# The mechanical properties of solid sulfur electrolytes: a local approach for a multiscale design

Kethsovann Var, Etienne Barthel, Sofiane Maiza, David Sicsic, Damien Bregiroux, Christel Laberty-Robert

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Kethsovann Var, Etienne Barthel, Sofiane Maiza, David Sicsic, Damien Bregiroux, et al.. The mechanical properties of solid sulfur electrolytes: a local approach for a multiscale design. Journal of Power Sources, 2026, 668, pp.239292. 10.1016/j.jpowsour.2026.239292. hal-05481169

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# The mechanical properties of solid sulfur electrolytes: a local approach for a multiscale design

Kethsovann Var<sup>a, c, 1)</sup>, Etienne Barthel<sup>d, *, 1)</sup>, Sofiane Maiza<sup>c)</sup>, David Sicsic<sup>c</sup>,
Damien Bregiroux<sup>a,)</sup>, Christel Laberty-Robert<sup>a, b, **, 1)</sup>

<figure><img src="image_2.png" /></figure>

## HIGHLIGHTS

* Fast nanoindentation quantifies micro-mechanical properties of Li₆PS₅Cl particles.

* Enables in-air probing of air-sensitive solid electrolytes under low load.

* Particle stiffness and size govern pellet densification and surface texture.

* Contact stiffness trends explain macroscopic density and surface smoothness.

* Framework guides compaction design for robust solid-state battery electrolytes.

## GRAPHICAL ABSTRACT

<figure><img src="image_3.png" /></figure>

## ARTICLE INFO

### Keywords:

Mechanical properties

Argyrodite

Nanoindentation

## ABSTRACT

Optimizing solid-state cathodes and electrolytes requires meeting stringent mechanical constraints, which demands precise knowledge of individual component properties. We show that fast, low-load nanoindentation effectively characterizes single particles in air-sensitive solid electrolytes, overcoming atmospheric control challenges. As a case study, argyrodite (Li₆PS₅Cl) pellets were fabricated under varying compaction pressures and particle sizes. Local-scale measurements reveal that smaller or softer particles achieve higher density and smoother surfaces at lower pressures, linking particle-scale mechanics to bulk behavior. These results rationalize macroscopic pellet density and surface quality, providing practical guidance for compaction optimization. Overall, this accessible methodology offers a multiscale framework for designing high-density, high-performance

<footnote><sup>a</sup> Sorbonne Université, CNRS, Laboratoire de Chimie de la Matière Condensée de Paris (LCMCP), F-75005, Paris, France</footnote>

<footnote><sup>b</sup> Réseau sur le Stockage Electrochimique de l'Energie, RS2E, FR 3459, F-80039, Amiens, France</footnote>

<footnote><sup>c</sup> Renault Group, Ampere, AMV-CPB5 - Battery Innovations, F-78280, Guyancourt, France</footnote>

<footnote><sup>d</sup> ESPCI Paris, PSL University, Sorbonne Université, CNRS, Laboratoire Sciences et Ingénierie de la Matière Molle, F-75005, Paris, France</footnote>

<footnote>* Corresponding author.</footnote>

<footnote>** Corresponding author. Sorbonne Université, CNRS, Laboratoire de Chimie de la Matière Condensée de Paris (LCMCP), F-75005, Paris, France.</footnote>

<footnote>E-mail addresses: etienne.barthel@espci.fr (E. Barthel), christel.laberty@sorbonne-universite.fr (C. Laberty-Robert).</footnote>

<footnote n="1">¹ These authors contributed equally.</footnote>
solid electrolytes, enabling informed choices of particle size, compaction pressure, and material properties to enhance the mechanical and electrochemical performance of solid-state batteries.

The growing demand for high-performance, safe, and durable energy storage systems has driven significant interest in all-solid-state batteries (ASSBs) as a promising alternative to conventional lithium-ion batteries [1]. By replacing the flammable liquid electrolyte with a solid counterpart, ASSBs offer the potential for enhanced energy density, improved safety, and a long-term stability. Despite these advantages, several technological challenges remain, particularly at the interfaces between electrodes and the solid electrolyte. Critical issues include electrochemical and chemical reactivity at interfaces [2–6], porosity, mechanical stresses [7–9], and plating/stripping phenomena [10–12].

Among these, electro-chemo-mechanical degradation presents a major barrier to performance. During lithiation and delithiation [13–18], volume changes in the active materials generate internal stresses that can lead to crack formation and interfacial delamination [19–21], resulting in reduced cyclability and increased interfacial resistance. Various strategies have been explored to mitigate these effects, such as tailoring the morphology of active particles to alleviate stress [22,23], selecting low-expansion active materials [24], optimizing the electrochemical operating window, or combining different active materials to achieve near-zero average expansion at the macroscopic scale [13]. Nonetheless, recurring difficulties highlight the need for a rational design of the battery architecture in relation to these stringent mechanical requirements.

In this context, the mechanical properties of the solid electrolyte itself are crucial. A mechanically compliant electrolyte could accommodate active material deformation and maintain intimate interfacial contact during cycling. Oxide-based electrolytes, such as garnets (LLZO), offer excellent chemical stability in air simplifying handling and mechanical testing. However, their exceptionally high stiffness (Young's modulus >200 GPa) [25–28] and intrinsic brittleness severely limit their ability to accommodate interfacial strain, posing significant challenges for interface stability. In contrast, sulfide-based (e.g., Li~6~PS~5~Cl, Li~10~GeP~2~S~12~, Li~2~S–P~2~S~5) and chloride-based (e.g., Li~3~YCl~6) electrolytes exhibit significantly greater ductility and are well-suited for cold pressing [29–34]. In addition to their high Li⁺ mobility, their superior mechanical compliance vs. oxides makes then highly promising candidates for ASSBs. However, their pronounced sensitivity to moisture and oxygen complicates mechanical characterization under ambient conditions, often necessitating controlled environments that hinder high throughput analysis. Pioneering studies, including those by Papakyr-iakou et al. [35] and Ai et al. [36], have employed nanoindentation systems integrated into gloveboxes or coupled with scanning electron microscopes (SEM) *via* inert transfer chambers, enabling mechanical characterization of air-sensitive solid electrolytes. While these approaches are effective, they rely on highly specialized and costly instrumentation, which limits accessibility, reproducibility, and broader adoption across research groups. This highlights the critical need for simplified, robust, and reproducible experimental protocols that enable mechanical evaluation of air-sensitive materials under ambient conditions.

In this study, we present a robust and practical methodology for the mechanical characterization of air-sensitive solid electrolytes, using a thin protective layer of mineral oil to enable nanoindentation measurements under ambient conditions. When coupled with ultra-fast mechanical mapping, this approach facilitates the acquisition of large, high-quality datasets, up to 4000 indentations per sample within just 6 h, while maintaining excellent reproducibility and spatial resolution. Beyond its efficiency, this technique provides a powerful means to resolve and identify distinct mechanical phases within composite materials, based on their unique mechanical signatures and spatial distributions. These capabilities open new opportunities for high-resolution,

local scale analysis of complex solid electrolyte systems, enabling the mechanical characterization of individual constituents essential for advanced material design and process optimization.

**Methodology** The setup used to prevent moisture exposure is inspired by the study of McGrogan et al. [34] from which we adopt the use of a mineral oil layer to protect the argyrodite pellet from ambient humidity (Fig. 1). Initially, 200 mg of argyrodite powder are pressed inside a glovebox under an inert atmosphere (H₂O level <1 ppm) at pressures ranging from 100 to 400 MPa, depending on the experimental conditions, in a home-made mold (Appendix 1). The resulting pellet typically has a diameter of 13 mm and a thickness between 0.8 and 1.2 mm, depending on the applied pressure. The pellet is formed and stored within the mold to avoid microcrack formation that could occur during demolding process. Next, 1–2 mL of mineral oil (Ultragrade performance vacuum oil - Edwards) is added to fully cover the pellet surface and protect it from air exposure. The mold can then be removed from the glovebox to perform indentation tests under ambient conditions. The absence of reactivity between argyrodite and oil was confirmed by X-ray diffraction (XRD), (Appendix 2), and by X-ray photoelectron spectroscopy (XPS) (Appendix 2). Indentation tests (Berkovich tip) and data analysis were performed with a Hysitron TI Premier nanomechanical test system (Bruker) and the associated Triboscan software (Appendix 2).

Several difficulties arise. The surface of this assembly of ca 10 µm diameter particles is rough. Second, due to the cold sintering, the particle assembly has a rather poor cohesion. For example, with an indentation experiment at high load (10 mN), the force curve typically exhibits displacement jumps (red circles in, Appendix 3 (Fig. S3) originating from particle rearrangements.

Faced with these challenges, our methodology resorts to low loads and fast mapping (XPM) to derive characterization of individual components. Typically, over a 20 µm × 20 µm square area of the pellet surface, 400 indentations at a 1 mN load are performed with a 1 µm spacing. Using the fast mapping mode, the mapping is completed in 8 min. For further data analysis, we also acquire topographical images using the Scanning Probe Microscopy (SPM) mode to evaluate the surface state after XPM mapping.

## 1. Data analysis

Fig. 2a shows a mechanical map of 400 indents, displaying the distribution of Young's modulus across an argyrodite pellet pressed at 400 MPa, while Fig. 2b presents the corresponding topography recorded in *situ* over a slightly larger area immediately after indentation. The local scale mechanical response at the grain size can be determined when heterogeneities, particularly e surface roughness, are taken into account. To achieve this, we applied a simple statistical analysis based on *k*-means clustering, which partitions the dataset into *k* clusters, each represented by a centroid. Data points were assigned to the nearest centroid using Euclidean distance, and the clustering process was optimized to minimize within-cluster variance. For this relatively simple sample, *k* was set to 2, effectively separating the measurements into two distinct subgroups. Additional methodological details are provided in Appendix 4.

Fig. 2c shows the superposition of the topography and the clusters map. Two distinct clusters, emerge, low modulus values in green and high modulus values in red, which are clearly spatially correlated. The high value cluster corresponds to the tops of the asperities, whereas the low values appear in the lower lying regions. Measurement artefacts, particularly multiple surface contacts caused by the relatively wide angle (146°) of the indenter tip, likely affect these depressions. This
observation reveals that clustering approach effectively isolates and averages the mechanical response over regions suitable for reliable nanoindentation probing (Fig. 2d), representative of the intrinsic mechanical properties of Li₆PS₅Cl grains. Consequently, the mean value from the cluster associated with particle tops is used to derive the mechanical properties of the particle material, while values from the other cluster are discarded. To further confirm the robustness of this approach, results for a Li₆PS₅Cl pellet pressed at a lower pressure of 100 MPa are presented in Appendix 5. We additionally performed nanoindentation measurements on Li₁.₅Al₀.₅Ti₁.₅(PO₄)₃ (LATP), a solid electrolyte that remains stable under ambient air. Indentations were carried out both with and without the protective oil layer. The measured Young's modulus—107.5 ± 2.4 GPa (without oil) and 110.6 ± 4.5 GPa (with oil) (see Appendix 6) were in excellent agreement and consistent with previously reported values. The negligible difference between these measurements confirms that the oil layer does not alter the mechanical response. These additional results extend the validation of the method beyond argyrodite and Li₃YBr₂Cl₄, demonstrating its robustness and broader applicability to other solid electrolytes.

## 2. Result and discussion

We applied this method to argyrodite pellets composed of ~10 µm particles, compacted at different pressures: 100 MPa (6 samples), 220 MPa (2 samples), and 400 MPa (15 samples), see Fig. 3a. The corresponding final relative density were 0.68, 0.73, and 0.78, respectively. Detailed compaction data are provided in Appendix 8. In parallel, we have measured the ionic conductivity of the sample pressed at these different pressures and we have shown that. As shown in Appendix 7, the ionic conductivity of the pellet increases with increasing compaction pressure, highlighting the strong correlation between mechanical densification and ion-transport performance. The corresponding final relative density were 0.68, 0.73, and 0.78, respectively. Detailed compaction data are provided in Appendix 7. This indicate that pressure help to compact the particles, confirming that higher pressures enhance densification and improve particle-particle contacts, thereby enabling better ionic transport [7]. The hardness (H), as derived from the clustering method, remains nearly constant within measurement dispersion, increasing moderately by ~20 %, from H = 545 MPa at 100 MPa to H = 665 MPa at 400 MPa. In contrast, the reduced modulus shows a much stronger dependence on compaction, increasing by ~60 %, with values of E = 15.3 ± 0.5 GPa, 19.7 ± 0.2 GPa, and 24.0 ± 1.0 GPa for 100, 220,

and 400 MPa, respectively.

These values are consistent with, though slightly lower than, previous reports: 28.5 ± 3.5 GPa by Papakyriakou et al. [35] (glovebox measurements), 33.0 ± 5.0 GPa by Ai et al. [39] (in-SEM measurements), and 24.7 GPa from DFT calculations [33]. They are, however, significantly higher than the ~4 GPa reported by Song et al. [38] from macroscopic beam bending experiments. This large discrepancy highlights the inherently multiscale nature of the mechanical behavior and the importance of accounting for local heterogeneities.

Interestingly, such an increase in modulus is not expected from a truly local measurement at the particle scale, as targeted by our method via low load indentation and clustering process. However, it is well established that indenting a stiff particle (modulus *E*<sub>p</sub>) embedded in a softer surrounding medium (modulus *E*<sub>s</sub> < *E*<sub>p</sub>) yields a reduced effective indentation modulus. In contrast, hardness, being governed by more localized plastic deformation, is much less influenced by the mechanical properties of the surrounding medium [40,41] compaction increases, the stiffness of the embedding matrix (*E*<sub>s</sub>) approaches that of the particle, leading the measured modulus to converge toward *E*<sub>p</sub>. While a comprehensive theoretical model for such granular systems is still lacking, we consider the modulus measured at the highest compaction density (24.0 ± 1.0 GPa) to be a reasonable approximation of *E*<sub>p</sub>.

The same methodology was applied to a commercial Li₆PS₅Cl powder (Ampcera) with particle sizes of 1 µm and <1 µm. The results show a moderate increase in both reduced Young's modulus and hardness as particle size decreases: E<sub>r</sub> = 24.0 ± 1.0 GPa/H = 670 MPa for 10 µm particles, 25.6 ± 0.4 GPa/780 MPa for 1 µm, and 28.6 ± 1.4 GPa/870 MPa for particles <1 µm (Fig. 3b). This trend likely reflects subtle structural changes induced during the powder fabrication or pellet compaction processes.

To place these values in context, we compared them with those obtained for another solid electrolyte, Li₃YBr₂Cl₄, with a supplier-reported particle size of 1–2 µm. At a compaction pressure of 400 MPa, the relative density reaches approximately 0.85, and the pellet surface appears significantly smoother (Fig. 3c), displaying shallow ridges imprinted by the punch texture. This improved surface quality resulted in a more homogeneous mechanical responses in XPM mapping (Fig. 3c and d). Consequently, the data are less affected by local microstructural variations, and clustering with k = 2 produced results close to the surface average.

Across four experiments on Li₃YBr₂Cl₄, we obtain average values of E<sub>r</sub> = 24.0 ± 0.4 GPa and H = 700 ± 52 MPa, indicating that Li₃YBr₂Cl₄

<figure><img src="image_4.png" /><figcaption>**Fig. 1.** Air free fast nanoindentation for local mechanical measurement on the electrolyte granular assembly: (1) pellet conditioning in situ (2) mechanical mapping (3) extraction of local mechanical information through statistical treatment.</figcaption></figure>
and Li₆PS₅Cl have comparable mechanical properties (Fig. 3e). Interestingly, Hennequart et al. [37] reported a significantly lower hardness value (H ≈ 300 MPa) for Li₃YBr₂Cl₄ compacted at the same pressure (400 MPa), using microindentation, where modulus is typically not measured. This discrepancy, together with the differences in surface quality discussed above, may result from plastic deformation behavior that are captured differently by microindentation and fast nanoindentation techniques.

To assess the influence of timescale on mechanical response, a different nanoindentation experiment was performed on large-grain (10 µm diameter) argyrodite pellets. A topographical scan was first conducted to identify the flat regions at the summits of surface asperities. Individual indentations were then performed at the center of these regions using standard exponential (constant strain rate) loading, with a slightly higher peak load (2 mN) and an extended hold period at peak load to allow to accommodate material creep, either 30 s or 120 s.

The corresponding force-displacement curves are shown in Fig. 4a. An initial indentation depth of ~350 nm increases to ~425 nm after 30 s and nearly 500 nm after 120 s. These simple tests clearly demonstrate the pronounced viscoplastic behavior of sulfide-based solid electrolytes. This finding supports earlier observations that chloro-sulfide electrolytes, in particular, exhibit strong time-dependent plasticity [35]. The viscoplastic nature of sulfide electrolytes allows them to adapt to stress variations during cycling, helping to limit immediate cracking or damage. During simple powder pressing for battery preparation, viscoplasticity also enables the material to absorb and dissipate energy, promoting more uniform densification and improved contact between particles. Therefore, such materials tend to show lower hardness in conventional microindentation experiments, which involve longer loading times, compared to fast nanoindentation measurements.

Finally, we illustrate how quantifying local mechanical properties at

the grain scale can be used to better understand, and even predict, the macroscopic behavior of solid electrolytes. As discussed above, for argyrodite, representative values are E<sub>r</sub> ≈ 25 GPa for the reduced Young's modulus and H ≈ 600 MPa for hardness. These values are directly relevant to the compaction process used to form the pellets.

As a simple example, Baumard et al. [42] proposed a model in which the compaction pressure P is given by

$$ \frac{P}{H} = \frac{d^2(d - d_0)}{(1 - d_0)} \qquad (1) $$

were d is the relative density and d₀ ≈ 0.64 is the initial packing density before compaction begins. This compaction curve is shown in Fig. 4b (long dashes) and qualitatively follows the trend of our experimental data, though it significantly underestimates the pressure required for a given density. This discrepancy arises from a key assumption in Baumard's model: that interparticle contacts are fully plastic.

Following Johnson's contact mechanics theory [43] fully plastic contacts are expected only when the plasticity index Iₚ exceeds ~100. The plasticity index is defined as Iₚ = 3Eₜa/HR where a is the radius of the contact zone between two spheres of radius R. Compaction from the initial density (~0.64) to the final density (~0.80) corresponds to a volumetric strain of ~30 %, or roughly 10 % linear strain, implying a/R ≈ 0.1. Given that 3Eₜ/H ≈ 125, when approaching maximum compaction, the plasticity index Iₚ ≈ 12, well below the threshold for fully plastic contacts. In this regime, the mean contact pressure pₘ is less than H, meaning that significantly higher compaction pressures are required than those predicted by the fully plastic assumption.

It is not clear how Baumard's model can be quantitatively adapted to this intermediate case but qualitatively, a reasonable match to the experimental data is obtained by scaling the contact pressure pₘ by a

<figure><img src="image_5.png" /><figcaption>Fig. 2. Li₆PS₅Cl pellet pressed at 400 MPa. (a) XPM map of the reduced modulus (Eₜ). (b) 3D topographical representation by SPM. (c) 2D topographical representation by SPM coupled with indent color distribution. (d) Indent distribution according to k-means clustering with k = 2.</figcaption></figure>
<figure><img src="image_6.png" /><figcaption>**Fig. 3.** (a–b) $Li_6PS_5Cl$ particles – nanoindentation experiments: (a) impact of compaction pressure for pellets made of 10 µm diameter particles: evolution of hardness (left) and modulus (right) as a function of applied pressure: also shown are the nanoindentation results obtained by Baranowski et al. [29] for $Li_3PS_4$. (b) effect of particle size on reduced modulus and hardness; (c–e) $Li_3YBr_2Cl_4$ particles – nanoindentation experiments: (c) 2D topographic representation by SPM; (d) XPM map of the reduced modulus. (e) Comparison of the mechanical properties of $Li_3YBr_2Cl_4$ and $Li_6PS_5Cl$ pellets with identical particle size (1 µm) and compacted under 400 MPa.</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>**Fig. 4.** a) Single indent experiment with long hold under load, demonstrating pronounced creep demonstrating the strong viscoplastic character of argyrodite; b) measured compaction pressure normalized to hardness as a function of relative pellet density. Also shown are the predictions for compaction following Baumard et al. [42] (see text).</figcaption></figure>

factor of three (Fig. 4b dotted line). Although this adjustment is only a crude approximation and quantitative interpretations should be made with caution, this model remains a crude approximation, and although quantitative conclusions should be drawn with caution, the results still offer practical insights for optimization. For instance, it suggests that for argyrodite, with the mechanical properties measured in this paper, the

10 µm diameter is slightly too large. Reducing particle size increases the plasticity index, thereby lowering the compaction pressure needed to achieve a given density. Likewise, the low hardness reported for $Li_3YBr_2Cl_4$ by Hennequart et al. [37], possibly due to strong viscoplastic creep, could explain (Eq. (1)) the relatively high density and improved surface quality of the corresponding pellets.
In summary, fast and low-load mechanical testing provides a powerful means of probing the local mechanical behavior of solid electrolyte constituents, while effectively mitigating challenges related to air sensitivity. When combined with *in situ* imaging and statistical data analysis, this approach offers a robust framework for extracting meaningful and reproducible mechanical parameters at the particle scale. Using argyrodite as a case study, we demonstrated both the strengths and limitations of the method. We also provided a simple example of how these intrinsic constituent mechanical parameters can be applied to the analysis of a macroscopic property, here the density, in the context of the fabrication process. Looking ahead, future work will aim to correlate these local mechanical insights with electrochemical performance, with the goal of informing more rational, multiscale material design strategies for next-generation all-solid-state batteries.

### CRediT authorship contribution statement

**Kethsovann Var:** Writing – original draft, Validation, Methodology, Formal analysis, Data curation, Conceptualization. **Etienne Barthel:** Writing – review & editing, Validation, Methodology, Investigation, Formal analysis, Data curation, Conceptualization. **Sofiane Maiza:** Writing – review & editing, Validation, Supervision, Conceptualization. **David Sicsic:** Writing – review & editing, Validation, Supervision, Conceptualization. **Damien Bregiroux:** Writing – review & editing, Validation, Supervision, Methodology, Funding acquisition, Conceptualization. **Christel Laberty-Robert:** Writing – review & editing, Validation, Supervision, Methodology, Funding acquisition, Formal analysis, Conceptualization.

### Declaration of competing interest

The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: Christel Laberty-Robert reports financial support was provided by Renault SAS. If there are other authors, they declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

### Acknowledgment

K.V, D.B. and ChL thanks Renault group-Ampere for the financial support. All the authors thanks the DIM Respore for financial support for the Nanoindenter.

### Appendix A. Supplementary data

Supplementary data to this article can be found online at https://doi.org/10.1016/j.jpowsour.2026.239292.

### Data availability

Data will be made available on request.

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