Crystal Structure of the Intermediate Na2V2(PO4)3 Phase and Electrochemical Reaction Mechanisms in NaxV2(PO4)3 (1 ≤ x ≤ 4) System

1Laboratoire de Réactivité et de Chimie des Solides, Université de Picardie Jules Verne, CNRS-UMR 7314, F-80039 Amiens Cedex 1, France 2CNRS, Univ. Bordeaux, Bordeaux INP, ICMCB UMR 5026, F-33600 Pessac, France 3TIAMAT, 15 Rue Baudelocque, 80000 Amiens 4Department of Materials Science and Engineering, National University of Singapore, Singapore 117575, Singapore 5Chemical and Biomolecular Engineering, National University of Singapore, 4 Engineering Drive 4, Singapore 117585 6CELLS-ALBA Synchrotron, Cerdanyola del Vallès, E-08290 Barcelona, Spain 7RS2E, Réseau Français sur le Stockage Electrochimique de l’Energie, FR CNRS 3459, F-80039 Amiens Cedex 1, France


Introduction
Na-superionic-conductor (NASICON) structured materials are considered as promising electrodes for sodium-ion batteries because of their 3D open-framework crystal structure, resulting in high cyclability and fast rate capability. [1][2][3][4][5] Among them, Na3V2(PO4)3 has been extensively studied, showing satisfactory energy density and rate performance as well as good thermal stability. [6][7][8][9][10][11][12][13] The crystal structure of Na3V2(PO4)3 is composed of repeating units called lanterns, into which two VO6 octahedra are joined together through three corner-sharing PO4 tetrahedra. Within the 3D framework generated by these lanterns, two crystallographic sodium sites, labeled Na(1) and Na (2), are usually reported. The Na(1) site is located between the lantern units along the [001]hexagonal direction and is surrounded by six oxygen atoms in its first coordination sphere and by six Na (2) atoms in its second one. At maximum, the Na(1) and Na(2) sites (of different multiplicities) can respectively generate one and three Na positions per formula unit, thus leading to the final stoichiometry Na4V2(PO4)3. During electrochemical reactions, although the Na(1) site is involved in the global Na-ion transport mechanism (Na(2) -Na(1) -Na(2) pathways), it tends to be almost fully occupied regardless of the total Na content into the material, whereas the Na(2) site is partially/fully emptied or filled depending on the compositions. 8,9,[14][15][16] It is well known that two Na + ions can be reversibly electrochemically extracted from a Na3V2(PO4)3 electrode, through a voltage-composition "plateau" at ~3.4 V (vs. Na + /Na) utilizing the V 4+/3+ redox couple (with a theoretical capacity of 117.6 mAh/g). 13,17- 22 The reaction has been described by many authors as a mechanism of two-phase reaction between Na3V2 3+ (PO4)3 and Na1V2 4+ (PO4)3. 13,17-22 Additionally, one Na + ion can be inserted into Na3V2(PO4)3 at ~1.6 V (vs. Na + /Na) through the V 3+/2+ redox couple towards the Na4V2(PO4)3 composition (theoretical capacity of 58.8 mAh/g). 18,19,[22][23][24][25][26][27] Recently, Zakharkin et al. 20 noticed the signature of an intermediate Na2V2(PO4)3 phase, which involves the V 4+/3+ redox couple. Nevertheless, no structural information on the intermediate phase was provided. Other previous reports also suggested the existence of Na2V2(PO4)3, but the authors barely contemplated the existence of a new intermediate phase. 18,19 This suggests that the widely believed two-phase reaction between Na3V2(PO4)3 and Na1V2(PO4)3 needs to be reinvestigated, in particular, providing structural information and the origin of the appearance of the intermediate Na2V2(PO4)3 phase.

Material Characterization:
The chemical composition of the synthesized material was quantified using inductively coupled plasma-optical emission spectroscopy (ICP-OES) with a Varian Model 720-ES spectrometer. The amount of carbon coating on the synthesized material was measured by thermogravimetric analyses (TGA) with a NETZSCH STA 449C. The morphology of the powder was examined by scanning electron microscopy (SEM) with a Hitachi Model S-4500 microscope.
Operando Synchrotron X-ray Diffraction: Operando synchrotron X-ray powder diffraction (SXRPD) measurements were performed on the MSPD beamline of the ALBA synchrotron in Spain 37 with Debye−Scherrer geometry (λ=0.8266 Å) using an in situ coin cell with glass windows. Prior to the operando measurements, the SXRPD pattern of the pristine Na3V2(PO4)3 was collected with a 0.3 mm diameter capillary. Two in situ cells containing Na3V2(PO4)3 electrodes were measured at the same time thanks to the eight-cells holder with an automatic positioning system available at the MSPD beamline. 38 Each SXRPD pattern was collected every 30 minutes with an acquisition time of ~3.5 minutes in the 2θ angular range of 2-40°, with a 2θ step size of 0.006° using a MYTHEN detector for rapid pattern collection. The working electrodes were composed of the Na3V2(PO4)3 powder and carbon black (80/20 in wt%), and Na metal was used as counter/reference electrode. The mass loadings of the active material in the electrodes were 5.33 and 6.12 mg, respectively. One sheet of Whatman glass fiber (GF/D) was used as a separator and the electrolyte was composed of 1 M NaPF6 in ethylene carbonate (EC) / dimethyl carbonate (DMC) (1:1, w/w) with 2 wt.% of fluoroethylene carbonate (FEC). The first cell was measured for one cycle with a slow electrochemical reaction rate of 0.11 C (1 C = 58.2 mA/g, or about 9 h for the exchange of 1Na + / 1e -) with a voltage window of 1 -3.75 V versus Na + /Na. The second cell was measured for six cycles with higher C-rates (i.e., 0.37-0.77-0.77-0.77-0.37-0.77 C). A large overpotential was observed during the measurements of the second cell, hence the voltage windows were adjusted with the respected C-rates (detailed cycling conditions can be found in Table S1 in the supporting information section).

Density Functional Theory Calculations:
To assess the thermodynamic stability of NaxV2(PO4)3 with distinct Na-vacancy orderings at 0 K, we used the spin-polarized density functional theory (DFT), as implemented in VASP. 39,40 The exchange-correlation was approximated by the strongly constrained and appropriately normed (SCAN) meta-generalized gradient approximation functional, 41 with a U correction of 1.0 eV on all vanadium atoms to improve the localization of 3d electrons. 42 The total energies were converged to within 10 -5 eV/cell, atomic forces (stresses) within 10 -2 eV/Å (0.29 GPa). The 1 st Brillouin zone was integrated over a G-centered k-point grid of 3 × 3 × 3 for all primitive structures containing 2 formula units (f.u.) with 42 atoms, a 1 × 3 × 3 k-point mesh for all supercells with 4 f.u. (84 atoms), and a 1 × 1 × 3 mesh for 8 f.u. (168 atoms). The valence electrons were treated in terms of plane-waves up to an energy cutoff of 520 eV, while projector augmented wave potentials were used to describe the core electrons, 43 with Na The average intercalation voltage was derived using Eq. 1.
where Δ ! is the change of Gibbs free energy, as approximated from our DFT total energies, which ignore the zero-point energy correction, the term, and entropic effects. Thus, ) () are the DFT total energies of stable Navacancy orderings at compositions + , and the Na chemical potential of Na metal, . is the Faraday constant. Mixing enthalpies ( *+"+,-) at different Na compositions, to construct the 0 K phase diagram were defined in Eq. 2.

Results and Discussion
The composition of the as-synthesized Na3V2(PO4)3 powder was determined by elemental analysis using ICP-OES. The Na/V/P ratio was found to be 3.03(2):1.97(3):2.99 (6), suggesting that the target composition Na3V2(PO4)3 was achieved through the sol-gel-assisted solidstate reaction. SEM images of the Na3V2(PO4)3 powder ( Figure S1) show that the particles have no particular shapes as similar to other studies. 11-13,17-22 However, relatively large agglomerates ranging from few microns to several tenths of microns were found with the primary particles in the size of a few hundreds of nanometers. The powder is carbon-coated on the surface, ca. 9 wt% of carbon as determined by TGA measurements in air, shown in Figure S2.
The SXRPD pattern of the as-synthesized Na3V2(PO4)3 powder is shown in Figure 1. No impurity phases were detected based on the XRD analysis. As previously reported, 44 at room temperature the crystal structure of Na3V2(PO4)3 cannot be indexed using a rhombohedral (R3c) cell, but a monoclinic distortion must be considered. This is illustrated by the splitting of the (116)rhombohedral reflection at dhkl ~ 2.8 Ǻ into (-511)monoclinic, (-422)monoclinic, and (-313)monoclinic, which are signatures of the monoclinic distortion (inset images of Figure 1).
Depending on the thermal history of the sample, Na3V2(PO4)3 can crystallize either in the monoclinic α or β form at room temperature (the reversible phase transition occurring very close to room temperature with about 10° of hysteresis). 44 In the present study, the crystal structure was refined with the monoclinic β phase since the (111) reflection at 6.74° (λ=0.8266 Å) was not observed, while it is allowed in the α (i.e., Na + ordered) phase, as shown in Figure S3.  To study the (de-)intercalated phases and the Na + insertion/extraction mechanisms in Na3V2(PO4)3, operando SXRPD measurements were performed. Figure 2a displays a 2D view of the SXRPD of a selected 2θ range during the first electrochemical charge-discharge cycle together with the corresponding galvanostatic data measured within a voltage window of 1.0 -3.75 V (vs. Na + /Na) at a C-rate of ~0.11 C (for wider 2θ range, see Figure S4). A total number of 89 scans were recorded during the first cycle. From scan number 1 to 30, Na3V2(PO4)3 is first oxidized up to 3.75 V vs. Na + /Na. During the charge process, two Na + cations are extracted leading to the composition Na1V2(PO4)3. Close to the mid-charge (i.e., after approximatively 10h of cycling) a weak reflection at 2θ ≈ 7.7° starts to appear together with the presence of Na3V2(PO4)3 (corresponding reflection at 2θ ≈ 7.63°) and Na1V2(PO4)3 (corresponding reflection at 2θ ≈ 7.85°). Na1V2(PO4)3 is then reduced back to Na3V2(PO4)3 (scan number 60) and further to Na4V2(PO4)3 (scan number 89) at a potential of ~1 V vs.
Na + /Na. During the discharge process, the very same peak at 2θ ≈ 7.7° re-appears with an increased intensity. This new reflection that is attributed to the new intermediate The intermediate Na2V2(PO4)3 phase tended to coexist with the Na3V2(PO4)3 and Na1V2(PO4)3 phases at low C-rate (0.11 C). However, when a higher current density was applied (i.e., towards a non-equilibrium state), the Na2V2(PO4)3 phase became more isolated. Similarly, in the operando study of LiFePO4, a higher C-rate (1 C to 10 C) allowed a more intense appearance of the intermediate LixFePO4 phase. 30 Even though the C-rates used in this study were relatively low, the battery cells already reached a non-equilibrium condition. This is probably because (i) the Na3V2(PO4)3 powder contains relatively large particles (see Figure   S1); and (ii) the electrodes without binder can induce a higher overpotential. 45 This is further confirmed by the observation of the large polarization of ~150 mV using the in situ cell compared to a low polarization of 30 mV observed using a normal coin cell, cycled at the same C-rate of 0.11 C ( Figure S5). Figure S6 shows operando SXRPD data collected during six cycles with the C-rates of 0.37-0.77-0.77-0.77-0.37-0.77 C (which are about three to seven times higher current densities than 0.11 C). To increase the chance of isolating a 'pure' Na2V2(PO4)3 phase, multiple cycles were measured. The SXRPD pattern which appears mostly composed by the Na2V2(PO4)3 phase was obtained during the last cycle (see Figure   S6 for more details). compositions. Importantly, a careful evaluation of the SXRPD pattern of Na2V2(PO4)3 reveals the appearance of weak Bragg peak at a very low 2θ angle (~ 3.85°, dhkl = 12.29 Å). With operando technic, this weak Bragg peak at such a low angle (equivalent to ~7.2° in CuKα radiation) may be missed with a standard laboratory X-ray equipment, while we clearly observed it with a synchrotron X-ray source. This provides critical information to solve the crystal structure of Na2V2(PO4)3. The powder pattern of Na2V2(PO4)3 presented in Figure 3 was then used to solve its crystal structure. The indexing of the powder pattern, the space group determination, and the cell transformation with group-subgroup relationships were carried out using Dicvol, 46 Chekcell, 47 and POWDERCELL 48 software, to fully resolve the crystal structure of Na2V2(PO4)3. During the steps of indexing and space group determination, it was found that the reflection at 2θ = 3.85° excludes the rhombohedral lattices ( Figure S7) as well as C-  (Table S2), it appears that the environment of both V(1a) and V(1b) are similar with an average V-O bond distance of 1.99(9) Å, which suggests that V 3+ and V 4+ are randomly distributed over the V(1a) and V(1b) positions. For the Na crystallographic sites, the Na(1) and Na(2) sites split into two Na(1) (labeled Na(1a) and Na(1b)) and three Na(2) positions (labeled Na(2a1), Na(2a2), and Na(2b)) in the space group P21/c. The refined occupancy factor for Na(2a2) position was 0.08 (7), which can be considered as fully empty.
To shed light on the thermodynamic stability of the intermediate Na2V2(PO4)3 phase, detected with our SXRPD diffraction, we performed dedicated DFT calculations. Figure 5 shows the thermodynamic properties of NaxV2(PO4)3 in the region of x = 1 -3 at 0 K, as computed by DFT. Figure 5a shows the DFT mixing enthalpies ( *+"+,-in eq. 2) for all Na/vacancy orderings of the NaxV2(PO4)3 compositions. Using a convex hull minimization algorithm, all the ground-state configurations were obtained. It can be concluded that besides the endmembers Na1V2(PO4)3 and Na3V2(PO4)3, which are assigned to rhombohedral and monoclinic symmetry, respectively, a new phase Na2V2(PO4)3 appears as a stable configuration. However, Na2V2(PO4)3 shows a relatively low mixing enthalpy (ca. -23 meV/f.u.) with respect to Na1V2(PO4)3 and Na3V2(PO4)3, and this suggests that the intermediate phase may be metastable at room temperature.  chemically as a pure phase will further clarify the discrepancies between the DFT data and our experimental models.
Notably, the Na ordering of Na2V2(PO4)3 give rise to a small voltage step (~50 mV). Having the crystal structures of the new Na2V2(PO4)3 phase determined (with the space group P21/c), the operando SXRPD data (shown in Figure 2) were analyzed by Rietveld refinements including the evolutions of phase transitions, cell volumes, and phase weights as shown in Figure 6. Five different regions can be distinguished during the charge and discharge processes (labeled from I to V) in Figure 6. In region I (solid solution part), only Na3-δV2(PO4)3 is present and its unit cell volume (V/Z) slightly decreases from 239.687(6) Å 3 to 239.384(8) Å 3 . Region II (plateau at 3.4 V vs. Na + /Na) can be divided into two sub-regions (II' and II''). The Na + extraction mechanism occurs first through an out-of-equilibrium "threephase" reaction, where the amount of Na3V2(PO4)3 phase decreases while those of Na1V2(PO4)3 and Na2V2(PO4)3 phases increase concomitantly up to mid-charge (region II').
When the pristine Na3V2(PO4)3 phase re-appears during discharge, the reaction mainly occurs through a two-phase reaction mechanism but a slight peak-shift to lower angles (Figure 6b) and an increase of V/Z were observed, which indicates that a partial solid solution mechanism is also involved. This behavior is typically observed in Na3V2(PO4)3 17-22 and other electrode materials, such as, Na3Al0.5V1.5(PO4)3, 51 Na4MnCr(PO4)3, 52 Na2TiV(PO4)3, 53 and LiVOPO4, 54 which involve a two-phase reaction mechanism upon cycling.
When multiple phase boundaries are possibly observed between two end-members, leading to strains, slight changes in cell parameters can occur as a signature of these strains. 51,53,54 Nevertheless, the SXRPD pattern of Na3V2(PO4)3 is maintained after the re-sodiation, implying that the overall electrochemical reaction is highly reversible.
From the phase fraction analysis, it is clear that the Na2V2(PO4)3 phase could not be observed as completely isolated but rather coexisting together with the Na1V2(PO4)3 and  (1) and Na(2) sites. Generally, Na + insertion in the NASICON structure increases the a parameter and decreases the c parameter (in hexagonal axes). When the Na(1) site is depopulated, the c parameter increases mainly due to an increasing repulsion between parallel O3 triangular faces of the MO6 octahedra through the Na(1) site, as less screened by the Na + ions. 15,52,55-57 In the case of NaxV2(PO4)3, the distances between adjacent VO6 octahedra through the Na (1) site along [001]hexagonal remain nearly constant, 6.269(4) Å in Na4V2(PO4)3 and 6.228(4) Å in Na1V2(PO4)3, (Figure 7), as the Na (1) Table S2.
Also, the volumes of the VO6 octahedra decrease in parallel from 11.69, to 10.73, to 10.16, and to 9.15 Å 3 , respectively (∆Voct/Voct = 21.7 %). As a comparison, the volume of the When it comes to the number of Na + in the Na(1) and Na(2) sites per formula unit (Table 3), our findings establish that the Na(1) site is almost fully occupied in all compositions except for Na3V2(PO4)3 as the occupancy factor of Na(1) site is 0.679(14). For the Na(2) site, when the Na + content changes from x=4 to 1 in NaxV2(PO4)3, the occupancy factor gradually decreases from almost 100 % down to ~0 %. This evidence appears in good agreement with the computational analysis on Na(1) and Na(2) sites at room temperature. 49 Other NASICON-type materials also show similar trends, i.e. the Na(1) site tends to keep its high occupancies while the Na(2) site is populated or depopulated depending on the compositions. 8,9,[14][15][16] Overall, the refined total number of Na + per formula unit shows very good agreement with the expected compositions.
Finally, from Na2V2(PO4)3 to Na1V2(PO4)3, the structure is back to rhombohedral unit cell (R3c), having the Na(2) site fully emptied. It is interesting that from Na4V2(PO4)3 to Na2V2(PO4)3, the Na(2b) position tends to be more occupied than the Na(2a) positions. This may be related to different connectivities of Na(2a) and Na(2b) with the Na(1) site. Figure 8 shows the polyhedra constructed from Na and O atoms in Na3V2(PO4)3 or Na2V2(PO4)3. The connectivity between Na(2a) and Na(1) forms distinct 2D Na + diffusion paths parallel to the (100) plane, while the connectivity between Na(2b) and Na(1) results in 1D Na + diffusion chains along the [101] direction. This suggests that Na + ions in Na(2a) position may show easier migration than those in Na(2b) position, and therefore explaining the lower occupancy factor observed for Na(2a) than Na(2b).

Conclusions
In this study, we report for the first time the crystal chemistry of the new intermediate         Table S2. Bottom: the SPXRD patterns containing the most Na2V2(PO4)3 phase during each cycle. Note that the Na3V2(PO4)3 phase during 2 nd and 3 rd discharge was not observed as data point missing (fewer data points) due to higher C-rate. Table S1. Changes in voltage windows and C-rates during operando XRD measurements performed upon cycling of the second cell ( Figure S5). The measurement was stopped in the middle of charge during the sixth cycle.     Figure S9. Comparison of the space group P21/c and P2/c for the structural determination of Na2V2(PO4)3 phase. The same intensity for the possible (010) reflection (from the P2/c structural model) was observed in the XRD patterns of Na3V2(PO4)3, Na2V2(PO4)3, and Na1V2(PO4)3, suggesting it is not a peak but noisy background. Figure S10. Rietveld refinement results of Na4V2(PO4)3. The XRD pattern was obtained from operando measurements. The contributions from Na metal and Al foil are removed