# Exploring the temperature-dependent structural evolution of mechanically synthesized Na\_3Ps\_4 solid electrolyte through in situ X-ray diffraction

Sergio Federico Mayer, Marta Mirolo, Alisson Andrea Iles Velez, Ove Korjus, Emmanuelle Suard, Laureline Lecarme, Jean-baptiste Ducros, Claire Villevieille

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Sergio Federico Mayer, Marta Mirolo, Alisson Andrea Iles Velez, Ove Korjus, Emmanuelle Suard, et al.. Exploring the temperature-dependent structural evolution of mechanically synthesized Na\_3Ps\_4 solid electrolyte through in situ X-ray diffraction. Small Structures, 2024, 2024, pp.2400225. 10.1002/sstr.202400225. hal-04710726

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# Exploring the Temperature-Dependent Structural Evolution of Mechanically Synthesized Na₃PS₄ Solid Electrolyte through In Situ X-Ray Diffraction

Sergio Federico Mayer,* Marta Mirolo, Alisson Andrea Iles Velez, Ove Korjus, Emmanuelle Suard, Laureline Lecarme, Jean-Baptiste Ducros, and Claire Villevieille*

Exploring the potential of sodium-based materials is of utmost importance, especially for next-generation solid-state batteries. Herein, Na₃PS₄ thiophosphate solid electrolyte is focused on. While its tetragonal α phase is initially studied for Na solid-state batteries, the impact of heat treatment and the phase transitions of amorphous and semicrystalline polymorphs obtained by mechanochemical synthesis remains poorly understood. The structural evolution is evaluated as function of the temperature of amorphous and semicrystalline Na₃PS₄ polymorphs obtained by mechanochemical processes. Both samples are heat-treated during an in situ synchrotron X-ray diffraction measurement, and multiple phase transitions are detected, some of them being irreversible. A novel and abundant orthorhombic intermediary phase is observed when the heat treatment is performed on the amorphous sample. The ionic conductivity of both amorphous and semicrystalline samples undergoes significant enhancement after heat treatment, reaching 0.09 and 0.16 × 10⁻³ S cm⁻¹, respectively. This research sheds light on the thermal dynamics of Na₃PS₄ polymorphs, providing valuable insights into their crystallization processes, especially in the amorphous-to-cubic transition. The discovered intermediate phases underscore the potential for further advancements in sodium-based solid-state battery technologies.

## 1. Introduction

Batteries are essential to tackle the challenges of global warming. However, to date they rely on lithium-based compounds that are also classified as of "high criticality" in global supply risk

surveys.[1,2] Replacing Li by Na is not straightforward especially in the field of solid-state batteries, where Na superionic conductors are yet to be further explored. Among the potential candidates, Na₃PS₄ is currently under investigation owing to its good ionic conductivity and rich polymorphism chemistry.[3-6]

The Na₂S-P₂S₅ solid solutions have been the subject of study in the field of material science since the 1980s, when Blachnik and Rabe determined the first phase diagram of the two sulfides and obtained the Na₂P₂S₆, Na₄P₂S₇, and Na₃PS₄ stable compositions.[7] In 1992, Na₃PS₄ (NPS) was synthesized by a solid-state reaction between the two precursors at a molar ratio of 3:1,[8] in analogy to Li₃PS₄ thiophosphate,[9] crystallizing in a tetragonal system with P\*42₁c (no. 114) space group, called α-NPS. The authors also assessed the ionic conductivity of the sample, demonstrating that Na solid-state batteries were a feasible technology. The reported ionic conductivity was

≈4 × 10⁻⁶ S cm⁻¹ at 50 °C, with an activation energy of 0.416 eV. Later on, it was demonstrated that the tetragonal polymorph can turn into a cubic system at around 260 °C, the so-called β-NPS, but its structure remained unknown until 2014 when Tanibata et al. properly indexed a cubic, Si-doped

S. F. Mayer, L. Lecarme, C. Villevieille

University Grenoble Alpes

University of Savoie Mont Blanc

CNRS

Grenoble INP

LEPMI

Grenoble 38000, France

E-mail: sergio-federico.mayer@grenoble-inp.fr;

claire.villevieille@grenoble-inp.fr

The ORCID identification number(s) for the author(s) of this article can be found under https://doi.org/10.1002/sstr.202400225.

© 2024 The Author(s). Small Structures published by Wiley-VCH GmbH. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

DOI: 10.1002/sstr.202400225

M. Mirolo, A. A. Iles Velez

European Synchrotron Radiation Facility (ESRF)

Experimental division

Grenoble 38000, France

O. Korjus, E. Suard

Institut Laue Langevin (ILL)

Grenoble 38042, France

S. F. Mayer, J.-B. Ducros

University Grenoble Alpes

CEA

Liten

DEHT

Grenoble 38000, France
NPS phase in the I4̄3m (no. 217) space group.[10] The crystalline structure of such material, obtained by mechanochemical synthesis followed by heat treatment (HT) at 220 °C, was then validated by structure refinements for undoped NPS samples.[4,11] Ongoing research revealed that several amorphous and semicrystalline polymorphs of NPS could be obtained using at least three different synthesis routes, namely, the liquid-phase reaction, the solid-state synthesis route and mechanical milling. This has led to a widespread improvement in ionic conductivities and lower overall activation energies.[3,12–14] In 2019, it was demonstrated that NPS with a mostly cubic structure can be obtained in 60 min through mechanochemical synthesis and reach an ionic conductivity of 2 × 10⁻⁴ S cm⁻¹ at room temperature (RT).[15] To get such results, the authors relied on a high-purity Na₂S source. Otherwise, the ionic conductivities of samples obtained by this route barely reach a few µS cm⁻¹ and thermal treatments become mandatory to attain values suitable for battery application.[3,14]

To date, however, the impact of such HTs on the structure of mechanically obtained NPS is poorly reported. Nishimura et al. conducted an X-ray diffraction (XRD) experiment during HT to investigate the α-to-β NPS transition,[4] but they made a 100 K-step screening, resulting in a limited number of diffractograms. Only two studies, both by Famprikis et al.[6,16] have delved into the in situ structural transitions of NPS through a “temperature-controlled” diffraction study, denoted hereafter as X-ray thermo-diffraction. These two reports describe the reversible α-to-β (at ≈250 °C) and β-to-γ (≈500 °C) NPS transitions, but exclusively for crystalline samples obtained by the solid-state route. Detailed pair distribution function analysis highlights the liquid-like behavior of the γ-NPS polymorph, and the sudden thermal expansion of the unit cell of about 10% during the β-to-γ phase transition. Finally, in a recent electron thermodiffraction analysis on NPS, Nakajima et al.[17] investigated the local nucleation of crystalline species on amorphous NPS grains obtained by mechanochemical precipitation. The coexistence of nanosized crystallites of cubic β-NPS and amorphous domains seems to play a key role in the enhanced ionic conductivity of Na₃PS₄ electrolyte. Prevailing X-ray thermodiffraction studies involve crystalline NPS samples obtained either via the solid-state route[6,16] or by crystallization at high temperature of amorphous NPS samples,[4] providing deficient information on the long-range crystallization process, particularly in the amorphous-to-cubic NPS transition.

In this study, we investigate the structural thermal behavior of one amorphous and one semicrystalline Na₃PS₄ samples, both obtained by mechanical milling. XRD performed at the ESRF synchrotron facility (ID31 beamline) reveals a different thermal behavior between the two samples. Our findings indicate a strong effect of the synthesis conditions on what phase transitions happen and at what temperature they occur. Furthermore, a novel series of intermediate phases is identified during the HT of the amorphous NPS, suggesting that additional phases from which super ionic conductors could emerge are yet to be discovered. Finally, the structural data were correlated to the ionic conductivities of both samples, showing that remaining secondary phases formed at lower temperatures during the HT can negatively affect the ionic conductivity of samples obtained by mechanochemical synthesis.

## 2. Results and Discussion

### 2.1. Pristine Powders Analysis

#### 2.1.1. Morphological Analysis

Two samples with nominal chemical formula Na₃PS₄ were synthesized by mechanical milling, as described in Experimental Section. An amorphous NPS sample, hereafter am-NPS, and a semicrystalline one, denoted sc-NPS, were obtained in the form of homogeneous yellowish powders, slightly darker in the latter case. Microscopy images of am-NPS and sc-NPS taken by field emission scanning electron microscopy (FE-SEM) are displayed in **Figure 1**. The am-NPS sample (Figure 1a,b) exhibits a uniform morphology of primary particles, with size ranging from 1 to 3 µm. These primary particles tend to aggregate into secondary particles measuring up to 50 µm. Conversely, the sc-NPS, as illustrated in Figure 1c,d, showcases individual, high-crystallinity particles of tens of micrometers with the tendency to form aggregates exceeding 150 µm.

#### 2.1.2. Structural Analysis

To account for the crystallinity of the pristine samples, they were explored by XRD and neutron powder diffraction (NPD). The am-NPS is amorphous, as observed in **Figure 2a**, so it cannot be classified into any crystal system. However, if it is assumed to have a cubic structure indexed in the I4̄3m (no. 217) space group as if it were β-NPS, a Lebail fit can be performed. When the synchrotron XRD (sXRD) data collected at RT are fitted (Figure S1a, Supporting Information), a unit cell with cubic symmetry and lattice parameter *a* = 7.166(4) Å is obtained. For the selected Thompson–Cox–Hastings pseudo-Voigt profile function,[18] the fitting leads to an enormous peak broadening of *U* = 417(23) (degree 2*θ*)², accounting for a severely strained structure.[19]

On the other hand, the pristine sc-NPS sample can be successfully indexed in the cubic I4̄3m (no. 217) space group as β-NPS (Figure 2a), although at RT, its diffractogram suggests that both crystalline and amorphous NPS phases are present. Based on the analysis of the am-NPS sample, an amorphous and the cubic β-NPS contributions were fitted from sc-NPS data by the Lebail method, as presented in Figure S1b (Supporting Information). The obtained results imply that, from a crystallographic point of view, the sc-NPS sample is a heterogeneous product.

Once an amorphous and a crystalline contributions were fitted from the sc-NPS data, the latter was refined by the Rietveld method from sXRD and neutron powder diffraction (NPD) data (Figure 2b,c, respectively). A cubic lattice with *a* = 6.9734(1) Å was obtained, where PS₄³⁻ groups are located in each corner and in the center of the unit cell. Statistically, less than one Na atom occupies the center of each face and edge of the cell, as represented in Figure 2d,e. The asymmetric unit is composed of one P, one S, and one Na species, respectively, labeled as P1, S1, and Na1 and located at 2*a* (0, 0, 0), 8*c* (x, x, x), and 24*f* (x, ½, 0) Wyckoff sites. A difference Fourier synthesis performed after the refinements only presents background noise,
<figure><img src="image_2.png" /><figcaption>**Figure 1.** FE-SEM images of Na₃PS₄. a,b) Microscopy images of am-NPS sample, with a more homogeneous primary particle size around 1–3 µm and a rather spherical shape that agglomerates into secondary particles of up to 50 µm. c,d) Image of sc-NPS electrolyte, exhibiting sharper individual particles and larger chunks that can reach the 80–100 µm in size and stand out from the smaller particles, also forming agglomerates higher than 150 µm.</figcaption></figure>

indicating there are no missing atoms and that the site occupancy factors (SOFs) are correctly determined. Hence, the structure of sc-NPS, obtained exclusively by mechanochemical synthesis, is similar to the one of β-NPS at 600 K as it was defined by Nishimura et al.,[4] in coherence with previous reports on NPS obtained by high-energy ball milling.[15] The displacement ellipsoids of S1 species suggests its electron cloud resonates perpendicularly to the P–S bond, with an equivalent atomic displacement “thermal” parameter (ADP) of 3.25(2) Å². The resulting lattice parameters, atomic coordinates, ADPs, and SOFs were summarized for each technique in Table S1 (Supporting Information), along with the reliability factors and the goodness-of-fit. Figure 2d shows the structure of sc-NPS with atomic SOFs. Only Na¹ species present a fractional occupancy, close to 24.3%. Statistically, less than ¼ of Na⁺ ions occupy the 24f (x, ½, 0) Wyckoff site, i.e., about 0.972(3) ions are located near the center of the face of the unit cell at coordinates (0, ½, ½). Figure 2e exhibits the displacement ellipsoids of each species, drawn with 95% probability.

Finally, if the obtained structure is treated as a rigid model of spheres with electrostatic charges, a bond-valence energy landscape (BVEL) can be calculated. The output, presented in Figure 2f, is an isosurface of potential that represents the ionic percolation pathway, in this case of Na⁺ ion, with a migration activation energy of Eₐ = 0.25 eV in all three directions. As foreseen, the Na¹ species, with a theoretical site-energy of −1.93 eV, can be found close to energy wells of −1.98 eV over the percolation pathway.

Once the structure of sc-NPS was determined, a combined XRD and neutron diffraction refinement, so called X–N map, was performed to extract the location of the two S1 electron lone pairs. The principle of the analysis is as follows: i) The high-resolution sXRD allows precise determination of both the relative positions of the electron clouds within the crystal lattice and the lattice parameters, ii) The NPD, on the other hand, is highly sensitive to the atomic positions due to the interaction between the neutron beam and atomic nuclei. Consequently, it is possible to determine the discrepancies from both techniques by fixing the atomic positions extracted from NPD data refinement and performing a difference Fourier synthesis from sXRD data. This allowed us to find the exact position of the electron lone pairs belonging to the S1 species, located at ≈1.7 Å from Na1 and 1.6 Å from S1 in tetrahedral coordination (Figure S2, Supporting Information).

### 2.1.3. Electrochemical Discussion

To evaluate the ionic conductivity of both pristine materials, electrochemical impedance spectroscopy (EIS) measurements were performed on pellets densified at RT. The cell preparation and measurement conditions are described in Experimental Section.

The Nyquist plots of the pristine samples (Figure 3a) display a semicircle related to the ionic conductivity of am-NPS and sc-NPS. The straight line in the low-frequency region corresponds to the blocking response of the current collector. The large discrepancy in the semicircle diameter represents a major
<figure><img src="image_3.png" /><figcaption>**Figure 2.** Diffraction patterns and structural representations of Na₃PS₄. a) Synchrotron X-ray diffractogram of semicrystalline (red curve) and amorphous (blue curve) NPS obtained by mechanochemical synthesis. The pattern of sc-NPS is indexed in the body-centered unit cell with space group *I*43*m*, for which main Bragg peaks are shown. b,c) Plots of the Rietveld refinement for the sc-NPS sample from sXRD (wavelength (λ) = 0.16530 Å) and NPD (λ = 1.593 Å) data, respectively. Experimental (red crosses), calculated (solid black line), and difference (solid blue line at the bottom) curves are plotted together with Bragg reflection positions as vertical green bars. d) Structure of β-NPS obtained upon Rietveld refinement from sc-NPS data, presenting the SOFs. e) Alternative representation, highlighting the asymmetrical displacement ellipsoids for the S1 and Na1 species, displayed with a probability of 95%. f) View of the Na⁺ percolation pathway, in pink. For simplicity, the Na1 species are hidden and the PS₄³⁻ tetrahedra are shown as sticks.</figcaption></figure>

difference in terms of ionic conductivity for both samples. The overall ionic conductivity of the amorphous and the semicrystalline samples are 0.5 × 10⁻⁶ S cm⁻¹ and 3.7 × 10⁻⁶ S cm⁻¹, respectively. The high resistances might be related to incomplete NPS synthesis reaction and/or a poor densification. The first hypothesis is consistent with similarly low ionic conductivities reported elsewhere[11] for mixtures of NPS precursor that were ball-milled and did not sufficiently reacted to form the β-NPS phase.

The impedance data should be deconvoluted in different con-
tributions to analyze the reasons behind the poor ionic conduc-
tivity. However, as their deconvolution at RT is far from trivial,
lower temperature measurements are necessary. Moreover, the
distribution of relaxation times (DRT) is used here to enhance
the resolution in separating electrochemical processes. The
advantage of DRT is that it needs no a priori assumptions,
e.g., there is no need for electrical, chemical, or physical models
or any knowledge about the electrochemical system.[20,21]

In the case of am-NPS, only one significant process contrib-
utes to the resistance (Figure 3b), as expected for the amorphous
material due to their lower grain boundary resistances. However,

the activation energy calculated from the Arrhenius plots
(Figure S3a, Supporting Information) is 2.33 eV, while a value
of 0.49 eV has been reported previously.[3] This means that, most
likely, the amorphous sample has only partially reacted and it is
unable to form an ionic conductive network of NPS, leading to
poor ionic conductivity and enormous activation energy.[11]

In the case of sc-NPS, three different processes (P₁, P₂, and P₃, in Figure 3c) can be distinguished with DRT. The P₂ is the most significant of the processes and almost dominates the sc-NPS conductivity. Surprisingly, according to previous studies, P₂'s activation energy (0.464 eV·7 eV) is more likely to correspond to amorphous NPS rather than crystalline α-NPS or β-NPS.[3,13,22,23] However, in Figure 2a–c, a significant amount of amorphous NPS is visible, which validates the impedance results. P₁ and P₃, in total, account for less than one-third of the impedance contribution. Their origin is unclear to date because their activation energies are too high for α-NPS or β-NPS (Figure S3b, Supporting Information), so it is likely a contribution from the crystalline part that is badly interconnected owing to partial mechanochemical reaction, leading to a discrepancy for the Eₐ values.
<figure><img src="image_4.png" /><figcaption>**Figure 3.** EIS data of am-NPS and sc-NPS. a) Nyquist plots of pristine am-NPS and sc-NPS samples collected at RT. b,c) DRT plots of pristine (b) am-NPS and (c) sc-NPS measured at different temperatures (noted in the figure). P₁, P₂, and P₃ correspond to different processes.</figcaption></figure>

## 2.2. Thermodiffraction Data Analysis

After the characterization of the pristine samples, the am-NPS and sc-NPS were introduced in quartz capillaries and subjected to HT while being monitored in situ sXRD. Following the sequence of HT steps summarized in Table 1 and depicted in Figure S4 (Supporting Information), the series of diffractograms displayed in Figure S5 (Supporting Information) were recorded.

<table><caption>**Table 1.** Temperature program of Na₃PS₄ HT. The whole sequence comprises 11 temperature steps grouped in four parts (stage I–IV). For each heating step, the initial (Tinitial) and final (Tfinal) temperatures, the temperature slope (Tslope), its duration (telapsed), and the difference in sample temperature between collected diffractograms (ΔTdiffractograms) are presented. Both stage I and II, where maximum resolution is sought, begin with moderate (2 K min⁻¹) and low (0.5 K min⁻¹) temperature slopes. During stage IV, the temperature is ramped up and down to assess the reversibility of phase transitions.</caption><thead><tr><th>Stage</th><th>Heating step</th><th>T<sub>initial</sub><br>[°C]</th><th>T<sub>final</sub><br>[°C]</th><th>T<sub>slope</sub><br>[K min<sup>-1</sup>]</th><th>t<sub>elapsed</sub><br>[min]</th><th>ΔT<sub>diffractograms</sub><br>[K]</th></tr></thead><tbody><tr><td rowspan="3">I</td><td>Ramp</td><td>21</td><td>150</td><td>2</td><td>64.5</td><td>7.8</td></tr><tr><td>Ramp</td><td>150</td><td>200</td><td>0.5</td><td>100</td><td>2</td></tr><tr><td>Plateau</td><td>200</td><td></td><td></td><td>90</td><td></td></tr><tr><td rowspan="3">II</td><td>Ramp</td><td>200</td><td>240</td><td>2</td><td>20</td><td>7.8</td></tr><tr><td>Ramp</td><td>240</td><td>290</td><td>0.5</td><td>100</td><td>2</td></tr><tr><td>Plateau</td><td>290</td><td></td><td></td><td>90</td><td></td></tr><tr><td rowspan="2">III</td><td>Ramp</td><td>290</td><td>500</td><td>2</td><td>105</td><td>7.8</td></tr><tr><td>Plateau</td><td>500</td><td></td><td></td><td>180</td><td></td></tr><tr><td rowspan="3">IV</td><td>Ramp</td><td>500</td><td>100</td><td>-10</td><td>40</td><td>≈26</td></tr><tr><td>Ramp</td><td>100</td><td>300</td><td>5</td><td>40</td><td>20</td></tr><tr><td>Ramp</td><td>300</td><td>80</td><td>Uncontrolled</td><td>30</td><td>≈20</td></tr></tbody></table>

Owing to the several structural changes monitored by Lebail and Rietveld refinements, and for the sake of clarity, these data will be discussed in four stages.

### 2.2.1. Stage I: Heating to 200°C and Plateau

As shown in Table 1, a two-slopes temperature ramp approach was used to both limit the thermal inertia of the gas blower and reach the targeted temperature plateau relatively fast without losing temporal resolution on the structural changes occurring in the critical phases of the HT. The close-up corresponding to this HT stage is displayed in **Figure 4**.

The sc-NPS sample presents subtle structural changes, as shown in Figure 4a and Video S1 (Supporting Information). The amorphous contribution to the diffractograms lowers, while the crystalline peaks shift to lower angles due to an increase of the lattice parameters linked to the rising temperature. A close-up of the diffractograms series, highlighting the initial and final patterns, is displayed in Figure S6 (Supporting Information). There is no presence of impurities other than the amorphous phase.

The am-NPS, on the other hand, remains amorphous from RT to 173 °C, as shown in Figure 4b. At this temperature, reported as the one for glass transition for the am-NPS.[14] new peaks appear at the expense of the amorphous phase. Judging by the evolution of the X-ray diffractograms and Bragg peaks with temperature, in the following it will be seen that this process seems to involve the formation and disappearance of at least three phases in a multi-phase crystallization process before the formation of β-NPS. At around 185 °C (red pattern), the main phase is an orthorhombic crystal system, hereafter called Orth-1. This crystal phase, a novel polysulfide or NPS polymorph that was not yet reported,
<figure><img src="image_5.png" /><figcaption>**Figure 4.** Stage I diffractograms: heating to 200 °C and plateau. Collected sXRD diffractograms (λ = 0.16530 Å) from a) sc-NPS and b) am-NPS samples during the stage I of HT. a) The crystallinity of the sc-NPS sample slightly increases with the temperature and during the plateau. b) The amorphous sample experiences a multiphase crystallization process starting from 173 °C with the predominance of Orth–1 crystalline phase at around 185 °C (red diffractogram). Then, the β-NPS polymorph becomes predominant. During the plateau at 200 °C, the secondary phases decrease but persist to some extent (purple triangles).</figcaption></figure>

is only obtained during the HT of the amorphous sample and crystallizes in either the *Pbam* (no. 55) or *Pba2* (no. 32) space groups. Determining its exact structure is challenging due to the substantial presence of amorphous and secondary phases. However, upon detailed observation of the diffractograms sequence in Video S2 (Supporting Information) in the 173–200 °C range, β-NPS is formed at expense of Orth–1, suggesting the latter could contain all three Na, P, and S atoms. When the volume of the obtained unit cell is divided by the molar volumes of Na₃PS₄ in its α and β forms, an average of 48 atoms per unit cell is calculated, with an atomic mean volume of 21.6 Å³. If Orth–1 were an NPS polymorph, the most likely Z value, or number of formula units in the unit cell, is 6. Other phases, such as Na₂P₂S₆ and Na₄P₂S₆,²⁴⁾ were considered, but these suggest a total of 44 atoms per cell, which does not correspond to an integer Z value. Several attempts to find the atomic structure of Orth–1 using ab initio methods failed, likely due to the presence of multiple phases and a significant amorphous component still present at this temperature. The other two phases found in the crystallization process of am–NPS a Orth–2 and Orth–3, likely crystallizing in the *Pccm* (no. 49) and *Pmmm* (no. 47) orthorhombic space groups, respectively. The Lebail fit involving the three orthorhombic phases, the β-NPS, and an undefined amorphous phase integrated in the background is presented in Figure S7 (Supporting Information), where the individual contribution of each pattern is highlighted. Table S2 (Supporting Information) summarizes the cell parameters for each phase present at 185 °C. Above this temperature, Orth–1 phase gradually fades while heating, giving way to the β-NPS polymorph, now main phase. At 200 °C there is a mixture of β-NPS and the remaining of the three orthorhombic phases. During the plateau at 200 °C, the latter decrease to some extent, as seen by the peaks tagged with purple triangles (Figure 4b).

### 2.2.2. Stage II: Heating to 290°C and Plateau

After the plateau at 200 °C for 90 min, the samples were heated up to 290 °C. The collected diffractograms are presented in **Figure 5**; panels (a) and (b) for sc-NPS and am-NPS, respectively. The diffractograms of sc-NPS sample shown in Figure 5a and in Video S3 (Supporting Information) reveal no changes aside from peak shifts toward lower angles during the heating. The absence of significant structural changes suggests that a HT performed at 200 °C on NPS should be enough to achieve the crystallization of β-NPS phase, as could be concluded from the glass-transition temperatures found by calorimetric analysis of glassy NPS.[3,14]

On the other hand, as shown for am-NPS in Video S4 (Supporting Information), the intensity of the small peaks mostly attributed to Orth–2 decrease upon heating, particularly before reaching 260 °C. However, after the 90 min dwell at 290 °C, these still remain visible, as marked with green triangles in Figure 5b. The close-up in the inset of Figure S8 (Supporting Information) shows that these peaks do not to belong to the cubic β-NPS phase. From the perspective of the long-range structure, this may seem to contradict the common approach of performing HTs at 250–280 °C to achieve the crystallization and structural changes in amorphous NPS polymorphs.[3,4] Hence, the reason behind the HTs performed at such temperatures on NPS samples[13,15,25] is likely related to change at the local level associated with an increase in their ionic conductivity.

### 2.2.3. Stage III: Heating to 500°C and Plateau

Following the plateau at 290 °C, the samples are heated up to 500 °C and held at this temperature for 3 h. The sequences of collected X-ray diffractograms can be visualized in
<figure><img src="image_6.png" /><figcaption>**Figure 5.** Stage II diffractograms: heating to 290 °C and plateau. Collected sXRD diffractograms (λ = 0.16530 Å) of a) sc-NPS and b) am-NPS samples during the stage II. Both series of diffractograms display the sharpening and intensification of peaks, indicative of crystallization processes. For am-NPS, some impurities marked with green triangles remain even after the 90 min plateau at 290 °C.</figcaption></figure>

Video S5 and S6 (Supporting Information) for sc-NPS and am-NPS, respectively, as well as in **Figure 6**. The sc-NPS experiments a phase evolution from β-NPS to γ-NPS starting at about 492 °C, as reported in the literature. The γ-NPS polymorph was originally predicted by calorimetric analysis[8] and coincides with the crystal phase recently indexed in the *Fddd* (no. 70) space group.[6,16] Interestingly, the sc-NPS does not achieve a full β-to-γ transition and peaks from β-NPS remain visible, even after 3 h at 500 °C, as evidenced by the remaining Bragg reflections in the green curve of Figure 6a. In fact, most of sc-NPS remains as β-NPS by the end of stage III, exemplified, for instance, by the peak at 2.72°,

corresponding to the (200) planes of the β-NPS. For a clearer view, the Figure S9 (Supporting Information) shows the Lebail fits of β-NPS and γ-NPS in the two samples at the beginning of the plateau at 500 °C.

In the case of am-NPS, the first noticeable change occurs at around 358 °C, where a new phase emerges during an accentuated process of crystallization of the β-NPS phase, with significant peak sharpening and peak intensity gain. Between 433 and 441 °C, all the secondary phases and the β-NPS suddenly disappear and γ-NPS is formed. The β-to-γ transition, highlighted with blue diffractograms in Figure 6, occurs for the am-NPS

<figure><img src="image_7.png" /><figcaption>**Figure 6.** Stage III diffractograms: heating to 500 °C and plateau. Collected sXRD diffractograms (λ = 0.16530 Å) from a) sc-NPS and b) am-NPS samples between 290 and 500 °C. The sc-NPS exhibits a β-NPS to γ-NPS transition toward 484–492 °C (panel (a), blue pattern). The am-NPS presents the formation of a secondary phase at around 358 °C that remains until the β-to-γ phase transition at 433–441 °C (panel (b), blue diffractogram). When both samples reach the 500 °C (green curve), a plateau of 180 min begins (not displayed).</figcaption></figure>
at the lowest temperature ever reported, i.e., 60–70 °C below previously stated conditions.[8,16]

### 2.2.4. Stage IV: Cooling to 100°C and ReHeating to 300°C

In this last stage involving a fast (10 K min⁻¹) cooling down to 100 °C and a reheating to 300 °C, the reversibility of the α-to-β phase transition is explored. In **Figure 7**, the bottom diffractograms of panels (a) and (b) correspond, respectively, to the sc-NPS and am-NPS samples at the end of the 500 °C plateau. For a facile comparison between the two samples, the several phase transitions occurring in this stage are summarized in **Table 2** and displayed in Video S7 and S8 (Supporting Information). During cooling, the γ-to-β transition occurs earlier for the sc-NPS at a temperature range of 445–420 °C, while in the case of am-NPS it happens between 420 and 395 °C. Interestingly, the sc-NPS is mostly β-NPS even after 3 h at 500 °C. Likewise, all the diffractograms spanning along the capillary and centered in the gas blower position (vertical frames, see Experimental Section) present a significant amount of β-NPS (Figure S10, Supporting Information). The main hypothesis is that the transition temperature is not completely reached, provided the proximity of the experiment temperature

to the one reported for the formation of the γ-NPS phase,[16] the temperature gradient along the capillary, and a reasonable uncertainty between the nominal and actual temperature of the gas blower.

During the first cooling step (Figure 7, purple series), the am-NPS experiences a full γ-NPS to β-NPS transition in the temperature range of 420–395 °C (green curve), 25 °C lower than for sc-NPS. When the sc-NPS reaches the 370 °C, α-NPS starts to be formed (red curve) and its amount increases along the cooling down, as can be seen from the profiling obtained by sequential Rietveld refinement involving the two species (Figure S11, Supporting Information). In the case of am-NPS, this transition begins at ≈265 °C, showing that the β-NPS is more stable when synthesized from am-NPS. At 100 °C, the amount of β-NPS in am-NPS and sc-NPS phases reaches the 52(1) wt% and 36(3) wt%, respectively. The remaining phase is α-NPS.

Finally, to evaluate the reversibility of the α-to-β phase transition, the samples are heated up to 300 °C (Figure 7, blue series). The α-to-β phase transition is completed when the temperature reaches 200 and 260 °C, respectively for am-NPS and sc-NPS. Above these temperatures, only β-NPS can be detected for both samples. During the last cooling down of the samples, the α-NPS phase is, respectively, observed at ≈200 and 260 °C for am-NPS

<figure><img src="image_8.png" /><figcaption>**Figure 7.** Stage IV diffractograms: cooling to 100 °C and reheating to 300 °C. Collected sXRD diffractograms (λ = 0.16530 Å) from a) sc-NPS and b) am-NPS samples during the stage IV. The successive phase transitions and their corresponding curves are summarized in Table 2.</figcaption></figure>

<table><caption>**Table 2.** Phase transitions in Na₃PS₄ during stage IV. Phase transitions occurring for am-NPS and sc-NPS during stage IV involve cooling from 500 to 100 °C at ~10 K min⁻¹, heating up to 300 °C at 5 K min⁻¹, and natural cooling to ≈80 °C. For each step, the initial (Tinitial) and final (Tfinal) temperatures are presented, along with the observed phase transitions, the transition mode, the temperature at which they occur (Ttrans), and the curve in Figure 7 indicating the phase change.</caption><thead><tr><th>Step</th><th>T<sub>initial</sub> [°C]</th><th>T<sub>final</sub> [°C]</th><th>Transition</th><th>Transition mode</th><th>sc-NPS T<sub>trans</sub> [°C]</th><th>am-NPS T<sub>trans</sub> [°C]</th><th>Curve (Figure 7)</th></tr></thead><tbody><tr><td rowspan="2">Cooling (purple series)</td><td rowspan="2">500</td><td rowspan="2">100</td><td>γ → β</td><td>Sudden</td><td>445–420</td><td>420–395</td><td>Green</td></tr><tr><td>β → α</td><td>Progressive</td><td>From 370</td><td>from 265</td><td>Red</td></tr><tr><td>Heating (blue series)</td><td>100</td><td>300</td><td>α → β</td><td>Progressive</td><td>Up to 260</td><td>up to 200</td><td>Black</td></tr><tr><td>Natural cooling (orange series)</td><td>300</td><td>80</td><td>β → α</td><td>Progressive</td><td>From 260</td><td>from 200</td><td>Black</td></tr></tbody></table>
and sc-NPS, showing the good reversibility of the α → β phase transition.

## 2.3. Electrochemical Performance of Heat-Treated Samples

To evaluate the well-known increase in ionic conductivity upon thermal crystallization of NPS samples obtained by mechanical methods, sc-NPS and am-NPS were heat-treated at 300 °C as described in Experimental Section. Both samples, namely, HT-sc-NPS and HT-am-NPS, were pelletized at RT at 380 MPa. Their ionic conductivity was evaluated by EIS. As foreseen, the HT significantly increases the ionic conductivities for both samples, as evidenced by the significant resistance reduction shown in the corresponding Nyquist plots (Figure 8). The ionic conductivity of HT-sc-NPS reaches the $0.16 \times 10^{-3}$ S cm$^{-1}$, while for HT-am-NPS it rises to $0.09 \times 10^{-3}$ S cm$^{-1}$, about two orders of magnitude higher than the raw materials. Such high increment in ionic conductivity after HT of the original samples is in good agreement with previous reports on NPS.[3,13] This also correlates well with the diffraction data, showing well-crystallized peaks and no amorphous contributions after HT. The fact that the HT-am-NPS is less conductive than HT-sc-NPS is likely due to the impurities that are still present in the am-NPS sample, as observed after the temperature plateau of stage II (Figure 5b).

It should be noted that the EIS measurements were performed at RT. Additionally, the pressure applied during the shaping process of the pellets proved to be an important variable, responsible for an increase of up to ≈10 fold in the ionic conductivity of NPS samples,[26] making these values difficult to be compared to other reports where the exact conditions are not reported.

However, although the ionic conductivity of both HT-sc-NPS and HT-am-NPS are significantly below 1 mS required for solid electrolytes to be widely implemented in batteries,[27-29] these are adequate values for the archetypical $Na_3PS_4$[3,11,22] with cubic long-range structure. Indeed, several studies based on pair distribution function and Raman spectroscopy suggest that the local arrangement of $PS_4^{3-}$ anions in cubic NPS polymorphs fit better

with a tetragonal local arrangement model regardless the synthesis method used.[6,22,26] $^{23}$Na solid-state nuclear magnetic resonance (NMR) spectra show strong similarities in cubic and tetragonal polymorphs at ambient and low temperatures,[11] and a thorough analysis of ball-milled and heat-treated NPS samples, including spectra of $^{23}$Na and $^{31}$P collected by magic-angle spinning NMR, suggests that multiple domains of coherent tetragonal distortion are distributed in each crystallite of β-NPS with a cubic long-range structure.[26]

## 3. Conclusions

In this study, we conducted a comprehensive investigation of the thermal dependence of the structure of two different types of sodium thiophosphate electrolytes synthesized through mecha-nochemical processes. Our analysis involved a thorough characterization of pristine amorphous (am-NPS) and semicrystalline (sc-NPS) samples using a series of state-of-the-art techniques. In a multistage HT program, we elucidated the structural changes occurring during thermal treatment. First, we observed distinct structural behaviors for both samples with respect to temperature. A series of novel orthorhombic phases were identified during the crystallization process of am-NPS. Through detailed evaluation of synchrotron XRD data by Lebail fits and Rietveld refinements, we found that the most significant phase changes, i.e., the α-to-β NPS, the β-to-γ NPS, and the reverse phase transitions, occur at 50 to 100 °C lower temperatures for am-NPS than for sc-NPS. This indicates that the high-conductivity phases are favored (i.e., they form at lower temperature) for the amorphous phase. Conversely, the am-NPS presents a series of secondary phases or impurities that only fade away during the formation of γ-NPS.

Our findings revealed that the HT induces an irreversible crystallization process of the amorphous phase, and a reversible α-to-β phase transition that leads to improved ionic conductivity of the NPS compared to the pristine samples. After crystallization at high temperature, the ionic conductivity of both am-NPS and sc-NPS samples increase by two orders of magnitudes, from $\approx 10^{-6}$ S cm$^{-1}$ to around $10^{-4}$ S cm$^{-1}$ at RT.

All in all, the am-NPS exhibits a pure γ-NPS phase formation and permanence at the lowest temperatures ever reported. The β-NPS/α-NPS ratio upon HT at 500 °C is larger for am-NPS at probed temperatures below α-NPS crystallization, i.e., below 370 °C. The sc-NPS is not only limited to partial γ-NPS formation from the β-NPS polymorph, but also consists mostly of α-NPS upon cooling down. Hence, we demonstrated that the ball milling conditions during the preparation of the thiophosphates seem to play a key role in how the crystallization processes occur upon HT, and in the presented scenario, am-NPS appears to be a more suitable candidate for a solid electrolyte if the HT temperature is high enough to remove any remaining traces of impurities.

## 4. Experimental Section

**Precursors and Synthesis:** The precursors used in this work were anhydrous sodium sulfide (96%, ThermoFisher Alfa Aesar) and phosphorus pentasulfide (99%, Sigma-Aldrich), both predried under vacuum ($P < 10^{-3}$ mbar) for 20 h in a Büchi oven at 250 and 130 °C, respectively.

<figure><img src="image_9.png" /><figcaption>**Figure 8.** EIS data of heat-treated samples. Nyquist plots of HT-sc-NPS and HT-am-NPS samples collected at RT.</figcaption></figure>
**Precursors and Synthesis: Mechanochemical Synthesis of Sodium Thiophosphate Electrolytes:** Both investigated samples were prepared by mechanochemical synthesis using a planetary ball mill (Fritsch, Pulverisette 7). The Na₂S and P₂S₅ were manually ground together in a 3:1 molar ratio in an agate mortar to ensure homogeneity. Subsequently, the mixture was ball-milled in 45 mL ZrO₂ jars using different conditions. For the am-NPS sample, 1.5 g of precursor mixture was ball-milled with ≈40 g of ZrO₂ balls with a diameter of Ø5 mm. The process involved an active milling time of 24 h at a rotation speed of 510 rpm. The ball milling scheme consisted of 5 min active milling, followed by 15 min resting periods. For obtaining the sc-NPS, 1.5 g of precursor mixture were placed in the ZrO₂ jar together with 40 g of ZrO₂ balls of Ø10 mm and rotated at 600 rpm. Milling periods of 2 h followed with resting periods of 10 min were used for a total active milling time of 10 h. Following the ball milling process, the resulting samples were ground by hand to break down any formed agglomerates. All the processes were performed in an Ar-filled glove box (<1 ppm of water and oxygen).

**Precursors and Synthesis: Heat-Treatment of NPS for Electrochemical Characterizations:** The heat-treated samples used for determining the ionic conductivity of well-crystallized NPS samples were prepared as follows: about 2 g of mechanically obtained sample were introduced in an alumina crucible in powder form, which, in turn, was placed in a quartz tube under Ar atmosphere. The tube was then placed in a Carbolite Gero 30-3000 tubular oven (Carbolite Gero Ltd.) and connected to an Ar gas line. The samples were heated under mild Ar flow at ambient pressure for 12 h at 300 °C, with temperature ramps of 2 °C min⁻¹.

**Characterizations: Synchrotron X-Ray Thermodiffraction Analysis (sXRD):** Measurements were carried out at ID31 beamline at the European synchrotron (ESRF, Grenoble, France), using high energy photon beam (75.00 keV, or a wavelength of 0.16530 Å) and Pilatus CdTe 2M detector. This combination allows for the acquisition of a wide reciprocal space (above 15 Å⁻¹ here) in short time (1 s in this study), reducing the possible beam damage of the solid electrolyte materials. For each sample, a diffractogram was taken each ≈234 s at a centered spot. Calibration of the sample-detector distance, detector tilts, and energy has been performed using CeO₂ reference powder from NIST. The scattered signal collected from the 2D detector is integrated into 1D XRD pattern using pyFAI package[³⁰] and the integrated data analyzed using FULLPROF[¹⁹] software for the refinement of structures by the Rietveld method[³¹] and the FullProfAPP[³²] appliance for the bulk treatment of sequential diffractograms.

The setup for the in situ X-ray thermodiffraction consists of two gas blowers manufactured at ESRF, each one positioned in front of a sealed quartz capillary of Ø0.7 mm containing the solid electrolyte under Ar protective atmosphere. The calibration of the temperature has been performed prior to the beamtime using thermocouples to confirm the exact reading of the temperature compared to the target temperature. To ensure that no temperature gradient occurs in the capillary during HT, a vertical profiling of the capillary was performed by scanning it over 1 cm length (0.5 mm below and 0.5 mm above the center of the heating area) corresponding to 25 separated frames. Besides, the setup is mounted on a translational motor, allowing for the acquisition in parallel of two samples, one after the other. An offset of the setup in the beam direction guarantees no shadowing effect on the detector while protecting the gas blowers from the heating of their counterpart. The different sample-detector position has been considered during the data processing phase.

The HTs were performed on both NPS samples from RT to 500 °C, with varying temperature slopes and several plateaus to precisely monitor the phase transitions. The full temperature program is composed of 11 sequential steps, as classified in Table 1. The temperature program used is depicted in Figure S4 (Supporting Information).

**Characterizations: Neutron Powder Diffraction (NPD):** D2B high-resolution beamline two-axis diffractometer was used (Institut Laue-Langevin, Grenoble, France) to perform measurement on the crystalline sample. Approximately 1 g of sc-NPS sample was introduced in a Ø5 mm vanadium can, sealed with In wire, and kept under Ar protective atmosphere. The diffractogram was collected at RT (about 21 °C) in high intensity mode for 2 h. A wavelength of 1.593 Å was selected from a Ge monochromator.

**Characterizations: Field Emission Scanning Electron Microscopy (FE-SEM):** The FE-SEM images were taken by a ZEISS Sigma 300 microscope, using a Gemini column. The images were generated using a secondary electron detector at an acceleration voltage of 10 kV.

**Electrochemical Characterizations: Cell Assembly:** For the evaluation of the ionic conductivity of the materials, full-stainless-steel electrochemical cells were used. In a standard cell preparation, about 30–40 mg of sample are introduced in a polyoxymethylene spacer, which acts both as a mechanical container for pressing the electrolyte powder and as an electrical insulator between the two opposite electrodes. The powder-form sample is pressed at RT at ≈380 MPa (3.88 ton cm⁻²) for 15 min. Afterward, two W-metal current collectors are introduced on each side of the shaped pellet, and the cell is hermetically closed with a stack pressure of ≈70 MPa. All the manipulations are performed in an Ar-filled glove box.

**Electrochemical Characterizations: EIS Measurements:** The EIS analyses were performed in potentiostatic mode on the described cells using a VMP3 multichannel potentiostat (Bio-Logic Science Instruments). For the temperature-controlled experiments, a CTS “T-series” (CTS Nederland B.V.) benchtop temperature chamber was used. The EIS spectra were collected at open-circuit voltage with a signal amplitude of 20 and 50 mV for heat-treated and nonheat-treated samples, respectively, in a frequency range from 7 MHz to 10 Hz. Three consecutive EIS spectra were collected upon temperature stabilization (2–4 h, depending on the temperature setpoint). The conductivity values were normalized to the pellet geometry. Both qualitative and quantitative distribution function of relaxation times analysis was conducted with the Relaxis3 software package (RHD instruments, Germany). For all the calculations, the regularization parameter, λ, was chosen using Lamda-plot and set to 0.001. The shape factor has been set to 0.5.

**Data Processing:** The FULLPROF[¹⁹] toolbar software (version 5.10), available from Institut Laue-Langevin Grenoble, France (https://www.ile.eu/sites/fullprof/), including WinPLOTR-2006 (version 0.50), was used for the Rietveld refinement of the structures. The embedded modules BondSTR (version 2010), and GFOURIER (Graphic Fourier Program, version 04.06) from Institut Laue-Langevin Grenoble, France, and the University of La Laguna, Tenerife, Spain, respectively, were employed for Fourier difference density maps calculation, and BVEL analysis. Data processing was conducted using OriginPro (version 2021) from OriginLab, Northampton, MA, USA (https://www.originlab.com). Crystal structure projections were generated using VESTA[³³] (Visualization for Electronic and Structural Analysis, version 3.5.5, 64-bit Edition) graphing tools, available at https://jp-minerals.org/vesta/en/. GSAS II[³⁴] software (version 5677) from Argonne National Laboratory Illinois, United States (https://subversion.xray.aps.anl.gov/trac/pyGSAS), was also used for evaluating the structural changes and for representing the diffractograms series.

## Supporting Information

Supporting Information is available from the Wiley Online Library or from the author.

## Acknowledgements

The authors are thankful for the financial support provided by Carnot Energie du futur funding agency through the “SONA” grant. Beamtime at the ESRF was granted through proposals IH-CH-1708[³⁵] and MA-5872,[³⁶] and beamtime at ILL was obtained through LTP-1-4 proposal.[³⁷] The authors also thank Dr. Julio Andrade for his guidance in the resolution of the structure of the orthorhombic phases formed during the HT of the am-NPS sample.

## Conflict of Interest

The authors declare no conflict of interest.
Data Availability Statement

The data that support the findings of this study are available from the
corresponding author upon reasonable request.

Keywords

energy storage, Na₃PS₄, sodium-ion, solid electrolytes, solid-state batteries, structure refinement, thiophosphates

Received: May 6, 2024

Revised: July 26, 2024

Published online:

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