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## Creator

Yuta Yasui, [Masataka Tansho](https://orcid.org/0000-0001-7986-3199), [Kotaro Fujii](https://orcid.org/0000-0003-3309-9118), Yuichi Sakuda, [Atsushi Goto](https://orcid.org/0000-0002-9472-4098), Shinobu Ohki, Yuuki Mogami, Takahiro Iijima, [Shintaro Kobayashi](https://orcid.org/0000-0002-7306-8458), [Shogo Kawaguchi](https://orcid.org/0000-0002-8498-0936), Keiichi Osaka, [Kazutaka Ikeda](https://orcid.org/0000-0002-1257-1850), [Toshiya Otomo](https://orcid.org/0000-0002-7210-8374), [Masatomo Yashima](https://orcid.org/0000-0001-5406-9183)

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[Hidden chemical order in disordered Ba7Nb4MoO20 revealed by resonant X-ray diffraction and solid-state NMR](https://mdr.nims.go.jp/datasets/4fb08df1-5961-48a5-9290-a9c4aa0d3866)

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Hidden chemical order in disordered Ba7Nb4MoO20 revealed by resonant X-ray diffraction and solid-state NMRArticle https://doi.org/10.1038/s41467-023-37802-4Hidden chemical order in disorderedBa7Nb4MoO20 revealed by resonant X-raydiffraction and solid-state NMRYuta Yasui1, Masataka Tansho2, Kotaro Fujii 1, Yuichi Sakuda1, Atsushi Goto 2,Shinobu Ohki2, Yuuki Mogami2, Takahiro Iijima3, Shintaro Kobayashi 4,Shogo Kawaguchi 4, Keiichi Osaka5, Kazutaka Ikeda 6,7,8,Toshiya Otomo 6,7,8,9 & Masatomo Yashima 1The chemical order and disorder of solids have a decisive influence on thematerial properties. There are numerous materials exhibiting chemical order/disorder of atoms with similar X-ray atomic scattering factors and similarneutron scattering lengths. It is difficult to investigate such order/disorderhidden in the data obtained from conventional diffraction methods. Herein,we quantitatively determined the Mo/Nb order in the high ion conductorBa7Nb4MoO20 by a technique combining resonant X-ray diffraction, solid-statenuclear magnetic resonance (NMR) and first-principle calculations. NMR pro-vided direct evidence that Mo atoms occupy only the M2 site near the intrin-sically oxygen-deficient ion-conducting layer. Resonant X-ray diffractiondetermined the occupancy factors ofMo atoms at theM2 and other sites to be0.50 and 0.00, respectively. These findings provide a basis for the develop-ment of ion conductors. This combined technique would open a new avenuefor in-depth investigation of the hidden chemical order/disorder in materials.Structural order and disorder have attracted considerable attentionbecause of their correlation with material properties1–16. Chemical(occupational) order and disorder have been studiedmainly by crystalstructure analysis using diffraction data. Such order and disorder areoften observed among elements demonstrating similar X-ray atomicscattering factors and similar neutron scattering lengths. Here, weconsider the chemical order between two elements X and Y (X/Y order)and define the ScatteringContrast Score of elements X and Y, SCS(X, Y)as a measure of the contrasts in X-ray and neutron scattering powersbetween the X and Y elements.SCS X ,Yð Þ= N Xð Þ � N Yð ÞN Xð Þ+N Yð Þ��������+Re b Xð Þ� �� Re b Yð Þ� �Re b Xð Þ� �+Re b Yð Þ� ����������� ð1ÞHereN(X) and Re[b(X)] are the number of electrons and real part of thecoherent neutron scattering length bof atomX, respectively. There arenumerous pairs of X and Y elements with low SCS values (ex. ~300 X/Ypairs with SCS lower than 0.15; red parts in Fig. 1). However, it isReceived: 24 December 2022Accepted: 30 March 2023Check for updates1Department of Chemistry, School of Science, Tokyo Institute of Technology, 2-12-1-W4-17, O-okayama, Meguro-ku, Tokyo 152-8551, Japan. 2NMR Station,National Institute for Materials Science (NIMS), 3-13 Sakura, Tsukuba, Ibaraki 305-0003, Japan. 3Institute of Arts and Sciences, Yamagata University, 1-4-12Kojirakawa-machi, Yamagata, Yamagata 990-8560, Japan. 4Diffraction and Scattering Division, Japan Synchrotron Radiation Research Institute (JASRI),SPring-8, 1-1-1 Kouto, Sayo-cho, Sayo-gun, Hyogo 679-5198, Japan. 5Industrial Application and Partnership Division, Japan Synchrotron Radiation ResearchInstitute (JASRI), SPring-8, 1-1-1 Kouto, Sayo-cho, Sayo-gun, Hyogo 679-5198, Japan. 6Institute of Materials Structure Science, High Energy AcceleratorResearch Organization (KEK), 203-1 Shirakata, Tokai, Ibaraki 319-1106, Japan. 7J-PARC Center, High Energy Accelerator Research Organization (KEK), 2-4Shirakata-Shirane, Tokai, Ibaraki 319-1106, Japan. 8School ofHigh EnergyAccelerator Science, TheGraduate University for AdvancedStudies, 203-1 Shirakata,Tokai, Ibaraki 319-1106, Japan. 9Graduate School of Science and Engineering, Ibaraki University, 162-1 Shirakata, Tokai, Ibaraki 319-1106, Japan.e-mail: yashima@cms.titech.ac.jpNature Communications |         (2023) 14:2337 11234567890():,;1234567890():,;http://orcid.org/0000-0003-3309-9118http://orcid.org/0000-0003-3309-9118http://orcid.org/0000-0003-3309-9118http://orcid.org/0000-0003-3309-9118http://orcid.org/0000-0003-3309-9118http://orcid.org/0000-0002-9472-4098http://orcid.org/0000-0002-9472-4098http://orcid.org/0000-0002-9472-4098http://orcid.org/0000-0002-9472-4098http://orcid.org/0000-0002-9472-4098http://orcid.org/0000-0002-7306-8458http://orcid.org/0000-0002-7306-8458http://orcid.org/0000-0002-7306-8458http://orcid.org/0000-0002-7306-8458http://orcid.org/0000-0002-7306-8458http://orcid.org/0000-0002-8498-0936http://orcid.org/0000-0002-8498-0936http://orcid.org/0000-0002-8498-0936http://orcid.org/0000-0002-8498-0936http://orcid.org/0000-0002-8498-0936http://orcid.org/0000-0002-1257-1850http://orcid.org/0000-0002-1257-1850http://orcid.org/0000-0002-1257-1850http://orcid.org/0000-0002-1257-1850http://orcid.org/0000-0002-1257-1850http://orcid.org/0000-0002-7210-8374http://orcid.org/0000-0002-7210-8374http://orcid.org/0000-0002-7210-8374http://orcid.org/0000-0002-7210-8374http://orcid.org/0000-0002-7210-8374http://orcid.org/0000-0001-5406-9183http://orcid.org/0000-0001-5406-9183http://orcid.org/0000-0001-5406-9183http://orcid.org/0000-0001-5406-9183http://orcid.org/0000-0001-5406-9183http://crossmark.crossref.org/dialog/?doi=10.1038/s41467-023-37802-4&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-023-37802-4&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-023-37802-4&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-023-37802-4&domain=pdfmailto:yashima@cms.titech.ac.jpdifficult to investigate the X/Y chemical order hidden in conventionalX-ray andneutrondiffraction. Thus, the chemical order is an importantunresolved issue with numerous materials (Supplementary Table 1).Herein, we propose a technique to elucidate the chemical order, whichis a combination of resonant X-ray powder diffraction (RXRD)17–21 andsolid-state nuclear magnetic resonance (NMR)22–25 assisted by densityfunctional theory (DFT) calculations26–33. Most materials are polycrys-talline or powdered. In contrast to single-crystal X-ray and neutrondiffraction, this combined technique can be widely applied to bothpolycrystalline and powdered samples. Direct evidence of thechemical order can be obtained by NMR23; however, it is difficult toquantitatively analyse the chemical order among the constituentelements. In contrast, RXRD enables the quantitative determination ofthe chemical order by the refinement of occupancy factors, althoughthe refinement results using powder diffraction data are oftendependent on the initial structural model. A reliable, quantitativechemical order can be obtained by the present combined technique ofNMR and RXRD. We call this combined technique as RXRD/NMRmethod.In this study, we aim to elucidate the Mo/Nb order/disorder in ahigh ion conductor Ba7Nb4MoO20·0.15 H2O using the RXRD/NMRmethod (Fig. 2a). We chose Ba7Nb4MoO20·0.15 H2O, becauseBa7Nb4MoO20-based oxides and related compounds are emergingmaterials with high ion conduction, structural disorder and high che-mical stability11,34–40. The crystal structures of Ba7Nb4MoO20-basedoxides have been extensively investigated. However, all the structuralrefinements were performed assuming the complete Mo/Nbdisorder11,34–36,38,39, because the Mo6+ and Nb5+ cations have both (i) thesame number of electrons leading to almost the same X-ray atomicscattering factors and (ii) almost the same neutron scattering lengths(6.715 and 7.054 fm forMo andNb, respectively). This indicates a smallSCS value for theMo/Nb pair of 0.037. Because the ionsmigrate in theoxygen-deficient c′ layers of Ba7Nb4MoO20-based oxides34,36,38,39, thedetermination of the chemical order/disorder of Mo and Nb atoms atH D Li Be Na Mg K Ca Ti V Cr Mn Fe Rb Sr Zr Nb Mo Tc Ru Cs Ba La Ce Pr Nd Pm Hf Ta W Re OsHDLiBeNaMgKCaTiVCrMnFeRbSrZrNbMoTcRuCsBaLaCePrNdPmHfTaWReOs0.20.10ScatteringContrastScore(SCS)Zr Nb Mo Tc RuZrNbMoTcRuElement XAtomicnumber 40 8020 60ElementY204060800.2ScatteringContrastScore(SCS)0.10Fig. 1 | Numerous pairs of X and Y elements having low scattering contrastscore SCS(X, Y). Each number stands for the SCS(X, Y) value. Neutron scatteringlengths are taken from the NIST website68. All the SCS(X, Y) values are available inSupplementary Data 1 and Supplementary Table 16.Elucidation ofMo/NbOrderProtonPosition+ NeutronDiffractionResonantX-rayDiffractionSolidStateNMRDFTCalculations01010011010010baM4M2 M3M1oxide-ion conductingBa1(O1)2–y(O5)ylayer (c′)Ba2(O2)3 layer (h)Ba2(O2)3 layer (h)Ba4(O4)3 layer (h)Ba4(O4)3 layer (h)Ba3(O3)3 layer (c)Ba3(O3)3 layer (c)oxide-ion conductingBa1(O1)2–y(O5)ylayer (c′)M2M2M4M4M3M1M1 M1M3Ba1Ba2Ba4Ba3O1O5O4O3O2 HNb Mo?a bcFig. 2 | Strategies for the elucidation of the Mo/Nb order and complete crystalstructure of Ba7Nb4MoO20·0.15 H2O. a Combined technique to determine thecrystal structure and Mo/Nb order of Ba7Nb4MoO20·0.15 H2O. b Refined crystalstructure showing the M1, M2,M3 and M4 sites of Mo and Nb atoms inBa7Nb4MoO20·0.15 H2O where theMo and Nb atoms are assumed to be completelydisordered.Article https://doi.org/10.1038/s41467-023-37802-4Nature Communications |         (2023) 14:2337 2the crystallographicM2 site near the c′ layer is essential (Fig. 2b). Thus,the chemical order of Mo and Nb atoms at theM2 site is an importantunsolved issue. Herein, we report the chemical order of Mo atoms atthe M2 site near the c′ layer, which offers unprecedented insight intothe understanding of the ion diffusion mechanism in hexagonalperovskite-related oxides.ResultsA single hexagonal phase of Ba7Nb4MoO20·0.15 H2O was prepared bythe solid-state reactions (Supplementary Fig. 1). The lattice para-meters of Ba7Nb4MoO20·0.15H2Oweredetermined tobea = 5.8654(3)and c = 16.5390(3) Å using the X-ray diffraction data of the mixture ofBa7Nb4MoO20·0.15 H2O sample and internal standard silicon. Todetermine the occupancy factors of Nb0.8Mo0.2, Ba and O atoms,preliminary Rietveld analyses of Ba7Nb4MoO20·0.15 H2O were per-formed using neutron diffraction (ND) data and conventional syn-chrotron X-ray diffraction (SXRD) data recorded with 0.6994806(5) ÅX-ray far from the Nb K-edge, based on the Mo/Nb disordered model(Supplementary Note 1 and Supplementary Fig. 2 for details).Ba7Nb4MoO20·0.15 H2O was confirmed to be a P�3m1 hexagonal per-ovskite polytype 7Hwith fourMo/Nb cation sites (M1,M2,M3 andM4)(Fig. 2b). The occupancy factors were determined as follows:gðNb;MiÞ+ gðMo;MiÞ = gðBa;BajÞ= gðO;OkÞ= 1,gðNb;M2Þ+ gðMo;M2Þ=0:92,gðNb;M4Þ+ gðMo;M4Þ =0:08,ði= 1 and 3; j = 1, 2, 3, and4; k =2, 3, and4Þð2ÞHere, g(Nb;Mi) + g(Mo;Mi) = g(Nb0.8Mo0.2;Mi), and the g(X; s) denotesthe occupancy factor of X atoms at s site. The refined crystal para-meters of Ba7Nb4MoO20·0.15 H2Owere consistent with those reportedin the literature11,38.Direct experimental evidence for Mo order at M2 site by NMRWe performed 93Nb and 95Mo solid-state NMR experiments onBa7Nb4MoO20·0.15 H2O at a highmagnetic field (18.8 T), which enabledthe selective observation of Nb and Mo cations, respectively23. Fig-ure 3a and Supplementary Fig. 3 show two-dimensional (2D) 93Nbtriple-quantum magic angle spinning (3QMAS) and one-dimensional(1D) 93Nb magic angle spinning (MAS) NMR spectra, respectively.Three peaks are observed in each 93Nb spectrum, indicating the pre-sence of three Nb sites in Ba7Nb4MoO20·0.15 H2O. In contrast, in the 1D95Mo MAS NMR spectrum, only one peak is observed (Fig. 3b), indi-cating a single Mo site and Mo order in Ba7Nb4MoO20·0.15 H2O.To assign the NMR peaks to different crystallographic sites, weperformed gauge-including projector augmented wave (GIPAW) DFTcalculations of NMR parameters26–29 with the VASP programme41.To validate this method, the calculated 93Nb and 95Mo NMR para-meters were computed for 13 niobates and 11 molybdates (Supple-mentary Tables 2, 3). The experimental and calculated 93Nb and 95MoNMR parameters show good correlations (Supplementary Fig. 5).Thus, we can assign the Nb and Mo peaks by comparing the experi-mental and calculated NMR parameters of Ba7Nb4MoO20·0.15 H2O.For this purpose, the atomic positions in ten possible structuralmodels with different Nb and Mo configurations were optimised byDFT calculations with the P1 space group (Supplementary Figs. 6, 7).The NMR parameters of the optimised structures were estimated bythe GIPAWDFT calculations. The calculated peak positions for (Mo2)O4 tetrahedron of Ba7Nb4MoO20 ranged from –29 to –36 ppmdepending on the structural model, which is close to the experi-mental peak position of –47 ppm for Ba7Nb4MoO20·0.15 H2O.(Table 1), where Mo2 is the Mo atom at the M2 site. The calculatedquadrupolar coupling constant |CQ | values ranged from 0.36 to0.90 depending on the structural model, which is consistent withthe observed value (≤ 2MHz). In contrast, the peaks calculated for–700 –800 –900 –1000δF2 (ppm)a– – –M2Mδ(95Mo) (ppm)bδ F1(ppm)–700–800–900–1000Fig. 3 | Solid-state NMR spectra of Ba7Nb4MoO20·0.15 H2O, showing the siteassignment and Mo order. a 2D 93Nb 3QMAS NMR spectrum and b 1D 95Mo MASNMR spectrum of Ba7Nb4MoO20·0.15 H2O. An asterisk * denotes spinningsidebands.Table 1 | Calculated and experimental 95Mo NMR parameters of Ba7Nb4MoO20, showing the peak assignment to the M2 siteDFT-calculated DFT-calculated Experimental ExperimentalModels a Site Polyhedron b peak position (ppm)c |CQ | (MHz)d peak position (ppm) |CQ | (MHz)d(4), (5) M1 (Mo1)O6 +261 ~ +291 1.47, 2.00 not observed(1)–(3), (5) M2 (Mo2)O4 –29.1 ~ –36.0 0.36–0.90 –47 ≤ 2(7)–(10) M2 (Mo2)O5 +135 ~ +601 5.1–10.7 not observed(6) M3 (Mo3)O6 +192.2 2.87 not observed(7), (8) M4 (Mo4)O6 +208, +202 5.17, 5.23 not observedaEach model is shown in Supplementary Figs. 6, 7.bMoi denotes the Mo atom at the Mi site.cDFT-calculated peak position under 18.79 T was obtained using the correlation in Supplementary Fig. 5a, including the second-order quadrupolar shift.dQuadrupolar coupling constant |CQ|. Experimental |CQ| was estimated from the NMR spectrum (Fig. 3b) with DMFIT69.Article https://doi.org/10.1038/s41467-023-37802-4Nature Communications |         (2023) 14:2337 3different sites were not observed in the experimental 95Mo NMRspectrum. Thus, the single 95Mo NMR peak was assigned to theM2 site. Similarly, observed 93Nb peaks at isotropic chemicalshifts δiso = –748, –952 and –928 ppm can be assigned to the M1,M2 and M3 sites, respectively (Supplementary Table 4). Theseresults lead us to conclude that the Mo cations are located at theM2 site near the ion-conducting c′ layer, indicating Mo order inBa7Nb4MoO20·0.15 H2O.Quantitative determination of the occupancy factors of Mo andNb atoms by resonant X-ray diffractionWeused resonant X-ray diffraction (RXRD) to quantify theoccupancyfactors of the Mo and Nb atoms in Ba7Nb4MoO20·0.15 H2O. Wemeasured the X-ray absorption near edge structure (XANES) spectraof Ba7Nb4MoO20·0.15 H2O and the resonant (anomalous) scatteringfactors of Nb atoms (Supplementary Table 5) were determinedby Kramers–Kronig transformation from the XANES spectra42 (Sup-plementary Fig. 8). In the Rietveld analyses of the RXRD data ofBa7Nb4MoO20·0.15 H2O, we used the linear constraints Eq. (2), whichwere obtained in the preliminary analyses of the ND andconventional SXRD data. The occupancy factors of the Nb and Moatoms at the M1, M2, M3 and M4 sites were not simultaneouslyrefined because of strong correlations. Therefore, we carefullyexamined the residual sum of squares (RSS) in the Rietveldanalysis for fixed occupancy values of Mo atoms at the Mi siteg(Mo; Mi) step-by-step (0.005 step interval for the finest case). Herethe RSS is defined asRSS=XNi = 11yobsiyobsi � ycali� �2ð3Þwhere N, yobsi and ycali are the total number of intensity data, theobserved and calculated intensities for the ith step, respectively, of theRXRDdata. Figure 4 shows RXRD results obtainedwith 0.6527887(5) ÅX-ray at the BL02B2 beamline of SPring-8, which indicates that theoccupancies ofMo atoms are 0.00 at theM1,M3 andM4 sites and 0.50at the M2 site:gðMo;M1Þ= gðMo;M3Þ= gðMo;M4Þ=0:00, gðMo;M2Þ=0:50 ð4ÞThus, gðNb;M1Þ= gðNb;M3Þ= 1:00,gðNb;M2Þ=0:42, gðNb;M4Þ=0:08 ð4′ÞThe same values were also obtained also in the Rietveld analysesfor the RXRD data taken with a 0.6523630(5) Å X-ray at the differentbeamline BL19B2 of SPring-8 (Supplementary Fig. 9), validating theMooccupancy values of Eq. (4). In preliminary analyses, the refinedoccupancy factors g(Mo; Mi) (i = 1, 3 and 4) were negative (Supple-mentary Tables 6–8), supporting the Mo occupancy factors of Eq. (4).850000800000750000700000650000600000550000RSS1.00.80.60.40.20.0g(Mo; M1)850000800000750000700000650000600000550000RSS0.50.40.30.20.10.0g(Mo; M3)850000800000750000700000650000600000550000RSS0.50.40.30.20.10.0g(Mo; M2)850000800000750000700000650000600000550000RSS0.080.060.040.020.00g(Mo; M4)g(Mo; M2)0 0.50.25acbdFig. 4 | Determination of the Mo occupancy factors in Ba7Nb4MoO20·0.15 H2O. Variation of the residual sum of squares (RSS; see the definition of Eq. (3)) with theoccupancy factor ofMo atom at the aM1, bM2, cM3 and dM4 sites in the Rietveld analyses for the RXRD datameasured with 0.6527887(5) Å X-ray at the BL02B2 beamline.Article https://doi.org/10.1038/s41467-023-37802-4Nature Communications |         (2023) 14:2337 4These results clearly indicate theMochemical order at theM2 site nearthe ion-conducting c′ layer, which is consistent with the NMR resultspreviously discussed.Complete crystal structure of Ba7Nb4MoO20·0.15 H2OToaccurately refine the structural parametersof hydrogen andoxygenatoms, we have analysed the crystal structure of Ba7Nb4MoO20·0.15H2Ousingneutrondiffraction (ND)data collected at 30 and300K.During this process, the occupancy factors of Mo and Nb atomswere fixed to the values of Eqs. (4) and (4′), respectively, which wereobtained from the analysis of the RXRD data. Excellent fittings wereobtained for both ND and RXRD data (Fig. 5 and SupplementaryFig. 10). The crystallographic parameters refined using ND and RXRDdata were consistent with each other (Table 2 and SupplementaryTable 9). The water content x in bulk crystalline Ba7Nb4MoO20–x(OH)2x(= Ba7Nb4MoO20+xH2x = Ba7Nb4MoO20·x H2O) was calculated to bex =0.151(5) using the refined occupancy factors at 30K (Supplemen-tary Table 10), which is consistent with the water content estimatedfrom the thermogravimetric-mass spectroscopic (TG-MS) analyses(Supplementary Fig. 11). TheO1–Hdistancewas estimated tobe 1.07(4)Å using the refined crystal structure of Ba7Nb4MoO20·x H2O at 300K,which agrees with the O–H distance of 0.99738(8) Å obtained fromits Raman spectrum (Supplementary Fig. 12), indicating the presenceof hydroxide ions formed by the hydration. The bond-valencesums (BVSs) of cations and anions for the refined structure ofBa7Nb4MoO20·0.15 H2O agree with their formal charges (Table 2).These results confirm the validity of the refined crystal structure ofBa7Nb4MoO20·0.15 H2O.Figure 6 shows the refined crystal structure of Ba7Nb4MoO20·0.15 H2O, with the sequence c′hhcchh. Oxygen-deficient lattice O1 andinterstitial O5 sites exist in the c′ layer. At high temperatures, oxideions can migrate via O1–O5 diffusion pathways and the interstitialcydiffusion mechanism as shown by the maximum-entropy method(MEM) neutron scattering length density (NSLD) distribution ofBa7Nb3.9Mo1.1O20.05 at 1073 K36. Similar O1–O5 paths were visualised inMEM NSLD distribution of wet Ba7Nb4MoO20·0.87 H2O at 368K34.Structural disorders have been reported in Ba7Nb4MoO20-basedmaterials11,34,36,38,39. In contrast, a striking feature is the presence of Moatoms only at the M2 site near the ion-conducting c′ layer, indicatingMo chemical order. DFT-optimised structures with Mo order at theM2 site have slightly lower energies than those with Mo disorder andMo atoms atM1 andM3 sites, which supports theMo chemical order atthe M2 site (Supplementary Table 11). This is the first report on thechemical order of Mo atoms in Ba7Nb4MoO20-based materials. In theliterature11,34–36,38,39, all structural analyses were performed based oncomplete Mo/Nb disorder. Meanwhile, in this study, the Mo order wasindicated not only by structural refinements using RXRD data but alsobyNMRmeasurements andDFT calculations. An important question iswhy the Mo order occurs. The probable explanation is as follows: theM2 site has a smaller space compared with otherMi sites (i = 1, 3 and 4)(Supplementary Table 12), and the size of theMo cation is smaller thanthat of the Nb cation; thus, Mo order occurs. Indeed, the BVS of Mo atM2 site 5.54 agrees with the formal charge 6 of Mo6+, which is higherthan the BVS values of Mo atoms at M1 (4.63), at M3 (4.76) and atM4(3.51) sites indicating the underbonding and instability of Mo atoms atMi sites (i = 1, 3 and 4).DiscussionThepresentwork has demonstrated the chemical orderofMoatoms attheM2 site near the ion-conducting c′ layer in Ba7Nb4MoO20·0.15 H2Oby the combined technique of solid-state NMR, resonant XRD andDFTcalculations, in addition to the neutron diffraction and conventionalSXRD. TheNMRspectra provided direct experimental evidence for theMo order, while the structural analyses using the RXRD data enabledthe quantitative determination of the occupancy factors of Mo andNb atoms. This combined technique can be used to investigate thehidden chemicalorder in various ion-conductinghexagonal perovskitederivatives such as Ba7Nb4−xMo1+xO20+x/236, Ba7Nb4−xWxMoO20+x/238,Ba7Nb4−xCrxMoO20+x/239 and Ba3MoNbO8.56,43,44 where the Mo occu-pancies at the Mi sites (i = 1, 2, 3 and 4) are unknown. Here x is thedopant or excess Mo content. Beyond the limits of the combinedtechnique of conventional X-ray diffraction and NMR (’SMARTER’crystallography45,46), this RXRD/NMR method can be applied tonumerous compounds such as thermoelectric Ag1–xCdxSbTe216 andsuperconducting Zr5Ir2Os47 exhibiting chemical order/disorder ofatoms with both similar X-ray atomic scattering factors and similar2θ (º)50201510Intensity(arb.units)432d (Å)1150000100000500000.0Intensity(counts)5040302010baFig. 5 | Rietveld fitting patterns of Ba7Nb4MoO20·0.15 H2O. a Resonant X-raydiffraction (RXRD) datameasured at 297 Kwith 0.6527887(5) Å X-ray at the BL02B2beamline. b Neutron diffraction data at 300K. The observed and calculatedintensities and difference plots are shown by red cross marks, blue solid lines, andblue dots, respectively. Green tick marks denote the calculated Bragg peakpositions.MM2M2M4M4M3M1M1 M1M3Ba1Ba2Ba4Ba3O1O5O4O3O2Hoxide-ion conductingBa1(O1)2–y(O5)ylayer (c′)a bcBa2(O2)3 layer (h)Ba2(O2)3 layer (h)Ba4(O4)3 layer (h)Ba4(O4)3 layer (h)Ba3(O3)3 layer (c)Ba3(O3)3 layer (c)oxide-ion conductingBa1(O1)2–y(O5)ylayer (c′)100% Nb42% Nb,50% Mo,8% Vacancy100% Nb8% Nb,92% VacancyFig. 6 | Crystal structure of Ba7Nb4MoO19.849(OH)0.302. Refined crystal structureof Ba7Nb4MoO19.849(OH)0.302 at 300K,which shows theMo chemical order and siteoccupancies of Nb and Mo atoms.Article https://doi.org/10.1038/s41467-023-37802-4Nature Communications |         (2023) 14:2337 5neutron scattering lengths (Fig. 1 and Supplementary Table 1). In con-trast to the single-crystal X-ray diffraction19,48 and X-ray fluorescenceholography49, the RXRD/NMRmethod uses powders or polycrystallinesamples, making it versatile and easily applicable to in situ measure-ments (e.g., at high temperatures). The combined technique would beuseful for investigatingnot only theperiodic average structurebut alsothe short- and intermediate-range order/disorder hidden in conven-tional diffraction and total scattering.Next, we discuss the influences of Mo chemical order on thematerial properties of Ba7Nb4MoO20. The flexibility of the coordina-tion ofM2 atoms near the c′ layer was suggested to determine the highion conduction in Ba7Nb4MoO20·0.5 H2O from the ab initio moleculardynamics simulations34. Since the present work has indicated that Mocations are localised at the M2 site near the ion-conducting c′ layer inBa7Nb4MoO20·0.15 H2O, the flexibility ofMo atoms is important for thehigh ion conduction in Ba7Nb4MoO20-based materials as well as inother Mo-containing ionic conductors such as La2Mo2O950. Therefore,the bulk conductivity of Ba7Nb4−xMo1+xO20+x/2 increases with increas-ing the excess amount of Mo atoms x from x = 0 to 0.136, which isascribed to not only a larger amount of excess oxygen atoms but alsothe larger amount of Mo atoms.The energy barriers for oxide-ion migration Eb/O of Mo-orderedand virtual Mo-disordered Ba7Nb4MoO20·0.15 H2O were calculatedusing the bond-valence method51,52. The Eb/O along the c axis in Mo-ordered Ba7Nb4MoO20·0.15 H2O (1.93 eV) is higher than that in thevirtual Mo-disordered Ba7Nb4MoO20·0.15 H2O (1.60 eV) [Supplemen-tary Table 13], which is attributable to the narrower bottleneck foroxide-ion migration along the c axis due to the higher occupancyfactor of larger Nb cations at the bottleneck triangle (Supplemen-tary Fig. 14).The substitution of Nb with Mo improves the oxide-ion con-ductivity because of the larger number of interstitial oxygen atoms(higher carrier concentration). The formation energies ΔHf of theMo-ordered and virtual Mo-disordered Ba7Nb3.5Mo1.5O20.25 oxideswere calculated using the DFT method. The calculated ΔHf values ofMo-ordered models are lower than those of virtual Mo-disorderedones (Supplementary Table 15), which indicates that Mo orderingstabilises Ba7Nb3.5Mo1.5O20.25 with interstitial oxygen atomsmore efficiently than Mo disordering, leading to higher oxide-ionconductivity. The hydration enthalpies ΔHhyd of Mo-orderedand Mo-disordered Ba7Nb4MoO20 were also investigated by DFT cal-culations, because the hydration is important for proton conductionin Ba7Nb4MoO20. Compared with the calculated ΔHhyd ofthe Mo-disordered Ba7Nb4MoO20 (1.70 kJmol−1), that of Mo-orderedBa7Nb4MoO20 (−22.7 kJmol−1) is close to the experimental value below300 °C (−24 kJmol−1)34. The calculated ΔHhyd for the Mo-orderedsystem (−22.7 kJmol−1) is lower than that of the Mo-disorderedone (1.70 kJmol−1), indicating that the Mo ordering also stabilisesthe hydrated Ba7Nb4MoO20 more efficiently compared with Modisordering. These results demonstrate that the Mo order inBa7Nb4MoO20 affects the material properties. The present findingsrepresent a major advance in the fundamental understanding of thecorrelation between the crystal structure and material properties ofionic conductors.MethodsSynthesis and characterisationThe Ba7Nb4MoO20·0.15 H2O samples were prepared by the solid-statereaction method. High-purity (>99.9%) BaCO3, Nb2O5 and MoO3 weremixed as ethanol slurries and ground as dry powders using an agatemortar and pestle. The obtained powders were calcined at 900 °C for12 h for decarbonation. The materials thus obtained were crushed andground into fine powders in an agate mortar for 1 h as dried powdersand ethanol slurries. The resultant powders were uniaxially pressedat 150MPa and then sintered in air at 1100 °C for 24 h. The sinteredpellets were crushed and ground into fine powders for X-ray powderTable 2 | Refined crystal parameters and reliability factors in Rietveld analysis of the neutron diffraction data ofBa7Nb4MoO19.849(OH)0.302 (= Ba7Nb4MoH0.302O20.151 = Ba7Nb4MoO20.151H0.302 = Ba7Nb4MoO20·0.151 H2O) at 300KSite / Atom label Atom Wyckoff position gf x y z Uiso (Å2)g BVSdBa1 Ba 1a 1e 0 0 0 0.0165(7) 2.02Ba2 Ba 2d 1e 1/3 2/3 0.82374(7) 0.0138(3) 2.19Ba3 Ba 2d 1e 1/3 2/3 0.57420(9) 0.0091(3) 2.29Ba4 Ba 2c 1e 0 0 0.27870(8) 0.0078(4) 1.91M1 Nb 1b 1e 0 0 1/2 0.0060(3) 4.57M2 Nb 2d 0.42 1/3 2/3 0.09489(6) 0.0060(3) 4.91M2 Mo 2d 0.5 1/3 2/3 0.09489(6) 0.0060(3) 5.54M3 Nb 2d 1e 1/3 2/3 0.34909(6) 0.0060(3) 4.61M4 Nb 2d 0.08 1/3 2/3 0.1926a 0.0060(3) 3.65O1 O 6i 1/3 0.3532(4) 0.7064(9) –0.01209(6) 0.0196(8) 1.84O2 O 6i 1e 0.16652(14) 0.3330(2) 0.13082(4) 0.01167(16) 1.94O3 O 6i 1e 0.16323(14) 0.3265(2) 0.43098(4) 0.01086(18) 1.95O4 O 6i 1e 0.49502(9) 0.50498(9) 0.29455(3) 0.00791(18) 1.98O5 O 3e 0.0504b 1/2 0 0 0.0196(8) 1.28H H 12j 0.0252b 0.346(4) 0.500(5) 0.9748(16) 0.041c 0.85Crystal system: trigonal. Spacegroup: P�3m1 (No.164, setting 1). Lattice parameters: a =b = 5.865653(4) Å, c = 16.53699(3) Å. The number of formula per unit cell: Z = 1. Reliability factors: Rwp = 2.719%,Rp = 2.254%, RB = 4.577%, RF = 3.872%, GoF = 19.857.az coordinate of the Nb4 atom was fixed to those from preliminary analyses.bOccupancy factors of O5 and H atoms were fixed to those from ND analysis at 30K.cAtomic displacement parameter of the H atom was fixed to those from preliminary analyses.dBVS bond-valence sums. Here the bond-valence parameters after ref. 70 were used for the calculations of BVSs. The low BVS values of O5 and H atoms than the formal charges of –2 and +1 areconsistent with the low occupancy values of 0.0504 and 0.0252, respectively.eThe occupancy factors of Ba1–Ba4,M1,M3, and O2–O4 atoms were fixed to unity, because the refined values agreed with unity within three times of estimated standard deviations (seeSupplementary Note 1 for details).fg = g(X; s): Occupancy factor of X atom at the s site. g(Ba; Ba1) = g(Ba; Ba2) = g(Ba; Ba3) =g(Ba; Ba4) =g(Nb;M1) = g(Nb;M3) =g(O; O2) =g(O; O3) =g(O; O4) = 1; g(Nb;M2) = 0.42, g(Mo;M2) = 0.5, g(Nb;M4) = 0.08; g(O; O1) = 1/3, g(O; O5) = 0.0504; g(H; H) = 0.0252. x, y, and z: atomic coordinates.gUiso(Xn) Isotropic atomic displacement parameter of X atom at the Xn site. Linear constraints in the Rietveld analysis: Uiso(Nb1) =Uiso(Nb2) =Uiso(Mo2) =Uiso(Nb3) =Uiso(Nb4).Article https://doi.org/10.1038/s41467-023-37802-4Nature Communications |         (2023) 14:2337 6diffraction (XRD), inductively coupled plasma atomic emission spec-troscopy (ICP-AES, Shimadzu ICPS-8100 spectrometer), and TG-MSmeasurements. The ICP-AES results indicated that the cation molarratio of Ba7Nb4MoO20·0.15 H2O was Ba: Nb: Mo = 6.89(12): 4.078(18):1.034(10), which is consistent with the nominal composition. TG-MSanalyses of Ba7Nb4MoO20·0.15 H2O were performed using RIGAKUThermoMass PhotounderHeflows at a heating rate of 20 Kmin–1 up to900 °C. The Raman spectrum of Ba7Nb4MoO20·0.15 H2O was collectedusing an NRS-4100 (JASCO Co.) instrument with an excitation wave-length of 532 nm.Synchrotron X-ray and neutron diffraction experiments anddata analysisSynchrotron X-ray diffraction (SXRD) experiments were performed atbeamlines BL02B2 (297K)53 and BL19B2 (300K)54 of SPring-8. X-raywavelengths for resonant X-ray diffraction experiments were selectedfrom the spectrum of Nb K-edge X-ray absorption near edge structure(XANES) for a Ba7Nb4MoO20·0.15 H2O powder. X-ray wavelengths weredetermined from the X-ray diffraction data of standard silicon powder(SRM 640c) using FullProf software55. Conventional SXRD data wererecorded with a 0.6994806(5) Å X-ray. RXRD measurements were per-formed using a 0.6527887(5) Å X-ray at the BL02B2 beamline and a0.6523630(5) Å X-ray at BL19B2. Both the conventional SXRD andRXRDdata were analysed using the Rietveld method with the computer pro-gramme RIETAN-FP56. We used atomic scattering factors in the form off= f0 + f’′+ if”, where f0 is the Thomson scattering factor and f’ and f” arethe resonant (anomalous) scattering factors. The f’ and f” factors of theNb atom were calculated from the XANES spectrum (SupplementaryFig. 8) recordedat BL19B2with theprogrammeDiffKK57, and the f’ and f”factors of Ba, Mo and O atoms were obtained from the theoreticalvalues reported by Cromer and Libermann58 (Supplementary Table 5).Time-of-flight (TOF) neutron diffraction data of Ba7Nb4MoO20·0.15 H2O were obtained at 30 and 300K using a high-intensity totaldiffractometer NOVA (BL-21) in the MLF of J-PARC. Rietveld analyseswere performed using Z-Rietveld59,60 using neutron diffraction dataobtained from the backscattering bank of the NOVA.The bond-valence-based energy (BVE) landscapes for a test oxideion and proton in Ba7Nb4MoO20·0.15 H2O were calculated usingrefined crystal parameters at 300K using the SoftBV programme51,52.The refined structures and BVE landscapes were depicted using theVESTA 361.Solid-state NMR experimentsNMR experiments of Ba7Nb4MoO20·0.15 H2O were performed with a3.2-mmhomemadeMAS probe at a spinning speed of 20 kHz under amagnetic field of 18.79 T, corresponding to 95Mo and 93Nb Larmorfrequencies of 52.16 and 195.84MHz, respectively. 1D 95Mo and 2D93Nb NMR spectra were recorded using a JEOL JNM-ECA 800 spec-trometer, whereas 1D 93Nb NMR spectra were obtained using a JEOLJNM-ECZ 800R spectrometer. 95Mo chemical shifts were referencedto 2.0M aqueous solution of Na2MoO4 at 0.00 ppm (refs. 62,63), and93Nb chemical shifts were externally referenced to NaNbO3 at −1093ppm (ref. 64). 95Mo NMR spectra of α-MoO3 and BaMoO4 were alsoobtained to investigate the relationships between the experimentaland DFT-calculated NMR parameters (Supplementary Figs. 4, 5). The1D 95Mo NMR spectra were acquired by accumulating 22,000 scansusing a 1.2 μs single-pulse sequence with a relaxation delay of 20 s.The 1D 93Nb spectra were measured using a spin-echo sequence(2.0 and 4.0 μs), accumulating 1024 scans with a relaxation delay of1 s. The 2D 93Nb 3QMAS NMR spectra were measured by the con-ventional three-pulse sequence with z-filter65 (2.0, 0.9 and 15 μs), andrecorded with 264 transients averaged for each of the 1024 t1 pointswith a relaxation delay of 0.2 s. Shearing transformation66 wasapplied to the spectra. Here, the centre of the F1 axis was set to thecentre of the F2 axis.Density functional theory (DFT)-based calculationsGeneralised gradient approximation (GGA) electronic calculationswere performed using Vienna Ab initio Simulation Package (VASP)41.We used projector augmented wave (PAW) potentials for Ba, Nb, Moand O atoms, plane-wave basis sets with a cutoff of 500 eV and thePerdew–Burke–Ernzerhof (PBE) GGA functionals. The crystal para-meters refined using the neutron diffraction data of Ba7Nb4MoO20·0.15 H2O at 300K were used as the initial parameters in the DFTstructural optimisations. Atomic coordinates of Ba7Nb4MoO20 wereoptimised in the space group P1, with the convergence condition of0.02 eVÅ–1. The supercell programme67 was used to generate supercellmodels. The formation energies of Ba7Nb3.5Mo1.5O20.25 ΔHf for theMo-ordered and virtual Mo-disordered models were calculatedaccording to the following equation:Ba7Nb4MoO20 + 1=2MoO3 ! Ba7Nb3:5Mo1:5O20:25 + 1=4Nb2O5The optimised structures are shown in Supplementary Fig. 15. Thehydration enthalpies ΔHhyd were also estimated for the Mo-orderedand virtual Mo-disordered models (Supplementary Fig. 16) accordingto the following reaction:Ba7Nb4MoO20� �4 +H2O ! Ba7Nb4MoO20:25H0:5� �4DFT calculations of the 93Nb and 95Mo chemical magnetic shield-ing and electric field gradient tensors were performed using the VASPcode with a cutoff energy of 700 eV for the plane-wave basis sets,where the total energy converged within 10–8 eV/atom. The GIPAWformalism28 was utilised for the calculations of the NMR chemicalshielding tensors.Data availabilityThe datasets generated during and/or analysed during the currentstudy are available from the corresponding author on request.References1. May, S. J. et al. Enhanced ordering temperatures in anti-ferromagnetic manganite superlattices. Nat. Mater. 8,892–897 (2009).2. Keen, D. A. & Goodwin, A. L. The crystallography of correlateddisorder. Nature 521, 303–309 (2015).3. Hogrefe, K. et al. Opening diffusion pathways through site disorder:the interplay of local structure and ion dynamics in the solid elec-trolyte Li6+xP1–xGexS5I as probed by neutron diffraction and NMR. J.Am. Chem. Soc. 144, 1795–1812 (2022).4. 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Tada ofthe Materials Analysis Division, Open Facility Center, Tokyo Institute ofTechnology, for their assistance in the TG-MS and Raman measure-ments, respectively.We acknowledgeKojundoChemical LaboratoryCo.for the ICP measurements and for supplying chemical materials. Neu-tron and synchrotron X-ray experiments were performed under projectNos. 2019BF2106, 2020L0801, 2020L0804, 2019A1052, 2020A1730,2021A1599 and 2021B1826. This study and travel expenses were sup-ported by a Grant-in-Aid for Scientific Research (KAKENHI, Nos.JP19H00821 (M.Y.), JP20J23124 (Y.Y.), JP21J22818 (Y.S.), JP21K18182(M.Y.) and JP22H04504 (K.F.)) from the Ministry of Education, Culture,Sports, Science and Technology of Japan, Adaptable and SeamlessTechnology Transfer Programme through Target-driven R&D (A-STEP)from the Japan Science and Technology Agency (JST) Grant NumberJPMJTR22TC (M.Y.), and JSPS Core-to-Core Programme, A. AdvancedResearch Networks ([i] Solid Oxide Interfaces for Faster Ion Transport(M.Y.) and [ii] Mixed Anion Research for Energy Conversion[JPJSCCA20200004] (M.Y.)). Y.Y. and Y.S. acknowledge support in theform of a JSPS Fellowship for Young Scientists DC1 (20J23124 and21J22818). A part of this work was supported by NIMS microstructuralcharacterisation platform as a programme of the ’NanotechnologyPlatform’ of the Ministry of Education, Culture, Sports, Science andTechnology (MEXT), Japan, Grant Numbers JPMXP09A19NM0110 (M.Y.).This work contains the result of using research equipment shared in theMEXT Project for promoting public utilisation of advanced researchinfrastructure (Programme for supporting the introduction of the newsharing system) Grant Number JPMXS0420900521.Author contributionsY.Y. andM.Y. designed research. Y.Y. and Y.S. prepared the samples andmeasured TG data. M.T., A.G., S.O. and Y.M. measured NMR data. Y.Y.,K.F., Y.S., S.KO., S.KA. and K.O. measured synchrotron XRD data. Y.Y.and T.I. performed the DFT calculations. Y.Y., K.F., Y.S., K.I. and T.O.collected the neutrondiffraction data. Y.Y. analysed the crystal structureand Raman data. Y.Y., M.T., K.F. and M.Y. wrote the original draft of themanuscript. M.Y. and Y.Y. edited the manuscript. M.Y. conceived theproject and supervised the research. All authors participated in the dataanalysis, discussed the results and read the manuscript.Competing interestsThe authors declare no competing interests.Additional informationSupplementary information The online version containssupplementary material available athttps://doi.org/10.1038/s41467-023-37802-4.Correspondence and requests for materials should be addressed toMasatomo Yashima.Peer review information Nature Communications thanks AbbieMclaughlin, Mohamed Haouas and the other, anonymous, reviewer(s)for their contribution to the peer review of this work. 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To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.© The Author(s) 2023Article https://doi.org/10.1038/s41467-023-37802-4Nature Communications |         (2023) 14:2337 10http://creativecommons.org/licenses/by/4.0/http://creativecommons.org/licenses/by/4.0/ Hidden chemical order in disordered Ba7Nb4MoO20 revealed by resonant X-ray diffraction and solid-state NMR Results Direct experimental evidence for Mo order at M2�site by NMR Quantitative determination of the occupancy factors of Mo and Nb atoms by resonant X-ray diffraction Complete crystal structure of Ba7Nb4MoO20·0.15 H2O Discussion Methods Synthesis and characterisation Synchrotron X-ray and neutron diffraction experiments and data analysis Solid-state NMR experiments Density functional theory (DFT)-based calculations Data availability References Acknowledgements Author contributions Competing interests Additional information