Hydride Conductivity in an Anion-ordered Fluorite Structure LnHO with

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Hydride Conductivity in an Anion-ordered Fluorite Structure LnHO with an Enlarged Bottleneck Hiroki Ubukata, Thibault Broux, Fumitaka Takeiri, Kazuki Shitara, Hiroki Yamashita, Akihide Kuwabara, Genki Kobayashi, and Hiroshi Kageyama Chem. Mater., Just Accepted Manuscript • DOI: 10.1021/acs.chemmater.9b01968 • Publication Date (Web): 12 Aug 2019 Downloaded from pubs.acs.org on August 12, 2019

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Chemistry of Materials

Hydride Conductivity in an Anion-ordered Fluorite Structure LnHO with an Enlarged Bottleneck Hiroki Ubukata1, Thibault Broux1, Fumitaka Takeiri2,3, Kazuki Shitara4, Hiroki Yamashita1, Akihide Kuwabara5, Genki Kobayashi2,3, and Hiroshi Kageyama1* Department of Energy and Hydrocarbon Chemistry, Graduate school of Engineering, Kyoto University, Nishikyoku, Kyoto 615-8510, Japan 1

2

Department of Materials Molecular Science, Institute for Molecular Science, Aichi 444-8585, Japan.

3

SOKENDAI (The Graduate University for Advanced Studies), Aichi 444-8585, Japan

4 Joining

and Welding Research Institute, Osaka University, Ibaraki, Osaka 567-0047, Japan

5 Nanostructures

Research Laboratory, Nagoya 456-8587, Japan

ABSTRACT: We report on the hydride (H‒) conductivity in fluorite-type LnHO oxyhydrides (Ln = lanthanide) using samples prepared under high pressure. It is found that, despite its ‘stoichiometric’ composition, the anion-ordered phase (Ln = La, Nd) exhibits hydride conductivity (e.g., 2.3  10‒5 S cm‒1 for NdHO at 300 °C), while the anion-disordered one (Ln = Gd, Er) is an ionic insulator. The systematic structural analysis combined with computational calculations has revealed the indirect interstitial mechanism, where H‒ anions migrate between the tetrahedral and octahedral sites through a triangular Ln3 bottleneck expanded by the anion order, with a critical bottleneck radius of 1.18 Å. This study may offer a general guide for the design and control of suitable anion diffusion pathways for oxyhydrides and more generally mixed-anion compounds.

1. Introduction The introduction of hydride (H‒) into an oxide leads to interesting properties that are impossible to achieve otherwise.1–3 The most feature of H‒ is its labile nature,4 making BaTi(O,H)3 perovskite a suitable precursor for anion-exchange reactions to access novel mixed-anion compounds including BaTi(O,N)3.5–7 The hydride lability (or hydride diffusion) is also one of the major reasons for BaTi(O,H)3 to work as a catalyst for NH3 synthesis and CO2 methanation by suppressing the so-called hydrogen poisoning.8–10 As such, hydride anion diffusion in oxide lattices offers considerable attention in various fields. For example, oxyhydrides could be useful toward realization of all-solid-state hydride-based electrochemical device. A ‘pure’ hydride conductivity in oxyhydrides was first demonstrated in layered perovskite La2LiHO3 and its Lasite substituted compounds.11 Subsequently, the H‒ anions in the isostructural Ln2LiHO3 (Ln = Pr, Nd)12 and Ba2ScHO3 13 are shown to be mobile. In comparison with oxide conductors, they exhibit relatively high conductivity at moderate temperatures, for example, 2.1  10‒4 S cm‒1 for La0.6Sr1.4LiH1.6O2 at 317 °C.11 Although it is obvious that the hydride amount, the presence of anion vacancy and the lattice size vary the H‒ conductivity, there remains a great deal of room for developing new structural variations and related concepts.

Figure 1. Fluorite-based LnHO structures. (a) anion order structure (𝑃4/𝑛𝑚𝑚) for Ln = La‒Nd.19,20 The Ln1, Ln2, and Ln3 cations are located at 2a, 2c, and 4e, respectively, and H and O anions at distinct 8i sites. (b) Anion-disordered structure (𝐹𝑚3𝑚) for Ln = Sm‒Er,23 with Ln and H/O ions at 4a and 8c. The dotted lines represent each unit cell. Fluorite-type structure is one of the best-known frameworks in solid state ionics, such as yttria-stabilized zirconia (YSZ), gadolinia-doped ceria (GDO),14,15 CaF2 and -PbF2.16–18 Oxyhydrides of this structural type are known,19–22 but properties studied so far are limited to luminescence22 and catalysis.23 We have recently found an unusual anion order-disorder transition in LnHO from the ordered form (𝑃4/𝑛𝑚𝑚) for lager Ln to the disordered one (𝐹𝑚3𝑚) for smaller Ln (Figure 1).23 The disordered form has a single anion-centered tetrahedron, with its volume increasing linearly with the Ln3+ radius, rLn, as shown in Figure 2. Upon the transition, it splits into two, with distinct tetrahedral volumes (Figure 2). Here,

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the H‒ size flexibility allows the HLn4 tetrahedron to be expanded, which is in order to reduce the OLn4 tetrahedral size and relieve otherwise underbonded oxygen.

residual CaH2 and byproduct CaO. These samples are labelled as LnHO-AP. For comparison, high-pressure polymorphs of LaHO (-LaHO and -LaHO) were also prepared as reported.25

Given the extensive research on anionic conductivity in fluorite-type compounds, LnHO could be promising as a hydride conductor. In this study, we used the highpressure (HP) methodology, which allowed for the preparation of stoichiometric LnHO, thus free from electronic conductivity. It is found that, while aniondisordered LnHO is ionic insulator, the anion-ordered one exhibits H‒ ion conductivity (e.g. 2.3  10‒5 S cm‒1 for NdHO at 300 °C). From the structural considerations combined with first principles calculations, what differentiates between the ordered and disordered phases is the size of the Ln3 triangular bottleneck for hydride migration between the lattice and interstitial sites, suggesting an anisotropic (i.e., two-dimensional) diffusion with a critical bottleneck radius of ~1.18 Å. This study may offer a general guide for the design and control of suitable diffusion pathways for mixed-anion compounds.

We measured powder X-ray diffraction (XRD) using a D8 ADVANCE diffractometer (Bruker AXS) with Mo-K radiation. Each sample was put into a Pyrex capillary with an inner diameter of 0.2 mm and sealed in under N2 atmosphere. We measured powder neutron diffraction at room temperature for NdHO-HP and ErHO-HP using a time-of-flight (TOF) neutron powder diffractometer, SPICA at J-PARC. The samples were installed in a vanadium can (diameter of 5.8 mm and height of 55 mm). The neutron profiles collected from the backscattering bank (average 2 = 160.77°, d = 0.1 ~ 4.1 Å) were refined by the Rietveld method using the Z-Rietveld program.26 Differential scanning calorimetry (DSC) was used to examine thermal stability of LnHO. The oxyhydride sample and the corundum reference material sealed in Al containers were subject to heat treatment under Ar atmosphere at a heating/cooling rate of 5 °C/min. Additionally, in-situ synchrotron XRD experiments were carried out in a range of temperature from 27 °C to 827 °C. The NdHO-HP sample was sealed as described above, but using a silica capillary. The diffraction profiles were collected after holding at each temperature for 3 min. The hydride exchangeability of NdHO under hydrogen atmosphere was tested by mass spectroscopy (MS) for the NdHO-HP sample after annealing with D2 gas for 1 h at 320 °C in a Pyrex tube.

Figure 2. The anion-centered tetrahedral volume as a function of the Shannon radius, rLn of the Ln3+ cation (8coordination)24 of LnHO (Ln = La-Er), reproduced from Ref. 23. 2. Experimental Procedure Lanthanide oxyhydrides LnHO (Ln = La, Nd, Gd, and Er) were synthesized under high pressure using LnH2+x (0 < x < 1; 99.9%, Kojundo) and dried Ln2O3 (99.9%, Wako). The starting materials were weighted in a 1:1 molar ratio, thoroughly mixed and pelletized in an N2-filled glovebox. The pellet was loaded into a BN sleeve inside a graphite heater, and sealed in a pyrophyllite cell, together with NH3BH3 pellet (which generates H2 upon heating). The assembled cell was heated at 900 °C for 1 h under 1 GPa using a cubic anvil press. Thus obtained products are denoted as LnHO-HP. For comparison, we prepared NdHO, GdHO, and ErHO using the reported method at ambient-pressure (AP);23 Ln2O3 (99.9%, Wako) was mixed with CaH2 (99%, Aldrich) in a 1:3 molar ratio, sealed in an evacuated silica tube, and heated at 650 °C for 20 h. After this procedure, the samples were washed with 0.1 M NH4Cl/methanol solution in order to completely remove

Electrical conductivities for all the compounds were measured by electrochemical impedance spectroscopy (EIS), using a Bio-Logic VSP-300 frequency response analyzer. The measurements were carried out under H2 atmosphere in a frequency range from 0.1 Hz to 7 MHz for 200 ‒ 300 °C. The as-prepared pellets were used for LnHO-HP, while the powder samples of LnHO-AP were pressed into pellet form at 1 GPa using the cubic anvil press. Gold was deposited on both sides of the sample pellets as the electrode. The measured impedance spectra were fitted with electrical equivalent circuits using the EC-Lab software. The DC electronic conductivity of NdHO-HP was measured using asymmetric (‒)Pd/NdHO/Au(+) cell at 300 °C, where Pd electrode was used as reversible electrode for H2 (see details in Supporting Information). We also conducted the conductivity experiments for -LaHO and -LaHO under the same conditions. First-principles calculations for the anion-ordered LaHO were performed using the projected augmented wave method as implemented in the VASP code.27–29 The exchange-correlation term was treated with the PerdewBurke-Ernzerhof functional revised for solid.30 The 5s and 5p electrons of the La atoms were treated as valence electrons for all calculations. A supercell containing 80 atoms was constructed by √2×√2×2 expansion of an optimized fluorite unit cell. The plane wave cutoff energies were set to 520 eV and integration in reciprocal


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Chemistry of Materials space was performed with 2×2×2 -point centered mesh. The total energies were minimized until the energy convergences were less than 10–5 eV during self-consistent cycles. The atomic positions and lattice constants were fully relaxed until the residual atomic forces become less than 0.02 eV Å‒1. The lattice parameters were calculated to be a = 7.995 Å and c = 5.651 Å. We considered point defects of vacancy and octahedral interstitial atoms of each elements, and antisite atoms of O and H. 2b, 2c, and 4d sites were calculated for the interstitial sites and 2a, 2c, and 4e sites for the La vacancy. The nudged elastic band (NEB) method31,32 was applied to the migration energy of the hydride hopping in LaHO lattice. The direct interstitial, indirect interstitial, and vacancy mechanisms were considered as migration path of the hydride ion (see Supporting Information). 3. Results and Discussions As displayed in Figure S1, XRD patterns for LnHO prepared at ambient pressure are similar to the previous results on LnHO, suggesting the formation of fluorite structure with anion order for Ln = La, Nd and without for Ln = Gd, Er.23 The anion order for the former was readily probed by the ½½1 superlattice reflection (based on the cubic fluorite cell), which was absent for the latter. The samples prepared under high pressure gave similar diffraction patterns (Figure S2), with the lattice constants being consistent with those of previously reported (Table S1).23,19,20 Despite the similarity of cell parameters, we observed a notable contrast in sample colour depending on the preparation method, as well as Ln3+ species (Figure 3 and Figure S3). GdHO-AP and ErHO-AP powder samples are black, but their high-pressure counterparts are light grey coloured. NdHO-AP and NdHO-HP, respectively, exhibit dark and pale violet derived from the 4f-5d transitions for Nd3+ ions.33 The substantial darkening for LnHO-AP samples (except for NdHO and LaHO) strongly suggests the presence of sizable Ln 5d electrons. We hence presumed that Ln3+ cations in “LnHO” are partially reduced, giving a slightly hydrogen-deficient composition of LnH1‒xO. Although the divalent state for lanthanide is rare in oxides (apart from Eu2+ and Yb2+), hydride materials can accommodate both divalent and trivalent states.34–36 For example, YHx films exhibit a reversible optical change between deep blue (YH2; metal) to transparent (YH3; semiconductor) by varying hydrogen pressure.37 Neutron refinement of ErHO-HP assuming the aniondisordered structure (𝐹𝑚3𝑚)23 with Er at 4a, O at 8c, and H at 8c (Figure 3a) yielded Rp = 3.17% and Rwp = 3.88% (Table S2). Occupancies of O and H were refined to 0.505(1) and 0.494(3), respectively, meaning that anion deficiency is at most less than 0.2%. For NdHO-HP, we used the anion-ordered structure (P4/nmm)20 by placing Nd1 at 2a, Nd2 at 2c, Nd3 at 4e, O at 8i, and H at 8i. The initial analysis gave the almost stoichiometric occupancy of gO = 0.985(4), which agrees with the expected

stoichiometry (Table S3). In contrast, there is a significant hydride deficiency, gH = 0.706(9), which is inconsistent with its colour and the result of conductivity measurements (shown later). Hinted at by LnH2+x, where excess hydride anions occupy the octahedral site,34,38 we allowed the hydride anions to occupy at the octahedral interstitial (2b, 2c and 4d) sites with a constraint of gH(2b) = gH(2c) = gH(4d) and the total hydride content of 1. This model resulted in gH = 0.897(3) and 0.103(3) at the tetrahedral and octahedral site, respectively, and the reliability factors of Rp = 2.11% and Rwp = 2.69% (Figure 3b and Table S4). Besides, from DFT calculations the formation probability of defects in the octahedral site (2c) is given by exp(‒0.3 eV/kBT), where kB is the Boltzmann constant and T is the synthesis temperature. It gives 5% at 1173 K, indicating that small amount of hydride anions can spontaneously move to the interstitial site. Interestingly, Fourier difference map calculated using the ideal anion-ordered structure without hydrogen showed significant negative scattering density only at the octahedral (2c) and tetrahedral (8i) sites (Figure S4). This observation led us to employ an alternate model, where hydride anions are exclusively occupied at 2c and 8i. The subsequent Rietveld analysis again with a constraint of the total hydride content of 1 yielded gH(8i) = 0.884(3) and gH(2c) = 0.46(1). Reliability factors of Rp = 2.11% and Rwp = 2.69% are similar to those of the initial model (Table S5). At present, it is difficult to conclude which of these two is more appropriate. In any event, a partial H‒ occupation at 2c at least takes place at room temperature. It should be pointed out that, as will be shown later, the long-range H‒ pathway cannot be formed by the 8i and 2c sites only, implying that the second model requires thermal hopping of H‒ to/from 4d at elevated temperature to account for the observed hydride conductivity.

Figure 3. Rietveld refinements for neutron data of (a) ErHO-HP and (b) NdHO-HP. The red crosses, black solid



line and blue solid lines represent the observed, calculated and residual curves, respectively. Green ticks indicate the peak positions. Several unindexed peaks (e.g., d ~ 2.25, 2.8 Å) in (a) come from Er2O3 (< 3%). The inset shows photos of AP and HP samples. The in-situ SXRD experiments on NdHO-HP to 827 °C exhibited an irreversible change in the lattice constants above 327 °C (Figure S5a). The DSC curve in the heating process showed a peak (endothermic) at 360 °C, which was absent in cooling process (Figure S6). These results indicate a thermal decomposition of NdHO around this temperature. The reversibility of the cell parameters between room temperature and 327 °C (Figure S5b) led us to conduct conductivity experiments in this temperature range. As inferred from the sample colour, the aniondisordered GdHO-AP and ErHO-AP suffered from the electronic contribution to the electric conductivity (Figure S7). Both samples showed high conductivities of the order of 10‒1 S cm‒1 (Gd) and 10‒3 S cm‒1 (Er), and there is no spike in the impedance spectra that are derived from the ion blocking electrodes. In a marked contrast, the anion-ordered NdHO-AP exhibited a rather low conductivity (10‒6 S cm‒1) with large temperature dependence (Figure S7c), suggesting that the electronic contribution is negligibly small. However, in the following we will show the results for NdHO-HP (and other LnHOHP samples) because the high-pressure samples give more promises of being electronically insulating. Hereafter LnHO-HP will be simply denoted as LnHO unless otherwise specified. The hydride exchangeability of NdHO with H2 (D2) gas was tested by annealing the NdHO specimen at 320 °C under D2 gas (5 atm) for 1 h in a stainless steel tube. The lattice parameters after this treatment does not change, while the MS experiment showed a substantial amount of HD and D2 gas, indicating the H/D exchange reaction to yield NdH1‒xDxO, as observed in BaTi(O,H)3.4,39 The EIS experiments on LnHO showed that the anion order/disorder plays a crucial role in the ionic conductivity. The resistivity of GdHO and ErHO with the anion-disordered structure was too high to be probed in the present setting (> 108  cm at least). In a stark contrast, the conductivities of the anion ordered LaHO and NdHO were measurable, with a spike in the impedance spectra in the low frequency region (Figure 4a, 4b). The two semicircles in the spectrum for LaHO corresponding to responses from the bulk and grainboundary component, respectively, were fitted using an equivalent circuit consisting of Rc + Rbulk/Qbulk + Rgb/Qgb (Figure 4a, Table S6). The bulk conductivity, for example, at 300 °C, was estimated as 1.32 × 10‒5 S cm‒1. Similarly, the impedance spectrum of NdHO could be resolved into a bulk and grain-boundary component (Figure 4b), yielding the bulk conductivity of 2.31 × 10‒5 S cm‒1 at 300 °C. The analysis by Hebb-Wagner polarization method40 gave an electronic conductivity of 2.15 × 10‒7 S cm‒1 for NdHO

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(Figure S8), which is much lower than the conductivity obtained by EIS. In addition, the ion transport number at 300 °C was calculated to be 99.1%, suggesting the predominant ionic conduction. From the linear slope of Arrhenius plots for LaHO and NdHO (Figure 4c), we estimated the activation energy as 97(2) kJ mol‒1 and 108(2) kJ mol‒1 for LaHO and NdHO, respectively. These values are comparable with those of previously reported oxyhydrides with the K2NiF4-based structure (95.4 kJ mol‒1 for La2LiHO3,11 62.3 kJ mol‒1 for Nd2LiHO3,12 86.4 kJ mol‒1 Ba2ScHO3 13). As for K2NiF4-type perovskite oxyhydrides, all-solid-state electrochemical cell based on La2LiHO3 demonstrated pure H‒ conduction at 300 °C,11 which is supported by firstprinciple calculations that gave the activation energies of 66‒75 kJ mol‒1 for H‒ migration and 116‒118 kJ mol‒1 for O2– migration.41,42 As shown in Figures S9 and S10, the formation energy related to hydrides is lower than that for oxides, and the Frenkel defect of H‒, in which the lattice H‒ moves to the interstitial (2c) site, is most reasonable with the lowest formation energy of 0.3 eV, as found in the room-temperature structure of LaHO. These results strongly suggest that the hydride ion is the main conducting species in LaHO and NdHO, although a possibility of oxide ion diffusion is not completely ruled out.

Figure 4. Cole-Cole plots for (a) LaHO-HP and (b) NdHO-HP at 300 °C. The equivalent circuit used for both plots are shown in the inset of (a). (c) Arrhenius plots of LaHO-HP (red) and NdHO-HP (blue), providing the activation energy of 97(2) and 108(2) kJ mol‒1, respectively. Let us consider the origin of the presence (absence) of hydride conductivity in the anion-ordered (disordered) structure in LnHO. The in-depth structural analysis of the anion-ordered NdHO phase at room temperature showed finite hydride deficiency at the tetrahedral (T) site owing to the partial occupation of the octahedral (O) sites. Thus, direct hopping between the neighboring T sites (via the so-called vacancy mechanism43) is in principle possible. However, this process would hardly occur since, as will be described later, it requires a rather high activation energy.


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Chemistry of Materials The alternative process, which we believe is likely to occur, involves a hopping between T and O sites. This indirect interstitial process has been discussed in various fluoride-type compounds such as -PbF2 44 and PbSnF4.17 While the anion-disordered (𝐹𝑚3𝑚) structure has a unique 𝑇H,O 8𝑐 ― 𝑂4𝑏 pathway ( 4), it splits into three pathways for hydride diffusion in the anion-ordered (P4/nmm) structure, 𝑇H8𝑖 ― 𝑂2𝑏 ( 1), 𝑇H8𝑖 ― 𝑂2𝑐 ( 1), and 𝑇H8𝑖 ― 𝑂4𝑑 ( 2), as shown in Figure 5. As reported previously,23 the (normalized) volume increases in proportion to the Ln3+ ionic radius (rLn), in the entire lanthanide series across the phase boundary, but the structural transition to the ordered phase leads to a marked expansion and reduction of the HLn4 and OLn4 tetrahedra, respectively. It means more specifically that the area of Ln3 triangles in the HLn4/OLn4 tetrahedron discontinuously jumps/drops at the structural transition.

and ideal opportunity to discuss the anion-diffusion pathway. The bottleneck radius, Rbn, of the cubic fluorite AX2 (or anion-disordered LnHO) is defined by 𝑙𝐴 ― 𝐴 𝑅𝑏𝑛 = ― 𝑟𝐴 (1) 3 where lA‒A is the distance between A cations and rA is the ionic radius of the A-site cation24 (see the inset of Figure 6). Fluorite-type compounds are one of the most wellknown anion conductors, as exemplified by YSZ and GDC.14,15 To our surprise, however, the bottleneck argument has not been performed, except for the ‘straight’ pathway through the center of two cations (vacancy mechanism between the lattice sites, Figure S11)45 though the carrier in fact takes a curved route.53,54 Figure 6 displays Rbn values as a function of rLn, where the averaged lLn‒Ln value was used for Ln = La, Nd. Although the tetrahedral volume in the disordered phase increases linearly with rLn, Rbn takes a nearly constant value of ~1.17 Å. In the ordered phase, there are six indirect interstitial pathways (Figure 6): 𝑇H8𝑖 ― 𝑂2𝑏, 𝑇H8𝑖 ― 𝑂2𝑐, 𝑇H8𝑖 ― 𝑂4𝑑 for H‒ and 𝑇O8𝑖 ― 𝑂2𝑏, 𝑇O8𝑖 ― 𝑂2𝑐, 𝑇O8𝑖 ― 𝑂4𝑑 for O2–. Regarding H‒, the 𝑇H8𝑖 ― 𝑂2𝑏 pathway has a similar Rbn to that of the disordered phase, while other two have much larger Rbn values. Since 𝑇H8𝑖 ― 𝑂2𝑐 with the largest Rbn (1.24 Å for La and 1.23 Å for Nd) provides only a shortrange diffusion (Figure S11), the addition of 𝑇H8𝑖 ― 𝑂4𝑑 with Rbn of 1.21 Å (La) and 1.20 Å (Nd) is necessary to allow a long-range diffusion. Figure 5c illustrates a twodimensional diffusion network by 𝑇H8𝑖 ― 𝑂2𝑐 and 𝑇H8𝑖 ― 𝑂4𝑑 provide. Given the nearly same hydride conductivities for LaHO and NdHO, the critical bottleneck radius should be around 1.18 Å.

Figure 5. Proposed anion diffusion pathways in LnHO, based on the indirect interstitial mechanism via Ln3 triangular bottleneck for (a) the anion-disordered and (b) the anion-ordered case. ‘T’ and ‘O’ denote tetrahedral and octahedral sites, respectively. The Ln cations marked by 1, 2, and 3 in (b) represent Ln1 (2a), Ln2 (2c) and Ln3 (4e). (c) Long-range H‒ diffusion pathway composed of 𝑇H8𝑖 ― 𝑂2𝑐 (dark blue line) and 𝑇H8𝑖 ― 𝑂4𝑑 (light blue line). To be more quantitative, let us introduce the effective bottleneck, which has been applied to argue cation/anion conductivity in a wide range of oxide materials such as perovskite (e.g., LnMO3 (M = In, Sc, Rh, Fe, Mn, and Al), La2/3‒xLi3xTiO3, and La0.95Sr0.05GaO3),45–48 brownmillerite (e.g., Ba2(In1‒xGax)2O5),49 apatite (e.g., La10Si5.8Mg0.2O26.8),50 NASICON-type materials (e.g., Na1+xMxZr2‒xP3O12),51 and melilite (La1.54Sr0.46Ga3O7.27).52 We would like to point out that all these compounds involve two (or more) different cations with distinct sites and valences. In a marked contrast, the LnHO system forms the bottleneck comprised only by Ln cations, thereby giving a unique

Figure 6. The rLn dependence of the bottleneck size, Rbn. Blue and red triangles represent Rbn for H‒ and O2‒ hopping from tetrahedral (T) lattice sites to octahedral (O) interstitial sites. Standard deviations are within the size of triangles. The dotted line represents a proposed threshold of the bottleneck for hydride ion conduction. The inset shows the bottleneck for anion migration in the ideal (anion-disordered) fluorite cell.



Using the Nudged-Elastic band (NEB) method, we estimated migration energies associated with hydride diffusion via indirect interstitial pathways (𝑂2𝑏 ― 𝑇H8𝑖 ― 𝑂2𝑐, 𝑂2𝑏 ― 𝑇H8𝑖 ― 𝑂4𝑑, 𝑂2𝑐 ― 𝑇H8𝑖 ― 𝑂4𝑑, and 𝑂4𝑑 ― 𝑇H8𝑖 ― 𝑂4𝑑) and obtained 1.2, 1.3, 0.6, and 0.7 eV (Figure S13). The latter two (responsible for the long-range diffusion network in Figure 4c) have lower energies (0.6 and 0.7 eV), while the former two involving the O2b site show higher energies (1.2 and 1.3 eV), in a good agreement with the result based on the bottleneck size. In addition, the calculated activation energy of 1.0 eV, given by the sum of the formation energy (0.3 eV) and the migration energy (0.7 eV for 𝑂4𝑑 ― 𝑇H8𝑖 ― 𝑂4𝑑), is in a reasonable agreement with the experimental value (1.01(2) eV for LaHO). For the direct interstitial and vacancy mechanisms, we found much higher activation energies of 1.6 and 2.3 eV (Figures S10, S13 and Table S7), supporting the indirect interstitial mechanism. We recently prepared two high-pressure polymorphs of LaHO, -LaHO (PbCl2-type) and -LaHO (Fe2P-type) (Figure S14).25 Although high-pressure phases of CaF2 (PbCl2- and Fe2P-type) are theoretically predicted to be excellent ionic conductors,55,56 the hydride conductivity for -LaHO and -LaHO appears to be impossible from the viewpoint of the bottleneck; -LaHO and -LaHO, respectively, require one and two pathways to allow a long-range diffusion (Figure S15). However, Rbn for LaHO is 1.10 Å and for -LaHO (smaller one) 1.01 Å, much smaller than the critical value of 1.18 Å. In fact, the EIS measurement show that the conductivity of both phases is less than 10‒8 S cm‒1 at 300 °C. The concept of the triangular bottleneck may be further applicable to other fluorite-type ion conductors. For example, alkaline-earth difluorides AF2 (A = Ca, Sr, and Ba) with the 𝐹𝑚3𝑚 space group have been studied as fluoride conductors. Despite a large difference in the cell parameters (5.44 Å, 5.80 Å, and 6.20 Å for A = Ca, Sr, and Ba), these fluorides exhibit similar activation energies of 197‒214 kJ mol‒1 and similar conductivities of 1.4‒6.8 × 10‒3 S cm‒1 at 777‒877 °C.18 These observations are understandable given the nearly same Rbn values: 1.10 Å for CaF2, 1.11 Å for SrF2, 1.11 Å for BaF2. 4. Conclusion We investigated the hydride conductivity of fluoritetype LnHO using the stoichiometric, electronically insulating samples prepared under high pressure. For NdHO, the hydride ion is partially present at the interstitial sites at ambient temperature. Electrochemical impedance measurements revealed that only the ordered phase (Ln = La, Nd) exhibits a hydride conductivity (e.g., 2.3  10‒5 S cm‒1 for NdHO at 300 °C). The enlarged hydride pathway as a result of the anion ordering is a key parameter for the hydride conduction based on the indirect interstitial mechanism. Namely, the bottleneck composed of the Ln3 triangle is greatly expanded as compared with the disordered case (5‒8%), giving the

critical bottleneck size of ~1.18 Å. The theoretical calculations support the indirect interstitial mechanism. Although ionic diffusion of materials is often discussed in terms of bottleneck, the simplicity of the bottleneck in the fluorite-type structure with the single-cation triangle allows for quantitative and comparative arguments. Combining the present finding with other well-known strategies such as aliovalent substitution (e.g. Ba2+ for Ln3+), we would be able to improve the ionic conduction property of LnHO and other fluorite-type mixed-anion compounds. ASSOCIATED CONTENT Supporting Information

The Supporting Information is available free of charge on the ACS Publications website. Methods: Hebb-Wagner polarization method and first-principles calculations. Supporting data: XRD patterns of LnHO-AP and LnHO-HP (Ln = La, Nd, Gd, Er), photos of ErHO-AP, ErHO-HP, NdHOAP, and NdHO-HP, crystallographic data for ErHO-HP and NdHO-HP, Fourier difference map for NdHO-HP, temperature dependence of the lattice parameters of NdHOHP, DSC result of NdHO-HP, EIS data for LnHO-AP (Ln = Nd, Gd, Er), the result of Hebb-Wagner polarization method for NdHO-HP, Formation energy of defects in stoichiometric LaHO, considerable hydride ion pathways in anion ordered LnHO, migration energies for interstitial hydride ions via indirect interstitial mechanism and direct interstitial mechanism and for hydride vacancy via vacancy mechanism, and crystal structures of LnHO polymorphs (-LaHO and LaHO).

AUTHOR INFORMATION Corresponding Author

* [email protected].

Notes

The authors declare no competing financial interests.

ACKNOWLEDGMENT This work was supported by CREST project (JPMJCR1421), Grants-in-Aid for Scientific Research on Innovative Areas “Mixed Anion” (No. JP16H06439; JP16H06440; and 17H05491), and by JSPS Core-to-Core Program (A) Advanced Research Networks (16H00888). The neutron experiments were conducted at J-PARC. The synchrotron radiation experiments were performed at the BL02B2 of SPring-8, with the approval of the Japan Synchrotron Radiation Research Institute (JASRI).

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Chemistry of Materials We report on the hydride (H‒) conductivity in fluorite-type LnHO oxyhydrides (Ln = lanthanide) with anion orderdisorder transition. It is found that, despite its ‘stoichiometric’ composition, the anion-ordered phase (Ln = La, Nd) exhibits hydride conductivity, while the anion-disordered one (Ln = Gd, Er) is an ionic insulator. The systematic structural analysis combined with computational calculations has revealed the indirect interstitial mechanism, where H‒ anions migrate through a triangular Ln3 bottleneck expanded by the anion-order. This study may offer a general guide for the design and control of suitable diffusion pathways for mixed-anion compounds.


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Hydride Conductivity in an Anion-ordered Fluorite Structure LnHO with

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