Impact of the Solid Electrolyte Particle Size Distribution in Sulfide‐Based Solid‐State Battery Composites

All solid‐state batteries are promising, as they are expected to offer increased energy density over conventional lithium‐ion batteries. Here, the microstructure of solid composite electrodes plays a crucial role in determining the characteristics of ionic and electronic pathways. Microstructural aspects that impede charge carrier transport can, for instance, be voids resulting from a general mismatch of particle sizes. Solid electrolyte materials with smaller particle size distribution represent a promising approach to limit the formation of voids and to match the smaller active materials. Therefore, a systematic investigation on the influence of the solid electrolyte particle size on the microstructural properties, charge carrier transport, and rate performance is essential. This study provides an understanding of the influence of the particle sizes of Li6PS5Cl on the charge carrier transport properties and their effect on the performance of solid‐state batteries. In conclusion, smaller Li6PS5Cl particles optimize the charge transport properties and offer a higher interface area with the active material, resulting in improved solid‐state battery performance.


Introduction
Access to sufficient electrochemical energy storage is essential for a successful energy and mobility transition from fossil fuels to renewable energies.So far, lithium-ion batteries with liquid electrolytes are the most widely used battery system.However, capability. [8]In addition, void spaces are present in solid-state electrodes.In contrast to the liquid electrolyte, solid electrolyte does not infiltrate small pores and the formation of voids leads to a decrease in the ionic conductivity.This was demonstrated by Bielefeld et al. by simulation and comparison of different geometry models of typical CAM arrangements. [9,10]Rana et al. [11] explored the particle size compatibility of CAM and solid electrolytes for an optimal packing density.Shi et al. [12] used microstructure simulations to show how CAM utilization depends on different ratios of CAM and solid electrolyte particle sizes, focusing on the influence on electrochemical performance.However, it is still open to how the charge transport correlates to void space formation and homogeneity as a function of the solid electrolyte particle size and how this impacts the electrochemical performance.
To answer these questions, this work systematically alters the particle size of Li 6 PS 5 Cl in cathode composites and focuses on changes in the microstructure, charge transport, and overall electrochemical performance.LiNi 0.83 Co 0.11 Mn 0.06 O 2 (NCM811) is used as CAM together with Li 6 PS 5 Cl of different particle size distributions as the catholyte.The Li 6 PS 5 Cl is first examined for structural differences at different particle sizes with X-ray diffraction and pair distribution function analyses.Rate performance tests and long-term cycling are performed on half cells to investigate the electrochemical performance of the composite electrodes.The effective electronic and ionic charge transport is determined by impedance spectroscopy using a transmission line model.Finally, the microstructure of the composite electrodes is modeled, and the resulting current density distributions are simulated and compared with the experimental results.This work underlines the importance of adjusting the particle sizes of the solid electrolyte to design an opti-mized microstructure for charge transport in solid-state battery composites.

Results and Discussion
To assess the influence of the solid electrolyte particle size distribution on the effective transport in solid-state battery composites, first, the Li 6 PS 5 Cl needs to be assessed in terms of potential structural and transport differences for different particle sizes.Figure 2a shows the volumetric particle size distribution of the different Li 6 PS 5 Cl samples.The particle size distribution range of the studied solid electrolytes covered 40, 20, 11, and 4 μm.To emphasize on the complex nature of the particle size distributions, the prepared composites are herein referred to as S (D50 vol = 4 μm), M (D50 vol = 11 μm), L (D50 vol = 20 μm), and XL (D50 vol = 40 μm), respectively.This particle size range was selected to investigate the optimum size ratio of the solid electrolyte with the CAM, which has a D50 value of 3.4 μm (see Figure S1, Supporting Information).Additional scanning electron microscopy images and a detailed discussion of the particle size distributions can be found in Figures S2, S16-S18 (Supporting Information).Figure 2b presents the impedance spectra of the Li 6 PS 5 Cl.Due to the high ionic conductivities, no process besides the blocking behavior of the electrodes can be seen and the data is fitted with an R-CPE equivalent circuit.The total ionic conductivities at room temperature of the different solid electrolytes calculated from the impedance spectra are 2.2 mS cm −1 .The only exception is the 20 μm Li 6 PS 5 Cl, which has a conductivity of 2.8 mS cm −1 .Nevertheless, this can be considered within the measurement and sample uncertainty. [13]emperature-dependent impedance measurements show similar activation barriers for ionic transport (see Figure S3, Supporting Information).All these ionic conductivities are within the range of the Li 6 PS 5 Cl argyrodites of 10 −3 -10 −2 S cm −1 , [14][15][16] suggesting no particular influence of the particle size distribution on the ionic conductivity.
Powder X-ray diffraction (Figure 2c) indicates phase purity of the Li 6 PS 5 Cl and no differences in the average structure and lattice parameters can be found for the different particle sizes (see Figure S4, Supporting Information).As different particle sizes may exhibit differences in the local structure of the materials, pair distribution function analyses were performed.The pair distribution functions are found in Figure 2d and their quantitative analyses by small-box modeling can be found in Figure S5 (Supporting Information).Despite the different particle sizes, no difference in the local structure or coherency can be found.Clearly, no impact of the particle size of Li 6 PS 5 Cl on the ionic conductivity as well as the average and local structure is evident.This can also be demonstrated by the similar Raman spectra (Figure S6, Supporting information S6).
To investigate the effects of the different particle sizes of Li 6 PS 5 Cl in the NCM composite electrode, cathode composites with 70 wt.%NCM811 and 30 wt.% Li 6 PS 5 Cl are produced.Scanning electron microscopy cross-sections with energy-dispersive X-ray spectroscopy (EDS)-mapping of the pressed composites from Figure 3a indicate a more homogeneous distribution of Li 6 PS 5 Cl for smaller particle sizes compared to larger particle sizes.Another magnification of the SEM images can be found in Figure S7 (Supporting Information).Figure 3b shows the modeled microstructure using the experimental microstructural inputs.Further details of the simulations and how the digital microstructures are derived can be found on Pages S9-S16 (Supporting Information).The modeled microstructure also indicates a better distribution of Li 6 PS 5 Cl with smaller particle sizes of the solid electrolyte.A decrease in void space with decreasing particle size is shown in Table S1 (Supporting Information).The different composites are used to build half-cells with Li 5.5 PS 4.5 Cl 1.5 as the separator and In/LiIn alloy as the counter electrode.Li 5.5 PS 4.5 Cl 1.5 was used as the separator because it has a conductivity of 8 mS cm −1 that ensures a low resistance of the separator and only a low effect on the performance of the cell. [14]he cells are either charged and discharged at various C-rates or at 0.1 C for 50 cycles.Triplicates of each measurement were made to assure reproducibility (see Figures S8 and S9, Supporting Information) and the resulting cell performance data are shown in Figure 4, together with their standard deviation.
Figure 4a,b shows the charge and discharge curves at 0.05 C (j = 0.107 mA cm −2 ) and 1 C (j = 2.14 mA cm −2 ) for the NCM811 composites with different particle sizes of Li 6 PS 5 Cl.
The general shape of the potential curve during charging and discharging at 0.05 C is identical and similar to the literature. [17]he composite S exhibits the highest initial charge capacity at 247 mAh g −1 (±24 mAh g −1 ).The initial charge capacities of the composites M and L are similar at 212 mAh g −1 (±4 mAh g −1 ).The composite XL has the lowest initial charge capacity at 205 mAh g −1 (±4 mAh g −1 ).Solid-state cells with a sulfide solid electrolyte and with a high nickel-content NCM typically show initial capacities of more than 200 mAh g −1 . [18]A similar trend can be observed for the discharge capacities.The composite S has a discharge capacity of 198 mAh g −1 (±18 mAh g −1 ).The discharge capacities of the composites M and L are similar at 165 mAh g −1 (±3 mAh g −1 ).The composite XL shows the lowest discharge capacity at 152 mAh g −1 (±3 mAh g −1 ).The difference in the charge and discharge capacity of the initial cycle is often reported and stems from structural rearrangements, chemomechanical effects, and loss of available lithium. [19]The Coulombic efficiencies of the composites are shown in Figures S8 and S9 (Supporting Information).For the charge and discharge curves at 1.0 C, the shape of the discharge curves changes as the particle sizes increase.The overpotential increases with increasing particle size of Li 6 PS 5 Cl.This may be due to kinetic limitations such as lithium-ion transport, [20] but needs to be corroborated below.Figure 4c presents the discharge capacity over 50 cycles.No difference can be seen in the capacity retention for the composites with different particle sizes of Li 6 PS 5 Cl.The initial decrease in capacity can likely be explained by the formation of solid electrolyte interphase of the decomposition reactions. [21]The resulting phosphate-and sulfate-like species are redox active, which could explain the small increase in the capacity after ten cycles of the S and M composites. [21,22]Figure 4d shows that all composites have constant capacities at all C-rates.However, the rate capability decreases with increasing particle size, which, at this point, we attribute to the higher overpotential shown in Figure 4b.Clearly, the reason for the lower overpotential and with-it better cycling and rate-capability of the smaller catholyte particle sizes needs to be evaluated.
To do so, electrochemical impedance spectroscopy and DC polarization measurements were carried out to determine the effective conductivity of the cathode composite.Triplicate measure-ments of the impedance spectroscopy can be found in Figures S10 and S11 (Supporting Information).The results of the DC polarization as a support of the impedance analyses are shown in Figures S12 and S13 (Supporting Information).The resulting Nyquist plots of the impedance spectra are shown in Figure 4.The cathode composite consists of two phases that conduct different species, namely lithium-ions that travel through the Li 6 PS 5 Cl, and electrons that are conducted by the CAM.In addition, charge transfer also takes place at the interface between the phases.Therefore, a transmission line model is required to describe the electrochemical system.This is commonly used to describe porous membranes [23] and was developed by Siroma et al. [24] for composite electrodes.Recently Minnmann et al. [8] extended it to sulfide-NCM systems.For these systems, the use of the transmission line model measured in half cells is limited due to the overall low cell resistances.This results in limitations of the resolution of the impedances.When cells with higher resistances are used, the transmission line model can also be used on half cells as has recently been shown by Hendriks et al., [7] Miß et al. [25] and Rana et al. [11] Figure 5a shows the impedance data of the composites with different particle sizes of Li 6 PS 5 Cl in an ionic blocking symmetric cell setup with the resulting "T-type" transmission line model that helps to extract the effective electronic transport of the composites.The cell impedance Z CC of the ionic blocking cell is described as It depends on the impedance of the electron-conducting phase z el and the impedance of the ion-conducting phase z ion as well as the impedance of the interface between these two phases z int .L is the thickness of the composite electrode. [24]he electronic impedance z el is represented by the electronic bulk resistance r el and an in-series connected electronic interfacial impedance z el,int of the NCM particles, as previously reported by Minnmann et al. [8] This electronic interfacial impedance is based on the electronic charge transfer across the NCM-NCM interface and is represented by a parallel R-CPE unit.The ionic impedance can be described by an ohmic resistance r ion .While other transmission line model approaches have shown the ionic path as a resistor in parallel with a constant phase element when using a solid electrolyte with lower ionic conductivity, the fast ionic transport of the sulfide electrolyte in this work requires only a resistor equivalent circuit element. [7]For the system, a nonfaradaic behavior can be assumed as there is no charge transfer between the ion-conducting and electron-conducting phases in the symmetric cell.This is represented by a CPE int for the z int.[8]   Figure 5b shows the impedance spectra and the "T-type" transmission line model of the symmetric electronic blocking cells.Since it represents the ionic pathway, the ionic and electronic pathways are interchanged.The ionic, electronic, and interface impedances are represented by the equivalent circuit elements previously described in Figure 5a.Additionally, the equivalent circuit has a resistor in series with a parallel R-CPE.This represents the bulk resistance from the electrolyte and the impedance of the interface of the electrolyte-In/LiIn electrode.
The effective electronic and ionic resistance R el and R ion are obtained as follows: Comparing the so-determined electronic and ionic resistances from the impedance analyses with the values determined by DC polarization measurements (Figures S12 and S13, Supporting Information) shows the validity of both approaches, see Figure S14 (Supporting Information).
From Figure 6a it is evident that the experimental effective ionic conductivity in the composite electrode is enhanced with decreasing particle size of Li 6 PS 5 Cl.The experimental conductivities are similar for the composites L and XL at 0.16 mS cm −1 (±0.03 mS cm −1 ) but increase to 0.25 mS cm −1 (±0.01 mS cm −1 ) in the composite S. Figure 6c shows the simulated current distribution through the composites and illustrates that this increase in ionic conductivity can be attributed to a more homogeneous distribution of Li 6 PS 5 Cl in the composite that leads to a more uniform distribution of the ionic current density.Here, the tortuosity factor , with  = volume fraction ⋅bulk conductivity effective conductivity , is decreasing with smaller particle sizes (Figure S15, Supporting Information) that is a result of a significantly smaller void space in composite S than the other composites (see Table S1, Supporting Information).Despite the same composition in terms of weight fraction, the overall volume occupied by Li 6 PS 5 Cl is larger, and that in turn has a positive effect on the effective ionic conductivity.Figure 6c further illustrates that the current distribution in the composites L and XL is rather local.The larger Li 6 PS 5 Cl particles exhibit a smaller surface area, so the possibility to form a well-connected conduction network is smaller.Practically, the ionic current is forced to pass through a few particle-to-particlepoint contacts that can be regarded as bottlenecks.
Compared to the effective ionic conductivity, its electronic equivalent shows less dependence on the Li 6 PS 5 Cl particle size with 0.40 mS cm −1 (±0.06 mS cm −1 ) for the composite XL and 0.38 mS cm −1 (±0.15 mS cm −1 ) for the composite S, in Figure 6a.While Minnmann et al [8] experimentally observed a reduction of the effective electronic conductivity with decreasing solid electrolyte particle size.In contrast, the simulated conductivities decrease with the solid electrolyte particle size.The simulated electronic current distribution in the composites is shown in Figure S21 (Supporting Information) and exhibits the same trend as the ionic current distribution.The composite S possesses less voids and a more homogeneous distribution of NCM811 and Li 6 PS 5 Cl that is generally favorable for both, ionic and electronic pathways.It is unclear why this effect is not evident in the experiment.At this stage, we assume this to stem from surface effects on the NCM leading to different resistances between NCM particles as any changes due to cycling-based decomposition or contact losses can be ruled out for these symmetric cells.
Taking all experimental data, Figure 6b compares the attainable capacity at 0.05 and 1 C with the ratio of the ionic and electronic conductivities.An increase in capacity can be observed when the conductivity is balanced and closer to unity.It becomes evident that for a high-performance electrode not only fast charge transport but also balanced charge transport is essential as an electrochemical reaction requires both electrons and ions to be supplied at comparable rates. [26]A similar effect was recently seen by Hendriks et al. using a LiMn 2 O 4 /Li 3 InCl 6 solidstate battery. [7]Concerning the attainable capacity, apart from the effective conduction pathways, the active interface area also acts in favor of composites with smaller particle sizes.Due to their higher surface area, small particle-containing composites offer more possibilities for contacts and, thus, a higher interface area.This is underlined by the specific active interface area of 142.7 × 10 5 m −1 for the composite S that is lowered by a factor of 3.5 for the composite M and decreases to 16.5 × 10 5 m −1 for the composite XL (see Figure S22, Supporting Information).

Conclusion
This study shows that the particle size distribution of Li 6 PS 5 Cl in solid-state battery composites is a key factor in determining the overall cell performance.In the studied range, the particle size distribution has no impact on the ionic conductivity and the structure of pure Li 6 PS 5 Cl.However, it significantly affects the performance of NCM811 composite electrodes.Smaller particle sizes of Li 6 PS 5 Cl result in higher capacities and better rate performance of the composite electrodes.Smaller Li 6 PS 5 Cl particle sizes ensure a larger contact interface, which provides more opportunities for contact between solid electrolytes and CAM.The effective ionic conductivity in the composite electrode is improved with decreasing particle size by a more homogeneous distribution of Li 6 PS 5 Cl, resulting in a more uniform distribution of ionic current density.In addition, the smaller void and larger volume fraction occupied by Li 6 PS 5 Cl in composites with smaller particle sizes contributed to the higher effective ionic conductivity and the lower ionic tortuosity factor.This work highlights the importance of balanced charge transport for high-performance electrodes in solid-state batteries, in which both fast and balanced transport of electrons and ions are critical for efficient electrochemical reactions.In the end, this needs to be achieved by tailoring the composite properties whenever active materials, additives, or catholyte materials are changed so that an optimum matching of particle sizes and transport parameters is achieved.

Experimental Section
Synthesis of Solid Electrolyte: Li 6 PS 5 Cl (provided by AMG Lithium) was used as a catholyte and Li 5.5 PS 4.5 Cl 1.5 as the separator.All synthetic steps were performed under inert conditions (O 2 < 0.1 ppm, H 2 O < 0.5 ppm).The Li 5.5 PS 4.5 Cl 1.5 was synthesized by a solid-state synthesis route as previously reported. [14]A stoichiometric amount of lithium chloride LiCl (LiCl, anhydrous, Alfa Aesar, 99%) was hand-ground with a mortar and pestle for 15 min.Lithium sulfide (Li 2 S, Alfa Aesar, 99.99%) and diphosphorus pentasulfide (P 2 S 5 , Sigma) were added and ground for another 15 min.The resulting mixture was densified into pellets and put in a silica ampoule with a carbon coating, which was then sealed under a vacuum.In the first reaction step, the ampoule was kept in the furnace for 72 h at 450 °C at a heating rate of 100 °C h −1 , followed by natural cooling after the reac-tion.The ampoule was then opened, and the obtained pellets were handgrounded for 15 min.The powder was pressed into pellets again and the first reaction step was repeated.After the second heating step, the pellets were ground, and the powder was characterized with X-ray diffraction and impedance spectroscopy.For the Li 6 PS 5 Cl, the analysis of the particle sizes was performed with a static laser diffraction particle size analyzer from Sympatec Helos.
X-Ray Diffraction: The phase purity of the synthesized Li 5.5 PS 4.5 Cl 1.5 and the Li 6 PS 5 Cl with different particle sizes was analyzed by X-ray powder diffraction using a StadiP from STOE in Debye-Scherrer geometry with Cu-K  radiation ( 1 = 1.545051Å).The samples were analyzed in sealed 0.5 mm capillaries.The measurements were taken at an angle range of 2 = 10°-70°and a step size of 0.1 and 15 s per step.
Pair Distribution Function Analyses: The Li 6 PS 5 Cl samples were measured in a sealed glass capillary with an STOE StadiP diffractometer (Ag K 1 radiation:  = 0.55941 Å, Ge 111 monochromator) in Debye-Scherrer geometry with four Dectris MYTHEN2 1K detectors.The scattering data were recorded over a Q-range of 0.8-20.5 Å -1 for 24 h.PDFgetX3 was used for data reduction with a Q-range cutoff of Q max = 18 Å −1 . [27]Small box modeling was performed using TOPAS Academic V7 where 1) scalefactor, 2) correlated motion factor, 3) lattice parameters, 4) atomic positions, and 5) isotropic atomic displacement parameters were subsequently refined over an r-range of 1.5-40 Å.
Scanning Electron Microscopy: The CAM, Li 6 PS 5 Cl samples, and the surface of the pressed composites were analyzed by scanning electron microscopy with EDS.The samples and the pressed composites were attached to the sample holder with double-sided carbon tape and coated with gold.The scanning electron microscopy was carried out at Carl Zeiss AURIGA CrossBeam working station (accelerating voltage of 3 kV) and an In-lens detector.The EDS was performed with an X-Max 80mm2detector (accelerating voltage 15 kV).
Preparation of Electrode Composites: Cathode composites were prepared by mixing lithium nickel cobalt manganese oxide (, MSE supplies, dried overnight in a B-585 oven (Büchi) in dynamic vacuum at 250 °C) and the respective Li 6 PS 5 Cl (AMG Lithium) in a weight ratio of 70:30.The two components were transferred into a 15 mL ZrO 2 cup with 3 mm sized zirconia spheres and mixed using a frequency ball mill (Fritsch pulverisette 23 Mini Mill) at a frequency of 15 Hz for 15 min.
Electrochemical Cell Assembly: For all electrochemical measurements a PEEK lined, airtight press cell with stainless steel stamps with a surface area of 0.785 cm 2 as current collectors were used. [28]For the half cells, 60 mg of Li 5.5 PS 4.5 Cl 1.5 was filled as the separator in the cell.A hand press was used to press the separator between the two stainless steel stamps in a uniformly distributed layer.Composite (12 mg), corresponding to an area loading of the CAM of 10.7 mg cm −2 , was layered on one side of the separator.Particular attention was given to ensure an even and complete coverage of the composite on the separator.The separator and the composite layer were densified with a uniaxial press with 3 tons for 3 min.After pressing, an indium foil (chemPUR, 100 μm thickness, 99.99%) with 9 mm diameter was placed on the other side of the separator.1.5 mg of lithium (Li, abcr, 99.8%) was pressed into a foil and was then placed on the indium foil.The cell was closed airtight.For electrochemical measurements, the cell was placed in a metal frame to apply a pressure of 50 MPa and was left for 6 h at 25 °C for equilibration.
Electrochemical Characterization: Long-term cycling tests were performed using the MACCOR in a climate chamber maintained at 25 °C.The half cells were cycled in a voltage window of 2.0 to 3.7 V versus In/LiIn with a C-rate of 0.1 C for 50 cycles.Rate performance tests were performed at a Biologic-VMP300 potentiostat in a climate chamber at a constant 25 °C.The applied charge and discharge currents were varied from C/20 (j = 0.107 mA cm −2 ), C/10 (j = 0.214 mA cm −2 ), C/5 (j = 0.428 mA cm −2 ), C/2 (j = 1.070 mA cm −2 ) and 1 C (j = 2.140 mA cm 2 ) in a voltage window from 2.0-3.7 V versus In/LiIn.
Effective Transport Characterization: Symmetric cells were prepared for the charge transport measurements.For effective electronic transport, steel stamps were used as ionic-blocking electrodes on both sides.100 mg of the composite was filled in the press cell and uniformly distributed.The cell was closed airtight and pressed with the uniaxial press with 3 tons for 3 min.For the determination of effective ionic transport, electronically blocking electrodes on both sides were used.For this, layers of 80 mg of Li 5.5 PS 4.5 Cl 1.5 were placed on both sides of the 100 mg prepressed composite.The cell was closed airtight and pressed in the uniaxial press with 3 tons for 3 min.Then indium foil (9 mm diameter) and 1.5 mg lithium foil were placed on both sides of the solid electrolyte layers.The cells were placed in a metal frame to apply a pressure of 50 MPa and were left for 6 h at 25 °C for equilibration. [29]o determine the effective electronic conductivity, impedance spectroscopy was performed on the symmetric cell with ionic blocking electrodes.Electrochemical impedance spectroscopy (EIS) was performed at 25 °C with a Biologic VMP 300 potentiostat at a perturbation amplitude of 10 mV and in a frequency range from 10 mHz to 7 MHz.After the impedance measurement, a subsequent DC polarization was performed to corroborate the AC data.Here, a voltage from 45 to 50 mV was applied in 5 mV steps.To reach an equilibrium state, each voltage step was kept for 2 h.For measuring the effective ionic conductivity, symmetrical cells with electronic blocking electrodes were used.First, impedance spectroscopy was performed with the same conditions as for electronic conductivity.The subsequent DC polarization measurement was performed in a voltage range from 0.5 to 5 mV.The voltage steps were 0.5 mV.For the adjustment of the equilibrium, each voltage step was measured for 5 h to ensure full polarization.The impedance data were evaluated with a transmission line model using RelaxIS 3 software.
Microstructure Modeling and Simulation: The simulation of ion flux through composite electrodes requires the reconstruction of microstructure models that consist of voxels.These models are generated based on the scanning electron microscopy images and EDS mappings of the pristine CAM (Figure S1, Supporting Information), Li 6 PS 5 Cl particles (Figure S2, Supporting Information), and the various composites (Figure S7, Supporting Information).The simulations and microstructure generations are performed on a Dell Precision 3650 Tower (96 GB RAM, 11th Gen Intel Core i7-11700 CPU) with the GeoDict [30] Modules GrainGeo, ProcessGeo, ConductoDict, and MatDict.
The microstructure models are constructed based on the particle size distributions and particle shapes of all electrode components, their volume fractions, the overall void space, and the homogeneity of the particle/component distribution (see Table S1, Figure S16, Pages S10 and S11, Supporting Information).To model the cathode composite, both CAM and Li 6 PS 5 Cl particles are randomly distributed within the model volume of (300 μm) 3 for the larger Li 6 PS 5 Cl particles and (90 μm) 3 for the smallest particles at a resolution of 600 and 300 nm voxel −1 , respectively.For each composite, three microstructure models are generated to provide an average.The flux simulations are performed as introduced previously [10] with a potential difference of 1 and 0.3 V for the smallest Li 6 PS 5 Cl particles.As the material bulk conductivity, 2.2 mS cm −1 (Li 6 PS 5 Cl) and 5.2 mS cm −1 (CAM) were employed.The simulation assumed that the ionic current was carried by the solid electrolyte, while the electronic current was carried by the CAM.Since the CAM has a high Young's modulus of 194 GPa, [31] the resulting overlap between the CAM and Li 6 PS 5 Cl was assigned to the CAM. [32]Before the simulation, the structure was cleansed from residual CAM particles within the Li 6 PS 5 Cl substructure.For a detailed explanation see Figures S19 and S20, and Pages S13-S15 (Supporting Information).

Figure 1 .
Figure 1.Scheme of a solid-state battery with tortuous charge transport pathways and microstructures of electrode composites with different solid electrolyte particle sizes.

Figure 2 .
Figure 2. Characterization of Li 6 PS 5 Cl with different particle sizes.a) Volumetric cumulative particle size distribution measured by a laser diffraction particle size analyzer.b) Impedance spectroscopy to determine the ionic conductivity, c) X-ray diffraction patterns, and d) pair distribution functions suggest no strong differences in the structure and transport at different particle sizes.

Figure 3 .
Figure 3. a) Scanning electron microscopy with EDS-mapping of the pressed composites with different particle sizes of Li 6 PS 5 Cl and b) modeled microstructures indicate a more homogeneous distribution of solid electrolyte.

Figure 4 .
Figure 4. Cell performance tests of composite electrodes with different solid electrolyte particle sizes in half-cell setups.a) First cycle charge and discharge curves at 0.05 C (j = 0.107 mA cm −2 ).b) Charge and discharge curve at 1 C (j = 2.14 mA cm −2 ).c) Discharge capacities for 50 cycles at 0.1 C (j = 0.214 mA cm −2 ).d) Discharge capacities of rate-performance test.All data show that with decreasing particle size distribution, higher capacities and better rate-performance can be obtained.

Figure 5 .
Figure 5. Nyquist plots of impedance data of composites with different particle sizes of Li 6 PS 5 Cl and the transmission line model.Impedance spectra measured in a) ionic blocking symmetric cells with electron-electron "T-type" connection for measuring the effective electronic transport and in b) electronic blocking symmetric cells with "T-type" ion-ion connection for measuring the effective ionic transport.

Figure 6 .
Figure 6.a) Effective electronic (blue) and ionic (yellow) conductivity of composites with different particle sizes of Li 6 PS 5 Cl measured with impedance spectroscopy and compared to simulated conductivities.The electronic conductivity keeps constant while the ionic conductivity increases with smaller particle size.b) Capacity of composite electrodes at C/20 and 1 C versus the ratio of ionic and electronic conductivity measured by impedance spectroscopy.The initial charge capacity is increasing when the ionic and electronic conductivity are more balanced.c) Comparison of the effective ionic conductivity from the flux-based simulation for all composites.The small Li 6 PS 5 Cl particles show a uniform current distribution, while the composite XL exhibits a localized ionic current flow.