Average structure analysis of LLNO (x = 0.20). (a)Rietveld refinement pattern (X-ray) and (b) refined average struc-ture. Color code: Li, light green; La, green; Nb, blue; and O, red.Journal of the Ceramic Society of Japan 134 [4] 225-231 2026 JCS-Japan227through the La-rich layer; thus, the electrical conductivityof Li+ along the c-axis is lower than that along the otherdirections.6,8–10,13) Considering these results, the volume ofthe La-poor layer seems to be too large for accommodatingLi+ diffusion.3.2 Local structureBecause average structure analysis cannot distinguishLi, La, and vacancies at the A-sites, RMC modeling wasperformed using the total scattering data in addition to theBragg profile. Figure 3 shows the fitting patterns obtainedvia the RMC modeling, and Fig. 4(a) shows the obtainedatomic configuration. As shown in Fig. 3, this atomic con-figuration can reproduce not only the Bragg profile butalso the total scattering data well. Similar to the Rietveldanalysis result described earlier, the RMC modeling resultindicates that part of the La occupies the La-poor layer[Fig. 4(a)].To gain further detailed insight into the distribution ofLi+, La3+, and vacancies, we investigated the atoms in theLa-rich layers surrounding La in the La-poor layer(Fig. S3). We found that, on average, 7.7 Li and 8.7 Laatoms surround La in the La-poor layer. Considering thelocal electroneutrality condition, La3+ is less likely to existaround La3+ than around Li+, but such a trend cannot beobserved at the scale of the surrounding atoms mentionedabove. Because our XFH analysis revealed La columnararrangements in the case of a single crystal of LLNO,19) Lamight tend to exist relatively easily around La in the A-site-deficient perovskite LLNO.Using the BVS mapping obtained from the snapshot ofthe atomic configuration, we also examined the spaceswhere Li+ is likely to exist, and the results are shown inyellow in Fig. 4(b). As shown in this figure, we map theregions where the BVS values range from 0.7 to 1.3. Inaddition, Table 1 shows the volumes of LiO12 and LaO12polyhedra in the La-rich and La-poor layers, along with theaverage AO12 volumes in both layers estimated from theaverage structure. It is apparent from the BVS mappingFig. 3. RMC modeling of LLNO. (a) Convolved neutron struc-ture factor, (b) neutron reduced pair distribution function, and(c) neutron Bragg profile. The red plus marks and blue solid linerepresent the experimental data and RMC model, respectively.Fig. 4. Atomic configuration of LLNO. (a) Snapshot of atomicconfiguration obtained via the RMC modeling. The color code isas in Fig. 2. (b) BVS mapping in the atomic configuration. Thered rectangles represent the mapping around vacant spaces in theLa-poor layers.Table 1. Polyhedral volumes of LiO12 and LaO12 in La-rich andpoor layers along with average AO12 volumes estimated fromaverage structurePolyhedron Layer Volume/¡3 Volume estimated fromaverage structure/¡3LiO12 La-rich47.446.8LaO12 47.2LaO12 La-poor 49.9 54.5Kitamura et al.: Cation distribution and diffusion-path topologies of A-site-deficient perovskite LixLa(1−x)/3NbO3JCS-Japan228that Li+ does not preferentially exist at the center of thevoids, particularly in the La-poor layers, as indicated bythe red rectangles. This suggests that the La-poor layer isless suitable for Li+ conduction compared to the La-richlayer although Li+ can conduct through the La-poor layer.Indeed, conductivity measurements using a single crystalof LLNO demonstrated that the conductivity in the layer-stacking direction, i.e., c-axis direction is lower than inthe ab plane.10) This difference in the Li+ conduction isconsidered to be due to the significantly larger volume ofthe La-poor layer, as determined by Rietveld refinement(Table 1), compared to the volume of LiO12: that is, thelarge volume of the La-poor layer may be unsuitable forLi+ conduction.It is also noteworthy that the volume of LaO12 in the La-poor layer is much smaller than that obtained via theRietveld refinement, suggesting that the volume of the La-poor layer is decreased by the partial occupancy of La. Toconfirm this, we also performed the Rietveld refinementfor LLNO with x = 0.10 (Fig. S4 and Table S2). Compar-ing the refinement results for the samples with different x(Table S3), it is found that the volume of the La-poor layerdecreases as the occupancy of La in the layer increases.Since the volume of the La-poor layer is too large for Li+conduction basically as mentioned above, these analyticalresults suggest that Li+ diffusion across the La-poor layerbecomes easily owing to the volume contraction by thepartial occupancy of La. Indeed, previous studies haveindicated through molecular dynamics simulations that Li+conduction along the c-axis improves when La partiallyoccupies the La-poor layer.8)3.3 Topologies of perovskite blocksIn recent years, our studies have focused on compoundswith the Wadsley–Roth phase containing perovskiteblocks in the crystals, and we have investigated the rela-tionship between the atomic configuration and negative-electrode properties.26,37,38) In particular, we have per-formed a detailed topological analysis based on PH forthe atomic configuration of TiNb2O7,26) revealing that theshape of the octahedral network formed by corner-sharingBO6 (TiO6 and NbO6) significantly influences the elec-trode properties. For the LLNO studied herein, Li+ isthought to diffuse through free space in the corner-sharingoctahedral network formed by NbO6. Considering thestructural similarity between LLNO and TiNb2O7, weherein applied this analysis to the atomic configuration ofLLNO and compared the shape of the BO6 (NbO6) net-work in LLNO with that in TiNb2O7 to reveal the reasonfor excellent lithium-ion diffusion in LLNO.Figure 5 shows the one-dimensional persistent dia-gram (PD) of this network in LLNO, along with that ofTiNb2O7.26) In our analysis, Li and La were not consideredfor examining only the shape of the octahedral network;that is, this figure only shows the Nb- and O-centric PD.As clearly shown, many plots are concentrated along thediagonal line, where the birth and death values are ratherclose. As previously reported for TiNb2O7, these plots canbe attributed to triangles within NbO6 and are thus notrelated to the Li+ diffusion pathway.26) Contrastingly, plotswith a birth value around 1.1¡ and death value around1.9¡ are supposed to be attributed to larger rings. Accord-ing to ring analysis based on a primitive method,39) thereare fourfold rings formed by four Nb and four O atoms,and sixfold rings detected due to the slight difference in theNb–O distance within the fourfold rings (Fig. S5). There-fore, the plots can be basically originated from the fourfoldring, as shown in Fig. 5(a). Considering the fact that Li+diffuses through the corner-sharing NbO6 network, thisfourfold ring (which is the O4 window) is regarded as abottleneck for Li+ diffusion.6,13) Indeed, in the perovskiteblock of TiNb2O7, the distortion of the fourfold ring isconsidered to hinder Li+ diffusion, leading to poor elec-trode properties.26)Considering these factors, we performed investigationsfor the ideal size and shape of the fourfold ring based onFig. 5. Analysis using persistent homology for a topological dimensionality of 1. (a) Nb- and O-centric PD forLLNO. (b) PD for TiNb2O7. Reproduced with permission from Ref. 26). (c) Schematic illustration of idealbottleneck for Li+ diffusion (O4 window).Journal of the Ceramic Society of Japan 134 [4] 225-231 2026 JCS-Japan229the BVS for Li+ at the center of the ring, and the resultshows that the BVS at the center becomes +1 when thedistance between the center and oxygen is ca. 1.98¡ in thecase of the square fourfold ring [Fig. 5(c)]. This corre-sponds to the birth value of 0.99¡ and death value of1.98¡. When this result is compared with that in Figs. 5(a)and 5(b), the death values of the fourfold rings in LLNOtend to be larger than those in TiNb2O7 and close to theideal value (1.98¡) although they are distributed in anarea smaller than the ideal value, probably due to displace-ments of Nb.6,13)According to previous studies which determined dif-fusion coefficients of Li+ via a galvanostatic intermittenttitration technique (GITT),16,40) the diffusion coefficientsin LLNO-based materials are approximately 2.5 © 10¹12and 9.5 © 10¹10 cm2 s¹1 for Li+ insertion and deinsertion,respectively, and appear to be much higher than that inTiNb2O7, which ranges from 1.2 © 10¹14 to 1.4 © 10¹13cm2 s¹1. This difference in diffusion coefficients can bewell explained by the result of the topological analysisshowing that the fourfold rings in LLNO are more favor-able for Li+ diffusion than those in TiNb2O7. Furthermore,such a tendency of Li+ diffusion with respect to the shapeof fourfold ring is consistent with discussions in previousstudies on LLNO.6,13) Therefore, the results demonstratethat the topological analyses based on PH performed inthis study are effective for elucidating the relationshipbetween ionic diffusion and atomic configuration inperovskite-related compounds. As an extension, system-atic investigations of various perovskite-related materialsare expected to lead to the design of corner-sharing octa-hedral networks suitable for ion conduction.4. ConclusionsThe atomic configuration of LLNO with an A-site-deficient perovskite structure was constructed herein viaRMC modeling employing total scattering data. The poly-hedral volumes of LaO12 suggest that the incorporation ofLa into the La-poor layer changed the volume of the layerand then facilitated Li+ diffusion across the layer. In addi-tion, the size of the bottleneck for Li+ diffusion in LLNOwas successfully evaluated via topological analysis basedon PH, and a large bottleneck was suggested as the reasonfor superior Li+ diffusion. Systematic studies of variousperovskite-related materials in the future will enable us touncover corner-sharing octahedral networks suitable forion conduction.Acknowledgments This research was financially sup-ported by the JSPS Grant-in-Aid for Transformative ResearchAreas (A) “Hyper-Ordered Structures Science” (Grant Nos.20H05880, 20H05881, and 20H05884) and JSPS KAKENHI(Grant No. 19KK0068). We are grateful to Dr. K. Osaka(JASRI) for his support with the X-ray diffraction measure-ments at SPring-8, Japan (Proposal No. 2019B1882). Wethank Dr. T. Honda (KEK) for his support of with neutrontotal scattering measurement conducted at J-PARC, Japan(Proposal No. 2024A0180).References1) D. Larcher and J.-M. Tarascon, Nat. Chem. 7, 19(2015).2) M. S. 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