Unraveling multiphase conversion pathways in Li-S batteries through cryo-TEM and ML-assisted operando small-angle neutron scattering

1 Unraveling multiphase conversion pathways in Li-S batteries through cryo-TEM and ML-assisted operando small-angle neutron scattering Jean-Marc von Mentlen1, Ayça Senol Güngör1, Thomas Demuth2, Jürgen Belz2, Milivoj Plodinec3, Pronoy Dutta4, Alen Vizintin5, Lionel Porcar6, Kerstin Volz2, Vanessa Wood1,*, Christian Prehal1,4,** 1 Department of Information Technology and Electrical Engineering, ETH Zürich, Gloriastrasse 35, 8092 Zürich, Switzerland 2 Materials Science Center and Faculty of Physics, Philipps University Marburg, Hans-Meerweinstraße 6, Marburg 35043, Germany 3 Scientific Center for Optical and Electron Microscopy, Department of Chemistry and Applied Biosciences, ETH-Zürich, Otto-Stern-Weg 3, 8093 Zürich, Switzerland 4 Department of Chemistry and Physics of Materials, Paris-Lodron-University of Salzburg, Jakob-HaringerStrasse 2a, 5020 Salzburg, Austria 5 Department of Materials Chemistry, National Institute of Chemistry, Hajdrihova 19, 1000 Ljubljana, Slovenia 6 Institut Laue–Langevin, 71 Avenue des Martyrs, Grenoble, 38042, France *Correspondence: vwoo[email protected] **Correspondence: christian.preh[email protected] Keywords lithium-sulfur batteries; cryogenic transmission electron microscopy; electron energy loss spectroscopy; small angle neutron scattering; machine learning; 2 Abstract Understanding the complex physicochemical processes in conversion-type batteries requires investigations across multiple length scales. Here, we present a novel approach to examine Li-S batteries at the nanoscale by combining cryogenic transmission electron microscopy (cryoTEM) with operando small-angle neutron scattering (SANS). CryoTEM revealed discharge products with a biphasic structure, consisting of nanocrystalline Li2S within an amorphous Li2Sx matrix. Data analysis of complementary operando SANS measurements was accelerated by a convolutional neural network trained to predict scattering curves based on plurigaussian random fields, enabling comprehensive parameter space exploration for model fitting. Our findings are in line with disproportionation-driven deposition of Li2S2 particles that agglomerate and partially reduce to Li2S via solid-state conversion. This challenges the conventional view of direct, stepwise electroreduction of polysulfides at the electrode-electrolyte interface. Overall, our multitechnique approach demonstrates the value of combining localized high-resolution imaging with time-resolved operando scattering measurements to understand complex electrochemical conversion pathways in next-generation energy storage systems. 3 Introduction As the world transitions to renewable power production to mitigate the growing climate crisis, batteries emerge as pivotal for electric mobility and stationary energy storage. Emerging technologies beyond lithium-ion batteries promise enhanced energy density and reduced environmental impact from raw materials. Among these, conversion-type systems, including metal-air (Me-Air)1, metal-sulfur (Me-S) batteries2, emerge as promising alternatives. Despite their potential, conversion-type batteries face common challenges that hinder their practical adoption. These challenges include poor ionic/electronic conductivity and charge transfer kinetics and large volume changes of active materials, as well as (partially) dissolved reaction products causing side reactions and suboptimal active material utilization, all of which constrain cycling rates, cycle life, and energy density1,3–5. Further progress is limited by a lack of understanding of the complex structural transitions and physicochemical processes, particularly at the nanometer scale6–10. The sulfur-to-sulfide conversion process in liquid-electrolyte lithiumsulfur (Li-S) batteries exemplifies these challenges. During discharge, crystalline sulfur (S₈) is reduced to crystalline lithium sulfide (Li₂S) through multiple soluble polysulfide intermediates (Li₂S₈, Li₂S₆, Li₂S₄, etc.). This solid-liquid-solid conversion process is critical for battery performance as it dictates active material utilization and side reactions. However, the details of these processes remain unclear. Recent studies have shown that the complex nanoand microstructures of solid discharge products can consist of several phases (Figure 1a), and do not fit traditional nucleation and growth models, leaving many aspects of the conversion mechanism unresolved11–17. To address this, advanced techniques are needed to probe sulfur-to-sulfide phase evolution at atomic and nanometer scales. Current techniques for studying conversion mechanisms at the atomicand nanoscale can be categorized into two groups: integral (or bulk) methods — including Raman, X-ray absorption spectroscopy, and both small and wide-angle scattering — and local techniques, such as electron microscopy. Integral methods give insights into the ensemble-averaged structural and chemical composition of the electrode at a given time. Conducting such measurements operando can yield a detailed picture of the structural and chemical changes during cycling6,14–16,18–24. In the case of scattering measurements, the data analysis relies heavily on the chosen model, leading to potential variations in the interpretations drawn from the same dataset15,25,26. Consequently, the process is susceptible to significant user bias, as the model selection can influence the conclusions reached. Microscopy techniques, on the other hand, offer model-free, localized chemical and structural insights. However, their utility is constrained by a limited field of view and the requirement for specialized cell designs for in situ measurements27–32. Additionally, the need for ultra-high vacuum conditions and the electron beam-induced damage imposes significant limitations, particularly for materials like sulfur or lithium sulfide that are sensitive to such conditions33. In this work, we present a novel methodological approach for investigating conversion-type batteries at the nanoscale, combining advanced microscopy and scattering techniques with machine learning-enhanced data analysis (Figure 1b). We demonstrate this approach using Li-S batteries as a prototypical system, leveraging the synergistic properties of transmission electron microscopy (TEM) and small angle neutron scattering (SANS). We investigate discharge products 4 in Li-S battery cathodes using ex-situ energy filtered TEM (EFTEM) and electron energy loss spectroscopy (EELS) under cryogenic conditions to mitigate beam-induced damage. Air sensitivity is addressed using a vacuum-transfer cryo holder (VTC), and beam sensitivity is assessed under both non-cryogenic and cryogenic conditions33,34. To expedite the curve fitting process and allowing for a broader parameter space exploration in SANS data analysis, we employ machine learning algorithms. We train a convolutional neural network (forwardCNN) to predict SANS intensity curves based on input parameters of the plurigaussian random field (PGRF) model, reducing computational time by three orders of magnitude. This significant speed-up enables the application of Bayesian optimization for efficient determination of optimal PGRF parameters. Our results reveal that the discharge product in Li-S battery cathodes comprises multiple solid phases, including nanocrystalline Li₂S embedded in an amorphous polysulfide matrix. Real-time structural data indicate that these phases do not change their mean size simultaneously during cycling, offering new insights into the electrochemical conversion mechanisms. This study further showcases the potential of combining advanced imaging and scattering techniques with computational analysis to study a variety of battery chemistries with complex conversion mechanisms. Figure 1 Multi-scale analysis of deposition processes in conversion-type batteries using complementary techniques. a) Schematic illustrating the hierarchical structure of a conversion-type cathode (here Li-S battery), from the macro-scale electrode to the nanoscale multi-phase discharge product. b) Complementary characterization methods: Small angle neutron scattering (SANS) for operando structural evolution studies and electron microscopy for high-resolution imaging of the electrode morphology and composition. 5 Results and Discussion CryoTEM Previous works investigating Li-S cathodes have employed different strategies to mitigate beam and low-pressure-induced changes to the sample. Most notable are encapsulations of sulfur in hollow carbon structures for solid-state Li-S batteries or the usage of liquid cell holders to measure electrochemical TEM13,27,28,32,35. While these methods yield deep insight into the local processes during (de-)lithiation, the carbons and cell geometry of such nanobatteries differ greatly from standard cells. Here, the ex-situ TEM sample was prepared by discharging a catholyte solution of 0.5 M Li2S8 and 1 M LiTFSI + 0.4 M LiNO3 in diethylene glycol dimethyl ether (diglyme, 2G) onto a binder-free Ketjenblack (KB) powder (Figure 2a). The use of the commercial high-surfacearea carbon black KB ensured comparability between the investigated structures and the structures found in standard Li-S battery cathodes. The discharge curve revealed a distinct plateau at 2.1 V vs. Li/Li+, indicating the formation of Li2S onto the KB powder (Figure 2b). After full discharge, the powder was vacuum-dried without washing, ground with a mortar, and then transferred onto a Lacey Carbon TEM grid in an inert argon atmosphere (Figure 2c). By omitting the washing steps, we avoid the risk of removing easily soluble compounds (such as higher-order polysulfides Li2Sx, x>1) and altering the structure of the discharge product14. Figure S4 shows the washing impact of different solvents on the structure. Next, the grid was loaded on the LN2 Vacuum Transfer Holder by MelBuild (Figure 2d) and transported under Ar atmosphere from the glove box to the TEM (Figure 2e). The holder was then cooled to -193°C by introducing liquid nitrogen (LN2) into the holder's dewar. A more comprehensive description of the experimental procedure is provided in the methods section. Figure 2 Cryo-TEM sample preparation and analysis worflow. A discharged cathode containing Ketjenblack carbon and Li2S8 catholyte is ground into a powder inside an Ar-filled glovebox. The sample is transferred to a TEM grid via direct immersion and loaded onto a vacuum-transfer cryo holder, which maintains inter conditions during transport to the microscope. In the TEM, the sample is investigated using high-resolution imaging (HRTEM) and spectroscopic measurements like EFTEM and TEM-EELS The measurements were conducted in TEM mode because of the low Z-contrast between sulfur and carbon in STEM mode (Figure S1b). Avoiding STEM further helped mitigate damage induced by the highly condensed electron beam. The mortared cathode particles on the TEM grid differ a lot in size. One such typical particle compromised of KB and discharge products is displayed in Figure 3a. The discharge particles range from a few dozen to hundreds of nanometers in size, consistent with previous SEM observations14,36. We focused on discharge material at the edge of the larger particle to get an unobscured view of its structure. High-resolution micrographs of the discharge products, taken under both ambient and cryogenic conditions (Figure 3b, c and S1 c- 6 f), demonstrate that the samples remained stable regardless of temperature. The discharge products are made of two distinct solid phases - a nanocrystalline and an amorphous one. The nanocrystalline phase can be assigned to Li2S based on the Fast Fourier Transform (FFT) showing spots which can be assigned to the 111, 200, 220, and 222 planes (inset in Figure 3b, c, and in Figure S1 in large). There are four candidates for the amorphous phase, based on the chemical composition of the battery: the salt LiTFSI, the solvent 2G, Li2S, or a higher order LiPS. LiTFSI salt is visible throughout the sample, as the cathode was not washed. However, the micrometer-sized salt particles are clearly identifiable by their strong contrast and crystallinity (Figure S1f, g). Next, we turn to EELS measurements to get a deeper understanding of the elements present. While the discharge product was stable under both ambient and cryogenic conditions for the HRTEM measurements, it degraded in under 1 sec during cryo-STEM EELS measurements, likely due to the increased local e--dose. We, therefore, turned towards cryo-TEM-EELS and cryo-EFTEM, sacrificing the local resolution of the elemental distribution. The e-dose were roughly 200 e/Å2 for EFTEM and up to 267 e/Å2 for STEM per frame. The discharge product in Figure 3d was measured at different energy levels and locations. The circles indicate the field-of-view during the TEM-EELS measurement, and their colors relate to the lowand core-loss spectrum shown in Figure 3e. The low-loss spectrum in blue shows a distinctive double peak plasmon feature (15.5 and 19.7 eV) that can be attributed to Li2S 27,28. The red curve shows a reference spectrum of Li2Sx taken from Yang et al28. The core-loss spectrum (yellow), acquired from the discharge product and supporting carbon structure, reveals two significant edges: sulfur (159 eV) and carbon (284 eV). Notably, the sulfur edge appears at lower energy compared to bulk sulfur (165 eV), consistent with previous reports for Li2S 27,28,32. The absence of nitrogen (402 eV) and oxygen (532 eV) edges further suggests that the amorphous phase consists of other amorphous Li2S or an amorphous solid Li2Sx (LiPS) phase. LiTFSI and residual 2G, both rich in oxygen and nitrogen, can be excluded as constituents of the amorphous phase. While EELS can typically differentiate between Li2S and polysulfides, particularly in the low-loss region28, our lack of STEM's local resolution prevents direct distinction without sample alteration. To address this limitation, we acquired a series of EFTEM micrographs with energies filtered around 13, 17, and 21 eV (Figure 3f). Insets in the micrographs show a detailed view of the lowloss EELS spectrum of Li2S and Li2Sx. The low-loss spectrum remains unaltered after isolating and subtracting the zero-loss peak (Figure S2a, b), which suggests the sample to be sufficiently thin for any brightness differences to arise from chemical composition rather than thickness variations. The first two micrographs, centered around the Li2S peaks (13 and 17 eV), reveal two distinct brightness regions: a brighter phase in the inner region, surrounded by a darker phase in the outer areas. At higher energies (21 eV), this brightness difference disappears, making the particle appear as a single phase. These findings indicate that the amorphous phase covering the particle must be a solid Li2Sx. Consequently, the solid discharge product in Li-S batteries comprises nanocrystalline Li2S embedded within amorphous Li2Sx, which is in line with our previous study combining Raman spectroscopy with neutron and X-ray scattering14. 7 c Figure 3 Multi-technique TEM analysis of discharged Li-S battery cathode. a) Overview of a typical cathode region with discharge particles highlighted in green (cryo-TEM). b, c) Fourier filtered and magnified views of a two-phase discharge particle under ambient and cryogenic conditions, respectively. Insets show FFT spots assigned to (111), (200), (220), and (222) planes of Li2S crystals. d) High-resolution image of a two-phase discharge product (Fourier filtered). The blue, yellow and grey circles indicate the measurement area for the corresponding TEM-EELS spectrum in e). The blue curve shows the characteristic Li2S double peak in the low-loss region. The sulfur edge onset (yellow) appears at 159 eV. Reference spectra for Li2Sx (red) 28 and carbon structure (grey) are overlaid. f) EFTEM series centered around the Li2S double-peak energies. The energy window for every micrograph is overlayed on the bottom right. Two distinct phases are visible at the double peak energies (13 ± 3 eV, 17 ± 3 eV), but the intensity difference diminishes at higher energy (21 ± 3 eV). 8 Machine Learning Enhanced Operando SANS Next, we turn towards operando small angle neutron scattering (SANS) to further understand the biphasic discharge product and its behavior during galvanostatic cycling. For operando SANS measurements we installed a custom-built operando SANS cell at the D22 beamline at ILL Grenoble (Figure 4a)14,24. A neutron beam of about 10 mm in diameter hit the Li metal, separator and the Li-S battery cathode. Control experiments ensured that we observed changes in the Li-S battery cathode only14. We used a battery chemistry equivalent to the one we used for cryoTEM measurements, using a free-standing sulfur infiltrated KB composite electrode (KB/S) with PTFE binder and 1 M LiTFSI + 0.4 M LiNO3 in 2G as electrolyte. The 2G solvent is deuterated to achieve a scattering length density (𝑆𝐿𝐷𝑒𝑙=5.63∙10−10 cm−2) that approximately matches the carbon’s scattering length density (𝑆𝐿𝐷𝐶=6.67∙10−10 cm−2) with a slight mismatch of 15.6%. The square of the SLD difference between active materials and both electrolyte/carbon is about 30 times higher than the square of the carbon-electrolyte SLD difference. This ensures that any variations in the SANS curves are predominantly due to changes in the nanostructure of the discharge products, as depicted in the sketch in Figure 4b. The galvanostatic dis-/charge curves, shown in Figure 4c, reveal the standard features of Li-S batteries with ether-based electrolytes: (i) a high voltage plateau around 2.3 – 2.4 V corresponding to the dissolution of sulfur and its electrochemical reduction into polysulfides (Li₂S₈), followed by (ii) a second plateau above 2.0 V, which marks the coexistence of dissolved polysulfides and solid discharge products like Li2S and (iii) a charging plateau above 2.2 V vs Li/Li+ 37. Prior to discharge, the SANS curve reflects the constant contribution from the separator, PTFE binder, and carbon black due to imperfect SLD matching between deuterated electrolyte and carbon. The constant background at higher scattering vector q originates from incoherent scattering and the electrolyte, carbon structure, and sulfur structure factor. During discharge, the overall SANS intensity increases, and two distinct features (intensity shoulders) emerge at low and high q, stemming from the nanostructure of the solid discharge products (Figure 4d). During charging, the SANS intensity goes down again (Figure 4e). The contour plot in Figure 4f reveals the relative intensity change (normalized by the SANS intensity prior to discharge) as a function of time and q; the shoulders in Figure 3d, e appear as intensity maxima. The intensity increase, indicative of the solid discharge product formation, starts with the onset of the lower voltage plateau. During charging, the overall intensity decreases, and the high-q intensity maximum shifts towards lower q-values. The position of low-q and high-q intensity shoulders at around (1) 0.2 nm-1 and (2) 1.5 nm-1 suggest structures with feature sizes of around 2π/0.2 nm-1 ≈ 30 nm and 2π/1.5 nm-1 ≈ 4 nm, respectively. During charging, the high-q shoulder shifts slightly towards the lower q, and both features decrease in intensity until they vanish completely (Figure 4e). A similar behavior was previously reported under different experimental settings with small angle neutron and x-ray scattering14,19. To identify the origin of the high-q intensity shoulder, we performed smalland wide-angle X-ray scattering (SAXS/WAXS) measurements on discharged KB/S electrodes (Figure S3). The WAXS data revealed the expected diffraction peaks of nanocrystalline Li2S (peaks (111) and (200)) in the discharged electrode. After washing the discharged electrode with diglyme, the Li2S diffraction peak remained, while the high-q SAXS feature disappeared - unlike in the unwashed sample. This 9 suggests that the high-q feature observed in the SANS data corresponds to the soluble Li2Sx phase seen in TEM. Based on our SAXS/WAXS analysis, previous Raman spectroscopy results, and other theoretical and experimental studies, we propose that this Li2Sx phase is an amorphous, particulate Li2S2 phase12–14,38. Hence, the low-q and high-q intensity shoulders observed in Figure 4d-f, along with the cryoTEM results, indicate that the nanostructure comprises larger Li2S aggregates (around 30 nm, associated with the low-q shoulder) and an amorphous nanoparticulate Li2S2 phase (feature size around 4 nm, associated with the high-q shoulder). These Li2S aggregates consist of individual crystallites with an average size of 14 nm, as confirmed by both Scherrer analysis (Figure S3c) and direct TEM observation (Figure 3b,c). This structural composition is the base assumption for the following operando SANS data modelling approach. 16 chemistries and beyond. Our work underlines that next to thermodynamic equilibrium states37 also the path to equilibrium, often complicated by metastable intermediate states, is crucial for understanding the properties of conversion-type battery systems. 37 17 Methods Materials For operando SANS measurements we used carbon/sulfur composite cathodes with a C/S massratio of 1:1. The carbon was a carbon black material (Ketjenblack EC-600JD, sourced from ANR Technologies) with a Brunauer-Emmett-Teller (BET) specific surface area of 1400 m2 g-1 and minimal metal contamination (<30 ppm). For melt infiltration, we first mixed the carbon with elemental sulfur at the mass ratio of 1:1, manually with pestle and mortar for about 5 min. The prepared mixture was then melt-infiltrated at 155°C for 7-8 h in a sealed evacuated glass oven (Büchi, Switzerland). The final sulfur mass content was verified by weight. To create free-standing electrodes, we combined the carbon/S composite with polytetrafluoroethylene (PTFE, acquired as a 60% aqueous suspension from Sigma Aldrich) in a 90:10 mass ratio, using isopropanol (≥99.8%, Sigma Aldrich) as a dispersant. The components were manually blended in a mortar for 10 minutes at room temperature (25 °C). We then rolled the resulting paste into films of 180 ± 10 µm thickness. These films underwent a cleaning process using a mixture of acetone (≥99.5%, Sigma Aldrich) and deionized water (18 MΩcm), followed by overnight vacuum drying at 120 °C and 10 mbar pressure. The deuterated electrolyte consisted of 1 M lithium bis(trifluoromethane)sulfonimide (LiTFSI, 99.95% trace metals basis), and 0.4 M lithium nitrate (LiNO3, 99.99% trace metals basis) dissolved in 100% deuterated diethylene glycol dimethyl ether (2G, anhydrous, 99.5%) from Cambridge Isotope Laboratories Inc. The catholyte used for TEM investigations consisted of 0.5 M Li2S8, 1 M LiTFSI, (99.95% trace metals basis), and 0.4 M LiNO3, 99.99% trace metals basis) dissolved in 2G (anhydrous, 99.5%). For the electron microscopy sample preparation, we fabricated a binder-free cathode. To achieve that, we created a thick paste by mixing the carbon black powder with the catholyte at a ratio of 20 mg/50 µL. This paste was applied to a glassy carbon disc (SIGRADUR G Discs, 16 mm diameter, 0.5 mm thickness) and assembled in in-house-made coin-cell-type cells (uniaxial pressure of 0.7 ± 0.1 MPa), utilizing a polyethylene (PE) separator (Targray, PE16A) and Whatman separator. We added 100 µL of extra catholyte to ensure proper wetting of the separators. The electrolyte-to-sulfur ratio (E/S) and electrolyte-to-carbon ratio (E/C) are 7.8 and 7.5 respectively. To synthesize Li2S8, we combined stoichiometric amounts of elemental sulfur (powder, 99.98% trace metals basis, Sigma Aldrich) and lithium metal (110 µm thick high-purity foil, FMC Lithium Corporation) in excess anhydrous tetrahydrofuran (THF, ≥99.9%, inhibitor-free, Sigma Aldrich). The THF underwent a multi-step drying process using Al2O3 and molecular sieves, followed by distillation. We verified the water content using Karl Fischer titration (Mettler Toledo C20), ensuring it remained below 2 ppm. The entire synthesis took place in an argon-filled glovebox with strictly controlled atmosphere (H2O and O2 <0.1 ppm). The mixture was heated to 50 °C and stirred until complete dissolution occurred. Finally, we removed the THF under vacuum (10 mbar) to obtain the dry polysulfide powders. 18 Experimental Methods Experimental operando small angle neutron scattering (SANS) experiments were conducted under galvanostatic discharge/charge conditions at the ILL's D-22 beamline, utilizing a wavelength of 0.5 nm and a 10 mm beam diameter48. The setup included two areal detectors positioned at distances of 17.6 m and 1.4 m for an overlapping q-region. The custom twoelectrode SANS cell14, consisted of a PEEK body and two aluminum elements contacting cathode and anode from the top and the bottom. 12 mm aluminum windows ensures enough transmission for incident and scattered Neutrons and uniform mechanical pressure. The cell stack comprised copper (≥99.9%, Schlenk Metallfolien) and aluminum foil current collectors (≥99.5%, Korf), a lithium metal anode (≥99.9%, Alfa Aesar, 0.75 mm thickness, 16 mm diameter), a glass fibre separator (Whatman GF/A, 21 mm diameter), and a KB/S cathode with 13 mm in diameter, prepared according to the procedure above. The operando cell, with E/S and E/C are 38.3 and 31.3 respectively, was discharged at C/10. The neutron beam hit all cell components, with only the cathode showing reversible and notable structural changes. The 2D detector signals were azimuthally averaged, and corrected for empty cell scattering, and the detector dark current. Finally, the SANS intensities were normalized to absolute intensities (in cm-1) using transmission correction, detector efficiency correction, D22 detector parallax correction and by dividing the data by the sample volume (assuming a sample thickness of 0.007 cm) and empty beam flux. The ex situ SAXS/WAXS measurements (Figure S3) of the discharged KB/S cathode (galvanostatic discharge at C/10) were carried out at a laboratory SAXS/WAXS system (Xeuss 3.0 HR, Xenocs) using a copper microsource (with CuKα radiation), a 2D areal SAXS detector (Eiger 2R 1M, Dectris), and a 2D areal WAXS detector (Eiger 2R 500K, Dectris). For TEM measurements, the cathode was prepared as described above. Next, the cell was discharged with C/20. After discharge, the cell was disassembled, and the KB was scratched off the GC disc. The KB flakes were subsequently dried under vacuum and ground into a fine powder using a mortar. This sample was then transferred to a Lacey Carbon Type-A Copper TEM grid (TedPella, Nr. 01890) by directly immersing the grid into the powder. The different cycling rates (C/10 for SANS, C/20 for TEM) were chosen based on the requirements of each technique. The slower rate for TEM samples optimized the preparation of binder-free cathodes, ensuring better sample transfer and higher discharge capacity. Similarly, for cryo-TEM experiments, Li₂S₈ catholyte was used instead of sulfur-infiltrated cathodes to ensure precise control of the active material amount and enable good electronic contact in the binder-free cathodes, which was essential for proper sample transfer onto the TEM grid. This difference in starting materials does not affect the mechanistic interpretations, as elemental sulfur initially dissolves and converts to high-order polysulfides (Li₂S₈) before following the same reduction pathway with identical voltage responses at 2.1 V. The effect of slightly different cycling rates (C/20 vs. C/10) on the nanostructure is minor14. The TEM grid was transferred under Ar atmosphere from the glovebox to the TEM using a double tilt LN2 vacuum transfer holder (VTC, MelBuild) and Gatan 648 double tilt vacuum holder. TEM measurements were carried out on a double Cs-corrected JEOL GrandARM operated at 300 kV (ETH Zürich) and at 80/200kV on a double Cs-corrected JEOL JEM 2200fs (Philipps-Universität 19 Marburg). We followed two different LN2 cryo-vacuum-transfer-holder transfer procedures, depending on the microscope. For measurements on GrandARM it works as follows: First, the holder loaded with the TEM-grid was transferred from the glovebox to the TEM. Once the sample was inside the airlock of the TEM, the chamber was purged three times with nitrogen. During the third pumping cycle, the tip was extended into the airlock at an ion pump current of 200 µA. Alternatively, for measurements on JEM 2200fs, which is equipped with a diffusion instead of turbomolecular pump, the holder is first pre-pumped at a pumping a pumping station overnight. The tip is again extended during pumping. The next morning, the tip is retracted and the holder transferred to the microscope. In this case, the tip is extended into the airlock at the later stages of pumping. After the vacuum has stabilized, the holder is inserted into the column. In both cases, the holder was then cooled to -193°C by introducing liquid nitrogen (LN2) into the holder's dewar. To mitigate LN2 boiling and associated vibrations, helium gas was introduced into the cryocontainer, further reducing the temperature to -198°C, at which point the bubbling ceased49,50. The system was allowed to equilibrate for one hour, after which the LN2 was replenished and the helium gas cycle repeated. Following a second hour of stabilization, the system reached thermal equilibrium with a drift rate of approximately 1.5 nm/min, at which point data acquisition commenced. During the cryo-measurements, the tip was cooled down to -165 °C to reduce drift. Machine Learning and SANS Data Fitting All simulations and fitting procedures were performed on a high-performance Linux-based system equipped with a 16-core AMD Threadripper PRO 5955WX processor (4 GHz), 64 GB DDR4 3200 MHz ECC memory, and an NVIDIA RTX 4090 GPU with 24 GB VRAM. We implemented a custom CNN model using PyTorch to predict SANS intensity curves from input parameters. The architecture comprises three blocks, each containing one deconvolutional and two convolutional layers with ReLU activation functions, followed by max pooling. The network takes 8 input parameters and outputs a 117-point intensity curve. Dropout layers (p = 0.5) were inserted throughout the blocks to mitigate overfitting. A flattening layer was employed to generate the final 1D output. The model's trainable parameters totaled approximately 3 million. Adam with a learning rate of 810-4 and at StepLR scheduler with a step size of 4 and gamma of 0.5 was chosen. A dataset of 250,000 simulated Small Angle Scattering (SAS) curves was generated based on the Plurigaussian Random Field (PGRF) model. The parameter ranges used for simulation are detailed in Table S1. This dataset was partitioned into training (80%), validation (10%), and test (10%) subsets. Prior to training, we added the experimental background, applied logarithmic transformation to the intensity values and normalized the intensity value and all parameters to the [0, 1] interval based on their respective global minima and maxima. Training was conducted over 40 epochs with consistent batch sizes of 256 for train, 128 for validation and test subsets. This process was repeated for four times. For the fitting process, the four networks were combined and their prediction averaged. Experimental data fitting was performed using the Optuna library, implementing a Bayesian optimization algorithm with mean squared error as the optimization metric. For handling the SANS intensity background at high q-values, we added the experimental background to the simulated 20 PGRF curves during CNN training rather than subtracting it from experimental data (we selected the background SANS curve at the point where all sulfur was dissolved and no other solid phases were present; Figure 4c, potential drop before onset of the second discharge plateau). This approach proved more robust as it improved the CNN's ability to recognize weak scattering features and enabled direct fitting to untreated scattering data (Figure S7). The experimental logarithmic intensity data underwent normalization based on the simulated dataset's minimum and maximum intensity values. Hence, all simulated SANS intensities are normalized between 0 and 1. This normalization approach is valid because our simulated dataset was designed to span the largest possible range of scattering curves, ensuring that the experimental data to be fitted falls within the boundaries established by the training set's intensity extremes. The optimization process evaluated 10,000 parameter combinations over a duration of 35 minutes. The PGRF SANS model In the following, we briefly describe the PGRF concept for calculating SANS intensities of a Li2SLi2S2 composite nanostructure, in line with recent works14,40. Figure S5 summarizes the procedure. The experimental SANS intensity of the discharged cathode in absolute units (cm-1) can be decomposed into two main components: 𝐼(𝑞)=𝐼Li2S,Li2S2(𝑞)+𝐵𝐺. (1) 𝐼Li2S,Li2S2(𝑞) corresponds to the scattering from the Li2S/Li2S2 structure. BG accounts for the constant background intensity, primarily from incoherent scattering and the atomic structure factor of the electrolyte and carbon. Scattering from the carbon black nanostructure is negligibly small as the deuterated electrolyte approximately matches the scattering length density of the carbon. The experimental SANS intensity of the Li2S/Li2S2 nanostructure (in units of cm-1) can be written as 𝐼Li2S,Li2S2(𝑞)=𝑉 𝑉max ⁄ [𝐴 𝑞−4+𝐼PGRF(𝑞)] , (2) 𝑉 𝑉max ⁄ is the relative volume of the deposited Li2S/Li2S2 nanostructure and allows us to account for the changing deposit volume during cycling. 𝑉𝑚𝑎𝑥 corresponds to the irradiated beam area (approx. 1 cm in diameter) times an effective Li2S/Li2S2 deposit thickness 𝑑𝑚𝑎𝑥 . We chose 0.007 cm as an initial estimate for 𝑑𝑚𝑎𝑥 and used this value for the normalization to absolute intensities. The first term, 𝐴 𝑞−4, describes the Porod decay from large Li2S/Li2S2 agglomerates (larger than 100 nm, see Figure 3a and Figure S1), with the SANS intensity being proportional to 𝑞−4 within the measured q-range. The second term, 𝐼PGRF(𝑞), models the nanostructure within the 1-50 nm range using plurigaussian random fields (PGRF). The SANS intensity 𝐼PGRF(𝑞) can be represented as the Fourier transform of the scattering length density (SLD) correlation function 𝐶(𝑟). This relationship is given by: 𝐼PGRF(𝑞)=∫ 𝐶(𝑟)sin(𝑞𝑟) 𝑞𝑟 4π𝑟2d𝑟 ∞ 0 . (3) For the three-phase system composed of Li2S, Li2S2, and Electrolyte, 𝐶(𝑟) can be expressed as: 21 𝐶(𝑟)=(𝜌Li2S−𝜌Li2S2)(𝜌Li2S−𝜌EL)[𝑃Li2SLi2S(𝑟)−𝜙Li2S2] +(𝜌Li2S2−𝜌Li2S)(𝜌Li2S2−𝜌EL)[𝑃Li2S2Li2S2(𝑟)−𝜙Li2S22] +(𝜌EL−𝜌Li2S)(𝜌EL−𝜌Li2S2)[𝑃ELEL(𝑟)−𝜙EL2] . (4) where, 𝜌i denotes the scattering length density, 𝜙i the volume fraction and 𝑃ii(𝑟) the two-point correlation function of phase i. By employing Gaussian random fields (GRF), one can create a 3D model of a two-phase pore structure from the fit to an experimental scattering curve. Plurigaussian random fields (PGRF) extend this concept by combining two GRFs to model SANS intensities and 3D structures in threephase systems. A GRF 𝑌(𝐱) is defined as: 𝑌(𝐱)=√2 𝑁∑cos(𝐤𝐢∙𝐱−𝜑i) , 𝑁 𝑖=1 (5) and a corresponding two-point correlation function of the GRF is given by 𝑔𝑌(𝑟)=1 cosh (𝑟 𝑙𝑌 ⁄)∙sin (2π𝑟 𝑑𝑌) ⁄ (2π𝑟 𝑑𝑌) ⁄ , (6) where 𝑙𝑌 is a correlation length parameter related to the feature size of the structure, and 𝑑𝑌 characterizes ordering effects. The power spectral density associated with 𝑔𝑌(𝑟) can be written as 𝑓𝑌(𝑘)=𝑘 π𝑙𝑌𝑑𝑌sinh(𝜋𝑘𝑙𝑌2 ⁄ ) sinh(π2𝑙𝑌𝑑𝑌) ⁄ cosh(𝜋𝑘𝑙𝑌)+cosh(2π2𝑙𝑌𝑑𝑌 ⁄) . (7) To generate a two-phase porous structure from the GRF, threshold values 𝛼 are introduced. All points 𝒙 for which 𝛼<𝑌(𝒙)≤ ∞ are assigned to the pore space (the combined Li2S2 + EL phase), while other coordinates correspond to the Li2S scaffold. The threshold 𝛼 is linked to the Li2S volume fraction 𝜙Li2S by 𝜙Li2S=1 √2π∫ exp(−𝑡2 2)d𝑡 ∞ 𝛼 . (8) For the three-phase system, a second independent GRF 𝑍(x) is generated sharing the same functional form of the correlation function but distinct parameters 𝑙𝑍 and 𝑑𝑍. The Li2S2 phase is obtained by combining 𝑍(x) and 𝑌(𝒙) and applying thresholds in the 𝑌,𝑍 partition plane (Figure S5): 𝜙Li2S2= ∬ 1 2π exp(−𝑌2+𝑍2 2) (𝑌,𝑍)𝜖𝐷Li2S2d𝑌 d𝑍 (9) 22 The two-point correlation function for the Li2S2 phase is: 𝑃Li2S2Li2S2= ∫ d𝑌1d𝑍1 𝐷Li2S2∫ d𝑌2d𝑍2 𝐷Li2S2𝐺𝑔𝑌(𝑟)(𝑌1,𝑌2)𝐺𝑔𝑍(𝑟)(𝑍1,𝑍2) (10) These distributions are obtained using Hermite polynomials 40 (similar considerations apply for Li2S). The corresponding scattering intensities can then be calculated from correlation functions using Equations 3 and 4. The morphology of the Li2S2 phase is influenced by the angle 𝛽 and the Li2S2/EL boundary line, as shown in Figure S5. When 𝛽→0, the Li2S2 phase forms a thin film perfectly coating the Li2S phase. Conversely, when the Li2S2/EL boundary is parallel to the Y-axis (𝛽→π/2), the Li2S2 (or EL) structure within the Li2S pores becomes statistically independent of the Li2S structure. 23 Data and Code Availability The Python implementation of the PGRF algorithm and the machine learning models are openly available on GitHub (https://github.com/JeanvonMentlen/machine_learning_enhanced_pgrf). All raw experimental data and the PGRF dataset used to train the CNN have been deposited in Zenodo and are accessible at DOI: 10.5281/zenodo.14532384. Acknowledgments We acknowledge the funding for the ALISA project (project number 9359) provided by the http://mERA.NET network (part of the European Union’s Horizon 2020 research and innovation program (under grant agreement No 958174)) and the Slovenian Ministry of Higher Education, Science, and Innovation. A.V. further acknowledges financial support from the Slovenian Research and Innovation Agency (ARIS), research core funding P2-0423, and project N2-0266. J-M.M. and A.S.G. acknowledge the financial support for the ALISA project from the Swiss Federal Office of Energy SFOE. J-M.M. acknowledges the help of Giovanni Volpe, Benjamin Midtvedt, Henrik Klein Moberg and Jesús Pineda (Chalmers University of Technology, Sweden) on the development of the machine learning model. Additionally, J-M.M. mentions the valuable help from Mario Mücklich (ETH Zürich) in the development of the neural network. Parts of the work were funded by the European Union (ERC-2022-STG, SOLIDCON, 101078271). Views and opinions expressed are, however, those of the authors only and do not necessarily reflect those of the European Union or the European Research Council Executive Agency. Neither the European Union nor the granting authority can be held responsible for them. 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