All-solid-state batteries are promising candidates for use in electric vehicles, aiming to contribute to a sustainable society (Bates et al., 2022; Lu et al., 2022; Schmaltz et al., 2023). Solid electrolytes are key components in all-solid-state batteries. Intensive research efforts have been conducted on oxides, sulfides, and polymer-based electrolytes to find the most suitable for solid-state batteries. Li₃PS₄ is the most common electrolyte among sulfur-based solid electrolytes. Li₃PS₄ exhibits three temperature-dependent polymorphic forms: α-Li₃PS₄ at high temperatures, β-Li₃PS₄ at medium temperatures, and γ-Li₃PS₄ at low temperatures. The β-Li₃PS₄ phase crystallized from heat-treated Li₃PS₄ glass becomes stable at room temperature (Ohtomo et al., 2013). Glassy Li₃PS₄ and β-Li₃PS₄ stabilized in glass matrix are well-known model materials that have been employed to investigate the relationship between structure and ionic conductivity. Recently, α-Li₃PS₄ was stabilized in a glass–ceramic structure and exhibited an ionic conductivity higher than 10^–3 Scm⁻¹ at room temperature (Kimura et al., 2023).

The ionic conductivity of glassy Li₃PS₄, which is often prepared using the planetary ball milling method, is ∼3.0 × 10⁻⁴ Scm⁻¹ at room temperature (Phuc et al., 2022), and that of the well-crystalline β-Li₃PS₄ is ∼1.6 × 10⁻⁴ Scm⁻¹ (Stöffler et al., 2019). The liquid-phase synthesis of Li₃PS₄ has attracted significant attention because the formed solid electrolyte suspension or solution can be directly applied to the battery preparation process (Gamo et al., 2022; Gamo et al., 2023). Tetrahydrofuran, ethyl acetate, acetonitrile, and pyridine have been employed as synthetic media to prepare the β-Li₃PS₄ solid electrolyte (Liu et al., 2013; Phuc et al., 2016; Calpa et al., 2021; Ghidiu et al., 2021). In addition, several studies showed that Li₂S reacts with P₂S₅ in organic solvents via a multistep reaction to form a Li₃PS₄ precursor and is transformed into a Li₃PS₄ solid electrolyte after solvent elimination (Phuc et al., 2017a; Calpa et al., 2020). The ionic conductivity of the Li₃PS₄ solid electrolyte, which is prepared via a liquid-phase synthesis, is lower than that of the amorphous Li₃PS₄ obtained using planetary ball milling. This is attributed to the formation of crystalline Li₃PS₄ during solvent elimination (Takahashi et al., 2021); another reason, is solvent residue (Yamamoto et al., 2020). The ionic conductivity of a low-crystalline Li₃PS₄ solid electrolyte produced from butyl acetate is ∼5.09 × 10⁻⁴ Scm⁻¹ at 25°C, which was comparable to that of glassy Li₃PS₄ (Yamamoto et al., 2021).

Broadband dielectric spectroscopy is used to describe the dielectric dispersion and absorption phenomena due to dipole relaxation and electrical conduction over a wide frequency range (10⁻⁶–10¹² Hz), which corresponds to a timescale from a few picoseconds to hours. AC EIS is typically used for frequencies in the 10 Hz–10 MHz range. EIS is a suitable and inexpensive measurement method, which is used in low-frequency and low-impedance ranges. Therefore, it is suitable for the characterization of materials with time-dependent dielectric properties. The complex dielectric constant ε*, complex impedance Z*, complex electric modulus M*, and tangent loss (tanδ) are the frequency-dependent electrical properties of materials; these parameters can be extracted from EIS measurements and provide important knowledge about the performance of localized charge carriers in the sample. The complex conductivity, σ*, of samples was determined from the complex impedance, Z*: σ * = σ ′ + j σ ″ = l A Z * = l A Z ′ + j l A Z ″ where A (cm²) and l (cm) are the contact area and the thickness of the pellets, respectively.

In the electric modulus formalism, the complex electric modulus M*(ω) is defined by: M * = 1 ε * = ε ′ − j ε ″ ε * 2 = M ′ + j M ″ = ε ′ ε ′ 2 + ε ″ 2 − j ε ″ ε ′ 2 + ε ″ 2 ε * = ε ′ − j ε ″ = σ ′ ω ε 0 − j σ ″ ω ε 0 where ω (= 2πf, radians/second) is a radial frequency and ε₀ is the permittivity of free space.

Although several studies on the liquid-phase synthesis of the Li₃PS₄ solid electrolyte have been reported in the literature, there is still a lack of knowledge on the Li ion movement in a Li₃PS₄ solid electrolyte prepared via liquid-phase synthesis. Solvents containing ester functional groups, such as ethyl acetate, ethyl propionate, methyl propionate, and butyl acetate, have been used to synthesize Li₃PS₄ (Phuc et al., 2016; Yamamoto et al., 2021; Phuc et al., 2017b; Phuc et al., 2019). To the best of our knowledge, the synthesis of Li₃PS₄ using ethyl isobutyrate, which features the ester functional group, has not been reported in the literature. In this work, a Li₃PS₄ solid electrolyte was prepared via liquid-phase synthesis using ethyl isobutyrate (EiB) as a reaction medium, and the electrical properties of the electrolyte were investigated to understand the ionic transport mechanism in the temperature range from room temperature to 110°C.

Figure 1A shows the TG–DTA curve of the powder obtained from the reaction mixture at room temperature after solvent elimination. The DTA curve exhibits two intense endothermic peaks centered at 76°C and 132°C, respectively. Since the boiling point of EiB is ∼110°C, the DTA results indicate that EiB was chemically bonded in the sample. The TG curve exhibits a plateau starting at ∼150°C after the sample has lost ∼50% of its initial mass due to EiB evaporation. We calculated the first-order derivatives of the TG–DTA curves (inset of Figure 1A) to further analyze the TG–DTA results. The derivative of the TG curve shows that the mass loss occurs in two simultaneous steps with two endothermic troughs shown in the derivative of the DTA curve. The first step ends at ∼92°C and corresponds to ∼33% mass loss. The second occurs after that and ends at ∼150°C and corresponds to ∼17% mass loss. The estimated formulas of the sample in the first and second trough are Li₃PS₄∙1EiB and 2Li₃PS₄∙1EiB, respectively. Overall, the formula of the sample obtained after EiB removal at room temperature is 3Li₃PS₄∙2EiB. This ratio is different from that of the powder prepared using ethyl acetate (Li₃PS₄∙2 EA) and shows the effect of the organic solvent structure on the synthesis of Li₃PS₄ (Phuc et al., 2016). The TG–DTA results show that the appropriate temperature for removing EiB from the precursor to obtain the Li₃PS₄ solid electrolyte is 170°C. Thus, the samples were heat treated at 170°C for 1 h and cooled down naturally at room temperature to obtain EiB Li₃PS₄.

Figure 1B shows the XRD patterns of the precursor and EiB Li₃PS₄. The 3Li₃PS₄∙2EiB pattern exhibits many peaks; thus, it cannot be assigned to any known phases. In addition, this pattern resembles that of the Li₃PS₄ precursor, which was prepared using ethyl propionate (Phuc et al., 2017b). The EiB Li₃PS₄ pattern can be matched with that of β-Li₃PS₄. This is consistent with the structure of the liquid-phase synthesized Li₃PS₄ solid electrolyte (Calpa et al., 2021; Takahashi et al., 2021). Therefore, we conclude that EiB was effectively removed after heat treatment at 170°C for 1 h.

Figure 2A shows the frequency dependence of the real part σ′ of the complex conductivity of EiB Li₃PS₄. The conductivity isotherms of the sample exhibits temperature dependence. The conductivity isotherms had electrode polarization at low frequencies, polarization conductivity at high frequencies, and a plateau in the intermediate frequency region. Electrode polarization is caused by the accumulation of ions at the blocking electrodes (Preishuber-Pflugl and Wilkening, 2016). The conductivity in the intermediate frequency region can be expressed as σ = σ_DC + A ω^k (Jonscher power law), where σ_DC is the direct current (DC) conductivity, A is a pre-factor, and k is the frequency exponent in the 0 < k < 1 range (Jonscher and White, 1979; Funke, 1997). The DC conductivity exhibits long-range ion transport and temperature dependence of σ_DC, indicating that the charge carrier concentration increases with temperature. σ_DC was obtained for each temperature by fitting the conductivity curves using the above equation. Figure 2B shows the fitting result of conductivity measured at room temperature. It could be seen that the conductivity of the sample followed Jonscher power law.

The relaxation process is the result of the transition from correlated to uncorrelated ion hopping. The electric modulus represents the relaxation of the electric field in a material with a constant electric displacement. The variation of the imaginary part M″ of the complex modulus of EiB Li₃PS₄ against frequency is shown in Figure 3A. The conductivity becomes very high at high temperatures (above 90°C), and the peaks are not fully visible. The region on the left of F_max (which is equal to the inverse relaxation time) shows the movement of charge carriers, and the region on the right is the region where ions are spatially confined within their potential wells. The Li ion movement in EiB Li₃PS₄ is observed in the 10⁵–10⁷ Hz and 10²–10⁵ Hz frequency regions. The relaxation time t_M″ is defined as the most probable conductivity relaxation time of the ions. The dependence of inverse relaxation time (t_M'' ⁻¹ = F_max) on the inverse temperature is shown in Figure 3B. The activation energy for relaxation at low- and high-frequency regions are 0.39 and 0.10 eV, respectively.

Figure 4 shows the dependence of the real part of the dielectric constant ε′ of EiB Li₃PS₄ on frequency for different temperatures. In all plots, the increase in the low-frequency region can be attributed to the electrode–electrolyte interface polarization due to the accumulation of ions near the electrode; this leads to the formation of the space charge layer, which, in turn, blocks the electric field and enhances the electrical polarization. The dielectric constant decreases with frequency. In all samples, ε′ increases with temperature, indicating that the charge carrier movement is thermally activated. The EiB Li₃PS₄ plots at room temperature, 50°C, and 70°C exhibit a continuously decreasing trend in the intermediate and high-frequency regions. The maxima are observed at 90°C and 110. The change in the shape of the ε′ plots indicates a change in the EiB Li₃PS₄ microstructure and this process was temperature dependence.

Figure 5A shows the dependence of the DC conductivities of EiB Li₃PS₄ on the inverse temperature. Both the bulk and grain boundary (denoted as GB) resistances contribute to the σ_DC value. It was observed that log₁₀ (σ_DC) follows the Arrhenius equation σ_DC = σ₀ exp (−E_a,DC/[k_B T]). The ionic conductivities of EiB Li₃PS₄ at 25°C was about 6.8 × 10⁻⁵ Scm⁻¹ and the activation energy was about 36 kJ mol⁻¹. The ionic conductivity of EiB Li₃PS₄ obtained in this study is of the same order as that of β-Li₃PS₄ prepared using pyridine (Ghidiu et al., 2021). The activation energy value obtained from the dependence of the relaxation time on temperature in the low-frequency region (Figure 3B) was close to the conduction value, indicating that the activation energy for the Li ion movement in the GB is the main component of the DC activation energy. Those results indicated that the GB resistance was the main issue in the EiB Li₃PS₄ ionic conductivity at room temperature; thus, the pellet of this sample was warm-pressed at 170°C and 60 MPa for 1 h to reduce the GB resistance. The temperature dependence of the ionic conductivity of the cold-pressed and warm-pressed pellets is shown in Figure 5B and denoted as ‟cold-pressed” and ‟warm-pressed,” respectively. We observed that the ionic conductivity at 25°C had been significantly improved from 6.8 × 10⁻⁵ to 3.6 × 10⁻⁴ Scm⁻¹. The activation energies for the Li ion movement in the cold-pressed and warm-pressed pellets are 0.373 eV and 0.24 eV, respectively. The resistance components of the cold-pressed and warm-pressed pellets were double checked using the distribution relaxation time (DRT) (Wan et al., 2015). The Nyquist plots with small inset showing equivalent circuit model and DRT spectra of the cold-pressed and warm-pressed EiB Li₃PS₄ pellets measured at room temperature are shown in Figures 5B, C, respectively. Each of the DRT spectra of the cold-pressed and warm-pressed pellets exhibit two peaks located in the low- and high-frequency regions, indicating the contribution of GB and bulk resistances to the ionic conductivity of the samples. The insets in Figure 5C show the contributions of GB and bulk resistances to the total resistance of each sample. The GB resistance contribution to the total resistance of the cold-pressed pellet is ∼27%; however, that of the warm-pressed pellet is ∼15%. The ratio between GB resistances in warm-pressed and cold-pressed pellets was about 15%. The ratio between bulk resistances in warm-pressed and cold-pressed pellets was about 79%. Thus, the warm pressing process reduced most of the resistance at the grain boundary.

A Li₃PS₄ solid electrolyte was successfully prepared using EiB as a synthetic medium. The TG results showed that the formula of the solid electrolyte precursor was 3Li₃PS₄∙2EiB. β-Li₃PS₄ was obtained after solvent elimination from the precursor at 170°C. The ionic conductivity of the cold-pressed pellet at 28°C was ∼6.8 × 10⁻⁵ Scm⁻¹. The conductivity of the warm-pressed pellet at 25°C was ∼3.6 × 10⁻⁴ Scm⁻¹, which was close to that of glassy Li₃PS₄. Two relaxation peaks at low and high frequencies indicated the concept of GB and bulk conduction. The relaxation activation energy was close to the activation energy obtained from the DC conductivity, indicating that the lithium-ion movement was responsible for both the ionic conduction and the relaxation process.