Energy storage mechanisms in vacancy-ordered Wadsley – Roth layered niobates †

Wadsley – Roth (WR) crystallographic shear structures demonstrate high energy and power densities as Li-ion battery anode materials. We report the (de)lithiation behavior of two WR-derived layered niobates: NaNb 3 O 8 and KNb 3 O 8 . Both demonstrate multi-electron (Nb 5+ /Nb 3+ ) redox on the ﬁ rst discharge, reacting with z 5 mol Li per mol A Nb 3 O 8 . Li intercalation in NaNb 3 O 8 is dominated by Li-di ﬀ usion kinetics and evolution of the interlayer structure, with Li initially ﬁ lling octahedral sites near the interlayer space to draw the layers together to form a (2 (cid:1) 2) N WR structure. This average structure change pushes Na ions into the square channels, blocking fast Li di ﬀ usion down the square channels that provide the fast Li-ion conduction in most WR materials. Upon charge, Li ions incorporated into the octahedral WR sites (ordered vacancies in the layered structure) are extracted, revealing a new, reversible Li site for additional capacity in WR-like materials. The behavior of KNb 3 O 8 is similar, but has additional hysteresis associated with its larger counter-cation. While neither layered niobate matches the demonstrated performance of WR materials, by studying them, we identify a route for increased capacity in WR-like frameworks. Additionally, we identify the important role of Li di ﬀ usion kinetics and counter-cations in the cycling behavior of WR-derived structures.

The parent structure of WR phases, ReO 3 [Fig.1a, International Crystal Structure Database (ICSD) 16810 (ref.21)], is formed of [ReO 6 ] octahedra in a corner-sharing arrangement.ReO 3 has poor charge storage properties due to correlated rotations of the [ReO 6 ] octahedra that occur upon Li insertion (Fig. 1b). 223][24][25] In WR materials, ReO 3like units form (m Â n) N blocks [e.g., the (3 Â 5) N in H-Nb 2 O 5 , Fig. 1c]. 12The blocks terminate at shear planes where the octahedra in the ReO 3 -like units are linked through their edges to neighboring blocks.These shear planes provide rigidity to the framework, preventing correlated rotations of the octahedra upon lithiation, during which diffusion is predominantly 1D, down square channels in the centers of the blocks. 7,8,23,26As a result, structural changes across a wide operating composition range are mostly limited to subtle expansions and contractions of lattice parameters. 7,8Because the WR framework structure does not change signicantly during lithiation, Li ions retain similar intercalation geometries across different states of charge that result in fast diffusion. 26,27Motivated by their excellent anode properties, we investigated the electrochemical energy storage behavior of variations on the WR structure using complex niobates with layered and orderedcation-vacancy motifs (Fig. 1d-f).
We report the lithiation mechanism, Li-ion diffusion pathways, and average structure evolution in layered niobates NaNb 3 O 8 and KNb 3 O 8 .These are derived from a hypothetical body-centred tetragonal (2 Â 2) N WR structure 28 by replacing a plane of framework Nb atoms with ordered vacancies, resulting in Nb 3 O 8 sheets with a combination of edge-and corner-sharing octahedra (Fig. 2a,b).Large K + or Na + countercations reside near the ordered vacancies and prop the sheets apart to form a layered framework [general example in Fig. 1f, specic cases in Fig. 2, ICSD 31994 (ref.29) and ICSD 202400, 30 respectively].The counter-cation size and preferred coordination impact the layer stacking, both in terms of interlayer distance and stacking sequence.In KNb 3 O 8 , adjacent Nb 3 O 8 layers are off-set from one-another by c 2 , giving AB stacking, while NaNb 3 O 8 has AA stacking, approximately halving the unit cell volume (Fig. 2).][33] To the best of our knowledge, this is the rst reported electrochemical cycling of NaNb 3 O 8 .In the previous electrochemical studies of KNb 3 O 8 , asymmetric cycling proles indicate a different path upon discharge and charge, as has been observed for other K-Nb-O compounds. 34,35Incorporation of specialized carbon additives and reduction of particle dimensions have been reported and show improved rate capabilities and capacity retention, 32,33 but the underlying intercalation mechanisms have not yet been discerned, and are our focus here.
The electrochemical energy-storage behavior of NaNb 3 O 8 and KNb 3 O 8 as Li-ion electrodes was analyzed using a combination of ex situ and operando X-ray diffraction (XRD), high-resolution transmission electron microscopy (HRTEM), solid-state nuclear magnetic resonance (NMR) spectroscopy of 93 Nb, 23 Na, and 7 Li nuclei, and hybrid-exchange densityfunctional-theory (DFT) calculations.The work reveals new insights into Li diffusion kinetics, structural transformations, and charge-storage mechanisms in WR-derived materials with layered and vacancy-ordered modications and countercations.

Synthesis and initial structures
Adapting previously reported molten-salt syntheses, 36,37 we produced KNb 3 O 8 by heating K 2 CO 3 and Nb 2 O 5 in molten KCl at 800 C for 5 h.High-resolution synchrotron XRD showed agreement with the published Amam structure. 29However, there appeared to be peak intensity mismatch for several reections, including some at low momentum transfer, Q (Fig. 3a).TEM micrographs indicate rectangular platelets with particle dimensions varying as a function of crystallographic direction (Fig. 4a-c).SAED patterns show well-dened diffraction spots without streaking, consistent with a regular stacking arrangement and the absence of stacking faults.
Rather than extended defects, the apparent peak intensity mismatch was in fact systematic index-dependent width mismatch for several reections, which resulted from anisotropic particle size along crystallographic directions.Integrated intensity of synchrotron XRD data was overall well-captured using Rietveld renement with an anisotropic size broadening model (based on linear combinations of spherical harmonics) and an isotropic strain parameter contributing to the Lorentzian line shape (Fig. 3).The dramatic shape anisotropy evident in micrographs is reected in rened average dimensions for the principal axes of 263.9 nm (h00), 78.6 nm (0k0), and 6511 nm (00l).It is important to note that the method for extracting these quantitative results gives only the average value of particle size along each direction, and does provide information on the distribution of particle sizes.The relative rened particle dimensions are consistent with TEM micrographs, which together indicate the platelets' shortest dimension in the stacking direction (lattice parameter b) and their longest dimension along the chains of edge-sharing polyhedra (lattice parameter c) (Fig. 4).The XRD t with isotropic size broadening and isotropic strain is shown for comparison in Fig. 3b, which highlights the index-dependent peak broadening.
9][40] While these studies did not model microstructure effects in their diffraction data, it is likely that the deviations resulted from anisotropic particle size, preferred orientation, or a combination thereof.These various distributions of peak intensities per reection character suggest a dependence of morphology on synthesis route (e.g., molten salt, solid state, hydrothermal).NaNb 3 O 8 was prepared from KNb 3 O 8 using so chemical methods, with intermediate hydrate phases. 30In several repetitions of the synthesis, there were variations in the phase purity of intermediate hydrates that resulted in a minor fraction of unidentied phase(s) (# 5% by volume) in addition to NaNb 3 O 8 (Fig. 3c).High-resolution XRD of NaNb 3 O 8 revealed a similar index-dependent variation of peak width as that observed for KNb 3 O 8 , and the general features were modeled using a similar combination of isotropic strain and anisotropic particle size broadening.SEM (Fig. 4d) shows a larger dispersity of particle dimensions for NaNb 3 O 8 than KNb 3 O 8 .This dispersity, as well as the impurity, leads to less condence in the quantitative particle size from renement due to the overall poorer t.However, the particles once again had their shortest dimension in the stacking direction (lattice parameter b) and their longest in the direction of the polyhedral chains (lattice parameter c).Additional complexity in the analysis of NaNb 3 O 8 may also arise from a higher degree of strain, which could be introduced during the low temperature ion-exchange process, though we are not able to quantitatively determine this with the dataset.
Further details about Rietveld analysis of KNb 3 O 8 and NaNb 3 O 8 are provided in the Methods and ESI † sections, including expanded plots of XRD data and ts (Fig. S1 and S2 †).
Average structure characterization is complemented by the local structure perspective from solid-state nuclear magnetic resonance (NMR) spectroscopy.Despite the change in stacking sequence upon ion-exchange from K + to Na + , and associated decrease in interlayer spacing, the intralayer structure remains very similar, as reected in the rened average structure as well as the similar features in the 93 Nb NMR spectra (Fig. 5a and b).For KNb 3 O 8 and NaNb 3 O 8 , the 93 Nb central-transition spectra, collected using the quadrupolar Carr-Purcell-Meiboom-Gill (QCPMG) sequence, span about 2000 ppm at 9.4 T at room temperature (Fig. 5a and b).The two Nb sites in the structures can be t using two quadrupolar lineshapes with numerical simulations guided by CASTEP PBE DFT calculations [41][42][43][44] and t to within 15% of the calculated quadrupolar coupling magnitudes.The local coordination is consistent with the structure models wherein the Nb(1) site in the double-width chain is considerably more distorted than Nb(2) in the single-width chain (see calculated and experimental NMR parameters in Tables S3 and S4, † respectively).For NaNb 3 O 8 , the observed 23 Na quadrupolar coupling (0.52 (5) MHz; the uncertainty value specied in parentheses refers to a single standard deviation associated with the tting procedure) is far smaller (< 40%) than the calculated value (1.36 MHz), which suggests fast roomtemperature Na-ion dynamics (Fig. 5c and d). 45,46

Cycling
Loose-powder electrodes of the active material mixed with conductive carbon additive (SuperP) were assembled into homebuilt Swagelok cells for electrochemical cycling against Li metal anodes.As structural evolution rather than absolute cycling performance is the focus of this work, cell construction and cycling parameters were not optimized.The assembled half cells were cycled at slow rates, reacting with 1 mol Li per mol  6).On the rst discharge (Fig. 6), both have a plateau near 1.5 V corresponding to a chemical formula of approximately LiANb 3 O 8 .This high-potential plateau is followed by a sloped region, over which an additional z2 mol Li react.A second plateau near 1 V is followed by another sloped region where an additional z2 mol Li react.
With the applied cycling conditions, both compounds react with about 6 mol Li per formula unit (or 2 mol Li per mol Nb) on the rst discharge.However, as reported by See et al., conductive carbon additives have considerable contributions to capacity during cycling to low potentials. 47This effect, in combination with solid electrolyte interphase (SEI) formation, undoubtedly contributes to the measured capacity at low potentials.Future consideration of these materials in applied studies should certainly consider a higher minimum potential limit, but here we focus on identifying charge-storage mechanisms, including at low potentials.
Beyond the rst cycle, there is a reversible capacity of z3 mol Li per mol KNb 3 O 8 (or 1 mol Li per Nb) and z2 mol Li per mol NaNb 3 O 8 , which slowly fades with each cycle in these unoptimized cells (Fig. 6).Second and later discharge cycles have a small plateau and a long sloped region, with the majority of the capacity coming from the latter.Charge cycles begin with a sloped region, which contributes less than half of the reversible capacity, and the majority of the charge capacity takes place over a plateau near 1.5 V.The difference in charge distribution over slopes and plateaus between discharge and charge indicates asymmetric processes, as has been observed for other intercalation electrode materials, including compositionally-related KNb 5 O 13 , 35 in which the order of Li sites lling and unlling varies.
The most notable difference in the cycling of KNb 3 O 8 and NaNb 3 O 8 is the voltage hysteresis of the high potential plateau between charge and discharge.For KNb 3 O 8 , the high potential plateaus are separated by about 0.3 V, as opposed to about 0.1 V for NaNb 3 O 8 .This difference in potentials indicates a difference in the charge-storage processes between these two compounds despite their structural and chemical similarities.To understand this difference, the previously mentioned asymmetric cycling proles, and generally how these compounds store charge, we detail below the structural evolution at various states of charge using ex situ and operando synchrotron X-ray scattering and DFT, complemented by ex situ NMR and electron microscopy.
2.3 NaNb 3 O 8 structural evolution with cycling 2.3.1 First discharge.Operando XRD shows a shi of the 010 and 020 reections to higher momentum transfer, Q, during the rst discharge, indicating a contraction of the b lattice parameter.This is most prominent during the high  potential plateau from 0 mol Li to 0.75 mol Li (1.45 V) (Fig. 7).Over the rst plateau, there is a discontinuous change of the 002 reection position to lower Q (Fig. 7c), indicating an expansion of the c lattice parameter.In contrast, ex situ XRD at a similar state of charge shows no apparent evolution from the starting material (NA, discharged to 1.4 V, and NaNb 3 O 8 , respectively, in Fig. 8, ex situ and operando plotted together in Fig. S3 †).Aer the rst plateau, the remainder of the operando discharge reveals only minor changes to the average structure, including some further shis in peak positions.Both operando and ex situ XRD show qualitatively consistent structures for the rst discharge products from cycling (NB, discharged to 0.1 V) (Fig. S3 †).Based on their initial and nal positions, the 010 and 002 reections reveal an z9% reduction in lattice parameter b (the stacking direction) and a 3.5% increase in c during the rst discharge, with an intermediate change in operando XRD data at the end of the high potential plateau (Table 1).
The difference between operando and ex situ XRD results for the intermediate discharge product (approximately LiNaNb 3 O 8 ) are resolved by DFT calculations of the energetics and kinetics of Li site lling.The DFT calculations identify two low-energy sites for Li in NaNb 3 O 8 under dilute conditions, labeled X and Y (Fig. 9c and d).Site X is a ve-fold coordinated squarepyramidal 'pocket' in the Nb 3 O 8 layers (Fig. 9a and c) and site Y is a distorted octahedral site in the interlayer space (Fig. 9b  and d).
8]13 To the best of our knowledge, octahedral Li ion sites have not been reported previously in WR-like materials.In the WR phases studied for Li intercalation, framework transition metal (TM) ions typically occupy all of the possible octahedral sites in the defect fcc O 2À sublattice. 48t a composition of LiNaNb 3 O 8 , the structure with Li ions lling site X is more stable than with Li ions lling site Y by 0.082 eV per formula unit (f.u.) NaNb 3 O 8 .The calculated lattice parameters (Table 2) show the framework structure is relatively unchanged with Li ions in the low-energy X sites, consistent with ex situ XRD (Fig. 8 and S3 †).In contrast, lling metastable Y sites leads to a contraction of the interlayer space (lattice parameter b) (Fig. 9b), in agreement with operando XRD data (Fig. 7 and S3 †).We nd the interlayer contraction occurs because the Li ions in Y sites (tucked into voids behind Na + ) bond to O ions across layers, drawing the Nb 3 O 8 layers closer together and pushing Na ions into the square channels.
Using DFT, we compared the kinetics of Li diffusion to ll X and Y sites.Li diffusion in NaNb 3 O 8 is one-dimensional and takes place along the c direction, either between or within the Nb 3 O 8 layers (Fig. 9e and f).To ll X sites, Li ions must move within the Nb 3 O 8 layers either via 'cross-block' hops (path 1), which have an activation barrier of 0.74 eV, or through the square channels via a metastable high-energy square-planar site 'W' (Fig. S13 †), overcoming a barrier of 1.04 eV (path 2) (Fig. 9h).The high barrier for the 'cross-block' hop is due to Li-Nb repulsion, while the still higher barrier to move along the square channel results from Li-Na repulsion: Li + must move past Na + to migrate down the channels.
In the interlayer space, Li moves between Y sites following a zig-zag pathway (path 3) through two metastable distorted tetrahedral sites (denoted 'Z') (Fig. 9e and g).The activation Table 1 The positions of the 010 and 002 reflections of Li x NaNb 3 O 8 at various states of charge, and the their corresponding interplanar spacing, d hkl , show the progression of these key features of the average structure during discharge barrier for mobility in the interlayer space is 0.29 eV, much lower than for paths 1 and 2 within the Nb 3 O 8 layers.Diffusion in the interlayer space is therefore kinetically favorable, and leads to the formation of the metastable intermediate cycling product with a contracted interlayer distance and Li in higher energy Y sites, as was observed at the end of the rst plateau in operando XRD.In ex situ experiments, Li ions relax to occupy the thermodynamically favorable X sites, allowing the interlayer separation to expand back to a similar distance in the pristine material.We note that Y and Z sites cannot be occupied simultaneously under dilute Li conditions, since the two sites face-share; occupation of a Y site will push an adjacent Li from a Z site into the next Y site.However, under non-dilute conditions, Z sites adjacent to Y sites can be lled, which is discussed in greater detail later.
At the end of the rst discharge, ex situ and operando XRD are consistent and indicate a nal structure with Li in interlayer and intralayer sites.Rietveld renement of the ex situ discharge product (NB) using DFT-predicted Li 5 NaNb 3 O 8 (with all X, Y and Z sites lled) captures the major reections (Fig. 10).This is in qualitative agreement with our rst discharge capacity (z6 mol Li) with some additional capacity resulting from side reactions at low potentials, a combination of reactions with carbon and solid electrolyte interphase formation. 47Additionally, NMR indicates the reduction of all Nb (discussed in detail later), which gives rise to electronic changes in the material and the resulting Nb spectra at the discharged state.Together, the XRD, DFT, and NMR results strongly suggest a complete reaction, or at least homogeneous reactivity, of NaNb 3 O 8 , even as loosepowder electrodes.The remainder of the rst charge takes place over a plateau at 1.5 V, aer which ex situ XRD indicates a nal average structure nearly identical to pristine NaNb 3 O 8 (ND, Fig. 8) despite some Li remaining in the structure (from NMR, the estimated composition is Li 2.2 NaNb 3 O 8 , see ESI Table S5 † for details).This suggests a recovery of the original, larger interlayer spacing, with the remaining Li predominantly occupying 'pocket' X sites.Based on our observations of the metastable intermediate discharge product, it is unclear if the ex situ charge product has again evolved between cycling and structural characterization.It is worth noting that operando XRD over only the high potential plateau shows electrochemical and structural reversibility of this interlayer contraction and expansion, as well as a more symmetric galvanostatic prole (Fig. S5 †).While the high potential process appears to have symmetric (de)lithiation, the difference in the nal composition between the two charge products does not allow for extrapolation of the nature of the charge product following a deeper discharge.
2.3.3Later cycling.In subsequent cycles, reversible capacity matches that of the rst charge.Ex situ XRD to deep on the second cycles shows the same interlayer contraction as the rst (NB and NF, Fig. 8).Based on our conclusions from experiment and theory regarding the rst charge product, we propose Li that lls the X sites during the rst discharge remains there through subsequent cycling, with reversible (de) insertion of Li in the Y and Z sites contributing to the reversible capacity of z2 mol Li.
This assignment of X sites as the primary origin of irreversible capacity is supported by our observations for cycling over only the high potential features (using a minimum potential of 1.4 V).Operando XRD over this potential range shows contraction and expansion of the interlayer space, indicating Li (de) insertion into the interlayer Y site and only mild, gradual capacity fade without deep discharge.Likewise, we propose that the reversible capacity in second and later cycles for NaNb 3 O 8 arises from the (de)insertion of Li in Z and Y sites.

NMR of Li
x NaNb 3 O 8 .The local structure during cycling was investigated with 93 Nb, 23 Na, and 7 Li NMR.Upon Li insertion, the two 93 Nb resonances corresponding to the two symmetry-independent sites in NaNb 3 O 8 do not change position or shape.Instead, they decrease in intensity, until there is no visible feature upon deep discharge (at x z 5) (Fig. 11a, B).This loss of signal can be attributed to the rapid relaxation of the 93 Nb nuclei that results from unpaired electrons when the transition metal ions are reduced (to d 1 and d 2 ) upon lithiation, though it cannot be distinguished whether this stems from Curie (localized) or Pauli (delocalized) paramagnetism.On charge, the two 93 Nb signals return, indicating that the local structure of some Nb is recovered upon delithiation.As z2 mol Li remain at the end of charge, Nb in the vicinity of residual Li remain in a reduced state and are not visible owing to rapid nuclear relaxation.Upon reaction with Li, the 23 Na resonance broadens and additional intensity is observed at higher frequencies (Fig. 11b,  A and B).The full-width at half maximum (FWHM), 2 ppm in pristine NaNb 3 O 8 (12.5 kHz MAS), increases to 16 ppm when fully discharged.Upon charge, the 23 Na resonance does not return to its original narrow lineshape and, unlike the Nb local environment, is irreversibly altered from that of the pure compound.This suggests that some Li remains in the structure aer charge, affecting the Na local environment.
Another insight from NMR is that no residual 93 Nb signal, nor sharp 23 Na signal, is present at the end of discharge, indicating a relatively homogeneous and complete reaction rather than the presence of unlithiated particles or an inhomogeneous distribution of composition across domains.Insights from 7 Li are limited due to the broad lineshape and narrow shi range; however, two apparent features are (i) the broadened signal at deep discharge and (ii) a resonance that comes in at À7.5 ppm (Fig. S12 †).The correlation between line broadening and Li concentration could be due to increased homonuclear dipolar coupling, an increase in the number of sites, or slower kinetics, which limit signal averaging.The negatively shied resonance is outside the range for diamagnetic Li, but has been observed in other Nb-based oxides, such as WR structure Li x TiNb 2 O 7 , where it was correlated with electron localization.In WR materials, rapid Li-ion diffusion typically occurs down the square channels, hopping from window-to-window site with low barriers of z0.3 eV to 0.4 eV. 8,26In pristine NaNb 3 O 8 , Li-Na repulsion results in a large barrier of 1.04 eV for Li diffusion  down the square channels (Fig. 9h).Calculations for Li diffusion along the same path at a composition of LiNaNb 3 O 8 with the interlayer sites lled show an increased barrier of 1.48 eV (Fig. S14 †).The interlayer contraction causes the Na ions to be pushed into the square channels, further impeding the mobility of Li along this path.Li ions must instead diffuse along the channels at the edges of the blocks, by 'cross-block' hops.To ll X sites, Li must move along channels between [NbO 6 ] octahedra (Fig. 9a, cyan channel), whereas to ll Z sites, the Li ions must move along channels between [LiO 6 ] and [NbO 6 ] octahedra (Fig. 9a, gold channel).
Previously published DFT calculations for TiNb 2 O 7 revealed the activation barrier for cross-block hops increases as the charge of the framework cation increases, due to greater electrostatic repulsion. 8This observation follows a similar principle to the models of Li diffusion in disordered rocksalt compounds, where the activation barrier varies depending on the number of faces the mobile Li shares with Li vs. TMs. 49,50We therefore expect Li diffusion in Li x NaNb 3 O 8 to be easier between Z sites, down channels formed by [LiO 6 ] and [NbO 6 ] octahedra, in which the mobile Li will experience a smaller electrostatic repulsion moving past octahedra containing Li + than Nb (4+/5+) .

Voltage prole from DFT calculations.
To examine the site lling mechanisms under dilute conditions and for x > 1 in Li x NaNb 3 O 8 , we calculated the energetics of different Li orderings in the range 0 < x # 5, constructed convex hulls, and computed three possible voltage proles to compare with experiment.
The thermodynamic ground-state hull results from lling X sites between 0 < x # 1 (Fig. 9a), followed by Y sites between 1 # x # 2 (Fig. 13c, structure D), then the remaining X sites between 2 # x # 3 (Fig. 13c, structure G), and nally Z sites between 3 # x # 5 (Fig. 13c, structure I).The calculated voltage curve based on these ground-state hull structures (blue curve in Fig. 13b) shows a plateau at 1.6 V for 0 < x # 2 with a slight step at x ¼ 1, followed by a large step at x ¼ 2 (to 0.7 V), a smaller step at x ¼ 3 (to 0.5 V), and a plateau to x ¼ 5.This is different than the experimental voltage curve, which shows a clear drop just before x ¼ 1, followed by two solid-solution-type regions when 1 # x # 5.
Such a difference between the experimental and computed voltage from the ground-state hull is additional evidence that Li diffusion kinetics determine the site lling in NaNb 3 O 8 , with metastable Y sites lled before more stable X sites.Two alternative calculated voltage curves are presented in Fig. 13b (red and orange), based on lling Y sites to x ¼ 1, corresponding to the operando XRD product, followed by lling of sites X and Z. From the metastable LiNaNb 3 O 8 structure, lling X sites down alternate channels (Fig. 13c, structure E) results in a low-energy structure, however, the step in the computed voltage curve at x ¼ 1 is relatively small.From LiNaNb 3 O 8 , lling Z sites instead involves Li ions moving down the block-edge channels bordered by [LiO 6 ] and [NbO 6 ].This results in a higher-energy structure (Fig. 13c, structure F), but a larger drop in the voltage curve at x ¼ 1 that better reproduces the experimental voltage.
Even so, none of the calculated voltage proles match with experiment perfectly.The experimental voltage prole between 1 # x # 5 is sloping, indicating solid-solution-type behavior that cannot be captured in the DFT calculations, which are limited to enumerating congurations within a small unit cell.We speculate that the site-lling mechanism for 1 # x # 3 involves the preferential lling of Z sites, based on the step in the voltage curve and the easier diffusion along channels to access Z sites, but we cannot rule out some diffusion to ll X sites.For 3 # x # 5, a second solid-solution mechanism occurs, lling the remaining empty X or Z sites along the shear planes.At a composition of Li 5 NaNb 3 O 8 , Na ions are pushed into the center of the square channels, as all the pocket sites surrounding the central cavity are occupied by Li ions (Fig. 13c, structure I).

KNb 3 O 8 structural evolution with cycling
The structural evolution of KNb 3 O 8 generally shows similarities to NaNb 3 O 8 , but a number of differences arise, which likely stem from the different stacking sequence for the two materials in their pristine state.
During the rst discharge of Li x KNb 3 O 8 , operando XRD shows a decrease in intensity of the 020 reection concurrent with the growth of a new reection at slightly higher Q (z7 nm À1 ) (Fig. 14a and b).The correlated exchange of intensity between these peaks suggests a two-phase transformation upon lithiation of KNb 3 O 8 .Based on our ndings for NaNb 3 O 8 , we interpret the new reection as corresponding to a smaller b lattice parameter arising from a reduction of the interlayer spacing.The position of this new reection is similar to that of the nal 010 reection for LiNaNb 3 O 8 , in further support of this proposed change.Also similar to the Na analogue, we see a gradual shi of the 002 reection to lower angle, indicating an expansion of the c lattice parameter.Similar trends in average structure evolution have been observed during electrochemical cycling of KNb 3 O 8 as a Na-ion electrode. 31s was found for NaNb 3 O 8 , we nd discrepancies between ex situ and operando characterization of KNb 3 O 8 cycling products.From operando XRD, we observe a two-phase coexistence at the end of the rst plateau (x z 1) (Fig. 14).However, ex situ XRD shows an average structure nearly identical to the pristine niobate (KNb 3 O 8 and KA, Fig. S6 †).Likewise, electron diffraction reveals discrete 020 spots at this intermediate state of charge, showing no evidence of a second stacking sequence (Fig. S9 †).However, we do nd domains within crystallites, separated by low-angle boundaries (z14 , Fig. 15a and b).The domains themselves maintain crystalline order and a single, well-ordered stacking sequence.
Over the remainder of the discharge, operando XRD shows relatively minor average structure changes, and at the end of the discharge some intensity remains at the original 020 reection position, while the new, higher Q reection is more intense (Fig. 14).The ex situ discharge product shows three peaks in this low Q range (KB, Fig. S6 †), suggesting different stacking sequences are present.The dominant stacking reection in the operando discharge product supports a reduction of the b lattice constant, as seen for Li 5 NaNb 3 O 8 .TEM of the rst discharge product shows lighter-contrast channels across crystallites and ordered stacking, with no sign of multiple stacking sequences within the crystallite (Fig. S9 †).While this is inconsistent with XRD data for the discharge product, the two techniques differ by their statistical sampling (i.e., selected particles suitable for electron diffraction and imaging in TEM versus ensemble average in XRD).Thus, one possible interpretation of this discrepancy is that the various reections associated with the stacking direction (and lithium composition) in XRD arise from variation between, rather than within, particles.Alternatively, such a phenomena could be the result of Li composition gradients within particles, as has been observed in V 2 O 5 . 51er several cycles, what appeared as channels aer the rst discharge resemble cracks in TEM micrographs (Fig. 15c, le).However, high-resolution TEM shows some of these regions have an amorphous structure, rather than being true cracks (Fig. 15c, right).The difference in density, rather than the atomic species present, results in the contrast between the channels and crystalline regions surrounding them.Electron energy loss spectroscopy (EELS) reveals that K, Nb, and O atoms are present in these amorphous channels (Fig. S10 †).We propose these channels are the result of defect aggregation (e.g., dislocations) to alleviate strain associated with structure evolution upon (de)lithiation or as a result of relaxation from a higher energy metastable product.Given the similar crystallographic orientation of these channels and the low-angle boundaries in the partial discharge product, it is possible that those boundaries are the origins of the channels observed upon continued cycling.
Upon charge, operando XRD shows the initial average structure is partly recovered, albeit with a decrease of peak intensity and some of the discharge product (with a smaller interlayer spacing) remaining.The former is likely  a consequence of reduced domain sizes, as observed in TEM for discharge products.The latter is consistent with ex situ XRD insofar as that various interlayer spacings (corresponding to different Li compositions) co-exist in the sample (KD, Fig. S6 †).The multiple peaks in the XRD aer discharge and charge indicate an incomplete reaction and heterogeneous products (chemically and structurally), in contrast to NMR and XRD indications of homogeneous NaNb 3 O 8 cycling products.This could have several origins, e.g., the generation of phases with sluggish Li diffusion or a loss of electrical conductivity across amorphous channels, each of which could result in electrochemically inactive regions or particles.
Building upon the similarity of the initial structures and average-structure changes indicated by XRD reections, especially the 0k0 and 002, we propose that the dominant structure evolution during (de)lithiation is the decrease (increase) of the interlayer spacing.There are several open questions regarding this change, for example, does such a change to the interlayer spacing involve a change of the stacking sequence (from AB to AA, Fig. 2a and b)?If so, this could involve staging or relaxation to intermediate stacking sequences, which would be supported by the multiple low Q reections in ex situ XRD.
Stacking changes in NaNb 3 O 8 are associated with Li between the layers, and result from the reduction of the interlayer spacing.In the pristine materials, we see that the counter-cation size and preferred coordination determine the interlayer spacing.Accordingly, it seems that intercalated Li between the layers has a similar effect in the cycling products of both compounds.In KNb 3 O 8 , however, the high potential plateau has more hysteresis between discharge and charge than NaNb 3 O 8 , suggestive of a more extensive atomic structure change over this feature during cycling, perhaps even a change of stacking sequence in addition to interlayer spacing.A similar reduction of interlayer spacing (indicated by a new reection near 7 nm À1 ) is observed in operando XRD over only the high potential plateau, as is the relatively large voltage hysteresis (Fig. S8 †).For KNb 3 O 8 , the average structure evolution is not as reversible as for the Na analogue, evidenced in the various low angle Bragg peaks in ex situ diffraction as well as the aggregation of defects to form amorphous channels within particles.However, we cannot conrm whether average-structure changes and their irreversibility are the cause or result of separate domains formed within particles during cycling.

Further discussion & context
It is interesting to compare how Li intercalation proceeds in layered, vacancy-ordered NaNb 3 O 8 , summarized in Fig. 16 (and KNb 3 O 8 ), and conventional WR materials.7][8] Some coupling and correlation between Li in different channels, identied in Li 8 Nb 12 WO 33 and Li 8 Nb 14 W 3 O 44 , changes the nature of the diffusion from purely 1D. 26n NaNb 3 O 8 , diffusion does not occur down the square channels, which are blocked by Na ions.Instead, Li ions initially move down channels in the interlayer space, pathways that are absent in conventional WR phases.In the interlayer space, Liions ll the ordered octahedral framework vacancies, forming a WR framework with (2 Â 2) N blocks.These octahedral 'vacancy' sites do not exist in conventional WR materials, where all octahedral sites not face-sharing with tetrahedral cations are occupied by framework cations (typically transition metals).Liion insertion sites in conventional WR materials are squareplanar or square-pyramidal, except for some 'in-tunnel' sites for Li in TiNb 2 O 7 under dilute conditions. 8Filling framework vacancies is a new charge-storage mechanism for WR-type materials.This results in high theoretical capacities for Li 5 NaNb 3 O 8 and Li 5 KNb 3 O 8 of z300 mA h g À1 .As the octahedral framework vacancies are lled upon Li intercalation in these layered niobates, the interlayer space contracts as Li ions bond to O in adjacent layers.The layer contraction pushes Na (or K) ions further into the square channels.With the Na ions further into the square channels, Li diffusion down these channels is even more strongly impeded.Li ions are forced to move down shear planes through 'cross-block' hops, which have high activation barriers.This is a different diffusion mechanism than in conventional WR materials, where diffusion via cross block hops is always prohibitively sluggish compared to diffusion down square channels. 8,26The low overall rate performance of NaNb 3 O 8 is likely due to Li ions moving down these high-energy pathways.On charge, some Li remains in the structure, which our results suggest is in the X sites; this suggests a charge product similar to the ex situ LiNaNb 3 O 8 structure in which Li moves from the metastable Y site to the more stable X site, resulting in an interlayer spacing resembling pristine NaNb 3 O 8 .We predict that Li is extracted rst from the Z sites along shear-plane channels, followed by the Y sites.The Li stuck in the structure lowers the reversible cycling capacity, resulting in an operating range of about 2 # x # 4 in Li The combination of relatively extensive average structure evolution and blocked square-channel diffusion pathways results in the poor rate capabilities of NaNb 3 O 8 and KNb 3 O 8 for Li transport.However, there may exist layered structures with larger block sizes that allow fast diffusion down square channels while also incorporating Li into framework vacancy sites to achieve high capacity.The incorporation of a lower valent ion (such as Li or Na) rather than high valent d 0 TMs along the shear plane lowers the electrostatic repulsion for mobile Li ions along these pathways, beneting ion diffusion, analogous to transport properties in cation-disordered rocksalt cathodes. 49,50Diffusion of Na ions down square channels in WR and structurally related materials is limited by high activation barriers. 8,27However, the dynamics of Na apparent in NMR of NaNb 3 O 8 , as well as the previously reported Na-ion storage in KNb 3 O 8 , 31 indicate that Na is mobile between the layers in these materials.Accordingly, WR-derived structures, such as the layered compounds studied here, may also be applicable hosts for other large cation species.

Conclusions
In the search for high-rate Li-ion electrode materials and their design rules, we investigated ANb 3 O 8 (A ¼ Na, K), which are layered, vacancy-ordered derivatives of Wadsley-Roth materials, to see how these structural modications inuence electrochemical performance.Overall, the rate performance is lower than other WR materials, and not all Li is reversibly extracted aer the rst cycle.However, this work supports previous studies indicating polyhedral connectivity stabilizes the WR framework against signicant structural changes upon cycling.Structure evolution during cycling is dominated by changes to the interlayer, rather than intralayer, structure.Li is incorporated into ordered framework vacancy sites between the layers, contracting the interlayer space and forming a WR framework with (2 Â 2) N blocks.The size and preferred coordination of counter-cations (Na, K) is signicant to average structure evolution and voltage, with a different hysteresis and suggestions of a stacking sequence change in KNb 3 O 8 upon lithiation.While fast Li-ion diffusion takes place down square channels in conventional WR materials, in these niobates the square channels are blocked by the counter-cations and diffusion takes place initially in the interlayer space, and subsequently along the shear planes, leading to the overall moderate performance.These results offer perspective on key motifs for fast ion transport, as well as opportunities to further improve capacity and ion transport in WR-derived electrode materials and beyond.

Synthesis
KNb 3 O 8 powders were prepared using molten salt synthesis adapted from reported methods. 36,37K 2 CO 3 (J.T. Baker, 99.9%), Nb 2 O 5 (AlfaAesar, 99.9987%), and KCl (J.T. Baker 99.9%) were combined in a 1 : 3 : 12 molar ratio (about a 1 : 1 mass ratio of reactant and ux).Powders were ball-milled in ethanol and dried at ambient conditions.The resulting ne powder was heated in a new, covered alumina crucible, which went into a 700 C furnace, was heated at 3 C min À1 to 800 C and held for 5 h, cooled at 3 C min À1 to 700 C, and then air-quenched to room temperature.‡ The product was isolated using hot distilled water and vacuum-assisted ltration (using Whatman Grade 50 hardened low-ash lter paper).NaNb 3 O 8 was prepared through so chemical methods through several steps of ion-exchange reactions.KNb 3 O 8 was stirred in a nitric acid solution (7 mol HNO 3 per 1 L H 2 O) for 3 days, aer which the powder was ltered and rinsed with roomtemperature distilled water. 52While the structure is not known, this intermediate is reported to be HNb 3 O 8 $H 2 O. 30,52 HNb 3 O 8 -$H 2 O was then stirred in a NaOH solution (1 mol NaOH per 1 L H 2 O) for 3 h, the product was collected by ltration and rinsed with room temperature distilled water; again, while there is not a reported structure, this intermediate is described as NaNb 3 -O 8 $2H 2 O based on thermogravimetric analysis. 30The hydrated sodium niobate was heated at 3 min À1 to 140 , held for 3 h, and furnace cooled to room temperature, resulting in NaNb 3 O 8 . 30

Battery assembly & testing
For battery testing and ex situ characterization, layered niobates and SuperP (conductive carbon additive, Alfa Aesar, 99+%) in a 7 : 3 mass ratio were ground using an agate mortar and pestle.Loose powders were the working electrodes in 1.27 cm (0.5 in.) diameter Swagelok cells against Li metal (Alfa Aesar, 99.9%, 1.5 mm thick), which served as counter and reference electrode.Cells were assembled in an argon-lled glovebox with two Whatman glass lter dryer (GFD) separators and an electrolyte solution of 1 M (mol L À1 ) lithium hexauorophosphate (LiPF 6 ) in an ethylene carbonate : dimethyl carbonate (EC : DMC) (1 : 1 volume ratio) solvent (Sigma Aldrich).Galvanostatic cycling with potential limitations (GCPL) at various rates and potential limitations was carried out using a Bio-Logic VSP-300 potentiostat.
For ex situ samples, aer cycling to a select state of charge, powders were collected from disassembled cells, rinsed with DMC in the glovebox, and dried under vacuum without airexposure.Dried powders were ground using an agate mortar and pestle and loaded into 1.2 mm outer-diameter Kapton tubes sealed with epoxy.Sealed tubes were packed in glass vials under Ar, wrapped with Paralm, and not exposed to air until just before X-ray scattering data was collected.

X-ray characterization
Lab diffraction was collected using a Panalytical X'Pert powder diffractometer.High-resolution synchrotron XRD of prepared KNb 3 O 8 and NaNb 3 O 8 was collected at beamline 11-BM-B (l ¼ 0.4127 Å) of the Advanced Photon Source (APS) at Argonne National Laboratory through the rapid-access mail-in program (GUP-59538).Finely ground powders were measured in 0.8 mm inner-diameter Kapton tubes sealed with epoxy at both ends.Data was analyzed using Rietveld renement and Fullprof 53 freeware.Additional details of the renement are provided in the Results and discussion section as well as in the ESI.† Ex situ and operando X-ray total scattering of high-energy Xrays (l ¼ 0.2113 Å, E ¼ 58.7 keV) was collected at beamline 11-ID-B of the Advanced Photon Source using a PerkinElmer amorphous Si-based area detector at a sample-to-detector distance of 995 mm for diffraction data suitable for average structure information and analysis.Ex situ cycled powders were loaded into 1.2 mm outer-diameter Kapton capillaries in an ‡ Products were phase pure when using a new crucible.Subsequent reactions in used crucibles resulted in increasing fractions of secondary products until eventually the crucible cracked.While we have not investigated the cause of this, we anticipate that KCl in combination with rapid cooling contributed to reactants being lost in cracks in the crucible and shiing to other nearby K-Nb-O phases, especially K 4 Nb 6 O 17 , K 3 Nb 7 O 19 , and ternary bronzes.
argon glovebox and sealed with epoxy at both ends.Capillaries were sealed in vials under argon until just prior to scattering measurements to minimize moisture effects.Ex situ experimental geometries were calibrated using CeO 2 standards and integrated using Fit2D freeware, 54 and Topas-Academic-v6 was used for ex situ XRD analysis. 55or operando data collection, AMPIX cells 56 were assembled in an argon glovebox.Layered niobate powders were mixed with graphite, VulcanC, and polytetrauoroethylene (6 : 1 : 1 : 2 ratio by mass) and pressed into a free-standing cathode pellet.Between the cathode and Li metal anode were 1 M LiPF 6 in EC : DMC (1 : 1 volume ratio) electrolyte and one GFD separator.X-ray scattering of assembled AMPIX cells, with all but the cathode, was collected as a background to subtract from operando data.LaB 6 standards were used to calibrate experimental geometries.Due to the time constraints of operando experiments, full potential window cells were cycled at faster rates than ex situ.

NMR
Solid-state NMR spectra were recorded with a Bruker Avance III HD spectrometer in a Bruker narrow-bore 9.4 T superconducting magnet.The pulse-acquire sequence was used to record 7 Li and 23 Na spectra while both pulse-acquire and the quadrupolar Carr-Purcell-Meiboom-Gill (QCPMG) sequences were used to record 93 Nb spectra.Quantitative relaxation delays ($5 T 1 ) were used for all spectra (0.5 s for 93 Nb, 15 s for 23 Na, 10 s for 7 Li), with some additional T 1 -ltered measurements with shorter relaxation delays of 1 s for 7 Li and 23 Na to differentiate between sites experiencing rapid relaxation due to interactions with unpaired electrons. 7Li, 23 Na, and 93 Nb were referenced to 1.0 M LiCl (aqueous) [1 mol LiCl per L H 2 O] at 0 ppm, 1.0 M NaCl (aqueous) [1 mol NaCl per L H 2 O] at 0 ppm, and LiNbO 3 at À1004 ppm, respectively.All spectra were recorded at ambient temperature.
NMR chemical shielding and quadrupolar parameters were calculated with plane wave DFT in CASTEP 41-43 (v19.11)aer geometry optimization of the experimental structures from the Inorganic Crystal Structure Database (NaNb 3 O 8 , ICSD 202400; 30 KNb 3 O 8 , ICSD 31994 29 ).Vanderbilt ultraso pseudopotentials 57 were generated on-the-y in CASTEP.The Perdew-Burke-Ernzerhof (PBE) functional 44 was used to approximate exchangecorrelation effects.A plane wave basis set cut-off energy of 700 eV and Monkhorst-Pack k-point grids 58 of 4 Â 4 Â 9 (NaNb 3 O 8 ) and 4 Â 2 Â 9 (KNb 3 O 8 ) were used in the calculations.The geometry optimization was performed with the limited Broyden-Fletcher-Goldfarb-Shanno (LBFGS) algorithm until the energy and force converged to less than 2 Â 10 À5 eV per atom and 1 meV ÅÀ1 respectively. 93Nb calculated isotropic shieldings were converted to shis using the absolute shielding value of 642 ppm taken from the calculated 59 vs. experimental value for LiNbO 3 , d iso ¼ Às iso À 642 ppm.

Computational methods
First-principles calculations to investigate structures, energies and Li diffusion in Li x NaNb 3 O 8 (0 < x # 5) were performed using the periodic density-functional-theory (DFT) code CRYSTAL17. 60Electronic exchange and correlation were approximated using the hybrid-exchange functional HSE06. 61All-electron, atom-centered Gaussian basis sets were used for all atoms, with details provided in the ESI.† The Coulomb and exchange series were truncated with thresholds of 10 À7 10 À7 10 À7 10 À7 10 À14 .Reciprocal space was sampled using a Pack-Monkhorst net, 58 with a shrinking factor of IS ¼ 8 along each periodic direction for a total of 125 k-points in the irreducible Brillouin zone of the orthorhombic unit cell of NaNb 3 O 8 .Modied k-point grids were used for supercell calculations for a consistent sampling of reciprocal space.Dispersion forces were included using Grimme's semiclassical D3 correction. 62The self-consistent eld (SCF) procedure was performed up to a convergence threshold of DE ¼ 10 À8 Hartree per unit cell.Full geometry optimizations (lattice parameters and atomic positions) were performed using the default convergence criteria in CRYSTAL17.Activation barriers for ionic migration were determined using constrained geometry optimisations, with full details of the procedure described in the ESI.† Supercells obtained from a (1 Â 1 Â 2) expansion of the crystallographic unit cell were used for the calculations of activation barriers to ensure a distance of >7 Å between periodic images.The same (1 Â 1 Â 2) supercell was used to calculate the site lling and voltage prole.Intercalation voltages in Li x NaNb 3 O 8 between the limits x 1 and x 2 were determined relative to lithium metal using the following equation: DE inse ¼ E total (Li x2 NaNb 3 O 8 ) À [(x 2 À x 1 )E total (Li s ) + E total (Li x1 NaNb 3 O 8 )].Hybrid-exchange functionals are unsuited for the calculation of metals.To evaluate the energy of lithium metal, we calculated the energy of a single isolated Li ion and added the experimentally determined energy of sublimation (E sub ) and the rst ionization energy (E i(1) ): E(Li (s) ) ¼ E(Li + ) + E sub (Li (s) ) + E i(1) (Li).Crystal structures were visualized using VESTA soware. 63

Electron microscopy
SEM was performed with powder samples on carbon tape using a Helios NanoLab DualBeam microscope (Thermo Fisher Scientic, Waltham, MA, USA).TEM was performed in an FEI Titan (S)TEM operated at 300 kV and equipped with a highangle annular dark eld detector and EELS spectrometer.In same cases, a tomography sample holder was used to enable sufficiently large tilting angles.
Pristine KNb 3 O 8 powder samples were prepared for TEM by mixing the powder with a small amount of epoxy.The mixture was embedded in a slotted brass rod, which was placed inside a tightly tting brass tube with an outer diameter of 3 mm.Aer curing the epoxy, the rod-in-tube sample was mechanically sectioned into thin disks, which were subsequently mechanically polished and dimpled to the nal thickness of 25 mm, followed by Ar-ion thinning at 4 kV until perforation.Cycled materials were washed with DMC in an argon glovebox and dried under vacuum.The resulting powders were dispersed in ethanol and deposited on copper grids coated with lacey carbon for TEM.

Disclaimer
Any mention of commercial products is for informational purposes only; it does not imply recommendation or endorsement by the NIST.

Fig. 1
Fig. 1 (a) ReO 3 square channels (b) change shape upon lithiation as [ReO 6 ] octahedra begin to tilt (ReO 3 framework of Li 0.2 ReO 3 , Li not shown).(c) Wadsley-Roth crystallographic shear structures can be considered as ReO 3 -like blocks connected by shear planes (at the orange block edges), across which neighboring blocks have edge-rather than corner-sharing [MO 6 ] octahedra.(d) Hypothetical WR structure with (2 Â 2) N blocks.(e) Ordered framework cation vacancies leave layers with the composition M 3 O 8 .(f) Counter-cations reside in sites near the framework vacancies and push the layers apart.

Fig. 2 Fig. 3
Fig. 2 In (a) KNb 3 O 8 and (b) NaNb 3 O 8 , Nb 3 O 8 layers are separated by counter-cations.The size and preferred coordination of countercation (K or Na) determine the interlayer spacing as well as the stacking sequence of adjacent layers, AB for KNb 3 O 8 (with B shifted by c 2 ) and AA in NaNb 3 O 8 .

Fig. 4
Fig. 4 (a) SEM reveals rectangular platelets of as-prepared KNb 3 O 8 powders.(b) Bright-field TEM image of a KNb 3 O 8 crystallite crosssection imaged along the [100] direction.(c) SAED along the [100] direction shows no extended defects, revealing sharp reflections without any diffuse streaking, suggesting a well-ordered layer-stacking sequence along the [010] direction.(d) SEM of NaNb 3 O 8 shows a decreased particle size and increased size dispersity, but still a platelet shape.

Fig. 5
Fig. 5 Solid-state NMR spectra of layered alkali niobates.The static 93 Nb spectra of (a) KNb 3 O 8 and (b) NaNb 3 O 8 , collected using the quadrupolar Carr-Purcell-Meiboom-Gill (QCPMG) sequence.Both sets of data (orange) are overlaid by the fit (black) and deconvoluted into signals from the two crystallographically-distinct Nb sites.(c) MAS and (d) static 23 Na spectra (orange) of NaNb 3 O 8 fit to a single Na site (black).The y-axis corresponds to intensity, which is shown here on an arbitrary scale.

Fig. 6
Fig. 6 Galvanostatic cycling of (a) KNb 3 O 8 and (b) NaNb 3 O 8 , with the first cycle in solid lines and increasingly broken lines for subsequent cycles.In their first cycle, KNb 3 O 8 and NaNb 3 O 8 have similar cycling profiles, consisting of a combination of plateaued and sloped regions, with asymmetry in the profiles between discharge and charge.Later cycling shows a slow fade in capacity for both compounds.

Fig. 7
Fig. 7 (a) Galvanostatic discharge of NaNb 3 O 8 during operando X-ray scattering and (b and c) operando XRD at select states of charge, marked in (a), shows the evolution of specific reflections during lithiation (* marks a reflection from a component of the operando cell).The y-axis in (b) and (c) corresponds to the intensity of X-ray scattering, which is shown here on a arbitrary scale.

Fig. 8
Fig. 8 (a) Galvanostatic cycling of the first 1.5 cycles of NaNb 3 O 8 and the states of charge of ex situ samples.(b and c) XRD of pristine NaNb 3 O 8 and ex situ cycling products, with (b) structures similar to NaNb 3 O 8 at higher potentials and (c) with a distinct average structure from low potentials [data in (c) are scaled up by a factor of 2.5 relative to (b)].The y-axis in (b) and (c) corresponds to the intensity of X-ray scattering, which is shown here on a arbitrary scale.

Fig. 9
Fig. 9 Structures obtained from DFT calculations for intercalation to (LiNaNb)3O 8 .(a) Ground-state structure with Li in five-fold coordinate 'pocket' sites within Nb 3 O 8 layers, corresponding to the structure from ex situ XRD analysis.(b) Metastable structure with Li in distorted octahedral interlayer sites, corresponding to the structure from operando XRD analysis.Figures (c) and (d) show detail of the Li geometry from (a) and (b) respectively.Red, blue, and gold quadrilaterals indicate pathways along the square channels, within the Nb 3 O 8 layers, and within the interlayer space, respectively.(e) Diffusion pathway 3 in the interlayer space.(f) Diffusion paths 1 and 2 within the Nb 3 O 8 layers.Calculated activation barriers for (g) diffusion along pathway 3 and (h) along paths 1 and 2.

2. 3 . 2
First charge.Due to unexpected side reactions at low potentials during the operando discharge of NaNb 3 O 8 , XRD over the full charge was not captured.However, over the collected potential range, over a slope from 0.1 V to 1.5 V, only minor changes in peak positions and intensities were observed in operando (Fig.S4 †) and ex situ XRD (NC, Fig.8), indicative of a solid solution reaction.In particular, the k-character reections show that the b lattice parameter remains similar to that of the discharge product (Li 5 NaNb 3 O 8 ) over this voltage range.Based on our understanding that occupation of Y sites contracts the interlayer space, this indicates that some Li remains between the layers, even aer the removal of z2.5 mol Li on charge.

Fig. 10
Fig. 10 Ex situ XRD of the first discharge product of NaNb 3 O 8 and a fit of the data based on a model with a decreased interlayer spacing and expanded c lattice parameter.The y-axis corresponds to the intensity of X-ray scattering, which is shown here on a arbitrary scale.

2. 4
Site-lling mechanisms in Li x NaNb 3 O 8 2.4.1 (2 Â 2) N WR structure of LiNaNb 3 O 8 formed during discharge.Guided by insights from ex situ and operando XRD and NMR, DFT calculations were employed to further probe structural changes and site lling during cycling.The interlayer contraction across the rst discharge plateau heavily inuences the subsequent Li intercalation mechanism, changing the preferred Li diffusion pathways.When viewed along the cdirection, the metastable LiNaNb 3 O 8 structure with occupied Y sites resembles a (2 Â 2) N WR structure (Fig. 1d), with channels at the edges of the blocks formed by either pairs of [NbO 6 ] octahedra (cyan) or by one [LiO 6 ] and one [NbO 6 ] octahedra (yellow) (Fig.12, as in Fig.9a and b).DFT calculations indicate that when octahedral Y sites are lled, Li ions introduced into site Z adopt a new 4-or 5-coordinate geometry, similar to 'pocket' type sites at the edges of the WR blocks (Fig.12b).In total, the crystallographic unit cell containing two formula units of NaNb 3 O 8 contains 10 Li intercalation sites; four X, two Y, and four Z sites.

Fig. 11
Fig. 11 Evolution of the ex situ (a) QCPMG 93 Nb MAS NMR and (b) 23 Na MAS NMR of Li x NaNb 3 O 8 at various states of charge.Sample labels correspond to the ex situ cycling and XRD data in Fig. 8: NaNb 3 O 8 before cycling, (A) after reaction with 1 mol Li, (B) end of first discharge, (C) halfway through first charge, and (D) at the end of the first charge.The y-axis corresponds to intensity, which is shown here on a relative scale.In (b), quantitative (black) and T 1 -filtered (red) spectra are overlaid, recycle delays are given in the legend, and maximum intensities are normalized to highlight the changes in lineshape.A small impurity from sample preparation is denoted with an asterisk.

Fig. 12 (
Fig. 12 (a) Structure of Li 1.5 NaNb 3 O 8 with Z sites filled, causing Li-Na repulsion and displacement of Na (red).(b) Geometry of the four-foldcoordinate Li ion in pocket site Z.

Fig. 13
Fig. 13 Lithiation of NaNb 3 O 8 from DFT calculations.(a) Convex hull, showing the ground-state hull, and two convex hulls based on site filling determined by diffusion kinetics.Letters indicate structures along the hull.Structures B and C are presented in Fig. 9.(b) Experimental and calculated voltage curves, from the convex hulls in (a).(c) Structures along the convex-hulls from (a).

Fig. 14 (
Fig. 14 (a) Galvanostatic discharge of KNb 3 O 8 during operando XRD and (b and c) operando XRD patterns at select states of charge [marked in (a)] shows the evolution of specific reflections during lithiation.The y-axis in (b) and (c) corresponds to the intensity of X-ray scattering, which is shown here on a relative scale.

Fig. 15 (
Fig. 15 (a) Dark-field TEM image of a KNb 3 O 8 crystallite after partial discharge (to about LiKNb 3 O 8 ) shows segmentation into domains (labeled 1, 2, and 3).(b) As revealed by selected-area electron diffraction patterns from the three domains in (a), the domains share the same crystal structure and are separated by low-angle boundaries.Domain 2 is oriented with its [010] direction parallel to the beam, while domains 1 and 3 are tilted by about 14 from the in-plane [100] direction of domain 2. The contrast in domain 2 is consistent with the presence of twin-like domains.(b) Electron diffraction patterns show that each region is crystalline, with evidence of twin-like domains across region 2. (c, left) STEM high-angle annular dark-field imaging after several cycles shows crack-like channels across the platelets of Li x KNb 3 O 8 .(c, right) High-resolution TEM (down the [010] zone axis) shows crystallinity is retained on either side of the 'crack' region, and reveals amorphous contrast within these features.EELS spectra in the amorphous channel and its adjacent crystalline areas each indicate K, Nb, and O are present (see Fig. S10 †).

x
NaNb 3 O 8 .A comparison of the cycling and structure evolution of Li x -NaNb 3 O 8 and Li x KNb 3 O 8 shows the general intercalation mechanism and order of Li site lling are similar.However, some subtle differences that arise are associated with the different stacking sequence for KNb 3 O 8 (AB) compared to NaNb 3 O 8 (AA), and are likely associated with a change in the stacking sequence for Li x KNb 3 O 8 from AB to AA over the highvoltage plateau.We propose this change in stacking sequence is the source of the additional hysteresis of the high-potential feature for KNb 3 O 8 .The general similarities in the cycling for both compounds highlight the stability of the WR-type Nb 3 O 8 layers, leaving the differences to arise from changes to the interlayer structure, dependent on the counter-cation.

Fig. 16
Fig. 16 Schematic summary of the intercalation behavior in Li x NaNb 3 O 8 .(a) Structure of pristine NaNb 3 O 8 .(b) Voltage profile for the first discharge with shaded regions indicating the first high-voltage plateau, followed by two solid solution regions, and a low-voltage region where reactions with carbon and SEI are expected to occur.(c) Structure of LiNaNb 3 O 8 from operando XRD with Y sites filled, the interlayer space contracted and Na ions pushed into the square channels.Filling Y sites (gold blocks) results in a (2 Â 2) N block structure.(d) Structure of LiNaNb 3 O 8 from ex situ XRD with 'pocket' X sites filled.(e) Structure of Li x NaNb 3 O 8 when 1 # x < 5, with partial occupancy of X and Z sites, filled by 'cross-block' Li diffusion along shear-plane channels.Depending on which X and Z pocket sites are filled, the Na ions are displaced within the (2 Â 2 Â 2) cavity.(f) Structure of Li 5 NaNb 3 O 8 with all X, Y, and Z sites filled and Na ions in the center of the square channels.

Table 2
Lattice parameters of key structures obtained from DFT calculations for Li x NaNb 3 O 8 .E above hull is the relative energy vs. the most stable structure at that composition a Corresponding to ex situ XRD analysis.b Corresponding to operando XRD analysis.