Pre-zeolite framework super-MIEC anodes for high-rate lithium-ion batteries

Zeolites, Prussian blue analogues (PBAs), and metal–organic frameworks (MOFs) rely on surface-like internal pore diffusions, which have generically low activation barriers to enable the rapid uptake of chemical species. Here we show that Wadsley–Roth oxides (WROs) with pore diameters of 2.5 Å o d


Introduction
Mixed ionic and electronic conductors (MIECs) are widely used in solid oxide fuel/electrolysis cells, batteries, electrochromic devices, neuromorphic computing, etc. [1][2][3][4][5] Lithium-ion battery (LIB)'s cathode and anode must be MIECs, and need to store large quantities of Li 0 on-demand in the lattice interior, accompanied by the redox of certain host elements, often transition metals (TMs). Rapid Li + and e À transport (thus effective Li 0 ''atomic'' diffusivity D Li ) should be maintained at all depths of discharge (DODs), which is the most crucial factor for fast charging and high discharge power batteries used in heavy transportation (e.g., boats, trains, and trucks), industrial equipment (e.g., cranes), household products, and electrical-grid regulation. [5][6][7][8][9][10][11][12][13][14][15] Drawing an analogy to superionic solid electrolytes, we define super-MIECs in the LIB context to mean having an effective activation energy Q of D Li inside the MIEC of less than 250 meV or about 10 k B T at T = 300 K, which would give D Li B n Li h Li 2 e À10 B 5 Â 10 À13 m 2 s À1 , for a typical hopping trial frequency n Li = 1 THz and a hopping distance h Li = 1 Å. This means in t = 100 seconds (the typical duration it takes to fill up a gasoline car), or in a full charge/discharge cycle at 36C, the diffusion distance L = (2D Li t) 1/2 = 10 mm, which is the desirable battery electrode particle size for slurry coating. Note that a super-MIEC with a large DOD range would allow fully dense, single-crystal particles of 10 mm size to be used without requiring electrolyte infiltration into polycrystalline secondary particles, greatly increasing the volumetric energy density and reducing the side reactions. This is superior to nano Li 4 Ti 5 O 12 (the most widely studied and commercialized anode for fast charging 16 ) with low D Li . Some reported oxide anodes can be viewed as super-MIECs 12,17-19 (especially for Nb-based materials with 41 mm size, Table S1, ESI †), which can support a full charge/discharge cycle within several minutes. The dual demands of large ''Li adsorption'' per volume and maintaining D Li Z 5 Â 10 À13 m 2 s À1 put stringent requirements on transition-metal oxide MIECs. Across material classes, diffusion barriers generically less than 250 meV are frequently encountered only in surface diffusion. Diffusion in tight-fitting atomic channels for the Li + cation (Shannon ionic diameters of 1.18 Å for 4-fold coordinated, 1.52 Å for 6-fold coordinated and 1.84 Å for 8-fold coordinated Li + ), such as inside LiFePO 4 , typically gives Q values ranging from 270 meV to 500 meV. 20 By tight-fitting, we mean that the diffusing species at some point strongly interact with the host on two or more sides (e.g., in the LiCoO 2 lattice; stoichiometric LiCoO 2 in a fully lithiated state has sluggish Li + diffusivity), unlike surface diffusion where the mobile species mainly interact with the host on one side. If the host framework has a large enough pore diameter 4 2 Å, then this allows for the Li + to adsorb on the side wall of the pore, rather than be constrained at the center of a channel. Adsorption/uptake of external species is well-known in the realm of framework materials and molecular sieves. For example, zeolites have internal pore diameters ranging from B3 Å to 10 Å, which can take up large quantities of H 2 O (molecular diameter 2.8 Å), H 2 , and CO 2 molecules. 21 The word ''zeolite'' originated from its hygroscopicity, which literally meant ''stones that give off water steam when heated''. 22 The open aluminosilicate framework of zeolite A often gives entropic elasticity and a negative coefficient of thermal expansion (CTE) when dehydrated, which however turns positive in its fully hydrated state, when the pore is filled up. 23 Wellknown framework crystals also include Prussian blue analogues (PBAs) and metal-organic frameworks (MOFs). These open frameworks often have a negative CTE, tolerance for a wide variety of molecules inside the pores, and surface-diffusion-like rapid mass transport for molecules that can fit inside the pores, making them ideal gas storage media. [24][25][26] Some PBAs and MOFs are even electronically conductive, making them super-MIECs. [27][28][29] But these large-pore open frameworks, even though generally showing diffusivity 45 Â 10 À13 m 2 s À1 , will not store too many alkali metal atoms per volume due to the excessively large pore sizes, and thus are not optimal for high-volumetric-energy density fast-charging electrodes.
As H 2 O is the second smallest simple molecule (slightly larger than NH 3 ), a basic question is if it is possible to exclude molecular adsorption, while still allowing alkali ions to have surface-like adsorption and diffusion on the sidewalls of the ''internal pore surfaces'' of the framework structures. In this work, we define a pre-zeolite framework to mean crystals with percolating open pores with a diameter smaller than 2.8 Å, and therefore exclude water adsorption and generally all molecular adsorptions, while allowing surface-diffusion-like transport of Li + . We are mainly interested in multi-valent TM-containing pre-zeolite frameworks, and will show that these frameworks, if electronically conductive, are generally all super-MIECs. We will demonstrate the structural and chemical design criteria for such pre-zeolite frameworks, in particular Wadsley-Roth structures containing multi-valent Nb, W, and Ti and having an anionto-cation ratio (ACR) around 2.5 (mostly between 2.33 and 2.8).
While some of the compositions have been shown before, the universality and robustness of these open-pore design rules provide a cornucopia of surface-diffusion-like high-capacity super-MIECs, that would allow 10 mm sized single crystals with 430C charging/ discharging rates, rivaling fossil-fuel vehicles in the charging rate.

Results and discussion
Wadsley-Roth pore with 2.5 Å o d o 2.8 Å is a sufficient condition for ultrafast Li + diffusion We selected a representative Wadsley-Roth oxide (WRO) H-Nb 2 O 5 , and conducted first-principles calculations to clarify the physical picture of surface-like diffusion. As shown in To study the storage and migration mechanism of Li + in the dilute lithiated state, we added one Li atom into a 1 Â 3 Â 1 supercell (containing 84 Nb and 210 O). Pore P6 (the same as P3 by symmetry) was picked randomly and Li + was placed on the interstitial site in the center of a pore surrounded by 12 O (consisting of six square planes, including two within the a-c plane perpendicular to the b axis and four parallel to the b axis on the sidewalls of the cage; see the schematic for a cubic cage in Fig. 1 where lattice distortions were neglected for simplicity). In conventional transition-metal oxides, such high-symmetry interstitial sites are typically preferred sites for Li + storage, for example, octahedral sites in layered LiCoO 2 and lithiated Li 4 Ti 5 O 12 (Li 7 Ti 5 O 12 ) and tetrahedral sites in spinel LiMn 2 O 4 . However, this does not apply to H-Nb 2 O 5 , whose interstitial site (pore) is so large that a pore-centered Li + would automatically relax to a sidewall and adopt a square planar geometry (such as sites Li 1 and Li 2 in Fig. 1(a)). We refer to such one-sided behavior as ''surface adsorption'' like. Such a storage mechanism has been reported in ReO 3 experimentally using the diffraction technique 30 and in Nb 2 TiO 7 31 and Nb 12 WO 33 32 by atomistic simulations. We next used the climbing image nudged elastic band (NEB) method to calculate the migration path and energy barrier for Li + hopping between two neighbouring square-planar sites from one on the sidewall to the one in the a-c plane. We found the former has an energy of 130 meV lower than the latter, with a forward migration barrier of 190 meV and a backward barrier of 60 meV (Fig. S1b, ESI †). Such low barriers are surfacediffusion like, which supports the super-MIEC behavior. Yet a more striking feature is the saddle-point configuration, where the coordination number of Li + decreases from 4 in the squareplanar ground-state (see the schematic Li + migration pathway from sites Li 1 to Li 2 in Fig. 1(a)) to a remarkably low coordination of 3 (marked as Li SD ), which is rare for lattice diffusion in crystals (The critical role of the ultra-low coordination number at the saddle point of Li + hopping was not realized in previous studies. 31,32 ). We recall that surface diffusion can take place via low-coordination-number adatoms which reside on adsorption sites on the surface plane, and it does not cost much elastic energy because these adatoms can veer into the vacuum halfspace (with zero moduli) instead of the solid. The analogy is thus: the saddle-point Li + veers into the pore with a large free volume like an adatom, and this minimizes elastic energy penalty, which typically applies to the crowded saddle-point configuration and slows down diffusion due to steric hindrance (for example, octahedral-to-tetrahedral-to-octahedral Li + diffusion in LiCoO 2 ). Therefore, one can justifiably call Li + diffusion in Wadsley-Roth H-Nb 2 O 5 surface-like diffusion, and these ''internal surfaces'' are distinguishable from physical surfaces as the pores are not large enough to allow even the smallest molecules like H 2 O to enter. The latter was proved by thermogravimetric analysis for wet WRO powders (Fig. S2, ESI †), where no weight loss occurred above 100 1C (surface water was mostly removed below 100 1C). Indeed, WROs have been reported as  3 , and (f) metal-organic frameworks IRMOF-1 and (g) IRMOF-16 with varying pore sizes. Marked in (b)-(g) are the cation-cation distances, which divided by 2 1/2 gives the characteristic pore size. WROs are termed ''pre-zeolite frameworks'' due to their considerably smaller pore size than zeolites with 3-10 Å, while PBAs and MOFs may be considered as ''zeolite-like'' and ''post-zeolite'' frameworks. bulk intercalation pseudocapacitors, and the bulk Li + diffusion kinetics share a similar dependence on the charge/discharge rate as the one observed for electric double-layer supercapacitors. 33 From a crystallographic perspective, WROs are related to the ReO 3 structure 34 ( Fig. 1(c), which differs from the parent perovskite structure ABO 3 , e.g., SrTiO 3 in Fig. 1(b), by removing the A-site cation) by condensing some of the corner-sharing octahedra in ReO 3 to edge-sharing ones on the boundaries of ''blocks''. 35 This results in better structural rigidity and d-d orbital coupling. (Compared to corner-sharing ones, edge-sharing octahedra give shorter metal-metal distance and suitable orbital orientations-d xy , d yz , and d xz point to edge centers-for d-d coupling). Meanwhile, there are still sufficient numbers of corner-sharing octahedra inside the ''blocks'' 35 that form pores for Li + surface-like diffusion. For cubic SrTiO 3 and ReO 3 , one may estimate the pore size by the cation-cation distance (marked in Fig. 1(b)-(g)) divided by 2 1/2 , thus being 2.79 Å for SrTiO 3 and 2.69 Å for ReO 3 . A similar pore size is also noted in H-Nb 2 O 5 , for example, 2.70-2.71 Å for P6 ( Fig. 1(d)), despite the lattice distortion and lower symmetry. Such pores allow for adatom-like Li + storage and internal surface-like diffusion, and are even large enough for interstitial Na + and K + storage (but not Na + /K + surfacelike diffusion), as cubic NaNbO 3 and KNbO 3 have cage sizes of 2.84 Å and 2.87 Å (e.g., see atomic structures at materialsproject.org 36 ), respectively. Therefore, the off-center Li + storage and Li + migration without steric hindrance are both verifiable, distinguishable features. Meanwhile, the framework oxygen can be replaced by other groups if large pore sizes are desired. The examples beyond LIB applications include replacing the O 2À for corner-sharing octahedra by (CN) À in Fe(CN) 3 ( Fig. 1(e)) and other PBAs for Na + battery cathodes 37 and proton battery cathodes (H 3 O + storage in the cage 29 ), and by larger chain-molecules in mesoporous metal-organic frameworks such as IRMOF-1 ( Fig. 1(f)) and IRMOF-16 ( Fig. 1(g)), with varying pore sizes for gas storage and catalysis. 34 A WRO is thus identified as a prezeolitic framework that does not have strong hygroscopy, but can take up a large amount of Li atoms electrochemically.
The calculations above rationalize the superfast Li + transport in a model WRO. The insights into surface-like diffusion, as opposed to diffusion in tight-fitting channels of lithium intercalation oxides, should apply to all open pore structures with pre-zeolitic pore diameters 2.5 Å o d o 2.8 Å. We thus hypothesize that the Wadsley-Roth structure by itself, with a pore channel locally similar to ReO 3 , has already ensured facile bulk diffusion. Thus in real batteries, bulk diffusion in these compounds is likely not the bottleneck. The real challenge is in the boundary conditions, where side reactions and solid electrolyte interphases (SEIs) at the oxide surface build up impedance and degrade the battery during both early and prolonged cycles. As long as the 2.5 Å o d o 2.8 Å pores are maintained, we can tune the compositional space to optimize anode-electrolyte interactions to improve the cyclability. Finally, the large free volume gives rise to other structural and physical properties, such as anomalously low coefficient of thermal expansion (CTE) and formation of planar defects, which suggest soft phonon modes that could buffer strain and facilitate transport during electrochemical cycling. These shall be investigated in the following sections.  9,17,38,39 For all the samples, we heat-treated the powders at high temperatures (1100-1125 1C) to grow them into micron-sized single crystals. The powders obtained are phase-pure (shown by X-ray diffraction (XRD) in Fig. 2(a)) with crystal sizes shown by scanning electron microscopy (SEM) in Fig. 2(b), (c), (e) and (f). Using synchrotron powder XRD data ( Fig. 2(d)), we analyzed the crystal structure of NWT926 and confirmed that it is a new phase with large pores and monoclinic symmetry (crystal structure in the inset of Fig. 2(d); data listed in Table S2, ESI †). To shed light on the free volume in the crystal lattice (critical for surface-like diffusion), we calculated the average atomic volume (defined as the supercell volume divided by the number of atoms in the supercell) of H-Nb 2 O 5 , NPO, NTO, NWO, and NWT926, which are in the range of 13.2-14.4 Å 3 . The average atomic volume has been shown to correlate well with the CTE, a phonon-controlled property, and could be abnormally low or even negative in framework materials like zeolites. 40 The obtained values in our materials are close to the critical value that leads to a crossover from positive to a negative CTE (Fig. S3, ESI †). (Local average atomic volume at the pores of WROs can also be estimated from the geometry by neglecting lattice distortion and assuming a cubic ReO 3 -type local structure. For example, for P6 of H-Nb 2 O 5 in Fig. 1(e), it is around 3.82 3 /4 = 13.9 Å 3 .) We measured the CTEs of our powder samples using in situ XRD measurements ( Fig. S4-S8, ESI †) conducted at 100-650 K, and the linear CTE a was obtained from the refined primary-cell volume V 0 (T). Compared to the CTE database for 260 compounds centered around B7 Â 10 À6 K À1 (Fig. S9 and Table S3, ESI †), H-Nb 2 O 5 , NPO, NTO, NWO, and NWT926 indeed all have negative or close-to-zero CTEs ( Fig. S4-S8, ESI †). Of particular interest is NWT926 which has negative CTEs along all three lattice axes ( Fig. 2(g)), which are rare and termed triaxial negative CTEs. The reason may be that the transverse vibrations of oxygen atoms in the M-O-M (M = Nb, Ti, W) with increasing temperature lead to the rotation of corner-sharing MO 6 polyhedra, giving rise to the contraction. 24,41,42 Such anomalously low CTEs, similar to other open frameworks such as zeolites, PBAs, and MOFs, indirectly support the notion of surface-like adsorption and diffusion in all WRO super-MIECs. We next measured the electrochemical performances of H-Nb 2 O 5 , NPO, NWT926, and NWT944 as LIB anodes in half cells and compared them with NTO and NWO references. By definition, super-MIEC materials should have high intrinsic electronic conductivity to assist electronic percolation. Therefore, we minimized the usage of conductive carbon in the composite electrode and tested all the anodes with 485 wt% active materials. At a low , and a stable charge-discharge profile upon cycling ( Fig. S10-S12, ESI †). When tested at higher rates (for both charge and discharge) up to 16 000 mA g À1 (roughly 200B300C), we found all six materials have good capacity retention (for the capacity at 200 mA g À1 , Fig. 2(j)). At 6000 mA g À1 , the capacity retentions are 450%, offering 116 mA h g À1 capacity for H-Nb 2 O 5 , 146 mA h g À1 for NPO, 142 mA h g À1 for NTO, 125 mA h g À1 for NWO, 110 mA h g À1 for NWT926, and 138 mA h g À1 for NWT944. These correspond to B60C, which would satisfy many high-rate applications, shifting the rate-limiting consideration to the cathode or electrolyte in the full cells. D Li is the composite of the Li + ion and e À polaron diffusivities in ambipolar diffusion theory. First, the electronic conductivities of Nb 2 O 5 and Li 0.1 Nb 2 O 5 were calculated to be 1.0 Â 10 À6 S m À1 , and 6.6 S m À1 , respectively, by measuring the 2probe electronic resistance, area, and thickness of the pellet   Fig. 2(h) and a particle size analyzer in Fig. S16d, ESI † were used to obtain an agglomeration size of D 50 = 49.0 mm) and again tested its electrochemical performance (216 mA h g À1 capacity at 200 mA g À1 , Fig. S16b, ESI †). Remarkably, H-Nb 2 O 5 -B shows superior rate capability at different mass loadings ( Fig. 2(i)), which is similar to H-Nb 2 O 5 ( Fig. 2(j)), despite B10 times larger grain size, and it can deliver an impressive capacity of 110 mA h g À1 at 6000 mA g À1 (B60C). The D Li value of H-Nb 2 O 5 -B from GITT measurements is also 410 times larger than H-Nb 2 O 5 . Therefore, we conclude that WROs have high D Li in electrochemical cells and superior rate performance, which is relatively insensitive to oxide compositions but more sensitive to SEIs. The formation and growth of SEIs depend on the electro-chemo-mechanical interactions between active electrode materials and the electrolytes, which affect the rate capability and cycling stability of the anode and the full cell.  We therefore evaluated the cycling stability of the synthesized super-MIEC anodes in half cells (i.e., with excess electrolyte and Li reservoir). As shown in Fig. 3(a), when cycled at 6000 mA g À1 (12 mA cm À2 , B60C), NTO, NPO, and NWO rapidly decay and have capacity retentions of 69%, 47%, and 36% after 1000 cycles, respectively. H-Nb 2 O 5 and NWT926 have better cycling stability, with 100% and 80% capacity retentions after 1000 cycles. In comparison, NWT944 shows remarkably improved stability ( Fig. 3(b)), with 62% capacity retention after 7000 cycles (5.4% decay per 1000 cycles). To exclude capacity decay drivers from the other battery components, we replaced the Li metal counter electrode and the electrolytes after 7300 and 11 500 cycles (severe degradation of the Li metal electrode is shown in Fig. S17, ESI †). 56% capacity retention over 15 000 cycles has thus been achieved in NWT944. On the other hand, by tailoring the morphology and increasing the particle size, we show in Fig. 3(c) that H-Nb 2 O 5 -B has 5% higher capacity after 1000 cycles than its initial capacity (attributed to the activation process occurring in electrochemical cycling 43 ), and it also has capacity retentions of 77% after 3000 cycles, and 60% after 5800 cycles when cycled at 4000 mA g À1 (similar areal current density of 12 mA cm À2 ), representing improvements over H-    Fig. S18, ESI †). Super-MIEC anodes compete with Li 4 Ti 5 O 12 in high-rate applications. We compared the gravimetric energy density and electrode density of super-MIEC anodes in Fig. 3(d), which gives volumetric energy density in the range of 1128B1550 W h L À1 (at 6000 mA g À1 , Fig. 3 (More detailed comparisons on characterized particle size, electrode density, initial Coulombic efficiency, capacity, rate retention, average voltage, energy density, and cyclability are listed in Tables S4 and S5, ESI †.) These values are much higher than 658 W h L À1 for Li 4 Ti 5 O 12 and 127 W h L À1 for meso-carbon microbeads, which are the commercially prevailing high-rate anodes. Through trial and error, it appears that Nb is the baseline element to form the Wadsley-Roth oxide structure, W is beneficial for increasing the crystal density and energy density, and Ti is beneficial for enhancing the structural stability. We note that in many applications, the cycle life is an important metric, which sets NWT944 and H-Nb 2 O 5 -B to be the best candidates among the super-MIEC anodes investigated.

Other lattice-structural and microstructural features
As an anode must host and disgorge a great amount of excess lithium reversibly, a robust atomic structure is required. As shown by the top surfaces and cross-sections of H-Nb 2 O 5 , NPO, and NWT944 electrodes (Fig. S19, ESI †), the single-crystal WRO particles did not fracture after cycling. This means the particles could survive the mechanical stresses and stress-corrosion cracking during cyclic electrochemical loading, which would benefit the long-term cycling stability. Indeed, the scanning  transmission electron microscopy -high-angle annular darkfield (STEM-HAADF) image in Fig. 4(a) shows well-ordered crystal lattices without point defects (corresponding atomic structure for the Nb sublattice in Fig. 4(b)). However, over a larger length scale of a few hundred nanometers, extended defects including stacking faults, nanotwins, and ripplocations 49 were found in the WRO single crystals (Fig. 4(c), (d) and Fig. S20, ESI †). Different levels of diffuse scattering exist in the nanobeam electron diffraction patterns (Fig. 4(e) and (f)) at different locations of Fig. 4(d), and mapping of stacking fault density in Fig. 4(g) and (h) further indicates spatial variations. As these planar defects are formed in pristine H-Nb 2 O 5 synthesized from high-temperature heat treatment, the observations indicate their relatively low formation energies. It is in contrast with the high formation energy of point defects, but consistent with the fact that the large free volume and low CTE in WROs are a result of low polyhedral packing density and their collective twisting/relaxation. In addition, strain mapping by four-dimensional scanning transmission electron microscopy (4D-STEM) at 10 nm spatial resolution ( Fig. 4(g)) visualizes the lattice at the mesoscale, with a standard deviation of 1.53% for e xx , 1.44% for e yy , 0.20% for e xy , and 0.12% for the rotation angle y (Fig. 4(i)-(l)).
Pair distribution function (PDF) analysis was conducted on unlithiated (Nb 2 O 5 in Fig. 5(a)) and slightly lithiated (Li 0.1 Nb 2 O 5 in Fig. 5(b)) H-Nb 2 O 5 powders using synchrotron X-ray total scattering. Experimentally, the raw total scattering data were collected and then transformed into the real-space PDF G(r). 50,51 For Nb 2 O 5 , we noted the measured G(r) significantly deviates from the calculated one from the ''perfect'' H-Nb 2 O 5 structure ( Fig. 1(a)), especially at large r up to 20 Å. We thus conducted reverse Monte Carlo (RMC) simulations to fit the experimental data (calculated G(r) shown in Fig. 5(a), (b)) and to analyze the structure. As shown by simulated atomic structures (Fig. 5(c) Fig. S21, ESI †). To compare the structure before and after lithiation, we focused on G(r) data at 1.5B4.0 Å (Fig. 5(d)), especially the B1.9 Å double peaks for nearest Nb-O bonds, the B3.3 Å double peaks for nearest Nb-Nb bonds for edge-sharing NbO 6 octahedra, and the B3.8 Å peak for Nb-Nb bonds for corner-sharing NbO 6 octahedra. When lithiating from Nb 2 O 5 to Li 0.1 Nb 2 O 5 , we found minimum changes in B1.9 Å Nb-O bonds (Fig. 5(f)) and B3.8 Å Nb-Nb bonds ( Fig. 5(h)) but shortened Nb-Nb bonds at B3.3 Å (Fig. 5(g)). It indicates the pore structure is relatively robust and does not involve much structural change upon lithiation. To confirm, we conducted STEM-HAADF on Li 0.1 Nb 2 O 5 , which provides contrasts for light-element O. As shown in Fig. 5(i), the lattice is again well ordered, yet slight distortions on the O sublattice are notable. Quantitative analysis of the atomic positions (Fig. 5(j)) shows 0.004 Å (with a standard deviation of 0.008 Å) displacements in the Nb sublattice and 0.02 Å (with a standard deviation of 0.02 Å) displacements in the O sublattice, and some O atoms are displaced further up to B0.45 Å. These results agree with the diffraction and RMC data.

Conclusions and outlook
We have explained why the WROs have fast Li + diffusion ability and abnormally low CTEs. The low topological constraints per atom and large free volume in the crystal lattice should be the fundamental cause of soft phonons, low CTE, low-coordination-number Li + storage, and surface-like diffusion, similar to other open frameworks such as zeolites, PBAs, and MOFs. But unlike those frameworks that take up molecules, the WRO frameworks with 2.5 Å o d o 2.8 Å can only take up atoms like Li. The phonon anomalies are expected to influence the preexponential factor of the Arrhenius-type diffusivity. There is literature on D Li measured by pulsed-field-gradient nuclear magnetic resonance (PFG NMR) spectroscopy, which is a bulk measurement and not sensitive to SEIs. In Fig. S2a, ESI † of ref. 9, in Li x Nb y W z O (5y+6z)/2 , we note that larger activation energy gives higher D Li values, because a large pre-exponential term not only compensates but also dominates (Table S6, ESI †), signifying perhaps collective Li motion in pores.
Another question is why Nb (group-5, period-5) is essential in forming WRO super-MIEC anodes. Turning back to the parent structure ReO 3 , partial condensation of the cornersharing octahedra to edge-sharing ones is necessary to enhance the structural rigidity (to suppress extensive phase transitions during electrochemical cycling; unalloyed ReO 3 has multiple phase transitions upon lithiation, which leads to slow kinetics, voltage hysteresis, and poor cycling 52 ) and d-d coupling for better electron transport. Therefore, an ACR around 2.5 is expected, which requires a +5 average cation valence, and thus group-5 elements (Zr/Hf likes to be +4, Mo/W likes to be +6). Meanwhile, as the octahedron majority should be maintained, the fact-that V 5+ is so small that it prefers to be coordinated by four neighboring O 2À as is the case for various V 2 O 5 polymorphs; while Ta 5+ is so large that it prefers mixed TaO 6 / TaO 7 occupancy as is the case for L-and H-Ta 2 O 5 -sets group-5 and period-5 Nb 5+ to be the best candidate for the major cation. Other elements (Ti, W) can be alloyed into the lattice, to tune the bulk redox and surface stability.
Finally, we provide some guidance on the search for other candidates in the multi-element compositional space.  35,53 Taking the limiting cases as n -N and known small n compositions (e.g., n = 3 for Nb 2 TiO 7 in Group A, n = 7 for Nb 22 O 54 in Group B, n = 8 for Nb 24 TiO 62 in Group C, n = 3 for Nb 9 TPO 25 in Group D, n = 3 for Nb 12 WO 33 in Group E, and n = 4 for Nb 16

Conflicts of interest
The authors declare that they have no competing interests.

Synchrotron high energy XRD and PDF measurements:
The high energy XRD and PDF data were collected using the 11-ID-C beamline at the Advanced Photon Source (APS) of Argonne National Laboratory (ANL), with the Xray wavelength of 0.1173 Å. Si (113) single crystal was used as a monochromator for an X-ray beam at 105.7 keV. In a typical data collection, the NWT926 powder sample (for high energy XRD measurement), H-Nb 2 O 5 , and Li 0.1 Nb 2 O 5 powder samples (for PDF measurements) were loaded into a 3 mm capillary with a data acquisition time of 20 minutes. The background was extracted from the same empty capillary. A two-dimensional Perkin-Elmer detector was used to record the scattering patterns in transmission mode. Fit 2D software was applied to calibrate the scattering patterns with the CeO 2 standard sample and integrate the 2D patterns into 1D profiles 3 . The G(r) function was computed by Fourier transform of reduced structural function (F(Q), up to 17.6 Å −1 ) with PDFgetX2 software 4 . The Rietveld method was used to determine the crystal structure of NWT926 using Fullprof software 2 . A monoclinic C2/c unit cell was built to describe the XRD pattern. The pseudo-Voigt peak-shape function was used to fit the full width at half maximum (FWHM) with fitting parameters U, V, W, and Gaussian/Lorentz ratio. Due to the structural complexity of NWT926, not all the atomic information can be extracted. The atomic coordination values in Table  S2, ESI † were inherited from the pristine NWO structure with undistorted octahedra, while the occupancies were calculated based on the stoichiometric ratio. The current structural model can describe the XRD pattern reasonably well. The resolution of the collected XRD data is insufficient to provide complete atomic information, and singlecrystal diffraction experiments need to be carried out to determine the exact structure of NWT926 in the future studies to fully resolve the structure.

Morphology and structural characterizations:
A scanning electron microscope (SEM, MERLIN VP Compact) was used to characterize the morphology. A Ga-focused ion beam (Ga-FIB) system (FEI Helios G4) was used to lift out a thin TEM lamella from H-Nb 2 O 5 particles. The H-Nb 2 O 5 particles were protected by Pt deposition before lift-out. During the thinning process, the energy of the ion beam was reduced from 30 to 16, 8, 5, 2, 1 keV step by step. TEAM-1, a double aberration-corrected TEM operating at 300 kV at the national center for electron microscopy S3 (NCEM) in the Lawrence Berkeley National Laboratory, was used to collect atomic-resolution STEM-HAADF images. Image pairs with orthogonal scan directions were collected and a MATLAB code developed by Ophus et al. 5 was used to correct the nonlinear scan distortion. The 4D-STEM experiments were performed on an FEI Titan operating at 300 keV. A 10 µm condenser C2 aperture and a convergence angle of 0.12 mrad were chosen to form a nanosized electron beam with a full width half maximum (FWHM) of about 12 nm. The scan step size was 10 nm. The camera length was 480 mm. The py4DSTEM package 6 was used for the analysis of 4D-STEM data.

Method of stacking fault mapping:
Conventional STEM-HAADF images cannot depict the location of SFs accurately due to the co-existence of multiple structural information. To better map the SFs/twins in the sample, a new method is developed. For regions with stacking faults (SFs), diffuse streaks between Bragg peaks will show up in the nanobeam electron diffraction (NBED) patterns. Because the streaks due to SFs tend to make the Bragg peaks more elliptical, the averaged aspect ratio (a/b, where a and b are the length of the long axis and length of the short axis, respectively) of Bragg peaks in an NBED pattern can be correlated to the relative density of SFs. When there are more SFs, a/b is smaller. While there are no SFs, a/b is close to 1. To calculate a/b, windows of 20 pixels by 20 pixels in size are chosen whose center overlaps with each Bragg peak. The standard deviation along the streak direction and perpendicular to the streak direction is calculated as a and b, respectively. py4DSTEM package 6 is used to find the location of each Bragg peak.

Methods of displacement analysis:
The cross-sectional Li 0.1 Nb 2 O 5 TEM specimen was prepared using a Thermo Fisher Helios 600 focused ion beam (FIB)/SEM microscope. The specimen was first coated with 10 nm carbon using Denton DV502A Evaporator to minimize the beam damage and charging effects. Additive protective layers were deposited by combining e-beam and ion-beam deposition in the FIB instrument, including an e-beam-deposited 100 nm Pt layer and an ion-beam-deposited 1 m carbon layer. The sample was thinned step by step by lowering ion voltages from 30 kV to 2 kV and currents from 0.92 nA to 89 pA. The surface damage caused by FIB is further removed by argon ion milling using a Fischione 1051 TEM Mill at room temperature with a voltage of 100 V and angle of 7°. The high-resolution HAADF images are taken in a Thermo Fisher Themis Z-STEM at MIT with an acceleration voltage of 200 kV. The potential atom positions were obtained by identifying the local maxima of the HAADF image. After manual correction of the misidentified positions, a Gaussian function was used to fit a 5×5 pixels area around each local maxima, which generated a list of 2D coordinates of the atoms from the experimental image. Then, a unit cell was selected by identifying and averaging the smallest repeating unit of the atomic structure. A reference lattice was generated by periodically repeating the averaged unit cell in two in-plane directions of the image. Finally, the displacement vectors were calculated by comparing the experimental atomic coordinates with the reference lattice.

Characterizations of H 2 O adsorption/desorption:
Thermogravimetric analysis (TGA) was carried out using NETZSCH-STA 449 F3 with a heating rate of 10 o C min −1 under an air atmosphere. The powder samples were suspended in deionized H 2 O for 10 mins, then collected and dried at 60 o C for 5 h.

Characterizations of chemical compositions and surface areas:
Because of the low volatility of Nb, Ti and W elements, the ratios of transition metal (TM) were determined by the ratios of the raw materials, and the ratio of TM/O was determined by balancing the valance (as the synthesis was conducted at oxidation environment, we assumed +5 for Nb, +6 for W, and +4 for Ti). Inductively coupled plasma mass spectroscopy (ICP-MS, iCP QC, Thermo Fisher Scientific) measurements were also conducted to confirm the ratios of TM. The specific surface area was measured by Autosorb-iQ2-MP (Quanta Chrome) and calculated following the Brunauer-Emmett-Teller (BET) method.

Electrochemical measurements Preparation of half cells:
To prepare the composite working electrodes, active materials, conductive carbon, and binder were mixed with a specific weight ratio to form a homogeneous slurry, spread on commercial Al foils (for H-  Table S7, ESI †.

Model and simulation
First-principles calculations: Spin-polarized first-principles calculations were conducted on Vienna ab initio simulation package (VASP) using projector augmented-wave (PAW) method with Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation (GGA) 7-10 . We used PAW potentials with 1 valence electron for Li, 13 valence electrons for Nb, 6 valence electrons for O, and plane-wave cutoff energy of 520 eV. Li storage in H-Nb 2 O 5 was simulated by adding 1 Li to the described sites in a 1×3×1 supercell containing 84 Nb and 210 O. Convergence was considered as reached when residue atomic forces were less than 0.05 eV Å −1 . Li + migration was simulated in the same supercell, using the climbing image nudged elastic band (NEB) method 11 . The convergence of NEB calculations was set to be reached when the residual atomic forces were less than 0.1 eV Å −1 . The Brillouin zone was sampled using the Monhorst-Pack scheme with a 1×1×1 k-point mesh. Atomic structures were visualized and plotted using VESTA 12 Fig. S1 (a) Atomic structure of block structure oxide H-Nb 2 O 5 . Tunnels marked as P1 to P14 within one unit cell. (b) Calculated migration barrier for Li + between two neighboring square-planar sites from one on the sidewall to the one in the a-c plane within the P6 tunnel.        ,000 cycles at 6,000 mA g -1 , the surface of NPO electrodes (c) before and (d) after 1,000 cycles at 6,000 mA g -1 , cross-sectional images of NPO electrodes (e) before and (f) after 1,000 cycles at 6,000 mA g -1 , the surface of NWT944 electrodes (g) before and (h) after 7,300 cycles at 6,000 mA g -1 .