High Proton Conduction in the Octahedral Layers of Fully Hydrated Hexagonal Perovskite-Related Oxides

Proton conductors have potential applications such as fuel cells, electrolysis cells, and sensors. These applications require new materials with high proton conductivity and high chemical stability at intermediate temperatures. Herein we report a series of new hexagonal perovskite-related oxides, Ba5R2Al2SnO13 (R = Gd, Dy, Ho, Y, Er, Tm, and Yb). Ba5Er2Al2SnO13 exhibited a high proton conductivity without chemical doping (e.g., 0.01 S cm–1 at 303 °C), which is attributed to its high proton concentration and diffusion coefficient. The high diffusion coefficient of Ba5Er2Al2SnO13 can be attributed to the fast proton migration in the octahedral layers. The high proton concentration is attributed to full hydration in hydrated Ba5Er2Al2SnO13 and the large amount of intrinsic oxygen vacancies in the dry sample, as evidenced by both neutron diffraction and thermogravimetric analysis. Ba5Er2Al2SnO13 was found to exhibit high chemical stability under wet atmospheres of O2, air, H2, and CO2. High proton conductivity and high chemical stability indicate that Ba5Er2Al2SnO13 is a superior proton conductor. Ba5R2Al2SnO13 (R = Gd, Dy, Ho, Y, Tm, and Yb) exhibited high electrical conductivity in wet N2, suggesting that these materials also exhibit high proton conductivity. These findings will open new avenues for proton conductors. The high proton conductivity via full hydration and fast proton migration in octahedral layers in highly oxygen-deficient hexagonal perovskite-related materials would be an effective strategy for developing next-generation proton conductors.


INTRODUCTION
−7 Solid oxide fuel cells (SOFCs) have advantages such as high energy efficiency and fuel flexibility.−19 To develop highperformance PCFCs, it is important to explore novel proton conductors that exhibit both high proton conductivity and high chemical stability.−5 For example, CsH 2 PO 4 solid acids exhibit high proton conductivity of over 0.01 S cm −1 within a limited temperature range of 230−254 °C. 3 However, their application is limited due to the decomposition above 254 °C.In contrast, oxides generally exhibit high chemical stability and low proton conductivity at intermediate temperatures.As a result, there are no materials that exhibit both high proton conductivity and high chemical stability at intermediate temperatures, 20,21 although the lack of suitable materials has stimulated the search for new proton conductors.The purpose of this work is to explore new oxide materials with high proton conductivity and chemical stability.
The hexagonal perovskite-related oxides are a class of perovskite-related materials.The crystal structure of a hexagonal perovskite-related oxide has hexagonal close-packed (h) AO 3 layer(s) and/or intrinsically oxygen-deficient hexagonal closepacked AO 3−δ (h′) layer(s), 22,23 where A is a large cation such as Ba 2+ and δ is the amount of oxygen vacancies.Many hexagonal perovskite-related oxides also contain cubic close-packed (c) and/or anion-deficient cubic close-packed (c′) layers.−35 Here, the intrinsic oxygen vacancies are the oxygen vacancies in a parent material.−38 Murakami et al. 28 reported Ba 5 Er 2 Al 2 ZrO 13 as a new class of proton conductors with high proton conductivity comparable to those of representative proton conductors (e.g., 10 −3 S cm −1 at 300 °C).They refined the crystal structure of hydrated Ba 5 Er 2 Al 2 ZrO 13 using neutron diffraction data.Ba 5 Er 2 Al 2 ZrO 13 is a hexagonal perovskite-related oxide with h′ layers and octahedral layers.Here, the octahedral layer is the [ErO 6 − ZrO 6 −ErO 6 ] triple octahedral layer, which consists of two ErO 6 octahedral layers and one ZrO 6 octahedral layer and can be regarded as a triple perovskite-like layer.Murakami et al. 28 proposed the water uptake leading to the formation of protons in the h′ layers, which undergo two-dimensional proton diffusion.Later, Youn et al. 33  ) have the same crystal structure as Ba 5 Er 2 Al 2 ZrO 13 (10H polytype, hexagonal crystal system, space group P6 3 /mmc) and also exhibit significant proton conductivity. 26,28,30,32,33n general, a high proton concentration y is required for high proton conductivity.Here, the y values of hydrated perovskitetype BaBO 3−δ and hexagonal perovskite-related oxide Ba  Ba 5 A 2 Al 2 ZrO 13 materials are not high due to partial hydration. 26,28,30For example, the proton concentration y in Ba 5 Er 2 Al 2 ZrO 13−5y/2 (OH) 5y is 0.092 (ref 28), which is lower than the theoretical proton concentration for full hydration (y = 0.4), as shown later.The proton concentration of fully hydrated hexagonal perovskite-related oxides will be higher compared to that of partially hydrated ones; thus, full hydration will result in higher proton conductivity.However, to the best of our knowledge, there are no reports of fully hydrated hexagonal perovskite-related materials.In addition, to the best of our knowledge, there are no reports on Ba 5 A 2 Al 2 MO 13 materials (A = La, Bi, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu, Sc, In, and Ga; M = Sn, Hf, Ce, Ge, and Ti) in the literature.Therefore, we searched for Ba 5 A 2 Al 2 MO 13 materials.In this work, we discovered new materials Ba 5 R 2 Al 2 SnO 13 (R = Gd, Dy, Ho, Y, Er, Tm, and Yb).Among them, Ba 5 Er 2 Al 2 SnO 13 (BEAS) was found to exhibit full hydration and high chemical stability.The full hydration of BEAS enables high proton concentration and conductivity (e.g., 0.01 S cm −1 at 303 °C, which is higher than those of other proton conductors).
To demonstrate the proton conduction of BEAS, H/D isotope exchange experiments were performed at 300 °C in D 2 O-saturated N 2 and H 2 O-saturated N 2 (vapor partial pressure of 0.021 atm) (Figure 1a).The atmosphere was switched from D 2 O-saturated N 2 to H 2 O-saturated N 2 (first switching in Figure 1a), from H 2 O-saturated N 2 to D 2 O-saturated N 2 (second switching in Figure 1a), and then from D 2 O-saturated N 2 to H 2 O-saturated N 2 (third switching in Figure 1a).The conductivity ratios σ DC (H 2 O)/σ DC (D 2 O) at the first, second, and third switchings were approximately 1.5, which is close to 1.41, as expected from the classical theory. 39Here, σ DC (H 2 O) and σ DC (D 2 O) stand for the direct current (DC) electrical conductivities in H 2 O-saturated N 2 and D 2 O-saturated N 2 , respectively, which were measured by the DC four-probe method.The σ DC of BEAS in wet atmospheres was almost independent of the oxygen partial pressure P(O 2 ) and had a constant value in the wide P(O 2 ) ranges from 2 × 10 −22 to 1 atm at 400 and 600 °C and from 6 × 10 −23 to 1 atm at 300 °C, indicating negligible electronic conduction and high chemical and electrical stability (Figures 1b and S4).In contrast, in dry atmospheres, the slope of log(σ DC ) versus log(P(O 2 )) of BEAS had a positive value in the high P(O 2 ) ranges from 3 × 10 −4 to 1 atm at 600 °C and 3 × 10 −2 to 1 atm at 400 °C, suggesting hole conduction.At low P(O 2 ) ranges from 1.6 × 10 −23 to 3 × 10 −4 atm in dry atmospheres at 600 °C and 6.6 × 10 −24 to 5.5 × 10 −5 atm at 400 °C, the σ DC of BEAS was almost independent of the P(O 2 ), showing a constant σ DC value, electrolyte domain, negligible electronic conduction, and high chemical and electrical stability.The constant σ DC values independent of P(O 2 ) can be regarded as ionic conductivities.The proton transport number in wet N 2 was close to unity between 350 and 500 °C (Figure S3).The proton transport number of BEAS was investigated by electromotive force (EMF) measurements using vapor and oxygen concentration cells and was estimated to be 1.0 at 500 °C.The mean square displacement (MSD) was obtained from ab initio molecular dynamics (AIMD) simulations.The MSD of protons was much higher than the MSDs of other constituents (Figure 1c).These results indicate that the dominant carrier in BEAS is the proton.
Impedance measurements of BEAS were performed to investigate its bulk conductivity σ b .To extract the σ b and grain boundary conductivity σ gb of BEAS, equivalent circuit analyses were performed (Figures S5−S9).The obtained bulk capacitance (0.75−7.2 × 10 −12 F/cm) and grain boundary capacitance 0.95−4.4× 10 −11 F/cm were consistent with the values in the literature (Table S1). 40The difference between the activation energies for bulk conductivity in D 2 O-saturated N 2 and H 2 O-saturated N 2 (E D − E H ) was 0.058 (5) eV (Table S2), which was close to the E D − E H value of 0.055 eV predicted by the semiclassical theory. 39Here, E D and E H are the activation energies for the bulk conductivity in D 2 O-saturated N 2 and H 2 O-saturated N 2 , respectively.The ratio of the pre-exponential factors A H /A D was 0.49, which was consistent with the ratios of other proton conductors. 36,39Here, A H and A D are the preexponential factors in H 2 O-saturated N 2 and D 2 O-saturated N 2 , respectively.The σ b in wet N 2 was much higher than that in dry N 2 in the temperature range from 409 to 128 °C (e.g., 2100 times higher at 356 °C; Figure 1d).The proton transport number in wet N 2 was close to unity between 151 and 409 °C (Figure S10).These results also indicate the proton conduction of BEAS in wet N 2 .
The bulk conductivity of BEAS in wet N 2 σ b (H 2 O) was high (e.g., 0.01 S cm −1 at 303 °C in Figure 2a).At 300 °C, BEAS exhibited higher σ b (H 2 O) than other proton-conducting perovskite-type and hexagonal perovskite-related oxides 13,34,36,41 (see the details in Supplementary Note 1).The high σ b (H 2 O) of BEAS is attributed to both the high concentration and diffusion coefficient of protons, as discussed later.
The chemical stability of BEAS was investigated by annealing at 600 °C under wet atmospheres of O 2 , H 2 , air, and CO 2 .There was no significant difference between the XRD patterns before and after annealing (Figures S11 and S12), indicating the high chemical stability of BEAS.The high proton conductivity, high proton transport number, high chemical stability, and high chemical and electrical stability indicate that BEAS is a superior proton conductor.
To discuss the origin of the high bulk proton conductivity σ b (H + ) of BEAS, we investigated the bulk proton concentration y and the proton diffusion coefficient D, because σ b (H + ) is proportional to y and D: σ b (H + ) ∝ y × D (Supplementary Note 2).The high y and D are the origins of the high σ b (H + ) of BEAS (Figure 2b−d), as discussed below.To estimate the y of BEAS, we performed thermogravimetric (TG) and thermogravimetric−mass spectrometry (TG-MS) measurements.The TG-MS results indicated that the weight loss on heating was mainly due to dehydration (loss of H 2 O from the BEAS powders) (Figure S13).The TG results of BEAS showed the typical hydration behavior with higher proton concentration at lower temperatures (Figure S14 and Supplementary Note 3).At 300 °C, the proton concentration of BEAS (y = 0.35) was higher than those o f B a Z r 0 .8 Y 0 . 2 O 2 .9 − y / 2 ( O H ) y ( y = 0 .0 6 ) , B a -Ce 0.9 Y 0.  2c).The higher proton concentration of BEAS is a source of higher proton conductivity compared to other materials.The proton concentration y of hydrated perovskite-type and hexagonal perovskite-related oxides increases with an increase in the amount of oxygen vacancies δ of dry materials (Figures S15a and 2d).The value of y also increases with increasing fractional water uptake F w (= y/ 2δ) (Figures S15b and 2d).Therefore, the higher proton concentration y in BEAS (= Ba 5 Er 2 Al 2 SnO 14−5δ ) is attributed to the larger amount of oxygen vacancies (δ = 0.2) in dry BEAS without water and higher F w of 1.0 in hydrated BEAS compared to other perovskites and perovskite derivatives 13,35,41−44 (see the details in Supplementary Note 4).These results indicate that the high proton concentration y due to the large amount of oxygen vacancies in BEAS without water and the high fractional water uptake (full hydration) is the origin of the high proton conductivity in BEAS.S3).The occupancy factor of oxygen atoms at the interstitial O4 site, g(O; O4), was 0.02(2), indicating no oxygen atoms at the O4 site.Thus, the O4 atom was not placed in the final refinement.The bond valence sums of all of the cations and anions for the refined structures of dry Ba 5 Er 2 Al 2 SnO 13 were consistent with their formal charges, validating the refined crystal structure (Figure 3a).
Next, we performed Rietveld analyses of ND data of the hydrated (deuterated) Ba 5 Er 2 Al 2 SnO 13−5y/2 (OD) 5y pellets using t h e c r y s t a l d a t a o f h e x a g o n a l P 6 3 / m m c Ba 5 Er 2 Al 2 ZrO 12.77 (OH) 0.46 in ref 28 as initial parameters (Figure S17b and Table S4).The occupancy factor of oxygen atoms at the interstitial O4 site g(O; O4) was 1.08(3), indicating the full occupation of oxygen atoms at the O4 site.Thus, g(O; O4) was fixed to 1.00 in the final refinement (see the details in Table S4 and Figure S18).The bond-valence-based energy (BVE) and DFT calculations indicated the oxygen O4 and O3 sites and no other oxygen sites in the h′ layer of BEAS (Figure S19).Therefore, the h′ layer of fully hydrated BEAS is not the BaO  the first example of full hydration in hexagonal perovskiterelated materials.The proton concentration calculated using the occupancy factor of the O4 atom g(O; O4) agreed with that calculated from TG data, indicating that the bulk proton concentration of BEAS can be determined by TG.The D atoms of hydrated Ba 5 Er 2 Al 2 SnO 12 (OD) 2 existed at the D1 site closest to the O4 atom in the h′ Ba(O3)(O4) layers and the D2 site near the O2 atom in the octahedral layers (Figure 3b).Similarly, a fraction of the D atoms of Ba 2 LuAlO 4.522 (7) (OD) 0.957 (14) existed in the octahedral layer. 29,34The presence of the D1 atom closest to the O4 atom and the D2 atom near the O2 atom observed in the refined crystal structure was consistent with the results of AIMD simulations, where protons mainly existed at the sites near the O4 and O2 atoms (Figure S21).
It is interesting to compare the crystal structure and proton conductivity of hydrated Ba 5 Er 2 Al 2 SnO 13 with those of isostructural hydrated Ba 5 Er 2 Al 2 ZrO 13 .The lattice parameters and lattice volume of Ba 5 Er 2 Al 2 SnO 12 (OD) 2 were smaller than those of Ba 5 Er 2 Al 2 ZrO 12.77 (OH) 0.46 due to the smaller ionic radius of Sn 4+ (0.69 Å for coordination number 6) compared to Zr 4+ (0.72 Å for coordination number 6).At 200 °C in wet atmospheres, the bulk conductivity of BEAS was higher than that of Ba 5 Er 2 Al 2 ZrO 13−5y/2 (OH) 5y (BEAZ). 33The higher bulk conductivity of BEAS compared to BEAZ is attributed to the higher proton concentration of Ba  S22), which corresponds to the higher occupancy at the O4 site of hydrated BEAS compared to hydrated BEAZ.It is likely that the higher proton concentration in BEAS compared to BEAZ is attributed to the higher ability to incorporate the extra oxygen atoms O4 due to hydration into the h′ layer of BEAS compared to BEAZ.
To investigate the proton migration in the crystal structure of BEAS, AIMD simulations of Ba 5 Er 2 Al 2 SnO 13 •H 2 O were performed at 1200 °C using a 2 × 2 × 1 supercell (Ba 4 0 Er  4b and S23).The crystal structure refined by using the ND data of hydrated Ba 5 Er 2 Al 2 SnO 13 •D 2 O was used as the initial structure for the DFT structural optimization.Here four protons H1−H4 were placed in an h′ layer, four protons H5−H8 were placed in the other h′ layer, four protons H9−H12 were placed in an octahedral layer, and the other four protons H13−H16 were placed in the other octahedral layer.The optimized structure was used as the initial structure in the AIMD simulations.
In the AIMD simulations, each proton of H1, H2, H4−H6, and H8 placed in the h′ layer of the initial structure was mainly located closest to an O4 atom (blue trajectories in Figures 4a  and S24), while each proton of H9−H13 and H15 placed in the octahedral layer of the initial structure exhibited long-range migrations (red trajectories in Figures 4a and S25) as discussed below and in Supplementary Note 6.For example, proton H8, which was placed closest to the O4a atom in the h′ layer of the initial structure, was located closest to the O4a atom during 0−7 ps, indicating proton trapping (Figure 5a).On the contrary, proton H10, which was placed near the O2a atom in the octahedral layer of the initial structure, showed long-range migrations by reorientation and hopping from the proton sites near an O2 atom to those near a nearest-neighbor O2 atom (Figure S26 and Video S1).The H10 proton migrated between 0 and 0.2 ps from the sites near O2a to those near O2b, which we denote as "O2a−O2b".Then the H10 proton migrated as O2b− O2a−O2c−O2a−O2d−O2a−O2e−O2a−O2f−O2g−O2h− O2i between 0.2 and 7 ps.The proton migrated from the sites near O2 to those near the nearest O2′ along the O2−O2′ edge of the corner-shared ErO 6 and SnO 6 octahedra (Figures S26 and  5a).The distance between the O4a and H8 atoms in the h′ layer was almost constant from 0 to 20 ps (Figure 5b), which also indicates the proton trapping.In contrast, the distance between the O2a and H10 atoms increased with time, showing longrange proton diffusion (Figure 5c).For example, the distance between the O2a and H10 atoms increased from 0 Å at 0 ps to approximately 20 Å at 20 ps.The distance between the O4a atom and the Oij atom closest to the H8 atom was zero during 0−20 ps (Figure 5d), indicating the proton trapping (the atom labels Oij are shown in Figure 5a).On the contrary, the distance between O2a and the Oij which was nearest to H10 abruptly changed due to proton hopping to the sites near different Oij atoms (Figures 5e,f).The distance between the O2a and Oij atoms increased in a staircase-like fashion from 0 Å at 0 ps (Oij = O2a) to approximately 20 Å at 20 ps (Oij = O2i).
The MSDs of protons along the a and b directions were much higher than that along the c direction (e.g., 3.3 times higher at 20 ps in Figure S27), indicating that the high proton diffusion coefficient is attributable to the high proton MSDs along the a and b directions (Figure S27).The crystal structure of BEAS has the octahedral and h′ layers, and the MSD of protons in the octahedral layers was much higher than that in the h′ layer (e.g., 16 times higher at 20 ps in Figure S28).Therefore, the high MSDs of protons along the a and b directions are ascribed to the high MSD of protons in the octahedral layers.These results indicate that the high MSD (diffusivity) of protons in the octahedral layers is responsible for the high proton diffusion coefficient, leading to high proton conductivity.
This work has demonstrated that the new hexagonal perovskite-related oxide Ba 5 Er 2 Al 2 SnO 13−5y/2 (OH) 5y achieved high proton conductivity (e.g., 0.01 S cm −1 at 303 °C).Ba 5 R 2 Al 2 SnO 13−5y/2 (OH) 5y (R = rare earth) is also expected to exhibit a high proton conductivity.Therefore, we synthesized new materials Ba 5 R 2 Al 2 SnO 13−5y/2 (OH) 5y (BRAS) (R = Gd, Dy, Ho, Y, Tm, and Yb), as shown in Figure S29.The XRD patterns showed the formation of hexagonal perovskite-related oxides BRAS, and the lattice parameters and lattice volume increased with an increase in the ionic radius of the R 3+ cation (Figure S30 and Table S5).Preliminary measurements of DC electrical conductivities were performed in wet air, which indicated high conductivities (Figure 6).These results suggest that many hexagonal perovskite-related oxides Ba 5 R 2 Al 2 SnO 13−5y/2 (OH) 5y are high proton conductors.Preliminary TG measurements of BRAS were also performed, which indicated different proton concentrations (0.19 ≤ y ≤ 0.40 at 100 °C) and fractional water uptakes (0.48 ≤ F w ≤ 1.00 at 100 °C) depending on the rare earth species R (Figure S31).Therefore, the proton concentration, fractional water uptake, and proton conductivity were suggested to depend on not only the M species (M = Sn and Zr) but also the R species of the [RO 6 −MO 6 −RO 6 ] triple octahedral layer in Ba 5 R 2 Al 2 MO 13−5y/2 (OH) 5y .

CONCLUSION
In this work, we have discovered a series of new hexagonal perovskite-related oxides, Ba 5 R 2 Al 2 SnO 13 (R = Gd, Dy, Ho, Y, Er, Tm, and Yb).Ba 5 Er 2 Al 2 SnO 13 (BEAS) exhibits high chemical stability and high proton conductivity (e.g., 0.01 S cm −1 at 303 °C, which is higher compared to other proton conductors).The high proton conductivity of BEAS is attributed to its high proton concentration y and diffusion coefficient D. The higher proton conductivity of BEAS compared with the leading proton conductors BSM and BLA is attributed to the higher D of BEAS compared to these materials.The high D of BEAS is attributed to the proton diffusion in the [ErO 6 −SnO 6 −ErO 6 ] octahedral layers.On the other hand, the high proton concentration in BEAS is attributed to the large amount of oxygen vacancies δ = 0.2 in Ba(Er 0.4 Sn 0.4 Al 0.2 )O 2.8−δ (= 0.2 Ba 5 Er 2 Al 2 SnO 13 ) without water and the full hydration (high fractional water uptake F w of 1.0).The water uptake was found to occur by the occupation of extra oxygen atoms due to hydration at the interstitial oxygen O4 site.Indeed, the neutron diffraction analyses showed that the occupancy factors of the O4 atom of dry Ba 5 Er 2 Al 2 SnO 13 and hydrated Ba 5 Er 2 Al 2 SnO 12 (OD) 2 are 0.00 and 1.00, respectively.Here, the occupancy factor of g(O4) = 1.00 also shows the full bulk hydration, as well as the TG data.To the best of our knowledge, this is the first example of full hydration in hexagonal perovskite-related materials.The fractional water uptake in the hexagonal perovskite-related oxides Ba 5 R 2 Al 2 MO 13 (R = Ho, Er, and Tm for M = Sn; R = Er for M = Zr) is strongly dependent on the R and M species from 0.48 to 1.00 at 100 °C, resulting in the different proton concentration (y) values from 0.19 to 0.40 at 100 °C in Ba 5 R 2 Al 2 MO 13−5y/2 (OH) 5y .Therefore, the fractional water uptake, proton concentration, and proton conductivity can be controlled by the chemical composition R and M species in Ba 5 R 2 Al 2 MO 13 .Previous works have focused on the ABO 3−δ perovskite-type oxides as the fast proton conductors.In this work, we have demonstrated the highest proton conductivity of novel hexagonal perovskite-related oxide Ba 5 Er 2 Al 2 SnO 13 among the ceramic proton conductors, which would be a breakthrough for the development of fast proton conductors.

S y n t h e s i s a n d C h a r a c t e r i z a t i o n o f B E A S .
Ba 5 Er 2 Al 2 SnO 13−5y/2 (OH) 5y (BEAS) samples were synthesized by solid-state reactions.The starting materials BaCO 3 (99.95%,Kojundo Chemical Laboratory Co., Ltd., Japan), Al 2 O 3 (99.99%,Kojundo Chemical Laboratory Co., Ltd., Japan), Er 2 O 3 (99.9%,Shin-Etsu Chemical Co., Ltd., Japan), and SnO 2 (99.9%,Kojundo Chemical Laboratory Co., Ltd., Japan) were mixed and ground as ethanol slurries and dry powders in an agate mortar for about 1 h.The mixture was ground with a planetary-type ball mill at a rotation speed of 300 rpm using yttria-stabilized zirconia balls in ethanol for 30 min.The mixed powders were calcined in an electric furnace at 1000 °C for 12 h in air to remove the carbonates.The calcined powders of BEAS were ground for about 1 h as dry powders, isostatically pressed into pellets at approximately 200 MPa, and sintered in air at 1500 °C for 10−20 h.We called the obtained pellets "as-prepared BEAS pellets".The asprepared BEAS pellets were crushed and ground in an agate mortar, and the powders thus obtained are called "as-prepared BEAS powders" and were used for Cu Kα X-ray powder diffraction (XRD), synchrotron XRD, thermogravimetric (TG), thermogravimetric−mass spectrometry (TG-MS), X-ray photoelectron spectroscopy (XPS), and IR measurements.The as-prepared BEAS pellets were used in electrical conductivity measurements and scanning electron microscopy− energy-dispersive X-ray spectroscopy (SEM-EDS) observation.The Cu Kα XRD data of the as-prepared BEAS powders were measured using RINT-2550 (Rigaku Co., Ltd., Japan) and Miniflex600 (Rigaku Co., Ltd., Japan) diffractometers with Cu Kα radiation.XPS spectra of the as-prepared BEAS powders were measured using a JPS 9010 X-ray photoelectron spectrometer (JEOL Ltd., Japan).IR data of the asprepared BEAS powders were measured with an FT/IR-4200 (JASCO Co., Japan).The as-prepared BEAS powders were annealed at 600 °C for 12 h under wet atmospheres of O 2 , H 2 , and CO 2 to investigate the chemical stability.The as-prepared BEAS powders were also annealed at 600 °C for 24 h under wet air to investigate the chemical stability.The SEM micrograph and EDS maps of the as-prepared BEAS pellet were acquired with a JSM-6510LA microscope (JEOL Ltd., Japan).The elemental distributions of the as-prepared BEAS pellet were homogeneous (Figure S32).TG-MS analyses of as-prepared BEAS powders were performed under a He flow at a heating rate of 20 °C min −1 up to 1000 °C using a Thermomass Photo system (Rigaku Co., Ltd., Japan).
Synchrotron X-ray Powder Diffraction Measurements and Data Analysis.The synchrotron XRD data of the as-prepared BRAS powders (R = Gd, Dy, Ho, Y, Er, Tm, and Yb) were measured in air at 27 °C in transmission geometry with six one-dimensional solid-state detectors on beamline BL02B2 at SPring-8. 48The wavelength was determined to be 0.4006422(7) Å using silicon powder (NIST SRM 640c).The lattice parameters of the as-prepared BRAS powders (R = Gd, Dy, Ho, Y, Er, Tm, and Yb) were refined by Le Bail fitting using the synchrotron XRD data and the computer program GSAS-II. 49G Measurements on As-Prepared Ba 5 R 2 Al 2 SnO 13−5y/2 (OH) 5y .TG measurements of the as-prepared BRAS powders (R = Gd, Ho, Er, and Tm) were performed with a NETZSCH STA 449 F3 Jupiter system in the temperature range from 1000 to 100 °C.In the TG measurements, the as-prepared BEAS powders were heated to 1000 °C in dry N 2 (water vapor pressure P(H 2 O) < 10 −4 atm) at the heating rate of 10 °C min −1 and kept at 1000 °C for 1 h in dry N 2 to dehydrate and decarbonate, and then the gas was switched to wet N 2 (water vapor pressure P(H 2 O) = 0.021 atm).In the cooling process, the sample was kept for 2 h at 1000, 900, 800, 700, 600, 500, 400, 300, 200, and 100 °C to reach equilibrium in wet N 2 .
Crystal Structure Analyses Using the Neutron Diffraction Data of Dry Ba 5 Er 2 Al 2 SnO 13 and Hydrated Ba 5 Er 2 Al 2 SnO 12 (OD) 2 ."Dry Ba 5 Er 2 Al 2 SnO 13 " pellets were prepared by heating the as-prepared BEAS pellets at 800 °C for 30 min in a vacuum quartz tube to dehydrate and decarbonate.The sample in the quartz tube was cooled in vacuum to 300 °C, and then the quartz tube containing the pellets was sealed at this temperature."Hydrated (deuterated) Ba 5 Er 2 Al 2 SnO 12 (OD) 2 " ["hydrated (deuterated) Ba 5 Er 2 Al 2 SnO 13−5y/2 (OD) 5y "] pellets were synthesized using the as-prepared BEAS pellets as follows.The asprepared BEAS pellets were heated to 1000 °C in a dry He flow and kept at this temperature in a dry He flow for 30 min to dehydrate and decarbonate, and then the dry He flow was switched to D 2 O-saturated He flow (water vapor pressure P(D 2 O) = 0.021 atm).The pellets were kept at 1000 °C for 2 h in the D 2 O-saturated He flow and then cooled to 100 °C at the cooling rate of 10 °C min −1 .In the cooling process, the sample was kept in a D 2 O-saturated He flow for 2 h at each temperature of 900, 800, 700, 600, 500, 400, 300, 200, and 100 °C to reach equilibrium.Neutron diffraction data of the dry Ba 5 Er 2 Al 2 SnO 13 and hydrated Ba 5 Er 2 Al 2 SnO 13−5y/2 (OD) 5y pellets were measured at 5 K with the fixed-wavelength neutron diffractometer HERMES 50 at the JRR-3 research reactor of JAEA (Tokai, Japan) (wavelength = 1.3428(3)Å).The collected data were analyzed by the Rietveld method with the program RIETAN-FP. 51The bond-valence-based energy landscape for a test oxide ion in dry Ba 5 Er 2 Al 2 SnO 13 was calculated using refined crystal parameters at 5 K with the SoftBV program. 52easurements of Electrical Properties.The impedance spectra of BEAS were measured in wet N 2 (P(H 2 O) = 0.021 atm) and dry N 2 (P(H 2 O) < 5.0 × 10 −3 atm) using the as-prepared BEAS pellets (4 mm diameter, 6 mm thickness, relative density of 85%) with Pt electrodes.Impedance spectra were recorded with a Solartron 1260 impedance analyzer in the frequency range from 10 MHz to 0.1 Hz at an alternating voltage of 100 mV.Equivalent-circuit analysis was performed to extract the bulk conductivity and grain boundary conductivity using ZView software (Scribner Associates, Inc.).−55 DC conductivities σ DC of the as-prepared BEAS and BRAS pellets (R = Gd, Dy, Ho, Y, Tm, and Yb) were measured by a four-probe method with Pt electrodes.The temperature dependencies of σ DC of the asprepared BEAS pellets were investigated in dry and wet N 2 .The temperature dependencies of σ DC of the as-prepared BEAS and BRAS pellets (R = Gd, Dy, Ho, Y, Tm, and Yb) were also measured in wet air.The oxygen partial pressure P(O 2 ) dependence of σ DC of the asprepared BEAS pellets was investigated at 600, 400, and 300 °C in wet atmospheres in the P(O 2 ) range from 1 to 2 × 10 −22 atm.The σ DC of the as-prepared BEAS pellets was also measured in dry atmospheres at 600 and 400 °C at different P(O 2 ) in the P(O 2 ) range from 1 to 7 × 10 −23 atm.The P(O 2 ) was controlled using N 2 , O 2 , and 5% H 2 in N 2 , and monitored with an oxygen sensor at the outlet of the measurement apparatus.
Measurements of Proton and Oxide Ion Transport Numbers.To investigate the proton transport number t H and oxide ion transport number t O , concentration cell measurements of BEAS were performed at 500 °C by using a sintered pellet (16 mm in diameter, 1 mm thickness, and 98% relative density) attached to an alumina tube with a sealing material.The sum of t H and t O was estimated using the following equation based on the Nernst equation for the oxygen concentration cell:

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The t H was estimated using the following equation for the water vapor concentration cell:

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DFT Calculations and AIMD Simulations.The static DFT calculations and AIMD simulations were performed with the Vienna Ab Initio Simulation Package (VASP) 56 with projector augmented wave (PAW) potentials and the Perdew−Burke−Ernzerhof generalized gradient approximation (PBE-GGA).The plane-wave basis set with a cutoff of 500 eV was used in the static DFT calculations.In selfconsistent cycles, the total energy was minimized until the energy convergence was less than 10 −7 eV.Sums over occupied electronic states were calculated by the Gaussian scheme on a 7 × 7 × 2 k-point mesh for the 1 × 1 × 1 cell and on a 4 × 4 × 2 k-point mesh for the 2 × 2 × 1 cell.The cell parameters and atomic coordinates were optimized with a convergence condition of 0.02 eV Å −1 .Possible positions of the extra interstitial oxygen atoms due to the hydration of BEAS were investigated in the h′ layer by the static DFT calculations as follows.First, the lattice parameters and atomic coordinates of the 1 × 1 × 1 cell Ba 10 Er 4 Al 4 Sn 2 O 26 were optimized.An additional interstitial oxygen atom was then placed at the atomic coordinate (x, y, 1/4) in the optimized Ba 10 Er 4 Al 4 Sn 2 O 26 with a step interval of 0.1 from 0 to 1 for x and y (100 positions) to calculate the total energy of Ba 10 Er 4 Al 4 Sn 2 O 27 (Figure S19b), where the excess charge due to the interstitial oxygen atom was compensated by a uniform background charge.Structural optimization of a 2 × 2 × 1 supercell (Ba 40 Er 16 Al 16 Sn 8 O 112 H 16 ) was also carried out in space group P1 by the DFT calculations (Figure S23).The refined crystal parameters of hydrated BEAS (Table S4) were used as the initial structure for structural optimization.
AIMD simulations were also carried out using the PAW method and the PBE-GGA for the exchange and correlation functionals.The simulations were performed on a 2 × 2 × 1 supercell (Ba 40 Er 16 Al 16 Sn 8 O 112 H 16 ).The optimized structure in the static DFT calculations (Figure S23) was heated from −273 to 1200 °C at a rate of 1 °C fs −1 .The system was further equilibrated for 2 ps, and the production trajectory was accumulated for the canonical (constant N, V, T) ensemble using a Noséthermostat for ∼30 ps with a time step of 1 fs.The cutoff energy was set to 300 eV, and the reciprocal-space integration was performed only at the Γ point.To visualize the AIMD snapshots and trajectories, we used the OVITO program. 57The mean square displacements of all atoms were obtained with MDANSE. 58The refined crystal structures, the bond-valence-based energy landscape, and the probability density distribution of H atoms from the AIMD simulations were drawn with VESTA 3. 59 The relative frequency of oxygens nearest to each proton (Figure S21) and time evolutions of the oxygen atoms closest to each proton (Figures S24 and S25) were obtained using the Pymatgen code. 60ASSOCIATED CONTENT * sı Supporting Information The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/jacs.4c04325.
XRD patterns; XPS spectra; DC electrical conductivities; equivalent circuits; complex impedance plots; Arrhenius plots of bulk conductivity and grain boundary conductivity; H/D isotope effect; proton diffusion coefficient calculation; TG and TG-MS data; van't Hoff plots; correlation among the oxygen vacancy concentration without water, proton concentration, and fractional water uptake; Rietveld patterns; refined crystal parameters and reliability factors; bond-valence-based energy landscape; total energy landscape; IR spectrum; relative frequencies of oxygens nearest to each proton; time evolutions of the oxygen atoms closest to each hydrogen atom; snapshots of the proton diffusion process; time dependence of MSDs; synchrotron XRD data; lattice parameters; and SEM micrograph and EDS maps (PDF) also showed the anisotropic proton migration in Ba 5 Er 2 Al 2 ZrO 13 experimentally and by density functional theory (DFT) calculations.Ba 5 A 2 Al 2 ZrO 13 -based oxides (A = Dy, Tm, Yb, Lu, In, Y 1/4 Ho 1/4 Er 1/4 Yb 1/4 , Y 1/5 Dy 1/5 Ho 1/5 Er 1/5 Yb 1/5 , and Y 0.5 In 1.5

Figure 1 .
Figure 1.Evidence of the proton conduction in Ba 5 Er 2 Al 2 SnO 13 (BEAS).(a) H/D isotope effect of the DC electrical conductivity σ DC of BEAS at 300 °C (vapor partial pressure of 0.021 atm).(b) Oxygen partial pressure dependencies of σ DC of BEAS at 300 °C in wet atmospheres (blue solid circles and line) and at 400 °C in wet atmospheres (red solid circles and line) and dry atmospheres (red open circles and line).(c) Mean square displacement (MSD) of atoms obtained by ab initio molecular dynamics simulation at 1200 °C.(d) Arrhenius plots of bulk proton conductivity σ b (H + ) (red closed circles and line) and bulk conductivity in wet N 2 σ b (H 2 O) (black open circles) and dry N 2 σ b (dry) (blue open circles and line).The σ b (H + ) was calculated by the equation: σ b (H + ) = σ b (H 2 O) − σ b (dry).

Figure 4 .
Figure 4. Long-range migration and trapping of protons in the octahedral and h′ layers, respectively, of BEAS, studied by the trajectories of protons from the AIMD simulations.(a) Trajectories of 16 protons of Ba 40 Er 16 Al 16 Sn 8 O 112 H 16 in the AIMD simulations at 1200 °C during 0−10 ps.The blue lines represent the trajectories of H1−H8 placed in the h′ layers of the initial structure.The red lines denote the trajectories of H9−H16 placed in the triple-octahedral layers of the initial structure.(b) Initial structure of Ba 40 Er 16 Al 16 Sn 8 O 112 H 16 for AIMD simulations at 1200 °C.The pink, gray, and light-blue polyhedra stand for ErO 6 octahedra, SnO 6 octahedra, and AlO 4 tetrahedra, respectively.

Figure 5 .
Figure 5. Long-range migration and trapping of protons in the octahedral and h′ layers, respectively, of BEAS, studied by the AIMD simulations of Ba 40 Er 16 Al 16 Sn 8 O 112 H 16 at 1200 °C.(a) Rainbow trajectories of the H8 and H10 protons from 0 to 7 ps with the atomic arrangement at 0 ps.The red balls represent the oxygen atoms (Oij: i = 2, 4; j = a−i).The pink, gray, and light-blue polyhedra stand for ErO 6 octahedra, SnO 6 octahedra, and AlO 4 tetrahedra, respectively.(b, c) Distances between (b) O4a and H8 and (c) O2a and H10 with the time evolutions from 0 to 20 ps.(d, e) Distances from (d) O4a to Oij and (e) O2a to Oij with the time evolutions, where Oij is closest to the H8 and H10 atom, respectively.(f) Distances between O2a and Oij with the time evolutions from 0 to 7 ps, where the Oij are shown in (a).The rainbow colors in (a−f) denote the time evolution in the AIMD simulations, as shown by the color scale in (a).

V i d e o S 1 :
P r o t o n d i ff u s i o n p r o c e s s o f Ba 40 Er 16 Al 16 Sn 8 O 112 H 16 at 1200 °C from 2116 to 2878 fs (MP4) ■ AUTHOR INFORMATION Corresponding Author Masatomo Yashima − Department of Chemistry, School of Science, Tokyo Institute of Technology, Meguro-ku, Tokyo 152-8551, Japan; orcid.org/0000-0001-5406-9183;Email: yashima@cms.titech.ac.jp 1 6 Al 1 6 Sn 8 O 1 1 2 H 1 6 ).First, the structure of Ba 40 Er 16 Al 16 Sn 8 O 112 H 16 was optimized by DFT calculations.The structure of Ba 40 Er 16 Al 16 Sn 8 O 112 H 16 had two h′ layers and two octahedral layers (Figures