Sodium-Ion Conducting Solid Electrolytes in the Na₂S–In₂S₃ System

Abstract

The development of solid electrolytes is necessary for practical applications of all-solid-state Na-ion batteries. In this study, we systematically developed sulfide Na-ion conductors with central In cations, prepared by solid-state reaction and mechanochemical methods. Thermodynamically stable crystals of Na₅InS₄ and NaInS₂ were obtained by the solid-state reaction method, whereas amorphous and/or metastable phases were produced by the mechanochemical method. Two new metastable phases, Na₅InS₄ and NaInS₂, are expected to be examined in the future as end-members of sulfide Na-ion conductors with central In cations.

1. Introduction

Solid electrolytes are key materials used for the construction and performance improvement of energy devices. Sulfides used as solid electrolytes exhibit advantageous properties, including high ionic conductivity and good formability.¹ In particular, sulfide Li-ion conductors Li₁₀MP₂S₁₂ (M = Ge, Sn), Li₂S–P₂S₅, and Li₆PS₅X (X = Cl, Br, I) exhibit high ionic conductivity.^2–7 Among the sulfide Na-ion conductors, Na_2.88Sb_0.88W_0.12S₄, Na₃PS₄, and Na₁₁Sn₂PS₁₂ are also characterized by high ionic conductivity, and W-doped Na₃SbS₄ exhibits the highest electrical conductivity of 3.2 × 10⁻² S cm⁻¹ at room temperature.^8–11 The substitution of W for Sb in the end-member Na₃SbS₄ generates Na-ion vacancies and increases the structural symmetry. Additionally, replacing S by Cl in Na₃SbS₄ results in an improvement in the electrochemical stability and ionic conductivity.^12,13 As an alternative to improve the electrical conductivity and electrochemical stability of solid electrolytes and suppress H₂S gas generation, cation and anion substitutions (cations: Si, Ge, Sn, Mo, W; anions: Br, Cl) of end-member crystalline electrolytes have been investigated,^14–17 resulting in the development of several solid electrolytes. Thus, identifying suitable end-members is important for the development of solid electrolytes with excellent properties such as high electrical conductivity.

The conductivities of major sulfide Na-ion conductors with central cations containing elements from groups 13, 14, and 15 are listed in Table 1.^8,18–27 For elements of group 13, the synthesis of In-containing compounds, such as Na₅InS₄ and NaInS₂, has been previously reported;^28,29 however, their electrical conductivities have not been determined yet. Because sulfide Na-ion conductors with elements of group 13 (B, Al, and Ga) as central cations are utilized as ionic conductors, similar compounds consisting of central In cations from the same group can also be potentially used for the same purpose.

Table 1. Electrical conductivities of various compounds with central cations containing elements from groups 13, 14, and 15.

Group	Element	Compound	State	Conductivity/S cm−1	Ref.
13	Boron	Na3BS3	Glass	1.1 × 10−5	18
	Aluminum	Na5AlS4	Crystal	3.2 × 10−7	19
	Gallium	80Na2S·20Ga2S3	Glass	1.9 × 10−6	20
	Indium	—	—	—
14	Silicon	Na4SiS4	Glass	2.0 × 10−5	21
	Germanium	60Na2S·40GeS2	Glass	7.3 × 10−6	22
	Tin	Na4SnS4	Crystal	1.4 × 10−8	23
15	Phosphorus	Na3PS4	Glass-ceramic	2.0 × 10−4	8
	Arsenic	Na3AsS4	Crystal	3.1 × 10−6	24
	Antimony	Na3SbS4	Crystal	1.0–3.0 × 10−3	25–27

In this study, sulfide Na-ion conductors with central In cations were systematically synthesized. Na₅InS₄ and NaInS₂ were prepared using the solid-state reaction (SSR) method, and their electrical conductivities were determined. In addition, solid electrolytes in the Na₂S–In₂S₃ system were synthesized using a mechanochemical method and characterized.

2. Experimental

2.1 Sample preparation

Na₂S (>99.1 %, Nagao, Japan) and In₂S₃ (99.99 %, Kojundo Chemical Laboratory Co., Ltd., Japan) powders were used to prepare Na₅InS₄ and NaInS₂ compounds by the SSR method. These reagents were mixed at stoichiometric ratios under an Ar atmosphere. The obtained mixture was pelletized, placed in a carbon crucible, and heated at 700 °C for 12 h in a quartz ampoule sealed under vacuum.

xNa₂S·(100 − x)In₂S₃ (x = 50, 60, 70, 75, 80, 83, and 90) samples were prepared using a mechanochemical method with a planetary ball mill apparatus (Pulverisette 7, Fritsch Japan Co. Ltd., Japan) with zirconia pots (volume: 45 mL) and zirconia balls (diameter: 4 mm, mass: 50 g). The total mass of the starting material in each pot was 0.5 g, and the rotational speed and milling duration were 510 rpm and 10 h, respectively.

2.2 Characterization

The obtained powder samples were characterized by X-ray diffraction (XRD) using CuKα radiation (Smart Lab, Rigaku, Japan). The crystalline structures were refined using SmartLab Studio II (SLS2) software (Rigaku, Japan), and the XRD pattern of the 83Na₂S·17In₂S₃ (mol%) sample prepared by the mechanochemical method was refined using the Rietveld method implemented in the software package RIETAN-FP.³⁰ The crystal model was obtained using VESTA software.³¹

The obtained samples were mixed with the reference Al₂O₃ sample at weight rations of 5 : 5 or 9 : 1, followed by XRD measurements. The weight ratio of each sample was obtained by a reference intensity ratio (RIR) method with whole powder pattern fitting (WPPF) using SLS2 software.

The densities of the compact samples (d₁) were calculated from the weight and volume of the pellets, and those of the powders (d₂) were measured using a gas pycnometer (AccuPyc II 1340, Shimadzu, Japan). The relative density is defined as d₁/d₂.

2.3 Electrochemical impedance spectroscopy

The powder samples obtained were pelletized at 360 MPa by uniaxial pressing. The Au thin-film electrodes were sputtered on both sides of the dense pellets. Electrical conductivities were measured by two-terminal AC electrochemical impedance spectroscopy in the temperature range of 23–67 °C at an amplitude of 10–100 mV and frequency of 1.0 × 10⁷–1 Hz using an impedance analyzer (Solatron 1260, Solartron Metrology, UK). Each pellet was sealed in a laminate-type pouch cell under vacuum to prevent air exposure.

3. Results and Discussion

Figure 1 shows the XRD patterns of Na₅InS₄ and NaInS₂ prepared using the SSR method and xNa₂S·(100 − x)In₂S₃ (x = 50, 60, 70, 75, 80, 83, and 90) synthesized using the mechanochemical method. The XRD patterns of the SSR samples were indexed to the P2₁/m space group (ICSD 300175) for Na₅InS₄ and $R\bar{3}m$ group (ICSD 25557) for NaInS₂, indicating that the target crystalline materials were successfully obtained. The samples prepared by the mechanochemical method exhibited broad XRD peaks owing to the presence of an amorphous phase. In addition, the x = 90 sample demonstrated a halo pattern and contained a fraction of the Na₂S reagent. The XRD patterns of the samples with x = 83 and x = 80 exhibited broad peak similar to those of crystalline Na₅InS₄, which can be attributed to the metastable phase with a higher symmetry of crystalline Na₅InS₄. To examine the crystalline structure of this phase, the XRD pattern of the sample with x = 83 was refined using the Rietveld method. The refinement data obtained are presented in Fig. 2a and Table 2, and the resulting crystal structure model is shown in Fig. 2b. The structural optimization of the new metastable phase produced a monoclinic crystal structure. The measured and calculated XRD patterns (marked by the red and light blue lines, respectively) were in good agreement, as indicated by their difference spectrum (blue line). The metastable phase contained octahedral Na sites and tetrahedral Na and In sites, suggesting that the cations located at the tetrahedral sites were mixed. The crystal structure data obtained in this study are the average structural information. To obtain detailed structural information (e.g., bond lengths, interatomic distances, and etc.), further structural analyses using neutron diffraction and/or synchrotron XRD are required.

Figure 1.

XRD patterns of the xNa₂S·(100 − x)In₂S₃ samples prepared using the SSR and mechanochemical methods.

Figure 2.

Crystal structure analysis of 83Na₂S·17In₂S₃. (a) X-ray Rietveld refinement profile of the 83Na₂S·17In₂S₃ sample prepared by the mechanochemical method. (b) Schematic diagrams of the 83Na₂S·17In₂S₃ crystal structure.

Table 2. Crystal parameters and atomic coordinates of the 83Na₂S·17In₂S₃ metastable phase.

Crystal system	Monoclinic
Space group	P2
Lattice parameters	a = 6.798(24) Å, b = 4.465(16) Å, c = 7.744(28) Å, β = 90.0(1)°, Z = 2
Volume	V = 235.055(1456) Å3

Atoms	x	y	z	Site	Occupancy	U/Å2
Na1	0.359(4)	0	1/3	2e	0.823(7)	0.045(8)
In1	= x(Na1)	0	1/3	2e	= 1 − g(Na1)	= U(Na1)
Na2	0	1/2	1/2	1b	1	0.108(4)
Na3	0.646(3)	1/2	0.170(3)	2e	= 1.5 − g(Na1)	0.040(5)
In3	= x(Na3)	1/2	= z(Na3)	2e	= g(Na1) − 0.5	= U(Na3)
Na4	0	0	0	1a	1	= U(Na2)
S1	1/4	0	2/3	2e	1	0.046(13)
S2	1/4	1/2	1/6	2e	1	0.048(12)

*R_wp = 1.33, R_F = 6.199, R_B = 5.805, S = R_wp/R_e = 1.489.

The XRD pattern of the x = 75 sample contained a halo owing to the formation of an amorphous phase. For the x = 70 sample, unknown peaks were observed, in addition to the peaks detected for the x = 83 sample. The XRD patterns of the x = 60 and x = 50 samples were indexed to space group $Fm\bar{3}m$. This structure differed from the previously reported structure of the thermodynamically stable NaInS₂ phase, and the observed pattern was attributed to the presence of a cation-disordered metastable phase.

The Nyquist plot obtained for the x = 75 sample at 26.2 °C is shown in Fig. 3a, and the temperature dependences of the electrical conductivities of the prepared Na₂S–In₂S₃ samples are presented in Fig. 3b. Table 3 lists the electrical conductivities, activation energies, densities of pellets (d₁) and powders (d₂), and relative densities (d₁/d₂) of the fabricated Na₂S–In₂S₃ samples. As shown in Fig. 3a, the Nyquist plot consisted of a semicircle in the high-frequency region and a sharp spike in the low-frequency region, suggesting that the prepared sample was a typical ionic conductor. The total resistance (R_total) of the sample, including the bulk and grain boundary resistances, was used to determine its conductivity. By comparing the electrical conductivities of the samples obtained by the SSR and mechanochemical methods at x = 83 and x = 50, the conductivities of the mechanochemically prepared samples were higher than those of the SSR samples. These results suggest that metastable and/or amorphous phases are more favorable for ionic conduction than the thermodynamically stable phase. The stable NaInS₂ phase (x = 50) prepared by SSR method exhibited a layered structure, whereas the mechanochemically prepared metastable phase (x = 50) had a cubic structure. The improved symmetry of the crystalline phase changed the ionic conduction pathway from two to three dimensions, which is considered to be the reason for the improved conductivity in the metastable phase. The electrical conductivity of the SSR sample with x = 83 was approximately three orders of magnitude higher than that of the SSR sample with x = 50. The electrical conductivities of the mechanochemically prepared samples were maximized at x = 75, reaching a value of 6.8 × 10⁻⁶ S cm⁻¹ at 25 °C. Except for the x = 50 sample, the electrical conductivities of most of the mechanochemically prepared samples were approximately 10⁻⁶ S cm⁻¹. According to the XRD patterns obtained, the mechanochemically prepared samples with high electrical conductivities contained both amorphous and metastable phases (Fig. 1). To investigate the effect of these phases on the electrical conductivity, we used the RIR method with WPPF to estimate the weight ratios of the amorphous phase in the studied samples. The volume ratio of the prepared samples was calculated from the results of the RIR method with WPPF and the obtained density, d₂. For the sample with x = 70, this experiment could not be performed owing to the presence of unidentified peaks. The XRD pattern of the x = 75 sample contained a halo pattern (Fig. 1), suggesting that this sample was dominated by the amorphous phase. Although there may be nano-sized crystals that cannot be detected by XRD, we will treat the x = 75 sample as 100% amorphous in this study. Table 4 lists the volume ratios of the amorphous phases of the mechanochemically prepared xNa₂S·(100 − x)In₂S₃ (x = 50, 60, 75, 80, 83, and 90) samples. The volume ratios of the amorphous phases in the x = 60–90 samples were approximately 70% or higher, whereas that of the x = 50 sample was only 17%. The x = 60–90 samples containing the amorphous phase as the main component exhibited higher electrical conductivities (Fig. 3b), indicating that this particular phase considerably contributed to the ionic conductivity. Amorphous electrolytes have an open structure that allows carrier ions to move three-dimensionally, achieving high ionic conductivity by increasing the number of mobile carrier ions.^20,32 Thus, the x = 60–90 samples containing Na-rich amorphous phases showed higher conductivity. The conductivity varied with the amorphous ratio in the samples because phases other than the amorphous phase partially prevented ionic conduction. For these reasons, the highest conductivity was achieved for the amorphous x = 75 sample.

Figure 3.

(a) Nyquist plot of 75Na₂S·25In₂S₃ measured at 26.2 °C. (b) Temperature dependences of the electrical conductivities of the xNa₂S·(100 − x)In₂S₃ samples prepared using the SSR and mechanochemical methods.

Table 3. Electrical conductivities, activation energies, densities of pellets (d₁) and powders (d₂), and relative densities (d₁/d₂) of the prepared xNa₂S·(100 − x)In₂S₃ samples.

x /mol%	σ25°C	Ea /eV	d1 /g cm−3	d2 /g cm−3	Relative density /%
90	5.2 × 10−6	0.48	1.83	2.25	81.1
83	4.6 × 10−6	0.47	1.95	2.52	77.4
83 (SSR)	1.2 × 10−8	0.61	2.23	2.56	87.2
80	6.1 × 10−6	0.39	2.08	2.60	79.9
75	6.8 × 10−6	0.44	2.14	2.76	77.3
70	1.5 × 10−6	0.38	2.22	2.91	76.4
60	6.3 × 10−7	0.51	2.40	3.25	73.9
50	1.5 × 10−10	0.66	2.40	3.89	61.7
50 (SSR)	1.4 × 10−11	0.61	3.09	4.09	75.5

Table 4. Amorphous volume ratios of the mechanochemically prepared xNa₂S·(100 − x)In₂S₃ (x = 50, 60, 75, 80, 83, and 90) samples.

x/mol%	Amorphous ratio/vol%
90	74
83	68
80	93
75	100*
60	74
50	17

*The estimated amorphous ratio of the x = 75 sample was 100% because its XRD pattern contained a halo pattern.

4. Conclusion

The structures and conductivities of Na-ion conductors xNa₂S·(100 − x)In₂S₃ were systematically examined in this study. Na₅InS₄ and NaInS₂ were synthesized using SSR and mechanochemical methods. In addition, the previously reported structures of Na₅InS₄ and NaInS₂ were obtained using SSR method. The x = 60–90 samples prepared using the mechanochemical method were mainly amorphous and contained two new metastable phases. The metastable phases in the x = 80 and x = 83 samples consisted of monoclinic crystals with partially disordered cations. The other metastable phase formed in the x = 50 and x = 60 samples represents a cation-disordered rock-salt structure. The ionic conductivity of the studied samples reached a maximum value of 6.8 × 10⁻⁶ S cm⁻¹ at x = 75 and temperature of 25 °C, indicating that the amorphous phase mainly contributed to the high conductivity of the prepared compounds. Moreover, the newly developed metastable phases can serve as the end-members of sulfide Na-ion conductors with central In cations, whose ionic conductivity can be enhanced by cation and/or anion substitution.

Acknowledgments

This study was supported by JSPS KAKENHI (Grant Nos. 19H05816 and 21H04701).

CRediT Authorship Contribution Statement

Kota Motohashi: Conceptualization (Lead), Data curation (Lead), Investigation (Lead), Writing – original draft (Lead)

Akira Nasu: Investigation (Supporting), Resources (Supporting)

Takuya Kimura: Formal analysis (Supporting), Resources (Supporting), Software (Supporting)

Chie Hotehama: Investigation (Supporting), Software (Supporting)

Atsushi Sakuda: Validation (Equal), Writing – review & editing (Equal)

Masahiro Tatsumisago: Visualization (Supporting), Writing – review & editing (Supporting)

Akitoshi Hayashi: Funding acquisition (Lead), Supervision (Lead), Writing – review & editing (Lead)

Conflict of Interest

The authors declare no conflict of interest in the manuscript.

Funding

JSPS: KAKENHI 19H05816 and 21H04701

Footnotes

K. Motohashi, A. Sakuda, M. Tatsumisago, and A. Hayashi: Presently, Osaka Metropolitan University

K. Motohashi, A. Sakuda, and A. Hayashi: ECSJ Active Members

A. Nasu and T. Kimura: ECSJ Student Members

M. Tatsumisago: ECSJ Fellow

References

• 1)  A. Sakuda, A. Hayashi, and M. Tatsumisago, Sci. Rep., 3, 2261 (2013).
• 2)  N. Kamaya, K. Homma, Y. Yamakawa, M. Hirayama, R. Kanno, M. Yonemura, T. Kamiyama, Y. Kato, S. Hama, and K. Kawamoto, Nat. Mater., 10, 682 (2011).
• 3)  P. Bron, S. Johansson, K. Zick, J. Schmedt auf der Günne, S. Dehnen, and B. Roling, J. Am. Chem. Soc., 135, 15694 (2013).
• 4)  F. Mizuno, A. Hayashi, K. Tadanaga, and M. Tatsumisago, Adv. Mater., 17, 918 (2005).
• 5)  Y. Seino, T. Ota, K. Takada, A. Hayashi, and M. Tatsumisago, Energy Environ. Sci., 7, 627 (2014).
• 6)  H. J. Deiseroth, S. T. Kong, H. Eckert, J. Vannahme, C. Reiner, T. Zaiß, and M. Schlosser, Angew. Chem., Int. Ed., 47, 755 (2008).
• 7)  P. R. Rayavarapu, N. Sharma, V. K. Peterson, and S. Adams, J. Solid State Electrochem., 16, 1807 (2012).
• 8)  A. Hayashi, K. Noi, A. Sakuda, and M. Tatsumisago, Nat. Commun., 3, 856 (2012).
• 9)  A. Hayashi, N. Masuzawa, S. Yubuchi, F. Tsuji, C. Hotehama, A. Sakuda, and M. Tatsumisago, Nat. Commun., 10, 5266 (2019).
• 10)  M. Duchardt, U. Ruschewitz, S. Adams, S. Dehnen, and B. Roling, Angew. Chem., Int. Ed., 130, 1365 (2018).
• 11)  Z. Zhang, E. Ramos, F. Lalère, A. Assoud, K. Kaup, P. Hartman, and L. F. Nazar, Energy Environ. Sci., 11, 87 (2018).
• 12)  F. Tsuji, S. Yubuchi, A. Sakuda, M. Tatsumisago, and A. Hayashi, J. Ceram. Soc. Jpn., 128, 641 (2020).
• 13)  H. Gamo, N. H. H. Phuc, H. Muto, and A. Matsuda, ACS Appl. Energy Mater., 4, 6125 (2021).
• 14)  F. Tsuji, N. Masuzawa, A. Sakuda, M. Tatsumisago, and A. Hayashi, ACS Appl. Energy Mater., 3, 11706 (2020).
• 15)  X. Zhang, K. C. Phuah, and S. Adams, Chem. Mater., 33, 9184 (2021).
• 16)  N. Wang, K. Yang, L. Zhang, X. Yan, L. Wang, and B. Xu, J. Mater. Sci., 53, 1987 (2018).
• 17)  S. Han, J. Y. Seo, W. B. Park, S. R. Prabakar, S. Park, K. S. Sohn, and M. Pyo, Inorg. Chem. Front., 9, 1233 (2022).
• 18)  F. Tsuji, A. Nasu, C. Hotehama, A. Sakuda, M. Tatsumisago, and A. Hayashi, Mater. Adv., 2, 1676 (2021).
• 19)  S. Harm, A. K. Hatz, C. Schneider, C. Hoefer, C. Hoch, and B. V. Lotsch, Front Chem., 8, 90 (2020).
• 20)  K. Denoue, L. E. David, C. Calers, A. Gautier, L. Verger, and L. Calvez, Mater. Res. Bull., 142, 111423 (2021).
• 21)  N. Tanibata, K. Noi, A. Hayashi, and M. Tatsumisago, RSC Adv., 4, 17120 (2014).
• 22)  M. Ribes, B. Barrau, and J. L. Souquet, J. Non-Cryst. Solids, 38–39, 271 (1980).
• 23)  L. Gao, G. Bian, Y. Yang, B. Zhang, X. Wu, and K. Wu, New J. Chem., 45, 12362 (2021).
• 24)  Z. Yu, S. L. Shang, J. H. Seo, D. Wang, X. Luo, Q. Huang, S. Chen, J. Lu, X. Li, Z. K. Liu, and D. Wang, Adv. Mater., 29, 1605561 (2017).
• 25)  L. Zhang, D. Zhang, K. Yang, X. Yan, L. Wang, J. Mi, B. Xu, and Y. Li, Adv. Sci., 3, 1600089 (2016).
• 26)  H. Wang, Y. Chen, Z. D. Hood, G. Sahu, A. S. Pandian, J. K. Keum, K. An, and C. Liang, Angew. Chem., Int. Ed., 55, 8551 (2016).
• 27)  A. Banerjee, K. H. Park, J. W. Heo, Y. J. Nam, C. K. Moon, S. M. Oh, S. T. Hong, and Y. S. Jung, Angew. Chem., Int. Ed., 55, 9634 (2016).
• 28)  R. Hoppe, W. Lidecke, and F. C. Frorath, Z. Anorg. Allg. Chem., 309, 49 (1961).
• 29)  B. Eisenmann and A. Hofmann, Z. Kristallogr.–Crystal. Mater., 197, 169 (1991).
• 30)  F. Izumi and K. Momma, Solid State Phenom., 130, 15 (2007).
• 31)  K. Momma and F. Izumi, J. Appl. Crystallogr., 44, 1272 (2011).
• 32)  K. Noi, A. Hayashi, and M. Tatsumisago, J. Power Sources, 269, 260 (2014).