Research ArticleMATERIALS SCIENCE

Anion ordering enables fast H conduction at low temperatures

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Science Advances  02 Jun 2021:
Vol. 7, no. 23, eabf7883
DOI: 10.1126/sciadv.abf7883

Abstract

The introduction of chemical disorder by substitutional chemistry into ionic conductors is the most commonly used strategy to stabilize high-symmetric phases while maintaining ionic conductivity at lower temperatures. In recent years, hydride materials have received much attention owing to their potential for new energy applications, but there remains room for development in ionic conductivity below 300°C. Here, we show that layered anion-ordered Ba2−δH3−2δX (X = Cl, Br, and I) exhibit a remarkable conductivity, reaching 1 mS cm−1 at 200°C, with low activation barriers allowing H conduction even at room temperature. In contrast to structurally related BaH2 (i.e., Ba2H4), the layered anion order in Ba2−δH3−2δX, along with Schottky defects, likely suppresses a structural transition, rather than the traditional chemical disorder, while retaining a highly symmetric hexagonal lattice. This discovery could open a new direction in electrochemical use of hydrogen in synthetic processes and energy devices.

INTRODUCTION

Solid-state materials with fast ionic conductivity find diverse applications such as batteries, sensors, and fuel cells. Reducing operating temperatures is an important issue, but some materials drastically lose their ionic conductivity by undergoing a structural phase transition to lower-symmetry structure upon cooling (1, 2). The best-known strategy to circumvent this problem is the introduction of chemical disorder to stabilize a high-temperature (HT) phase. For example, in yttria-stabilized zirconia (YSZ), a Y3+-for-Zr4+ substitution for the cubic ZrO2 suppresses the transition to a tetragonal or monoclinic form and induces oxide ion conductivity (1). Likewise, the hexagonal HT phase of Li(CB9H10) can be stabilized by forming a solid solution with Li(CB11H12), which enables a fast lithium ion conductivity at room temperature (3). Other host materials that have successfully stabilized HT forms via chemical disorder include AgI (1), O2− conductors [e.g., Ba2In2O5 (1, 2) and La2Mo2O9 (4)], Li+ conductors [e.g., Li7La3Zr2O12 (5) and LiBH4 (6)], and Na+ conductors [e.g., Na2B12H12 (7) and Na4Zn(PO4)2 (8)].

Hydride materials have raised recent interest due to the unique characteristics of H anions such as high lability, high polarizability, and high compressibility, which have opened up new synthesis routes (9, 10) and lead to novel properties including catalysis (11, 12). In view of the light mass of H, its monovalence, and the redox potential of H2/H (−2.23 V versus standard hydrogen electrode), hydride ion conductivity appears promising as next-generation electrochemical energy storage systems with high voltage and high energy density (13, 14). In 2015, BaH2 with a hexagonal close packing (hcp) of Ba cations (Fig. 1A) was shown to achieve a H conductivity of 0.04 to 0.2 S cm−1 at 450° to 630°C, an order of magnitude higher than that of typical oxide ion conductors and proton conductors (e.g., YSZ and Nd-doped BaCeO3) (13). However, its conductivity drops rapidly at 450°C when it undergoes a transition to an orthorhombic phase with a distorted hcp (Ba) lattice (fig. S1). Subsequent studies of H conduction have shifted to oxyhydrides including Ln2−xySrx + yLiH1−x + yO3−y (Ln = La, Pr, Nd) (14, 15), Ba2MHO3 (M = Sc and Y) (16, 17), and LaH3−2xOx (18, 19). Although the inclusion of oxide ions may improve thermal stability, high H conductivity over 10−3 S cm−1 is only reached above 300°C.

Fig. 1 Structural comparison between BaH2 and Ba2H3X.

(A) The HT phase of BaH2 (space group, P63/mmc), composed of faced-shared hexagonal stacking of H1Ba6 octahedra (anti-NiAs structure), with additional hydride anions at H2Ba5 bipyramidal interstitials (13). (B) Ordered anion substitution in HT-BaH2 (“Ba2H4”) results in Ba2H3X (X = Cl, Br, and I; space group, P3¯m1), composed of alternate stacking of faced-shared H1Ba6 and XBa6 octahedra, with hydride anions at H2Ba4 tetrahedral interstitials.

Hydride-based antiperovskites with a soft anion sublattice have recently shown promise as alkali ion conductors (20). The use of soft anions compared to oxide ions would also be beneficial for hydride conductivity. Thus, we aimed to investigate Ba2H3X hydride-halides (X = Cl, Br, and I) with the anti-Li3LaSb2 structure (space group: P3¯m1) (21, 22), which consists of alternating stacking of face-sharing HBa6 and XBa6 octahedral layers along the hexagonal c axis, with additional hydride anions in a distorted tetrahedral (HBa4) environment (Fig. 1B). It can be also considered anion-ordered HT-BaH2 in which half of H1 is replaced by X (see Fig. 1). We found that the “stabilization” of the HT-BaH2 structure at low temperature by anion ordering makes Ba2H3X excellent H conductors together with low activation energies (ca. 35 to 50 kJ mol−1). The highest conductivity was achieved for X = I with 1.4 × 10−3 S cm−1 at 200°C. This result could open new avenues for hydride-based energy devices and material conversion systems that operate at low temperatures.

RESULTS

Crystal structure and nonstoichiometry

Polycrystalline Ba2H3X (X = Cl, Br, and I) samples were prepared by reacting stoichiometric quantities of BaH2 and BaX2 at 650°C for 20 hours in an Al2O3 tube loaded into an evacuated silica tube. All the powder specimens obtained are white, and their bandgaps were estimated from the diffuse reflectance spectrum to be around 3.1 eV, which are in agreement with those from first-principles calculations (Fig. 2A and fig. S2). The synchrotron x-ray diffraction (SXRD) pattern for X = I (Fig. 2B) could be indexed by a hexagonal lattice of a = 4.51276(4) Å and c = 8.0832(10) Å. These values are in reasonable agreement with those of the single crystal Ba2H3I [a = 4.5186(12) Å and c = 8.118(2) Å] (21), although they are slightly different. The lattice constants for X = Cl and Br are also compatible with the reported values (table S1) (22). Note that each SXRD profile contains a minor impurity BaHX (< 5%).

Fig. 2 Characterizations of polycrystalline Ba2H3X (X = Cl, Br, and I).

(A) Ultraviolet-visible diffuse reflectance spectra demonstrating the presence of a wide bandgap. The inset represents a photograph of Ba2H3X pellets. (B) SXRD patterns of Ba2H3Cl (blue), Ba2H3Br (green), and Ba2H3I (orange), indexed to the space group P3¯m1. Triangles denote a small amount (< 5%) of impurity BaHX. (C) Rietveld refinement on NPD pattern of deuterated sample of X = I, assuming Schottky defects (Ba2+:D = 1:2). Red circles, black line, and blue line represent observed, calculated, difference intensities, respectively. Green and orange ticks indicate Bragg peak positions of Ba1.764(3)D2.529(3)I and BaDI. See details in table S2. (D) The refined structure of Ba1.764(3)D2.529(3)I, where the occupancy factor g of each site is given. a.u., arbitrary units.

In the previous studies (21, 22), the structure of Ba2H3X was determined by single-crystal x-ray diffraction, and the hydrogen positions (1a and 2d) were only deduced from the analysis of the Madelung potentials and the bond valence sum. We therefore measured neutron powder diffraction (NPD) using the deuterated sample Ba2D3I and performed the Rietveld refinement. This readily converged with reasonable reliability factors (Rp = 4.51% and Rwp = 6.61%), but with large residual peaks (e.g., 101 at d ~ 3.5 Å), as shown in fig. S3. No improvement in the fit assuming different crystallographic sites for each atom suggests a nonstoichiometric composition, such as hydride vacancies that generate F-centers. However, given the sample color (white) and the bandgap of 3.1 eV (Fig. 2A), it is unlikely that electrons trapped in impurity levels are present. Furthermore, the absence of sizable defect-induced electrons is supported by the very small and nearly temperature-independent magnetic susceptibility (fig. S4). These results strongly suggest that under our synthetic condition, charge-neutral Schottky defects of Ba2+ and 2H are generated, thus resulting in the composition of Ba2−δH3−2δX.

The inclusion of the Schottky defects in the refinement substantially improved the agreement (Rp = 3.29% and Rwp = 4.41%; Fig. 2, C and D, and table S2) and gave Ba1.764(3)D2.529(3)I (δ = 0.236). The occupancy factor of the tetrahedral (H2) site is higher than that of the octahedral (H1) site. Furthermore, the Ba/I ratio of 1.73 estimated by ion chromatography (IC) agrees well with the value from NPD. The refinements for X = Cl and Br with the Schottky defects resulted in Ba1.724(3)D2.447(2)Cl (δ = 0.276) and Ba1.812(4)D2.618(3)Br (δ = 0.188), with the same tendency in the hydride occupancy (figs. S5 and S6 and tables S3 and S4). IC measurements also showed consistent Ba/X ratios of 1.60 (Cl) and 1.64 (Br). The formation of the Schottky defects of Ba2+ and 2H probably causes the discrepancy in the lattice parameters between the single crystals (21, 22) and our powder samples. We found a linear relationship between the Ba/I ratio and the lattice volume in Ba2−δH3−2δI (fig. S7). However, such lattice variation (or the amount of Schottky defects) does not substantially affect the ionic conductivity, at least within the range examined. It should be noted that the hydride vacancies in BaH2–δ (δ ~ 0.2) determined from NPD are similar to our compound, although the resulting electrons were assumed to be localized as F-centers (13).

To obtain further insight into the Schottky defects, we estimated the formation energies of point defects under hydrogen-rich conditions using first-principles calculations, but the results did not fully explain the experimental observations (fig. S8). For example, in Ba2H3I, the formation energies of VH1b· and VBa″, which are found as major defects, are only 0.2 eV lower than that of Hi′. This implies the presence of Hi to some extent, but hydrogen was not detected at the Hi site within the experimental accuracy by neutron diffraction. In addition, although the binding energy of a VH and VBa pair is reasonably high (e.g., 0.37 eV for X = I), the formation energy of associated defect of a pair of VH· and VBa′ is also high (e.g., 0.69 eV for X = I). Considering the high concentration of Schottky defects observed in Ba2−δH3−2δX, interactions among Schottky defects (clustered Schottky defects) may be taken into account, as reported in TiO2 (23) and UO2 (24). We also point out that some low-energy phonon vibrations of hydride anions are involved in the defect formation, as seen in hydrogen storage alloys (25) and Li3HCh and Na3HCh (Ch = S, Se, and Te) (20).

Hydride conductivity

The ionic conductivities of Ba2−δH3−2δX (δ ~ 0.2) were measured by electrochemical impedance spectroscopy (EIS) for 20° to 400°C using as-synthesized pellets. Note that there is no noticeable change in the XRD profiles before and after the EIS experiments (figs. S9 and S10 and table S5). Figure 3A displays the representative Cole-Cole plots at 200°C with a semicircle in the high-frequency region and a sharp rise in the low-frequency region, corresponding to the contribution from the bulk/grain boundary and the electrode, respectively (details in fig. S11 and table S6). The temperature evolution of total conductivity (σtotal) for Ba2–δH3–2δX, calculated from the sum of the bulk and grain boundary resistances, is shown in Fig. 3B. The Hebb-Wagner polarization (26) for X = I was measured to identify the charge carriers. We obtained a sufficiently small electronic conductivity σe,h = 7.98 × 10−6 S cm−1 at 200°C (fig. S12), indicating that the main contribution to the observed conductivity is ionic, with a transport number of tion = (σtotal − σe,h)/σtotal > 0.99. The high total conductivity observed in the relatively low temperature region is hardly conceivable for the divalent Ba2+ conduction. Negligible halide ion conduction is supported theoretically by the much higher formation energy of VX· (1.3 eV) compared to that of VH· (fig. S8) and experimentally by the higher conductivity for the larger X, along with a lower concentration (X/H ~ 1/3). Overall, these factors indicate that the H ion is the only carrier.

Fig. 3 Hydride conductive properties of Ba2−δH3−2δX (X = Cl, Br, and I; δ ~ 0.2).

(A) Impedance plots for Ba2−δH3−2δX at 200°C. The black and gray filled circles indicate measured frequencies of 106 and 102 Hz, respectively. (B) Arrhenius plots of the total conductivity of Ba2−δH3−2δX. The open green circles represent the bulk conductivity of X = Br, which could be separated from the total conductivity only at low temperatures (≤ 75°C). The dotted black line is an extrapolation of the total conductivity of the HT phase of BaH2 to low temperatures. (C) Thermal evolution of the total conductivity of the hydride-halides Ba2−δH3−2δX, together with those of other hydride conductors (1317, 27). Note that the bulk conductivities are shown for LaH2.52O0.24 and NdHO (18, 19).

In Fig. 3C, we compare the thermal evolution of total conductivities of Ba2−δH3−2δX (δ ~ 0.2) with those of the reported H conductors (1319, 27). The conductivities in the range of 10−3 to 10−2 S cm−1 above 300°C are comparable to those of known representative materials such as BaH2 (~5 × 10−3 S cm−1 at 420°C) (13) and LaH2.52O0.24 (2.6 × 10−2 S cm−1 at 342°C) (18). Ba2−δH3−2δX exhibit excellent total conductivities below 300°C. Even at 200°C, the total conductivity is as high as 10−4 to 10−3 S cm−1. It is also worth noting that the H conductivity can be measured down to room temperature in all samples, where a distinct semicircle is consistently observed at high frequencies (fig. S11 and table S6). Clearly, such fast conduction over a lower-temperature range is enabled by the low activation energy (35 to 50 kJ mol−1), in contrast to LaH2.52O0.24 with an activation energy of 125 kJ mol−1 (18).

DISCUSSION

The key to understanding the superior H conductivity of Ba2−δH3−2δX becomes clearer by comparing it with the structurally related BaH2. As mentioned above, the rapid decrease in the conductivity of BaH2 at 450°C results from the structural transition from the hexagonal structure (Fig. 1A) to the distorted orthorhombic one (fig. S1) (13). Extrapolation of the conductivity of the HT phase of BaH2 to low temperatures (broken line in Fig. 3B) is roughly in agreement with that of Ba2−δH3−2δX. This observation strongly suggests that the superior conductivity in Ba2−δH3−2δX is achieved by “stabilizing” the HT-BaH2 structure through ordered anion substitution with halide anions (Fig. 1), in a stark contrast to the introduction of chemical disorder applied to conventional ionic conductors including YSZ (1, 2). One might be surprised to see the correspondence in conductivity between Ba2−δH3−2δX and the “hypothetical” HT-BaH2 (broken line in Fig. 3B), because the latter has a three-dimensional (3D) H network and contains ca. 33% more H ions. However, this result is coherent with the preferential 2D conduction that is proposed in HT-BaH2 based on the large anisotropic thermal vibrations of H1 (13).

From the crystal structure of Ba2−δH3−2δX, it is evident that the H migration occurs within the Ba2−δH3−2δ slab. This was also verified by the climbing image nudged elastic band (CI-NEB) calculations for Ba2H3X. Among the possible H vacancy hopping routes, the lowest migration energy of 0.22 eV (X = Cl), 0.20 eV (X = Br), and 0.17 eV (X = I) is found for the nearest-neighbor H1–H2 path (Fig. 4, fig. S13, and table S7). Given the relatively lower values compared to the experimental activation energy (0.37 to 0.5 eV), the binding energy of a VH and VBa pair must be considered. The sum of the migration energy and the binding energy is 0.63 eV (X = Cl), 0.64 eV (X = Br), and 0.54 eV (X = I), which is higher but comparable to the experimental activation energy. This overestimation is probably due to the effects of phonon vibrations and interactions among multiple point defects as described above. For a more quantitative analysis, these effects need to be taken into account in the calculations. The higher ionic conductivity in the order of X = Cl < Br < I (e.g., 0.23, 0.63, and 1.4 mS cm−1 at 200°C) is not simply explained in terms of the size effect, because both H1–H2 distance and bottleneck size for H diffusion hardly depend on X species (fig. S14). Important here could be the softness of anions (Cl < Br < I) (28), as underlined in Li+ conductors such as LGPS (Li10GeP2S12) and argyrodite (Li6PS5X; X = Cl, Br, and I) (2931).

Fig. 4 Proposed hydride conduction in Ba2−δH3−2δX (X = Cl, Br, and I).

(A) H diffusion pathway via the vacancy mechanism in Ba2−δH3−2δ layer. The white spheres are barium ions. The blue and purple spheres indicate hydride ions at H1 (Wyckoff position 1a) and H2 (2d) sites, respectively. (B) Migration energy from CI-NEB calculation of H1–H2–H1 pathway.

Chemical disorder induced by substitution with dopants randomly distributed in the immobile ion sublattice is, apart from morphological control (3234), a general strategy to stabilize HT phases at lower temperatures and achieve fast ionic conductivity (18). Such chemical substitution inevitably introduces different parameters at the same time, including changes in local bonding nature and coordination environment (3538), that might complicate a thorough understanding of the mechanism of ionic conductivity. In marked contrast, the present study demonstrates the case where an ordered arrangement of anions can maintain the lattice free from or minimized chemical disorder, giving an ideal opportunity to study the intrinsic nature of H conductivity. Because many mixed-anion compounds adopt layered anion-ordered structures based on the concept of HSAB (hard and soft acids and bases) and the Hume-Rothery rule (39), ordered mixed anionization will lead to a new development in a variety of ion conducting materials, not only in the hydride system.

Perspectives

The observation of H conduction at low temperatures may give rise to various functions such as catalysis, not limited to ionic conductivity. For example, several oxyhydrides such as BaTi(O,H)3 BaCe(O,N,H)3−δ have recently been shown as catalytically active in NH3 synthesis and CO2 methanation at about 300°C, indicating that the lability of the H ions, combined with the strong basicity, is involved in these catalytic activities (11, 40, 41). An isotope experiment is a facile method to examine the exchangeability of H ions in a solid with hydrogen species in the outer atmosphere (9, 42). To see this, the Ba2−δH3−2δX powder was heated in a D2 gas stream, and the downstream gas was analyzed by quadrupole mass spectroscopy (see Materials and Methods). Figure 5 shows that H/D exchange started already at 100°C, much lower than for typical oxyhydride compounds [e.g., 350°C for BaTi(O,H)3] (9, 42). Such a low temperature H/D exchange makes Ba2−δH3−2δX a promising candidate material that could allow various inorganic hydrogenations under milder conditions, with much room for material optimization, e.g., by chemical substitution. Furthermore, labile H ions at (near) room temperature could even offer a new direction in organic synthesis chemistry. The hydride-halides are stable for several gases and aprotic solvents (fig. S15). The strong reducing property and high nucleophilicity of “free” H ions, instead of hydride clusters in conventional reductive reagents such as LiAlH4 and NaBH4, may convert various unsaturated bonds into useful saturated ones by allowing free H ions to react directly with hydrocarbons, possibly leading to unexplored reaction routes that are crucial for fine chemical synthesis including pharmaceuticals.

Fig. 5 Mass spectroscopy during isotope exchange for Ba2−δH3−2δX (X = Cl, Br, and I).

Each powder sample of Ba2−δH3−2δX was heated under a flow of D2/Ar gas, while ion current of evolved HD gas was monitored. The black dotted line indicates the temperature as a function of time. After this treatment, x-ray diffraction showed no noticeable change in lattice parameters or crystallinity.

MATERIALS AND METHODS

Synthesis of Ba2H3X (X = Cl, Br, and I)

We prepared the powder samples of Ba2H3X (X = Cl, Br, and I) using a conventional solid-state reaction. Powders of BaH2 (Mitsuwa Chemical, 99.5%) and BaX2 (X = Cl, Ba, and I) (Wako, 99.99%) were thoroughly ground and mixed, and then the mixture was pressed into a pellet (4 to 10 mm in diameter and 1 to 2 mm in thickness). The pellets were loaded into an alumina tube. The tube was then placed in a sealed and evacuated silica tube, followed by heating at 650°C for 20 hours. For neutron diffraction experiments, we prepared deuterated samples of Ba2D3X in the same method but using BaD2. BaD2 was synthesized by reacting barium metal (Sigma-Aldrich, > 99%) with deuterium gas (Taiyo Nippon Sanso, 99.8%). After Ba chunks were loaded into a SUS (steel use stainless) container, the container was evacuated and filled with deuterium gas, which was repeated five times to remove the residual N2. The sample was heated at 550°C for 30 min in 0.2 MPa of D2 gas, with two intermediate grindings. Owing to the air- and moisture-sensitive nature of the reactants and products, all handling was carried out in a nitrogen-filled glovebox. The quality of the sample was determined using a Rigaku SmartLab powder XRD apparatus.

Sample characterizations

High-resolution SXRD experiments were performed at room temperature using a large Debye-Scherrer camera installed at SPring-8 BL02B2 with λ = 0.420344(1) Å. Powder samples were loaded into capillaries (0.5 mm in diameter). During measurements, the capillaries were rotated for better averaging of the powder pattern intensities and removal of possible preferential orientation effects. The obtained SXRD profiles were analyzed by the Le Bail method using the Fullprof program (43). Using powder samples of Ba2D3X (X = Cl, Br, and I), time-of-flight NPD experiments were carried out at room temperature using a SPICA diffractometer at J-PARC. Approximately 1 g of powder sample was loaded in a vanadium-nickel cell (radius of 6 mm and height of 55 mm). The obtained NPD profiles were analyzed by the Rietveld method using the Z-Rietveld program (44).

The ultraviolet-visible spectra were collected using a Shimadzu UV-2600 spectrophotometer. The temperature dependence of magnetic susceptibility was measured by using a Quantum Design MPMS-XL SQUID magnetometer between 5 and 300 K at a constant magnetic field of 1 T. The Ba/X ratio of the sample was estimated by IC using a Thermo Fisher Scientific ICS-1600 for Ba2+ and using an ICS-2000 for X.

Electrochemical characterizations

Electrochemical measurements were carried out on sintered pellets of Ba2H3X (X = Cl, Br, and I) specimens with the relative density of around 80% (4 to 10 mm in diameter and 1 to 2 mm in thickness) using a Bio-Logic MTZ-35 frequency response analyzer. Ionic conductivity was measured by AC impedance methods with an applied frequency of 0.1 Hz to 35 MHz using gold electrodes for both sides in a flow of H2 gas for 27° to 400°C. The temperature in the measurement container was controlled by a TOYO Corporation HT-Z3-800 furnace control system. The obtained impedance spectra were analyzed using the EC-Lab software. The equivalent circuits used in the analysis were described in the Supplementary Materials. Electrical conductivities were estimated by the Hebb-Wagner polarization method (26) using an asymmetric (−)Pd/Ba2H3I/Au(+) cell, where Pd electrode was used as a reversible electrode for H2. The measurement was carried out using a Bio-Logic VSP-300 multichannel potentiostat in a flow of H2 gas at 200°C, with an applied potential between 0.3 and 1.9 V.

H/D exchange experiment

H/D exchange experiments were performed at heating rate of 5°C min−1 over the temperature range of 20° to 350°C under flowing 5% D2/Ar. The Ba2H3X (X = Cl, Br, and I) samples (typically ~30 mg) were placed in an Al crucible. The evolved gas species (m/z = 2 and 3 for H2 and HD) were recorded as a function of time using the Bruker MS9610 mass spectrometer.

First-principles calculations

First-principles calculations based on the density functional theory were performed to investigate the band structures and the migration energies using the projector augmented-wave method implemented in the Vienna Ab initio Simulation Package (VASP) code (4548). The band structures were calculated using the unit cell of Ba2H3X (X = Cl, Br, and I) shown in Fig. 1B. The supercell containing 3 × 3 × 2 unit cells was constructed to calculate point defect formation energies (49, 50) of Ba vacancy (VBa), H vacancy (VH), X vacancy (VX), interstitial H (Hi), and interstitial X (Xi). The binding energy (51) of a pair of VH and VBa was also estimated in Ba2H3X. All the symmetrically independent structures including one VH and one VBa were calculated. On the basis of the results of the experimental crystal structure analysis and the calculation of defect formation energies, the migration energies were calculated for the diffusion paths of H1–H1, H1–H2, and H2–H2 sites of H ion vacancy with the charge state +1, VH·. In the calculation models, the vacancy concentration of 1.85% (154), corresponding to δ ~ 0.04 in Ba2−δH3−2δX, was used. This concentration is lower than the experimentally obtained value of δ ~ 0.2, but it is known that the migration energy obtained from a model with low defect concentration usually agrees well with the experimental results for samples with high degree of defects (52, 53). The exchange-correlation term was treated with the Heyd-Scuseria-Ernzerhof hybrid functional (HSE06) (54) for the calculation of the band structure and Generalized Gradient Approximation and Perdew-Burke-Ernzerhof functional (GGA-PBE) (55) for the point defect formation and migration energies. The plane-wave cutoff energy was set to be 520 eV. The integration in the reciprocal space was performed using 6 × 6 × 3 and 2 × 2 × 2 Γ-centered grids for the unit cell and the supercell, respectively. Structure optimization was carried out until that all residual forces acting on each atom become less than 0.02 eV/Å. The migration energies of H ion via vacancy mechanisms were calculated using the CI-NEB method with three intermediate images (56, 57).

SUPPLEMENTARY MATERIALS

Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/7/23/eabf7883/DC1

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REFERENCES AND NOTES

Acknowledgments: Funding: This work was partly supported by CREST grant nos. JPMJCR1421 and JPMJCR20R2; JSPS KAKENHI grant nos. JP16H06438, JP16H06439, JP16H06440, JP16H06441, and JP19H04710; Nanotechnology Platform Program (Molecule and Material Synthesis) (S-20-MS-0015) from the Ministry of Education, Culture, Sports, Science and Technology (MEXT) of Japan; and Japan Society for the Promotion of Science (JSPS) Core-to-Core Program (JPJSCCA20200004). The SXRD experiments were performed at SPring-8 with the approval of JASRI. The NPD experiment was performed at J-PARC (2019S10). The IC measurements were conducted by Sumika Chemical Analysis Service Ltd. H.U. was supported by JSPS Research Fellowships for Young Scientists. G.K. acknowledges support from JSPS, grant numbers 17H05492 and 20H02828. Author contributions: H.K. designed the study. H.U. performed the synthesis, characterizations, and H/D exchange experiments. H.U., C.T., and T.B. performed the structural refinements of the neutron data collected by T.S and T.K. The electrochemical measurements were supervised by G.K. and performed by H.U. and F.T., K.S., and A.K. conducted the DFT calculations. All authors discussed the results. H.U., F.T., and H.K. wrote the manuscript, with contributions from other authors. Competing interests: The authors declare that they have no competing financial interests. Data and materials availability: All data needed to evaluate the conclusions in the paper are present in the paper and/or the Supplementary Materials.

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