Topochemical stabilization and single-crystal transformations of a metastable 2D (cid:33) '-V 2 O 5 intercalation cathode

The atomistic design of positive electrode materials requires understanding of (i) how guest cations diffuse through an intercalation host to fill empty interstices and (ii) the distortions of the host lattice induced as a result of ion intercalation. Here, we report the use of topochemistry to access single-crystals of a metastable 2D van der Waals solid, (cid:33) (cid:33) -V 2 O 5 , and examine its single-crystal-to-single-crystal transformations upon lithiation up to (cid:33) - LiV 2 O 5 . High-resolution single-crystal diffraction provides an atomistic view of preferred interstitial sites occupied by Li ions and distortions of the 2D lattice in an extended solid-solution lithiation regime, which stands in stark contrast to the thermodynamic (cid:34) -V 2 O 5 phase. These results illustrate the potential of metastable compounds with reconfigured atomic connectivity to unlock lithiation pathways and mechanisms that are profoundly different from their thermodynamic counterparts. The study furthermore demonstrates the viability of combining topochemical modification with single-crystal diffraction to image intercalation phenomena with atomic resolution.


INTRODUCTION
In Li ion batteries that are the mainstay of modern electrochemical energy storage, Li ions are intercalated and de-intercalated from transition metal oxide cathodes during discharging and charging of the battery. 1,24][5] Li ion insertion inevitably perturbs the structure of the host lattice; in some cases (e.g., LiCoO2), 6 the inserted ions are accommodated through extended solid-solution regimes wherein interstitial sites are sequentially filled while essentially preserving the host crystal lattice.In other cases (e.g., LiFePO4 and -V2O5) 7,8 lithiation triggers a series of The bigger picture (1000 characters max) The ability to grow proteins as single crystals paved the way to the determination of high-resolution structures, enabling the design of targeted approaches to modulate protein function.In intercalation electrodes used in energy storage, the insertion of cations and their transport through the crystal lattice brings about a dynamical modulation of structure that remains poorly understood.Much present knowledge of diffusion pathways is derived from mapping of lithiation inhomogeneities using electron and X-ray microscopy at larger length scales (yielding particle-and electrode-level information), ensemble nuclear magnetic resonance spectroscopy studies of local ion dynamics, or rely on density functional theory calculations (prone to substantial inaccuracies for strongly correlated systems).0][11] Deciphering lithiation mechanisms, the specific interstitial sites occupied by Li ions, lithiation-induced modification(s) of the crystal structure of the host lattice, and the coupling of Li ion diffusion to specific phonon modes 12 is of pivotal importance to materials design and for tuning the thermodynamics and kinetics of ion insertion. 13In particular, atomistic design of electrode materials requires a clear understanding of (i) how guest cations diffuse through the structure to fill empty available interstices; and (ii) the long-range transformations that intercalating ions induce in the host lattice away from equilibrium.In this article, we use single-crystal-to-single-crystal transformations to first stabilize a metastable van der Waals bonded -V2O5 phase, and then to topochemically insert Li ions at various stoichiometries between the layers up to a stoichiometry of -LiV2O5.We thus obtain high-resolution crystallographic "snapshots" with Ångstrom resolution depicting Li-ions located not just at the most stable interstitial sites but traversing diffusion pathways between these sites.
Diffusion pathways traversed by cations in electrodes have been mapped at relatively coarse mesoscale levels using electron and X-ray microscopy and have illuminated the role of particle morphologies and interconnectivity. 14Ensemble nuclear magnetic resonance spectroscopy studies have provided insights into local ion dynamics. 15However, with the exception of a few studies combining X-ray and neutron diffraction to locate cation sites, [16][17][18] the dynamical modulation of the structure of intercalation hosts upon lithiation remains poorly understood.Much of our current knowledge comes from first-principles density functional theory calculations, which are prone to substantial inaccuracies for strongly correlated systems and often do not precisely capture entropic contributions to site preferences and structure types.Single-crystal diffraction holds promise for high-resolution structure solutions that identify the site preferences of inserted cations with atomic resolution, 19 but has seldom been applied to electrode materials given challenges in growing macroscopic single-crystals and achieving topochemical ion insertion in a manner that mimics the 'far-from-equilibrium' processes operational within a battery.In this article, we demonstrate the stabilization of single-crystals of -V2O5, a metastable V2O5 polymorph comprising stacked 2D puckered sheets held together by van der Waals interactions.While electrochemical cycling of '-V2O5 powders has been previously investigated; [20][21][22] this represents the first success with stabilizing single crystals, which enables atomic resolution mapping of individual metastable crystal domains, investigation of site preferences and mapping of diffuse electron density reflecting diffusion pathways at discrete stages of Li ion intercalation, while simultaneously tracking intercalation-induced periodic distortions of the lattice structure of the intercalation host again with ngstrom resolution.Unlike powder XRD methods that have been indexed on the basis of 10-20 reflections, the 17,000+ reflections in single-crystal X-ray diffraction allow for unambiguous identification of Li sites with spatial resolution down to 0.77Å.
4][25] From the perspective of energy storage, such compounds afford opportunities for tuning ion transport through reconfiguration of diffusion pathways, for instance, confining cations within frustrated coordination environments. 8,261][32][33] In this work, we report the stabilization of single-crystals of a 2D metastable -V2O5 phase and explore its singlecrystal transformations at multiple stages of Li ion intercalation, enabling delineation of high-resolution electron density maps of cation occupancies during layer filling.
Single-crystal topochemical transformations performed using chemical lithiation reagents at room temperature provide a view of sites occupied by inserted cations that capture 'out-of-equilibrium' processes not accessible from ternary crystals (LixV2O5) prepared by direct synthesis wherein due to high synthesis temperatures, intercalated cations are able to locate within lowest energy sites. 34

RESULTS AND DISCUSSION
Single-Crystals of -LixV2O5 are Topochemically Delithiated and Lithiated in Sequence Single-crystals of -LiV2O5 were synthesized as described in the Experimental section.
tracks the results of single-crystal delithiation and lithiation in the Li--V2O5 system, with accompanying digital photographs of crystals (Figure 1A-E, F, top row); atomic structures delineating unit cell boundaries (Figure 1A-E, middle row); and a plot of lattice parameters and unit cell volume as a function of Li stoichiometry (Figure 1A-E, bottom row).These parameters as well as other crystallographic and topochemical information are also presented in in the Supporting Information.
shows optical images of the lustrous black crystals of -LiV2O5 (Structure A) with approximately rectangular cross-sections alongside the crystal structure viewed down the b-axis.Slow topochemical delithiation of -LiV2O5 was accomplished by treatment with NOBF4 as per: Leached single-crystals of -V2O5 (Structure B) retain excellent crystallinity and exhibit almost complete de-lithiation for small crystals (<300 m).The completeness of the leaching process is indicated by the transformation to a translucent yellow appearance caused by oxidation of V 4+ to V 5+ ( top panel); the total absence of electron density corresponding to Li atoms in the structure refined from highresolution single-crystal XRD (Figure 1B, middle panel); and the substantial distortion of lattice parameters and diminution in unit cell volume ( , lower panel).ICP-MS results acquired for an ensemble of crystals is shown in Table S22.The top-right panel of Figure 1B shows a low-magnification image of an ensemble of larger crystals, which are characterized by a variously dappled or striped appearance-dark regions in the otherwise bright-yellow crystals correspond to remnant LixV2O5 phases; the residual lithium content derives from incomplete leaching of Li ions from the centers of the largest crystalline domains owing to the extremely long diffusion path lengths.Such inhomogeneities and slow diffusion kinetics also induce strain gradients that account for the substantial cracking of the largest crystals.6][37] Further topochemical transformations have been performed for homogeneously deintercalated small (<300 m) single-crystals of -V2O5.While the structure of -V2O5 has previously been inferred from Rietveld refinement of powder X-ray diffraction patterns, 38 this is the first report of the isolation of metastable -V2O5 in the form of single-crystals (shown in ).Based on high-resolution structure solutions, the unit cell volume is substantially decreased from 370.1Å 3 to 354.4Å 3 , a 4.2% reduction in volume, upon delithiation of -LiV2O5 to stabilize metastable -V2O5.This loss can be entirely attributed to the removal of Li atoms from the galleries between the layers and the subsequent shrinkage along the c-axis to reduce void space.A minor expansion (2.4%) is observed along the adirection as the layers of VO5 square pyramids "un-buckle".The decrease of unit cell volume despite the small increase in the a parameter is a direct consequence of the 2D nature of the structure, which in the absence of Li ions is held together primarily by van der Waals interactions.contrasts the thermodynamically stable polymorph, orthorhombic -V2O5 (panel A) with that of the metastable -V2O5 (panel B).
Structural Distortions in Stable and Metastable Layered V2O5 are Calculated from High-resolution Single-Crystal XRD Owing to the symmetry of the unit cell and configuration of VO5 polyhedra, -V2O5 contains two crystallographically distinct vanadium sites, whereas -V2O5 contains a singular vanadium site.The average separation between extended layer centroids is shown with a dashed blue line in ; this value is equivalent to the length of the c lattice parameter in -V2O5, and c/2 in -V2O5 and -LiV2O5.
tracks the expansion of this metric for interlayer separation across a selection of polymorphs, which stretches from 4.342Å in -V2O5 to 4.996Å in -V2O5 (Structure B), and continues to expand with topochemical Li ion insertion between layers to 5.243Å in -Li0.5V2O5(Structure D) and 5.325Å in -Li1.0V2O5(Structure E).The shortest inter-layer V-O distance in -LiV2O5 (Structures A and E) is 3.053Å (shown as a red dashed line in Figure 2A-D).The equivalent bond in the fully delithiated Structure B shrinks to 2.692Å, which is almost short enough to constitute a quasi-octahedral arrangement around this V atom, corner-sharing with the opposite-facing square pyramid; and is even shorter than the quasi-octahedral bond distance in -V2O5, which is 2.753Å.For reference, 2.5Å is "long" for a true V-O bond, with an upper limit estimated to be 2.7Å. 39AFM analysis of a crystal of exfoliated '-V2O5 is shown in .shows the results of cleavage energies calculated from density functional theory (DFT) in order to contextualize the interlayer binding forces of the metastable y'-V2O5 phase in comparison to the thermodynamic -V2O5 polymorph, and to graphene, a model van der Waals solid, that both similarly undergo Li intercalation phenomena.The energy required to cleave layers of -V2O5 to an interlayer separation of 10Å from a starting interlayer separation of 4.996Å is 0.1035 J/m 2 , which is significantly lower as compared to the corresponding value of 0.2076 J/m 2 for -V2O5; both values are notably lower than the cleavage energy required to separate individual graphene layers from graphite (0.3405 J/m 2 ) calculated using the same exchange-correlation functional and van der Waals correction).This substantial reduction in cleavage energy relative to other layered insertion materials highlights the capacity for topochemically-accessed metastable materials with emptied layers to have substantially lower activation energies for mechanical cleavage as well as diffusion and for creation of stacked van der Waals heterostructures with precisely tunable diffusion pathways.
The relatively slow transformation kinetics in single-crystals, owing to their large diffusion path lengths relative to powders and nanomaterials, 14,19 provides the opportunity to isolate metastable structures at intermediate lithiations whose structure can be difficult to resolve from operando powder XRD experiments; in the case of -V2O5, only lattice trends have been examined and scarce little is known about atom positions and site occupancies. 19,20,22We have used topochemical transformations of -V2O5 single-crystals to access two intermediate -LixV2O5 phases (Figs.1C and D) as well as a "filled" -LiV2O5 phase (Fig. 1E), herein referred to as Structures C, D, and E, respectively.High-resolution structures provide a detailed perspective of the site preferences of Li ions and the concomitant distortion of the -V2O5 square pyramids.We observe that the space group and atomic positions in the unit cell remain identical, and only the Li atomic occupancy and lattice parameters are modulated in tandem (traced in Figure 1A-E).The unit cell volume is increased to 363.5Å 3 in Structure C at 0.41 Li, then to 367.9Å 3 in Structure D at 0.50 Li.With lithiation, O-Li-O bridges become the principle means of connectivity across layers; the shortest interlayer V-O distance in Structure D stretches to 2.971Å (Fig. 2C).The angle of "puckering" across the V1 and V2 square pyramids becomes more acute with increasing lithiation (and subsequent shrinkage of the a-axis).The puckering angle changes dramatically from 120.1° to 118.1° to 114.9° with increasing lithiation from -V2O5 to -Li0.50V2O5 to -LiV2O5, respectively ( , Structures B, D, and E).This trend is shown in in comparison to the essentially unpuckered -V2O5 structure, where the angle across corner-sharing square pyramids is almost exactly 180°.
During lithiation, the Li ions that are inserted between V2O5 layers are observed in all measured crystals to occupy a single 6-coordinate insertion site within the structure.Both Structure C (~41% Li occupancy) and Structure D (~50% Li occupancy) refined to the same Pnma unit cell as the empty (Structure B) and filled (Structures A and E) structures, with a random distribution of Li modeled as partial occupancy at the six-coordinated interlayer site, which we will refer to as the "A" site for Li ions in the structure.The favorability of randomly-distributed Li in the structure is reflective of the strong energetic preference for this 6-coordinated site (as shown in ).A second putative "B" site with tetrahedral coordination in a plausible intermediate position has been derived from the electron density map of Structure C (shown in ) where fewer than half of A-sites are occupied, and its energetics relative to a structure where only A-sites are occupied have been calculated with DFT ( ).

DFT Elucidates Energies for Layer Cleavage, Site Occupancy, and Ion-by-Ion Filling Configurations
Using the partial atomic occupancy data provided by single-crystal experiments as a basis, DFT calculations have also been performed to understand the evident preference for random site-filling over ordering phenomena such as staging, and glean further insight into local perturbations induced by individual Li-ions given that the single crystal structure solution represents an averaged view of an entire domain that has been trapped outside of thermodynamic equilibrium and may be undergoing dynamic effects at the local level.The energetics of layer-by-layer sitefilling in a relaxed superstructure of the -V2O5 lattice, shown in , is analyzed in comparison to more disordered configuration of lattice occupancies.The configurations that correspond to an ordered staging phenomenon, where alternating layers are filled preferentially, are represented by configurations 8 and 9 for -Li0.25V2O5, 12 and 13 for -Li0.375V2O5, and 17 for -Li0.5V2O5.Disordered configurations were found in all cases to be energetically similar or more favorable at each stoichiometry.These results corroborate well with ensemble crystallographic data (Figure 1) that by contrast give an average view of the overall crystal domain at each extent of lithiation, and are consistent with a preference for random Li distribution across local environments.These results further reflect that maintaining optimal separation of inserted Li ions (and accompanying local structure perturbations) is energetically more preferable as compared to a configuration with alternating distorted and undistorted layers as would be expected from stage ordering and superlattice formation.Upon lithiation, as also shown in Figures 2C and  D, the Li-O bonds transform the 2D lattice to a 3D interconnected structure.
DFT has also been used to analyze the energetic preference of the tetrahedral "B" site identified from the high-resolution electron density map of Structure C. The observation of this site only in the -Li0.41V2O5structure and its relatively minor contribution to the total electron density compared to the stable sixcoordinate A-site, suggests that it is an intermediate position that is filled transiently by Li-ions diffusing through the open ab plane of the structure to fill A-sites, which are very stable relative to an empty structure ( ). DFT calculations performed on relaxed unit cells where a single B-site is occupied support this hypothesis: shows the energy of unit cells containing one filled B-site, relative to unit cells of the same total Li-content containing only filled A-sites at adjacent positions.At very low levels of lithiation, when nearly all A-sites are empty and diffusion can be expected to be highest, an occupied B-site is slightly preferred (by about 78 meV/unit cell), and this slight preference is maintained when some, but not all adjacent A-sites are filled (slightly less stable, at about 26 meV/unit cell relative to an A-only structure).Such an "intermediate" structure, where some-but-not-all A-sites are filled and the Bsite is very slightly stabilized, corresponds well to Structure C from which the B-site is experimentally derived (shown in detail in ).When all adjacent A-sites are filled however, necessarily closing off potential diffusion routes and corresponding to a structure with total Li occupancy of 0.5, the B-site ceases to be favored and instead corresponds to a higher energy unit cell by nearly 140 meV; and correspondingly, an electron density peak is not observed at this position in Structure D. The observation of the B-site only in the intermediately-lithiated crystal highlights the potential for high-resolution diffraction of metastable crystals to provide insights into preferred diffusion pathways that may not be observable in equilibrium structures.
Treatment of -V2O5 single-crystals with 1.0 molar equivalents of n-BuLi effects a virtually perfect return of the crystal structure to that of the precursor material prepared using solid-state reaction conditions.The pristine Structure A exhibits a solved unit cell volume of 370.11Å 3 at 110K, while the fully re-lithiated Structure E has a nearly identical unit cell volume of 370.15Å 3 .The similarity between Structure A and Structure E is further reflected in the values of the refined Li site occupancies; the final occupancy of Li at the A-site in both structures is best refined at 100%.The transformations described here thus represent a complete topochemical "cycling" of the material from full occupancy in crystals of Structure A, to zero occupancy in crystals of Structure B, and finally back to full occupancy in crystals of Structure E. The absence of irreversible structural changes or indicators of topochemical deformation by high-resolution XRD reflects the thermodynamic stability of the fully-lithiated -LiV2O5 structure and the robustness of the -V2O5 framework.
Notably, previous studies have shown that the -LixV2O5 phase is characterized by a much wider solid solution region than demonstrated here (0.0<x<2.0) before it is irreversibly transformed to the amorphous quasi-rock salt structured -phase. 40,41However, attempts to lithiate large single crystals of -V2O5 beyond x = 1 in LixV2O5 resulted in cracking and exfoliation of the crystals in a distinctive, accordion-like fashion as shown in Figure 1F.Due to the observed decrease in crystal quality at these high levels of lithiation, it is no longer possible to obtain single-crystal XRD.Since at x = 1 the lowest energy Li ion sites are shown to be fully occupied, additional higher energy sites are necessarily occupied at x > 1.The filling of these additional sites likely drives an intercalation-induced structural transformation that contributes to the total loss of crystal integrity.
A "Lithium's-Eye View" of the 2D Layered '-V2O5 Structure At intermediate extents of lithiation (Structures C and D), the highlyresolved view provided by single-crystal XRD also allows for analysis of the Fo-Fc structure-factor maps for peaks and troughs of electron density, further providing insights into the diffusion behavior of topochemically inserted Li ions at resolutions entirely unattainable from powder XRD.The residual electron density map for Structure C, which has a comparatively low average Li content of about 0.4 Li per V2O5, includes a peak at an intermediate site located between principle sixcoordinated "A" sites.While too small and diffuse a region of electron density to refine stably as a partially-occupied Li site, its position at a four-coordinate tetrahedral position correlates with previous DFT calculations that predicted a 4-coordinate intermediate between stable 6-coordinate sites; the electron density distribution thus indicates low-energy diffusion proceeding along an octahedral-tetrahedraloctahedral pathway. 23,42hows the structure-factor map (positive residual indicated by a green mesh) in this crystallographic region in relation to the surrounding V2O5 framework and partially-occupied A-sites in Structure C. Notably, this peak also resides in the main void space between A-sites along both b-and a-axes, suggesting that two-dimensional diffusion within the ab-plane is plausible in the -V2O5 structure.Furthermore, DFT-calculated energies shown in confirm that this position is stabilized by ca.20-80 meV at low total occupancies by empty adjacent A-sites when diffusion between void spaces to fill available interstices is most favorable.In another metastable polymorph, -V2O5, Li ions are accommodated in a plethora of adjacent intercalation sites with closely spaced energetics and a substantial amount of diffuse electron density is observed in intermediate positions. 19n stark contrast, the vast majority of Li electron density in '-V2O5 is concentrated at the single 6-coordinated A-site, even at intermediate extents of lithiation.This is likely due to the ease of diffusion between these stable sites, which thus gives rise to an extended solid-solution intercalation regime from x = 0-1 in LixV2O5.The openness of the layered '-V2O5 structure (highlighted in ) allows comparatively easy hopping between thermodynamically stable insertion sites without the cations dwelling for long in intermediate positions.It is worth noting that -V2O5 is metastable; however, being only ca. 6 meV above hull as compared to -V2O5, 29 it is within the range accessible at finite temperatures kBT and thus can be stabilized under ambient conditions; albeit only indirectly via topochemical routes. 43FT calculations show that the total energy of -V2O5 is 0.36 eV/f.u.greater as compared to -V2O5 (Fig. 3A).However, the fully-lithiated -LiV2O5 structure is the thermodynamic minimum in the phase diagram for the Li-V-O system at these stoichiometries.This explains the seamless transformation of single-crystals in this study back to the fully-lithiated -LiV2O5 phase and the extended solid-solution intercalation mechanism with relatively minor lattice distortions at each point of lithiation.
The results demonstrate that unlike its thermodynamically stable counterpart -V2O5, which is a canonical phase-separating material, 8 intercalated Li ions are accommodated in -V2O5 through a solid-solution mechanism across an extended range of lithiation.The mechanism is furthermore quite distinct from another metastable polymorph, 1D tunnel-structured -V2O5, where increasing concentrations of Li ions are accommodated through extensive cation reordering and the sequential occupancy of interstitial sites. 29

Conclusions
Topochemically modifying single-crystals of -LiV2O5 has allowed us to stabilize single-crystals of a 2D metastable polymorph of V2O5.The van der Waals solid comprises stacked layers of highly puckered V2O5 with up-down-up-down orientations of edge-and corner-sharing VO5 square pyramids that fold and unfold at angles ranging from 114.9°-120.1°as a function of lithiation.The layered structure defines a vast abundance of interlayer interstitial sites that can accommodate Li ions.Single-crystal-to-single-crystal topochemical transformations have been realized at a series of points across the Li-V2O5 phase diagram, enabling the use of single-crystal X-ray diffraction to elucidate the site preferences of inserted Li ions and the accompanying lattice distortion at Ångstrom resolution.The open structure of the -V2O5 intercalation host allows for continuous Li ion diffusion into highly-stable octahedral sites with random distribution suggesting a solid-solution lithiation mechanism from x = 0 to at least 1 in LixV2O5.A six-coordinated site is found to be strongly energetically favored across this range and is fully occupied in -LiV2O5; further lithiation brings about structural transformations that shear the layers with respect to each other resulting in exfoliation into accordion-like morphologies.Electron density maps indicate a tetrahedral position at a plausible intermediate site between 6-coordinated sites, supporting facile pathways for Li ion diffusion available across the ab-plane, and DFT calculations confirm that this position is slightly stabilized on the order of 100 meV/unit cell at low levels of total lithiation when adjacent A-sites are empty and diffusion between these low-lying A-sites is most energetically favorable.The continuity of site-occupancy changes, minimal structural distortion, and the complete reversibility of transformation in the layered -V2O5 structure stands in contrast to the series of intercalation-induced transformations required to accommodate Li ions in the thermodynamically stable polymorph, -V2O5, and the extensive cation-reordering mechanism observed in 1D tunnelstructured -V2O5.This comparison highlights the potential advantages of open 2D polymorphs in rendering accessible extensive solid-solution ranges, as required for reducing phase separation, non-uniform stress gradients, and enabling high-rate electrochemistry. 14,44More generally, the results illustrate the potential of metastable compounds with reconfigured atomic connectivity to unlock lithiation pathways and mechanisms that are profoundly different from their thermodynamic counterparts.In providing an atomistic view of the layered orthorhombic -V2O5 system, this study also demonstrates the viability of combining topochemistry with single-crystal XRD in order to image intercalation phenomena at atomic resolution.These results in conjunction with mapping of Li-ion diffusion pathways in -V2O5 with a substantially different structural motif and pattern of extended atomic connectivity, 19 illustrates the generalizability of this approach.Topochemical transformations of large single crystals are particularly relevant to rigid extended frameworks, crystal lattices exhibiting high Li-ion diffusivity, and lattices that undergo relatively modest structural distortions upon insertion of guest cations.Powders of intercalation compounds with a variety of chemical and structural compositions have been long known to be amenable to cation insertion by topochemical reagents; 45 to the extent that any species can be isolated as large high-quality single-crystals, then, it is likely that transformations of the sort discussed herein may be effected under reaction conditions that favor insertion/removal over reconstitution and are slow enough so as to develop large stress gradients inevitably introduced across extremely long diffusion paths.Achieving topochemical single-crystal-to-single-crystal transformations to generalize the applicability of this method thus requires (1) availability of high-quality single crystals; (2) identifying conditions wherein insertion or leaching reactions are strongly preferred over dissolution/recrystallization or oxygen evolution; and (3) careful control of Li diffusion kinetics across millimeter-sized dimensions to ensure structural integrity of the single crystals as they undergo lattice expansion and contraction.Given the great diversity of polymorphs within the V2O5 family and other transition metal oxide systems, we expect that topochemical routes for the modification of large single-crystals will provide a means of atomic scale mapping of diffusion pathways and structural transformations in intercalation materials.

Lead contact
Further information and requests for resources should be directed to and will be fulfilled by the lead contact, Sarbajit Banerjee (banerjee@chem.tamu.edu).

Materials availability
All materials generated in this study are available from the lead contact.

Data and code availability
The crystallographic information files (CIF files) generated by the refinements of all structures in this study and including structure factors have been deposited in the Cambridge Structural Database and are available for access with deposition numbers 2084509, 2084510, 2084511, 2084512, and 2084513 for Structures A, B, C, D, and E, respectively.
-LiV2O5 was first synthesized as a powder using a solvothermal process.Stoichiometric amounts of LiOH (Sigma Aldrich, 98%) and V2O5 (Sigma Aldrich, 99.6%) and 86 mL of EtOH were added to a PTFE-lined stainless steel autoclave (Parr, 125 ml capacity) and allowed to react for 72 h at 210°C.The resulting black powder was filtered and allowed to dry under air overnight.The powder was ground and further annealed at 600°C in a tube furnace under a flow of Ar gas for 12 h to remove any residual moisture.The as-obtained powder was shown to be phase-pure by powder X-ray diffraction.To obtain large crystals, powder -LiV2O5 product was ballmilled again, sealed in quartz ampoules under vacuum, and then melted at 800°C and cooled at a rate of 2°C/h in a programmable furnace (Thermo Scientific, Lindberg Blue M with UT150 controller) to obtain large, lustrous black block-shaped single crystals.
It is important to note that under the synthetic conditions used to obtain the powder samples, -LiV2O5 is observed to be the only stable phase.Despite the mixture of phases in the melt, the large single crystals measured were observed to be phase-pure -LiV2O5.Topochemical de-intercalation of Li-ions to access crystals of -V2O5 was effected by treating them with 1.5M equivalents of NOBF4 (Alfa Aesar, 98%) in dry acetonitrile (ca.0.01M solution) for 24 h.The leaching of Li ions and corresponding oxidation of tetravalent vanadium to pentavalent vanadium caused a drastic change in appearance from lustrous black to translucent yellow ( ); cracks are observed along the blocks in a layer-like habit, reflecting the 2D nature of the V2O5 structure.
Topochemical lithiation was performed by treating 50 mg of -V2O5 crystals with 0.25, 0.50, and 1.0 molar equivalents of LiI (Alfa Aesar, 99%) dissolved in acetonitrile (results of ICP-MS elemental analyses are shown in Table S22 of the supporting information).Small differences between Li content in individual measured crystals and average Li content in bulk samples measured by ICP-MS suggest some inhomogeneity across crystal domains, likely due to variety in diffusion path lengths; however, it should be noted that each solved crystal structure reported in this study corresponds to a single domain at each Li content.DFT calculations of various possible site-filling regimes shown in support the notion that a given crystal domain at each total lithiation corresponds to a disordered solid-solution regime.
At molar ratios above 1.0 Li per V2O5, large cracks appear within the crystals, which are fractured into accordion-like morphologies (highlighted in the optical images in Figure 1).Beyond this point there was substantial loss of diffraction intensity and severe twinning during attempts to collect further single-crystal structures.The -V2O5 single crystals were also mechanically exfoliated onto a clean silicon wafer by the classical scotch tape method.The resulting extremely thin 2D flakes were characterized by tapping mode AFM with a silicon cantilever (AC240TS-R3, nominal spring constant 2 N/m) using an MFP-3D Infinity AFM instrument (Asylum Research, an Oxford Instrument Company, CA).
Single-crystal diffraction data was collected on a BRUKER Quest X-ray diffractometer utilizing the APEX3 software suite, with X-Ray radiation generated from a Mo-I s X-ray tube (K = 0.71073Å).All crystals were placed in a cold N2 stream maintained at 110K.Following unit cell determination, extended data collection was performed using omega and phi scans.Data reduction, integration of frames, merging, and scaling were performed with the program APEX3, and absorption correction was performed utilizing the program SADABS. 46,47Structures were solved using intrinsic phasing, and least-squares refinement for all structures was carried out on F 2 .9][50] Crystallographic Information Files pertaining to structures used in this study have been deposited in the Cambridge Structural Database and are available for access with deposition numbers 2084509, 2084510, 2084511, 2084512, and 2084513 for Structures A, B, C, D, and E, respectively.The atomic labeling scheme used for structures in this study is shown in in the Supporting Information; and crystallographic and refinement information is listed in in the Supporting Information.Total energies of relaxed atomistic structures were calculated using firstprinciples DFT, 51,52 as implemented in the Vienna ab initio simulation package (VASP).The exchange-correlation energy functional was modeled using the GGA with the Perdew-Burke-Ernzerhof (PBE) form. 53Considering the strongly correlated 3d electrons of vanadium, a Hubbard parameter U was applied to the PBE functional in the approach proposed by Dudarev et al., 54 with Ueff = 3.0 eV and D3 van der Waals corrections utilized.Atomic structures were derived from the refined CIF files obtained from single-crystal X-ray diffraction and comprised a 1 1 2 supercell containing 4 layers, and were fully relaxed.In the cleavage energy calculation, the bulk layered materials (V2O5 and graphite) are gradually separated by inserting additional interlayer distance in the van der Waals gap at the middle of the cell.The atomic positions are fully relaxed, while keeping the total cell length along the normal direction of the van der Waals plane fixed.Periodic boundary conditions are applied as the van der Waals gap is located at the middle of the cell, and at the cell boundary the system is treated periodically.To understand the energetically preferred site for Li in layered V2O5, DFT total energy calculations have been performed for different configurations with Li at different interstitial sites.Specifically, a supercell of 1 1 2 atoms with 4 atomic layers was examined the model a low Li-ion intercalation scenario.Total energies were calculated with the periodic boundary condition, at a specific Li concentration, to represent the infinite V2O5 crystal with a certain amount of Li atoms intercalated in practice.In this case, the supercell is also treated periodically to model alternating intercalation patterns.
The authors declare no competing interests.

(
A-E, F, top row) Digital photographs of single-crystals used in this study, tracking changes in color and habit upon topochemical transformation.The photographs highlight transformation from lustrous black blocks (panel A) to translucent yellow blocks with visible layers and defects arising from leaching Li ions from the layered -V2O5 structure (panel B).Intermediate lithiation of -V2O5 produces black plates that have a metallic blue hue when sufficiently thin (panels C and D); full re-lithiation yields irregular black plates with substantial edge damage but retaining singlecrystalline integrity (panel E).Lithiation above 1 equivalent partially-exfoliates the crystals, which show an accordion-like habit (panel F).Left-hand panels in the top row of B, C, D, and E show crystals used for diffraction experiments.(A-E, middle row) Atomic structures of crystals used in this study as refined from single-crystal X-ray diffraction at 110K, viewed down the b-axis to show extended layers, with unit cell boundaries indicated by blue lines.Key: Red = Oxygen; Teal = Vanadium; Green = Lithium.Partial site occupancy of Li indicated with partially-shaded spheres.VO5 square pyramids shaded in gray for lithiated structures (structures A, C, D, and E) and yellow for empty -V2O5 (structure B). (A-E, bottom row) Lattice parameters a (red triangles), b (green triangles), c (blue triangles), and Volume (black squares) of Pmna unit cell from refined single-crystal structures at 110K.Left axis = unit cell volume; Right axis = lattice parameter length.(G) AFM height map image of a -V2O5 single crystal (structure B) exfoliated to a thickness of ca.40 unit cells; showing clear steps along the crystal surface.An optical image of the same crystal is shown as a lowerright inset.Crystal surface height as a function of distance across this crystal is shown in the top half of the panel (indicated by a dashed yellow line).

Figure 2 .
Figure 2. Structural Distortions in Thermodynamically Stable and Metastable Layered V2O5 Polymorphs as Calculated from Single-Crystal XRD.

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A) Comparison of DFT-calculated layer cleavage energy as a function of vacuum thickness; and total energy per formula unit for orthorhombic '-V2O5 relative to stable orthorhombic -V2O5; with calculated cleavage energy values for graphite also shown.(B) Perspective view comparing 6-coordinate A-site and 4-coordinate B-site identified in Structure C of this study in context of the '-V2O5 framework, with interatomic distance (3.185A) shown; alongside a plot of DFT-calculated energies for relaxed unit cells where one B-site is filled, and any other sites in the unit cell correspond to filled adjacent A-sites, showing how the B-site is effectively stabilized by adjacent empty A-sites.(C) DFT-calculated energies of a sequence of Li site-filling configurations performed on a 1 1 2 relaxed-volume supercell model of the '-V2O5 structure, in order to compare relative stabilities of various possible ion-by-ion sitefilling configurations.The number of Li atoms inserted into each configuration, and hence the average stoichiometry represented by each configuration, is color-coded according to: Yellow = empty '-V2O5; light green = -Li0.125V2O5(one Li atom); dark green = -Li0.25V2O5(two Li atoms); teal = -Li0.375V2O5(three Li atoms); blue = -Li0.50V2O5(four Li atoms).Energies relative to the empty configuration 1 are listed on the right-hand side, in increasing order of stability.

Figure 4 .
Figure 4.A "Lithium's-Eye View" of the 2D Layered '-V2O5 Structure (A) Perspective views of extended atomic layers of partially-intercalated Structure C, viewed down the b-axis to emphasize interstitial sites accessible to intercalating Li ions.Key: Red = Oxygen, Green = Lithium, Gray polyhedra = VO5.All thermal ellipsoids shown at 50% probability.Li atomic site occupancy is 41%.Residual electron density surface derived from Fo-Fc structure factor map in the final refinement of Structure C is shown at select locations, with a white dotted circle around the peak of electron density at a tetrahedral "B" position between principle 6-coordinate Li "A" sites and mirrored along the b-direction.Green mesh = positive density; gray mesh = negative density.A-and B-sites are labeled in white.The atomic radius of Li (1.52Å) is labeled and indicated by a dotted gray circle.The nearest Li-Li distance in the a-direction (4.918Å) is highlighted.(B) The same structure, viewed down the aaxis, with important distances highlighted, including the nearest Li-Li distance in the b-direction (3.594Å), the A-site to B-site distance (3.185Å), and the distance between adjacent B-sites (1.103Å).O atoms bridging Li atoms are omitted for clarity.