Effect of grain boundary resistance on the ionic conductivity of amorphous xLi2S-(100-x)LiI binary system

Solid-state electrolytes (SSEs) hold the key position in the progress of cutting-edge all-solid-state batteries (ASSBs). The ionic conductivity of solid-state electrolytes is linked to the presence of both amorphous and crystalline phases. This study employs the synthesis method of mechanochemical milling on binary xLi2S-(100-x)LiI system to investigate the effect of amorphization on its ionic conductivity. Powder X-ray diffraction (PXRD) shows that the stoichiometry of Li2S and LiI has a significant impact on the amorphization of xLi2S-(100-x)LiI system. Furthermore, the analysis of electrochemical impedance spectroscopy (EIS) indicates that the amorphization of xLi2S-(100-x)LiI system is strongly correlated with its ionic conductivity, which is primarily attributed to the effect of grain boundary resistance. These findings uncover the latent connections between amorphization, grain boundary resistance, and ionic conductivity, offering insight into the design of innovative amorphous SSEs.

The ionic conductivity of SSEs can be optimized by manipulating lattice structure, element substitution, phase change, amorphization, etc (Asano et al., 2018;Wang et al., 2019;Luo et al., 2021;Kwak et al., 2022;Schweiger et al., 2022;Szczuka et al., 2022). Among these methods, amorphization has gained attention due to the emergence of mechanochemical synthesis methods, which is an effective approach to synthesizing SSEs with lower grain boundary resistance (Dalvi and Shahi, 2004;Morimoto et al., 2004;Kim and Martin, 2006;Enayati and Mohamed, 2014). Representatively, the amorphous Li 2 S-P 2 S 5 binary system SSEs can be prepared by mechanical milling and exhibit a high ionic conductivity (>10 -4 S/cm) (Hayashi et al., 2004). In addition, some SSEs such as Li 6 PS 5 I (Brinek et al., 2020), Li 2 B 4 O 7 (Wohlmuth et al., 2016), Li 2 ZrCl 6 (Chen et al., 2021), and Li 3 YCl 6 (Asano et al., 2018) show higher ionic conductivity after undergoing amorphization. However, the impact of amorphization on the ionic conductivity varies depending on the specific SSEs system, crystalline structures play a critical role in ionic conductivity for numerous SSEs. (Zhao et al., 2019;Schweiger et al., 2022). For instance, a recent study by Schweiger et al. revealed that Li 10 GeP 2 S 12 experienced an increase in grain boundary resistance and a decrease in ionic conductivity with increasing milling time against the behavior of other SSEs. The mechanism behind this phenomenon is that defects and site disorder caused by ball milling impede the migration of lithium ions within the lattice (Schweiger et al., 2022). Therefore, it is essential to investigate the impact of amorphization on the grain boundary resistance and ionic conductivity of SSEs, while also elucidating the underlying mechanism.
In this study, the amorphous SSEs of binary xLi 2 S-(100-x)LiI (10 ≤ x ≤ 90) were synthesized by mechanical ball-milling method for the first time. PXRD analysis indicates that the amorphization degree of xLi 2 S-(100-x)LiI system is significantly influenced by the stoichiometry of Li 2 S and LiI. Furthermore, electrochemical impedance spectroscopy (EIS) analysis reveals a strong correlation between the amorphization degree of the xLi 2 S-(100x)LiI system and its ionic conductivity, with the effect of grain boundary resistance being the primary contributing factor. Additionally, the increase of Li 2 S content in xLi 2 S-(100-x)LiI may restrict the grain boundary impedance reduction caused by amorphization.

Materials synthesis
The amorphous SSEs of binary xLi 2 S-(100-x)LiI (x = 10, 30, 50, 70, 90) were synthesized through a ball milling process. First, the starting materials of Li 2 S (Alfa Aesar, 99.9%) and LiI (Energy chemical, 98%) were ground in an agate mortar for 30 min to get the homogeneous mixture. Then, the stoichiometric mixtures of Li 2 S and LiI were ball-milled at 500 rpm for 33 h in a grinding jar with ZrO 2 balls using planetary ball mill (Pulverisette 7 PL, Fritsch). The ball-to-powder mass ratio is 20:1 during sample preparation, and each cycle running for 15 min and resting for 5 min. The entire preparation process were carried out under an argon atmosphere (O 2 < 0.1 ppm, H 2 O < 0.1 ppm).

X-ray diffraction measurements
PXRD measurements were conducted at room temperature on an Empyrean diffractometer from Malvern Panalytical using Cu Kα (λ = 1.541,874 Å) and a Bragg-Brentano geometry, for identify the phases of xLi 2 S-(100-x)LiI binary system. PXRD data were collected with 2θ ranging from 20°to 90°at a scan rate of 0.14°s −1 . Before measurements, each sample was placed on a zero-background sample holder in an Ar-filled glovebox and protected by a Kapton film for the hygroscopicity of xLi 2 S-(100-x)LiI.

Electrochemical impedance spectroscopy measurements
Ionic conductivities of xLi 2 S-(100-x)LiI binary system were obtained through EIS measurement. Powder samples of xLi 2 S-(100-x)LiI were cold pressed into pellets under 4 tons in an insulative mold, and the pellets were placed between two stainless steel rods served as blocking electrodes. EIS measurement was performed on electrochemical workstation analyzer (AUTOLAB M204) in a frequency range from 1 MHz to 1 Hz with an amplitude of 50 mV. Moreover, the Nyquist curves were fitted by equivalent circuit to obtain the bulk resistance and grain boundary resistance of xLi 2 S-(100-x)LiI SSEs.

Results and discussion
As presented in Figure 1, the amorphous degree of xLi 2 S-(100-x) LiI (x = 10, 30, 50, 70 and 90) system significantly depends on the stoichiometry of Li 2 S and LiI. Before ball-milling, all PXRD patterns of xLi 2 S-(100-x)LiI exhibit sharp-peak feature, which indicates their good crystallinity ( Figure 1A). In contrast, the PXRD patterns of xLi 2 S-(100-x)LiI after ball-milling exhibit different degrees of broadening ( Figure 1B). Representatively, FWHM of the PXRD peaks in the range of 40°-50°is used here to quantitatively analyze the amorphization degree of xLi 2 S-(100-x)LiI binary system (Indris et al., 2000;Sasano et al., 2011;Holder and Schaak, 2019;Londono-Restrepo et al., 2019;Schweiger et al., 2022;Sun et al., 2022). It should be emphasized that the peak positions and FWHM of Li 2 S or LiI at x = 10 or 90 are not discernible from the PXRD pattern due to the low content. Surprisingly, different stoichiometric ratios of Li 2 S and LiI in xLi 2 S-(100-x)LiI lead to obviously different amorphization degrees, even under the same ball-milling conditions. As shown in Figures 1C, D, the FWHM of LiI presents an increasing trend with the increase of Li 2 S and changes from 0.239 (x = 10) to 1.124 (x = 70), which demonstrates that the presence of Li 2 S can promote the amorphization of LiI. In contrast, the FWHM of Li 2 S seems to tend to remain constant as x increases in xLi 2 S-(100-x)LiI (x ≥ 50). Interestingly, the amorphization degree of the xLi 2 S-(100-x)P 2 S 5 binary system is also dependent on the stoichiometric ratios of Li 2 S Frontiers in Chemistry frontiersin.org and P 2 S 5 (Minami et al., 2006;Tatsumisago and Hayashi, 2012;Kudu et al., 2018). However, the amorphization degree of xLi 2 S-(100-x)P 2 S 5 diminishes as Li 2 S increases, accompanied by the appearance of sharp peaks of Li 2 S in the PXRD patterns (Hayashi et al., 2004). Therefore, the difference between the xLi 2 S-(100-x)LiI and xLi 2 S-(100-x)P 2 S 5 suggests that the amorphization degree depends not only on the stoichiometric ratios but also on the composition of the compound in the binary system. The stoichiometric ratios of Li 2 S and LiI determine the amorphization degree of the xLi 2 S-(100-x)LiI binary system, which significantly affects its ionic conductivity. Figure 2A shows the Nyquist plots of amorphous xLi 2 S-(100-x)LiI binary system at room temperature (RT), and each curve exhibits a typical semicircle at high frequency representing the resistance and the linear part at low frequency representing ion blocking electrode. The EIS data were processed based on the formula: Z = (Z 0 × S)/l to eliminate the effect of SSE pellet thickness and area on the impedance, in which Z 0 is the raw data of the measured EIS, l is the thickness, and S is the area of SSE pellet. Fitting the plot by the equivalent circuit leads to the resistance R, which corresponds to the value of the real part of the Nyquist curve, and the ionic conductivity is calculated according to the formula of σ = l/(R × S). As presented in Figure 2B, the ionic conductivities of xLi 2 S-(100-x)LiI show a non-monotonic variation with the increase of x. As x increased from 10 to 70, the ionic conductivity of xLi 2 S-(100-x)LiI increased from 1.03 × 10 −6 S/ cm to 8.43 × 10 −6 S/cm. Subsequently, after x continued to increase to 90, the ionic conductivity appeared to drop significantly to 1.78 × 10 −7 S/cm. The above non-monotonic ionic conductivity changes may be attributed to both the amorphization degree of LiI and the content of Li 2 S in xLi 2 S-(100-x)LiI. In the first stage (x from 10 to 70), the amorphization of LiI is the dominant factor in influencing the ionic conductivity of xLi 2 S-(100-x)LiI ( Figure 1C). However, in the next stage (x from 70 to 90), the adverse effect of Li 2 S content on ionic conductivity may play a major role.
To understand the ionic transport mechanism of the amorphous xLi 2 S-(100-x)LiI in depth, the Nyquist plots were fitted with the equivalent circuit consisting of bulk resistance (R b ), grain boundary  Frontiers in Chemistry frontiersin.org resistance (R gb ) and constant phase element (CPE). As illustrated in Figure 3A, lithium ions transport in the bulk phase and grain boundary of SSEs, which determines the overall ionic conductivity of xLi 2 S-(100-x)LiI (Gao et al., 2016;Goswami and Kant, 2019;Vadhva et al., 2021). Obviously, the hindrance of lithium ions transport at the grain boundaries is stronger than that of the bulk phase according to Figures 3B-F. For 10Li 2 S-90LiI, for example, its R gb is 947.7 kΩ cm, which is much higher than that of R b (8,403 Ω cm). Besides, the variation of R gb is significantly higher than that of R b . The R b and R gb of 70Li 2 S-30LiI with the highest ionic conductivity are 3,632 Ω cm and 116.1 kΩ cm respectively. In contrast, the R b and R gb of 90Li 2 S-10LiI with the lowest ionic conductivity are 9,925 Ω cm and 5,566.4 kΩ cm respectively. Furthermore, to present the dependence of R b and R gb on x in xLi 2 S-(100-x)LiI, the differences between R b and R gb on logarithmic scale are presented in Figure 4A. While the ionic conductivity of xLi 2 S-(100-x)LiI undergoes the significant change with x from 10 to 90 (Figure 2), R b does not undergo a distinct fluctuation, as well as the bulk phase conductivity σ b . In contrast, R gb and the grain boundary conductivity σ gb show the significant changes and are in agreement with the trend of the ionic conductivity ( Figure 4B). Also, the conductivity isotherms extracted from EIS can reflect the FIGURE 3 (A) Equivalent circuit model for SSEs, consisting of R b , R gb and CPE. The fitting results of Nyquist plots of (B) 10Li 2 S-90LiI (C) 30Li 2 S-70LiI (D) 50Li 2 S-50LiI (E) 70Li 2 S-30LiI (F) 90Li 2 S-10LiI. Frontiers in Chemistry frontiersin.org dependence of the grain boundary conductivity on x in xLi 2 S-(100x)LiI, which is consistent with the results of the Nyquist curves fitted with the equivalent circuit. As shown in Figure 5A, conductivity isotherms are plotted from the real part (σ′) of the complex ionic conductivity as a function of frequency. Typically, the frequency independent plateaus (marked by arrow) correspond to the ionic conductivities at the grain boundary of SSEs (Schweiger et al., 2022). As x increases, the plateau of σ′ gradually reaches a maximum of 8.50 × 10 −6 S/cm at x = 70, then dropping to a minimum of 1.79 × 10 −6 S/cm at x = 90. It is worth emphasizing that the feature of conductivity isotherms not only agrees with the analysis of the Nyquist curve, but also the values corresponding to the plateau of σ′ are very close to the grain boundary conductivity σ gb in Figure 4B, which confirms the above analysis of ionic conductivity of amorphous xLi 2 S-(100-x)LiI. In addition, the imaginary part (Z″) of the complex impedance as a function of frequency is plotted in Figure 5B, and the Z″ peak height is usually considered to be equal to half of the most resistive elements (here, i.e., the grain boundary resistance) in SSEs (Irvine et al., 1990). Consistently, the dependence of Z″ peak height on x can also corroborate the results of Nyquist curves fitted with the equivalent circuit. Obviously, the above results indicate that the ionic conductivity change of amorphous xLi 2 S-(100-x)LiI depends directly on the grain boundary conductivity σ gb and is almost unaffected by the bulk phase conductivity σ b . On the other hand, in combination with the PXRD data of xLi 2 S-(100-x)LiI (Figure 1), it can be concluded that the increase in grain boundary conductivity σ gb may depend on the enhanced amorphization of LiI as x increases from 10 to 70, while the decrease in grain boundary conductivity σ gb may be mainly affected by the increase in Li 2 S content as x increases from 70 to 90. In other words, there is a competitive relationship between the amorphization of LiI and the content of Li 2 S in affecting the grain boundary conductivity of amorphous xLi 2 S-(100-x)LiI.

Conclusion
In conclusion, the amorphous xLi 2 S-(100-x)LiI (10 ≤ x ≤ 90) binary system was synthesized by mechanical ball-milling method. The PXRD analysis significantly demonstrated that the increase of Li 2 S content can promote the amorphization of LiI, and the amorphous degree of Li 2 S tend to remain constant as x increases in xLi 2 S-(100-x)LiI (x ≥ 50). The EIS analysis revealed that the change in ionic conductivity of amorphous xLi 2 S-(100-x)LiI depends on the grain boundary conductivity and is almost unaffected by the bulk phase conductivity. In addition, the competitive mechanism between the amorphization of LiI and the content of Li 2 S in affecting the grain boundary conductivity was found. The findings of xLi 2 S-(100-x)LiI binary system provide insights into the future design of new amorphous SSEs.

Data availability statement
The raw data supporting the conclusion of this article will be made available by the authors, without undue reservation.

Author contributions
SH and LG designed the project. LD carried out the experiments; LG and LD performed the electrochemical properties and analyzed all the data. LG and JP wrote the manuscript. All authors contributed to the article and approved the submitted version.