Investigation of Effect of Heterovalent Element Doping on Ionic Conductivity in Li₃InCl₆ System Using Neural-network Potential

Abstract

For the halide solid electrolyte Li₃InCl₆, which has both high water resistance and high ionic conductivity, doping with different elements to further increase the conductivity is attracting attention. In this study, we investigated co-doping Li₃InCl₆ with Nb⁵⁺ and Zr⁴⁺. A pretrained neural-network potential was used for molecular dynamics simulations, and the results indicated that doping with a high concentration of Zr⁴⁺ and low concentration of Nb⁵⁺ promotes disorder in the Li⁺/vacancy arrangement on the diffusion path, even at relatively low temperatures. Bayesian optimization revealed the optimal composition with fewer samples, highlighting its utility for exploring complex compositions and expensive experimental investigations.

1. Introduction

Storage batteries are important devices for achieving carbon neutrality. Additionally, the reevaluation of energy devices, such as switching from gasoline-powered vehicles to electric vehicles, is attracting global attention.¹ Among them, all-solid-state Li batteries are promising because of their high theoretical energy density and safety, making them the next-generation technology for liquid Li-ion batteries with organic electrolytes.^2–5 Numerous studies have been performed on sulfide solid electrolytes (SEs)^6–9 and oxide SEs^10–13 owing to their high ionic conductivity and high stability, respectively. In 2018, Asano et al. reported halide SEs (Li₃YCl₆, Li₃YBr₆) that combined high Li-ion conductivity with a wide electrochemical window.¹⁴ In 2019, Li et al. reported Li₃InCl₆ with excellent water resistance.¹⁵ Since then, interest in improving the material properties and performance of halide SEs has grown.^16–23 In previous research,²⁴ we systematically evaluated Zr⁴⁺- and Nb⁵⁺-doped Li₃InCl₆ SEs using first-principles molecular dynamics (FPMD). The results indicated that the ionic-conductivity changes could be explained by the trapping effect of vacancies created by doping and a phase transition where the ordered array of Li and vacancies became disordered. In particular, doping with high-valent Nb⁵⁺ significantly reduces the ionic conductivity at room temperature owing to the trapping effect, while promoting phase transition and ensuring high ionic conductivity even at relatively low temperatures. Considering this tradeoff, in the present study, we explored co-doping with Zr⁴⁺ and Nb⁵⁺ via comprehensive material simulations to weaken the trapping effect while promoting phase transitions. The exploration employed molecular dynamics (MD) with neural-network potentials (NNPs), offering a precision comparable to that of first-principles calculations and a higher computational speed. Specifically, we used the pretrained NNP implemented in M3GNet.py.²⁵ Additionally, Bayesian optimization—a material informatics method—was applied using the exhaustively calculated ionic conductivities. Bayesian optimization can shorten the process of maximizing the ionic conductivity, making it effective for complex compositions and time-consuming experimental evaluations.

2. Methods

2.1 Experimental procedures

SEs were synthesized using a mechanochemical method with a planetary ball mill (P-7 Classic Line, Fritsch Japan K.K.). Stoichiometric mixtures of LiCl (99.9 %, Sigma–Aldrich, St. Louis, USA), InCl₃ (99.99 %, Kojundo Chemical Laboratory Co., Ltd., Saitama, Japan), ZrCl₄ (99.9 %, Kojundo Chemical Laboratory Co., Ltd., Saitama, Japan), and NbCl₅ (99.9 %, Kojundo Chemical Laboratory Co., Ltd., Saitama, Japan) were placed in a 45-mL ZrO₂ pot with 34 ZrO₂ balls (diameter = 8 mm). The mixtures were milled at 500 rpm for 1 h, followed by 15 min of rest, and this was repeated for 20 sets to synthesize the SEs. The resulting samples were subjected to heat treatment at 300 °C for 3 h. They were then characterized using X-ray diffraction (XRD; MiniFlex 600, Rigaku Corp.). The ionic conductivity was measured at 298 and 333 K using AC impedance (VSP electrochemical analyzer, BioLogic, Grenoble, France) with an applied voltage of 10 mV in the frequency range of 10²–10⁷ Hz. The pellets used for the measurements were prepared by compressing the SE powder with stainless-steel pins at 509 MPa (diameter of 10 mm, thickness of ∼0.50 mm). All the procedures, including heat treatment in an electric furnace, were conducted in a dry-Ar-gas atmosphere maintained at a dew point below −80 °C to prevent material and moisture reactions.

2.2 Calculation procedures

2.2.1 NNP MD

MD simulations were performed using an NNP based on a graph neural network architecture that represents the composition and crystal structure and considers three-body interactions within the crystal structure.²⁵ A superstructure of Li₂₈₈In₉₆Cl₅₇₆ was created, and the In was partially replaced with Zr⁴⁺ and Nb⁵⁺. The calculations were performed with the maximum Zr and Nb substitution amounts set as 50 % and 30 % of the total number of In sites, respectively, which were experimentally confirmed solubility limits of Zr and Nb according to a previous study.²⁴ Considering the solubility limits of Zr and Nb, 38 samples of co-doped compositions were selected to ensure that the total doping amount of both the elements remained less than 50 %. The NNP, which was implemented in M3GNet.py, calculates the energy and forces acting on the ions in the given structure. Structural relaxation and MD simulations were performed using the Atomic Simulation Environment (ASE).²⁶ The NNP MD simulations were performed at 400 K in a canonical ensemble (NVT) with a timestep of 1 fs for 100 ps.

2.2.2 Bayesian optimization

Bayesian optimization was performed to determine the optimal doping amounts of Zr⁴⁺ and Nb⁵⁺ for increasing the ionic conductivity. A Gaussian process was used to evaluate the prediction uncertainty as the prediction variance. Using the predictions and variance obtained from the Gaussian process, the acquisition function was calculated using the Expected Improvement (EI) strategy, where the next candidates were selected according to the acquisition-function scores.²⁷ The target compositions for the Bayes optimization were set as those of the NNP MD simulations (38 compositions).

3. Results and Discussion

The accuracy of the NNP calculations was verified using our previous DFT-MD calculations for Li_3−2xIn_1−xNb_xCl₆ and Li_3−yIn_1−yZr_yCl₆ with x = y = 0.125.²⁴ The snapshot of the crystal structure was extracted from the DFT-MD trajectory and the calculated energies of the lattices and forces acting on atoms by the NNP. The obtained energies and forces were compared with those obtained using DFT and the NNP. Figure 1 illustrates the diagnostic plots for Li_3−2xIn_1−xNb_xCl₆ and Li_3−yIn_1−yZr_yCl₆ with x = y = 0.125. Good linearity is observed in all the plots, where the root-mean-square errors for energies and forces are 2.6 meV/atom and 0.19 eV/Å, respectively, for Li_3−2xIn_1−xNb_xCl₆ and 2.2 meV/atom (energy) and 0.18 eV/Å (force), respectively, for Li_3−yIn_1−yZr_yCl₆.

Figure 1.

Comparison of DFT- and NNP-calculated energies and forces corresponding to x = y = 0.125 for the compositions Li_3−2xIn_1−xNb_xCl₆ and Li_3−yIn_1−yZr_yCl₆. Panels (a) and (b) show the results for Nb-doped LIC, and panels (c) and (d) show the results for Zr-doped LIC.

Figure 2 illustrates examples of mean square displacements (MSD) plots for Li₂₅₈In₇₈Nb₁₂Zr₆Cl₅₇₆ and Li₂₆₄In₇₈Nb₆Zr₁₂Cl₅₇₆, approximately corresponding to Li_2.68In_0.81Nb_0.13Zr_0.06Cl₆ and Li_2.65In_0.81Nb_0.06Zr_0.13Cl₆, respectively. These results confirm Li diffusion in all the computed systems. The MSD for ions other than Li indicated only thermal vibrations, confirming that the crystal structure framework was maintained during the MD simulations.

Figure 2.

Plots of the mean square displacements (MSD) at 400 K calculated via the NNP. Panels (a) and (b) show the results for Li₂₅₈In₇₈Nb₁₂Zr₆Cl₅₇₆ and Li₂₆₄In₇₈Nb₆Zr₁₂Cl₅₇₆, respectively.

Figure 3 illustrates a heatmap of the diffusion coefficients for various compositions obtained from the NNP-MD calculations. The diffusion coefficients for single Nb doping into Li₃InCl₆ were higher than those for single Zr doping. Li₃InCl₆ forms a two-dimensional layered structure consisting of In-rich and In-poor layers, with Li ions preferentially located in the In-poor layer at room temperature.²⁸ Therefore, Li selectively diffuses in two dimensions within the In-poor layer. However, our FPMD analysis²⁴ revealed that at high temperatures, a phase transition occurs where Li is disordered between the In-rich and In-poor layers, enabling three-dimensional diffusion and resulting in increased conductivity. Nb doping facilitates this phase transition at approximately 400 K, whereas Zr doping exhibits a similar but less pronounced effect. Consequently, Li diffusion is enhanced more by Nb doping than by Zr doping, suggesting that increasing the concentration of Nb in the Nb and Zr co-doped compositions may improve the low-temperature diffusion coefficients. However, compositions with relatively low Nb doping, such as Li₂₄₀In₅₄Nb₆Zr₃₆Cl₅₇₆, also exhibited good diffusion coefficients as shown in Fig. 3. This result is attributed to the combination of the large doping amount of Zr⁴⁺, which has a weak Li-vacancy trapping effect, and the superior phase-transition promotion by Nb⁵⁺. Therefore, it is challenging to understand the diffusion trends of co-doped samples on the basis of single-doping qualitative insights alone.

Figure 3.

Color map of diffusion coefficients at 400 K calculated using NNP-MD for Li_288-2a-bIn_96-a-bNb_aZr_bCl₅₇₆. Numbers represents logarithm of diffusion coefficients (cm² s⁻¹) at 400 K.

The diffusion capabilities of the Li ions in the co-doped samples obtained from the NNP-MD simulations were experimentally validated by synthesizing SEs. Three compositions Li₂₄₆In₇₂Nb₁₈Zr₆Cl₅₇₆, Li₂₄₀In₇₂Nb₁₂Zr₂₄Cl₅₇₆, and Li₂₄₀In₇₂Nb₆Zr₃₆Cl₅₇₆, corresponding to Li_2.56In_0.75Nb_0.19Zr_0.06Cl₆, Li_2.51In_0.63Nb_0.12Zr_0.25Cl₆, and Li_2.50In_0.56Nb_0.06Zr_0.38Cl₆, respectively, were targeted to represent materials with low, medium, and high ionic conductivities at 400 K (Fig. 3) and varied Nb and Zr doping amounts. The XRD patterns (Fig. 4) confirmed the successful synthesis of the desired electrolytes without significant impurities. The measured ionic conductivities are presented in Table 1. No significant difference was observed in the ionic conductivity at 298 K; however, a significant difference was observed at 333 K. The experimental composition of Li_2.50In_0.56Nb_0.06Zr_0.38Cl₆, which corresponds to the calculated composition of Li₂₄₀In₇₂Nb₆Zr₃₆Cl₅₇₆, exhibited a good diffusion coefficient at 400 K and the highest ionic conductivity. Despite the differences due to temperature variations and grain-boundary resistance considerations, these findings serve as useful indicators for identifying compositions with good ionic conductivity.

Figure 4.

XRD patterns of the experimentally synthesized samples. The bars at the bottom of each correspond to the collection code of Li₃InCl₆ (89617). The black, red, blue, and green lines indicate the results for Li₃InCl₆, Li_2.56In_0.75Zr_0.06Nb_0.19Cl₆, Li_2.51In_0.62Zr_0.25Nb_0.12Cl₆, and Li_2.50In_0.56Zr_0.38Nb_0.06Cl₆.

Table 1. Ionic conductivities measured in the experiments.

Composition	Ionic conductivity/mS cm−1
	298 K	333 K
Li2.56In0.75Nb0.19Zr0.06Cl6	0.57	1.94
Li2.51In0.63Nb0.12Zr0.25Cl6	0.64	1.60
Li2.50In0.56Nb0.06Zr0.38Cl6	0.53	3.24

From the three experimental evaluation examples, we identified materials with high ionic conductivity in the Li_2.50In_0.56Nb_0.06Zr_0.38Cl₆ composition through comprehensive NNP calculations. Additionally, NNP calculations for single-doped compositions showed an increase in ionic conductivity with Nb and Zr doping, with the conductivity enhancement due to Nb surpassing that due to Zr, consistent with previous experimental results.²⁴ However, discrepancies were observed between the NNP-derived Li⁺ ionic conductivity and experimental results for compositions with medium and low conductivities. These differences could be attributed to temperature variations between the calculations and experiments as well as the exclusion of grain boundary resistance in the calculations, suggesting the requirement of further investigations.

In this study, we aimed to optimize ionic conductivity via co-doping with multiple elements. Previous research has revealed that the factors controlling ionic conductivity are 1) the trapping effect of dopants and 2) the promotion of disorder in the Li-vacancy arrangement by dopants, and the tradeoff effects between these factors must be considered. Consequently, optimization must be performed through trial and error using conventional experimental methods. Exhaustive NNP-MD simulations are useful for determining the approximate optimal composition candidates because of their fast and accurate computational approach. However, experimental optimization is ultimately required because of the discrepancy in the assumptions between the simulation conditions and experimental results. Recently, Bayesian optimization has proven to be effective in reducing trial and error in terms of materials property. However, studies on optimizing the functional properties of ion-conductive materials via Bayesian optimization have been rarely reported. While several studies on oxide materials have been reported,^29–35 this is the first case of optimizing Li-ion conductivity in chloride materials. Thus, we evaluated whether Bayesian optimization could efficiently and quickly identify the optimal compositions using NNP-calculated ionic-conductivity tables. Notably, in this study, the conductivity of all the compositions was evaluated through comprehensive NNP calculations. However, this paper presents only the conductivity data for the compositions selected through the Bayesian optimization process to facilitate quantification of the efficiency of Bayesian optimization. Figure 5a compares the average ionic conductivities and accuracy rates per search step between random and Bayesian searches at 400 K, demonstrating a significant improvement in the Bayesian optimization after approximately 20 steps. This result indicates that Bayesian optimization prioritizes uncertain compositions early on, understanding the composition dependence after half the range is explored and selecting materials with higher ionic conductivities. Figure 5b shows the average ranking of the compositions selected by Bayesian optimization for each composition. Assuming that the first sample selection is random, the next selected composition is mostly (Nb, Zr) = (0, 6), indicating that information about nearly nondoped compositions is obtained early on. Subsequently, regions with relatively high co-doping amounts of Nb and Zr, such as (Nb, Zr) = (18, 18), are explored up to an average rank of approximately 10. This process is indicative of inadequate data for predictions in the early stages of exploration, and thus, compositions near the compositional endpoints are prioritized. Furthermore, the first 10 samples are likely selected to explore the entire compositional space. Later, areas with higher Nb and Zr doping amounts are preferentially examined possibly owing to the tendency for higher diffusion coefficients. Conversely, compositions close to the nondoped regions, where diffusion coefficients tend to be low, exhibit average ranks of 20 or higher, indicating lower priority. Figure 5c illustrates the correlation between the sample diffusion coefficient (logarithmic values) and average ranking, demonstrating that, with the exception of the result for (Nb, Zr) = (0, 6), specimens with higher diffusion coefficients exhibit a greater likelihood of identification through Bayesian optimization, thus indicating efficient sampling. However, the first 10–15 samples are selected based on comprehensively evaluation of all the compositions, and approximately 20 samples are necessary to reliably identify the optimal composition possibly because of the small variation in the diffusion coefficients for compositions with high doping amounts. Our study demonstrates the utility of Bayesian optimization and NNP calculations for systems with two tradeoff effects.

Figure 5.

Bayesian optimization results for the Li-ion conductivity at 400 K. (a) Discovery rate of the best sample identified by Bayesian optimization (red plots) and random sampling (black dash line) as a function of number of observations. (b) Numbers in cells represent the average ranking of the compositions selected by Bayesian optimization for Li_288-2a-bIn_96-a-bNb_aZr_bCl₅₇₆. (c) Bayesian optimization-driven averaged rank plotted as a function of the logarithm of diffusion coefficients at 400 K.

4. Conclusion

In this study, we attempted to increase the ionic conductivity of Li₃InCl₆—a promising halide SE—by co-doping it with Nb⁵⁺ and Zr⁴⁺. We performed a comprehensive search using NNP calculations, known for their low computational costs, to optimize the composition of Li-ion conductivity. Nb⁵⁺ exhibits a strong Li-vacancy trapping effect but can reduce the temperature of a phase transition where the ordered array of Li and vacancies becomes disordered. Conversely, Zr⁴⁺ demonstrates the opposite tendency. Owing to such tradeoff effects, it is difficult to derive the optimal composition intuitively; however, NNP-MD calculations allow fast and comprehensive evaluation. In addition, we performed experimental evaluation of the composition selected based on the results of the comprehensive calculations, and a relatively high ionic conductivity was obtained (3.24 mS cm⁻¹ at 333 K for Li_2.50In_0.56Nb_0.06Zr_0.38Cl₆). Because there were slight discrepancies between the experimental and calculated results, we used exhaustive calculation results to evaluate whether it is possible to efficiently determine the optimal composition using Bayesian optimization. Thus, we confirmed that the number of steps needed to determine the optimal material can be reduced. This method is considered useful in this field, where research is currently underway.

Acknowledgments

Computations were performed using the facilities at the Technology Center of Nagoya University, Japan. English language editing was performed by Editage (www.editage.com). This work was financially supported by Aichi Steel Corporation. MN expresses gratitude for the financial support from Grants-in-Aid for Scientific Research (grant numbers 24K01157 and 24H02203) funded by the Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan; the Data Creation and Utilization-Type Material Research and Development Project (grant number JPMXP1122712807) funded by MEXT; and JST CREST (grant number JPMJCR21D3).

CRediT Authorship Contribution Statement

Takeshi Usami: Conceptualization (Lead), Investigation (Lead), Writing – original draft (Lead)

Koichi Gocho: Data curation (Equal), Investigation (Equal), Validation (Equal)

Naoto Tanibata: Writing – review & editing (Equal)

Hayami Takeda: Writing – review & editing (Equal)

Masanobu Nakayama: Conceptualization (Lead), Funding acquisition (Lead), Methodology (Lead), Writing – original draft (Lead)

Conflict of Interest

The authors declare no conflict of interest in the manuscript.

Funding

Aichi Steel Corporation

mext: 24K01157, 24H02203

mext: JPMXP1122712807

Core Research for Evolutional Science and Technology: JPMJCR21D3

Footnotes

The content of this paper will be published by Takeshi Usami as a PhD thesis at Nagoya Institute of Technology in 2025.

N. Tanibata and M. Nakayama: ECSJ Active Members

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