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# Niobium tungsten oxides for high-rate lithium-ion energy storage

## Abstract

The maximum power output and minimum charging time of a lithium-ion battery depend on both ionic and electronic transport. Ionic diffusion within the electrochemically active particles generally represents a fundamental limitation to the rate at which a battery can be charged and discharged. To compensate for the relatively slow solid-state ionic diffusion and to enable high power and rapid charging, the active particles are frequently reduced to nanometre dimensions, to the detriment of volumetric packing density, cost, stability and sustainability. As an alternative to nanoscaling, here we show that two complex niobium tungsten oxides—Nb16W5O55 and Nb18W16O93, which adopt crystallographic shear and bronze-like structures, respectively—can intercalate large quantities of lithium at high rates, even when the sizes of the niobium tungsten oxide particles are of the order of micrometres. Measurements of lithium-ion diffusion coefficients in both structures reveal room-temperature values that are several orders of magnitude higher than those in typical electrode materials such as Li4Ti5O12 and LiMn2O4. Multielectron redox, buffered volume expansion, topologically frustrated niobium/tungsten polyhedral arrangements and rapid solid-state lithium transport lead to extremely high volumetric capacities and rate performance. Unconventional materials and mechanisms that enable lithiation of micrometre-sized particles in minutes have implications for high-power applications, fast-charging devices, all-solid-state energy storage systems, electrode design and material discovery.

## Main

New high-rate electrode materials that can store large quantities of charge in a few minutes, rather than hours, are required to increase power and decrease charging time in lithium-ion batteries. Such materials can thus help to alleviate technological challenges associated with the adoption of electric vehicles and grid-scale batteries and enable the development of new power-intensive devices. The most intuitive and commonly used approach to increase rate performance is to create nanometre-sized or porous (and often hierarchical) structures, which minimize Li+ solid-state diffusion distances, enable more rapid Li+ transport through the composite electrode and increase the surface area of electrode materials in contact with electrolyte. Carbonaceous hierarchical structures and carbon-coating are also frequently used to improve electronic conductivity, which is another prerequisite for the application of high current densities.

In practice, despite excellent lithium mobility, graphite cannot be used at high rates owing to particle fracture and the risk of Li dendrite formation, the latter leading to short circuits and potentially fires and explosions1,2,3. The dendrite issue inherently limits the use of low-voltage anodes in high-rate applications because electrode inhomogeneity, or any source of increased overpotential, can lead to Li plating potentials on the surface of the electrode3. Li4Ti5O12, with an average voltage of 1.55 V (Supplementary Fig. 1), enables high-rate Li (de)intercalation without the risk of Li dendrites or substantial solid–electrolyte interphase formation, albeit with an undesirable but necessary decrease in full-cell voltage and thus energy density. In this well-established ‘high’-voltage and high-rate anode, the capacity of 1-μm particles from solid-state synthesis reaches only 60–65 mA h g−1 at a rate4 of 10C, where the C-rate is defined as the inverse of the number of hours required to reach a defined theoretical capacity; for example, 10C corresponds to a 6-min discharge or charge time (see Methods). By contrast, through two decades of research, present carbon-coated nanoparticles of Li4Ti5O12 can reach at least 150 mA h g–1 at 10C5,6, which corresponds to approximately 0.5 lithium ions per transition metal (Li+/TM). However, using nanometre-sized and porous materials for electrochemical energy storage applications inherently results in a severe penalty in terms of volumetric energy density. Furthermore, these carefully designed porous and nano-architectures are time consuming and expensive to synthesize, characterize and manufacture. The relevant synthesis methods often result in relatively low yields or the generation of large quantities of chemical waste7, while also being more susceptible to degradation during electrochemical cycling (from processes such as catalytic decomposition of the electrolyte8, morphological changes that result in loss of nanostructuring9 and higher first-cycle capacity loss10).

In this work, we break from the conventional strategy of nanoscaling and nanostructuring of electrode materials to overcome poor ionic diffusion and electronic properties (found in TiO2 and Li4Ti5O12 for example). We demonstrate that with the appropriate host lattice, none of the usual size, structure or porosity criteria are required to achieve a practical high-rate battery electrode. Instead, we use insight obtained from previous investigations of complex binary niobium oxides, such as the low-temperature polymorph T-Nb2O511, and of superionic conductors, such as lithium lanthanum titanate perovskite (LLTO)12, to identify structural motifs that should exhibit favourable Li diffusion properties, and thus superior performance, allowing micrometre-sized particles to be used at extremely high rates. We show that when multi-redox 4d and 5d transition metals are used with the appropriate three-dimensional oxide structure, we can achieve extremely high volumetric energy densities and impressive rates. The bulk compounds studied are a series of complex ‘block’ or ‘bronze-like’ oxide structures (Fig. 1) largely comprising corner- and edge-sharing NbO6 and WO6 octahedra, and both oxides are prepared via gram-scale solid-state synthesis. Their unusual electrochemical performance is first illustrated by studying large (3–10 μm primary, 10–30 μm agglomerate) dense particles of the block structure Nb16W5O55 (Fig. 1a–c). Even on a mass-normalized basis, the lithium storage performance of Nb16W5O55 exceeds that of nanostructured versions of the heavily studied Li4Ti5O125,13,14,15, TiO2(B)16,17,18 and T-Nb2O519,20,21 under similar loading conditions. Given the high density of the crystal structure and the high tap density of bulk Nb16W5O55 compared with nanomaterials, this leads to exceptionally high volumetric performance. We further demonstrate the generality of this bulk phenomenon by exploring another new electrode material, bronze-like Nb18W16O93 (Fig. 1d–f).

## Complex oxides for energy storage

Nb16W5O55 is a metastable member of the system Nb2O5–WO322, with a monoclinic structure composed of subunits of corner-shared octahedra arranged into ReO3-like blocks that are four octahedra wide by five octahedra long and infinite in the third dimension (Fig. 1a)23. The block subunits are connected by crystallographic shear planes along the edges and by tetrahedra at each corner, and the structure is expressed as (4 × 5)1; in the notation (m × n)p, m and n denote block length in units of octahedra and p relates to the connectivity of the blocks, which may also be joined in pairs (p = 2) or infinite ribbons (p = ∞). To the best of our knowledge, this is the first reported application of any kind for Nb16W5O55 since its discovery in 196523,24. Nb18W16O93 is orthorhombic, a 1 × 3 × 1 superstructure of the classic tetragonal tungsten bronze (Fig. 1d, Supplementary Fig. 2). The superstructure25 results from partial filling of pentagonal tunnels by –M–O– chains to form pentagonal bipyramids, in addition to the distorted octahedra of the tetragonal tungsten bronzes. Nb16W5O55 and Nb18W16O93 were prepared via co-thermal oxidation of pellets of NbO2 and WO2. Details and alternative synthetic routes are described in Methods (Supplementary Figs. 37).

Reaction of Nb16W5O55 with lithium (Fig. 2a) proceeds in three regions from 2.5 V to 1.0 V, with an average voltage of 1.57 V (Supplementary Fig. 1), comparable to the average voltage26 of 1.55 V of Li4Ti5O12. The three regions, more easily observed in the derivative plot (Fig. 2b), are characterized by their slope and are reminiscent of the three regions observed in other crystallographic shear structures27, such as a second niobium oxide polymorph, H-Nb2O528, PNb9O2529, TiNb2O730 and Nb12WO3331. When the kinetics were examined over a range of current densities from C/5 (34.3 mA g−1) to 60C (10.3 A g−1), Nb16W5O55 showed unprecedented bulk rate performance (Fig. 2a, b, e) in standard electrode formulations (see Methods and Supplementary Fig. 8). At C/5, around 1.3 Li+/TM can be reversibly intercalated for a gravimetric capacity of about 225 mA h g−1. When the rate is increased by a factor of 25 to 5C, Nb16W5O55 maintains a capacity of 1.0 Li+/TM (171 mA h g−1). At 20C, which corresponds to a three-minute discharge, it is still possible to exchange 0.86 Li+/TM and access 148 mA h g−1. Rate tests on Nb16W5O55 were performed with a potentiostatic hold at the top of charge to ensure a reliable starting point for discharge. To test the performance under more demanding conditions, 1,000 cycles were measured with fixed galvanostatic discharge and charge conditions of 10C for 250 cycles followed by 20C for 750 cycles with no voltage hold (Fig. 2f). Under these conditions, 0.90 Li+/TM (average 155 mA h g−1) were reversibly intercalated at 10C with 95% capacity retention after 250 cycles on non-optimized or calendared electrodes. At 20C, the capacity was 0.75 Li+/TM (average 128 mA h g−1) and the capacity retention was again 95% over 750 cycles at 20C.

Excellent electrochemical energy storage was also discovered in another niobium tungsten oxide with distinct structural motifs: micrometre-scale particles of the bronze-like phase Nb18W16O93 (Fig. 1d–f) showed enhanced rate performance and could be cycled at extremely high rates (Fig. 2c–f). The average voltage of Nb18W16O93 is 1.67 V (Supplementary Fig. 1). In terms of gravimetric capacity, Nb18W16O93 stores about 20 mA h g−1 less than Nb16W5O55 at C/5 and 1C owing to the higher molar mass of the tungsten-rich bronze phase. However, at 20C, Nb18W16O93 is still able to accommodate a full unit of Li+/TM for a capacity of approximately 150 mA h g−1. At 60C and 100C (14.9 A g−1), the capacity is 105 and 70 mA h g–1, respectively.

Other cycling conditions, such as long-term cycling at C/5, and the effect of current collectors, which cannot be ignored at high rates32, were examined (Supplementary Fig. 9, 10). As a control, Li||Li symmetric cells were cycled at current densities corresponding to those applied for C/5–100C in Fig. 2 (Extended Data Fig. 1a). The overpotentials in the symmetric cell closely match those observed in the electrochemical cycling curves of Fig. 2a–d. This suggests that the extremely high rates in a bulk electrode approach the limits of Li metal plating/stripping or lithium-ion desolvation and transport in carbonate ester electrolytes at room temperature; that is, a considerable fraction of the ohmic loss during fast charging results from the Li metal and electrolyte rather than the complex oxide electrode materials.

## Measuring diffusion coefficients in mixed ionic–electronic conductors

The extremely high mobility of Li+ ions in these systems enabled the direct measurement of lithium diffusion with the pulsed-field-gradient nuclear magnetic resonance (PFG NMR) spectroscopy technique, which has previously only been applied to liquids or diamagnetic superionic solid electrolytes (Extended Data Table 1). To handle the short T2 (spin–spin) relaxation times of 7Li nuclei, which generally prevent these measurements in electrode materials because they are mixed ionic–electronic conductors, experiments were performed in the temperature range 333–453 K, at which the T2 relaxation times were longer than at room temperature. Analysis of the data (Extended Data Fig. 2, Methods) for LixNb16W5O55 (x = 6.3, 8.4) and LixNb18W16O93 (x = 3.4, 6.8, 10.2) showed lithium transport above 10−13 m2 s−1 at 333 K and 10−12 m2 s−1 at 373 K. Assuming Arrhenius behaviour and the extremely low measured activation energies of 0.10–0.30 eV, the room-temperature lithium diffusion coefficients are estimated to be greater than 1 × 10−13 m2 s−1 for all the materials (Table 1). The different samples exhibited similar diffusion coefficients and activation energies, consistent with the transport measurements made with the galvanostatic intermittent titration technique (GITT) (see Methods and Extended Data Fig. 1b, c) at low-to-moderate lithium contents. Lithium diffusion in both niobium tungsten oxide structures is markedly faster than that of Li4+xTi5O12 or LixTiO2 (about 10−16–10−15 m2 s−1) and is close to that of the best known lithium solid electrolytes (Extended Data Table 1). GITT and 7Li PFG NMR spectroscopy results (Extended Data Figs. 1b and 2, respectively) indicate that this rapid motion is maintained to high lithium contents (≥1.5 Li+/TM), and then the diffusion drops by about two orders of magnitude towards 2.0 Li+/TM. These complementary techniques suggest that the inherent range of the niobium tungsten oxide electrode materials for high-rate multi-redox extends to approximately 1.5 Li+/TM. The diffusion coefficients, of the order of 10−12–10−13 m2 s−1, measured for these materials are consistent with the values required to achieve full lithiation of 10-μm particles on a 60C timescale (Supplementary Table 1).

## Redox activity and local atomic structure

To understand (i) the nature of the charge-transfer sequence as a function of lithiation and (ii) the origin of multielectron redox behaviour in Nb16W5O55 and Nb18W16O93, the X-ray absorption near-edge structure (XANES) of the Nb K edge and W L edges was analysed (Supplementary Fig. 11, Methods). For Nb16W5O55, operando and ex situ Nb K edge XANES spectra show a nearly linear trend between the number of electrons (and Li+) transferred and the oxidation state of niobium, extracted from the shift of the absorption edge (Fig. 3a, Extended Data Fig. 3, Supplementary Fig. 12). Similarly, ex situ samples measured at the W Lii,i edges show a steadily negative correlation between capacity and edge position; however, there appears to be a larger shift in the tungsten absorption edge for the first 0.5 Li+/TM inserted (Fig. 3b, Extended Data Fig. 3, Supplementary Fig. 12), indicating a slight preference for tungsten reduction initially. The situation for Nb18W16O93 (Fig. 3, Extended Data Fig. 4, Supplementary Fig. 12) is analogous in that the niobium oxidation state decreases nearly linearly and tungsten reduction is slightly favoured initially. However, there is a clear preference for multielectron reduction on the tungsten throughout the lithiation, with Nb3+ appearing only beyond 1.5 Li+/TM, which may be related to cation occupancy variation on octahedral versus pentagonal bipyramidal sites.

The redox centres Nb5+ and W6+ in Nb16W5O55 are both d0 and both of these cations located in six-coordinate environments experience second-order Jahn–Teller (SOJT) distortions, which give rise to a pre-edge feature before the main absorption edge in the Nb K and W Li edge X-ray absorption spectra (Extended Data Figs. 3, 4, Supplementary Figs. 13, 14, Methods); this serves as a direct probe of local symmetry and an additional measure of the oxidation state. As the d0 cations are reduced, the energy of the d states moves up and the SOJT distortion is reduced (Methods), which increases the local octahedral symmetry and decreases the pre-edge states and intensity monotonically (Fig. 3c, Extended Data Figs. 3, 4, Supplementary Fig. 13)23, again with a slightly larger effect on tungsten at low lithium concentrations and a bigger difference between tungsten and niobium in Nb18W16O93. By about 0.8–1.0 Li+/TM, both the Nb K and W Li distinct pre-edges of both the block and bronze phase have decreased and no substantial further changes are observed in compositions corresponding to multi-redox; thus, lithiation is associated with an increase in local symmetry for the d0 oxide intercalation hosts. The XANES edge shifts and pre-edge evolution for Nb16W5O55 and Nb18W16O93 observed in this work indicate a parallel reduction pathway and multielectron charge storage of both transition metals.

## Anisotropic host-lattice response to Li intercalation

To probe the lattice evolution of these complex oxides upon lithiation, operando synchrotron X-ray diffraction was performed at different cycling rates. At C/2, Nb16W5O55 evolves through a complex, three-stage solid-solution mechanism (Fig. 4a, c, Extended Data Figs. 5, 6) that correlates with the following observed electrochemical regions: (i) high voltage (until about 65 mA h g−1 or 0.4 Li+/TM): ac-plane expansion of the blocks, along with a slight expansion perpendicular to the block plane; (ii) about 65–170 mA h g−1 (0.4–1.0 Li+/TM): anisotropic behaviour involving a contraction of the blocks and a substantial expansion in the (perpendicular) b direction; (iii) multi-redox (beyond 1.0 Li+/TM): linear expansion in all dimensions. The volume expansion is considerably buffered by the block contraction in the second stage, and the lattice undergoes only 5.5% expansion at lithiation to 1.0 Li+/TM. The diffraction results show that although the second electrochemical process has a relatively small gradient it is not two-phase, in agreement with the GITT measurements (Extended Data Fig. 1b, c). Upon charging, the stages are reversed (Extended Data Fig. 6k, l), although there is some first-cycle capacity loss. This capacity loss is ascribed, at least in part, to residual Li in the structure (Extended Data Fig. 7), rather than the usual solid–electrolyte interphase formation, because the final lithium ions are considerably harder to extract as their removal would lead to the formation of insulating domains. At a ten-times-higher rate (5C), only the first two stages of lattice evolution are observed (Extended Data Figs. 5, 6), which is consistent with the degree of loss of capacity at higher rates. In addition, there is more strain and reaction inhomogeneity at 5C, consistent with previous in situ studies that clearly showed that at these rates, lithium transport within the electrolyte results in internal (electrolyte) inhomogeneities and concentration gradients33,34. Nevertheless, the mechanism remains solid-solution in nature, which is evident from the high inter-peak intensity (Extended Data Fig. 6j).

Operando diffraction measurements of Nb18W16O93 were performed at rates of up to 10C (Fig. 4b, d; Extended Data Figs. 5, 8, Supplementary Fig. 15). Like the block phase, the bronze phase shows a complicated but reversible nonlinear and strongly anisotropic structural evolution upon lithiation (Fig. 4b, d; see Methods for further discussion). Interestingly, the b ≈ 3a pseudo-superstructure relationship persists until the fourth intercalation region, at >0.5 Li+/TM. From this point, the unit-cell volume actually decreases with increasing lithium intercalation and is the same at 1.0 Li+/TM as at 0.5 Li+/TM—a total increase of only 2.8% from the unlithiated host. This volume contraction upon lithium insertion is phenomenologically related to negative thermal expansion35,36 or negative linear compressibility37 and may have shared origins related to tilting of the polyhedral units (see ‘Host features and design considerations’). The small volume change has implications for the suppression of intergranular cracking and long-term cycle performance38. Unlike in the shear structure, the bronze phase exhibits a compositionally narrow two-phase reaction between approximately Li6.6Nb18W16O93 and Li10.2Nb18W16O93 (0.2–0.3 Li+/TM); the phase transition preserves the Pbam space-group symmetry and is characterized by ab-plane expansion and contraction of the bronze layers. The structural stability of both the block and bronze phases is also reflected in the stability of the energy storage capacity over 1,000 discharge–charge cycles (Fig. 2f).

## Host features and design considerations

Relative to the parent ReO3 structure, the niobium tungsten oxides accommodate anion-deficient nonstoichiometry by forming topologically distinct condensed phases. This has important consequences for Li motion because the intersecting crystallographic shear planes (block phase) or twisted octahedra locked to pentagonal columns (bronze-like) (Fig. 1a, d) decrease the structural degrees of freedom. Both the block (Nb16W5O55) and bronze (Nb18W16O93) structural motifs are derived from the parent ReO3 structure type, of which WO3 is a locally distorted analogue and LLTO is a version with Li+ and La3+ cations on the A site (Supplementary Fig. 16). In ReO3, WO3 and LLTO, Li ions occupy 4- and 5-coordinate sites and diffuse through square planar window transition states. It is well established that this process is fast; an activation energy of 120–220 meV is found in LLTO, whose framework is stabilized by the large lanthanum ions39,40,41,42,43,44,45. By contrast, although ReO3 and WO3 should also be suitable for rapid three-dimensional lithium motion, their open and flexible framework can undergo a structural phase transition that locks the Li+ in place, reducing Li mobility considerably40.

The shear and bronze structure formation mechanisms result in frustrated polyhedral networks that can no longer undergo tilts upon lithiation that would clamp the lithium ions, preventing their motion. These concepts are well established in perovskites, where the so-called rigid-unit modes drive long-range cooperative distortions despite the framework structure46,47. By contrast, crystallographic shear and twisted, locked octahedra (Supplementary Fig. 16) lead to two fundamentally different—but effectively three-dimensional—conduction networks for lithium, while stabilizing the framework and precluding substantial Li-induced rigid-unit mode displacements that lead to local and long-range structural rearrangements.

Structural analyses and bond-valence energy landscape calculations (Extended Data Fig. 9a, b) indicate that infinite lithium diffusion in the Nb16W5O55 block phase is one-dimensional along the b axis, but the twelve parallel tunnels act as a metaphorical multi-lane highway, enabling lithium to change ‘lanes’ via local hops in the ac plane. Lithium sites and diffusion in this twelve-channel path may be analogous to those of the ReO3 and LLTO structure types (Extended Data Fig. 9c), but without the phase transition of ReO3 or the blocking La3+ ions of LLTO. Furthermore, given this mechanism, Nb16W5O55 should not be susceptible to the tunnel-blocking defects that hinder micrometre-sized one-dimensional conductors, such as LiFePO448,49,50. The Nb18W16O93 bronze-like phase has an infinite two-dimensional lithium pathway similarly to high-rate T-Nb2O5 in the ab crystallographic plane, with the additional benefit of four- and five-membered windows and channels along the c axis to increase the dimensionality of long-range diffusion to three dimensions. As a result, the structure appears to exhibit better performance, certainly under comparable morphologies and conditions, than the recently intensely studied T-Nb2O511,19,28,51,52. The bronze comparisons stress the complementary benefits of the open room-and-pillar host structure found in T-Nb2O511 and Nb18W16O93 and the additional perpendicular lithium diffusion channels in Nb18W16O93. In addition, both Nb16W5O55 and Nb18W16O93 may benefit from the randomly distributed Nb and W occupancy throughout the metal sites, which prevents rate-inhibiting long-range lithium ordering(s). Nb16W5O55 and Nb18W16O93 are compared to their binary counterparts H- and T-Nb2O5, respectively, as a function of capacity and Li+/TM (Extended Data Fig. 9d–g). Although the niobium tungsten oxide hosts are d0 insulators, their three-dimensional –M–O– connectivity enables effective electronic pathways because the structure is n-doped upon lithiation. In addition, variations of the bronze and crystallographic shear structure types are abundant and tunable for specific applications and beyond Li electrochemical energy storage (see Methods for further discussion regarding structure family extensions).

## Volumetric energy density and future applications

When compared strictly on the basis of the theoretical 1.0 Li+/TM reaction and crystallographic density of the active material, titania, niobia and graphite could all display charge densities of greater than 800 A h l−1 (Supplementary Fig. 17). Once experimental capacities, multielectron redox and tap density are considered (Fig. 5a, Supplementary Table 2), the bulk, unoptimized niobium tungsten oxides presented here maintain volumetric charge storage densities greater than 500 A h l−1 at 1C and up to 400 A h l−1 at 20C—performance that even the most optimized versions of TiO2, Nb2O5 and Li4Ti5O12 cannot achieve. This does not mean that the compounds presented here cannot be improved by methods such as nanostructuring, calendaring or carbon coating (see, for example, ref. 52), but proves that large, micrometre-sized particles can be used for high-rate electrodes and illustrates that nanoscaling is not always the most appropriate strategy to improve performance. This is evident in a Ragone plot (Fig. 5b), which shows the higher energy and power densities of the new bulk niobium tungsten oxides compared with literature values for state-of-the-art high-rate anode materials and with graphite (see expanded dataset including other electrode materials, details and references in Supplementary Table 2).

The ability to intercalate lithium into microscopic particles in minutes, with transport numbers approaching the best liquid and solid electrolytes, calls for a different paradigm for electrode structuring. Rather than focusing on particle dimensions, other aspects—such as electrolyte transport or counter electrode diffusivity and overpotential—may become more critical to enhancing performance. The strict requirements for carbon coating and intricately wiring nanoparticles are relaxed and issues stemming from surface reactivity and stability are also diminished. Other applications of these materials can be envisaged. For example, in the field of all-solid-state batteries, there has been a mismatch between lithium transport in superionic solid electrolytes compared with electrode materials. If both components have similar diffusivities, it may be possible to design and implement new, simplified composite structures to speed up the realization of safe all-solid-state energy storage.

In conclusion, extremely high-rate performance has been achieved without nanoscaling by identifying appropriate three-dimensional oxide crystal structures. The two new electrode materials, Nb16W5O55 and Nb18W16O93, effectively use superstructure motifs to provide stable host structures for lithium intercalation with facile and defect-tolerant lithium diffusion and multielectron redox. Volume expansion is mitigated by structural contraction along specific crystallographic axes in response to increased lithium content, which may enable the extended cycling of these large particles53. The materials investigated here operate in a similar voltage region to the well-studied, and generally considered to be ‘safe’, anode materials Li4Ti5O12 and TiO2(B). In contrast to approaches that try to overcome physical properties (such as ionic and electronic conductivity) extrinsically (for example, by nanoscaling and carbon coating), the high-rate, high-capacity properties of the niobium tungsten oxide block and bronze phases presented here are intrinsic to the complex atomic and electronic networks. The path forward for new fast ionic conductors should consider host structures with open yet frustrated topologies (that prevent structural rearrangements that reduce Li transport) and that also contain ‘disorder’ in the sense of a multitude of guest sites for Li+ and limited interaction between the host and guest (that is, no strong coupling between the diffusing Li+ and associated electron, as found in LiFePO454, or between the Li+ and the host structure itself). This leads to a relatively flat potential energy surface with small kinetic diffusion barriers for Li transport. These criteria, which lead to extremely high power and energy densities (Fig. 5b), are satisfied in Nb16W5O55 and Nb18W16O93 via crystallographic shear and pentagonal columns that prop open the framework structures and through transition-metal disorder that prevents Li ordering.

## Methods

### Synthesis and structure characterization

Nb16W5O55 and Nb18W16O93 were synthesized by co-thermal oxidation of dark-blue NbO2 (Alfa Aesar, 99+%) and brown WO2 (Alfa Aesar, 99.9%) in batches of approximately 1–5 g. The partially reduced oxides were massed to within 0.001 g of the 16:5 or 18:16 stoichiometric ratios, ground together by hand with an agate mortar and pestle, pressed into a pellet at 10 MPa, heated in a platinum crucible at a rate of 10 K min−1 to 1,473 K, and naturally cooled in the furnace over approximately 2 h. Both phases formed subhedral particles with approximately 3–10-μm primary particles that appeared in the electron microscope to be intergrown/‘cemented’ into larger secondary particles of around 10–30 μm (Fig. 1, Supplementary Fig. 3a, b). As synthesized, Nb16W5O55 is pale yellow–green and Nb18W16O93 is off-white (Supplementary Fig. 3c) (we note that the colours of both mixed metal oxides are between those of light-green WO3 and white Nb2O5). Energy-dispersive X-ray spectroscopy (EDX) revealed a uniform distribution of niobium, tungsten and oxygen, with no apparent phase-segregated particles and no presence of any other elements (besides those on the background adhesive carbon) (Supplementary Figs. 4, 5). We note that although phases such as Nb2O5 and WO3 would be distinct via EDX, particles of niobium tungsten oxide phases with similar composition to that of Nb16W5O55 or Nb18W16O93 would not be distinguishable. Although the phase diagram55 suggests that Nb16W5O55 is only formed at about 1,363–1,658 K and is a metastable phase that should disproportionate to Nb14W3O44 and Nb2WO8 on cooling, this was not observed. Nb16W5O55 retains its high-temperature structure on quenching56 and even with more modest cooling. In the original synthetic report24, Roth and Wadsley also noted that phase-pure Nb16W5O55 was obtained even after annealing at 1,273 K for one to three days after an initial heat treatment at 1,623 K for 24 h. To investigate other synthetic methods, samples were also prepared by quenching the samples from 1,473 K onto a steel plate, as well as from analogous pellets or loose mixed powders of Nb2O5 (Alfa Aesar, 99.9985%, H-phase) and WO3 (Sigma-Aldrich, ≥99%, γ-phase) precursors. Large (20 g) single batches of Nb16W5O55 and Nb18W16O93 were produced by hand grinding (agate, 5 min) or ball milling (SPEX 8000M high-energy mixer/mill; zirconia jar with two 5-g zirconia balls, 90 min) Nb2O5 and WO3 powder, followed by heating in a platinum crucible covered with a platinum lid in air at 973 K for 12 h and then at 1,473 K for 12 h. The large batches were heated at 10 K min–1 and the samples were allowed to cool naturally in the furnace over about 2 h. Thermogravimetric analysis (TGA, Supplementary Fig. 6) revealed that WO2 oxidizes to WO3 starting at around 700 K and NbO2 oxidizes to Nb2O5 starting at around 550 K. At 1,273 K, the WO2 sample had gained 7.8% mass versus the expected 7.4%, and NbO2 had gained 5.8% compared to the expected 6.4%. These small differences may arise from slight off-stoichiometry in the starting material. WO3 undergoes sublimation at temperatures near or above 1,273 K; however, the reaction with niobium oxide apparently stabilizes the volatile tungsten to considerably higher temperatures. After 24 h at 1,473 K, the mass change was –0.4% for Nb16W5O55 and –0.3% for Nb18W16O93 compared with the expected values, which is within the error of the expected mass changes for NbO2 and WO2 oxidation.

Laboratory powder X-ray diffraction patterns were measured at ambient temperature with a Cu Kα source in Bragg–Brentano geometry at a scan rate of 0.83° min–1. The sample stage rotated continuously to improve powder averaging. Sample phase and purity were determined by Rietveld refinement in GSAS-II (Supplementary Fig. 7)57. Given the synthesis time and temperature (24 h and 1,473 K), the block-phase Nb16W5O55 samples are expected to contain several per cent of Wadsley defect fringes, as suggested by the laborious study of Allpress and Roth58.

TGA measurements were performed on a Mettler Toledo TGA/SDTA 851 thermobalance. Samples were placed in a tared 100-μl alumina crucible and the mass was recorded from 323 K to 1,273 K in steps of 1 K min–1 under a constant air flow (50 ml min–1). A blank with an empty crucible was recorded under the same conditions and subtracted from the NbOx/WOx data. The raw data were numerically differentiated to obtain differential thermogravimetry curves.

Scanning electron microscopy images were taken with a Sigma VP instrument (Zeiss) at 3.0 kV and a MIRA3 instrument (TESCAN) at 5.0 kV with secondary-electron detection.

Tap density was recorded on an AutoTap (Quantachrome Instruments) instrument operating at 257 taps per minute. Tap densities were measured according to the ASTM international standard B527-15, modified to accommodate a 5–10 cm3 graduated cylinder.

### Electrochemical characterization

All electrochemical measurements were conducted in stainless-steel 2032 coin cells (Cambridge Energy Solutions) with a stainless-steel conical spring, two 0.5-mm-thick stainless-steel spacer disks, a plastic gasket and a glass microfibre separator (Whatman). The electrode had an active material:carbon:binder mass ratio of 8:1:1, active material loading of 2–3 mg cm−2 and an area of 1.27 cm2. The metal oxide and conductive carbon (Super P, TIMCAL) were ground by hand in an agate mortar and pestle in an 8:1 mass ratio. This powder was ground in a 9:1 mass ratio with poly(vinylidene difluoride) (PVDF, Kynar) dispersed in N-methyl pyrrolidone (NMP; Sigma-Aldrich, anhydrous, 99.5%). Although standard, SuperP carbon is a nanoparticulate powder and NMP is a hazardous organic solvent, so appropriate nanoparticle cabinets and fume hoods should be used. This metal oxide/carbon/polymer electrode served as the cathode against a Li metal-disk (LTS Research, 99.95%) anode in half-cell geometry. The electrolyte for all experiments was 1.0 M LiPF6 dissolved in 1:1 v/v ethylene carbonate/dimethyl carbonate (EC/DMC; Sigma-Aldrich, battery grade). No additives were used. Electrochemistry measurements were performed in a temperature-controlled room at 293 ± 2 K. A galvanostat/potentiostat (BioLogic) with EC-Laboratory software was used to perform the electrochemical measurements. All potentials are reported with respect to Li+/Li0.

In this work, the C-rate is always defined relative to one-electron transfer per transition metal; for example, for Nb16W5O55, 1C = 171.3 mA g–1 and 20C = 3,426 mA g–1. Theoretical capacity is calculated by:

$${Q}_{{\rm{theoretical}}}=\frac{nF}{3.6m}=\frac{21\hspace{2.77626pt}\times \hspace{2.77626pt}{\rm{96,485}}{\rm{.3}}\hspace{2.22144pt}{\rm{C}}\hspace{2.22144pt}{{\rm{mol}}}^{-1}}{3.6\hspace{2.22144pt}{\rm{C}}\hspace{2.22144pt}{{\rm{mA}}}^{-1}\hspace{2.22144pt}{{\rm{h}}}^{-{\rm{1}}}\times \hspace{2.77626pt}{\rm{3,285}}{\rm{.65}}\hspace{2.22144pt}{\rm{g}}\hspace{2.22144pt}{{\rm{mol}}}^{-{\rm{1}}}}=171.3\hspace{2.22144pt}{\rm{mA}}\hspace{2.22144pt}{\rm{h}}\hspace{2.22144pt}{{\rm{g}}}^{-{\rm{1}}}$$

where n is the number of electrons transferred per formula unit, F is Faraday’s constant, 3.6 is a conversion factor between coulombs and the conventional milliampere-hour and m is the mass per formula unit.

In a Ragone plot59, the energy density of a battery cathode material or full cell is the product of capacity (Q) and voltage (V); however, this quantity is not appropriate when comparing anode materials, where energy and voltage have an inverse relationship. In the calculation of the anode-material Ragone plot in Fig. 5b, the energy (E) is computed on the basis of the voltage difference versus a 4.0-V cathode. Thus, normalized to the anode, Eanode = Qanode(Vcathode − Vanode). Literature values for the Ragone plot were extracted with WebPlotDigitizer60.

### Operando synchrotron X-ray diffraction

Operando powder diffraction measurements were carried out at beamline 17BM (bending magnet) at the Advanced Photon Source at Argonne National Laboratory. The samples were measured at ambient temperature in transmission geometry at 17.0 keV (0.7295 Å or 0.72768 Å) with an area detector. All operando measurements were performed in the AMPIX cell, which has been described elsewhere61. In brief, it contains a hard, conductive glassy carbon window to prevent inhomogeneous electrochemical reactions, which are a concern with flexible or non-conductive X-ray windows61. Owing to the absorbing nature of niobium and tungsten and the absence of a current collector, self-standing electrodes were made with a 3:6:1 (Nb16W5O55 at C/2) or 5:4:1 (Nb16W5O55 at 5C and N18W16O93 at 1C, 5C and 10C) mass ratio of metal oxide:SuperP carbon:poly(tetrafluoroethylene). The resulting electrodes were approximately 1.0 cm in diameter and contained 5.3 mg, 8.7 mg and 8.0 mg of active material for Nb16W5O55 (C/2), Nb16W5O55 (5C) and N18W16O93 (1C, 5C and 10C), respectively. These electrodes correspond to areal metal-oxide mass loadings of 6.8–11.1 mg cm−2. AMPIX cells were constructed in an argon glovebox with lithium-metal counter-electrodes, glass-fibre separators (Whatman) and 1.0 M LiPF6 dissolved in 1:1 v/v ethylene carbonate/diethyl carbonate (EC/DEC). Two-dimensional image data were converted to conventional one-dimensional diffraction patterns through integration in GSAS-II after calibration with LaB657. Background subtraction, primarily from the glassy carbon window, and normalization to incident X-ray intensity were performed on the one-dimensional integrated diffraction data.

Sequential Rietveld refinement of the unit-cell parameters of Nb16W5O55 and Nb18W16O93 during operando galvanostatic electrochemical lithiation was performed in GSAS-II. The initial structure model was based on Rietveld refinement of the atomic coordinates, unit-cell parameters, background, zero offset and peak-shape parameters (U, V and W; peak width squared (H2) = Utan2θ + Vtanθ + W)62 of the first in situ diffraction pattern before the application of a current. For the sequential refinement, only the unit-cell parameters and Chebyshev background coefficients were allowed to vary. Refinement of the atomic coordinates was not attempted owing to the large number of variables this would introduce, the weak relative scattering of lithium and oxygen versus niobium and tungsten, and the optimization of experiments towards rapid data collection. Nb16W5O55 contains 11 metal sites and 28 oxygen sites and Nb18W16O93 contains 10 metal sites and 25 oxygen sites in the asymmetric unit. Two-dimensional diffraction images (integrated to one-dimensional patterns) were collected in 7–15 s (Supplementary Table 3).

Nb18W16O93, which exhibits a region of two-phase behaviour, was fitted using a double-ended sequential Rietveld refinement, in which the process described above was also initiated from the structure at the end of the discharge and a ‘backward’ refinement was performed. Error bars (Extended Data Fig. 5) are derived from the refinements. The unit-cell parameters in the two-phase region of Nb18W16O93 and the inhomogeneous solid-solution region of Nb16W5O55 were estimated by fitting individual reflections to two sets of lattice parameters (Nb18W16O93) and measuring the range of individual reflections (Nb16W5O55); thus, error bars in these regions cannot be calculated using the whole pattern-refinement method. Owing to the unit-cell dimensions and pseudosymmetry, there is severe overlap of reflections in the powder diffraction patterns of both Nb18W16O93 and Nb16W5O55, even at the high resolution available at a synchrotron X-ray source. Furthermore, anisotropic lattice expansion results in reflections crossing during discharge (Fig. 4), which introduces challenges for sequential refinement. At 145–155 mA h g–1 in Nb16W5O55, this crossover (Fig. 4a, Extended Data Fig. 6k) resulted in strongly correlated and inconsistent fits for four consecutive diffraction patterns. These patterns were fitted according to the individual reflection model described above assuming linear changes—an approximation over the small change in lithium content and unit-cell dimensions.

For the crystallographic shear structure with monoclinic symmetry (Nb16W5O55; Fig. 1a, Fig. 4c), the b axis represents the ‘layered’ direction and the ‘block area’ is parameterized by acsinβ, where the a and c axes define the plane of the block and β is the angle between a and c. The unit-cell volume of this phase is the product of the block area and the layer spacing, (acsinβ)b. For the bronze-like phase with orthorhombic symmetry (Nb18W16O93, Fig. 1d, Fig. 4d), the unit-cell volume is simply the product of the crystallographic axes, abc.

### Operando and ex situ synchrotron X-ray absorption spectroscopy

Operando X-ray absorption spectroscopy (XAS) was performed at beamline 9BM (bending magnet) at the Advanced Photon Source at Argonne National Laboratory. Nb K edge spectra were recorded at ambient temperature in transmission mode above and below the absorption edge of 18,986 eV. The same AMPIX cells were used as for the diffraction measurements, but with a higher metal-oxide loading of 22.5 mg and lower carbon content (8:1:1 ratio of oxide:carbon:binder) at C/3.

Ex situ XAS was performed at beamline B18 (bending magnet) at the Diamond Light Source. Spectra of the Nb K edge, W Li, Lii and Liii edges were measured at ambient temperature in transmission mode using energy scans above and below the absorption edges of 18,986 eV, 12,100 eV, 11,544 eV and 10,207 eV, respectively. The X-ray energy ranges were scanned over 1,000 eV (W Li + Lii) or 1,500 eV (Nb K, W Liii) in steps of about 0.4 eV. To synthesize powders for ex situ characterization, pure Nb16W5O55 powder was pressed into pellets at 1–2 MPa, discharged to the relevant lithium content in coin cells as previously described, then extracted in an argon glovebox where it was rinsed three times with 2 ml DMC (Sigma-Aldrich, anhydrous, ≥99%) and hand-ground (agate) back into powder. Upon lithiation, the colour of Nb16W5O55 changed from a pale yellow–green to light blue, then to dark blue, and through to dark maroon above approximately 0.5 Li+/TM. Samples for XAS were prepared in an argon glovebox by carefully grinding the active material (typically 15–18 mg) with dried cellulose (to a total mass of 60 ± 5 mg) in an agate mortar and pestle to achieve a fine homogeneous sample with a change in absorption coefficient of about 1 across the Nb K and W Liii absorption edges. The thoroughly ground powders were pressed into 8-mm-diameter pellets (about 1 mm thick) in the glovebox. Non-air-sensitive samples (pristine and reference) were measured in air and lithiated samples were transferred from the glovebox in a custom-built (Diamond Light Source) transfer chamber with X-ray-transparent windows. The argon in the chamber was flushed with helium to reduce background absorption of the incident X-rays and the samples were measured at a slight overpressure of helium to ensure the exclusion of air. Multiple spectra were collected from each sample to improve the signal-to-noise ratio and to ensure sample stability with respect to possible air contamination or beam damage. The oxides appeared to be stable; no changes were observed for any sample between the first and last measurement (typically 2–6 spectra per sample per absorption edge) over several hours in the sample chamber and 30–60 min in the X-ray beam.

For all XAS measurements, simultaneous measurement of a reference Nb or W foil was performed with each spectrum to ensure X-ray beam stability and for energy calibration. Data merging, calibration/alignment, analysis and peak fitting were performed within the Athena program in the Demeter package running IFEFFIT63,64. The Nb K edge, W Li, Lii and Liii edges were calibrated to the reference Nb and W metal foils by setting the first maximum in the derivative plot of absorption versus energy equal to the standard electron binding energy65. The Nb16W5O55 operando calibration was set to be equivalent to the ex situ calibration to simultaneously compare edge shifts of both datasets.

XAS of the Nb K edge probes excitations from 1s to 5p at energies around 19,000 eV, which is well suited for standard synchrotron analysis. In principle, the same type of analysis could be performed with excitations from 1s to 6p at the W K edge, but at 69,500 eV, it is impractically high in energy for standard beamline configurations and suffers from severe core-hole lifetime broadening66. The W L edges, however, at 12,100–10,200 eV are suitable for high-resolution XAS. The W Li edge measures 2s to 6p excitations whereas the W Lii and Liii edges correspond to transitions of 2p to (near-)valence 5d states. The Lii and Liii edges are split by about 1,337 eV by spin–orbit coupling; in the octahedral sites present in Nb16W5O55, these edges are further split by about 4 eV by ligand-field effects into transitions to t2g and eg orbitals. Recent studies have demonstrated the use of the 5d Li edges for oxidation-state analysis in periodic11 and molecular67,68 structures. We considered this; however, the edge position of the W Li edge in Nb16W5O55 is severely complicated by the strong pre-edge feature. In this system, the Lii edge offered an excellent alternative, with a stronger signal and a single contribution from excitations from 2p1/2 to 5d3/2. We note that the contribution expected for 2p to 6s transitions can be neglected at the absorption edge for early-third-row transition metals69. Meanwhile, the W Li pre-edge peaks that are problematic for energy calibration provide direct evidence for local geometry around the tungsten ions.

An SOJT distortion moves Nb5+ and W6+ off-centre in the otherwise centrosymmetric environments of the octahedral MO6 transition-metal sites in Nb16W5O55 and Nb18W16O93. The SOJT results from the vibronic mixing of nondegenerate electronic states under nuclear displacements70. In a d0 metal oxide, the energy difference between the ground and excited states is small owing to the pseudodegeneracy of the filled valence p orbitals and empty d orbitals in the first excited state. This off-centre distortion enables mixing of the dipole-transition-allowed p states (for example, 5p for the Nb K edge) with lower-energy d states (4d for the Nb K edge), which gives rise to a pre-edge feature before the main absorption edge in the XAS spectra of the Nb K and W Li edges and serves as a direct probe of local symmetry and an additional measure of the oxidation state. As the d0 cations are reduced, the energy of the d states moves up and the SOJT distortion is reduced, which increases the local octahedral symmetry and decreases the pre-edge states and intensity. X-ray absorption pre-edge features are well known in tetrahedral and other noncentrosymmetric local-coordination environments, so the SOJT distortion and d0 electronic configuration are not prerequisites for pre-edge peak intensity from those sites. Nb16W5O55 has 40 distorted octahedral sites and 2 tetrahedral sites per unit cell whereas Nb18W16O93 has 30 octahedral sites and 4 occupied pentagonal bipyramidal sites per unit cell, so some pre-edge intensity may be expected, even beyond lithiation to the d1 electronic configuration. Interestingly, it has been shown that the tetragonal bronze structure cannot be constructed from identical, regular octahedra71, so some local distortion is topologically required regardless of the oxidation state or SOJT.

We note that for the related shear-phase Nb12WO33, the three observed electrochemical regions have tentatively been assigned to the sequential reduction of W6+/5+, Nb5+/4+ and Nb4+/3+ on discharge, but these proposed oxidation changes have not been experimentally verified31,72.

### 7Li PFG NMR spectroscopy

7Li NMR diffusion spectra were recorded on a Bruker Avance III 300 MHz (7.0 T) spectrometer using a Diff50 probe head equipped with an extended variable-temperature 5-mm single-tuned 7Li saddle coil insert. All of the materials examined here had spin–lattice (T1) relaxation times greater than spin–spin (T2) relaxation times. Therefore, spectra were recorded with the stimulated-echo PFG sequence shown in Extended Data Fig. 2b to minimize T2 losses. After the first 90° radiofrequency pulse, the net magnetization loses coherence owing to T2 relaxation; thus, the time period following this pulse, which includes the first PFG pulse (to encode spin position), must be shorter than T2. In the stimulated-echo sequence used here, a second 90° radiofrequency pulse was applied to store the net magnetization along the z axis, allowing diffusion times, Δ, commensurate with the comparatively longer T1 value, as no T2 relaxation occurred. During Δ, a short spoiler gradient (SINE.100) was applied to remove residual transverse magnetization. Afterwards, a third 90° radiofrequency pulse was applied, followed by a PFG pulse to decode the spin position. Sufficiently long delays (1 ms) were used between PFG and radiofrequency pulses to minimize eddy currents in the diffusion measurements.

During this sequence, the gradient strength, g, was varied from 0.87 to 1,800 or 2,300 G cm–1, and 16 gradient steps were acquired using ‘opt’-shaped pulses with 1,024–4,096 transients. The opt shape is a composite pulse that starts with a quarter of a sine wave, followed by a constant gradient, and ends with a ramp down (Extended Data Fig. 2b). The opt gradient pulses provided the largest gradient integral for a given time period, maximizing the range of diffusion coefficients that we could assess in this experiment.

Spectra were analysed in phase-sensitive mode and the response of the integrated NMR signal intensity, I, to variation in g is described by the Stejskal–Tanner equation73:

$$\frac{I}{{I}_{0}}=exp\left[-{g}^{2}{\gamma }^{2}{\delta }^{2}\left(\Delta -\frac{\delta }{3}\right)D\right]$$

where I0 is the intensity in the absence of gradients, γ is the gyromagnetic ratio (γ7Li = 103.962 × 106 s–1 T–1), δ is the effective gradient pulse duration and D is the diffusion coefficient. Typical δ values ranged from 0.8 ms to 1.5 ms and Δ values were 50–150 ms for the bronze- and the block-phase samples, respectively.

Diffusion spectra were recorded at elevated temperatures owing to the increase in T2 observed at high temperature (for example, T2 for Li3.4Nb18W16O93 is approximately 700 μs at room temperature and 1.9 ms at 453 K). (No attempt was made to calibrate the temperature for this experimental setup because a single-tuned 7Li coil was used and no reliable 7Li reference is routinely used for temperature calibration. The Bruker manual states that for static measurements, the temperature calibration should be within ±7 K of the set value.) The increase in T2 allowed the use of longer gradient pulses, δ, that were necessary to measure diffusion coefficients in the solid oxides.

Representative 7Li diffusion decay curves for the five samples studied, LixNb16W5O55 (x = 6.3, 8.4) and LixNb18W16O93 (x = 3.4, 6.8, 10.2), and a representative one-dimensional 7Li NMR spectrum are shown in Extended Data Fig. 2.

Concerning the difficulties associated with measuring self-diffusion coefficients with PFG NMR spectroscopy, it is worth noting that even if the T2 of these materials was sufficiently long, the cumulative length of δ applied before Δ in the pulse sequence of choice (Extended Data Fig. 2b) should not exceed 5 ms to mitigate probe damage. The limitation of cumulative δ = 5 ms places an inherent limitation on the diffusion coefficients that can be extracted using PFG NMR spectroscopy and effectively places the burden on the length of T1, which determines the length of Δ.

The PFG data were initially fitted with a single exponential to extract the diffusion coefficients. In the case of the block phase, Li6.3Nb16W5O55, fitting the data with two components for biexponential decay resulted in an improvement (on average) of a factor of two in the residual sum of squares of the fit to the PFG data. Therefore, the 7Li NMR signal of the Li6.3Nb16W5O55 sample presented in Table 1 can be interpreted as consisting of two Li species, one that diffuses rapidly and one that diffuses more slowly (we note that both diffusion coefficients are markedly faster than those reported for Li4Ti5O12 and LiFePO4). For the higher-Li-content block phase, Li8.4Nb16W5O55, the data were fitted well by a single-component exponential that yielded a similar diffusion coefficient and activation energy to the majority lithium phase in Li6.3Nb16W5O55. This suggests that within the two-component model, the fastest diffusing phase is present at lower lithium concentrations, and by the second stage of the electrochemical profile the structure is composed entirely of the phase with room-temperature lithium diffusion of about 1.6 × 10−13 m2 s−1.

For all measured stages of lithiation for the bronze phase (Li3.4Nb18W16O93, Li6.8Nb18W16O93 and Li10.2Nb18W16O93), the data were fitted well by a single-component exponential decay (as reflected in the error bars in Extended Data Fig. 2a, which represent 2σ values obtained from the fit), and no remarkable improvement was observed upon fitting by a biexponential.

Linear fits of the 7Li diffusion coefficients of both the block and bronze phases as a function of temperature allow extraction of the activation energy, assuming Arrhenius behaviour (Extended Data Fig. 2a). Extrapolation using the activation energy allows estimation of 7Li diffusion at room temperature and facilitates comparison to other materials (Table 1, Extended Data Table 1).

### GITT diffusion coefficient and diffusion length

Information on electrode thermodynamics, including phase transitions, and lithium kinetics74 can in principle be extracted from GITT measurements by tracking the voltage evolution after a brief current pulse as lithium diffuses and the chemical potential equilibrates within the electrode/particles. Reliable quantitative diffusion coefficients, DLi, are however difficult to extract from GITT alone. To determine a diffusion coefficient from GITT measurements, a diffusion length (L) must be defined. However, a battery electrode is a heterogeneous system. First, it is a composite of active material (here, metal oxide), porous carbon and polymeric binder. Within this composite, there is a distribution of particle sizes (unless single crystals75 or well defined particles are used; even then, diffusion varies with lattice direction). Furthermore, different regimes of diffusion must exist because of the presence of solid/liquid interfaces and porous electrode structure. Nevertheless, in an electrode that does not undergo severe pulverization (for example, an intercalation electrode), L is a fixed quantity throughout the experiment. Variation in L—a parameter required to relate the rate of relaxation to the diffusion—causes values of DLi to vary considerably between reports, even for the same material28,76. Thus, although a physically meaningful diffusion coefficient may not be extracted, a relative measure of diffusion is readily obtained. For this reason, we use an extracted proxy for lithium diffusion (DLiL–2; Extended Data Fig. 1), which removes the uncertainty in L and enables self-consistent analysis of a single electrode and electrodes prepared under identical conditions. The addition of quantitative information from another method (for example, NMR spectroscopy or tracer diffusion) allows us to calibrate relative changes in Li+ kinetics to quantitative diffusion values throughout a range of lithiation.

### Nb18W16O93 operando diffraction mechanism

As shown in Fig. 4d, lithiation from 0 to 0.2 Li+/TM is characterized by ab-plane expansion. The plateau-like region from 0.2 to 0.3 Li+/TM is associated with further ab-plane expansion, still maintaining the b ≈ 3a superstructure and contraction of the layers (c axis). From 0.3 to 0.55 Li+/TM, the structure expands nearly isotropically, whereas at about 0.55 Li+/TM, the pseudo-superstructure relationship collapses. From this point until 0.75 Li+/TM, b contracts rapidly, a expands and c is constant. At 0.75 Li+/TM, the layers begin to expand back to their initial interlayer spacing while b continues contracting, albeit at a slower rate, to its initial length, and a continues its expansion. Thus, when fully lithiated to 1.0 Li+/TM (Li34Nb18W16O93), b and c are within ±0.1% of the unlithiated host, while a, and thus the total volume expansion, is +2.8%. In the multi-redox region beyond 1.0 Li+/TM, the structure again expands somewhat isotropically.

### Structure family extensions

Regarding the electronic structure changes of Nb16W5O55 and Nb18W16O93 upon lithiation, related partially reduced phases may be considered. Very high electronic conductivities are known to exist in the crystallographic shear niobium tungsten oxides77, as well as related partially reduced versions of both families, for example, shear Nb12O2978 and bronze A0.3WO379 (A = alkali metal cation), which exhibit resistivities lower than 10−2 Ω cm.

For ionic diffusion, there are also analogies between the new lithiated complex oxides and superionic conductors, such as α-AgI80 and Li10GeP2S1281,82, in that there are multiple sites for the cations to occupy within a disordered three-dimensional structure83,84.

In the composition and phase space of block and bronze structures, cation (such as early transition metals, p-block elements, aliovalent mixed metals)27,75,77,85,86 and anion (such as oxyfluorides27,87,88) dopants make it possible to tune the ionic and electronic properties and thereby affect voltage, capacity, power capability and stability. Analogues are known with Na+, K+, Mg2+ and Ca2+, which suggests that the variety of possible tunnel shapes and sizes, vacant sites and three-dimensional connectivities is also promising for beyond-Li electrochemical energy storage, according to the insights into high rate and capacity discovered here.

### Application considerations

Fast charging or high-power delivery from a full cell requires a cathode to match the anode. Although LiFePO4 has been used as a promising high-rate cathode89, along with Li4Ti5O12, both of these electrodes have exceptionally flat voltage profiles. The LiFePO4–Li4Ti5O12 cathode–anode combination provides a constant voltage but presents a serious challenge in terms of battery management systems (BMS). Simple and accurate BMS are crucial for battery applications in electric vehicles and mobile technology and are even more important at high rates for preventing dangerous and degradative over(dis)charging while maximizing utility. BMS rely on their ability to measure the state of charge, which cannot be done by charge counting alone as the battery degrades. The open-circuit voltage is a more reliable measure and a thermodynamic quantity. In contrast to the Li4Ti5O12/LiFePO4 battery, the sloping voltage profiles of the new high-rate materials presented herein provide an opportunity for the modelling and electrochemical engineering/industrial communities to develop BMS based on sloping voltage profiles, which may prove to be a substantial commercial advantage for Nb16W5O55, Nb18W16O93 and related materials in the growing area of high-power/fast-charging applications.

High-voltage anode materials, such as the niobium tungsten oxides, have several further advantages. Above 1.0 V versus Li+/Li0, the formation of solid–electrolyte interphase is minimal, which means that Li will not be lost into side reactions with the electrolyte. Furthermore, in a full cell against, for example, LiFePO4, LiN(CF3SO2)2 can be used to replace the more toxic LiPF6 electrolyte salt without degrading Al current collector(s)89, and Al can be used as the current collector instead of the more expensive Cu while avoiding LiAl alloying potentials (≤0.3 V versus Li+/Li)90. Another incentive to find replacements for nano-Li4Ti5O12 is the issue of gas evolution and associated swelling or pressure build-up91,92, which stems from heterogeneous catalysis between the metal-oxide surface and the organic electrolyte. The small particle sizes required to compensate for poor Li+ and electronic diffusion in Li4Ti5O12 increase the reactive surface area, and the much smaller surface area of the ~5-μm Nb16W5O55 or Nb18W16O93 particles potentially reduces side reactions.

### Data availability

The data that support the findings of this study are available from www.repository.cam.ac.uk and the corresponding author upon reasonable request.

Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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## Acknowledgements

K.J.G. acknowledges support from The Winston Churchill Foundation of the United States, a Herchel Smith Scholarship and a Science and Technology Facilities Council Futures Early Career Award. K.J.G. and C.P.G. thank the EPSRC for a LIBATT grant (EP/M009521/1). L.E.M. acknowledges support from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska–Curie grant agreement number 750294 and a Charles and Katharine Darwin Research Fellowship. We thank I. Seymour from the University of Cambridge and B. Dunn from the University of California, Los Angeles for fruitful discussions. We thank J. Skepper and H. Greer from the University of Cambridge for assistance with electron microscopy and M. Avdeev from the Bragg Institute for the bond valence sum mapping program. We thank O. Borkiewicz from the Advanced Photon Source at Argonne National Laboratory and A. Kasam from the University of Cambridge for diffraction data reduction scripts. We thank Diamond Light Source for access to beamline B18 (SP11433, SP14956, SP16387, SP17913), where we obtained results presented here. This research used resources of the Advanced Photon Source (GUP40466, GUP41657, GUP47967), a US Department of Energy (DOE) Office of Science User Facility operated for the DOE Office of Science by Argonne National Laboratory under contract number DE-AC02-06CH11357.

### Reviewer information

Nature thanks S. Greenbaum, P. Woodward and the other anonymous reviewer(s) for their contribution to the peer review of this work.

## Author information

### Affiliations

1. #### Department of Chemistry, University of Cambridge, Cambridge, UK

• Kent J. Griffith
• , Lauren E. Marbella
•  & Clare P. Grey

3. #### Diamond Light Source, Harwell Science and Innovation Campus, Didcot, UK

• Giannantonio Cibin

### Contributions

K.J.G. and C.P.G. conceived the idea. K.J.G. synthesized and characterized the materials and performed the electrochemistry experiments. K.J.G. performed the synchrotron diffraction and absorption experiments and analysed the data with support from K.M.W. and G.C. L.E.M. and K.J.G. performed the PFG NMR measurements. K.J.G. and C.P.G. wrote the manuscript with input from all co-authors.

### Competing interests

K.J.G. and C.P.G., via Cambridge Enterprise, have filed a UK patent application (GB1809467.2) covering the materials and high-rate energy storage application described in this manuscript.

### Corresponding author

Correspondence to Clare P. Grey.

## Extended data figures and tables

1. ### Extended Data Fig. 1 Overpotential in Li||Li symmetric cells and GITT of niobium tungsten oxides.

a, Li||Li symmetric cells were configured identically to those used for metal-oxide testing, with the exception of a second Li disk replacing the composite electrode. Rate testing was carried out with current densities corresponding to the rates shown in Fig. 2a–e, with 5 cycles at 100 μA (C/5), 500 μA (1C), 1 mA (2C), 2.5 mA (5C) and 5 mA (10C) and 10 cycles at 10 mA (20C), 20 mA (40C), 30 mA (60C) and 50 mA (100C). The ‘rates’ in parentheses indicate the inverse of the time (in hours) that the current was applied, simulating the conditions (current densities, periods of applied current and thus total charge transferred) of the rate test experiments. An excerpt of the results is shown here from the fifth cycle at C/5 until the end of the test; the test was performed twice with the same overpotentials observed in both cells. At low current densities, below 1 mA (2C), the overpotential is below 100 mV; however, at 5 mA (10C) the overpotential rises to 200 mV and increases to about 700 mV at 100C. b, c, Relative changes in lithium diffusion as a function of open-circuit voltage (Voc; b) and open-circuit voltage versus closed-circuit voltage (Vcc; c) from the GITT measurements. The plot in c shows the ‘thermodynamic’ electrochemical profiles at C/20 with a 12-h rest period at each point, reaching a full discharge in approximately one month. In Nb16W5O55, the fastest diffusion is observed from the dilute limit to Li4.5(5)Nb16W5O55, dropping by two orders of magnitude in the low-voltage window, where more than 1 Li+/TM are incorporated. The GITT data indicate that the second electrochemical region of Nb16W5O55 is broader than typically observed in a two-phase reaction, but the observed discontinuity in the DLiL–2 values in this region suggests that Nb16W5O55 approaches two-phase behaviour. The average diffusion coefficient in Nb18W16O93 is similar to that of Nb16W5O55. The bronze also displays discontinuities in DLiL–2 at 2.1, 1.85 and 1.7 V. In both phases, the low-voltage region (below 1.25 V, well over 1 Li+/TM) is characterized by an increasing overpotential and suppressed kinetics.

2. ### Extended Data Fig. 2 Lithium diffusion from 7Li PFG NMR spectroscopy.

a, The lithium diffusion coefficients of LixNb16W5O55 (x = 6.3, 8.4) and LixNb18W16O93 (x = 3.4, 6.8, 10.2) were measured in the temperature range 333–453 K (Table 1). The filled (85% signal contribution) and empty (15% signal contribution) symbols for Li6.3Nb16W5O55 correspond to the observed two-component diffusion (see main text and Methods). In most cases, the error bars (2σ, obtained from the fit) are smaller than the sizes of the points. b, Stimulated-echo PFG sequence used to measure 7Li diffusivities, showing both radiofrequency (7Li) and magnetic-field-gradient (Gz) pulses. Here, the gradient pulse duration (tg) includes the up-ramping, time on and down-ramping of the opt composite gradient pulses. During Δ, a short spoiler gradient was used to remove residual transverse magnetization. c–g, Representative 7Li decay curves showing the normalized NMR signal intensity as a function of gradient strength for the bronze structures Li10.2Nb18W16O93 at 453 K (c), Li6.8Nb18W16O93 at 453 K (d) and Li3.4Nb18W16O93 at 453 K (e) and the block structures Li6.3Nb16W5O55 at 353 K (f) and Li8.4Nb16W5O55 at 383 K (g). Black circles represent experimental data points and red lines represent mono- (c–e, g) or biexponential (f) fits to the data by the Stejskal–Tanner equation. Biexponential fits to all samples except Li6.3Nb16W5O55 did not lead to improved fits over those obtained with monoexponential fits. The poor signal-to-noise ratio of Li6.3Nb16W5O55, even with more than 100 mg of electrode sample, did not allow us to explore alternative models beyond the mono- and biexponential models, such as models considering the effect of anisotropic diffusion, which manifests as subtle differences in echo attenuation94. h, A representative one-dimensional 7Li NMR spectrum (Li8.4Nb16W5O55, static, 403 K) showing the shift (δ 7Li) region and lineshape.

3. ### Extended Data Fig. 3 Nb16W5O55 X-ray absorption spectroscopy.

ad, LixNb16W5O55 ex situ (see Supplementary Fig. 14) Nb K edge XANES spectra (a, b) and derivative spectra (c, d). e, f, Operando Nb K edge XANES spectra of Nb16W5O55 and 22 discharge spectra, with each successive spectrum at about +11 mA h g–1 (e), and operando derivative spectra (f; 23 spectra shown, 5 colours labelled). The pre-edge and main edge are at about 18,991 and 19,004 eV, respectively. Spectra in b and d are vertically offset by 0.2 and 0.02, respectively, for clarity. gl, LixNb16W5O55 ex situ W Lii edge XANES spectra (g, h), derivative spectra (i, j) and second-derivative spectra (k, l). Spectra in h, j and l are vertically offset by 0.5, 0.2 and 0.4, respectively, for clarity. mp, LixNb16W5O55 ex situ W Li edge XANES spectra (m, n) and derivative spectra (o, p) near the W Li absorption edge. The pre-edge is at about 12,104 eV and the main edge at about 12,117 eV. Spectra are vertically offset by 0.5 in n and by 0.02 in p for clarity.

4. ### Extended Data Fig. 4 Nb18W16O93 X-ray absorption spectroscopy.

a–d, LixNb18W16O93 ex situ Nb K edge XANES spectra (a, b) and derivative spectra (c, d). The pre-edge and main edge are at about 18,991 and 19,004 eV, respectively. Spectra in b and d are vertically offset by 0.2 and 0.02, respectively, for clarity. e–j, LixNb18W16O93 ex situ W Lii edge XANES spectra (e, f), derivative spectra (g, h) and second-derivative spectra (i, j). Spectra in f, h and j are vertically offset by 0.5, 0.2 and 0.4, respectively, for clarity. k–m, LixNb18W16O93 ex situ W Li edge XANES spectra (k, l) and derivative spectra (m, n) near the W Li absorption edge. The pre-edge is at about 12,104 eV and the main edge at about 12,117 eV. Spectra are vertically offset by 0.25 in l and by 0.02 in n for clarity.

5. ### Extended Data Fig. 5 Lattice evolution of Nb16W5O55 and Nb18W16O93 upon lithiation.

a, b, Absolute lattice parameter values resulting from Rietveld refinement of operando diffraction data, analogous to that of Fig. 4c, Nb16W5O55 (a) and Fig. 4d, Nb18W16O93 (b). Error bars show the standard deviation of each parameter, as estimated from the fits (approximately equal to the symbol height in b). Shading distinguishes the different structural regions. For Nb18W16O93, the second stage (two-phase region) contains two sets of lattice parameters. c, Structure evolution of Nb16W5O55 as a function of rate. At high rates, the lithiation reaction becomes inhomogeneous (Extended Data Fig. 6) and cannot be fitted with a single set of lattice parameters over the whole electrode. The shaded grey area for the 5C data corresponds to the range of each unit-cell parameter. d, Structure evolution of Nb18W16O93 as a function of rate. The mechanism of LixNb18W16O93 lattice evolution does not appear to be strongly rate-dependent. The reaction extends further at lower rates within the same voltage range, partly because of a smaller overpotential at lower current densities (Extended Data Fig. 1a).

6. ### Extended Data Fig. 6 Solid-solution structure evolution and reversibility of Nb16W5O55.

ac, Profile evolution of selected reflections at C/2 and d, the corresponding electrochemical discharge profile. eg, Profile evolution of selected reflections at 5C and h, the corresponding electrochemical discharge profile. a, e, ($$60\bar{4}$$). b, f, overlapping (110) and ($$11\bar{1}$$). c, g, ($$10\hspace{2.77626pt}0\bar{1}$$) (left) and ($$60\bar{9}$$) (right), with smaller overlapping reflections. The evolution in each case commences analogously; as lithiation increases, the structure evolution at high rate becomes inhomogeneous and the contraction of the ac block is not fully realized. i, The overlapping (110) and ($$11\bar{1}$$) reflections shift smoothly to larger d spacing (smaller 2θ) for the entire sample at C/2, whereas in j, there is substantial intensity across a range of 2θ values at high rate. This inter-peak intensity is shown more clearly in the inset of j. The intensity range represents a range of lattice parameters (Extended Data Fig. 5c) and an inhomogeneous solid-solution reaction probably resulting from inhomogeneous lithium transport and concentration gradients within the electrolyte33,34. Diffraction patterns are shown from 0 to about 145 mA h g−1 (ascending), which corresponds to the full 5C discharge and partial C/2 discharge. k, l, Structure reversibility over a full electrochemical lithiation/delithiation cycle of Nb16W5O55 at C/2. In k, the ($$14\hspace{2.77626pt}0\bar{9}$$)/(407) (left) and (020) (right) reflections are displayed over a full operando synchrotron X-ray diffraction discharge–charge cycle from 3.0 to 1.0 V with multi-redox (de)lithiation. The symmetry of discharge and charge is apparent, although a small amount of lithium remains in the structure after charging (Extended Data Fig. 7).

7. ### Extended Data Fig. 7 Electrochemical profile evolution and early-cycle lithium retention of Nb16W5O55 and Nb18W16O93.

af, There is an activation process on the first cycle for Nb16W5O55 (a–c) and Nb18W16O93 (d–f), which extends to a much smaller extent in the next several cycles, leading to an increase in intercalation voltage at the first ‘plateau-like’ feature and a broadening of the dQ/dV peaks (b, c, e, f). The phenomenon is associated with a retention of lithium in the structure. The occurrence of this activation phenomenon is structure-independent, indicating that it may have an electronic origin. The electrochemical data in a–f were collected at C/5 but the phenomenon is also observed at other rates. g, Diffraction patterns of Nb16W5O55 before lithiation and after the first charge from operando measurements at C/2. h, Lattice parameters of the pristine and charged structure show changes that indicate that some lithium was retained in the structure after charging the electrode, commensurate with the changes from first- to second-cycle electrochemistry.

8. ### Extended Data Fig. 8 Operando X-ray diffraction patterns of Nb18W16O93 from 1C to 10C.

al, The profile evolution of selected reflections and the corresponding electrochemical discharge profile is shown at 1C (ad), 5C (eh) and 10C (il). a, e, i, (040); b, f, j, overlapped (230) and (160); c, g, k, (001) (left, initially) and overlapped (330) and (190) (right, initially). The evolution in each case is similar in mechanism and differs in the extent of reaction, consistent with the electrochemical profiles. mx, The two-phase region of LixNb18W16O93 for x ≈ 6.6–10.2 as a function of rate. Selected regions of the diffraction pattern at shown at 1C (mp), 5C (qt) and 10C (ux). m, q, u, (040); n, r, v, overlapped (230) and (160); o, s, w, (001) (left, initially) and overlapped (330) and (190) (right, initially). The arrows from the electrochemical discharge profiles in p, t and x correspond to the first and last diffraction patterns collected in the two-phase region (about 29–45 mA h g–1), as indicated. Metastable intermediates that can occur at high rates in two-phase systems such as LiFePO4 would be difficult to distinguish in this system owing to the small compositional and structural changes that are associated with the Li6.6Nb18W16O93 to Li10.2Nb18W16O93 two-phase reaction.

9. ### Extended Data Fig. 9 Prospective lithium positions and pathways in block-type and bronze-type ternary niobium tungsten oxides and electrochemical comparisons to binary niobium oxides.

a, b, Bond valence sum maps of Nb16W5O55 (a) and Nb18W16O93 (b) depict stable lithium positions and pathways according to bond valence energy landscape calculations performed in 3DBVSMAPPER121. Calculations were performed over a fine grid with 149 × 20 × 116 points computed for Nb16W5O55 and 61 × 184 × 20 points computed for Nb18W16O93 along their respective crystallographic axes. Isosurface levels are shown at ‘2.0 eV’, which is a parameter used to visualize ionic pathways and not a quantitative estimation. The bond valence sum and bond valence energy landscape provide an indication of lithium positions and diffusion pathways in complex or novel systems and have shown good agreement with experimental and computational investigations of structure and dynamics121,122,123. c, Possible intrablock lithium positions for Nb16W5O55 based on LixMO3 in the low-lithium regime, before it undergoes intercalant-induced distortion. d, e, Block phases Nb16W5O55 and H-Nb2O5 are compared on the basis of Li+/TM (d) and gravimetric capacity (e) on the third cycle at C/5. f, g, Bronze-like phases Nb18W16O93 and T-Nb2O5 are compared on the basis of Li+/TM (f) and gravimetric capacity (g) on the third cycle at C/5.

## Supplementary information

1. ### Supplementary Information

This file contains seventeen supplementary figures and three supplementary tables that support the niobium tungsten oxide synthesis, characterization, and mechanistic analysis.

### DOI

https://doi.org/10.1038/s41586-018-0347-0