Kinetic Control of Anion Stoichiometry in Hexagonal BaTiO 3

: The cubic oxyhydride perovskite BaTiO 3 − x H x , where the well-known ferroelectric oxide BaTiO 3 is partially hydridized, exhibits a variety of functions such as being a catalyst and precursor for the synthesis of mixed-anion compounds by utilizing the labile nature of hydride anions. In this study, we present a hexagonal version, BaTi(O 3 − x H x ) ( x < 0.6) with the 6H-type structure, synthesized by a topochemical reaction using hydride reduction, unlike reported hexagonal oxyhydrides obtained under high pressure. The conversion of cubic BaTiO 3 (150 nm) to the hexagonal phase by heat treatment at low temperature (950~1025 ◦ C) using a Mg getter allows the introduction of large oxygen defects (BaTiO 3 − x ; x − 0.28) while preventing the crystal growth of hexagonal BaTiO 3 , which has been accessible at high temperatures of ~1500 ◦ C, contributing to the increase of the hydrogen content. Hydride anions in 6H-BaTiO 3 − x H x preferentially occupy face-sharing sites, as do other oxyhydrides.


Introduction
Mixed-anion compounds have been attracting attention as a new class of materials that exhibit novel functions such as high-temperature superconductivity and photocatalysis [1]. Oxyhydrides with the perovskite structure ( Figure 1a) and its layered analogues have made remarkable progress in recent years. These include Sr n+1 V n O 2n+1 H n showing insulatormetal transition under pressure, SrCrO 2 H and LaSrCoO 3 H 0.7 with a high magnetic ordering temperature, and Sr n+1 VnO 2n+1 H n (n = 1 and n → ∞), SrCrO 2 H, LaSrCoO 3 H 0.7 along with Ba 2−δ H 3−2δ X (X = Cl, Br, and I) exhibiting hydride (H − ) anion conductivity [2][3][4][5]. A partial hydridization of the well-known ferroelectric oxide BaTiO 3 results in an ammonia synthesis catalyst BaTiO 3-x H x , which is unprecedented given the strong Ti-N bonding. BaTiO 3−x H x is also a stable catalyst for CO 2 hydrogenation despite the generation of water [6][7][8][9]. Epitaxial thin film study shows that ATiO 3−x H x (A = Ba, Sr, Ca) is metallic, with a high conductivity of 10 2 -10 4 S/cm.
Due to the significant difference in the character of oxides and hydrides, oxyhydrides cannot be synthesized by conventional high-temperature solid-state reactions, with a few exceptions [10]. Some of the perovskite-related oxyhydrides such as LaSrCoO 3 H 0.7 , BaTiO 3−x H x , and SrVO 2 H are synthesized by low-temperature topochemical reactions using metal hydrides in vacuo [5,7,11]. An alternate approach is high-pressure synthesis, In contrast to the cubic perovskite (3C-BaTiO3) with only corner-sharing octahedra, hexagonal perovskite oxyhydrides BaVO3−xHx and BaCrO2H with the 6H structure (space group P63/mmc), composed of alternating face-and corner-sharing octahedral layers (Figure 1b), have been recently obtained by high-pressure synthesis. BaCrO2H is a magnetic insulator [14,15]. The preferential occupation of the hydride anion at the facesharing (6h) crystallographic site enhances the magnetic interaction and provides a high magnetic transition temperature [3]. BaVO3−xHx also has the hydride anions preferentially occupied at the face-sharing sites, but unlike BaCrO2H it is a Pauli-paramagnetic metal, with the variable hydride content depending on the synthesis conditions [14]. In this paper, we first show that the oxygen content of the hexagonal perovskite 6H-BaTiO3 can be tuned widely. We used Mg metal as an oxygen getter to convert the cubic BaTiO3 to the hexagonal one, 6H-BaTiO3−x, with the maximum content of x = 0.28. A subsequent low-temperature topochemical reduction with CaH2 introduces hydride anions into the hexagonal perovskite lattice, yielding 6H-BaTiO3−xHx, with the tunable hydride content (0 ≤ x ≤ 0.45) by changing the reducing conditions. The structural characterization has revealed the preferential occupation of the oxygen vacancies in 6H-BaTiO3−x and the hydride anions in 6H-BaTiO3−xHx, at the face-sharing site, which is supported by DFT calculations. The initial introduction of oxygen defects, along with the small grain size, are critically important for the hydride ion content of the final product, indicating the importance of the kinetic control to obtain the desired structures and compositions.

Experimental Section
We carried out hydride reductions using two types of hexagonal perovskite BaTiO3. One is 6H-BaTiO3 (BTO-L) with large particles of ~100 μm, provided by Murata Manufacturing Co. BTO-L was fabricated by H2 reduction of BaTiO3 (Sakai Chemicals, BT-03) at 1450 °C for 1 h. A mixture of BTO-L and CaH2 (99.7%, Aldrich) at a molar ratio of 10:1 was vacuum-sealed in a Pyrex tube and heat-treated at 520 °C for 72 h (L-1), 120 h (L-2), and 168 h (L-3), respectively. The large particle size of BTO-L is consistent with the fact that the synthesis of 6H-BaTiO3 requires calcination at high temperatures (1400~1500 °C) in a reducing atmosphere, but this is not suitable for anion (H − /O 2− ) exchange reactions, as will be shown later [11,16].
In order to obtain 6H-BaTiO3 with a smaller grain size to promote the anion exchange, we have developed a new method to convert cubic BaTiO3 into the hexagonal phase (BTO-S) by treating it with Mg at relatively low temperatures. First, BaTiO3 (~100 nm), provided by Sakai Chemicals (BT-01), was pelletized, and the pellet was sandwiched between pellets of equal weight mixtures of cubic BaTiO3 and Mg (>99.7%, Fujifilm Wako In contrast to the cubic perovskite (3C-BaTiO 3 ) with only corner-sharing octahedra, hexagonal perovskite oxyhydrides BaVO 3−x H x and BaCrO 2 H with the 6H structure (space group P6 3 /mmc), composed of alternating face-and corner-sharing octahedral layers (Figure 1b), have been recently obtained by high-pressure synthesis. BaCrO 2 H is a magnetic insulator [14,15]. The preferential occupation of the hydride anion at the face-sharing (6h) crystallographic site enhances the magnetic interaction and provides a high magnetic transition temperature [3]. BaVO 3−x H x also has the hydride anions preferentially occupied at the face-sharing sites, but unlike BaCrO 2 H it is a Pauli-paramagnetic metal, with the variable hydride content depending on the synthesis conditions [14].
In this paper, we first show that the oxygen content of the hexagonal perovskite 6H-BaTiO 3 can be tuned widely. We used Mg metal as an oxygen getter to convert the cubic BaTiO 3 to the hexagonal one, 6H-BaTiO 3−x , with the maximum content of x = 0.28. A subsequent low-temperature topochemical reduction with CaH 2 introduces hydride anions into the hexagonal perovskite lattice, yielding 6H-BaTiO 3−x H x , with the tunable hydride content (0 ≤ x ≤ 0.45) by changing the reducing conditions. The structural characterization has revealed the preferential occupation of the oxygen vacancies in 6H-BaTiO 3−x and the hydride anions in 6H-BaTiO 3−x H x , at the face-sharing site, which is supported by DFT calculations. The initial introduction of oxygen defects, along with the small grain size, are critically important for the hydride ion content of the final product, indicating the importance of the kinetic control to obtain the desired structures and compositions.

Experimental Section
We carried out hydride reductions using two types of hexagonal perovskite BaTiO 3 . One is 6H-BaTiO 3 (BTO-L) with large particles of~100 µm, provided by Murata Manufacturing Co. BTO-L was fabricated by H 2 reduction of BaTiO 3 (Sakai Chemicals, BT-03) at 1450 • C for 1 h. A mixture of BTO-L and CaH 2 (99.7%, Aldrich) at a molar ratio of 10:1 was vacuum-sealed in a Pyrex tube and heat-treated at 520 • C for 72 h (L-1), 120 h (L-2), and 168 h (L-3), respectively. The large particle size of BTO-L is consistent with the fact that the synthesis of 6H-BaTiO 3 requires calcination at high temperatures (1400~1500 • C) in a reducing atmosphere, but this is not suitable for anion (H − /O 2− ) exchange reactions, as will be shown later [11,16].
In order to obtain 6H-BaTiO 3 with a smaller grain size to promote the anion exchange, we have developed a new method to convert cubic BaTiO 3 into the hexagonal phase (BTO-S) by treating it with Mg at relatively low temperatures. First, BaTiO 3 (~100 nm), provided by Sakai Chemicals (BT-01), was pelletized, and the pellet was sandwiched between pellets of equal weight mixtures of cubic BaTiO 3 and Mg (>99.7%, Fujifilm Wako Chemicals Corporation) as a sacrificial reagent, sealed in a quartz tube under vacuum, and heat-treated at 950~1025 • C for 10 h. This procedure was repeated until the starting cubic BaTiO 3 phase disappeared, as observed by XRD analysis. Next, the obtained 6H-BaTiO 3 was washed with a 1:3 mixture of acetic acid and methanol at 60 • C for more than 10 h to remove MgO. Then, the BTO-S powder was mixed with 10 molar ratio CaH 2 in an immersion mortar, vacuum-sealed in a Pyrex tube, and heat-treated at 450~520 • C for 120 h to obtain hydride samples. The conditions for the samples synthesized in this study are shown in Table S1.
The crystal structures of the samples were examined by laboratory X-ray diffraction (XRD) measurements using a Smart Lab diffractometer (Rigaku) with Cu Kα radiation. High-resolution powder synchrotron XRD (SXRD) experiments were performed at room temperature (RT) using the BL02B2 beamline of the Japan Synchrotron Radiation Research Institute (JASRI). Incident beams from a bending magnet were monochromatized either to λ = 0.419839(1), 0.42015(1), or 0.42053(1) Å. Powder samples were loaded into Pyrex capillaries with an inner diameter of 0.3 mm. The sealed capillary was rotated during the measurements to reduce the effect of preferred orientation of crystallites. Neutron powder diffraction (NPD) data were collected at RT using the BL09 SPICA beamline at the Japan Proton Accelerator Research Complex (J-PARC). The collected SXRD and NPD patterns were analyzed by the Rietveld method using RIETAN-FP program for SXRD data and Z-Rietveld program for NPD data [17][18][19][20].
The release of hydrogen was monitored upon heating using a Bruker MS9610 quadrupole mass spectrometer (QMS). The sample was heated up to 800 • C under flowing Ar gas at a 300 mL/min rate. Thermogravimetric (TG) measurements were performed with a Netzsch TG-DTA 2000SE up to 800 • C under flowing O 2 gas at 300 mL/min rate. Platinum pans were used to hold both the sample and Al 2 O 3 as a reference. A Quantum Design MPMS-XL SQUID magnetometer was used to measure the magnetic susceptibility of the sample with an applied magnetic field of 0.1 T from 2 K to 350 K.
DFT calculations were performed using the projector augmented wave method as implemented in the VASP code [21,22]. An exchange correlation term was treated with the Perdew−Burke−Ernzerhof functional [23]. We considered all possible structures of the symmetrically independent O/H configurations in the hexagonal cell with compositions of Ba 6 Ti 6 O 18−n H n (where n = 1, 2, . . . , 6). For n = 1, we introduced one H into the symmetrically independent O site, O1 or O2. Symmetrically nonequivalent configurations for n = 1 amount to 2, as shown in Table S2. For n = 2, an additional H was placed to the symmetrically independent anion site into these structures. Symmetrically independent sites were searched based on space group using spglib library [24]. This process was repeated 6 times, preparing all the possible symmetrically independent O/H configurations up to n = 6. All the symmetrically nonequivalent configurations amount to 1496, shown in Table S2. We constructed 1496 input models, and for each model the total energy was minimized until the energy convergences became less than 10 −5 eV during self-consistent cycles. Atomic positions and lattice constants were relaxed until the residual atomic forces became less than 0.02 eV Å −1 . Correlation effects of 3d orbitals with the effective U potential of 4.49 eV were taken into account within the framework of the GGA+U method [25][26][27]. The effective plane-wave cutoff energy was set to 550 eV. Integration in reciprocal space was performed with a 5 × 5 × 2 grid. Furthermore, we analyzed the relationship between formation energies and structural parameters using a linear regression method. A database of the formation energies and the structural parameters was constructed from the calculations of 1496 independent configurations. Figure 2 shows the XRD patterns of BTO-L and its reduced products. The diffraction pattern of the precursor BTO-L can be indexed with a hexagonal lattice and the cell parameters of a = 5.726(1) Å and c = 13.970(1) Å, in good agreement with the reported values of 6H-BaTiO 3 [28]. After hydride reduction at 520 • C for 72 h, all the peaks shifted to the lower angles, yielding the elongated lattice constants of a = 5.753(1) Å and c = 14.070(1) Å. The lattice expansion is attributed to the partial reduction of Ti 4+ to Ti 3+ by anion (H − /O 2− ) exchange, as observed in the reduction of tetragonal BaTiO 3 to cubic BaTiO 2.4 H 0.6 [8]. No impurity phases were observed. The TG measurement of the sample after hydride reduction showed a substantial weight gain ( Figure S1a), and the QMS measurement under argon atmosphere showed the hydrogen gas release as observed in other oxyhydrides ( Figure S1b), suggesting the successful formation of an oxyhydride [6,8,11,15,28].

Results and Discussion
Inorganics 2022, 10, x FOR PEER REVIEW 4 of 10 to the lower angles, yielding the elongated lattice constants of a = 5.753(1) Å and c = 14.070(1) Å. The lattice expansion is attributed to the partial reduction of Ti 4+ to Ti 3+ by anion (H − /O 2− ) exchange, as observed in the reduction of tetragonal BaTiO3 to cubic BaTiO2.4H0.6 [8]. No impurity phases were observed. The TG measurement of the sample after hydride reduction showed a substantial weight gain ( Figure S1a), and the QMS measurement under argon atmosphere showed the hydrogen gas release as observed in other oxyhydrides ( Figure S1b), suggesting the successful formation of an oxyhydride [6,8,11,15,28].

Figure 2.
XRD patterns of the polycrystalline 6H-BaTiO3−x and 6H-BaTiO3−xHx. The S-2 sample was synthesized by the Mg reduction twice at 1000 °C for 10 h, which was further subject to hydride reduction with CaH2 at 520 °C for 120 h to produce S-2-2, in contrast to BTO-L prepared by H2 reduction at 1450 °C for 1 h.
The longer reaction time of hydride reduction (520 °C) with BTO-L (L-1, L-2, L-3) resulted in the larger lattice parameters ( Figure S2), similar to the case of cubic perovskite ATi(O3−xHx) (A = Ba, Sr, Ca) [8,29]. The elongation of the c-axis relative to its precursor oxide is more pronounced than that of the in-plane axes ( Figure S2), which is also consistent with the trend observed in other hexagonal (6H) perovskite oxyhydrides, BaV(O3−xHx) and BaCrO2H, in comparison with corresponding oxides [15,28]. However, several XRD peaks of BTO-L after hydride reduction exhibit shoulders, which could be due to a distribution in hydrogen content caused by the use of large particles, as also observed in cubic perovskite ATi(O3−xHx) (A = Ba, Sr, Ca) [8]. This prevented precise structural and compositional analysis of the oxyhydride phases.
The hexagonal barium titanate is stabilized by introducing oxygen vacancies (x in 6H-BaTiO3-x) with a tendency of the lattice constant increasing with x [30]. As mentioned earlier, this phase is accessible at 1400~1500 °C in flowing H2, but we hypothesized that further removal of the lattice oxygen would stabilize the hexagonal phase at lower temperatures where particle growth can be suppressed [16]. Figure 2 shows the XRD pattern of sample S-2, obtained by the heat treatment of cubic BaTiO3 (~100 nm) at 1000 °C for 10 h (×2) in a vacuum using Mg as an oxygen getter. All the diffraction peaks were assigned with the hexagonal cell (P63/mmc) structure, indicating the complete conversion from the cubic phase even at low temperatures. The SEM images of BTO-S revealed that the articles grew only slightly (~250 nm) ( Figure S3).
The Rietveld analysis of the SXRD data of sample S-2 (6H-BaTiO3−x) was performed using the P63/mmc model ( Figure 3). The occupancy factors (g) for the two oxygen sites are determined to be g = 0.72 (1) for the O1 (6h) site and g = 0.995(1) for the O2 (12k) site. Thus, the O2 site was assumed to be fully occupied (thus giving 6H-BaTiO0.72) in the following analysis. The dominant creation of oxygen vacancy at the face-sharing site is consistent with previous studies [30]. By changing the severity of the Mg reduction conditions (950~1025 °C for 10 h), we are able to widely tune the oxygen-vacancy content (Table S1). The lattice parameters as a function of oxygen vacancy content x (6H-BaTiO3−x)  [8,29]. The elongation of the c-axis relative to its precursor oxide is more pronounced than that of the in-plane axes ( Figure S2), which is also consistent with the trend observed in other hexagonal (6H) perovskite oxyhydrides, BaV(O 3−x H x ) and BaCrO 2 H, in comparison with corresponding oxides [15,28]. However, several XRD peaks of BTO-L after hydride reduction exhibit shoulders, which could be due to a distribution in hydrogen content caused by the use of large particles, as also observed in cubic perovskite ATi(O 3−x H x ) (A = Ba, Sr, Ca) [8]. This prevented precise structural and compositional analysis of the oxyhydride phases.
The hexagonal barium titanate is stabilized by introducing oxygen vacancies (x in 6H-BaTiO 3-x ) with a tendency of the lattice constant increasing with x [30]. As mentioned earlier, this phase is accessible at 1400~1500 • C in flowing H 2 , but we hypothesized that further removal of the lattice oxygen would stabilize the hexagonal phase at lower temperatures where particle growth can be suppressed [16]. Figure 2 shows the XRD pattern of sample S-2, obtained by the heat treatment of cubic BaTiO 3 (~100 nm) at 1000 • C for 10 h (×2) in a vacuum using Mg as an oxygen getter. All the diffraction peaks were assigned with the hexagonal cell (P6 3 /mmc) structure, indicating the complete conversion from the cubic phase even at low temperatures. The SEM images of BTO-S revealed that the articles grew only slightly (~250 nm) ( Figure S3).
The Rietveld analysis of the SXRD data of sample S-2 (6H-BaTiO 3−x ) was performed using the P6 3 /mmc model ( Figure 3). The occupancy factors (g) for the two oxygen sites are determined to be g = 0.72 (1) for the O1 (6h) site and g = 0.995(1) for the O2 (12k) site. Thus, the O2 site was assumed to be fully occupied (thus giving 6H-BaTiO 0.72 ) in the following analysis. The dominant creation of oxygen vacancy at the face-sharing site is consistent with previous studies [30]. By changing the severity of the Mg reduction conditions (950~1025 • C for 10 h), we are able to widely tune the oxygen-vacancy content (Table S1). The lattice parameters as a function of oxygen vacancy content x (6H-BaTiO 3−x ) are shown in Figure 4, along with those presented by Akimoto [28] and Sinclair [30]. Both the a-axis and the c-axis increase in proportion with oxygen deficiency. SXRD data of 6H-BaTiO 3−x prepared under different Mg-reduction conditions of BTO-S were analyzed by Rietveld analysis. The crystallographic parameters and the compositions estimated from the occupancy of O1 (6h) sites are summarized in Table S3, and lattice parameters in terms of oxygen contents are shown in Figure 4, along with those presented by Akimoto et al. and Sinclair et al. [28,30]. Both the in-plane and out-of-plane axes are elongated with increasing oxygen deficiency, which can be understood in terms of the enhanced Coulombic repulsion between Ti2 and Ti2.
Inorganics 2022, 10, x FOR PEER REVIEW 5 of 10 are shown in Figure 4, along with those presented by Akimoto [28] and Sinclair [30]. Both the a-axis and the c-axis increase in proportion with oxygen deficiency. SXRD data of 6H-BaTiO3−x prepared under different Mg-reduction conditions of BTO-S were analyzed by Rietveld analysis. The crystallographic parameters and the compositions estimated from the occupancy of O1 (6h) sites are summarized in Table S3, and lattice parameters in terms of oxygen contents are shown in Figure 4, along with those presented by Akimoto et al. and Sinclair et al. [28,30]. Both the in-plane and out-of-plane axes are elongated with increasing oxygen deficiency, which can be understood in terms of the enhanced Coulombic repulsion between Ti2 and Ti2.  Lattice parameters of (a) V, (b) a, and c as a function of x taken from 6H-BaTiO3 (after Akimoto [28]), 6H-BaTiO2.83 (after Sinclair [30]), and 6H-BaTiO3−x in this work (see Table S3-5). The errors are within the size of the symbols.
When 6H-BaTiO2.72 (derived from sample S-2 in Table S3-2) was reacted at 520 °C for 120 h using CaH2, the XRD peaks shifted to lower angles than those of 6H-BaTiO3 (BTO-L) after the same hydride treatment, and the elongated lattice constants of a = 5.7664(1) Å and c = 14.0713(1) Å were obtained as shown in Table S4-5. The SXRD data of 6H-BaTiO2.72 after hydride reduction (sample S-2-2) were analyzed by the Rietveld analysis assuming an oxygen-deficient 6H-BaTiO3−x (space group P63/mmc), without considering hydride anions (Figure 5a and Table S4-5), which yielded the occupancy factor of O2 of 0.99(1); thus, we fixed it as unity for later refinements. On the other hand, the occupancy factor at the O1 site was determined as 0.55(1), giving x = 0.45 (1). The tendency of the hydride anion to occupy the face-sharing site is similar to that of 6H-BaV(O3−xHx) and 6H-BaCrO2H [15,16].  are shown in Figure 4, along with those presented by Akimoto [28] and Sinclair [30]. Both the a-axis and the c-axis increase in proportion with oxygen deficiency. SXRD data of 6H-BaTiO3−x prepared under different Mg-reduction conditions of BTO-S were analyzed by Rietveld analysis. The crystallographic parameters and the compositions estimated from the occupancy of O1 (6h) sites are summarized in Table S3, and lattice parameters in terms of oxygen contents are shown in Figure 4, along with those presented by Akimoto et al. and Sinclair et al. [28,30]. Both the in-plane and out-of-plane axes are elongated with increasing oxygen deficiency, which can be understood in terms of the enhanced Coulombic repulsion between Ti2 and Ti2.  Lattice parameters of (a) V, (b) a, and c as a function of x taken from 6H-BaTiO3 (after Akimoto [28]), 6H-BaTiO2.83 (after Sinclair [30]), and 6H-BaTiO3−x in this work (see Table S3-5). The errors are within the size of the symbols.
When 6H-BaTiO2.72 (derived from sample S-2 in Table S3-2) was reacted at 520 °C for 120 h using CaH2, the XRD peaks shifted to lower angles than those of 6H-BaTiO3 (BTO-L) after the same hydride treatment, and the elongated lattice constants of a = 5.7664(1) Å and c = 14.0713(1) Å were obtained as shown in Table S4-5. The SXRD data of 6H-BaTiO2.72 after hydride reduction (sample S-2-2) were analyzed by the Rietveld analysis assuming an oxygen-deficient 6H-BaTiO3−x (space group P63/mmc), without considering hydride anions (Figure 5a and Table S4-5), which yielded the occupancy factor of O2 of 0.99(1); thus, we fixed it as unity for later refinements. On the other hand, the occupancy factor at the O1 site was determined as 0.55(1), giving x = 0.45 (1). The tendency of the hydride anion to occupy the face-sharing site is similar to that of 6H-BaV(O3−xHx) and 6H-BaCrO2H [15,16]. Lattice parameters of (a) V, (b) a, and c as a function of x taken from 6H-BaTiO 3 (after Akimoto [28]), 6H-BaTiO 2.83 (after Sinclair [30]), and 6H-BaTiO 3−x in this work (see Table S3-5). The errors are within the size of the symbols.
When 6H-BaTiO 2.72 (derived from sample S-2 in Table S3-2) was reacted at 520 • C for 120 h using CaH 2 , the XRD peaks shifted to lower angles than those of 6H-BaTiO 3 (BTO-L) after the same hydride treatment, and the elongated lattice constants of a = 5.7664(1) Å and c = 14.0713(1) Å were obtained as shown in Table S4-5. The SXRD data of 6H-BaTiO 2.72 after hydride reduction (sample S-2-2) were analyzed by the Rietveld analysis assuming an oxygen-deficient 6H-BaTiO 3−x (space group P6 3 /mmc), without considering hydride anions (Figure 5a and Table S4-5), which yielded the occupancy factor of O2 of 0.99(1); thus, we fixed it as unity for later refinements. On the other hand, the occupancy factor at the O1 site was determined as 0.55(1), giving x = 0.45 (1). The tendency of the hydride anion to occupy the face-sharing site is similar to that of 6H-BaV(O 3−x H x ) and 6H-BaCrO 2 H [15,16]. The Rietveld analysis was carried out using the time-of-flight neutron diffraction data of the same specimen ( Figure 5b and Table S4-5; sample S-2-2). According to the synchrotron result, the occupancy of the O2 site was set to unity, and anion vacancies at the O1 were not considered. The occupancy factors of oxide and hydride anions at the O1 site were obtained as 0.54(2) and 0.46(2), respectively, yielding the composition of BaTiO2.54H0.46. The result of QMS in Ar gas flow, shown in Figure 6, supports the inclusion of a large amount of hydride anions in the hexagonal perovskite structure. The magnetic susceptibility of S-2-2 ( Figure 7) is nearly temperature-independent, a typical behavior for paramagnetic metal, and no difference is seen between field cooling (FC) and zero field cooling (ZFC) processes. These facts indicate that the reaction proceeded further than in the case of the BTO-L case with the replacement of O 2− and the vacancies with H − [6,11,31].  The Rietveld analysis was carried out using the time-of-flight neutron diffraction data of the same specimen ( Figure 5b and Table S4-5; sample S-2-2). According to the synchrotron result, the occupancy of the O2 site was set to unity, and anion vacancies at the O1 were not considered. The occupancy factors of oxide and hydride anions at the O1 site were obtained as 0.54(2) and 0.46(2), respectively, yielding the composition of BaTiO 2.54 H 0.46 . The result of QMS in Ar gas flow, shown in Figure 6, supports the inclusion of a large amount of hydride anions in the hexagonal perovskite structure. The magnetic susceptibility of S-2-2 ( Figure 7) is nearly temperature-independent, a typical behavior for paramagnetic metal, and no difference is seen between field cooling (FC) and zero field cooling (ZFC) processes. These facts indicate that the reaction proceeded further than in the case of the BTO-L case with the replacement of O 2− and the vacancies with H − [6,11,31]. The Rietveld analysis was carried out using the time-of-flight neutron diffraction data of the same specimen ( Figure 5b and Table S4-5; sample S-2-2). According to the synchrotron result, the occupancy of the O2 site was set to unity, and anion vacancies at the O1 were not considered. The occupancy factors of oxide and hydride anions at the O1 site were obtained as 0.54(2) and 0.46(2), respectively, yielding the composition of BaTiO2.54H0.46. The result of QMS in Ar gas flow, shown in Figure 6, supports the inclusion of a large amount of hydride anions in the hexagonal perovskite structure. The magnetic susceptibility of S-2-2 ( Figure 7) is nearly temperature-independent, a typical behavior for paramagnetic metal, and no difference is seen between field cooling (FC) and zero field cooling (ZFC) processes. These facts indicate that the reaction proceeded further than in the case of the BTO-L case with the replacement of O 2− and the vacancies with H − [6,11,31]. Figure 6. Quadrupole mass spectrometry of H2 during heating of the S-2-2 which is prepared by twice heat treatment at 1000 °C for 10 h and subsequent hydrogenation with CaH2 at 520 °C for 120 h. Figure 6. Quadrupole mass spectrometry of H 2 during heating of the S-2-2 which is prepared by twice heat treatment at 1000 • C for 10 h and subsequent hydrogenation with CaH 2 at 520 • C for 120 h.
As in the case of BTO-L, by changing the reaction temperature and duration for hydride reduction of BTO-S, the amount of hydride can be varied. Note that the hydride topochemical reaction above 560 • C for BTO-L and those above 500 • C for BTO-S resulted in the appearance of TiH 2 impurity. We additionally found that the amount of oxygen vacancy in the parent oxide 6H-BaTiO 3−x affects the insertion efficiency of hydride anions; the higher/longer the reaction temperature/time of the CaH 2 reduction, the higher the amount of H − is. Samples of S-1-1~S-1-3, S-2-1, S-2-2, S-3-1, and S-4-1 (Table S4) show varied H − anion content, depending on CaH 2 reduction conditions ( Figure S4). With increasing CaH 2 -reduction temperature, Hanion content increases. The Hcontents are estimated from the occupancy (g) of oxygen assuming 'oxygen deficiencies' are filled fully with H − anions. As shown in Table S3-5 (sample S-2-2), the occupancy of H − in O1 site from the ND analysis is 0.46(2), in good agreement with the value of 0.45 (1) obtained from SXRD analysis, supporting the above assumption. The importance of the initial inclusion of anion deficiency for anion exchange reactions has been underlined in the topochemical synthesis of oxyhydrides of Sr(Ti 1−x Sc x )(O,H) 3    As shown in Figure 8, the aand c-axes and volume tend to increase with the H − content. Interestingly, this trend is suppressed beyond a hydride content of x − 0.4. The atomic distance between Ti2 and Ti2 nearest neighbors obtained from Rietveld analysis (see Figure 9a,b), i.e., titanium cations in face-sharing octahedra, increases in response to the increase in oxygen deficiency in 6H-BaTiO 3−x (Figure 9c), but in 6H-BaTiO 3−x H x the Ti2-Ti2 interatomic distance decreases in contrast to the Ba1-O1 distance (Figure 9d). In 6H-BaCrO 2 H, the Cr-Cr distance at the face-sharing site is greatly extended compared to BaCrO 3 , which is discussed together with enhanced magnetic interactions in terms of the highly polarized H ions [15]. A simple explanation for this behavior of our compounds is not possible at present, but various factors such as kinetic factors and local distortions are likely to be involved. We believe that further studies, including local structure analysis and in-depth theoretical studies, are needed in the future. As in the case of BTO-L, by changing the reaction temperature and duration for hydride reduction of BTO-S, the amount of hydride can be varied. Note that the hydride topochemical reaction above 560 °C for BTO-L and those above 500 °C for BTO-S resulted in the appearance of TiH2 impurity. We additionally found that the amount of oxygen vacancy in the parent oxide 6H-BaTiO3−x affects the insertion efficiency of hydride anions; the higher/longer the reaction temperature/time of the CaH2 reduction, the higher the amount of H − is. Samples of S-1-1~S-1-3, S-2-1, S-2-2, S-3-1, and S-4-1 (Table S4) show varied H − anion content, depending on CaH2 reduction conditions ( Figure S4). With increasing CaH2-reduction temperature, Hanion content increases. The Hcontents are estimated from the occupancy (g) of oxygen assuming 'oxygen deficiencies' are filled fully with H − anions. As shown in Table S3-5 (sample S-2-2), the occupancy of H − in O1 site from the ND analysis is 0.46(2), in good agreement with the value of 0.45(1) obtained from SXRD analysis, supporting the above assumption. The importance of the initial inclusion of anion deficiency for anion exchange reactions has been underlined in the topochemical synthesis of oxyhydrides of Sr(Ti1−xScx)(O,H)3 and CaV(O3−xHx) and oxynitrides of EuTiO2N [31][32][33].
As shown in Figure 8, the a-and c-axes and volume tend to increase with the H − content. Interestingly, this trend is suppressed beyond a hydride content of x − 0.4. The atomic distance between Ti2 and Ti2 nearest neighbors obtained from Rietveld analysis (see Figure 9a,b), i.e., titanium cations in face-sharing octahedra, increases in response to the increase in oxygen deficiency in 6H-BaTiO3−x (Figure 9c), but in 6H-BaTiO3−xHx the Ti2-Ti2 interatomic distance decreases in contrast to the Ba1-O1 distance (Figure 9d). In 6H-BaCrO2H, the Cr-Cr distance at the face-sharing site is greatly extended compared to BaCrO3, which is discussed together with enhanced magnetic interactions in terms of the highly polarized H ions [15]. A simple explanation for this behavior of our compounds is not possible at present, but various factors such as kinetic factors and local distortions are likely to be involved. We believe that further studies, including local structure analysis and in-depth theoretical studies, are needed in the future.   Table S4-8). The errors are within the size of the symbols. The values for x = 0 (open symbols) are taken after Akimoto [28]. DFT calculations were also performed for the transition metal Ti (d 1 ) to examine the site preference of the hydride anion in 6H-BaTiO3−xHx. We have calculated the energies of all possible structures of the independent 1496 coordination in Ba6Ti6O18−nHn (n = 1, 2, …, 6; Table S2) to know which site the hydrogen ion is more likely to occupy. The most stable configurations obtained for each n are shown in Figure S5, showing that when n is one to five, hydride anions preferentially occupy the face-sharing site. When n is six, hydride anions start to occupy the corner-sharing site, but the preference of cis-and trans-seems to be weaker than that of BaVO3−xHx [14] (see supporting information, Figures S6 and S7 and Table S2). Furthermore, theoretically, the H − anion in BaTiO3−xHx has a stronger tendency to occupy the 6h site (vs. the 12k site) than that of V in BaVO3−xHx, in particular for x < 0.33 (Table S4-5). This is consistent with the experimental observation in BaVO2.7H0.3 [14].
During the final preparation stage of this manuscript, we become aware of the report of 6H-BaTiO2.01H0.96, which was prepared from the direct reaction of BaH2 and TiO2 [34]. The material catalyzes the hydrogenation of the unsaturated C-C bonds when used as a support of Pd nanoparticles.

Conclusions
The hexagonal form of BaTiO3−x in a wide range of oxygen deficiencies, with the maximum content of x = 0.28, was synthesized from cubic BaTiO3 under strong reducing condition using Mg as an oxygen getter. In 6H-BaTiO3−x, oxygen vacancies are exclusively introduced into the face-sharing Ti-centered octahedral site O1. Low-temperature CaH2 reduction of the obtained 6H-BaTiO3−x yielded oxyhydride 6H-BaTiO3−xHx with H − ions occupying only at the face-sharing site O1, which is supported by DFT calculations. The initial introduction of oxygen defects, along with small grain size, is critically important for the hydride ion content of the final product, indicating the importance of the kinetic control to obtain the desired structures and compositions.  Table S2) to know which site the hydrogen ion is more likely to occupy. The most stable configurations obtained for each n are shown in Figure S5, showing that when n is one to five, hydride anions preferentially occupy the face-sharing site. When n is six, hydride anions start to occupy the corner-sharing site, but the preference of cisand transseems to be weaker than that of BaVO 3−x H x [14] (see supporting information, Figures S6 and S7 and Table S2). Furthermore, theoretically, the H − anion in BaTiO 3−x H x has a stronger tendency to occupy the 6h site (vs. the 12k site) than that of V in BaVO 3−x H x , in particular for x < 0.33 (Table S4-5). This is consistent with the experimental observation in BaVO 2.7 H 0.3 [14].
During the final preparation stage of this manuscript, we become aware of the report of 6H-BaTiO 2.01 H 0.96 , which was prepared from the direct reaction of BaH 2 and TiO 2 [34]. The material catalyzes the hydrogenation of the unsaturated C-C bonds when used as a support of Pd nanoparticles.

Conclusions
The hexagonal form of BaTiO 3−x in a wide range of oxygen deficiencies, with the maximum content of x = 0.28, was synthesized from cubic BaTiO 3 under strong reducing condition using Mg as an oxygen getter. In 6H-BaTiO 3−x , oxygen vacancies are exclusively introduced into the face-sharing Ti-centered octahedral site O1. Low-temperature CaH 2 reduction of the obtained 6H-BaTiO 3−x yielded oxyhydride 6H-BaTiO 3−x H x with H − ions occupying only at the face-sharing site O1, which is supported by DFT calculations. The initial introduction of oxygen defects, along with small grain size, is critically important for the hydride ion content of the final product, indicating the importance of the kinetic control to obtain the desired structures and compositions.
Supplementary Materials: The following supporting information can be downloaded at: https: //www.mdpi.com/article/10.3390/inorganics10060073/s1, Figure S1: Results of (a) thermogravimetric analysis, which was performed in oxygen flow at a rate of 300 mL/min; (b) quadruple mass spectrometry of H 2 ; Figure S2: The relationship between lattice parameters (a) c, (b) a, and reaction time for the 6H-BaTiO 3−x H x reduced by H 2 at 1450 • C for 1 h and hydrogenated with CaH 2 at 520 • C; Figure S3: SEM images of 6H BaTiO 3−x . (a) Specimen prepared by H 2 reduction at 1450 • C for 1 h (BTO-L); (b) specimen prepared by Mg reduction twice at 1000 • C for 10 h (BTO-S); Figure S4: Variation of hydrogen content in 6H-BaTiO 3−x H x as a function of hydrogenation temperature by CaH 2 reduction; Figure S5: The (a) 1st, (b) 2nd, and (c) 5th most stable structures in 6H-type system for Ba 6 Ti 6 O 16 H 2 obtained by the DFT calculations; Figure S6: Relationship between predicted energies from LASSO regression [35] and DFT calculations for Ba 6 Ti 6 O 16 H 2 ; Figure S7: Obtained coefficients from LASSO regression; Table S1: Sample lists. (a) BaTiO 3 (BT03, Sakai) was reduced in H 2 atmosphere and hydrided by CaH 2 . (b-e) BaTiO 3 (BT01, Sakai) was prepared by Mg reduction method and hydrided by CaH 2 ; Table S2: Number of symmetrically independent O/H configurations of a hexagonal unit cell with the composition of Ba6Ti6O 18−n H n (n = 1~6); Table S3: Crystallographic parameters of 6H-BaTiO 3−x with varied oxygen deficiencies prepared by Mg reduction; Table S4: Crystallographic data analyzed by the Rietveld analysis against SXRD and the NPD patterns of 6H-BaTiO 3−x H x prepared by Mg reduction in different conditions; Table S5: List of descriptors of structural parameters.