Is there a common reaction pathway for chromium sulfides as anodes in sodium-ion batteries? A case study about sodium storage properties of MCr2S4 (M = Cr, Ti, Fe)

We present new insights into the electrochemical properties of three metal sulfides MCr2S4 (M = Cr, Ti, Fe) probed as anode materials in sodium-ion batteries for the first time. The electrodes deliver decent reversible capacities and good long-term cycle stability, e.g., 470, 375, and 524 mAh g−1 are obtained after 200 cycles applying 0.5 A g−1 for M = Cr, Ti, and Fe, respectively. The reaction mechanisms are investigated via synchrotron-based X-ray powder diffraction and pair distribution function analyses. The highly crystalline educts are decomposed into Na2S nanoparticles and ultra-small metal particles during initial discharge without formation of intermediate NaCrS2 domains as previously reported for CuCrS2 and NiCr2S4. After a full cycle, the structural integrity of MCr2S4 (M = Cr, Ti, Fe) is not recovered. Thus, the Na storage properties are attributed to redox reactions between nanoscopic to X-ray amorphous conversion products with only local atomic correlations M···S/S···S in the charged and M···M/Na···S in the discharged state.

Compounds with the general composition MCr 2 S 4 (M = 3d transition metals) crystallize either in the Cr 3 S 4 structure type (Fig. 1a, space group (SG) I12/m1, no. 12) (M = Ti, V, Cr, and Ni) or in the spinel structure type (Fig. 1b, SG Fd3m, no. 227) (M = Mn, Fe, Co, Cu, and Zn) [60,61]. The Cr 3 S 4 structure type can be described as an ordered defect variant intermediate between the NiAs and CdI 2 structure types: Edge-sharing CrS 6 octahedra form fully occupied layers with the stoichiometry CrS 2 and 50% of octahedral sites between these [CrS 2 ] x− slabs are occupied by M 2+ , and 50% are empty [62]. Thus, compounds crystallizing in this structure type are regarded as layer-like materials (Fig. 1a). The precise structural description is, however, more complicated for each MCr 2 S 4 , because the cation distributions M 2+/3+ :Cr 3+/2+ in fully and half occupied layers depend on the choice of M [52,63,64]. For example, Ti and Cr atoms share octahedral sites in fully occupied layers and remaining Cr atoms are located in the half occupied layers for TiCr 2 S 4 as revealed by neutron scattering experiments [65]. The few investigations about accurate cation distributions in monoclinic M 1 M 2 X 4 (M = Ti, V, Cr, Ni; X = S, Se, Te) indicate that the site preference in fully occupied layers decreases in the order Ti > Cr ≈ V > Ni [52]. In contrast, the spinel structure is composed of S 2− anions arranged in a close-packed fcc lattice with M 2+ cations occupying 1/8 of the tetrahedral and Cr 3+ cations 1/2 of the octahedral voids ( Fig. 1b) [66][67][68][69]. The thermodynamically favored arrangement of cations in MCr 2 S 4 mainly depends on the octahedral site preference energy (OSPE) of M 2+/3+ [70]. Thus, high OSPEs (e.g., V 2+ and Ni 2+ ) drive crystallization in the Cr 3 S 4 structure type, whereas low OSPEs (e.g., Fe 2+ and Zn 2+ ) prefer crystallization in the spinel structure [70].
We selected Cr 3 S 4 (CS) and TiCr 2 S 4 (TCS), both crystallizing in the Cr 3 S 4 -type, as well as cubic FeCr 2 S 4 (FCS) for our investigations. High theoretical capacities Q(CS) = 754.3 mAh g −1 , Q(TCS) = 765.4 mAh g −1 , and Q(FCS) = 744.2 mAh g −1 are calculated for full conversion reaction of all cations to their elemental states according to the following: here, we present the first study about electrochemical performances of the title compounds as anode materials for SIBs analyzed by galvanostatic discharge-charge (GDC) cycling and cyclic voltammetry (CV). Moreover, new insights into charge storage properties during Na uptake and release of Cr sulfides in terms of a structural, mechanistic view are presented by results of synchrotron-based, high-energy X-ray powder diffraction (XRPD), and total scattering X-ray experiments to calculate pair distribution functions (PDFs).

Synthesis of pristine materials
The pristine materials were synthesized by high-temperature solid-state reactions. Stoichiometric amounts of Cr (Alfa Aesar, 99%), Fe (Alfa Aesar, 99.9%), Ti (Chempur, 99.5%), and S (Chempur, 99.999%) corresponding to Cr 3 S 4 , TiCr 2 S 4 , and FeCr 2 S 4 were each mixed and ground in mortars. The mixtures were placed in quartz tubes, which were sealed under vacuum (< 10 −4 mbar) and heated at 450 °C for 24 h and subsequently at 800 °C (FCS) or 1000 °C (CS, TCS) for 72 h in a furnace before cooling to room temperature. Each (1) MCr 2 S 4 + 8 Na + + 8 e − → M 0 + 2 Cr 0 + 4 Na 2 S Fig. 1 Crystal structures of a monoclinic MCr 2 S 4 with S (yellow atoms), Cr (in gray and/ or red octahedra), M = Ti, V, Ni, Cr (in gray and/or red octahedra) and b cubic MCr 2 S 4 with S (yellow atoms), Cr (in blue octahedra), M = Mn, Fe, Co, Cu, Zn (in green tetrahedra). Created with Vesta v3 [71] product was crushed in a mortar, followed by characterization with XRPD. For CS and FCS, pellets were pressed and annealed at 800 °C (FCS) and 1000 °C (CS) for 168 h again, cooled to room temperature and crushed in mortars.

Electrochemical characterization
Film electrodes were prepared by suspending mixtures of 70 wt% MCr 2 S 4 , 20 wt% Super C65 carbon (Timcal), and 10 wt% polyvinylidene difluoride (PVDF) (Solvay) in N-methyl-2-pyrrolidone (Fisher Bioreagens, 99.8%) in a Retsch MM400 ball mill for 20 min at 15 Hz. The suspensions were spread on carbon coated Cu foil via doctor-blade casting method. Afterwards, they were dried for > 24 h at room temperature and at 60 °C in vacuum for about 12 h. For ex situ characterization, pellet electrodes were prepared by first mixing 70 wt% MCr 2 S 4 and 30 wt% Super C65 (Timcal) in a Retsch MM400 ball mill for 30 min at 10 Hz and then pressing parts of these mixtures into pellets. Swagelok®-type test cells were assembled in an Ar-filled glovebox. In each cell, either a circular electrode disk (d = 10 mm, active material mass m(CS) = 1. was covered by a Celgard® membrane and two glass fiber filter disks (Whatman) as separators, wetted by 1 m sodium trifluoromethanesulfonate NaCF 3 SO 3 (Sigma-Aldrich, 98%) in bis(2-methoxyethyl)ether (diglyme, Acros, 99 + %, anhydrous) as electrolyte solution, and layered by a circular Na metal disk as the counter electrode. GDC measurements were performed on a Neware BTS 3000 and an MTI BST8-WA battery analyzer applying constant current constant voltage (CCCV) mode for performance tests (film electrodes). A current density of 0.1 A g −1 was always applied for the 1st cycle and the end current of the CCCV mode. For ex situ characterization (pellet electrodes), current rates of I(CS) = 18.9 mA g −1 , I(TCS) = 19.1 mA g −1 , and I(FCS) = 18.6 mA g −1 were chosen for GDC interruptions, corresponding to an uptake or release of 8 Na/MCr 2 S 4 (Eq. 1) in 40 h (C/40). CV curves (film electrodes) were recorded in the potential range 3.0-0.1 V with a scan rate v = 0.1 mV s −1 on a Biologic VSP potentiostat.

Material characterizations
Initial characterization of pristine samples was carried out by in-house XRPD (PANalytical Empyrean diffractometer with PIXcel 1D detector, Cu-K α radiation, Debye-Scherrer geometry), energy-dispersive X-ray spectroscopy (EDX) and scanning electron microscopy (SEM) (Zeiss Gemini Ultra-55Plus with Oxford SD detector), and elemental analysis (Elementar vario MICRO Cube). The final pristine products and ex situ samples, obtained at distinct GDC interruption points, were packed in glass capillaries (d = 0.7 mm, Hilgenberg, Germany) in an Ar-filled glovebox and sealed with beeswax. High-energy (~ 60 keV) synchrotron-based experiments were performed at beamline P02.1, PETRA III (DESY, Hamburg): XRPD patterns and total scattering data were collected in Debye-Scherrer geometry at a wavelength of λ(CS) = λ(TCS) = 0.20703 Å and λ(FCS) = 0.20697 Å utilizing a Perkin Elmer XRD1621 amorphous silicon area detector placed at sample to detector distances of 1015(1) mm (XRPD) and 356(1) mm (total scattering). For calibration, to account for instrumental line broadening (XRPD) and for Q-damping (PDF), LaB 6 (NIST 660b) was measured as standard applying the same conditions. An empty capillary was measured to subtract glass contributions from the total scattering patterns. Raw data processing was performed with DAWN Science [72] and total scattering data were transformed into atomic PDFs, G(r), applying Q max = 24 Å −1 using xPDFsuite [73]. Joint refinements of XRPD and PDF data were performed for the pristine samples using Topas Academic v6 [74,75]. For the XRPD patterns, 9th order polynomial functions were applied to model backgrounds and Thompson-Cox-Hasting pseudo-Voigt profiles to contribute for instrumental line broadening [76]. For the PDF data, pseudo-Voigt Q-damping functions were applied to account for instrumental parameters and spherical peak shape functions with lower cutoff were used to consider the transition from correlated (small r values) to uncorrelated (high r values) atomic motion. Lattice parameters, atomic positions, Debye-Waller (DW) factors, and site occupancy factors (SOF) were co-refined during global optimization applying a weighting scheme such that parts of χ 2 were about equal for the XPRD and PDF data sets [77,78]. Special coordinates and SOFs of S atoms were fixed during the refinements. ICSD structure data were used for simulation of reference patterns and for starting parameters of the refinements: Cr 3 S 4 (ICSD-16722), TiCr 2 S 4 (ICSD-42907), FeCr 2 S 4 (ICSD-625938), Cr 2 O 3 (ICSD-25781), Na 2 S (ICSD-644959), bcc-Cr (ICSD-64711), bcc-Fe (ICSD-64795), and hcp-Ti (ICSD-43416).

Characterization of pristine compounds
The stoichiometry was determined by EDX yielding compositions of Cr 3.00(6) S 4.00 (6) , Ti 0.99(9) Cr 2.04(8) S 3.97 (6) , and Fe 0.98(2) Cr 2.03(7) S 3.99 (9) in line with nominal values (Table S1 and Fig. S1). Further elemental analysis demonstrates good agreement of the S content in all compounds with expected values (Table S2). The layered nature of CS and TCS is clearly visible in the SEM images, whereas the product FCS exhibits no specific particle shape morphology (Fig. S2).
In accordance to literature, the compounds CS and TCS crystallize in the monoclinic SG I12/m1, whereas FCS crystallizes in the cubic SG Fd3m (cf. "Introduction"). This is evidenced by joint Rietveld-like least-squares refinements of XRPD and PDF data yielding good agreement of the averaged long-range structure and local order for all compounds (Fig. 2, structural parameters in Table 1). For CS, minute amounts of Cr 2 O 3 (≈ 1.0 wt%) were detected, Fig. 2 Results of joint Rietveld-like least-squares XRPD-PDF refinements: a, c, and e XRPD patterns for CS, TCS, and FCS, respectively, each co-refined with corresponding PDFs shown in b, d, and f. Details are listed in Table 1 presumably resulting from reaction of Cr with the quartz ampoule. Moreover, the refinement reveals the presence of about 3% Cr atoms on Wyckoff position 2a, which represents the empty octahedral sites in the ideal Cr 3 S 4 structure type (Table 1). Lattice parameters and atomic fractional coordinates are in good agreement with previous results reported for this compound [79]. For TCS, it is not possible to distinguish between Ti and Cr via XRPD; hence, both elements are refined together (Fig. 2c, d). In contrast to CS, no atoms are located on site 2a in TCS (Table 1). For the joint XRPD-PDF refinement of FCS (Fig. 2e, f), the positions of Fe and Cr were fixed to tetrahedral and octahedral sites, respectively (cf. "Introduction"). The results for TCS and FCS demonstrate phase-pure products and yield structural parameters in accordance to values reported for TCS [65,79] and FCS [66,[80][81][82][83][84][85].

Electrochemical properties in SIBs
GDC (Fig. 3a, b) and CV (Fig. 3c, d) profiles were recorded during the 1st, 2nd, and 5th cycle using film electrodes in Na half-cells. The main electrochemical features are summarized in Table 2. During initial discharge of the CS electrode, one pronounced pseudo-plateau is visible around 0.41 V (GDC, Fig. 3a), which corresponds to a narrow cathodic peak in the 1st CV cycle (Fig. 3c). Although the capacities during the 1st discharge (8.0 Na/CS, CV; 8.3 Na/CS, GDC) match with the expected value for ideal conversion (8.0 Na/ CS, cf. Eq. 1), contributions of chemical side-reactions and formation of a solid electrolyte interphase (SEI) must be considered. Thus, a full conversion reaction of CS is hindered applying the selected conditions, which will be further discussed in the next chapter. Irreversible redox reactions of Cr 3+ cations and SEI formation cause an irreversible capacity loss of 30% in the 1st GDC cycle close to values reported for Na/CuCrS 2 (33%) [21], Na/NiCr 2 S 4 (28%) [22], and Na/CuV 2 S 4 (27.5%) [86], where very similar cell and electrode conditions were applied. One pronounced, peak is observed in the subsequent cathodic and anodic CV curves (Fig. 3c, d and Table 2) demonstrating that a single, reversible redox event between Cr x+ cations and Cr 0 accounts for the high capacities obtained after the 1st GDC and CV cycle (capacities fade < 2%, cf. Table 2). Almost equal capacities are delivered during subsequent cycles and correspond to ≈ 6 Na/CS uptake and release. Hence, the redox reaction in Eq.
(2) most likely occurs: Discharging the FCS electrode in the 1st cycle yields a pronounced pseudo-plateau at 0.43 V (GDC, Fig. 3a), which corresponds to the narrow cathodic CV peak at 0.36 V (Fig. 3c). Both electrochemical features are comparable to those observed for CS but higher discharge capacities are achieved (9.3 Na/FCS, CV; 9.7 Na/CS, GDC). Thus, a full conversion reaction (Eq. 1) occurs in addition to SEI (2) 3 Cr 0 + 6 Na + ⇌ 3 Cr 2+ + 6 Na 0   Table 2 Main redox events, capacities and corresponding Na uptake/ release observed during the 1st, 2nd, and 5th cycle of GDC (I = 0.1 A g −1 ) and CV (v = 0.1 mV s −1 ) measurements for Na/CS, Na/TCS, and Na/FCS cells. GDC potentials were extracted using differential capacity dQ/dV analysis of respective curves in Fig. 3a, b, whereas CV capacities were calculated by integration of respective curves in Fig. 3c  formation leading to an irreversible capacity loss of 26% during the 1st cycle. In contrast to CS, two cathodic peaks and two less resolved anodic events are observed in subsequent CV cycles (Fig. 3c, d and Table 2). This observation strongly indicates that Fe and Cr both participate in the redox reactions. The reversible capacities obtained in the 2nd to 5th GDC and CV cycles (capacities fade < 5%, cf. Table 2) correspond to a shuttle of ≈ 7 Na/FCS. Taking also the observations for CS into account (Eq. 2), a redox reaction according to Eq. (3) may be formulated for FCS: The lowest reduction voltage of the three metal sulfides during the initial discharge is observed for TCS, also exhibiting a less distinct pseudo-plateau (GDC, Fig. 3a) and a broader cathodic CV peak (Fig. 3c) compared to CS and FCS. This point towards a higher internal resistance for the TCS electrodes resulting in a larger polarization voltage. The conversion process of TCS is obviously incomplete if discharged to 0.1 V, clearly evidenced by the interruption at V low = 0.1 V of the cathodic event (1st CV curve, Fig. 3c). This is further confirmed by the initial discharge capacities (6.8 Na/TCS, CV; 7.9 Na/TCS, GDC), which is smaller than expected (Eq. 1). Again, additional contributions from SEI formation and chemical side-reactions need to be considered, in particular because the irreversible capacity loss (31%, TCS) during the 1st GDC cycle is close to the findings for CS and FCS. During subsequent GDC and CV cycles, the TCS electrodes deliver the smallest capacities of the three sulfides (Table 2) and ≈ 5 Na/TCS are reversibly shuttled (capacity fade < 4%). The incomplete reduction in the 1st cycle also causes a cathodic peak located at 0.1 V in the 2nd CV cycle (Fig. 3d). In contrast to the results for CS, (3) Fe 0 + 2 Cr 0 + 7 Na + ⇌ Fe 3+ + 2 Cr 2+ + 7 Na 0 two anodic CV signals are clearly visible for TCS indicating that both metal centers, Ti and Cr, participate in the redox reactions. We note that the reduction of Ti cations to elemental state was recently observed during discharge of TiO 2 [87] and TiS 2 [88] anodes. However, only one cathodic CV signal occurs after the 1st cycle for TCS. The area of the one cathodic CV peak corresponds to the sum of the two anodic CV peak areas; thus, the reduction of Ti and Cr cations seems to occur at a similar voltage vs. Na + /Na. However, a distinct assignment of electrochemical features to redox pairs remains speculative for TCS.
GDC performance tests were conducted for all electrode materials to evaluate long-term ( Fig. 4a and Table 3) and rate stabilities (Fig. 4b and Table 4). Applying a current rate of 0.5 A g −1 after the 1st cycle (I 1st = 0.1 A g −1 ), all electrodes deliver high capacities for 200 cycles accompanied by Coloumbic Efficiencies > 99% after the 5th cycle. The highest capacities are observed for FCS but it decreases by 14% (to 524 mAh g −1 ≈ 5.6 Na/FCS) until the 200th cycle. These high capacities can be explained by an almost full conversion reaction as discussed further below (XRPD and PDF analyses). In contrast, CS exhibits the best long-term stability and 5.0 Na/CS (470 mAh g −1 ) are reversibly shuttled after 200 cycles corresponding to a superior capacity retention of 93%. As evidences further below (XRPD and PDF analyses), the crystalline material CS is completely decomposed to X-ray amorphous products during sodiation and insulating Na 2 S does not crystallize, which boosts the long-term stability. Although the TCS electrode delivers the lowest capacities during cycling, e.g., 375 mAh g −1 (≈ 3.9 Na/TCS, capacity retention: 85%) after 200 cycles, this electrode offers the best rate capability in SIBs comparing the three sulfides. For example, the TCS electrode still delivers 264 mAh g −1 (≈ 2.8 Na/TCS, capacity retention: 58%) at a Fig. 4 GDC performance tests of Na/CS (blue), Na/TCS (red), and Na/FCS (green) test cells in the potential window 3.0-0.1 V: a long-term stability tests applying a current density of 0.5 A g −1 (1st cycle: I = 0.1 A g −1 ) and b charge capacities of rate capability tests current rate of 3.0 A g −1 , whereas the charge storage at this high rate is significantly worse using CS (125 mAh g −1 ≈ 1.3 Na/CS, capacity retention: 24%) or FCS (92 mAh g −1 ≈ 1.0 Na/FCS, capacity retention: 15%). The poor rate performance of the CS and FCS electrodes might result from diffusion limiting processes at higher current rates, but detailed studies about the reaction kinetics are necessary in future work. Comparing the overall performance of MCr 2 S 4 electrodes (rate capability, cycle life, and magnitude of capacity, cf. Tables 3 and 4), NiCr 2 S 4 offers the best electrochemical properties [22].

Structural changes during the 1st GDC cycle
The sodium storage mechanisms during the 1st GDC cycle were investigated at selected interruption points (Fig. 5) by high-energy XRPD (Fig. 6) and PDF (Fig. 7) analyses. Ex situ samples were collected using pellet electrodes. A comparison (Fig. S3) of the initial galvanostatic discharge profiles to 0.1 V using common film electrodes with and pellet electrodes without PVDF (cf. "Experimental") demonstrates that smaller capacities are obtained (≈ 6.8 Na/CS, ≈ 6.0 Na/TCS, and ≈ 7.3 Na/FCS) for the latter. This is not surprising since (i) PVDF contributes to SEI formation in SIBs, i.e., additional Na is consumed by decomposition of PVDF into NaF [22,[89][90][91] and (ii) different cell conditions influence the electrochemical kinetics, i.e. the electron and Na + ion diffusion. Thus, we selected a potential window of 3.0-0.01 V (Fig. 5), also because the former electrochemical experiments indicated that the full conversion is incomplete for CS and TCS at V = 0.1 V. Even so, the capacities obtained by discharging the pellet electrodes to 0.01 V (Fig. 5) demonstrate full conversion only for FCS (≈ 8.0 Na/ FCS) and incomplete conversion for CS and TCS (≈ 7.4 Na/ CS, ≈ 7.1 Na/TCS).
The results from XRPD (Fig. 6, cf. Figs. S4, S5 and S6) evidence that the sodium insertion-transition metal extrusion mechanism found for CuCrS 2 [21] and NiCr 2 S 4 [22] Table 3 Results of long-term stability tests (I = 0.5 A g −1 ): charge capacities after several cycles for Na cells using CS, TCS, and FCS electrodes. Results for NiCr 2 S 4 electrodes are shown for comparison. The capacity retention is related to the capacity of the 2nd cycle CS TCS FCS NiCr 2 S 4 [22] Cycle number Capacity (mAh g −1 ) Capacity retention (%) Capacity (mAh g −1 ) Capacity retention (%) Capacity (mAh g −1 ) Capacity retention (%) Capacity (mAh g −1 ) Capacity retention (%)   2  504  100  441  100  611  100  593  100  10  490  97  431  98  597  98  581  98  50  479  95  390  88  562  92  548  92  100  473  94  379  86  543  89  539  91  150  472  94  379  86  542  89  553  93  200  470  93  375  85  524  86 558 94  Fig. 6), the reflection intensities of the educts successively decrease. For CS, these reflections completely vanish at 6 Na/CS and two small reflections at ≈ 4.63° and ≈ 6.66° 2θ appear (marked with asterisks in Fig. 6a). They cannot be related to any known phases with compositions including Cr, S, and Na but indicate the formation of an intermediate at this point. Very small reflections, which does not change for the CS XRPD series (marked with "x" in Fig. 6a), correspond to the Cr 2 O 3 impurity already detected in the pristine material, not taking part in Na storage as an electric isolator [92]. Even after discharge to 0.01 V (C5), XRPD does not yield distinct evidence for the formation of nanoscopic Na 2 S or for crystalline, elemental Cr. However, very broad signals around ≈ 5.6° 2θ and ≈ 9.7° 2θ may be caused by ultra-small, X-ray amorphous Cr particles (cf. Fig. S4). The charged sample (C6) contains only X-ray amorphous products (besides crystalline Cr 2 O 3 ). These findings are typical phenomena reported for conversion-type materials. For TCS, a comparable picture is obtained including a charge storage mechanism via generation of X-ray amorphous conversion products (Figs. 6e and S5). The formation of nanocrystalline Na 2 S is observed between 4 and 7 Na/TCS (T3-T5). At 6 Na/TCS (T4, V ≈ 0.1 V), pronounced reflections of the starting material are still detected. These reflections remain after uptake of 7 Na/TCS (T5) and after a full cycle (T6) with smaller scattering intensity, unambiguously demonstrating the incomplete conversion at the selected conditions for TCS. This explains the lower capacities detected for TCS in all electrochemical GDC and CV tests compared to CS and FCS. Also during discharge of the FCS electrode, neither crystalline elemental Fe nor Cr is observed (Figs. 6f and S6). The formation of nanocrystalline Na 2 S is, on the contrary, clearly evidenced after an uptake of 8 Na/FCS (F5), and the charge product (F6) is again X-ray amorphous. More distinct reflections for Na 2 S at full discharge are a good hint that the conversion of FCS is in an advanced state after full discharge compared to CS and TCS, which explains the higher capacities observed during GDC and CV tests for Na/ FCS cells. The crystallization of an insulating Na 2 S matrix observed for FCS and TCS is accompanied by additional volume expansion, forcing the contacts between X-ray amorphous products and the electric conductor to break. This explains the worse capacity retention observed for FCS and TCS during long-term cycling ( Fig. 4 and Table 3) compared to CS. Atomic PDFs corresponding to the samples M1-M6 of CS, TCS, and FCS are shown in Fig. 7, representing the evolution in the averaged local environments (1.9-3.9 Å) during Na uptake and release (cf. Fig. S7 for r = 1 to 21 Å). In agreement with the observations from XRPD, a look at the mid-range order (Fig. S7) confirms that all samples lose their structural integrity and barely any total scattering intensity is observed at r > 7 Å after uptake of 6 Na per formula unit (M4-M6). Hence, only very small conversion products account for the charge storage properties after initial structural disintegration. Total scattering intensities Chemical structures were created with Vesta v3 [71] corresponding to M-S (M = Cr, Ti, Fe) bonds decrease during all initial discharge processes (Fig. 7). In addition, very short interatomic separations M···M and S···S, which are apparent in the pristine compounds MCr 2 S 4 , completely disappear after discharging to 0.01 V (for TCS and FCS already at 6 Na/MCS). Thus, these conversion products are not related to the pristine materials, but after charging the electrodes to 3.0 V (M6), PDF peaks reappear in the short range at very similar positions as observed for the pristine compounds. Hence, the local environments of the charged products resemble that expected for very small metal sulfides. Because the charge products lost their structural integrity in the mid-to long-range order, a relation to particular sulfidic phases is obviously speculative. The PDFs of all discharged samples (V = 0.01 V, M5) are comparable to each other and point towards the formation of Na-S bonds as well as metal-metal separations in the elemental metals. However, differentiation between PDF signals corresponding to similar bonds in the first shells of bcc-Cr, bcc-Fe, and hcp-Ti is not possible because the PDFs represent histograms of all interatomic distances in the sample. Representatively, PDFs and XRPD patterns corresponding to the discharged and charged state of FCS electrodes in the 2nd cycle are shown in Fig. S8. Although no reflections of Na 2 S are visible in the XRPD pattern after the 2nd discharge, the local environments in both discharged products (1st and 2nd cycle) are very similar as the PDFs are almost superimposable. Also, the PDFs and XRPD patterns of the charged samples in the 1st and 2nd cycle are very similar evidencing a high reversibility of the charge storage mechanism involving very small conversion products.

Conclusion
In this comparative study, the three highly crystalline chromium sulfides Cr 3 S 4 (CS), TiCr 2 S 4 (TCS), and FeCr 2 S 4 (FCS) were analyzed as anode materials in SIBs for the first time. Galvanostatic and voltammetric investigations provide insights into the Na storage properties and extend the overall picture for sulfidic SIB-anodes. The three metal sulfides offer good long-term stability with high capacity retention between 0.1 and 3.0 V and deliver remarkably high capacities even after 200 cycles at 0.5 A g −1 . From the results of CV, we propose reversible redox reactions (Eqs. 2 and 3) for discharge and charge processes after the 1st cycle. Moreover, analyses of high-energy X-ray diffraction patterns and pair distribution functions provide a fundamental understanding of structural changes during the 1st cycle. In contrast to the Na insertion-Cu/Ni extrusion mechanisms observed for CuCrS 2 [21] and NiCr 2 S 4 [32], neither crystalline NaCrS 2 -like intermediates nor crystalline Cr, Ti, or Fe is formed during discharge of Na/CS, Na/TCS, or Na/FCS cells. During Na uptake, these metal sulfides are directly decomposed into X-ray amorphous conversion products embedded in a nanocrystalline Na 2 S matrix, and structural integrity of the sulfides is not recovered during Na release. We conclude that the charge storage reactions occur on a very small nanoscale for the three title compounds and rather depend on the metals redox activity than on the structure of the starting compounds.