Mechanism of Li2S formation and dissolution in Lithium-Sulphur batteries

Insufficient understanding of the mechanism that reversibly converts sulphur into lithium sulphide 18 (Li 2 S) via soluble polysulphides (PS) hampers the realization of high performance lithium-sulphur 19 cells. Typically Li 2 S formation is explained by direct electroreduction of a PS to Li 2 S; however, this is 20 not consistent with the size of the insulating Li 2 S deposits. Here, we use in situ small and wide angle 21 X-ray scattering (SAXS/WAXS) to track the growth and dissolution of crystalline and amorphous 22 deposits from atomic to sub-micron scales during charge and discharge. Stochastic modelling based 23 on the SAXS data allows quantification of the chemical phase evolution during discharge and charge. 24 We show that Li 2 S deposits predominantly via disproportionation of transient, solid Li 2 S 2 to form 25 primary Li 2 S crystallites and solid Li 2 S 4 particles. We further demonstrate that this process happens 26 in reverse during charge. These findings show that the discharge capacity and rate capability in Li-S 27 battery cathodes are

deposits from atomic to sub-micron scales during charge and discharge. Stochastic modelling based 23 on the SAXS data allows quantification of the chemical phase evolution during discharge and charge. 24 We show that Li2S deposits predominantly via disproportionation of transient, solid Li2S2 to form 25 primary Li2S crystallites and solid Li2S4 particles. We further demonstrate that this process happens 26 in reverse during charge. These findings show that the discharge capacity and rate capability in Li-S 27 battery cathodes are therefore limited by mass transport through the increasingly tortuous network 28 of Li2S / Li2S4 / carbon pores rather than electron transport through a passivating surface film. 29 30 Main 1 Lithium-sulphur (Li-S) batteries are considered strategic candidates to reduce the environmental impact of 2 current Li-ion batteries 1 . The high expectations arise from the large theoretical capacities, abundance, and 3 low cost of sulphur [2][3][4] . Li-S batteries reversibly cycle sulfur to lithium sulfide (S / Li2S), typically in a highly 4 porous carbon cathode soaked with a liquid, non-aqueous electrolyte and using a lithium metal anode. 5 Discharge converts S to Li2S stepwise via polysulfides (PSs) Li2Sx (2 < x < 8). Practical realization of  cells is hindered by incomplete S utilization, poor S/Li2S mass loadings, rapid capacity fading, low rate 7 capabilities, and irreversible reactions of PSs at the anode 3,5,6 . These issues all trace back to insufficient 8 understanding of S-to-Li2S conversion. 9 The physical-chemical mechanism to reversibly form and dissolve solid Li2S remains controversial 7,8 . Many 10 studies consider Li2S to form via direct electroreduction of Li2S2 (or higher-order PSs) at the carbon-electrolyte 11 interface 8-12 . However, as electrodeposition of an insulator is in principle self-limited, the fact that Li2S deposits 12 are beyond tens and hundreds of nm in size 13-15 suggest that they form via a solution-mediated process. This 13 is supported by the finding that capacity is limited by mass transport in the tortuous Li2S-carbon pore 14 network. [16][17][18] Such a solution-mediated processes could be the direct electroreduction of molecular Li2S2 to 15 dissolved Li2S (2 Li + , S 2-), which then precipitates solid Li2S crystallites, similar to the electrodeposition of 16 NaO2 or KO2 in Na-O2 and K-O2 batteries 19 . However, large deposits beyond tens or hundreds of nanometers 17 would require a solubility of Li2S beyond the reported 10 -6 M 15 . Disproportionation of PSs is widely accepted, 7 18 and some studies consider Li2S to form via disproportionation of dissolved Li2S4 13,16,20 . 19 While operando x-ray diffraction 21,22 and spectroscopy 23-26 provide insights into the chemistries occurring 20 during (de)lithiation, a complete understanding of the mechanisms of Li2S formation requires a detailed 21 chemical as well as structural picture. While the structures within Li-S has been studied using (operando) 22 electron and X-ray microscopy 27-30 , these techniques are limited by impractical cell designs, the Li2S stability, 23 the resolution, field of view, and the challenges of 3D imaging. Small angle scattering can provide 24 complementary structural sensitivity from sub-nm to 100 nm, regardless of whether the probed phases are 25 crystalline, amorphous or liquid 31 . A recent operando small angle neutron scattering study confirmed the 26 ability to follow the evolution of Li2S particles not much larger than a few nm 32 . Neutron and x-ray scattering 27 are complementary methods since the phases are probed with different scattering contrasts. 28 Here, we perform in situ small and wide-angle X-ray scattering (SAXS/WAXS) to gain simultaneous structural 29 and chemical insights from atomic to sub-micrometer scales with time resolutions of several seconds. 33 Fig. 1). SAXS and WAXS intensities are recorded on 46 separate areal detectors (Fig. 1a) with a time resolution of 1 min during potentiostatic discharge/charge. The 47 x-ray beam hit the Li metal anode, the catholyte soaked separator and the carbon black cathode. All reversible 1 structural changes seen by in situ SAXS/WAXS stem from the reversible deposition / dissolution of active 2 material in the carbon black cathode only ( Supplementary Fig. 2). More details are given in the Methods. on the carbon black electrode after potentiostatic discharge at 2.0 V vs. Li/Li + to a capacity of 1520 mAh gC -1 .

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The (dis)charge profile in the in situ cell shows the expected behavior of a Li-S system (Fig. 1b). The absolute 11 current during potentiostatic discharge at 2.0 V vs. Li/Li + exhibits a distinct minimum indicating the onset of 12 Li2S nucleation. After nucleation, the current (i.e., the Li2S formation rate) increases, since growth of Li2S on 13 existing Li2S nuclei occurs at a lower activation energy than initial nucleation. The reduction in current after 14 ~4500 s indicates the onset of capacity-limiting processes. The discharge is stopped after 2.5 h at a capacity 15 of 1520 mAh gC -1 (normalized by the carbon mass, as there is no defined amount of sulphur present at the 16 cathode). The maximum theoretical capacity of Li2S8 in the 60 µl catholyte corresponds to ca. 2000 mAh gC -17 1 , which is larger than the maximum values in Fig.1b. Consistent with literature 15,16 , SEM images of electrodes 18 after full potentiostatic discharge show large structures with particle sizes beyond 100 nm (Fig. 1c) Due to the 19 poor electronic conductivity of Li2S, the resolution of SEM is not sufficient to resolve the nanostructure below 20 100 nm properly; however, these insights can be obtained by SAXS. During charge at 2.45 V vs. Li/Li + for the 21 same time, initially high currents fade quickly after ~2/3 of the capacity. 22 The initial SAXS intensity prior to discharge shows a roughly linear decay in the double-logarithmic plot 23 (Fig. 2a). Such power law behavior is typical for the fractal-like structure of carbon black electrodes. During 24 discharge, the SAXS intensity generally increases, with a larger increase at high q around 1.5 nm -1 and at 25 low q around 0.2 nm -1 . The background-corrected WAXS intensities indicate the formation of Li2S crystallites 1 during discharge (Fig. 2b). 2 To visualize the subtle SAXS intensity changes during the full potentiostatic discharge / charge cycle, we plot 3 the relative SAXS intensity change with respect to the initial SAXS intensity prior to discharge as a function 4 of time and scattering vector length q (Fig. 2c, d). The WAXS intensity is also plotted as a function of time 5 and scattering angle in Fig. 2e. As solid Li2S starts to form (as evidenced by the decreasing current at ~5000 6 s in Fig. 2c and the emergence of the Li2S crystallites in Fig. 2e), two distinct SAXS intensity maxima appear 7 at low q (regime qA) and at high q (regime qB). In line with the high currents during charge (Fig. 1b, 2c), these 8 features disappear quickly during charge compared to their emergence during discharge. 9 Comparing the changes in intensities of the SAXS and WAXS features (Fig. 2f) shows similarities in 10 emergence of the WAXS and the high q SAXS feature during discharge. Meanwhile the low q SAXS feature 11 decreases at the end of discharge. During charge, the low q SAXS feature decreases quickest. The WAXS 12 signal from the Li2S crystallites decreases slower, with the high q feature decreasing even slower. These 13 observations suggest that the SAXS intensity maxima, while related to Li2S deposition and dissolution, do not 14 correlate directly to the Li2S crystallites probed by WAXS. 15 This suggestion is further supported when considering the sizes of the features. From WAXS, we use the 16 Scherrer equation to estimate that the Li2S crystallite size (i.e., mean diameter) increases and plateaus at 17 about ~7 nm (Fig. 2g). Spherical 7 nm single crystal particles should in a first approximation cause a broad 18 SAXS intensity peak around 0.6 nm -1 ( Supplementary Fig. 3). However, neither the high-q (1.5 nm -1 ) nor the 19 low-q (0.2 nm -1 ) SAXS intensity maximum relates to this primary Li2S crystallite size, instead indicating 20 features of approximately 2.5 nm and 24 nm, respectively. 21 To verify whether the features seen in the SAXS / WAXS data are specific to our selected materials and 22 operating conditions, we galvanostatically discharge a sulphur / carbon black electrode (ENSACO 350G, 23 Imerys) in a 1 M LiTFSI / TEGDME:DOL (1:1 vol.%) electrolyte at three different currents (Supplementary 24 Fig. 1). For all currents, we find a 6 -7 nm Li2S crystallite size from the WAXS diffraction peak fitting and a 25 high q SAXS intensity maximum between 1 -2 nm -1 . Primary Li2S crystallite formation can therefore not be 26 explained by classical nucleation and continuous growth 37,38 , which would result in a crystallite size that 27 strongly depends on current. 28 On the other hand, the low q intensity maximum depends on the applied current ( Supplementary Fig. 1). With 29 increasing current, the intensity shifts to higher q-values (from ~0.1 nm-1 at C/3 to <<0.08 nm -1 at C/30). We 30 therefore attribute our low q feature to aggregates comprised of the smaller primary Li2S crystallites. At higher 31 current, we have more, smaller aggregates which is in principle consistent with heterogenous nucleation and 32 growth 39 . 33 These SAXS/WAXS findings are in line with previous experimental data. Independently of the used materials 34 or applied current 13,15,16,22,39 , the Li2S primary crystallite size has been shown to remain around 10 nm. Size 35 and shape of the super-structures on the other hand, are very sensitive to the used materials and conditions 36 such as current density 11,15,16,39 . A feature similar to our signal at low-q was observed using small angle 37 neutron scattering 32 . Finally, the Li2S deposits observed with SEM are known to be larger than the primary 38 crystallite size estimated by XRD via the Scherrer equation 15,16 . 39 New in this work is the high-q SAXS intensity maximum corresponding to a feature with ~2.5 nm diameter. 40 Understanding the origin of this feature can provide the missing piece of the puzzle in quantifying Li2S 41 formation and dissolution. the low-q (qA) and high-q (qB) regimes during potentiostatic discharge / charge (black and grey) and (111) diffraction peak 10 height A in blue (obtained from Lorentzian peak fit). g, Shift of the SAXS intensity maximum in qB, obtained by calculating 11 the "center of mass" in the qB regime (black) and Li2S crystallite size in blue (obtained from the (111) peak width and the 12 Scherrer equation) during potentiostatic discharge / charge.

Li2S formation via polysulfide disproportionation
14 To develop a model for the chemical phase evolution and observed hierarchical structures that can be 15 validated with the SAXS data, we consider potential scenarios for Li2S formation. The observed aggregate 16 sizes of more than 100 nm combined with the insulating nature of Li2S mean that is highly improbable that 17 Li2S forms via direct electroreduction and growth at the carbon/electrolyte interface or Li2S/electrolyte 18 interface 34 . Instead, the structural features point to species in the electrolyte supporting growth. This could be 19 Li2S if it redissolves (Li + , S 2-) and precipitates after having formed by direct reduction at the carbon; however, 20 the extremely low solubility of Li2S 15 suggests that dissolved Li + and S2could only form small Li2S crystallites 1 on or in close proximity to the carbon surface. Alternatively, it could be solution transport of PSs, which after 2 diffusing in solution to a nucleation site disproportionate to form Li2S (for example, Li2S2 → 2/3 Li2S + 1/3 3 Li2S4) (Fig. 3a). 4 If Li2S forms via disproportionation of PSs, we also expect PSs synthesized via chemical routes to 5 disproportionate to Li2S and a higher-order PS. To test this, we prepare solid PSs from their solutions and 6 investigate whether Li2S forms. We mix sulphur and Li metal in a solution of tetrahydrofuran (THF) at 50 °C 7 to obtain nominal stoichiometries of Li2S2, Li2S3, Li2S5 and Li2S7. The stirring time to completely dissolve all S 8 and Li varies between 1 day for nominally Li2S7 to 2 weeks for Li2S2. The solutions are dried under vacuum 9 to obtain solid PS powders (details in the Methods). 10 X-ray diffraction patterns of the resulting solid PSs (Fig. 3b) show that the low-order PSs (nominal 11 stoichiometry Li2S2 and Li2S3) contain crystalline Li2S. Sharp diffraction peaks in the higher-order PSs indicate 12 larger sulphur (α-S) crystallites. Ex situ nuclear magnetic resonance (NMR) spectra of PS powders confirm 13 the coexistence of Li2S and other higher order PS (or S) 40 . Interestingly, SAXS intensities of the nominally 14 Li2S2 and Li2S3 solids ( Supplementary Fig. 4) reveal a high-q SAXS intensity shoulder as observed for the 15 electrochemically discharged electrode ( Fig. 2d and Fig. 4a). The Li2S diffraction peak width of the Li2S2 16 powder is nearly identical to the peak width of Li2S obtained from electrochemical discharge, resulting in 17 crystallite size of 5-7 nm. This indicates that Li2S forms both in the electrochemical cell and upon drying PS 18 solutions via disproportionation from solution species. 19 The fact that only low order PSs show crystalline Li2S implies that the disproportionation educt is either Li2S2 20 or Li2S3. Since the latter is typically absent in glyme-based electrolytes, 20 we hypothesize that Li2S forms and 21 dissolves predominantly via 22 and that the high-q SAXS intensity maximum therefore stems from solid Li2S4 particles. 23  Li2S4, we perform a simple experiment. Higher order polysulfides are soluble in glymes 43 so washing a dried, 33 discharged electrode with fresh 2G should dissolve most Li2S4. Indeed, ex-situ SAXS of the dried electrode 34 shows a pronounced high-q SAXS intensity shoulder that disappears after washing ( Supplementary Fig. 2). 1 Alternative but unlikely SAXS data interpretations are discussed in Supplementary Note 1. 2

3
Our experiments point to the following process for the formation and dissolution of Li2S: during discharge, 4 solid Li2S2 precipitates and disproportionates, forming a composite structure consisting of solid Li2S and Li2S4 5 particles (Fig. 3a). The solid Li2S4 particles are responsible for the SAXS feature in region qB in Fig. 2d and  6 have a mean size around 2.5 nm. The 7 nm Li2S crystallites (WAXS) and these Li2S4 particles aggregate to 7 form features with a mean size (diameter) around 24 nm (region qA SAXS). These polycrystalline aggregates 8 arrange into the larger structures >100 nm seen by SEM (Fig. 1c). During charge, the aggregates first dissolve 9 into primary Li2S and Li2S4 particles. Li2S4 dissolution lagging behind Li2S dissolution during the entire charge 10 (in Fig 2f, the low-q maximum disappears faster than WAXS diffraction peaks and high-q shoulder). 11 To validate this and gain further insights into the structural evolution of the Li2S/Li2S4 nanostructure, we use 12 the concept of plurigaussian random fields 33,44 to create the three-phase Li2S / Li2S4 / electrolyte structure 13 (Methods). With this structure, we then model the expected time-dependent SAXS intensity change during 14 discharge and charge based on our proposed mechanism and compare it to the measured SAXS data. 15 To remove the scattering contribution of carbon black and electrolyte structure factor from the evolving Li2S / 16 Li2S4 composite structure, we subtract the SAXS intensity prior to discharge as well as a constant background 17 from all in situ SAXS intensities (Methods). The remaining, reduced SAXS intensities correspond to the Li2S 18 / Li2S4 scattering contribution, assuming negligible correlations between Li2S / Li2S4 and carbon black 19 structures (Fig. 4a). 20 By fitting the SAXS intensity of the fully discharged electrode (Fig. 4a), we extract parameters for (i) the feature 21 sizes of Li2S and Li2S4, (ii) the respective volume fractions of Li2S and Li2S4, and (iii) a parameter accounting 22 for the spatial correlation between the Li2S and Li2S4 structures (Table S1). The latter parameter (δ, see 23 Methods) defines whether Li2S4 particles are preferably located close to the Li2S surface (δ → 0°) or randomly 24 distributed across cavities that form amongst the Li2S particles (δ → 90°). The value of δ = 45° shows that 25 Li2S4 particles are growing in close proximity to the Li2S crystallites. This is in line with the disproportionation 26 reaction in Equation 1 and Fig. 3a. With these parameters, we generate a 3D representation of the Li2S/Li2S4 27 nanostructure on a 3D lattice shown in Fig. 4b (cross section) and Fig. 4c (3D visualization). This visualization 28 highlights the smaller size of Li2S4 particles compared to Li2S particles, the Li2S4 growth in close proximity to 29 the solid Li2S, and the mean aggregate size around 24 nm. 30 With the time-dependent input parameters described in Supplementary Note 2, we model the SAXS intensity 31 during discharge and charge. The salient features of the experimental in situ data (Fig. 4d) are reproduced 32 by the model (Fig. 4e) for the full discharge/charge cycle. Deviations between the model and experiment can 33 be explained by carbon-Li2S/Li2S4 correlations, which were not considered here. The comparatively better 34 model fit for Li2S/Li2S4 deposited on glassy carbon beads confirm this ( Supplementary Fig. 5). 35  Supplementary Fig. 10). We see that the Li2S4 volume grows 38 at initial stages of charge, and so do the Li2S4 particles (high-q maximum shifting to smaller q as shown in 39 Fig. 4d). Li2S4 dissolution lags behind Li2S dissolution during the entire charge, shifting relative volume 40 fractions towards Li2S4, and suggesting that Li2S4 is the driver for Li2S dissolution. 41 The Li2S and Li2S4 pair distance distribution functions (Fig. 4g-h)  dotted black curves in g-h correspond to a Li2S and Li2S4 particle correlation length, respectively, and serves as a guide 15 for the eye for the time-dependency of particle sizes. The correlation length is arbitrarily defined as the distance where the 16 correlation function equals 0.2 ( Supplementary Fig. 6). Details are given in the methods section.

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Solid-state disproportionation 18 We next investigate whether the dis-and com-proportionation reactions can in principle occur in the solid 19 state. The relatively constant Li2S crystallite sizes independent of the used electrolytes and experimental 20 conditions suggest diffusion-limitation dictated by the solid phase rather than by the electrolyte, and hence a 1 solid-state process to be involved. We rolled crystalline sulphur onto a piece of Li metal in a molar ratio of 2:1 2 under Ar atmosphere and recorded the XRD pattern of the resulting mixture from 3 to 20 hours after mixing 3 (Fig. 5, details see Methods). The crystallite size obtained from the diffraction peak widths remained constant 4 for the different resting times and similar to the Li2S size obtained from electrochemical discharge (Fig. 5). 5 This suggests that Li2S during Li-S battery discharge is formed by solid-state disproportionation.  Li2S4 is both the educt to form Li2S2 via electron transfer and the product of disproportionation. Upon charge, 30 Li2S4 is both the product of Li2S2 oxidation and the educt of comproportionation. Hence, the very right hand 31 side of Equation 2 feeds back to the very left. Except for the electron transfer step, all steps are equilibria. 32 The direction of electron transfer will, therefore, create a net flow with the same direction in these equilibria; 33 disproportionation (DISP) following reduction and comproportionation (COMP) following oxidation. Spatially, 34 According to Equation 2, some Li2S2 and Li2S4 will remain dissolved at the end of discharge. This is because 8 neither is directly electrochemically converted to Li2S. This is in accord with a relative Li2S-to-Li2S4 volume 9 fraction of 2:1 (Fig. 4f). The 2:1 Li2S:Li2S4 molar ratio from disproportionation in Equation 1 would result in .a 10 Li2S:Li2S4 volume ratio of 0.7:1. 11 During charge, dissolved Li2S2 is electrochemically oxidized to Li2S4(sol). Hence, solid Li2S4(s) can still grow (as 12 seen in Fig. 4d). Li2S4(sol) thus acts as mediator to oxidize and dissolve Li2S without any electronic conduction 13 through Li2S deposits. Galvanostatic charging of a discharged electrode after washing and drying confirms 14 this ( Supplementary Fig. 7). Since washing removes part of the dissolved Li2S2 and Li2S4, charging after 15 washing leads to higher overpotentials at initial stages of charge. 48

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In conclusion, we provide direct experimental evidence that solid Li2S in Li-S batteries forms via precipitation 28 of short-chain polysulfides (such as Li2S2) and subsequent solid-sate disproportionation or phase separation. 29 Besides solid Li2S, the SAXS data indicate the formation of a second solid PS phase (such as Li2S4), with 30 smaller particle size. During charge, the particles of this second phase initially grow while Li2S already 31 disappears. The behavior is consistent with a DISP/COMP equilibrium between the short-chain PS and Li2S 32 plus a longer-chain PS. Electron transfer interconverts the short-and longer-chain PSs and its direction 33 determines the net flux through the equilibrium, giving rise to Li2S formation/dissolution on discharge/charge 34 without the need for electron transport across the insulating Li2S. 35 Converting Li2S2 to Li2S affords half of the theoretical capacity of Li-S cells and is -as we show -a chemical 1 rather than electrochemical reaction. It means that discharge capacity of a Li-S battery cathode is limited by 2 mass transport 16,17 through the tortuous network of Li2S / Li2S4 / carbon pores rather than electron transport 3 through a passivating surface film 11 (note that macroscopic PS transport through the separator and PS 4 reactions at the anode might be limiting as well in practical systems). Knowing this, shifts paradigms of how 5 to control the discharge capacity. The achievable Li2S pore filling and hence the discharge capacity is not 6 only limited by the electrolyte solvation strength, but equally by the applied current density and the mobility of 7 the reactive species. Theoretical sulphur capacities may never be achieved as a certain amount of higher-8 order PSs remains in solution and/or as a second solid phase. Concerning the initial overpotential during 9 charging, remaining PSs are beneficial as they mediate charge transfer via solution, bypassing the insulating 10 Li2S. 11 Given the known relation between electrolyte solvation and Li2S morphology 13,15 (i.e., Li2S nucleation and 12 growth), we believe that solvation energies influence on the one hand Li2S2 crystallization in terms of 13 nucleation and size/shape, of which the Li2S deposits form replicas. On the other hand, the electrolyte 14 determines redissolution and diffusion of the longer-chain DISP product, which is critical for approaching 15 theoretical capacities. 16 More broadly, the solid-state disproportionation mechanism indicates solid state DISP of precipitated Li2S2 to 17 have similar kinetics to precipitation of Li2S2 and redissolution of Li2S4. Solid state DISP requires Li 18 redistribution from the Li2S2 into the Li2S and Li2S4 phases, which appears sufficiently facile on a scale of up 19 to 10 nm, as indicated by the Li2S crystallite sizes. This implies that solid-state S-to-Li2S conversion (SSC) is 20 possible at practical rates if S/Li2S structures are properly engineered, which is a very important message for 21 all Li-S design strategies that avoid the polysulfide shuttling problem by utilizing SSC, but so far struggled to 22 convert practical S amounts. 23 24 Methods 1 Materials 2 As cathode material we used a high-surface area carbon black (Ketjenblack, EC-600JD, ANR Technologies)  3 with a BET area of 1400 m 2 gC -1 . The free-standing film electrodes were prepared by mixing carbon with 4 polytetrafluoroethylene (PTFE, 60 mass% suspension in water, Aldrich) at 90/10 mass ratio with isopropanol. 5 The resulting dough-like material was rolled to a 50-70 µm thick film, washed in acetone/H2O mixture and 6 finally dried at 120 °C under vacuum overnight. As catholyte we used a solution of 0.5 M Li2S8 + 1 M lithium 7 bis(trifluoromethane)sulfonimide (LiTFSI) + 0.4 M lithium nitrate (LiNO3) in diethylene glycol dimethyl ether 8 (2G). In Supplementary Fig. 1 we show in situ SAXS/WAXS data using a sulphur infiltrated carbon black 9 cathode (ENSACO 350G/S) with a solution of 1 M LiTFSI + 0.1 M LiNO3 in 1:1 (v:v) 1,3-dioxolan (DOL) + 10 tetraethylene glycol dimethyl ether (TEGDME) as electrolyte. The ENSACO 350G carbon (Imerys) / sulphur 11 composite was prepared in a C:S = 1:2 mass ratio by melt infiltration under Ar atmosphere at 155 °C. The 12 electrode was prepared by adding Printex (Degussa) conductivity additive and PVdF binder to the C/S 13 composite in a mass ratio of 1:1:8. All solvents were used as received and dried under freshly activated 14 Molecular Sieves (type 4 Å). All salts were dried at elevated temperature (90 °C) and reduced pressure. 15 Lithium polysulfide powders were synthesized by mixing a stoichiometric amount of elemental sulphur (Sigma 16 Aldrich) and lithium metal (FMC) in excess of dried THF (the THF was dried in a multistep process using 17 Al2O3, molecular sieves, and distillation, after which the water content was measured by Karl Fischer titration 18 (Mettler Toledo, C20) and kept below 2 ppm.). The synthesis procedure was conducted in an argon filled dry 19 box with controlled levels of water and oxygen content (below 0.1 ppm). The mixture was stirred at slightly 20 elevated temperatures (50 °C) until all the reactants dissolved. THF was then removed under reduced 21 pressure to obtain dry polysulfide powders. 22 The solid 2 Li + S mixture was prepared by rolling fine sulphur powder (large S crystals crushed with mortar 23 and pestle) onto a thin piece of Li metal on a glass plate in inert atmosphere. The Li and S mass correspond 24 to a molar ratio of 2:1. After a short time of rolling the Li/S piece was turning brittle, indicating immediate Li2S 25 crystal formation. 26

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In situ SAXS/WAXS and XRD measurements were carried out with a commercial electrochemical in situ 28 scattering cell (BatterycellSAXS, Anton Paar, Austria). We used polytetrafluoroethylene (PTFE) X-ray 29 windows due to their chemical stability and relatively low background in the SAXS regime. The small diameter 30 of the windows (2 mm) ensures a relatively equal pressure distribution across the cell assembly. It consisted 31 of a Li metal anode, a Celgard separator, a Freudenberg (FS 2125) separator, a carbon black cathode, and 32 an Aluminium grid current collector. The X-ray beam irradiates all cell materials; reversible and significant 33 structural changes are only detected in the cathode. A Biologic SP240potentiostat/galvanostat was used for 34 electrochemical cycling. 35 In situ SAXS/WAXS measurements were carried out on the Austrian SAXS beamline at the Synchrotron 36 ELETTRA 36 (Trieste, Italy) using an X-ray wavelength of 0.154 nm and a Pilatus 1M SAXS and Pilatus 100K 37 WAXS detector (Dectris, Switzerland). During potentiostatic discharge / charge measurements, SAXS and 38 WAXS patterns were collected with 1 s exposure time (to avoid radiation damage) and 60 s period (to avoid 39 huge amounts of data). We discharged the cell at 2.0 V vs. Li/Li + for 2.5 hours (giving a capacity of 1520 mAh 40 gC -1 ) and charged it at 2.45 V vs. Li/Li + for maximum 2.5 hours (to reverse the capacity of 1520 mAh gC -1 ). In 41 situ SAXS data shown in Supplementary Fig. 1 were recorded on a laboratory SAXS/WAXS instrument 42 (SAXSpoint 2.0, Anton Paar, Austria) with an EIGER2 R 1M area detector (Dectris, Switzerland) and a time 43 resolution of XX min. All recorded SAXS patterns were azimuthally averaged and normalized by transmission 44 values. The SAXS background intensity was recorded separately for each cell after removing the cathode. 45 The averaged and normalized background intensity was then subtracted from all recorded in situ SAXS 46 1 prior to discharge (at OCV). 2 Scanning Electron Microscopy (SEM) images were collected with a Hitachi SU-8200 at 5.0 kV acceleration 3 voltage using a secondary electron detector. Ex situ XRD (and SAXS) measurements (Fig. 3b, Fig. 5 In situ SAXS data modelling via plurigaussian random fields 7 The SAXS intensity of the discharged cathode can be split into three terms, 8 The first term $ Li 2 S,Li 2 S 4 % corresponds to the scattering contribution of the Li2S / Li2S4 structure, the second 9 term $ * % to the scattering contribution of the electrolyte-filled carbon structure and the third background term 10 to the constant (low-q) intensity of electrolyte (and carbon) atomic structure factor. Correlations between 11 carbon black and the Li2S / Li2S4 structure are neglected (see discussion in Supplementary Note 1 and 12 Supplementary Fig. 5). 13 To separate the SAXS intensity of the Li2S / Li2S4 structure we subtract $ * % , i.e., the SAXS intensity 14 measured prior to discharge at OCV. Further, we subtract the electrolyte (and carbon) structure factor 15 background BG by a Porod background subtraction in a q-range from 3-5 nm -1 . 16 The SAXS intensity of the Li2S / Li2S4 nanostructure (Fig. 4a) with + being a constant that depends on instrumental parameters, such as detector efficiency and irradiated 18 sample volume, and , , -./ ⁄ the relative volume of the deposited Li2S / Li2S4 nanostructure. The first power 19 law term stems from the large Li2S (Li2S4) agglomerates beyond 100 nm (see SEM images in Fig. 1c. Given 20 their large expansion, the SAXS intensity in the measured q range is proportional to % (Porod decay). The 21 second term accounts for the Li2S / Li2S4 nanostructure in the size regime between 1 to 50 nm and is modelled 22 via plurigaussian random fields, as described further below. The least square error sum is minimized by 23 particle swarm optimization 49 with reasonable parameter constraints. Deviations between model fit (blue curve 24 in Fig. 4a) and experimental data (black curve in Fig. 4a) can explained by carbon black -Li2S/Li2S4 25 correlations. Li2S / Li2S4 nanostructures deposited on a planar Glassy carbon substrate with negligible cross 26 correlations show an improved fit quality ( Supplementary Fig. 5). 27 Time-dependent SAXS intensity change during discharge and charge are modelled by using the fit 28 parameters of the model fit to the fully discharged electrode in Fig. 4a (Table S1) as a starting point. All input 29 parameters for the modelled in situ SAXS data are given in Supplementary Note 2. 30 We model the reduced in situ SAXS data $ 3456 % using the concept of plurigaussian random fields (PGRF) 44 . 31 This allows retrieving 3D real space models of the solid Li2S / Li2S4 nanostructure during discharge and charge 32 (Fig. 4). A detailed theoretical description of the PGRF method is given by Gommes et al. 44 . 33 The SAXS intensity $ 89:; % is the Fourier transform of the electron density correlation function < = Here, F H is the electron density, H the volume fraction and N HH = the two-point correlation function of phase i. 1 Using clipped Gaussian random fields, a 3D model of a two-phase nanopore structure can be generated from 2 a fit to the structure's experimental SAXS intensity 50-53 . Plurigaussian random fields use a second Gaussian 3 random field to model SAXS intensities and 3D real space structures of disordered three-phase systems. A 4 Gaussian random field P Q is the sum of cosine waves with wave vector lengths distributed according to 5 their power spectral density R S T and phase factors U H randomly distributed between 0 and 2V 44,50,54,55 . 6 A suitable analytic two-point correlation function of the GRF is 53 7 where e P is a correlation parameter related to the mean size of the structure and f P a parameter accounting 8 for ordering effects via the second oscillation term. Equation 7 translates into the following analytic expression 9 for the power spectral density: 10 T π e S f S sinh VTe S 2 ⁄ sinh π e S f S ⁄ cosh VTe S cosh 2π e S f S ⁄ .
To generate a two-phase porous structure from the GRF, we define the threshold values g for the Gaussian 11 distributed P Q values. All spatial coordinates Q with g < P Q ≤ ∞ are assigned to the pore space (i.e. (10) To model SAXS intensities and real space structures of the three phase system, we generate a second 15 independent GRF r x using the same correlation function (Equation 8-9) with different input parameters e s 16 and f s (Supplementary Fig. 8c). The Li2S4 phase with the volume fraction GH I is generated by cutting r x 17 and P x according to Equation 11 and the cut-offs visualized in Supplementary Fig. 8. 18 with ) z P b , P being the bivariate Gaussian distribution with mean 0, variance 1, and covariance G. Their 1 calculation via Hermite polynomials is described in Ref. 44 . Depending on the angle ~ and the Li2S4/EL 2 boundary line in Supplementary Fig. 8d-f, the morphology of the Li2S4 phase will be different. The Li2S4 phase 3 will perfectly cover/wet the Li2S phase in form of a thin film if ~→ 0 ( Supplementary Fig. 8d,g). In contrast, for 4 an Li2S4/EL boundary parallel to the Y-axis (~→ π/2) the Li2S4 (EL) structure inside the Li2S cavities is 5 statistically independent from the Li2S structure ( Supplementary Fig. 8f,i). Inserting Equation 12 into 6 Equation 5-6 gives the corresponding scattering intensities (Fig. 4). 7 The modelled relative SAXS intensity change (Fig. 4e) is obtained by calculating $ , % via Equation 4 8 using the fit parameters shown in Supplementary Fig. 10 and adding $ • % () (i.e. the experimental SAXS 9 intensity at OCV). Finally, the generated SAXS intensities are normalized by the modeled SAXS intensity at 10 t = 0, prior to discharge. 11 The pair distance distribution functions ‚ ƒƒ = of phase X in Fig. 4g