(Na,□)5[MnO2]13 nanorods: a new tunnel structure for electrode materials determined ab initio and refined through a combination of electron and synchrotron diffraction data

Octahedral molecular sieves (OMS) attract increasing interest in the search for novel electrode materials for energy storage and water desalination. While a nanometric particle size is desirable for such applications, this makes ordinary single-crystal characterization difficult and many OMS structures are still waiting for elucidation. Here we present the long awaited structure of a well known material, (Na,□)5[MnO2]13, resolved by a combination of electron diffraction tomography, dynamical scattering theory and X-ray powder Rietveld refinement. A new type of tunnel structure was found, able to explain previously reported electrochemical properties. This structure also suggests a possible mechanism for topotactic transformations between different manganese oxide OMS frameworks.


Introduction
(Na,&) 5 [MnO 2 ] 13 belongs to an emergent group of compounds which is now usually referred to as octahedral molecular sieves (OMS; Suib, 2008), in allusion to their open framework structures resembling zeolite molecular sieves, the well known tetrahedral counterpart. Zeolites are widely used in chemical processes (ion exchange, shape selective catalysis, semipermeable membranes etc.; Breck, 1974;Gorgojo et al., 2008) and their unique properties can be explained in terms of crystal structure: there are presently 231 different framework topologies (cf. http://www.iza-online.org) and efforts are ongoing to find new frameworks and applications (Cundy & Cox, 2003;Camblor & Hong, 2010;Bellussi et al., 2012).
The most promising features which distinguish OMS frameworks are with regard to their electronic properties. While zeolite frameworks are typically electronic insulators, the octahedrally coordinated elements in OMS structures (mostly transition elements from Ti to Co and their homologs) have easily accessible 3d (4d, 5d) orbitals and many different oxidation states may occur.
The title compound (Na,&) 5 [MnO 2 ] 13 (Tsuda et al., 2003;Hu & Doeff, 2004;La Mantia et al., 2011;Liu et al., 2011), along with other binary or ternary manganese oxides (Doeff, 1996;Wei et al., 2011;Lee et al., 2014;Yabuuchi & Komaba, 2014;Wang et al., 2015;Fang et al., 2016), have recently attracted much interest for their use as electrodes in batteries or in supercapacitors for energy storage or capacitive water desalination, but its properties were so far little understood. Since its first synthesis by Parant et al. (1971), (Na,&) 5 [MnO 2 ] 13 has been assumed to be based on the romanè chite framework, & 2 [MnO 2 ] 5 , which exhibits large rectangular 2 Â 3 tunnels confined by walls of double and triple octahedral chains (for an exhaustive presentation of these tunnel structures see Pasero, 2005). In this structure, there is only one crystallographically distinct site for the channel cations, but electrochemical results (Tsuda et al., 2003;Hu & Doeff, 2004;Liu et al., 2011) clearly show 3-4 peaks and plateaus for cation insertion-desorption during charge-discharge and cyclic voltammetry experiments, difficult to reconcile with the expected behaviour of a romanè chite framework. Parant et al. (1971) already mentioned that several lines in the diffraction pattern of (Na,&) 5 [MnO 2 ] 13 were incompatible with the side centring of the romanè chite unit cell found by Wadsley (1953). Later, Hu & Doeff (2004) mention that they were unable to simulate the observed diffraction pattern using the monoclinic unit-cell parameters of Parant et al. (1971) and the romanè chite atom parameters of Turner & Post (1988).
We found (Na,&) 5 [MnO 2 ] 13 in a more general study about the formation of Na x MnO 2 compounds and, as usual with OMS materials, we invariably obtained fine-grained powders made up of needles of < 4 mm in length and 30-60 nm in thickness. While a high degree of dispersion is desirable for most applications, this precludes ordinary single-crystal work to establish the crystal structure. In addition, impurity phases are generally present and make work with these powders difficult.
In the present study, we could overcome this problem using the recently developed (Kolb et al., 2007 electron diffraction tomography (EDT) technique which allows the collection of quasi-kinematical three-dimensional electron diffraction data sets on crystals of a few hundreds of nanometres or smaller. The technique has been used successfully for solving the structure of a variety of nanocrystalline materials (Mugnaioli & Kolb, 2013;Mugnaioli, 2015). Here, EDT data collected on selected single needles allowed us to conduct a single-crystal ab initio structure determination and, in a second step, to undertake a full parameter refinement based on the dynamical theory of diffraction using the methodology recently established by Palatinus et al. (2013 and . The model yielded by EDT was independently refined using the Rietveld method based on synchrotron radiation (SR) data, allowing us to establish the chemical formula (Na x & 1 À x ) 5 [MnO 2 ] 13 , x = 0.80, along with a refined model about Mn 3+ -Mn 4+ order and the distribution of Na in the channels.
In the last section of this study, the electrochemical properties of (Na,&) 5 [MnO 2 ] 13 are extensively discussed on the basis of the new structure and compared with other tunnel structures (including romanè chite proper), in the perspective of the development of novel OMS materials.

Experimental methods
(Na,&) 5 [MnO 2 ] 13 was prepared in a two-step procedure similar to that used by Lan et al. (2011) for the synthesis of manjiroite (Na-hollandite). A solution of 0.8 g NaOH in $ 20 ml deionized and freshly boiled water is added slowly, using a magnetic stirrer, to a solution of 1.97 g of MnCl 2 Á4H 2 O in $ 30 ml of deionized water. The brown precipitate is filtered and washed with deionized water until the effluent reaches pH = 7 and subsequently dried at 363 K for 24 h. For the second step, a small quantity (0.1-0.2 g) of the dry powder is mixed with 4 g NaNO 3 and heated in a porcelain crucible at 778 K for 24 h. The product of this reaction, mainly (Na,&) 5 [MnO 2 ] 13 , is a dark brown powder ( Fig. 1) which was isolated from NaNO 3 through washing with water and filtration. Reagents were MnCl 2 Á4H 2 O (Panreac, PRS), NaOH (Baker Analyzed) and NaNO 3 (Merck Suprapur).
Elemental composition was determined from energydispersive X-ray (EDX) spectra obtained on a Philips XL30 scanning electron microscope (SEM) at 20 kV acceleration voltage, averaging data taken from three different homogeneous areas of $ 10 Â 10 mm 2 , and on an EDS-ISIS Oxford spectrometer mounted on a Jeol 2010 TEM working at 200 kV, averaging data taken from nine areas on four different single rods.
Electron diffraction data collection was carried out using the EDT method (Kolb et al., 2007. In EDT a series of patterns is collected while the crystal is tilted in steps around the goniometer axis. The reciprocal space falling between the recorded orientations is integrated by collecting the patterns  The product obtained at 778 K/24 h. (a) Sample as prepared in a silicon holder for Bragg-Brentano X-ray diffraction (11 Â 17 mm). (b) SEM microphotograph showing needles of (Na,&) 5 [MnO 2 ] 13 and some flakes of Na 2 Mn 3 O 7 /birnessite. in precession mode, i.e. the electron beam is precessed on a cone surface with the vertex fixed on the sample (Vincent & Midgley, 1994). The collected patterns are used to obtain a three-dimensional reconstruction of the investigated angular range of reciprocal space from which the unit-cell parameters and the extinction group can be derived. The combined effect of collecting patterns in random orientations and integrating the diffracted intensities over the excitation error makes the intensities extracted for these data sets close to the kinematical approximation and therefore suitable for structure solution (Mugnaioli et al., 2009).
EDT data were collected on a Zeiss Libra 120 operating at 120 kV. The microscope is equipped with an in-column omega filter for energy-filtered imaging and a Nanomegas Digistar P1000 for precession electron diffraction. Data collection was performed by tilting the sample around the goniometer axis in an angular range of 110 (from À50 to +60 ) in steps of 1 , and with a precession semiangle of 1 . The EDT patterns were energy filtered with a slit of 20 eV centred around the zero loss peak. It has been demonstrated that energy filtering is generally not strictly necessary for structure solution and refinement (Gemmi & Oleynikov, 2013;, but the patterns collected in this way show sharper peaks and a lower inelastic background. The intensities were integrated using the PETS software (Palatinus, 2011). Ab initio structure determination was performed both by the direct methods implemented in SIR2011 (Burla et al., 2012) and by charge flipping implemented in the SUPERFLIP software (Palatinus & Chapuis, 2007) embedded in JANA2006 (Petříček et al., 2014). Refinement was performed both in a standard kinematical approach using SHELX (Sheldrick, 2008) and in the recently proposed dynamical approach of Palatinus et al. (2013),  and  included in JANA2006. For the dynamical refinement only 1 pattern out of 111 was excluded from the final calculation where the following parameters were used: g max = 2 Å À1 , S max g (matrix) = 0.01 Å À1 , S max g (refine) = 0.1 Å À1 , R max S g = 0.75, N steps = 128. No geometrical restraint was imposed.
Laboratory X-ray diffraction patterns were obtained using a Panalytical X'pert powder diffractometer with Bragg-Brentano geometry, Ni-filtered Cu K radiation ( = 1.5405981 and 1.5444183 Å ) and an X'Celerator linear position sensitive detector (more details in x1.1 and x2.1 of the supporting information).
A synchrotron X-ray diffraction pattern was obtained at the ID09 beamline at ESRF (Grenoble, France), using the standard beamline setup (Merlini & Hanfland, 2013), monochromatic radiation of = 0.415352 Å , glass capillary of 0.2 mm in diameter, beam diameter 0.8 mm, flat panel MAR555 detector at a distance of 300 mm, pixel size 139 Â 139 mm. The X-ray powder pattern was collected during a full rotation of the sample and the two-dimensional powder rings were integrated into a conventional one-dimensional powder pattern using the FIT2D software (Hammersley, 1997), taking into account the geometrical and intensity corrections needed. High-quality diffraction data were obtained in the range 2 = 1.309 to 32.245 , step size 0.012 , corresponding to a resolution of d = 18.2 to 0.748 Å . The GSAS program system (Larson & Von Dreele, 2004 for Linux) combined with the EXPGUI graphical interface (Toby, 2001) was used for Rietveld refinement least-squares calculations. The background was simulated using a 15-term (up to 36 for synchrotron data) Chebyshev function, a correction of the pattern origin was allowed for, and peak profiles were calculated using a pseudo-Voigt function (Thompson et al., 1987) providing for both instrument and material dependent parameters. The three instrument dependent profile parameters used (the Gaussian variances U, V and W of Caglioti et al., 1958) were found from independent refinements using standard materials (3 mm silicon powder) and held constant throughout all calculations (laboratory data) or constrained to be equal for all phases (W in SR data).

Synthesis and composition
The brown precipitate obtained after the first reaction of the two-step synthesis procedure, once dry, gives the diffraction pattern of hausmannite, a (possibly defective) spinel of composition Mn 3 O 4 (or Mn 2 O 3 = Mn 2.67 O 4 ), whose structure is tetragonally distorted due to a Jahn-Teller effect in the 3d 4 electron configuration of Mn 3+ . The occurrence of Mn 3+ indicates that, during the first reaction, manganese has been oxidized from 2 to 2.7 or 3.0. Subsequent calcination in NaNO 3 gives the final product (Na x & 1 À x ) 5 [MnO 2 ] 13 whose composition corresponds, with x = 0.80, to an average oxidation state of 3.69 for manganese, i.e. oxidation must also accompany the second reaction, possibly through decomposition of nitrate NO 3 À + e À ! NO 2 + O 2À . SEM images reveal that the sample consists of rods of < 4 mm in length and 30-60 nm in thickness ( Fig. 1). Chemical composition was first determined using SEM-EDX on the loose powder samples, giving the ratio Na/Mn = 0.5 (2), with a high standard deviation due to sample rugosity and impurities. Some points, corresponding to denser masses in the SEM image, gave higher Na contents and might reflect Na 2 Mn 3 O 7 / birnessite impurities. Birnessite was also detected in the powder diffraction pattern (Fig. S1), and it cannot be excluded that particles of this compound are dispersed in the whole product and unavoidably sampled by the SEM-EDX probe (10 mm in diameter).
TEM-EDX was used to obtain chemical information from single rods. The analysis gave a ratio of Na/Mn = 0.22 (2) for nine points on four different crystals. This is probably more accurate, but values may tend to fall short due to Na evaporation during the electron bombardment, which is more important in TEM. Such evaporation could be observed from the fact that, at the beginning of some analyses, the Na peak at 1041 eV grew more rapidly than afterwards. It was anyway not possible to precisely quantify this effect. The best estimate is therefore the intermediate taken from structure refinement [Na/Mn = 0.306 (14)].

Crystal structure model from single-crystal electron diffraction intensities
From EDT (Fig. 2), a C-centred monoclinic unit cell, a = 22.63 (12), b = 2.826 (14), c = 14.91 (7) Å , = 104.6 (5) , was unequivocally derived, the a, c and parameters being very different from those in the romanè chite cell (C2/m, a = 13.929, b = 2.8459, c = 9.678 Å , = 92.39 ; Turner & Post, 1988). The main direction of growth of the rods is always b. The diffraction symbol is 2/mC--leaving C12/m1, C121 and C1m1 as possible space groups. SUPERFLIP gave space group C2/m as first choice for the correct solution. In order to obtain a confirmation about this space group, we conducted a supplementary statistical analysis of intensities using the program suite DIFRASYM (Gregorkiewitz & Vezzalini, 1989). A value of pwys(h0l) = 0.900 suggests that -1/m-is either absent or most atoms lie on the reflection plane (which is actually the case), and the intensity distribution parameters (Ramachandran & Srinivasan, 1959) NYQ1(hkl) = 0.456 and NYQ1(h0l) = 0.699 comply with the presence of the centre 1 and the binary -2-, respectively (NYQ1 = 1.960 for acentric and 0.776 for centric distribution). We therefore choose C2/m to start with model search and parameter refinement. The internal error for averaging over Laue equivalent intensities is R sym = 0.135 and clearly within the mean error of all intensities R = AEI/AEI = 0.157 (Table S1).
In the structure solutions obtained both with SUPERFLIP and SIR2011 we recognized a preliminary model which contained all framework atoms (7 Mn and 13 O sites). In addition, as for other tunneled structures solved by EDT data (Rozhdestvenskaya et al., 2010), electron densities in the channels showed up in a difference Fourier map and were assigned, in this case, to different Na sites. In Fig. 3 we report the reconstructed electron density, given by the SUPERFLIP solution in which the framework topology is evident, and the difference Fourier map superimposed to the final structure model, where two main Na sites, one inside the S-shaped 10ring channel and the other in the 8-ring channel, are clearly visible along with some weaker residuals in the channels.

Structure refinement
The so-obtained structure was subsequently refined by the Rietveld method. The first trial, using laboratory X-ray powder diffraction data, confirmed the EDT overall model providing for improved unit-cell parameters, but convergence was achieved only after the Mn-O distances were restrained using the distance least squares (DLS) method (Meier & Villiger, 1969) and no improved structural parameters could be obtained, probably due to a problem with peak resolution (see xS4.1).
We therefore substituted the laboratory pattern with a synchrotron radiation (SR) powder diffraction pattern. Their detailed inspection (Fig. S1) shows that in the SR pattern the reflection width is reduced by a factor of $ 3 (the FWHM of reflection 602 passes from 0.14 to 0.042 2), but resolution in terms of (@(2)/@NR)/FWHM remains approximately the same due to the much shorter SR wavelength. However, the total number of peaks is halved (no 2 component), and a huge improvement of the signal-to-noise ratio can be seen, especially at high angles (Figs. S1 and 4).
With these improvements Rietveld refinement converged rapidly. For the final model, presented in Fig. 5 as well as in Table S2 and the CIF file in the supporting information, refinement included several parameters of the impurity phases birnessite (those specified in Table 1 plus eight atom parameters) and Na 2 Mn 3 O 7 (unit cell and Lorentzian broadening only). Attempts to refine anisotropic grain shape, microstrain (Stephens, 1999) and preferred orientation (ODF) were made and showed that these phenomena have little relevance. A final agreement of 2 = 0.690, R wp = 0.051, R p = 0.037, R F2 = 0.035 was reached (Table 1). With respect to the refinement using the laboratory X-ray pattern, the structural agreement for the (Na,&) 5 [MnO 2 ] 13 phase alone, R F2 = 0.036 instead of 0.10, has greatly improved. The model, corroborated by extensive significance tests in the final stage of refinement (see xS4.2 and S7.1), clearly shows that Na occupies all three channels while Mn-O distances in the framework, now free from restraints, diversify to comply with an ordered Mn 3+ -Mn 4+ distribution. These details are fundamental to the chemical behaviour and will be discussed later.
The excellent agreement between observed and calculated intensities can also be judged from the patterns in Fig. 4 where all discrepancies with |Y o À Y c |/Y > 3 lie in regions of important birnessite peaks, i.e. they are due to errors in the model used to describe the birnessite and not the (Na,&) 5 [MnO 2 ] 13 structure. Details about the modeling of birnessite are interesting in their own right and suggest (see xS4.2) that this typically hydrothermal phase, not expected in our salt melt synthesis, was derived from Na 2 Mn 3 O 7 , a layered structure which forms at high temperatures (Chang & Jansen, 1985;Raekelboom et al., 2001) and may then hydrate (Parant et al., 1971;Chen et al., 1996;Caballero et al., 2002;Nam et al., 2015), during the washing procedure when isolating the product from NaNO 3 . In order to further confirm the details of the structural model for   Table 1 Crystal data and overall parameters obtained from Rietveld refinement using SR data.
The title compound is (Na x & 1 À x ) 5 [MnO 2 ] 13 , x = 0.80 (4), space group C2/m, Z = 2; for refined atom parameters see Table S1. Atom parameters of impurities were taken from Post & Veblen (1990) for birnessite and Raekelboom et al. (2001) for Na 2 Mn 3 O 7 . Estimated standard deviations (in parentheses) refer to the last digits of the preceding value. Linear absorption coefficient for = 0.415352 Å calculated from Henke et al. (1993). NY, NR and NP give the number of observations, reflections and refined parameters, respectively.

Parameter
Global 0.035 0.036 0.018 0.043 undertook several refinements using single-crystal electron diffraction intensities. A comparison with the results from powder diffraction also gives the opportunity to check if the bulk structure corresponds to the model obtained from a single crystal a few hundred nanometres in size.
In a first approach, the raw model was input to a regular singlecrystal structure refinement through least squares and Fourier cycles using the kinematical approximation by the program SHELX97 (Sheldrick, 2008). Refinement was stable and converged rapidly, without imposing any geometrical restraint, to R1(F) = 0.263 (Table S1), but the framework geometry still showed some dispersion (cf. Table S4) and, among the three sites for Na, only the two in the 10-and the 8-ring channels were resolved.
In a second trial, refinement was continued using the recently developed method based on dynamical diffraction theory (Palatinus et al., 2013;. Convergence was now reached at a residual of R(F) = 0.07 (0.24) for observed (all) intensities, and the resulting model (Table S2 and the CIF file in the supporting information) contains all atoms, including individual atomic displacement parameters, and atom parameters are near to those obtained from Rietveld refinement. These results are remarkably reliable for a structure derived from electron diffraction intensities, especially when compared with the model derived by kinematical theory. Details about structural features and related uncertainties will be discussed later.  Table 2 Interatomic distances (Å ) for (Na x & 1 À x ) 5 [MnO 2 ] 13 , x = 0.80 (4) as obtained from Rietveld refinement using SR data (the corresponding values obtained from dynamical refinement can be found in Table S3).

Figure 5
Crystal structure of (Na In addition, a pronounced Jahn-Teller distortion, expected for high-spin 3d 4 electron configuration, can be recognized for both Mn4 and Mn7. In Mn4, the longer distances are found on the O6-Mn-O8 axis (2.150 and 2.037 Å , in the ca plane) defining the filled e g orbital, and Mn7 lies far away from the vertex [d(Mn7-O3) = 2.172 Å ], practically on the basis of the square pyramid (2 O5 + 2 O12). According to the model refined on the basis of EDT data and dynamical theory, Mn2 also presents a (less pronounced) Jahn-Teller distortion, that was not evident in the PXRD Rietveld refined model (Tables 2  and S3).
In order to establish the CN of sodium, distances were calculated up to 4 Å and a clear gap between the first [d(Na-O) < 2.9 Å ] and the second [d(Na-O) > 3.1 Å ] coordination shell was found. Distances in the first shell are reported in Table 2 and give the canonical coordination environment of sodium with CN = 7, 8 and 6 for Na1, Na2 and Na3, respectively. For the dynamics of the structure it is important to realise that Na1 and Na2 stay in a trigonal prism with one (Na1) or two (Na2) more oxygen ligands on their faces, which provides reasonable electrostatic shielding. Na3, on the other hand, stays at the centre of a trigonal antiprism, extremely flattened along b, which lacks shielding along the tunnel axis. The alternative Na3 position at y = 0, mentioned in the results section xS4.2, has CN = 9 with highly dispersed Na-O distances ranging from 2.07 to 2.85 Å , i.e. neither of the two positions provides a suitable environment for Na + and it is possible that, as a consequence, Na3 may move more easily along the channel.

A new framework: tunnels and possible transformations
The framework of (Na,&) 5 [MnO 2 ] 13 (Fig. 5) is very different from that of romanè chite {2 Â 3 tunnel structure, chemical formula (Ba,H 2 O) 2 [MnO 2 ] 5 } and resembles the one first found by Mumme (1968) for Na 4 [Mn 4 Ti 5 O 18 ] and later refined (Richardson et al., 1998;Akimoto et al., 2011;Chu et al., 2011;Kruk et al., 2011) for Na 3.6-4.5 Mn 9 O 18 = Na 0.4-0.5 [MnO 2 ]. In both structures there are tunnels, running along the short (2.8 Å ) axis, which are defined by walls of double and triple chains of octahedra, occasionally replaced by a single chain made up of square pyramid Mn V O 5 polyhedra. The most visible difference among the two frameworks is that the Mumme (1968) structure is reminiscent of ramsdellite with its 1 Â 2 tunnels, while our compound recalls the 2 Â 2 tunnels of hollandite.
The existence of such disproportionations suggests possible pathways in the synthesis of OMS frameworks. Solid-state transformations from a birnessite layer structure to one of the different tunnel structures are presently much discussed (Drits et al., 1997;Lanson et al., 2002;Li & Wu, 2009;Grangeon et al., 2014 Detail of the crystal structure of (Na,&) 5 [MnO 2 ] 13 , showing the possible topotactic transition of an Sshaped tunnel (a) to a 2 Â 3 romanè chite tunnel (b). Oxidation of the framework NaMn 3+ ! &Mn 4+ induces the nucleophilic attack of O13 at Mn7. nè chite tunnel (Fig. 6). Independent support for such speculations comes from a recent DFT study on alkali hollandites (Tompsett & Islam, 2013), where a progressive increase of the in-plane Mn-O distances was seen to accompany reduction. The coupling between redox and topotactic transformation mechanisms is important not only for synthesis but also for electrochemical applications of manganese oxide materials. Much of the limits in x for the (de)intercalation reaction [MnO 2 ] + xM + + xe À $ M x [MnO 2 ] are indeed due to structural transformations that compromise reversibility (see e.g. the discussion of deep discharge in Hu & Doeff, 2004).

Chemical formula and preferred compositions
(Na,&) 5 [MnO 2 ] 13 has three different channels which are only partially filled with Na, evidently also a consequence of the relatively short period along b = 2.84 Å which implies strong repulsive Na + -Na + interactions in the Na chains along b (comparatively, the lateral distance between the adjacent Na1 chains in the S-shaped tunnel is 3.94 Å ). From structure refinement, we find an average degree of filling of 0.8 in all Na chains and, in principle, there might be some multiple or incommensurate period to accommodate sodium in an orderly way. However, inspection of overexposed electron diffraction patterns showed only a very weak diffuseness along 10 " 1 1 and no satellite peaks, suggesting an essentially statistical Na distribution. Dynamical refinement on the basis of EDT data allowed anisotropic displacement parameters to be introduced for all metal atoms except Na3 and it turned out that Na atoms have a relatively larger U 22 component compared with Mn atoms. This supports the idea of a certain disordered distribution of cations along the channels (see Table S2).
The actual number of Na per unit cell is 8, even if there is place for 10 Na (see Table S2). The exact match of 8 Na with 2 Â 4 = 8 Mn 3+ positions suggests that charging of the framework, e.g. in a redox reaction during synthesis or in electrochemical cycling, is not a fully statistical process but follows a stepwise reduction of different Mn sites, so we expect pronounced voltage/composition plateaus.
The highest charge, corresponding to a load of 10 Na per unit cell, corresponds to the ratio Na/Mn = 10/26 = 0.385, near to the composition Na 0.40 [MnO 2 ] first suggested by Parant et al. (1971). There are few analytical data. Tsuda et al. (2003) give Na/Mn = 0.31 for a product calcined at 873 K in air, exactly the same value as found for our material, and (Li + Na)/Mn = 0.38 for an ion-exchanged derivative (LiNO 3 , 623 K, under Ar). Hu & Doeff (2004) found instead Na/Mn = 0.41 for calcination at 873 K in the presence of an organic reducing agent, and (Li + Na)/Mn = 0.33 and 0.40 for the ionexchanged derivatives (LiBr in EtOH, 353 K, air, and LiNO 3 / LiNO 2 , 473 K, air, respectively). It would be interesting to check the structure of these materials: if the framework of (Na,&) 5 [MnO 2 ] 13 is conserved, as the published X-ray diffraction patterns suggest, we might have a transition between structures with x = 0.80 and x = 1.00 as predicted from our chemical formula. Correspondingly, a further 2 Mn per unit cell must undergo reduction to Mn 3+ , possibly at Mn2 which has the longest mean Mn-O distance [d(Mn-O) ! 1.94 Å , Table 2] after Mn4 and Mn7, but a rearrangement of charges cannot be excluded.
Regarding the lowest sodium content, both Tsuda et al. (2003) and Hu & Doeff (2004) conclude, from electrochemical measurements, that higher oxidation states of the framework (down to x = 0.07) should also exist. Our results suggest that each oxidation state should comply with an ordered Mn 3+ -Mn 4+ distribution, i.e. we expect a preference for x = 0, 0.15, 0.31 and 0.39, in excellent agreement with the results from chemical analysis and electrochemical measurements.
Interestingly, and in contrast with our material, the Mumme (1968) framework cannot be fully oxidized and always retains Mn 3+ in the square pyramid (Mn4 site, see xS6.1). This may be a consequence of the different environments of the square pyramids: on oxidation, in our case the square pyramid can easily convert to an octahedron through incorporation of O13 (Fig. 6), whereas in the Mumme (1968) framework (cf. Fig. 1 in Doeff et al., 2004) there are no 'under-shared' O atoms (like O13 in Fig. 6) at reach and a similar mechanism would be hard to explain. This reduces the theoretical capacity from 182 mAh g À1 to (8/12) Â 182 = 121 mAh g À1 , coming near to the capacity of (Na,&) 5 [MnO 2 ] 13 which is 108 mAh g À1 (calculated from structure) and $ 90 mAh g À1 (measured from electrochemical cycling; Tsuda et al., 2003;Hu & Doeff, 2004).

Contrasting with the romanèchite framework
Knowledge about synthetic materials with the 'true' romanè chite framework (2 Â 3 tunnels, right part of Fig. 6) is limited. Tsuda et al. (2001) synthesized (453 K, autogenous pressure) an analog to the natural material, with composition Ba 0.18 MnO 2.10 Á0.42H 2 O, and studied its performance as a positive electrode in a Li cell. The charge-discharge curves from 2 to 4 V are almost featureless, without the intermediate plateaus observed by the same authors (Tsuda et al., 2003) for (Na,&) 5 [MnO 2 ] 13 . The corresponding material is actually a mixture between barian and lithian compositions and interpretations must be done with caution, but in principle the romanè chite structure (M,H 2 O) 2 [MnO 2 ] 5 possesses only one crystallographically distinct site for the tunnel cation M or water and would be in agreement with a monotonous chargedischarge curve.
Later, Shen et al. (2004) reported the synthesis of a sodian romanè chite with composition (Na 0.24 (H 2 O) 0.16 )-[MnO 2 ]Á0.55H 2 O. Again, the material was obtained from hydrothermal synthesis ($ 493 K, autoclave), and from thermal analysis it was concluded that water occupies part of the tunnel sites where it has also been found for the mineral (Wadsley, 1953;Turner & Post, 1988).
The structural identity of the above two materials was inferred (Tsuda et al., 2001;Shen et al., 2004) from their powder X-ray diffraction patterns which resemble the reference pattern for natural romanè chite (PDF Powder Diffraction File, Card #14-627, JCPDS -International Centre for Diffraction Data 1 , 12 Campus Blvd, Newtown Square, PA research papers 19073-3273 USA, 199719073-3273 USA, -2015. Neither of the two patterns has been indexed, but for the sodian material, the typical unit-cell dimensions of romanè chite were confirmed from high-resolution transmission electron micrographs. Also, the pattern of the sodian material ( Fig. 1 in Shen et al., 2004) grossly differs from our pattern (Fig. S1), especially for the all important lowangle peaks. A romanè chite proper material therefore appears to be well distinguished from our (Na,&)

Reliability of results from EDT single-crystal and X-ray powder diffraction
The structure of (Na,&) 5 [MnO 2 ] 13 was finally revealed combining EDT based ab initio structure model determination and Rietveld PXRD structure refinement. As excellently pointed out by McCusker & Baerlocher (2009), electron diffraction and PXRD are rather complementary methods, whose combination may be extremely powerful for the structure investigation of nanocrystalline materials. Crucial steps forward for electron diffraction derived from the development of beam precession (Vincent & Midgley, 1994) and tomographic methods for data collection and analysis (Kolb et al., 2007;Mugnaioli et al., 2009;Zhang et al., 2010) which made it possible to acquire more complete and more kinematical electron diffraction data sets, are able alone to deliver ab initio a first structure model that can be subsequently refined by Rietveld methods. This strategy has proved successful for the characterization of tetrahedral molecular sieves (Jiang et al., 2011;Bellussi et al., 2012;Martínez-Franco et al., 2013).
In the present case, we were also able to perform a singlecrystal refinement on the basis of EDT intensities using the dynamical refinement method recently developed by Palatinus et al. (2013;. This is one of the first cases where this new approach was applied for the refinement of an unknown structure, giving us the opportunity to compare between results obtained from different data and methods (details in xS7.1).
Atom positions obtained ab initio (by a kinematical approach) on the basis of EDT data already embodied a reasonably correct model for the MnO 2 octahedral framework of (Na,&) 5 [MnO 2 ] 13 , despite the structure residual of about R1(F) = 0.263 (Table S1). Mn and O atom positions could be straightforwardly assigned and were stable after least-squares refinement without imposing any restraint or constraint. Most of the Na positions could be deduced from the difference Fourier map, even if their occupancy and displacement factor could not be refined.
Rietveld refinement using laboratory X-ray powder data served, in our case, for a first improvement of the unit cell (where EDT gives uncertainties on the order of 0.5%) and to check the correctness of the EDT model which, after introducing DLS restraints to avoid correlations, refined to a theory-biased rough model (R F2 = 0.10) where Mn-O distances scatter tightly around the imposed mean [hMnOi = 1.89 (2) Å ].
SR powder data, beyond a further improvement of the unitcell parameters (uncertainties are now less than 5 Â 10 À5 , Table 1), allowed unrestrained Rietveld refinement and gave details like the ordered Mn 3+ -Mn 4+ distribution and the Na3 site occupation factor which was important to fit the intensities of the low-angle peaks (see Fig. 4).
EDT data combined with dynamical scattering refinement essentially confirm the model obtained from SR data. By using the Bilbao Crystallographic Server (Tasci et al., 2012), the average (maximum) discrepancies between the two coordinate sets were found to be 8 (21) pm for all and 3 (5) pm for the Mn atoms. This is $ 5 (10) times the uncertainty estimated from least-squares calculations with SR(EDT) data, and $ 4 times the discrepancies reported in test runs for dynamical scattering refinements . For future work it will be interesting to explore the significance of these discrepancies.
Here we are mainly concerned with the structural results, and their detailed inspection (xS7.1) shows that differences do not affect the interpretations put forward in the preceding sections, i.e. the similarity of two independent results can be taken as an additional warranty of their correctness. One discrepancy which should be highlighted regards the Mn2 octahedron. While both SR data Rietveld refinement and EDT dynamical refinement give very much the same mean hMn-Oi distances [1.94 (8) and 1.94 (5) Å , respectively], complying with some Mn 3+ substitution, only the latter shows clearly the expected Jahn-Teller distortion with the long axis (O2-Mn2-O4) in the ca plane.
Finally, we point out that EDT dynamical refinement allowed to refine all structure parameters without any constraint, including displacement parameters for all atoms, up to very reasonable values. For all Mn and two out of three Na atoms it was also possible to refine anisotropic displacement parameters, showing that for all Mn atoms U 22 is systematically smaller than U 11 and U 33 and that, conversely, for at least one Na atom U 22 (parallel to the channel direction) is larger.

Conclusions
(Na x & 1 À x ) 5 [MnO 2 ] 13 was synthesized using a new and facile procedure which yielded nanorods with the Na load x = 0.80. The long-awaited crystal structure of this material has been resolved and shows a novel OMS framework containing three distinct types of tunnel, which differs radically from the previously assumed romanè chite framework containing only one type of tunnel. A particularly interesting detail of the new framework is the existence of MnO 5 square pyramids which, on oxidation from Mn 3+ to Mn 4+ , may act as centres for nucleophilic attack from a nearby under-shared oxygen. This mechanism is likely to play a fundamental role for both synthesis and electrochemical behaviour of manganese-based OMS structures.
The elucidation of this particular and quite complex structure has become possible through EDT-based ab initio model determination combined with SR powder diffraction based Rietveld refinement. The procedure was straightforward and led rapidly to a model whose precision (positional errors < 1.5 pm) can be compared with ordinary single-crystal refinement except for atomic displacement parameters. This opens new opportunities for the development of OMS materials where progress is often difficult due to their cryptocrystalline and polyphasic nature.
As a novelty for an unknown structure, a single-crystal refinement based on EDT data and dynamical scattering theory has been performed and it could be shown that results compete in precision with those obtained from SR data and can be taken to confirm the reliability of the final model.