# Bromine-rich argyrodites compositions: Enhancing lithium-ion conductivity for improved solid-state battery performance

Dhanush Shanbhag, Ajay Gautam, Elodie Salager, Laura Albero-Blanquer, Florencia Marchini, Jean-Noël Chotard, François Fauth, Emmanuelle Suard, François Rabuel, Houssny Bouyanfif, et al.

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Dhanush Shanbhag, Ajay Gautam, Elodie Salager, Laura Albero-Blanquer, Florencia Marchini, et al. Bromine-rich argyrodites compositions: Enhancing lithium-ion conductivity for improved solid-state battery performance. Journal of Power Sources, 2025, 657, pp.238175. 10.1016/j.jpowsour.2025.238175. hal-05228518

HAL Id: hal-05228518

https://u-picardie.hal.science/hal-05228518v1

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# Bromine-rich argyrodites compositions: Enhancing lithium-ion conductivity for improved solid-state battery performance

Dhanush Shanbhag<sup>a,b,c</sup>, Ajay Gautam<sup>d</sup>, Elodie Salager<sup>b,e</sup>, Laura Albero-Blanquer<sup>c</sup>, Florencia Marchini<sup>c</sup>, Jean-Noël Chotard<sup>a,b</sup>, François Fauth<sup>f</sup>, Emmanuelle Suard<sup>g</sup>, François Rabuel<sup>a,b</sup>, Houssny Bouyanif<sup>h</sup>, Andrey D. Poletayev<sup>i</sup>, Christopher Davies<sup>i</sup>, Benjamin Zelin<sup>i</sup>, M. Saiful Islam<sup>i</sup>, Virginie Viallet<sup>a,b</sup>, Christian Masquelier<sup>a,b,j,*</sup>

## HIGHLIGHTS

* A new compositional range of Argyrodite ionic conductors has been discovered.

* The $Li_{5.4}PS_{4.4}BrCl_{0.6}$ composition achieves an ionic conductivity of 10 mS/cm, at RT.

* Superior air stability compared to conventional lithium argyrodites is achieved.

* Well-performing all solid-state batteries were built.

## ARTICLE INFO

### Keywords:

- Solid electrolytes

- Ionic conductivity

- Structure-transport correlations

- Solid state batteries

- CCD

## ABSTRACT

Halide-enriched lithium argyrodite superionic conductors are considered as promising candidates for all-solid-state batteries due to their soft structure and high ionic conductivity. Challenges remain, including chemical instability and incompatibility with anode materials, and in addition a deeper understanding of the fundamental aspects of ionic transport and performance is required. In this study, we investigated two argyrodite mixed-halide series of compositions, $Li_{6-x}PS_{5-x}BrCl_x$ and $Li_{5.5}PS_{4.5}Br_{1.5-x}Cl_x$. By employing a range of techniques including X-ray diffraction (XRD), neutron diffraction, nuclear magnetic resonance (NMR) spectroscopy, electrochemical impedance spectroscopy and machine learning based molecular dynamics, we found that increasing the halide substitution enhances ionic conductivity. Notably, the $Li_{5.4}PS_{4.4}BrCl_{0.6}$ composition achieves an ionic conductivity of 10 mS/cm, demonstrates superior air stability compared to conventional lithium argyrodites and allows for the fabrication of well-performing all solid-state batteries. Our results reveal that in lithium-poor compositions the lithium environments in the 4a and 4d cages become more alike, facilitating fast long-range lithium-ion transport. This work paves the way for the development of air-stable, high-conductivity sulfide electrolytes, advancing the practical implementation of solid-state batteries.

This article is part of a special issue entitled: In memory of Professor Bruno Scrosati published in Journal of Power Sources.

<footnote><sup>a</sup> Laboratoire de Réactivité et de Chimie des Solides, UMR CNRS 7314, Université de Picardie Jules Verne, Cedex 1, 80039, Amiens, France</footnote>

<footnote><sup>b</sup> RS2E, Réseau Français sur le Stockage Electrochimique de l'Energie, FRCNRS 3459, Cedex 1, F80039, Amiens, France</footnote>

<footnote><sup>c</sup> Umicore, 31 Rue du marais, Brussels, BE-100, Belgium</footnote>

<footnote><sup>d</sup> Storage of Electrochemical Energy, Department of Radiation Science and Technology, Faculty of Applied Sciences, Delft University of Technology, 2629 JB Delft, the Netherlands</footnote>

<footnote><sup>e</sup> CNRS, Université d'Orléans, CEMHTI UPR3079, 1D avenue de la recherche scientifique, Cedex, F45071, Orléans, France</footnote>

<footnote><sup>f</sup> CELLS-ALBA Synchrotron, Cerdanyola del Vallès, E-08290, Barcelona, Spain</footnote>

<footnote><sup>g</sup> Institut Laue-Langevin (ILL), BP 156, 71 Avenue des Martyrs, 38042 Grenoble, France</footnote>

<footnote><sup>h</sup> Laboratoire de Physique de la Matière Condensée (LPMC), UR 2081, Université de Picardie Jules Verne, Amiens 80039, France</footnote>

<footnote><sup>i</sup> Department of Materials, University of Oxford, Oxford OX1 3PH, UK</footnote>

<footnote><sup>j</sup> Institut Universitaire de France, 103 boulevard Saint-Michel, 75005 Paris, France</footnote>

<footnote>* Corresponding author. Laboratoire de Réactivité et de Chimie des Solides, UMR CNRS 7314, Université de Picardie Jules Verne, Cedex 1, 80039 Amiens, France
E-mail address: christian.masquelier@u-picardie.fr (C. Masquelier).</footnote>
# 1. Introduction

Lithium-ion batteries (LIBs) are widely used in portable electronics and electric vehicles due to their high electrochemical performance and long cycle life. However, the liquid electrolytes in LIBs present safety risks, such as flammability, leakage, and lithium dendrite formation, which can reduce battery lifespan [1–3]. Solid-state batteries (SSBs), which use solid electrolytes, offer a safer alternative while enabling higher energy densities and broader operational temperatures [4,5]. Various lithium-ion solid electrolytes, including oxides, phosphates, halides, and argyrodites, have been studied [6,7]. Oxide-based electrolytes generally have a wide electrochemical window and good stability in air. However, their ionic conductivity at room temperature is usually low, as seen in $Li_{6.75}La_3Zr_{1.75}Ta_{0.25}O_{12}$ (LLZTO, 0.9 mS cm⁻¹). Additionally, their synthesis often involves complex procedures, including high-temperature sintering. On the other hand, halide electrolytes present several benefits, such as high ionic conductivity at room temperature and excellent oxidation stability, demonstrated by materials such as $Li_3InCl_6$ (1.49 mS cm⁻¹) [8], $Li_2Sc_{2/3}Cl_4$ (1.5 mS cm⁻¹) [8], and $LiTaCl_6$ (10 mS cm⁻¹) [9]. However, the high cost of raw materials including $ScCl_3$, $InCl_3$, and $TaCl_5$ limits their potential for large-scale use [10].

Lithium argyrodites have attracted significant interest due to their high ionic conductivity, low cost, good ductility, excellent electrode stability, and simple synthesis process. The most common form, $Li_6PS_5X$ (where halide X = Cl, Br, I), achieves ionic conductivities ranging from 0.001 to 4 mS/cm [11–17]. By adjusting the halide composition, particularly increasing the Cl content, the disorder between $S^2^-/X^-$ at the 4a/4d sites enhances ionic conductivity [18–20]. Computer simulation studies suggest that maximum conductivity is achieved when Cl⁻ occupies 75 % of the 4d site [21,22]. Substituting P with aliovalent elements (e.g., Ge or Si) further increases $Li^+$ substructure disorder, significantly boosting conductivity, as seen in compounds like $Li_{6.6}P_{0.4}Ge_{0.6}Sb_5I$ (5.4 mS/cm) and $Li_{6.6}Si_{0.6}Sb_{0.4}S_5I$ (14.8 mS cm⁻¹) [23–25]. However, the high cost and instability of Ge- or Sb-containing argyrodites with lithium metal anodes and high-voltage cathodes limit their use [26].

Another widely explored strategy to enhance ionic conductivity in argyrodite $Li_6(PS_4)(S)(X)$ is substituting the "free" sulfur with halogen atoms. This substitution not only increases the concentration of $Li^+$ vacancies but also introduces greater $S^2^-/X^-$ site disorder, both of which synergistically improve ionic mobility. Notably, halide-rich argyrodites with the composition $Li_6-yPS_5-yXy$ ($y > 1$) demonstrate substantially higher ionic conductivity (up to 24 mS cm⁻¹) compared to conventional $Li_6PS_5X$ counterparts [27,28]. Nazar et al. [29] investigated chloride-rich $Li_6-xPS_5-xCl_{1+x}$ ($x \le 0.5$) compositions of high conductivity of 9 mS cm⁻¹ (12 mS cm⁻¹ upon sintering) and a lower activation energy of 0.29 eV for $Li_{5.5}PS_{4.5}Cl_{1.5}$. Following this work, Feng et al. [30] further increased Cl⁻ content and found a solubility limit up to $x = 0.7$ and reported 17 mS cm⁻¹ at 25°C and low activation energy of 0.22 eV for $Li_{5.3}PS_{4.3}Cl_{1.7}$. Janek et al. [31] have shown that $Li_{5.5}PS_{4.5}Cl_{1.5}$ performs better in ASSBs when compared with $Li_6PS_5Cl$. Bromine-rich compositions $Li_6-xPS_5-xBr_{1+x}$ ($x \le 0.7$) were recently investigated by Wang et al. [32] who reported a high ionic conductivity of 11 mS cm⁻¹ and a low activation energy of 0.18 eV. Recently, Wagemaker et al. [33] conducted a neutron diffraction study of the same compositions and showed that with increasing Br⁻ content in the structure, an expansion of the dimensions of the $Li^+$ cages occurs, which enables an alternative jump route (T5-T4-T5) for $Li^+$ with a lower migration energy barrier [33]. In this case the ionic conductivity increases from 0.78 to 6.2 mS cm⁻¹ from $Li_6PS_5Br$ to $Li_{5.5}PS_{4.5}Br_{1.5}$ along with the increase in activation energy 0.36–0.40 eV [33].

A contrasting difference exists between two reports by Wang et al. [32] and Wagemaker et al. [33], where with increasing Br⁻ content, the former reports the increase in lattice constant and decrease in activation energy whereas the latter reports the opposite trend. Although Br⁻ (196 p.m.)) is larger than $S^2^-$ (184 p.m.), and one might expect the lattice to

always expand when Br⁻ replaces $S^2^-$, this is not always the case. In slow-cooled samples, the lattice parameter decreases with more Br⁻, while in fast-cooled (quenched) samples, it increases. Wagemaker et al. suggest that in slow-cooled samples, the Br⁻ content at the 4a site stays almost the same, so the lattice shrinkage might be due to more $Li^+$ vacancies or changes in $Li^+$ distribution. Furthermore Zhang et al. [34] reported the synthesis of iodine-rich $Li_{6-x}PS_{5-x}I_{1+x}$ by ball milling which resulted in the improvement of ionic conductivity from 0.15 to 0.31 mS cm⁻¹ from $x = 0$ to 0.5. However, after annealing the halide-rich $Li_{5.5}PS_{4.5}I_{1.5}$ showed a significant impurity content, suggesting the unlikely possibility of synthesizing pure $Li_{5.5}PS_{4.5}I_{1.5}$.

Instead of a single type of halide, there exists a possibility to mix the halides to achieve an even higher degree of occupational disorder. Among Cl⁻/Br⁻ mixing, Patel et al. [28] investigated a mixed halide composition $Li_{6-x}PS_{5-x}ClBr_x$ ($0 \le x \le 0.8$) and achieved a remarkably high ionic conductivity of 24 mS cm⁻¹ and an unusually low activation energy of 0.15 eV. Masuda et al. [35] studied $Li_{7-x-y}PS_4$ ($S_{2-x-y}Cl_xBr_y$) compositions and showed that an ionic conductivity of 11.2 mS cm⁻¹ can be achieved for $Li_{5.4}PS_{4.4}BrCl_{0.6}$ and $Li_{5.4}PS_{4.4}ClBr_{0.6}$ while $Li_{5.4}PS_{4.4}Cl_{1.6}$ and $Li_{5.4}PS_{4.4}Br_{1.6}$ showed slightly inferior ionic conductivity. This is due to the higher configurational entropy ($\Delta S_{conf} > 1.5 R$) which arises from shared occupancies by $S^2^-/Cl^-/Br^-$ on a single crystallographic site as recently shown by Strauss et al. [36] in $Li_{5.5}PS_{4.5}Br_{1.5}Cl_x$. Among Cl⁻/I⁻ mixed halide compositions, Yan et al. [37] synthesized $Li_{5.7-x}PS_{4.7-x}Cl_{1.3}I_x$ ($x = 0$ to 0.3) and achieved higher ionic conductivity and better stability against Li metal when compared to $Li_6PS_5Cl$. Along with improved ionic conductivity, halide-rich argyrodites also show greater moisture stability when compared to $Li_6PS_5X$ [38]. In general, all the halide-rich compositions have shown better ionic conductivity and electrochemical properties when compared to $Li_6PS_5X$ compositions. Hence, the majority of the aforementioned studies are devoted to detailed structural investigations and ionic conductivity measurements, but with less emphasis on performance in ASSBs in a comparative manner. In a patent application by Hu et al. [39] a wide range of halide rich compositions such as, $Li_{6-x}PS_5-xCl_{1+x}$, $Li_{6-x}PS_5-xBr_{1+x}$, $Li_{6-x}PS_5-xClBr_x$ and $Li_{6-x}PS_5-xClI_x$ have already been covered. However, to the best of our knowledge there are no reports on the $Li_{6-x}PS_5-xBrCl_x$ and $Li_{6-x}PS_5-xBrI_x$ series. Although, $Li_{6-x}PS_5-xBrCl_x$ appears similar to $Li_{6-x}PS_5-xClBr_x$, the latter shows an increase in lattice volume with increasing $x$, whereas we anticipate a decrease in lattice volume for $Li_{6-x}PS_5-xBrCl_x$. Additionally, Zeier et al. [14] have shown that having softer and more polarizable anion leads to lower activation energy, thereby in principle Br⁻ rich compositions would exhibit lower activation energy compared to Cl⁻ rich compositions. Another added advantage of halide-rich compositions is that they require a reduced amount of the high cost $Li_2S$ precursor (50g = ~800 €, Sigma-Aldrich). For instance, $Li_{5.4}PS_{4.4}Cl_{1.6}$ can be synthesized by utilizing 10 % less amount of $Li_2S$ when compared to $Li_6PS_5Cl$ and hence economically more viable.

With a key aim to find synergy between ionic conductivity and activation energy in the mixed halide compositional space, we have studied several mixed-halide rich argyrodite compositions with a primary focus on a new $Li_{6-x}PS_5-xBrCl_x$ and $Li_{5.5}PS_{4.5}Br_{1.5-x}Cl_x$ series. All samples were synthesized by a mechanochemical method followed by annealing at 450°C. The structure and transport properties were investigated by a range of techniques including X-Ray and neutron diffraction, Raman spectroscopy, ³¹P magic angle spinning (MAS) NMR, and electrochemical impedance spectroscopy. The moisture stability was investigated by monitoring the amount of $H_2S$ release as a function of time in controlled conditions. To complement the experimental work and to probe atomic-scale mechanisms, we used ab initio and machine learning based molecular dynamics methods. Finally, we present the results of electronic conductivity measurements and a detailed investigation of all solid-state batteries.
## 2. Results and discussions

### 2.1. Structural changes in $Li_{6-x}PS_{5-x}BrCl_x$ with increasing Cl content

Lithium argyrodites, $Li_6PS_5X$ ($X$ = Cl, Br, or I), exhibit structural disorder, particularly between $X^-$ and $S^{2-}$ ions at the 4d sites, which has been linked to Li-ion conductivity. Recent studies have shown that increasing halide content for $X = Cl$ and Br enhances ionic conductivity [15,18,28,30,32,35,40]. This improvement is rationalized in several ways: (i) the substitution of divalent $S^{2-}$ with monovalent $X^-$ at the 4d site could reduce the electrostatic interaction between Li ions and anions occupying the 4d sites, (ii), the occupation of the lithium T4 site could offer an additional path for inter-4d-cage movement [25,33], (iii) configurational entropy and increased similarity between 4a and 4d cages could enable effective long-range transport [15,40]. Overall, the substitution of S with a mix of Cl and Br in the $Li_{6-x}PS_{5-x}BrCl_x$ system, and its impacts on air stability, lithium substructure, the structural framework, and ionic transport mechanisms, remain underexplored and require further investigation.

To investigate the impact of halide substitution on the structure, the $Li_{6-x}PS_{5-x}BrCl_x$ series ($0 \le x \le 0.8$) was synthesized using ball milling followed by heat treatment at 450°C. Structural analysis was conducted using X-ray diffraction (XRD) and neutron diffraction, with Rietveld refinements applied to examine both structural changes and $Li^+$ substructures. In this series, the Cl content was systematically increased in steps of $x = 0.1$, up to a maximum of $x = 0.8$. Representative XRD patterns for $Li_{6-x}PS_{5-x}BrCl_x$ compositions ($0 \le x \le 0.8$) are shown in

Fig. 1a & b, revealing the argyrodite phase within the $F\bar{4}3m$ space group for compositions up to $x = 0.7$. The absence of impurity or precursor diffraction peaks indicates the high purity of the samples. For nominal $x = 0.8$, phase segregation occurred, as evidenced by the splitting of a single peak into two distinct peaks, corresponding to separate $Li_6PS_5Br$ and $Li_6PS_5Cl$ phases, which indicates that the solubility limit of $Cl^-$ in the $Li_{6-x}PS_{5-x}BrCl_x$ system is $x = 0.7$. This solubility limit is consistent with other halide-rich compositions, such as $Li_{6-x}PS_{5-x}Cl_{1+x}$, $Li_{6-x}PS_{5-x}Br_{1+x}$ and $Li_{6-x}PS_{5-x}ClBr_x$, reported in the literature [18,28].

As the Cl content increases up to $x = 0.7$, the XRD peaks' positions shift to higher $2\theta$ values, as illustrated in Fig. 1b, which signifies a decrease of the lattice parameter, $a$, of the cubic unit cell. Decrease in the lattice constant may be primarily due to the $Li^+$ vacancies created upon $Cl^-$ incorporation and increased disorder on the 4a and 4d sites, similar to simpler compositions [20]. Simulation results (detailed below) further confine this effect to a compression of the lithium cages around the 4a sites, whereas the geometries of the lithium 4d cages remain virtually unchanged. The lattice parameter obtained from profile matching of the XRD patterns linearly decreases from 9.992(1) to 9.908 (1) Å as shown in Fig. 1c, supporting $x = 0.7$ as the solubility limit of $Cl^-$ in the system. This finding aligns with other halide-rich compositions ($Li_{6-x}PS_{5-x}Cl_{1+x}$, $Li_{6-x}PS_{5-x}Br_{1+x}$ and $Li_{6-x}PS_{5-x}ClBr_x$) and suggests that a nominal $Li^+$ content of 5.3 in the composition is necessary to stabilize the argyrodite phase.

High-resolution neutron powder diffraction (NPD) measurements were conducted to study the lithium substructure and the occupancies of Cl and S at the 4a and 4d sites. The measurements were collected at room

<figure><img src="image_3.png" /><figcaption>**Fig. 1.** (a) and (b) XRD patterns of $Li_{6-x}PS_{5-x}BrCl_x$ with increasing x values. (c) Variation of lattice parameter as a function of x in $Li_{6-x}PS_{5-x}BrCl_x$. (d) XRD patterns of $Li_{5.5}PS_{4.5}Br_{1.5-x}Cl_x$ with increasing x and (e) variation of lattice constant 'a' with increasing x in $Li_{5.5}PS_{4.5}Br_{1.5-x}Cl_x$. The lattice constants of $Li_6PS_5Br$ and $Li_6PS_5Cl$ are also shown for comparison. (f) Raman spectra of $Li_{6-x}PS_{5-x}BrCl_x$ with increasing x. (g) and (h) show the shift of the Raman peaks corresponding to symmetric stretches and deformation mode of S-P-S of $PS_4$ units respectively. (i) to (l) 31P MAS NMR spectrum of $Li_6PS_5Br$, $Li_{5.7}PS_{4.7}BrCl_{0.3}$, $Li_{5.5}PS_{4.5}BrCl_{0.5}$ and $Li_{5.4}PS_{4.4}BrCl_{0.6}$ respectively, obtained at 17.4 T (10 kHz MAS).</figcaption></figure>
temperature from selected samples of Li₆⁻ₓPS₅⁻ₓBrClₓ, with x = 0, 0.3, 0.5, and 0.6. A representative diffraction pattern for Li₅.₄PS₄.₄BrCl₀.₆ along with the corresponding Rietveld refinement profile is depicted in Fig. 2a (other plots are shown in Supplementary Information Fig. S1). The calculated lattice constants from XRD and NPD are in excellent agreement with each other and the obtained structure is shown in Fig. 2b, In the mixed halide argyrodites, the three anions (S²⁻, Cl⁻, and Br⁻) are distributed over two distinct crystallographic sites (4a and 4d). Due to the complexity of having three atoms occupying the same positions, we constrained the total occupancy of both the 4a and 4d sites to equal 1 for each. By refining all the occupancies together under this constraint, we achieved the best possible fit for the data. Structural data are tabulated in supplementary information.

The obtained S²⁻/Cl⁻/Br⁻ occupancy % on the 4a and 4d site for x = 0, 0.3, 0.5 and 0.6 are shown in Fig. 2c and d. At x = 0 (Li₆PS₅Br), the Br⁻ occupancies over the 4a and 4d sites are 81 % and 19 % respectively. Although Br⁻ prefers to occupy the larger 4a site in Li₆PS₅Br, with increasing x, the Br⁻ occupancy on the 4d site increases from 19 % to 30 % between x = 0 to x = 0.6. This increased Br⁻ occupancy % on the 4d site (increased site-disorder) is beneficial to obtain a higher ionic conductivity, as already identified by Zeier et al. [18,20,33,41] Similarly, as the chloride content increases with x, the Cl⁻ occupancy on the 4d site increases from 0 % to 42 % between x = 0 and x = 0.5. At x = 0.6, the 4d site is occupied by 40 % Br⁻, 36 % Cl⁻, and 24 % S²⁻. The randomness in the halogen distribution in the crystal structure also affects the Li sub-structure. For the mixed halide argyrodites, 4 different Li positions, namely T5 (Wyckoff 48h), T4 (Wyckoff 16e), T5a (Wyckoff 24g) and T2 (Wyckoff 48h) shown in Fig. S2, were identified by Masuda et al. [35] In our case, for x = 0 and 0.6 three Li positions, namely T2, T4, and T5, were identified as yielding meaningful Bᵢₚₐ₉ and occupancy values. For all of our compositions, without constraining the Li occupancies, the refined Li occupancies were always less than targeted values. In this series, as the chloride content increases, the occupancy of the T4 site increases. Since T4 sites are approximately as close to 4a sites as T2 sites

are (although along differing crystallographic directions), their population signifies an increasingly uniform lithium distribution throughout the material and increasing similarity between 4a lithium cages and 4d lithium cages. We return to this point below when discussing computational results. Additionally, with increasing Cl content, the overall lithium content decreases and site disorder increases, both of which can contribute to shrinking the lattice parameter.

As a next step, we maintained the nominal Li content constant (Li₅.₅) and varied the halide distribution starting from Br⁻ rich to Cl⁻ rich composition in the series, Li₅.₅PS₄.₅Br₁.₅⁻ₓClₓ with 0 ≤ x ≤ 1.5. The XRD patterns of the representative samples in Li₅.₅PS₄.₅Br₁.₅⁻ₓClₓ are depicted in Fig. 1d. All the diffraction peaks can be assigned to the argyrodite phase in the space group: F̅43m. The lattice parameter 'a' derived from the profile matching as a function of varying x in Li₅.₅PS₄.₅Br₁.₅⁻ₓClₓ are shown in Fig. 1e and the lattice constants of Li₆PS₅Br and Li₆PS₅Cl are also shown for the comparison. The linear decrease in lattice constant across the entire compositional range substantiates the solid solution behaviour, primarily attributed to the lower ionic radii of Cl⁻ relative to Br⁻, while maintaining the same nominal levels of lithium, sulfur, and phosphorus. Notably, the lattice constant of Li₅.₅PS₄.₅Br₁.₅ is lower than that of Li₆PS₅Br, which is an observation contradictory to that of Hu et al. [32] but in agreement with the recent report from Wagemaker et al. [33]. In the case of Li₅.₅PS₄.₅Br₁.₅, in contrast to the expected increase in lattice constant arising from the larger Br⁻ ions, the concomitant decrease in the nominal Li content and increase in the anion site disorder exert a superseding effect on lattice shrinkage, thereby resulting in a lower lattice constant compared to Li₆PS₅Br [33].

Raman spectroscopy measurements were performed to confirm the sample purity and provide hints on structural changes resulting from the increasing Cl⁻ in Li₆⁻ₓPS₅⁻ₓBrClₓ. The Raman spectra of Li₆⁻ₓPS₅⁻ₓBrClₓ (0 ≤ x ≤ 0.8), shown in Fig. 1f contain four prominent peaks at around 204, 276, 421, and 571 cm⁻¹ (for x = 0) attributed to the different vibrational modes of PS₄³⁻ tetrahedra. With increasing 'x'

<figure><img src="image_4.png" /><figcaption>**Fig. 2.** (a) Neutron powder diffraction pattern and Rietveld refinement profile for Li₅.₄PS₄.₄BrCl₀.₆. (b) crystal structure of Li₅.₄PS₄.₄BrCl₀.₆ with the different Wyckoff positions and elemental constituents indicated in the legend to the right. (c) and (d) The normalized occupancies of the 4d and 4a Wyckoff positions depicted in the panels.</figcaption></figure>
the Raman peak corresponding to the symmetric stretches of the PS₄ units (Fig. 1g) is broadened and is gradually shifted to higher wave-numbers, from 421 to 424.3 cm⁻¹ for x = 0.0 to 0.7. This is most likely due to the decreasing unit-cell and to the altered bond lengths due to random distribution of Br⁻ and Cl⁻ in the structure. However, the Raman peak at 571 cm⁻¹ corresponding to the asymmetric stretching mode remains mostly unaltered except for x = 0.8, which is due to the phase segregation, as observed from XRD. Additionally, a small peak around 470 cm⁻¹ is observed corresponding to S-S stretching and bending modes [42]. Notably, the two peaks at 204 and 276 cm⁻¹ corresponding to the deformation modes of S-P-S in PS₄⁻ shift to lower wavenumbers upon increasing the amount of Cl as shown in Fig. 1h. The opposite trend in the phonon shift (hardening for the 421 cm⁻¹ phonon and softening for the 204 - 276 cm⁻¹ doublet) is indeed reminiscent of melting behavior (weaker influence of lattice environment/Li sublattice on internal PS₄ frequencies) as previously observed in Na₃PS₄ and isolated PS₄ phonon frequencies measured in aqueous solution [43,44].

To gain a deeper understanding of the P environment in this series of new compositions, we conducted ³¹P MAS NMR measurement of Li₆PS₅Br, Li₅.₇PS₄.₇BrCl₀.₃, Li₅.₅PS₄.₅BrCl₀.₅ and Li₅.₄PS₄.₄BrCl₀.₆ as shown in Fig. 1i–l. The ³¹P NMR spectra of the four samples are centered in the range 80–95 ppm, as expected from literature for PS₄⁻ tetrahedra [45,46]. The multiple components of each spectrum arise from the superposition of slightly differing local environments for the phosphorus atoms, which we assign to the 4 s anionic neighbours that occupy the 4d sites around the PS₄⁻ tetrahedron (P-4d distance = a/2).

In the Li₆PS₅Br structure, due to the mixed occupation Wyckoff 4d site occupation by Br⁻/S²⁻, five distinct local ³¹P environments are expected, corresponding to 4S, 3SBr, 2S2Br, 1S3Br and 4Br on the Wyckoff 4d positions. The ³¹P NMR spectrum of Li₆PS₅Br was fitted into a set of 3 relatively narrow Gaussian-shaped functions centered at 93.3 ppm, 92.2 ppm, and 90.3 ppm, assigned previously to PS₄⁻ units with configurations 4S, 3S1Br and 2S2Br on the 4 neighbouring 4d sites (no 4Br environments). Contrary to recent reports for Li₆PS₅Br [32] or for the endmembers Li₅.₅PS₄.₅Cl₁.₅ and Li₅.₅PS₄.₅Br₁.₅ [36] or Li₆-xPS₅-xBr₁+x [15], an additional extremely broad Gaussian-shaped peak centered at 91.3 ppm was necessary for a reasonable fit, which we tentatively assign to a PS₄⁻ environment with a less well-defined second coordination sphere, possibly due to increased mobility of Li next to the PS₄⁻ units, to a slight tilting of the PS₄⁻ orientation, or to an additional effect of third anionic neighbours on the 4a sites (only slightly further away: P-4a distance = a/√3/4) [47]. In contrast, for Li₆-xPS₅-xBrClₓ, where Wyckoff 4d position is potentially occupied by Br⁻/S²⁻/Cl⁻, the complexity of the potential phosphorus local environments arises, with the potential for 15 distinct local arrangements of the neighbouring second anionic neighbours, including 4S, 3S-1Br, 3S-1Cl, 2S-1Cl-1Br, 2S-2Cl, 2S-2Br, 1S-1Cl-2Br, and so forth. Experimentally with increasing Cl⁻ content, the relative proportion of the peaks at lower ppm increase, in agreement with previous reports [15,36,

48].

Owing to the difficulty of under-constrained fitting of the NMR data with 15 Gaussian-shaped functions, we decided to constrain the fit to the minimal amount (10) of relatively narrow Gaussian-shaped functions that enabled a reasonable fit of all the data while keeping identical the positions and widths across the series of samples. The 10 resulting ³¹P environments in the fit for Li₅.₇PS₄.₇BrCl₀.₃, Li₅.₅PS₄.₅BrCl₀.₅ and Li₅.₄PS₄.₄BrCl₀.₆ are centered between 93.09 ppm and 82.08 ppm, with varying relative areas (Table 1). As for Li₆PS₅Br, an additional broad Gaussian shaped function (peak 11) was necessary to obtain good fits. The shift and width of peak 11 had to vary across the series to ensure correct fitting. The increase of relative integral of peak 11 (Table 1) with increasing Cl⁻ content may indicate towards an increased Li mobility or increased disorder in the PS₄⁻ units tilting.

By considering the multinomial distribution of S, Br, Cl and the 4d occupancies (x1; x2, x3) obtained from neutron diffraction, the relative populations of the 15 expected environments can be predicted by using the probability function below, with populations tabulated in Table S5 in the case of independent populations

$$P(S = x_1, Br = x_2, Cl = x_3) = \frac{4!}{x_1! \cdot x_2! \cdot x_3!} S^{x_1} \cdot Br^{x_2} \cdot Cl^{x_3}$$

A good agreement of this probability function with the areas of the individual peaks of the fit would indicate that the probability of one type of atom occupying one of the 4d sites does not affect the probability of other atoms occupying the remaining three 4d sites. As the fit for each composition contains fewer environments than expected, it was not possible to assign directly each peak to a particular configuration of S, Br, and Cl on 4d site. Still, we tentatively added the calculated probabilities of the arrangement containing the same total number of (Br + Cl), assuming that they are the main cause for displacing the 31P peaks to lower shifts. A weak trend towards decreasing shift with decreasing S content (increasing Br + Cl content) of the neighbouring 4d sites is indeed reproduced in first-principles calculations (Supplementary Information).

Our approach reduces the number of arrangements for the 4d sites around the PS₄⁻ units down to six (namely 4Cl/4Br, 4X, 1S2X, 2S2X, 3S1X, 4S with X = Br or Cl, detailed list in Table S5). The multinomial probabilities for random arrangement are plotted in grey in Fig. S4. We managed to add peaks together from the experimental fit for Li₅.₇PS₄.₇BrCl₀.₃ to reduce it to 6 environments with areas in reasonable agreement with the calculated probabilities for a random arrangement (multinomial), as plotted in orange in Fig. S4a. However, this treatment of the experimental fits provided discrepancies for Li₅.₅PS₄.₅BrCl₀.₅ and Li₅.₄PS₄.₄BrCl₀.₆. These discrepancies between the multinomial distribution and the experimental fit may be due to a non-random arrangement, for example if the presence of Cl restricts the probability of Br being in the same coordination shell. This would not change the average probability as measured from neutron diffraction, but would modify the

<caption>**Table 1**</caption>

Characteristics of the Gaussian peaks used for the ³¹P NMR fits for Li₆-xPS₅-xBrClₓ Areas are obtained by integration of the isotropic peak, neglecting differences in chemical shift anisotropy.

<table><thead><tr><th rowspan="2">Peak #<br>Composition</th><th colspan="3">Shift/ppm</th><th colspan="3">Width/ppm</th><th colspan="3">Area/%</th></tr><tr><th>x = 0.3</th><th>x = 0.5</th><th>x = 0.6</th><th>x = 0.3</th><th>x = 0.5</th><th>x = 0.6</th><th>x = 0.3</th><th>x = 0.5</th><th>x = 0.6</th></tr></thead><tbody><tr><td>1</td><td>93.09</td><td>93.09</td><td>93.09</td><td>0.68</td><td>0.68</td><td>0.68</td><td>6.4</td><td>0.67</td><td>0</td></tr><tr><td>2</td><td>92.07</td><td>92.07</td><td>92.07</td><td>1.27</td><td>1.27</td><td>1.27</td><td>14.7</td><td>5.02</td><td>1.5</td></tr><tr><td>3</td><td>90.76</td><td>90.76</td><td>90.76</td><td>0.96</td><td>0.96</td><td>0.96</td><td>14.08</td><td>6.58</td><td>2.28</td></tr><tr><td>4</td><td>90.05</td><td>90.05</td><td>90.05</td><td>0.94</td><td>0.94</td><td>0.94</td><td>4.58</td><td>3.05</td><td>1.53</td></tr><tr><td>5</td><td>89.27</td><td>89.27</td><td>89.27</td><td>1.17</td><td>1.17</td><td>1.17</td><td>9.96</td><td>6.3</td><td>2.24</td></tr><tr><td>6</td><td>88</td><td>88</td><td>88</td><td>1.39</td><td>1.39</td><td>1.39</td><td>6.95</td><td>6.44</td><td>3.08</td></tr><tr><td>7</td><td>86.32</td><td>86.32</td><td>86.32</td><td>0.96</td><td>0.96</td><td>0.96</td><td>1.02</td><td>2.91</td><td>3.39</td></tr><tr><td>8</td><td>85.07</td><td>85.07</td><td>85.07</td><td>1.02</td><td>1.02</td><td>1.02</td><td>0.08</td><td>1.69</td><td>2.47</td></tr><tr><td>9</td><td>83.72</td><td>83.72</td><td>83.72</td><td>2.25</td><td>2.25</td><td>2.25</td><td>0</td><td>3.6</td><td>6.79</td></tr><tr><td>10</td><td>82.08</td><td>82.08</td><td>82.08</td><td>1.79</td><td>1.79</td><td>1.79</td><td>0.1</td><td>0.36</td><td>0.62</td></tr><tr><td>11</td><td>88.21</td><td>87.61</td><td>87.41</td><td>5.59</td><td>5.22</td><td>5.27</td><td>42.14</td><td>63.39</td><td>76.09</td></tr></tbody></table>
relative intensities in the NMR spectrum. Alternatively, changes in lithium mobility or in tilting of the $PS_4^{3-}$ with varying lithium and chlorine contents may be responsible for changing peak widths, which we did not allow in the present analysis.

Although similar compositions were studied by Hu et al.30,3248, Wagemaker et al. [15] and Strauss et al. [36], yet a comprehensive understanding of the spectra of the mixed halide compositions still needs to be pursued. A more robust simulation of ³¹P spectra would require

averaging configurations over the timescale of the Larmor frequency of the measurement [49], which is left to further study.

## 2.2. Ionic transport within $Li_{6-x}PS_{5-x}BrCl_x$ and $Li_{5.5}PS_{4.5}Br_{1.5-x}Cl_x$

To assess the ion transport properties, temperature-dependent impedance spectroscopy measurements were performed in the temperature range of -20 °C–50 °C. All the measurements were carried out on

<figure><img src="image_5.png" /><figcaption>**Fig. 3.** Nyquist plots of $Li_{6-x}PS_{5-x}BrCl_x$ at (a) -10°C and (b) 25°C. The Inset shows the equivalent circuit model used to fit the data. (c) Variation of ionic conductivity and activation energy as a function of increasing x in $Li_{6-x}PS_{5-x}BrCl_x$ at 298 K (d) Arrhenius plots of $Li_{6-x}PS_{5-x}BrCl_x$. (e) Variation of ionic conductivity measured at 298 K and activation energy as a function of increasing x in $Li_{5.5}PS_{4.5}Br_{1.5-x}Cl_x$. (f) Arrhenius plots of $Li_{5.5}PS_{4.5}Br_{1.5-x}Cl_x$.</figcaption></figure>
pellets of 10 mm diameter and about 1.25–1.3 mm thickness which were pressed under 5 Tons, resulting in density of 85–87 %. Thin indium foils of thickness ~60 µm and 10 mm diameter were used as ion-blocking electrodes in all the cases. Normalized Nyquist plots of Li₆⁻ₓPS₅⁻ₓBrClₓ at -10°C and 25°C are represented in Fig. 3a and b respectively. For the Nyquist plots at -10 °C (Fig. 3a), a semicircle representing contributions from both the bulk and grain boundaries was observed. The data was fitted with an equivalent circuit model (R_c-(R|CPE)-CPE), where R_c represents the resistance from contacts and wires, R/CPE corresponds to the sample contribution, and CPE represents the blocking electrodes. At 25 °C, all samples except the one with x = 0.1 showed capacitive blocking behaviour of the electrodes, which is commonly observed in materials with low resistance or very high ionic conductivity [25,50]. Consequently, all data were fitted with an equivalent circuit containing a resistor in series with a constant phase element (R-CPE), where R represents the total resistance (including both bulk and grain-boundary resistance), and the CPE represents the blocking electrodes. By visual inspection, it is evident that resistance decreases as x increases in Li₆⁻ₓPS₅⁻ₓBrClₓ, with the lowest resistance observed at x = 0.6 for Li₅.₄PS₄.₄BrCl₀.₆. Arrhenius plots for compositions with x values from 0.0 to 0.6 are shown in Fig. 3c that shows the temperature-dependent ionic conductivity, which increases with temperature, following a linear trend consistent with an Arrhenius behaviour. Ionic conductivity increases gradually from 1.2 mS cm⁻¹ for x = 0 to 9.8 mS cm⁻¹ for x = 0.6 within the Li₆⁻ₓPS₅⁻ₓBrClₓ series. This was confirmed by additional measurements for same composition by making pellets of thickness 0.13, 0.25 and 0.31 cm and the Nyquist plots at 25 °C and -10 °C are shown in Fig. S3a and S3b respectively. All the data were fitted with an equivalent circuit (R-CPE) and the ionic conductivity at 25 °C for three pellets with (t) = 0.13, 0.25 and 0.31 cm are 9.8, 10.2 and 10.4 mS cm⁻¹ respectively. At -10 °C, a single semicircle is observed comprising of bulk and grain boundary contributions. Calculated ionic conductivities at -10 °C are 1.8, 1.9 and 2.0 mS cm⁻¹. All three values are well within the error limit, and validates our good measurement protocol and measured ionic conductivity values. Further increase in x to 0.7 leads to minor decrease in ionic conductivity to 8 mS cm⁻¹. The activation energies, calculated from the linear fit of the Arrhenius plot, slightly increase from 0.32 to 0.34 eV from x = 0 to 0.6. Notably, even at -10⁰°C Li₅.₄PS₄.₄BrCl₀.₆ shows a high ionic conductivity of 2 mS cm⁻¹. Enhanced ionic conductivity can be mainly attributed to the higher degree of disorder of Cl⁻, Br⁻ and S²⁻ on the 4a and 4d sites and increased similarity of the 4a and 4d cages.

We further investigated Li-deficient argyrodite compositions of same Li nominal content (5.5) by changing the Br and Cl ratio. The variations of the ionic conductivity and of the activation energy as a function of increasing ‘x’ from 0 to 1.5 in Li₅.₅PS₄.₅Br₁.₅-xClₓ are depicted in Fig. 3e and corresponding Arrhenius plots are shown in Fig. 3f. The ionic conductivity ranges from 3.7 to 9.8 mS cm⁻¹ from Li₅.₅PS₄.₅Br₁.₅ (x = 0) to Li₅.₅PS₄.₅Br₀.₅Cl (x = 1). Notably, when the Br and Cl mixing is maximum (ClBr₀.₅ and BrCl₀.₅), the ionic conductivity is higher compared to the end members, while the activation energy significantly increases from 0.32 to 0.39 eV when transitioning from Br-rich (Br₁.₅) to Cl-rich (Cl₁.₅) compositions. Comparing the two highly conductive compositions, i.e. Li₅.₅PS₄.₅ClBr₀.₅ with Li₅.₅PS₄.₅BrCl₀.₅, the former exhibits a higher ionic conductivity of 9.8 mS cm⁻¹ at 298K accompanied by a slightly higher activation energy of 0.36 eV. Conversely, the latter displays a marginally lower ionic conductivity of 8.9 mS cm⁻¹ at 298 K but features a lower activation energy of 0.33 eV. Hence, at 273 K, both compositions exhibit identical ionic conductivities as indicated on the Arrhenius plot. To choose the best composition, the trade-off between ionic conductivity and activation energy is a critical consideration. While higher ionic conductivity is generally desirable, the impact of increased activation energy on overall performance cannot be overlooked.

## 2.3. Atomic-scale mechanism of conductivity improvement in Li₆⁻ₓPS₅⁻ₓBrClₓ

To gain atomic-scale mechanistic insights into fast lithium-ion transport, we used ab initio methods and molecular dynamics (MD) simulations based on machine learning interatomic potentials (MLIP). We simulated the structural, dynamic, and transport properties of the Li₆⁻ₓPS₅⁻ₓBrClₓ composition series for x = 0, 0.3, and 0.6 to determine the mechanism of the enhancement in lithium-ion conductivity with Cl substitution. The MLIP simulation reproduced the experimental lattice parameters to better than 0.01 Å, i.e., to within about 0.1 % (Fig. 4). For further validation of our model, the simulation also reproduces all the experimental fingerprints of Raman spectra using the sulfur vibrational density of states as a proxy. Here, we only target frequencies and their shifts with composition and do not simulate intensities to avoid computing polarizabilities.

The S-P-S distortion peaks at 204 and 276 cm⁻¹ are accurate to within ≤5 cm⁻¹, and their softening with Cl substitution is reproduced (compare Figs. 4 and 1). The peak at 571 cm⁻¹, by contrast, does not soften with Cl substitution, and the peak at 421 cm⁻¹ instead hardens (Fig. 4). Precise agreement with experiment allowed us to interpret three more features of the vibrational spectra. First, we assigned the feature near 150 cm⁻¹ to S cages (4a and 4d) based on their disappearance with decreasing S content. This was only a weak feature in the experimental Raman spectra, likely due to low polarizability. Second, based on the softening of the modes at ≤100 cm⁻¹, which most likely are acoustic and phononic, we concluded that the lattice softens with Cl substitution; a more detailed analysis of PS₄ vibrations is left for future work. Third, the Br vibrations, instead harden with Cl substitution, demonstrating an opposing trend. We interpret this below but note that in Li₆PS₅Br the Br occupies predominantly the 4a site, which can be expected to be soft. Finally, the simulation also reproduces the increasing trend in ionic conductivities with Cl substitution at 323 K, although it overestimates their absolute magnitudes. The agreement at x = 0.6 is within a factor of 2.3x, and at x = 0.3 within a factor of 3.0x. We note that in lieu of simulating diffusivity at elevated temperatures (500 K and above) and relying on Arrhenius extrapolations or assuming a unity Haven ratio, we benchmarked directly to experimental values using long-duration simulations and ascertaining that the dispersive Jonscher regime (power-law increase of conductivity with increasing a.c. frequency) is surpassed.

We then investigated the origin of increased conductivities with Cl substitution by examining the pairwise radial distribution functions (RDF, g(r)) between cage anions and lithium as a proxy for cage structure following the approach by Morgan [51] but dis-aggregating cage structure by anion and cage type. With increasing x in Li₆⁻ₓPS₅⁻ₓBrClₓ, the 4d cages remain unchanged (Fig. 4, orange); this can be further seen in the corresponding coordination numbers (Fig. S9). However, the 4a cages (Fig. 4, blue) harden and compress as they accommodate the decrease in lithium stoichiometry. This occurs for both S, Cl, and Br 4a cages (see again Fig. S9 for Cl coordination numbers). As a result, the lithium cage structure around every 4a anion approximates that around the same anion on the 4d site by x = 0.6: the lithium environments around the 4a and 4d cages become more similar with Cl substitution. Together with increasing anion disorder (Fig. 2), this helps to explain the improvement in lithium conductivity: instead of any particular cage type (4a or 4d) serving as a bottleneck to transport, the landscape for lithium-ion conduction becomes effectively more uniform even if the individual hopping distances may not substantively change. A T4 site would be found at ≈3.7 Å from 4d anions, but these are not pronounced in simulation. However, the experimental identification of T4 occupancy similarly serves to make the 4a cages more akin to the well-defined 4d cages.

## 2.4. Critical current density tests (CCD)

Although there is no direct correlation between ionic conductivity
<figure><img src="image_6.png" /><figcaption>**Fig. 4.** Simulated structure, conductivity, and vibrational dynamics of Li₆-xPS₅-xBrClₓ. (a) Lattice constants from simulation (green) reproduce experiment to within 0.01 Å; experimental values from Fig. 1. (b) Li-ion conductivity simulated at 323 K reproduces the experimental trend with composition. (c) S vibrational density of states (vDOS); vertical guidelines are Raman peaks from Fig. 1. (d) Br vDOS shows broadening and hardening with Cl substitution. (e) The strong experimental S mode at 421 cm⁻¹ in Li₆PS₅Br and its hardening upon Cl substitution are reproduced. Pairwise radial distribution functions between cage-center anions and Li in Li₆-xPS₅-xBrClₓ from the MD simulations (f–h) Br–Li, (i–k) S–Li. Blue: 4a cage anions, orange: 4d cage anions. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)</figcaption></figure>

and CCD, it is commonly observed that compositions with higher conductivity tend to show higher CCD values [52–55]. To study the impact of Cl substitution on the Li dendrite suppression capability of Li₆-xPS₅-xBrClₓ compositions (x = 0.0, 0.3, 0.5, 0.6), Li | SE | Li symmetric cells were constructed.

Li plating/stripping profiles for Li₆-xPS₅-xBrClₓ (x = 0.0, 0.3, 0.6) are presented in Fig. 5a, b and 5c, respectively. For a given current density, the overpotential value decreases with increasing Cl content. In Li₆PS₅Br, the overpotential increases to 93 mV at 0.6 mA cm⁻², leading to a short circuit in the cell. In contrast, at the same current density, Li₅.7PS₄.7BrCl₀.3 exhibits a significantly lower overpotential of 34 mV

that further decreases to 24 mV for Li₅.5PS₄.5BrCl₀.5 and Li₅.4PS₄.4BrCl₀.6. At higher current densities of >0.7 mA cm⁻² the overpotential of Li₅.7PS₄.7BrCl₀.3 starts to increase and eventually the cell undergoes a short circuit at 0.9 mA cm⁻². Despite showing a lower overpotential, the CCD of Li₅.4PS₄.4BrCl₀.6 is also 0.9 mA cm⁻². Among the measured samples, a highest CCD of 1 mA cm⁻² is achieved for Li₅.5PS₄.5BrCl₀.5. These observations suggest that the high ionic conductivity observed in mixed halide compositions also translates into better stability against Li metal. Since all the compositions exhibited similar particle sizes, we can speculate that mixed halide compositions may also contribute to the formation of a stable SEI layer. The SEI layer,
<figure><img src="image_7.png" /><figcaption>Fig. 5. Time-controlled Li plating/stripping profiles of symmetric Li | SE | Li cells under constant stack pressure of 25 MPa for (a) Li₆PS₅Br, (b) Li₅.₇PS₄.₇BrCl₀.₃, (c) Li₅.₅PS₄.₅BrCl₀.₅, (d) Li₅.₄PS₄.₄BrCl₀.₆. A constant current was applied for 1 h during each charge/discharge cycle, with the current density incrementally increased from 0.05 mA.cm⁻² until cell failure occurred. (d) and (f) DC polarization curves for the applied voltages of 10–50 mV for Li₆PS₅Br and Li₅.₄PS₄.₄BrCl₀.₆ pellets respectively. (e) and (g) Typical I-V curves of Li₆PS₅Br and Li₅.₄PS₄.₄BrCl₀.₆ plotted using current values derived from polarization curves.</figcaption></figure>

likely containing both LiCl and LiBr along with Li₂S/Li₃P, probably exhibits synergistic properties. LiCl may contribute to enhanced mechanical strength and electronic passivation, while LiBr may facilitate efficient Li⁺ diffusion [56,57] This improved SEI may promote homogeneous lithium deposition and robust dendrite suppression, thereby enabling a superior and stable critical current density. consequently leading to higher critical current density [58,59].

## 2.5. Electronic conductivity of Li₅.₄PS₄.₄BrCl₀.₆ in comparison to Li₆PS₅Br

The electronic conductivity was measured by performing “classical” DC polarization experiments, for which after a small voltage applied, the resulting leakage current was measured over time. From these measurements the electronic resistance (Rₑ) values were determined using the relation

$$V_{DC} = I_{DC} \times R_{e}$$

DC polarization measurements were performed on two samples, Li₆PS₅Br and Li₅.₄PS₄.₄BrCl₀.₆ (Fig. 5d and e). Small voltages of 10, 20, 30, 40 and 50 mV were applied for 2 h each and the current values were recorded as a function of time. From the I-V curves shown in Fig. 5f and g, a clear linear relationship was observed between the applied voltage (Vₐ) and the measured current (Iₐ). The calculated resistance values from the slopes of these curves indicate an electronic resistance of 5.1 MΩ for Li₆PS₅Br, whereas Li₅.₄PS₄.₄BrCl₀.₆ displays a lower resistance of

1.02 MΩ. The room temperature electronic conductivity was therefore determined as 3.3 × 10⁻⁸ S cm⁻¹ for Li₆PS₅Br and 16.2 × 10⁻⁸ S cm⁻¹ for Li₅.₄PS₄.₄BrCl₀.₆. Although five times higher electronic conductivity is observed for Li₅.₄PS₄.₄BrCl₀.₆, the value is still in a similar range as observed for other Li-argyrodites [12,60].

## 2.6. Comparative electrochemical performances of Li₅.₄PS₄.₄BrCl₀.₆ and Li₆PS₅Cl

To evaluate the electrochemical performance of Li₅.₄PS₄.₄BrCl₀.₆ (referred to as Br₁₀Cl₆), all solid-state batteries were assembled using LiNi₀.₆Mn₀.₂Co₀.₂O₂ (NMC-622) as the cathode active material and Li₀.₅In-Li₆PS₅Cl (60-40 wt%) as the anode composite.

We have chosen two samples: the highly-conducting Li₅.₄PS₄.₄BrCl₀.₆ composition isolated in this study (Br₁₀Cl₆) and a commercial Li₆PS₅Cl, widely utilized worldwide in ASSB research activities [61–63]. SEM micrographs of Li₆PS₅Cl, Br₁₀Cl₆ and NMC622 are shown in Fig. S5. While assembling the ASSBs, the cathode composite was prepared in a standard weight ratio of 70:30 of cathode: solid electrolyte, as often used (Kitaura et al. [64]). An optimal ratio is crucial to achieve optimal percolation in the composite cathode, ensuring the conduction pathways for ions and electrons and the composite microstructure, influencing both ionic and electronic conductivities, must be optimized to mitigate high tortuosity [65]. Whenever a new material has to be investigated, finding the optimal ratios of cathode and solid electrolyte becomes essential for ideal transport characteristics, as partial resistances within
the composite don't scale linearly with volume fractions of constituents [66].

As a first step, to choose the optimal weight ratio of SE and cathode active material in the catholyte, ASSBs were assembled with catholyte containing different weight ratio of NMC-622 and Br10Cl6. Catholyte powder made by manually grinding four distinct weight ratios of NMC-622 and Br10Cl6 (60-40, 70-30, 80-20 and 88-12 wt%) in an agate mortar and pestle. In all the cells, 20 mg of catholyte (different wt%), Br10Cl6 as separator and Li₀.₅In-Li₆PS₅Cl (60-40 wt%) was used as anode composite. The ASSB fabrication pressure was 325 MPa, and a constant stack pressure (applied by torque wrench) of approximately 100 MPa was applied during electrochemical analyses.

The first charge-discharge cycles shown in Fig. 6a were conducted at a rate of C/30 and the upper cut-off voltage was set at 3.6 V vs. Li/LiIn. The initial specific charge capacities for all weight ratios of the catholyte are in the range of 179–185 mAh.g⁻¹, with an increasing trend observed as the ratio of NMC-622 increases, as shown in the inset of Fig. 6a. A columbic efficiency of 87 % is achieved for the ASSB with 60-40 wt% catholyte, while the batteries built with 70-30, 80-20, and 88-12 wt% of catholyte exhibit columbic efficiencies higher than 90 %. Notably, the columbic efficiencies are higher than those reported by Tarascon et al. [67] for NMC-622 and Li₆PS₅Cl, which were approximately 81 %. Although no significant difference is observed during the initial cycle at C/30, a notable difference becomes apparent when the cells are subjected to charge/discharge at different C rates (Fig. 6b). The ASSB with 88-12 wt% catholyte exhibits faster capacity fade, especially at higher C rates, while the ASSB with 70-30 wt% catholyte shows higher specific capacity over other cells at all C rates. Based on these observations, a catholyte with a 70-30 wt ratio of NMC-622 to solid electrolyte was selected as the optimal weight ratio to achieve the best electrochemical performance for later studies.

### 2.6.1. Towards higher cathode active material loadings

To achieve a practical ASSB with higher gravimetric energy density involves a ubiquitous strategy of increasing the cathode active material content of the positive electrode. Achieving better performance at

higher loading of the cathode active material depends on several factors such as particle size distribution of cathode/solid electrolyte, tortuosity, etc; the ionic conductivity of the solid electrolyte also plays a crucial role [68]. To assess electrochemical performance at higher cathode loadings, ASSBs were assembled with a catholyte composition of 88-12 wt% of NMC-622 and Br10Cl6/Li₆PS₅Cl, allowing for a comparison. It is to be noted that specific capacities are calculated based on the mass of the cathode composite (around 20 mg).

The first charge-discharge cycle at C/30 of ASSB with catholyte containing different weight ratio of NMC-622 and Br10Cl6 are shown in Fig. 6c. This is basically the same data as in Fig. 6a, but represented in terms of total mass of the cathode composite. When the total mass of the cathode composite is considered, the initial charge capacities of 107.2 mAh.g⁻¹ is obtained for 60-40 wt% catholyte, whereas 88-12 wt% catholyte exhibits 166.2 mAh.g⁻¹ with a coulombic efficiency of 90 %. Under similar conditions, the ASSB with Li₆PS₅Cl delivers only 142 mAh.g⁻¹ with higher polarization and lower columbic efficiency of 83.6 % (Fig. 6d). Although at higher C rates the capacity fade is faster in Br10Cl6, it can still deliver around 43 mAh.g⁻¹ at C/2, while Li₆PS₅Cl delivers only 11 mAh.g⁻¹. To assess the long-term stability, both cells were subjected to charge/discharge at C/5 for 65 cycles. For the battery containing Br₁₀Cl₆ as the solid electrolyte, the specific discharge capacity decreased from 60.5 to 50.9 mAh.g⁻¹ (84.1 % retention) over 65 cycles, whereas in the case of Li₆PS₅Cl, the capacity decreases from 25.4 to 21.1 mAh.g⁻¹ (83 % retention) (Fig. 6d). Although both cells undergo significant capacity fade, Br₁₀Cl₆ exhibits much higher capacity compared to Li₆PS₅Cl even at cathode loading of 88 wt%. The overall improvement is ascribed to the higher ionic conductivity of Br₁₀Cl₆ which offers both higher ionic conductivity in cathode composite and facilitates faster ion transport in separator.

To deconvolute the effect of higher ionic conductivity in cathode composite and separator and to understand which factor affects most for the rate capability, four ASSBs were assembled in four different configurations (Fig. 7b).

(a) Li₀.₅In-Li₆PS₅Cl | Br10Cl6 | Br10Cl6/NMC-622 (70-30 wt%)

<figure><img src="image_8.png" /><figcaption>**Fig. 6.** Electrochemical performance of ASSBs assembled with catholyte of different wt % of NMC-622 and Li₅.₄PS₄.₄BrCl₀.₆. (a) First charge/discharge cycle at C/30 (b) Discharge capacity at different C rates and long-term charge/discharge at C/5. (c) First charge discharge cycle at C/30 of ASSB with different weight ratio of NMC-622 and Br10Cl6 with capacity represented in terms of mass of cathode composite. ASSB cycling results for cathode composite in the weight ratio of 88-12 wt% of NMC-622 and Li₅.₄PS₄.₄BrCl₀.₆/Li₆PS₅Cl (d) Comparative first charge discharge cycles at C/30 of Li₅.₄PS₄.₄BrCl₀.₆ and Li₆PS₅Cl then compared at different cycling rates in (e).</figcaption></figure>
<figure><img src="image_9.png" /><figcaption>Fig. 7. (a) and (c) Galvanostatic charge/discharge curves at C/30 for the four ASSBs configurations depicted in (b). Br10Cl6 refers to $Li_{5.4}PS_{4.4}BrCl_{0.6}$. (d) Comparison of the rate capability of the four configurations.</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>Fig. 8. Galvanostatic charge/discharge curves at C/30 for $Li_6PS_5Cl$ at 3 different stack pressures for (a) $Li_6PS_5Cl$ (b) $Li_{5.4}PS_{4.4}BrCl_{0.6}$ ASSB vs Li metal anode: Cycling results of $Li_{5.4}PS_{4.4}BrCl_{0.6}$ and $Li_6PS_5Cl$ (c) First charge/discharge cycle at C/30 vs. Li metal and corresponding discharge capacity at different C rates and long-term charge/discharge at C/5 in (d).</figcaption></figure>
(b) $Li_{0.5}In-Li_6PS_5Cl$ | $Li_6PS_5Cl$ | $Br_{10}Cl_6$/NMC-622 (70-30 wt%)

(c) $Li_{0.5}In-Li_6PS_5Cl$ | $Br_{10}Cl_6$ | $Li_6PS_5Cl$/NMC-622 (70-30 wt%)

(d) $Li_{0.5}In-Li_6PS_5Cl$ | $Li_6PS_5Cl$ | $Li_6PS_5Cl$/NMC-622 (70-30 wt%)

Galvanostatic charge/discharge curves at C/30 for 4 configurations are shown in Fig. 7a and c.

The 2 cells with $Br_{10}Cl_6$ in cathode composite deliver specific discharge capacity of 163.5 and 159.4 mAh.g⁻¹ with coulombic efficiencies of ~90 %. While the 2 cells with $Li_6PS_5Cl$ in cathode composite deliver specific discharge capacity of 152.4 and 145.1 mAh.g⁻¹ with coulombic efficiency of 86.5 and 88.9 % respectively. Notably, the 2 cells with $Br_{10}Cl_6$ in the separator show higher specific capacity at higher C-rates. At 1C the 2 cells ((a) and (c)) with $Br_{10}Cl_6$ in the separator delivers the specific discharge capacity of 76.6 and 73.24 mAh.g⁻¹. These results suggest that at low C rates the limiting step is associated with the ionic conductivity of the cathode composite, while the ionic conductivity of the separator dominates the rate capability at higher C rates. Overall, the higher ionic conductivity of $Br_{10}Cl_6$ is favourable in the ASSBs compared to $Li_6PS_5Cl$.

## 2.7. Effect of stack pressure

So far, all the ASSBs we reported have been tested at a constant stack pressure of approximately 100 MPa, which corresponds to a torque of 21 Nm applied with a torque wrench. To evaluate the electrochemical performance of $Br_{10}Cl_6$ at lower stack pressures, three different ASSBs were assembled and the stack pressure of 100, 66 and 33 MPa were applied that corresponds to 21, 14 and 7 Nm torque (Fig. 8b). Similarly, ASSBs with $Li_6PS_5Cl$ were also assembled for comparison and the galvanostatic charge/discharge curves at C/30 (Fig. 8a). At 33 MPa stack pressure, $Li_6PS_5Cl$ shows low specific charge and discharge capacities of 63 and 51.9 mAh.g⁻¹ and high polarization. Whereas under same conditions, $Br_{10}Cl_6$ delivers a specific charge and discharge capacities of 155 and 130.3 mAh.g⁻¹ respectively. Even at 66 MPa the electrochemical performance of $Li_6PS_5Cl$ is very low compared to $Br_{10}Cl_6$. Although at this point, we do not know the exact reason for this improvement, we suspect that there might be changes in the mechanical properties and the high ionic conductivity and moderate elastic modulus of $Br_{10}Cl_6$ that facilitates overall enhancement in the performance [69].

### 2.7.1. Performance of argyrodite electrolytes against lithium metal anode

ASSBs were assembled with lithium metal as the anode, considered to be the "Holy Grail" anode for use in ASSBs despite being extremely challenging due to issues related to the formation of Li dendrites, leading to internal short circuits. This issue stems from the inherent morphological instability during the plating and stripping of lithium metal at the SE separator interface [70]. Meng et al. [71] have demonstrated that controlling both fabrication and/or stack pressure play a crucial role during battery operation. However, controlling all the parameters was beyond the scope of this study, as our focus was solely on the comparative study of $Br_{10}Cl_6$ and $Li_6PS_5Cl$ used under similar conditions.

ASSBs with Li metal were assembled using 14 mg of cathode composite (70-30 wt%) and 80 mg of solid electrolyte in the separator. These two layers were stacked, and a fabrication pressure of 375 MPa was applied for 3 min. Finally, a thin Li metal foil was attached to the other side, and a stack pressure of ~25 MPa was applied during electrochemical analyses. This specific stack pressure was determined after multiple trials within the range of 15–40 MPa. The initial charge-discharge cycles for $Br_{10}Cl_6$ and $Li_6PS_5Cl$, performed at a rate of at C/30 (54.7 µA g⁻¹) and with an upper cut-off voltage at 4.2 V vs. $Li/Li^+$ are shown in Fig. 8c and d. In the initial cycle, specific charge and discharge capacities of 173 and 153.1 mAh.g⁻¹, respectively, were attained for $Br_{10}Cl_6$, corresponding to a coulombic efficiency of 89.3 %. The ASSB incorporating $Li_6PS_5Cl$ demonstrated comparable specific charge capacities of 170.3 mAh.g⁻¹. However, it exhibited a higher overpotential and a reduced specific discharge capacity of 136.6 mAh.g⁻¹, resulting in

a coulombic efficiency of only 80 %. Even at different C rates, $Br_{10}Cl_6$ consistently delivers a higher capacity than $Li_6PS_5Cl$. At C/2 (0.821 mA g⁻¹), $Br_{10}Cl_6$ delivers 75.9 mAh.g⁻¹, while $Li_6PS_5Cl$ undergoes a short circuit after four cycles at C/2. This observation may be attributed to the higher critical current density of $Br_{10}Cl_6$, which impedes the formation of dendrites. To assess the long-term stability of the $Br_{10}Cl_6$ cell, it was subjected to charge/discharge at C/5 for 85 cycles. The specific discharge capacity at C/5 decreases from 96.7 to 89.6 mAh.g⁻¹ with a capacity retention of 92.6 % retention over 85 cycles. The enhanced electrochemical performance can be attributed to the higher ionic conductivity and excellent stability of the $Li/Br_{10}Cl_6$ interface, as indicated by critical current density measurements.

To summarise the ASSB measurements, our comprehensive analysis conducted under various conditions consistently demonstrates that $Br_{10}Cl_6$ exhibits enhanced electrochemical performance when compared to commercial $Li_6PS_5Cl$.

## 3. Conclusions

This study investigates the structural and ionic transport properties of the $Li_{6-x}PS_{5-x}BrCl_x$ and $Li_{5.5}PS_{4.5}Br_{1.5-x}Cl_x$ argyrodite series using XRD, neutron diffraction, Raman spectroscopy, ³¹P MAS NMR, impedance spectroscopy, and machine learning based MD simulations. The ionic conductivity of $Li_{5.4}PS_{4.4}BrCl_{0.6}$ reaches 9.8 mS cm⁻¹ at 25 °C and remains notable at 1 mS cm⁻¹ at -20 °C. The study identifies that the enhanced ionic conductivity arises from increased site disorder at the 4d and 4a sites and increased similarity between local lithium environments around the 4a and 4d sites contributing to a more uniform Li-ion hopping landscape; this is consistent with the experimental identification of T4 16e sites. Notably, solid-state batteries constructed with NMC-622 cathodes, $Li_{0.5}In$ anodes, and $Li_{5.4}PS_{4.4}BrCl_{0.6}$ electrolyte exhibit superior performance, including higher specific capacities, improved coulombic efficiencies, and better rate capabilities compared to the conventional electrolyte $Li_6PS_5Cl$. In addition, under various applied pressures and with lithium metal anodes, $Li_{5.4}PS_{4.4}BrCl_{0.6}$ demonstrates consistent electrochemical stability and exceptional cycling performance. These findings provide key insights into the role of halide substitution in improving ionic conductivity within the argyrodite structure. Further research into halogen-rich compositions could further enhance ionic conductivity and electrolyte stability, thereby accelerating the development and practical implementation of all-solid-state batteries.

## 4. Experimental and computational methods

**Synthesis method:** All the synthesis work and sample treatments were conducted in an argon-filled glovebox with O₂ and H₂O levels below 0.1 ppm. To synthesise both $Li_{6-x}PS_{5-x}BrCl_x$

$(0 \le x \le 0.8)$ and $Li_{5.5}PS_{4.5}Br_{1.5-y}Cl_y$ $(0.0 \le y \le 1.5)$ compositions, stoichiometric ratios of reagents, $Li_2S$ (Sigma Aldrich, 99.98 %), $P_2S_5$ (Sigma Aldrich, 99 %) (3 wt% excess added), $LiCl$ (Alfa Aesar, 99 %) and $LiBr$ (Alfa Aesar, 99 %), were mixed to obtain 2g batches of precursors. The precursors were transferred into a Fritsch Pulverisette 7 premium line 80 mL zirconia ball-milling jar, along with 20 zirconia balls of 10 mm diameter (the ball-to-powder ratio was 30:1). Initially, the precursors were milled at 150 rpm for 30 min to homogenize the mixture. Ball milling was carried out at 600 rpm for 20 h in total. Each milling cycle consisted of 15 min of milling and 10 min of rest to dissipate the excess of heat. Throughout the milling process, the milling jars were periodically opened inside the glovebox, and any sample adhering to the walls and the cap was dislodged. After 20 h of ball milling, the obtained powder was pelletized into 10 mm pellets and sealed in quartz ampoules under vacuum of $10^{-2}$ mbar. Annealing was carried out at 450°C for 5 h, followed by normal cooling (2–3 °C/min). Finally, the annealed pellets were pulverized by grinding in a mortar and pestle and used for further characterization.
**X-Ray Diffraction:** XRD measurements of annealed powders were measured using a Bruker D8 Discover diffractometer equipped with CuKα radiation in reflection geometry for a 2θ range of 10°–50°, a step size of 0.02°, and a scan rate of 0.9 s/step. To mitigate sample sensitivity to moisture and air, PXRD data were collected using a custom airtight sample holder equipped with a Be window. Unit cell parameters were refined using the Le Bail fit method implemented in the FullProf software.

**Neutron diffraction:** Neutron powder diffraction experiments were conducted at the high-resolution powder diffractometer D2B beamline of the Institut Laue-Langevin (ILL), Grenoble, France. Approximately 2 g of sample was hermetically sealed in cylindrical vanadium containers. Diffraction data were collected at room temperature in transmission geometry and high intensity configuration without any collimation. A neutron wavelength of 1.594 Å was selected using the Ge(335) reflection from a germanium monochromator.

**Solid-State NMR:** NMR spectra were recorded on a Bruker Avance III HD spectrometer and a 17.6 T magnet operating at 303.6 MHz for ³¹P, with a Bruker 4 mm triple resonance wide bore probe (used in double mode). The samples were packed into 4 mm zirconia rotors in an Ar-filled glovebox, sealed with a Kel-F cap and spun at the magic angle under dry nitrogen gas at a spinning rate of 10 kHz. One-pulse spectra were collected using a direct RF pulse of 4.75 µs (52.6 kHz), setting the spectral width to 100 kHz and co-adding 64 transients. The recycling delays (d1) were set to 35–70s, chosen to be more than five times the longest measured longitudinal relaxation time for the PS₄³⁻ zone to ensure quantitative measurements. The FID were Fourier-transform without apodization and all the spectra were referenced to 85 % H₃PO₄ at 0 ppm. The fits of the NMR spectra were performed with the dmfit software [72] after a baseline correction (spline on spectrum), using 10 Gaussian-shaped functions optimized on Li₅.₇PS₄.₇BrClO₃ and kept the same for the other samples except for the area. An additional broad Gaussian shaped function was necessary to obtain good fits, and its position, width and area were optimized individually for each sample. The contributions of the spinning sidebands were ignored as they did not modify the relative quantities of each peak significantly (similar anisotropies).

**RAMAN Spectroscopy:** Spectra were collected using a Raman DXR Microscope (Thermo Fischer Scientific) equipped with a green laser of excitation wavelength of 532 nm. A laser power of 0.1 mW was used to avoid sample damage due to excessive local heating. Spectra were collected by 1 s exposure time and 180 exposures.

**Electrochemical Impedance Spectroscopy:** Total conductivity was measured using AC impedance spectroscopy. About 200 mg of sample were uniaxially cold-pressed in a 10 mm die at 625 MPa. The relative density of the pellet was 85–87 % and the thickness was 1.4 mm approximately. Indium foils were pressed on the surface of pellets as ion-blocking electrodes. AC impedance spectroscopy was performed on these pellets by mounting them in BioLogic CESH cell and spectra were recorded using MTZ 35 frequency response analyzer by applying 50 mV AC perturbation in the frequency range from 30 MHz to 1 Hz. Spectra were collected between the temperature of range of –20 to 50 °C with 10 °C intervals in the ITS temperature controller. The AC impedance data were analyzed using Zview (Scribner) or RelaxIS software (rhD instruments, Darmstadt, Germany).

**Critical current density measurement:** Li | SE | Li symmetric cells were fabricated by densifying 150 mg of solid electrolyte powder at 375 MPa between two stainless steel pistons (10 mm diameter). Subsequently, Li metal foils (10 mm diameter) were pressed onto both sides of the solid electrolyte layer under a maintained uniaxial stack pressure of 25 MPa throughout operation. Electrochemical testing utilized a time-controlled measurement method, where a constant current was applied for 1 h during each charge and discharge cycle. The current density was initially set at 0.05 mA/cm² and incrementally increased until short-circuit failure was observed.

**Cell fabrication:** The cathode composite was prepared by grinding

70 wt% of LiNi₀.₆Mn₀.₂Co₀.₂O₂ (NMC-622) and 30 wt% of solid electrolyte for 20 min. In specific cases, the cathode composition was adjusted as indicated in the respective sections. The anode composite was obtained by grinding a 60:40 wt% ratio of Li₀.₅In alloy and Li₆PS₅Cl for 1 h to form a dark grey powder. To assemble the battery, approximately 49 mg of solid electrolyte (SE) powder was introduced into a 10 mm polymer mold and densified by cold pressing under 125 MPa for 1 min. Subsequently, 20–22 mg of the cathode composite (containing 14–15 mg NMC-622) was uniformly layered on one side of the solid electrolyte, while 85 mg of the anode composite was applied to the opposite side. The stack was pressed at 375 MPa for 5 min, assembled into a stainless-steel frame, and subjected to a uniaxial stack pressure of 100 MPa using a torque wrench.

**First-principles calculations:** Density-functional theory (DFT) calculations were used to train a machine-learning interatomic potential (MLIP) for argyrodites spanning the composition space from Li₇PS₆ to Li₅PS₄Cl₂ and Li₅PS₄Br₂. Training structures were sampled from ab initio molecular dynamics and single-point calculations using VASP [73] and the projector-augmented wave method [74,75]. The strongly constrained and appropriately normed (SCAN) functional with the revised Vydrov-van Voorhees dispersion correction [76] (rVV10) were used, with a plane-wave cutoff of 600 eV and k-point spacing 0.25 Å⁻¹. The convergence cutoff for energy was 10⁻⁶ eV with an “accurate” precision setting. Ab initio molecular dynamics (AIMD) were carried out at temperatures between 300 K and 1200 K in isobaric and isovolumetric ensembles at compositions spanning the above chemical space. Enhanced sampling was used to improve sampling of lithium hopping and stresses. The same settings were used for single-point calculations during active learning loops.

**MLIP settings and training:** the equivariant graph neural network architecture allegro [77] was used to train the MLIP (nequip 0.6.1) [78, 79]. For all models, the key network parameters were 5 Å radial cutoff and tensorial feature maximum dimension $l_{max} = 1$ with initial embedding multiplicity 32 and final edge layer 128. The dimensions of the two-body perceptron layers were 64, 128, 256, and 256, and those of the latent perceptron layers 256, 256, and 256. The training with starting learning rate 0.005 was conducted on one NVIDIA A100 GPU per model for up to 1 day. Uncertainty was estimated in active learning cycles as the standard deviation of predicted force components a committee of models. The model was evaluated on a fully out-of-distribution test set of stoichiometries (Br/Cl) not seen during training and whose configurations were sampled from AIMD at 600k, the allegro model reproduces SCAN-DFT reference data (retroactively) with an energy RMSE of 0.0021 eV Å⁻¹ (MAE 0.0020 eV Å⁻¹, R = 0.9952) and a force RMSE of 0.0714 eV Å⁻¹ atom⁻¹ (MAE 0.0527 eV Å⁻¹ atom⁻¹, R = 0.9942), while element-resolved force RMSEs remain low—0.0499 eV Å⁻¹ atom⁻¹ for Li, 0.1346 eV Å⁻¹ atom⁻¹ for P, 0.0785 eV Å⁻¹ atom⁻¹ for S, 0.0516 eV Å⁻¹ atom⁻¹ for Br, and 0.0537 eV Å⁻¹ atom⁻¹ for Cl.

**Molecular dynamics (MD) simulations:** The allegro model was used in LAMMPS [80] for MD simulations of Li₆ₓPS₅ₓBrClₓ for x = 0, 0.3, 0.6 at 323 K. The simulations used a 3 × 3 × 3 supercell of the conventional unit cell. The occupancies of the Wyckoff 4a and 4d sites were the same as in Fig. 2(cd). No other ordering or correlations were assumed: the cage-center sites were populated randomly in accordance with the experimentally determined occupancies. Constant-pressure simulations were carried out with a timestep of 5 fs for 45–90 ns (which is much longer than typical AIMD simulations of 100ps). To calculate the vibrational density of states as a fast proxy for spectroscopic observables, velocity autocorrelation functions were computed up to 50 ps in time lag. The lithium ionic conductivity was calculated by window-averaging the center-of-mass mean-square displacement for log-spaced time lags up to 10 ns, equivalent to 100 MHz. Since the conductivities at 1–10 ns (1 GHz–100 MHz) were independent of frequency, they were averaged to represent the d.c. conductivity.

**Simulation of ³¹P NMR spectra:** NMR shifts were computed from structures sampling all 15 arrangements of S, Br, and Cl on 4d sites
adjacent to a PS₄ polyhedron. For each set of 4d neighbours of a PS₄ tetrahedron, every possible configuration of 4a neighbours was also considered. Structures used for NMR calculations were of size 1 conventional unit cell. Lithium positions were randomized via isobaric molecular dynamics and sample structures were relaxed. The NMR magnetic shielding tensors were calculated with the CASTEP 23.11 plane-wave pseudopotential code using the GIPAW approach [81]. All calculations used ultrasoft pseudopotentials with a cutoff energy 900 eV and k-point spacing 0.05 Å⁻¹ for sampling the Brillouin zone. For these values the ³¹P isotropic shifts for individual atoms were converged to within 1 ppm. All calculations used the PBE functional, which has been shown to generally give good agreement with experiment [82]. Arbitrary reference shieldings, σ<sub>ref</sub>, are required to convert NMR shieldings, σ, to chemical shifts, δ, viz. δ = σ<sub>ref</sub> - σ. The reference shieldings were determined by taking the intercept of a linear fit of a set of experimental δ<sub>iso</sub> and calculated σ<sub>iso</sub> values for a diverse set of reference compounds.

### CRediT authorship contribution statement

**Dhanush Shanbhag:** Writing – review & editing, Writing – original draft, Investigation, Formal analysis, Data curation, Conceptualization.
**Ajay Gautam:** Formal analysis, Elodie Salager: Writing – review & editing, Investigation, Formal analysis, Data curation. Laura Albero-Blanquer: Writing – review & editing, Supervision, Investigation, Funding acquisition.
**Florencia Marchini:** Writing – review & editing, Validation, Supervision, Investigation, Funding acquisition, Conceptualization.
**Jean-Noël Chotard:** Writing – review & editing, Investigation, Formal analysis, Data curation.
**François Fauth:** Writing – review & editing, Formal analysis, Data curation.
**Emmanuelle Suard:** Writing – review & editing, Investigation, Formal analysis, Data curation.
**François Rabuel:** Writing – review & editing, Investigation, Data curation, Conceptualization.
**Houssny Bouyanfif:** Writing – review & editing, Investigation, Formal analysis, Data curation.
**Andrey D. Poletayev:** Writing – review & editing, Methodology, Investigation, Formal analysis, Conceptualization.
**Christopher Davies:** Writing – review & editing, Methodology, Investigation, Formal analysis, Data curation.
**Benjamin Zelin:** Writing – review & editing, Methodology, Investigation, Formal analysis, Conceptualization.
**M. Saiful Islam:** Writing – review & editing, Methodology, Investigation, Funding acquisition, Formal analysis, Conceptualization.
**Virginie Viallet:** Writing – review & editing, Supervision, Project administration, Methodology, Investigation, Funding acquisition, Conceptualization.
**Christian Masquelier:** Writing – review & editing, Supervision, Project administration, Investigation, Funding acquisition, Conceptualization.

### Declaration of competing interest

The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: Dhanush Shanbhag reports financial support was provided by UMICORE Group Research and Development. 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.

### Acknowledgement

D.S. and C.M. gratefully acknowledges UMICORE for financial support provided through a joint Ph.D. project between with LRCS. The authors thank the Institut Laue-Langevin (ILL) for beam time allocation on the D2B diffractometer for powder diffraction measurements, the ALBA synchrotron for beam time on the MSPD diffractometer, and CEMHTI (Orléans) for access to solid-state NMR facilities. Computational work was carried out using the UK Materials and Molecular Modelling Hub, which is partially funded by EPSRC (EP/T022213/1, EP/W032260/1 and EP/P020194/1) and the ARCHER2 high-

performance computing facility through the HEC Materials Chemistry Consortium (EP/R029431). A.D.P. and S.I. gratefully acknowledge the Faraday Institution (EP/S003053/1, FIRG016).

## Appendix A. Supplementary data

Supplementary data to this article can be found online at https://doi.org/10.1016/j.jpowsour.2025.238175.

### Data availability

Data will be made available on request.

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