On the Arrangement of Pentagonal Columns in Tetragonal Tungsten Bronze-Type Nb 18 W 16 O 93

: The evaluation of HAADF-STEM images of a sample with the composition Nb 18 W 16 O 93 provided new insights in its real structure. The basic structure comprises an intact octahedral framework of the tetragonal tungsten bronze (TTB) type. The partial occupation of the pentagonal tunnels (PT) by metal-oxygen strings determines the oxygen to metal ratio (O/  M with M = Nb,W). For a large area, the O/  M was determined to be 2.755 which is smaller than the value of Nb 18 W 16 O 93 which is O/  M = 2. 735. To a large extent, the threefold TTB superstructure structure of Nb 8 W 9 O 47 with a high oxygen content is present (O/  M = 2.765). In addition, a new fourfold TTB superstructure was found in small domains: Nb 12 W 11 O 63 with an O/  M = 2.739 obviously accommodates a part of the sample’s metal excess compared to the stable phase Nb 8 W 9 O 47 .


Introduction
At present, there is a broad interest in niobium tungsten oxides since they have application potential as high-performance anode materials in lithium ion batteries. The recent world-wide research activities have been induced in 2018 by a report of extremely fast reversible Li exchange and high cycling stability for the block-type phase Nb16W5O55 and for a sample with the composition Nb18W16O93, the structure of which was found to be based on the tetragonal tungsten bronze (TTB) type [1]. This structure type comprises corner-sharing octahedra MO6 that are arranged in such a way that trigonal, square, and pentagonal tunnels arise (Figure 1, bottom left). In the structure of Nb8W9O47, one third of the pentagonal tunnels (PTs) are systematically occupied by metal-oxygen (MO) strings resulting in a threefold superstructure of the TTB type (Figure 1, top). The metal inside the PT has got a pentagonal bi-pyramidal coordination by oxygen. The unit comprising this polyhedron and the five equatorially connected octahedra is designated a pentagonal column (PC) [2]. Two of such PCs are grouped to pairs by sharing a square of octahedra (so-called diamond link [2]). Four orientations of these PC pairs are possible in the TTB framework, and at a time two of them occur in each of the two unit cell orientations of the Nb8W9O47 structure ( Figure 1). The threefold TTB superstructure realized in Nb8W9O47 exhibits a high thermodynamic stability, apparently because the interactions between the MO strings inside the TTB substructure are optimized in this arrangement. Iijima and Allpress postulated rules for a stable dense packing of PCs [3]: (i) PTs directly adjacent to a PC (dPC-PT  0.6 -0.65 nm) remain empty; (ii) one of the two PTs with the next-nearest distance to a PC (dPC-PT  0.9 nm) is occupied forming a pair of diamond-linked PCs. These rules are strictly obeyed in the structure of Nb8W9O47. Any deviation from the composition M17O47 (M = Nb,W) therefore leads to a less ordered real structure. An occupation of directly adjacent PTs, which breaches the first rule, has rarely been observed in TTB-type niobium tungsten oxides up to now. In contrast, the second rule is strictly valid for the composition M17O47 only and chains of diamond-linked PCs have frequently been observed in W-richer structural variants like Nb6W8O39 (Figure 1) [4]. Already in 1979, Li-containing phases LixNb8W9O47 with x = 2 and 4 could be synthesized by the reaction of LiNbO3 and WO3 [5]. In 1998, the insertion of Li into Nb8W9O47 by both electrochemical and chemical reactions could be achieved [6]. A reversible electrochemical uptake of up to 20 Li ions per formula unit was reported for Nb8W9O47 and for the not fully oxidized members of the solid solution series Nb8-xW9+xO47 (1≤x≤ 6) [7]. As already mentioned above, the electrochemical investigations on TTB-type NbW oxides gained momentum after the study on Nb18W16O93 had been published by Griffith et al. in 2018 [1]. Several follow-up investigations confirmed the outstanding electrochemical performance of samples with this composition [8][9][10][11][12][13]. An orthorhombic structure Nb18W16O93 was proposed by Stephenson in 1968 to explain split reflections observed in higher order Laue zones of a twinned crystal with the composition Nb12W11O63 (6Nb2O5:11WO3) [14]. For this composition, congruent melting was found in the course of the exploration of the phase diagram Nb2O5/WO3 by Roth and Waring [15]. The structure of the hypothetical Nb18W16O93 could never been confirmed, neither by single crystal X-ray diffraction nor by transmission electron microscopy studies [3,16,17]. As both the structural model of Nb18W16O93 and the well-established phase Nb8W9O47 are described by a threefold TTB superstructure with similar symmetry and practically the same unit cell metric, the differentiation of the two structures by powder XRD is difficult but possible if a comparative Rietveld refinement is performed [18]. The difference between these structures is the occupation of PTs in the TTB host lattice, and thus the appropriate characterization method is to image the metal positions in the ab plane by high-resolution transmission electron microscopy (HRTEM) [3,19] or by high-angle annular dark field scanning transmission electron microscopy (HAADF-STEM) [20][21][22]. The conclusions drawn from the analysis of HAADF-STEM images of a sample Nb18W16O93 are reported here.

Synthesis
The sample with composition Nb18W16O93 was prepared by the solid state reaction of Nb2O5 and WO3 powers (molar ratio Nb2O5:WO3 = 9:16). After grinding the powders in an agate mortar, the resulting mixture was pressed into pellets and then annealed in a Pt crucible covered with a Pt lid at 700 °C for 12 h followed by 1200 °C for 12 h. For details, see [12].

Electron Microscopy
Scanning transmission electron microscopy images were recorded on a JEM-ARM300F (JEOL) using a high-angle annular dark field detector (HAADF-STEM), as described elsewhere [12].  Figures 2b,c). In this structure, they are oriented nearly perpendicular in respect to each other so that two regularly arranged PCs are directly adjacent to each other (red arrows in Figure 2d). While this close distance breaks the first rule proposed for a stable PC arrangement, it enables a denser PC packing and thus a decrease of the oxygen/metal ratio O/M (M = Nb,W). A fourfold TTB supercell with a = b = aTTB, c = cTTB describes this structure (Figures 2d). The metric of this cell is approximately tetragonal, but the peculiar PC arrangement decreases its symmetry to orthorhombic. In this cell, six of the sixteen PTs are occupied according to (MO)6(M10O30)4 or normalized to a single TTB unit (MO)1.5(M10O30). Thus, the number of PCs is higher than in Nb8W9O47 corresponding to (MO)1.33(M10O30), which moreover leads to a decreased ratio O/M: 2.739 vs. 2.765. The general formula (MO)6(M10O30)4 corresponds to a composition Nb12W11O63, which is that of the so-called 6:11 phase (6Nb2O5:11WO3) [15]. Interestingly, the structural model contains TTB cells in which all four PTs are empty as indicated by red frames in Figure 2d, an array that does not occur in the Nb8W9O47 structure. These empty TTB units and such in which two PTs are occupied (blue PC pairs) are alternatingly arranged in the structural model of Nb12W11O63 (Figure 2d). The domains of Nb8W9O47 and Nb12W11O63 are intimately intergrown with each other by sharing a slab of PC pairs (yellow in Figure 2c) that run along the crystallographic a axis of Nb8W9O47. The domain of the new structure is terminated on the left side by a defective area which contains the blue PC pairs as a slab in perpendicular orientation.

HAADF
A larger area which contains mainly the Nb8W9O47 structure is shown in Figure 3. Two distinct defects that are typical for this structure occur, namely an out-of-phase boundary on the lower left side and rotational twinning by 90° on the right side. The threefold TTB superstructure is perfectly ordered on the upper left side (Figure 3a). The inclusion of a row of five PC pairs with perpendicular orientation (blue) causes a shift of the adjacent domains of Nb8W9O47 by 1/3 b (= bTTB) in respect to each other (Figure 3b,c). In the lower part of the boundary, the structure is semiregular: the slabs of yellow PC pairs in the two domains are connected via a chain of four diamond-linked PCs with each slab contributing two PCs. The slabs with green PC pairs are not connected. Instead, they are directly neighbored to an isolated yellow PC. This structure is depicted in the lower left side of Figure 4a. Four-membered PC chains had been observed before, e. g. in zigzag out-of-phase and twin boundaries in Nb8W9O47 [3] and as a regular structural element in Nb6W8O39 (Figure 1) [4]. At the top of this boundary, the occupation of PTs is less regular and includes a three-membered PC chain, in which die middle PC belongs to two perpendicularly oriented slabs of PC pairs (blue and green). Here, a small block of six PCs with perpendicular orientation (90° rotation twin) is incorporated (light blue area). Interestingly, this block connects two slabs of green PC pairs, and the two PCs at the top and at the bottom can be regarded as a part of the small section of 3 PC pairs (light blue area) as well as a part of the connected slabs of green PCs.
Another example for such rotational twinning appears on the right side of Figure 3 with the corresponding structural model shown in Figure 4b. In the upper part, slabs of blue and magenta PC pairs are connected to perpendicularly oriented slabs of green and yellow PC pairs. The arrangement there is frequently observed at boundaries between rotational twin domains: the central PC of a triple PC chain belongs to the two perpendicular PCs slabs. This is also the case of the isolated PC that is quasi the extension of the not directly connected PC rows. This frequently appearing array is marked by dotted lines for the two just described units in Figure 4b (top center). It should be mentioned that such a connection of 90° rotational twin domains by three-membered PC chains was already observed in the first HRTEM investigation of this material in 1974 [3]. Like here, empty TTB cell and directly adjacent simultaneously occupied PTs were found then.  Figure 4. The magnified area (inset in (a)) demonstrates the varying dot intensities with white arrows pointing to W-rich and yellow ones to Nb-rich positions, respectively.
As the HAADF-STEM method generates images with the intensity I increasing with the atomic number Z (I ~ Z 2 ; Z contrast imaging [23]), the metal positions appear as bright dots with their brightness increasing with the W content of the particular atomic column (ZW = 74 > ZNb = 41) [19,21]. Thus, the observation of the relative brightness of the individual atomic columns provides some information about the distribution of the metals (inset in Figure 3a). The relative darkness of the metal position inside the PTs indicates that is preferentially occupied by Nb as it is also the case in W-richer samples [21]. Thus, the Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 12 November 2021 doi:10.20944/preprints202111.0234.v1 preference of Nb for this position as it was found during the structure determination of Nb8W9O47 from single-crystal X-ray diffraction data [18,24] has been preserved. This is also the case for a W-rich position that appears with high brightness (inset in Figure 3a).

Discussion
According to the evaluation of HAADF-STEM images, the sample Nb18W16O93 comprises an intact TTB framework that hosts intimately intergrown domains of the Nb8W9O47 phase and such with an increased amount of filled PTs. In the latter domains, the occupation of directly neighbored PTs by MO strings compensates the decreased O/M: (MO)x(M10O30) with x > 4/3 compared to x = 4/3 in Nb8W9O47. This is the case in the structure of Nb12W11O63 (= (MO)6(M10O30)4 with x = 1.5) that has been observed in small domains in the sample Nb18W16O93 for the first time. In fact, the ratio O/M of Nb12W11O63 (2.739) is close to that of Nb18W16O93 (2.735). This dense occupation of PTs violating the first rule for a stable array of PCs is enforced by the decreased O content that must be somehow adjusted by structural adaptions. Nonetheless, the most stable PC arrangement, namely that of Nb8W9O47, is still the dominating structure in the sample Nb18W16O93 and present in many domains with typical diameters of several 10 nm. In contrast, the O-poorer domains are smaller and heavily disordered with regular structures appearing as rather small inclusions only. Both TTB superstructures Nb8W9O47 and Nb12W11O63 do occur in different orientation variants (Figure 5b) with the respective nanometer-sized domains coherently intergrown with each other. This flexibility is caused by the unaffected TTB-type framework with the structural modifications realized by filling PTs in different ways.  [18,25]. It is important to state that the PCs in all TTB-based structures and variants tend to be connected to form pairs or chains via the diamond link rather than being isolated or directly adjacent. In the structure Nb12W11O63 corresponding to (MO)6(M10O30)4, diamond linked PCs pairs are directly adjacent to each other which might represent a moderately stable arrangement as it is present as an intact structure in nanodomains.

Conclusions
The present HAADF-STEM investigation reveals that the sample Nb18W16O93 cannot be considered as a separate phase. The arrangement of PCs embedded in a perfectly ordered TTB substructure corresponds in wide areas to that of the well-known and stable phase Nb8W9O47 but is little ordered in small domains. No evidence for the existence of a PC array as suggested by Stephenson for the structure of Nb18W16O93 [14] could be found. In general, most PCs are connected via the diamond link to form pairs or less frequently three or four membered chains of PCs. The decreased O content compared to Nb8W9O47 is structurally compensated by a denser packing of PTs filled with M-O strings. This unavoidably leads to the occupation of directly adjacent PTs as they are present in the structural model proposed for Nb12W11O63 here. This structure appears in the investigated sample only in nanometer-sized domains, but future synthetic efforts might be successful in indeed preparing a phase Nb12W11O63 in pure form.