A Theoretical Raman Spectra Analysis of the Effect of the Li₂S and Li₃PS₄ Content on the Interface Formation Between (110)Li₂S and (100)β-Li₃PS₄

Abstract

In this study, we perform density functional theory (DFT) simulations to investigate the Raman spectra of the bulk and surface phases of β-Li₃PS₄ (LPS) and Li₂S, as well as their interfaces at varying compositional ratios. This analysis is relevant given the widespread application of these materials in Li–S solid-state batteries, where Li₂S functions not only as a cathode material but also as a protective layer for the lithium anode. Understanding the interfacial structure and how compositional variations influence its chemical and mechanical stability is therefore crucial. Our results demonstrate that the LPS/Li₂S interface remains stable regardless of the compositional ratio. However, when the content of both materials is low, the Raman-active vibrational mode associated with the [PS₄]³⁻ tetrahedral cluster dominates the interface spectrum, effectively obscuring the characteristic peaks of Li₂S and other interfacial features. Only when sufficient amounts of both LPS and Li₂S are present does the coupling between their vibrational modes become sufficiently pronounced to alter the Raman profile and reveal distinct interfacial fingerprints.

1. Introduction

In the past decades, energy shortage problems have become increasingly serious, and the search for clean energy and batteries with high storage capacity, in addition to being economically viable, has become a main research focus [1]. High-energy-density batteries are considered to be one of the most efficient ways to store energy. Lithium–sulfur (Li–S) batteries are one of the most promising candidates for the next generation of batteries due to their characteristics of cost efficiency, natural abundance, environmental friendliness, and a high theoretical energy density of 2500 W h kg⁻¹ (or 2800 W h L⁻¹) [2]. Furthermore, all-solid-state lithium batteries (ASSLBs) have shown superior performance compared to liquid electrolyte batteries, as ASSLBs are more stable and less flammable. However, the interface problem between materials arises, where the formation of Li dendrites or by-products, in addition to interfacial defects, can hinder proper functioning [3].

In this scenario, the choice of solid electrolyte is important given the low fluidity and insufficient wettability of the ASSLBs. No matter how high the ionic conductivity of the solid electrolyte is, the distribution of active materials, solid electrolytes, and electrically conductive materials must be homogeneous in the electrodes to obtain solid-state cells with high levels of performance [4]. Among sulfide-type electrolytes, β-Li₃PS₄ (LPS) stands out for its high ionic conductivity (3.0 × 10⁻² Scm⁻¹ at 573 K) [5]. Unfortunately, the interface between LPS and the Li anode is not electrochemically stable, and the decomposition of the electrolyte into Li₂S and Li₃P affects Li transport, increasing cell resistivity. A possible solution for this problem is to insert a functional buffer layer between the LPS electrolyte and the Li anode, preserving the cell components and their properties. Li₂S seems to be one of the best choices given its electrochemical inertness with respect to Li metal and the stability of the LPS/Li₂S and Li₂S/Li interfaces [6,7,8].

The Raman spectrum is a useful tool for identifying the chemical composition of materials and determining the degree of purity based on the appearance (disappearance) of the characteristic vibrational mode peaks of the product (reactant) after synthesis is complete. This non-invasive technique allows one to investigate the chemical nature of components in both ex situ and in situ conditions. In ASSLBs, Raman spectroscopy has also been employed to monitor the evolution of interfaces within practical electrode composites after or during electrochemical treatment [9,10,11]. In particular, the LPS/Li₂S interface can be characterized through Raman spectroscopy, taking into account the effects of electrochemical cycling. Identifying characteristic peaks in Raman spectra is key to understanding whether precursors have reacted to form the LPS/Li₂S interface and for determining whether undesired degradation products or Li₂S₂ clusters have been formed [12,13,14,15,16].

Therefore, in this paper, we theoretically discuss the Raman spectra for the (100) LPS and (110) Li₂S surfaces and the interfaces formed by modulating the Li₂S and LPS content in the heterostructure. For the first time, the simulated Raman spectra of β-LPS and Li₂S surfaces have been reported. DFT hybrid calculations carried out with the CRYSTAL23 program [17] were applied in order to precisely characterize this stable interface, whose structure has been already described in a previous publication [6]. Specific spectral features will be identified and related to the atomic structure and the local environment (thickness of the slabs).

2. Materials and Methods

The density functional theory (DFT) approach was combined with the hybrid PBE0 functional [18,19] and all-electron basis set 6–11G [20], 86–311G* [21], and 85–211dG [22] for Li, S, and P, respectively, as implemented in the CRYSTAL program.The adopted computational approach, which was already applied in our previous studies [6,23], has provided structures and energies in good accordance with data available in the literature. The accuracy of the truncation criteria for the bi-electronic integrals, Coulomb, and HF exchange series was controlled by a set of five thresholds with values of [8, 8, 8, 8, 16]. The reciprocal space was sampled according to a sublattice with shrinking factor 8, corresponding to 25 independent k-points in the irreducible part of the Brillouin zone. The LPS/Li₂S heterostructures are completely relaxed in order to avoid the appearance of imaginary frequencies caused by geometrical constraints.

Adhesion energy ($E_{adh}$) is a key parameter for evaluating the interaction and stability of interfaces between solid materials, calculated according to the following equation:

$$E_{adh}={\displaystyle \frac{E_{interface}-{(E}_{Li2S}+E_{LPS})}{A}}$$

(1)

where $E_{interface}$ is the total energy of the heterostructure, A is the surface area of the interface, and $E_{{Li}_{2}S}$ and $E_{LPS}$ are the total energies of the two structures relaxed at the lattice parameters defining the interface. All $E_{adh}$ values have been corrected for basis set superposition error (BSSE) using the counterpoise method [24]. The BSSE correction does not exceed +3.55 meV/Ų for PBE0 and +2.95 meV/Ų for MN15. Both components are therefore either stretched or compressed during the interface formation process, and the energy cost for this deformation defines the strain energy (per surface unit), $E_{strain}$, which has to be taken into account for a proper estimate of the overall stability of the composite. $E_{strain}$ was computed as

$$E_{strain}({\mathrm{L}\mathrm{i}}_2\mathrm{S};\mathrm{L}\mathrm{P}\mathrm{S})={\displaystyle \frac{E_{({\mathrm{L}\mathrm{i}}_2\mathrm{S};\mathrm{L}\mathrm{P}\mathrm{S})}-E_{({\mathrm{L}\mathrm{i}}_2\mathrm{S};\mathrm{L}\mathrm{P}\mathrm{S})}^{\mathit{\text{'}}}}{2A}}$$

(2)

where $E_{({\mathrm{L}\mathrm{i}}_2\mathrm{S};\mathrm{L}\mathrm{P}\mathrm{S})}^{\prime }$ is the energy of the fully relaxed LPS or Li₂S.

As in previous studies [25,26], to better estimate noncovalent interactions involved in the interface formation, energy estimates have also been made by using the Minnesota hybrid functional (MN15) [27] by computing single-point energy calculations on the PBE0 optimized structures.

The vibrational frequencies at the Γ point were computed within the harmonic approximation by diagonalizing the mass-weighted Hessian matrix of the second derivatives of the total energy per cell with respect to the pair of atomic displacements in the reference cell. Once the vibrational frequencies are calculated, the Raman intensities and the simulated Raman spectra can also be obtained. A temperature of 298 K is considered, along with laser wavelengths selected to recreate experimental conditions, with 632.8 nm for LPS, 488.0 nm for Li₂S, and 532.0 nm for the interfaces [28,29,30]. More details on the computational vibrational frequencies calculated with the CRYSTAL program can be found in Ref. [31].

3. Results and Discussion

3.1. Bulk and Isolated Surfaces

Before discussing the modifications in the Raman spectra of the β-LPS/Li₂S heterostructures, we first examine the Raman spectra of the pristine bulk and surface structures, previously presented and characterized in Ref. [6]. To our knowledge, this is the first time the Raman spectrum of the (100) surface of β-LPS has been computed.

Figure 1a–c shows the Raman spectra of the bulk and (100) surface β-LPS with four and eight layers (4L and 8L). Both the general shape of the spectra and the position of the characteristic peak of the [PS₄]³⁻ vibration at ~425 cm⁻¹ agree well with previous experimental and theoretical studies on bulk LPS [12,15,28,30,32]. This characteristic peak presents similar intensities in both the bulk and surface structures. In the [PS₄]³⁻ tetrahedron, the P–S bonds are covalent, and the overall structure is only moderately affected by the surrounding chemical environment. This limited influence is also reflected in the corresponding Raman features, which exhibit minimal variation. In addition to the intense main peak at 425 cm⁻¹, the Raman spectra of both bulk and surface LPS also exhibit several signals in the 500–600 cm⁻¹ range. These features are associated with vibrational modes involving the P–S within the PS₄ tetrahedral units. At lower frequencies, additional peaks are observed, which are primarily attributed to the vibrational contributions of Li–S bonds present in the broader framework of the material. The complete description of vibrational modes, symmetry, and intensity are shown in Table S1.

When comparing the calculated Raman spectrum of bulk LPS with the experimental spectrum presented in Figure 1a, it is essential to emphasize that the peaks observed in the theoretical spectrum result from an idealized, perfectly ordered, and defect-free simulated structure. Conversely, the experimental sample exhibits a certain degree of structural disorder and defects (or are related to impurities during the synthesis), which leads to the broadening and attenuation of these peaks, making them less distinct and more challenging to resolve.

The Raman spectrum for the bulk Li₂S has also been widely discussed in several articles in the literature [12,33], but to our knowledge, the experimentally acquired Raman spectrum for the (110) Li₂S surface has not been reported. In contrast to LPS, Li₂S exhibits a more pronounced difference between bulk and surface Raman spectra. The Raman spectrum of the bulk structure is characterized by a single peak at approximately 389 cm⁻¹, which corresponds to Li–S stretching vibrations, as shown in Figure 1c. This well-defined feature reflects the high symmetry and long-range order of the crystalline bulk material. At the surface, however, the situation changes significantly. The reduced symmetry and increased degrees of freedom for the Li–S bonds lead to a splitting of at 389 cm⁻¹ and the appearance of additional low-intensity peaks, particularly at lower and higher frequencies. These spectral changes are a direct consequence of structural rearrangements and local distortions confined to the outermost layers. As the number of layers increases, the Raman spectrum of the surface begins to resemble that of the bulk: the peaks gradually merge and become more defined, indicating a progressive restoration of the bulk-like crystallinity (compare the spectra reported in Figure 1e–h). For example, in the 36L_Li₂S system, Figure 1h, the original 389 cm⁻¹; peak is split into three components (at 390, 391, and 392 cm⁻¹), and additional features appear around 344 cm⁻¹ and 520 cm⁻¹. These are attributed to S–Li–S bending, Li–S stretching, and mixed modes activated by surface symmetry breaking and to the Li–S–Li vibrational modes involving mainly the topmost surface layers (see Table S2 for more details).

3.2. LPS/Li₂S Heterostructure

After having identified the characteristic Raman peaks of each material and their isolated surfaces, we can proceed to analyze the LPS/Li₂S heterostructures. As previously discussed, these materials are widely employed in sulfur-based solid-state lithium batteries. Their interface commonly arises either at the cathode/solid-electrolyte boundary [34] or when Li₂S is used as a protective layer for the lithium anode in contact with LPS [6,7,8]. In this context, understanding and identifying the features of the interface is essential to evaluating the behavior and stability of the system. Previous studies [6] conducted by our group have examined the LPS/Li₂S interface particularly under conditions where only a limited amount of Li₂S was introduced (4L of Li₂S was considered). The results showed that the interface is chemically and mechanically stable, indicating a good intrinsic compatibility between the two materials.

Based on this, we decided to analyze the same interface (100)LPS/(110)Li₂S, its stability, and its Raman spectrum profile, taking into account different amounts of LPS and Li₂S. We simulated the following interfaces:

(1)

8L of LPS with 12L of Li₂S (8L_LPS/12L_Li₂S);

(2)

4L of LPS with 12L of Li₂S (4L_LPS/12L_Li₂S);

(3)

4L of LPS with 24L of Li₂S (4L_LPS/24L_Li₂S);

(4)

4L of LPS with 36L of Li₂S (4L_LPS/36L_Li₂S);

(5)

8L of LPS with 36L of Li₂S (8L_LPS/36L_Li₂S).

The optimized interface models are shown in Figure 2 and Figure S1, and their adhesion energies are shown in

Table 1. E_adh and E_strain (meV/Ų) of all interface models computed as in Equations (1) and (2). a and b represent the cell parameters of the surfaces and interfaces.

	a	b	Estrain (Li2S)	Estrain (LPS)	${\mathit{E}}_{\mathit{a}\mathit{d}\mathit{h}}$	${\mathit{E}}_{\mathit{a}\mathit{d}\mathit{h}}$
PBE0						MN15
(110)Li2S	5.70	8.06	-	-	-
(100)LPS	6.23	8.28	-	-	-
4L_LPS/12L_Li2S	5.82	8.04	1.39	7.36	−29.15	−48.32
8L_LPS/12L_Li2S	5.88	8.05	4.03	5.29	−28.79	−47.81
4L_LPS/24L_Li2S	5.82	8.04	0.33	7.45	−27.76	−50.54
4L_LPS/36L_Li2S	5.82	8.04	1.02	7.50	−31.23	−48.99
8L_LPS/36L_Li2S	5.88	8.06	0.74	5.34	−29.12	−47.82

. According to our results, the content of Li₂S and LPS at the interface has little effect on its chemical and mechanical stability, the E_adh values are between –27 and –31 meV/Ų, and only slight structural changes are observed, mostly confined to the interfacial region, with the non-interfacial layers remaining largely unaffected. The 4L_LPS/36L_Li₂S and 8L_LPS/36L_Li₂S models present a reduction in ~1 meV/Ų in E_adh, which may be due to the high structural stability of Li₂S that is mostly undisturbed by the presence of LPS and that recovers its bulk structure after the first 12 layers. Although the MN15 functional yields significantly larger energy values (ranging from –47 to –50 meV·Å⁻²), the predicted stability order of the heterostructures remains consistent with that computed using the PBE0 functional. The stability of the heterostructures can be assed evaluating the work of adhesion [35,36,37], W_adh = –(E_adh + E_strain). W_adh quantifies the energy required to separate the heterostructure into two isolated slabs, accounting for both the adhesion energy and the strain induced by heterostructure formation. In all the heterostructure examined in this work, E_strain is only a fraction of the E_adh, indicating thermodynamic stability. As a result, a positive W_adh must be supplied to separate the interfaces. Although the computed E_adh may appear relatively small, it is important to consider that such heterostructures are likely to form under experimental conditions, as the synthesis and stability of the interface in the device involves the application of external pressure [38,39].

From now on, we will analyze the simulated Raman spectra of all interfaces. Figure 3 contains the Raman spectra for the heterostructures and, for the sake of comparison, the pristine surfaces. As can be seen in Figure 3, the characteristic peak related to [PS₄]³⁻ of LPS appears in all the Raman spectra regardless of LPS content. The intensity of this peak is not significantly affected by the formation of the interface, although a slight shift in its position is observed. In general, the vibrational peaks associated with LPS remain identifiable in the Raman spectra of the interface, showing only subtle changes in both intensity and frequency compared to the pristine LPS surface. These variations can be attributed to the relative LPS content within the interface region.

It is important to note that the vibrational modes related to LPS—particularly those associated with the [PS₄]³⁻ tetrahedral unit—exhibit much higher intensities than those originating from the Li₂S surface. As the Li₂S content increases, however, more prominent and partially degenerate Li₂S-related peaks begin to emerge. This effect is clearly illustrated by comparing the spectra of the 8L_LPS/4L_Li₂S and 8L_LPS/12L_Li₂S heterostructures (see Figure S2 and Figure 3b). In the latter, characteristic Li₂S peaks become distinguishable at approximately 365 cm⁻¹, 392 cm⁻¹, and 511 cm⁻¹, corresponding to Li–S bond stretching modes. This observation aligns with previous reports highlighting the experimental challenges in detecting Li₂S during the synthesis of Li₃PS₄. In such cases, Raman measurements often fail to capture Li₂S-related peaks following the formation of Li₃PS₄, likely due to their lower intensity and possible overlap with LPS signals [40].

In our case, significant modifications to the Raman spectra are observed for the 8L_LPS/36L_Li₂S interface, where both LPS and Li₂S are present in high concentrations. Under these conditions, the main LPS peak couples with the stretching vibrational modes of Li₂S, resulting in the formation of three distinct peaks characteristic of the interface at 435 cm⁻¹, 456 cm⁻¹, and 468 cm⁻¹. Additionally, typical Li₂S vibrations appear at the interface as a split peak at 388 cm⁻¹, a broad band around 300 cm⁻¹ due to the overlap of Li–S stretching modes from both Li₂S and LPS, and a distinct peak at 558 cm⁻¹. Notably, the region between 570 cm⁻¹ and 590 cm⁻¹ continues to display LPS-related vibrations, with no significant contribution from Li₂S modes. The details of the peaks and their descriptions are reported in Table S3 and discussed in Section S1 of Supplementary Information. The broadening and splitting of the peak around ~450 cm⁻¹ can thus be regarded as a distinctive spectroscopic fingerprint indicative of the LPS/Li₂S interface reflecting changes in local bonding environments and structural heterogeneity. The simulated spectrum likely represents the most accurate model of what would be observed experimentally in a well-formed interface with a balanced composition, providing an important reference for interpreting Raman data. This highlights the importance of detailed spectral analysis, which is essential not only for elucidating how the relative amounts of Li₂S and LPS influence the Raman spectrum but also for enabling a reliable interpretation of the experimental results.

Li₂S may be intentionally introduced to promote the formation of a stable interface with LPS, where it plays a beneficial role as a passivating coating that prevents the decomposition of LPS in contact with a lithium metal anode. However, Li₂S can also arise as an unintended residual byproduct from the synthesis of LPS. In this context, residual Li₂S impurities have been shown to adversely affect the ionic conductivity of the solid electrolyte, thereby compromising lithium metal battery performance by increasing overpotentials and shortening cycle life.

Therefore, understanding and controlling the interfacial composition through spectroscopic evaluation is essential for optimizing solid-state battery performance. According to Mirmira et al. [30], Raman spectroscopy could detect residual Li₂S in LPS samples when the impurity concentration was above 12 mol%. However, for concentrations below this threshold, Raman spectroscopy’s sensitivity diminished, making it challenging to identify smaller amounts of Li₂S impurities. They found that until 30 mol% of Li₂S in the sample, the peaks related to the Li-S vibration of Li₂S (at ~380 cm⁻¹) are evident, and then the intensity decreases with the Li₂S concentration due to the higher intensity of LPS vibrations. The same peak was also evident in the Li₂S-LPS composite obtained by Jiang and co-workers [39]. The composite structure was evaluated by Raman spectroscopy and XRD diffraction, and the authors observed that when the lithium sulfide in the starting material was excessive, such as a 45% and 62.5% mass fraction of Li₂S, the phase LPS was generated with a residual lithium sulfide, and the characteristic peaks related to LPS (at 420 cm⁻¹ related to [PS₄]³⁻ cluster) and Li₂S (at 380 cm⁻¹ attributed to Li–S–Li vibration) were apparent in the Raman spectra of the composite. Thus, the presence of these signals does not necessarily indicate the formation of a stable interface but may instead correspond to residual impurities and, even more critically, residual Li₂S may be present below the detection limit of Raman spectroscopy, making its presence difficult to identify and potentially leading to underestimated impurity levels that can adversely affect battery performance.

4. Conclusions

In this study, we performed a theoretical Raman spectra analysis to investigate the effect of Li₂S and Li₃PS₄ content on the interface formation between (110) Li₂S and (100) β-Li₃PS₄. Our results confirm that the LPS/Li₂S interface remains stable regardless of its content. However, we observed that a higher concentration of LPS complicates the spectral identification of the interface, as the intense vibrational peak of the [PS₄]³⁻ cluster overshadows the characteristic Li₂S peaks and other interface-related signals.

The analysis of heterostructures with different LPS and Li₂S contents showed that, while small amounts of Li₂S induce minimal modifications in the Raman spectrum, a significant increase in Li₂S leads to substantial spectral changes. Notably, the broadening and splitting of the peak at ~450 cm⁻¹, attributed to the coupling of [PS₄]³⁻ and Li₂S vibrations, can be considered a spectral fingerprint of the formed interface. This feature was only observed at higher amounts of LPS and Li₂S, suggesting its importance for identifying the interface experimentally.

Our findings provide valuable insights into the Raman spectral characteristics of LPS/Li₂S interfaces, emphasizing the need for careful spectral interpretation, especially when working with low Li₂S content. This study contributes to the understanding of interface formation in all-solid-state lithium batteries, which is key for optimizing their performance and stability.