Polymorphism in Weberite Na2Fe2F7 and its Effects on Electrochemical Properties as a Na-Ion Cathode

Weberite-type sodium transition metal fluorides (Na2M2+M′3+F7) have emerged as potential high-performance sodium intercalation cathodes, with predicted energy densities in the 600–800 W h/kg range and fast Na-ion transport. One of the few weberites that have been electrochemically tested is Na2Fe2F7, yet inconsistencies in its reported structure and electrochemical properties have hampered the establishment of clear structure–property relationships. In this study, we reconcile structural characteristics and electrochemical behavior using a combined experimental–computational approach. First-principles calculations reveal the inherent metastability of weberite-type phases, the close energetics of several Na2Fe2F7 weberite polymorphs, and their predicted (de)intercalation behavior. We find that the as-prepared Na2Fe2F7 samples inevitably contain a mixture of polymorphs, with local probes such as solid-state nuclear magnetic resonance (NMR) and Mössbauer spectroscopy providing unique insights into the distribution of Na and Fe local environments. Polymorphic Na2Fe2F7 exhibits a respectable initial capacity yet steady capacity fade, a consequence of the transformation of the Na2Fe2F7 weberite phases to the more stable perovskite-type NaFeF3 phase upon cycling, as revealed by ex situ synchrotron X-ray diffraction and solid-state NMR. Overall, these findings highlight the need for greater control over weberite polymorphism and phase stability through compositional tuning and synthesis optimization.

the A, B, C layers, respectively; c) and 4M, monoclinic where B1 chains are parallel to [ 10] and [110] for 1 the A and B layers, respectively. Each slab (denoted by A, B, or C) corresponds to one AB3 and one A3B Kagomé-like layer. Note that within each AA and BB pair of the 4M structure, the A3B layers differ slightly while the AB3 layers remain identical.  Table S1. DFT-computed energy, formation energy (EF), and energy above the hull (EHull) for all compounds within the NaF-FeF2-FeF3 phase space. The binary fluorides were used to compute the formation energies of the ternary phases.  Figure S4. Laboratory XRD patterns of various synthesis conditions used to obtain Na2Fe2F7. All syntheses began with a 36 hr ball-milling (BM) step (resulting XRD pattern shown in red) that was then followed by an anneal at the temperature and time specified in the figure. Na3FeF6 impurities were identified in all patterns besides the one obtained after a 500°C 30 min anneal, which was selected for the remainder of this work.  Figure S5. a) SXRD pattern collected on pristine Na2Fe2F7 and refined using the Rietveld method and only the 3T and 4M weberite variants (χ 2 = 2.16, RWP = 9.94%). An enlarged version of the refinement results of the main weberite peaks is shown in b), and compared to the best refinement results (χ 2 = 2.12, RWP = 9.75%) over the same Q range obtained using all three weberite polymorphs (2O, 3T, and 4M, see Figure  2a) in c). Individual profiles are shown for the 2O (blue), 3T (purple), and 4M (orange) polymorphs. Table S4. Refined lattice constants and weight percentages for all phases used to fit the SXRD data for carbon-coated Na2Fe2F7. The fit residuals are: χ 2 = 1.31 and RWP =7.01%. Note that the 4M weberite polymorph was used to fit the low crystallinity, carbon-coated data as it was the majority weberite variant in the pristine material.

Supplemental Note 1. First principles computations of NMR parameters using CRYSTAL17 and comparison with experimental results
The computed hyperfine (paramagnetic) NMR properties were obtained at 0 K for the Na2Fe2F7 2O, 3T, and 4M weberite polymorphs using a 2x1x2 supercell for the 2O variant, and a 1x1x1 cell for the 3T and 4M variants. All computations were carried out on ferromagnetically-aligned cells. To compare CRYSTAL17 calculation results with experimental data acquired at room temperature, the computed shifts were subsequently scaled to a value consistent with the paramagnetic state of the system at the temperature of the NMR experiments, using a magnetic scaling factor Φ of the form: where Msat is the saturated (ferromagnetic) Fe 2.5+ magnetic moment at 0 K, and 〈 ( !"# )〉 the bulk average magnetic moment measured at the sample experimental temperature, Texp. Here, Texp is set to 320 K to account for frictional heating caused by fast (60 kHz) sample rotation during NMR data acquisition.
The magnetic scaling factor in eq. (1) can be evaluated from the experimental magnetic properties of the material: where B0 is the external magnetic field, μeff is the effective magnetic moment per Fe site, kB is Boltzmann's constant, ge is the free electron g-value, μB is the Bohr magneton, S is the formal spin of Fe 2.5+ (S = 4.5/2), and Θ is the Weiss constant. A derivation of eq. (2), starting from the Brillouin function in the low field, high temperature limit, can be found in a previous study by Kim et al. 1 Eq. (2) uses the "spin-only" expression for the magnetic moment and is only strictly valid when the orbital angular momentum is quenched. 2 Yet, for systems where spin-orbit coupling effects are negligible, such as Na2Fe2F7, the spinonly expression is a good approximation of the magnetic behavior of the system.
Given the multi-phasic nature of Na2Fe2F7 samples, we are unable to obtain the magnetic properties (μeff and Θ) of individual Na2Fe2F7 polymorphs experimentally. However, similar magnetic properties may be expected for the different polymorphs as they all retain a similar transition metal network, solely differentiated by variations in layer stacking. 3 Thus, we approximated μeff by the theoretical, "spin-only" magnetic moment (μSO = 5.41 μB/Fe 2.5+ ), and used a previously-reported value 3 of Θ = −104 K for Na2Fe2F7 to compute the magnetic scaling factor. A bulk magnetic scaling factor, Φ, of 0.008066 was obtained at T = 320 K and B0 = 2.35 T using eq. (1), which was used to scale the computed 23 Na and parameters listed in Table S7. Table S7. First principles 23 Na NMR parameters computed using the CRYSTAL17 code on 2O, 3T, and 4M Na2Fe2F7 structures optimized with VASP. The predicted NMR properties were scaled using a scaling factor Φ = 0.008066 to compare them to room temperature 23 Na solid-state NMR data obtained at an external magnetic field of B0 = 2.35 T. There are two unique Na local environments in 2O, three in 3T, and six in 4M Na2Fe2F7, with multiplicities specified in parentheses in the table below. δiso is the isotropic Fermi contact shift, Δδ and η are the electron-nuclear dipolar anisotropy and asymmetry parameters, respectively, CQ is the quadrupolar coupling constant, ηQ is the quadrupolar asymmetry, δQ is the second-order quadrupolar shift, and δobs= δiso + δQ is the observed chemical shift.  Figure S6. Comparison of 23 Na solid-state NMR spin echo spectra collected with a π/2 excitation pulse on Na3FeF6, and on pristine and carbon-coated Na2Fe2F7. All spectra are scaled according to the intensity of the 1800 ppm Na3FeF6 signal. Asterisks indicate spinning sidebands.

Supplementary Note 2. Optimization of the carbon-coating method for the preparation of Na2Fe2F7 cathode films
As the 24 hr carbon-coating process affects the weberite structure (based on the SXRD and Mössbauer results in Figure 2-3, and 23 Na ss-NMR results presented in Figure 4 in the main text), several shorter mechanochemical milling times and an in situ carbon-coating method were investigated to reduce structural disordering. The in situ carbon-coating method involved mixing the Na2Fe2F7 material with sugar prior to the annealing step and then heating the mixture to 650°C for 30 min. The laboratory XRD patterns collected on the various cathode films are shown in Figure S7a. These cathode films were galvanostatically cycled at a rate of C/20 (full (dis)charge in 20 hrs assuming the transfer of 2 Na per formula unit) by first charging to 4.3 V vs. Na + /Na and subsequent cycling between 4.3 V and 1.5 V. The resulting electrochemical profiles are shown in Figure S7b. While the in situ carbon-coating method led to a highly crystalline cathode, it also resulted in significant decomposition of the weberite phases. Further, the shorter milling procedures all resulted in reduced crystallinity and worse electrochemistry than the 24 hr ball-milled carbon-coated Na2Fe2F7 cathode considered thus far. Hence, carbon-coating using a 24 hr ball-milling step was deemed optimal and used for the remainder of this study. Figure S7. a) Laboratory XRD patterns, and b) galvanostatic charge-discharge curves obtained for Na2Fe2F7 after different carbon-coating methods. Asterisks denote impurity/decomposition phases formed during the carbon-coating step. Figure S8. a) Plots of discharge capacity retention and coulombic efficiency and b) average discharge voltage and voltage hysteresis vs. cycle number for the galvanostatic data shown in Figure 5. dQ/dV plots for cycles 1 (c), 2 (d), 10 (e), and 20 (f) from the galvanostatic data shown in Figure 5b. The cycle 1 charge data is shown in black with the remaining data coloring analogous to that in Figure 5b.  Table S10. Refined lattice constants and weight percentages for all phases used to fit the SXRD data collected on ex situ 10 th discharge Na2Fe2F7. The fit residuals are: χ 2 = 1.19 and RWP = 4.98%.   Figure S10. Quantitative 19 F ss-NMR spin echo spectra obtained on ex situ NaxFe2F7 samples collected after the 1 st and 10 th discharge using a long interpulse delay of 60 s. Both spectra show a prominent signal at −120 ppm assigned to the PTFE binder, and very minor signals at −74.5 ppm and −224 ppm, which we attribute to decomposed electrolyte species containing PF6 − , 7 and NaF, respectively. The NaF signal is indicated with a dashed line. By taking the ratio of NaF to PTFE integrated signal intensity (assuming the presence of 10 wt% PTFE in the sample, as used to prepare the cathode films), we find that the NaF content in the two ex situ samples is < 0.05 wt%. Thus, NaF is not related to the phase transformation process occurring in the bulk of the cathode and most likely arises from electrolyte decomposition during cycling. We note that NMR signals from 19 F nuclei directly bonded to paramagnetic Fe species (as is the case for all F environments in NaxFe2F7 and NayFeF3) in the cathode materials are too broad (and short-lived) to be observed experimentally.

Supplemental Note 3. Selection of Na-vacancy enumerated structures
All calculations were performed on 1x1x1 cells of the different weberite variants, leading to cells containing 44, 66, and 176 atoms for 2O, 3T, and 4M Na2Fe2F7, respectively. As each weberite polymorph contains many individual Na sites, it is impractical to consider all possible Na-vacancy orderings. For example, there are 17,000 Na-vacancy orderings between x = 1 and 2 for the 4M polymorph. Thus, select configurations were considered for each polymorph at x = 0, 0.75, 1, 1.25, 1.5, 1.75, 2, 2.25, 2.5, and 3, and for the 4M polymorph only full or zero occupation of each of the Wyckoff sites was considered. Symmetrically-unique Na-vacancy orderings were enumerated and ranked according to their Ewald Sum Energy using Pymatgen (Python Materials Genomics) 8 and the five lowest energy orderings were considered. In total, 71 NaxFe2F7 structures were calculated for the 2O polymorph, 12 for the 3T polymorph, and 85 for the 4M polymorph.
Only a small number of structures were calculated for the 3T NaxFe2F7 polymorph as a convex hull has already been reported for this variant, although only down to x = 0.5. 5 As the 2O and 4M polymorphs contain no intrinsic Na vacancies, bond valence sum mapping using the SoftBV 9-11 software program was used to identify possible intercalation sites. This resulted in three and five possible intercalation sites for the 2O and 4M polymorphs, respectively. The coordinates for these possible intercalation sites are listed in Table S11. As the 3T structure contains two half-filled Na sites at x = 2, no additional intercalation sites were investigated. Below x = 2, only the Na sites that are occupied at x = 2 were considered. Table S11. Possible Na-ion intercalation sites in 2O, 3T, and 4M NaxFe2F7. Crystallographic information for sites that may be able to accommodate Na-ions in the various polymorphs, including sites occupied in the Na2Fe2F7 crystal structures and those predicted by SoftBV. [9][10][11] The occupancy (occ.) is given at x = 2. The relative site energy is calculated using bond valence sum mapping within SoftBV. The coordination environment for each site is also provided, including the number of nearest neighbors (NN) and coordination environment.  Figure S11. Predicted % volume change with respect to the Na2Fe2F7 structure upon Na insertion and extraction for the three Na2Fe2F7 weberite polymorphs. The volume expansion is plotted for each Navacancy ordering within 10 meV/atom of the lowest energy ordering at a given NaxFe2F7 composition.