Machine Learning Approach for the Material Search of Fluoride-Ion Conductors
Authors: Matsui Naoki , Seki Tomoaki , Suzuki Kota , Hirayama Masaaki , Kanno Ryoji 
Published: February 2024

Fluoride-ion conductors are key materials for realizing all-solid-state fluoride batteries, which theoretically exhibit high energy densities of 4,400 Wh L–1 using Cu cathode and LaF3 anode1-2. To date, a high fluoride-ion conductivity has been reported for limited compounds, such as fluorite-type MSnF4 (M = Pb or Ba)3, tysonite-type Ln
1−x

AEx
F3−x
(Ln = La–Sm, AE = Ca, Sr, or Ba)4, and ASn2F5 (A = Na, K, Rb, or NH4)5. However, the conductivities of these structures can be improved only to a limited extent, necessitating the search for novel phases in multielement systems6. Material search in a multielement system is cost- and effort-intensive due to the extremely large compositional space. In this study, we used regression learning of the ionic conductivities based on compositional descriptors aiming to accelerate the material search for fluoride-ion conductors. Training data on ionic conductivity at room temperature for 317 crystalline or amorphous fluorides were collected from the literature. Descriptors were prepared using only compositional properties (e.g., polarizability, ionic radius, and electronegativity). Regression learning using lasso, ridge, elastic net, support vector machine, and random forest were performed. Fig. 1 shows the correlation between the measured and predicted conductivities from random forest regression. Random forest yields the highest R
2 values of 0.96 and 0.85 for the training and test data, respectively. The highest permutation importance was given for the descriptor of the cation polarizability. Highly polarizable cations such as Bi3+, Sb3+, Pb2+, Sn2+, Tl+, Ag+, Cs+, and Rb+ are essential for achieving a high fluoride-ion conductivity. Moreover, the mean of melting point of metal fluorides and mean of M–F binding energy exhibit high importance scores, suggesting that a weak interaction between the metal cation and fluoride ion is preferred for fluoride-ion conduction. The predictive performance was experimentally verified, and the correlation between the measured and predicted ionic conductivities of the BaF2–SnF2–LaF3 (or KF) pseudo-ternary system was demonstrated. The ionic conductivities of the experimentally obtained samples, as illustrated as green circles in Fig.1, suitably match the predicted values. During experimental verification, new tysonite-type Ba0.2Sn0.8F2 was identified in the SnF2-rich composition region, where a high ionic conductivity was predicted. Rietveld analysis was performed using synchrotron X-ray diffraction (SXRD) data. Refinement was conducted with space group of P63/mmc. Barium and tin simultaneously occupy the 4e site with occupancies of 0.2 and 0.8, respectively, and form a hexagonal close-packed structure. Fluoride ions occupy two distinct sites, 2b and 4f, which adopt three- and four-fold coordination by M
2+ ions (M = Ba0.2Sn0.8), respectively. The occupancies of the fluoride ions at the 2b and 4f sites are 0.626 and 0.687, respectively, suggesting that numerous vacancies are randomly distributed at both sites, which is a unique feature of Ba0.2Sn0.8F2. The composition-based model for the prediction of the ionic conductivity enables to ascertain the compositional regions with high predicted ionic conductivities; consequently, it reduces the cost of material search and accelerates the discovery of fast fluoride-ion-conducting materials.
Acknowledgement: This presentation is based on results obtained from a project, JPNP21006, commissioned by the New Energy and Industrial Technology Development Organization (NEDO).
Reference: (1) M. A. Reddy, et al., J. Mater. Chem.,
21, 17059 (2011). (2) F. Gschwind, et al., J. Fluorine Chem.,
182, 76 (2016). (3) G. Denes, et al., Solid State Ionics,
13 , 213 (1984). (4) C. Rongeat, et al., ACS Appl. Mater. Inter.
6 , 2103 (2014). (5) J. P. Battut, et al., Solid State Ionics, 22 , 247 (1987). (6) K. Suzuki, et al., J. Mater. Chem. A,
8 , 11582 (2020).
Figure 1. Predicted versus measured logarithm of the ionic conductivity. Red, blue, and green circles correspond to the training, test, and experimental data of the newly synthesized compounds. The black line represents the ideal line, i.e., where the predicted and measured conductivities are equal.

Figure 1