Improved Oxide Ion Conductivity of Hexagonal Perovskite-Related Oxides Ba 3 W 1+ x V 1 − x O 8.5+ x /2

: Hexagonal perovskite-related oxides such as Ba 3 WVO 8.5 have attracted much attention due to their unique crystal structures and signiﬁcant oxide ion conduction. However, the oxide ion conductivity of Ba 3 WVO 8.5 is not very high. Herein, we report new hexagonal perovskite-related oxides Ba 3 W 1+ x V 1 − x O 8.5+ x /2 ( x = − 0.1, − 0.05, 0.05, 0.1, 0.25, 0.4, 0.5, 0.6, and 0.75). The bulk conductivity of Ba 3 W 1.6 V 0.4 O 8.8 was found to be 21 times higher than that of the mother material Ba 3 WVO 8.5 at 500 ◦ C. Maximum entropy method (MEM) neutron scattering length density (NSLD) analyses of neutron diffraction data at 800 ◦ C experimentally visualized the oxide ion diffusion pathways through the octahedral O2 and tetrahedral O3 sites in intrinsically oxygen-deﬁcient layers. By increasing the excess W content x in Ba 3 W 1+ x V 1 − x O 8.5+ x /2 , the excess oxygen content x /2 increases, which leads to more oxygen atoms at the O2 and O3 oxygen sites, a higher minimum NSLD on the O2–O3 path, and a higher level of conductivity. Another reason for the increased conductivity of Ba 3 W 1.6 V 0.4 O 8.8 is the lower activation energy for oxide ion conduction, which can be ascribed to the longer (W/V)–O2 and (W/V)–O3 distances due to the substitution of V atoms with large-sized W species. The present ﬁndings open new avenues in the science and technology of oxide ion conductors.


Introduction
Oxide ion and proton conductors are important materials for clean energy and environment [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. For example, oxide ion conductors can be used in electrochemical devices such as solid oxide fuel cells (SOFCs) and solid oxide electrolyzer cells (SOECs). High oxide ion conductivity is needed for high-performance electrochemical devices and is attained in materials with specific crystal structures such as the fluorite-type and AMO 3 perovskite-type structures [10,11,[15][16][17]. Here, A and M are relatively larger and smaller cations. The conventional yttria-stabilized zirconia (YSZ) electrolytes exhibit low levels of oxide ion conductivity at intermediate temperatures, which restrict the widespread use of SOFCs with YSZ electrolytes. To solve this problem, it is of vital importance to search for new oxide ion conductors that exhibit higher conductivities.
There are four main groups of perovskite-type and perovskite-related structures: (i) the AMO 3 -perovskite-type structure, (ii) AMO 3 -perovskite-related structure, (iii) hexagonal perovskite-related structure, and (iv) modular structure [18,19]. Layered perovskites are emerging materials with layered structures that have perovskite or perovskite-like units [11]. The hexagonal perovskite-related oxides (iii) have a layered structure containing a hexagonal close-packed AO 3 h layer or an oxygen-deficient, hexagonal close-packed AO 3-δ h' layer [9,11,12,[18][19][20][21][22][23][24][25][26][27]. Compared with other perovskites, high levels of oxide ion and proton conduction were rarely found in hexagonal perovskite-related materials. Recently, high oxide ion conduction has been reported in various hexagonal perovskite-related oxides such as Ba 3 MoNbO 8.5 , Ba 3 WVO 8.5 , and Ba 7 Nb 3.9 Mo 1. 1 O 20.05 [18,20,21,[24][25][26][27]. Ba 3 M 2 O 8.5 oxides (e.g., M 2 = MoNb, WV, and WNb) exhibit structural disorder in the oxygen-deficient, cubic close-packed c' layer, leading to significant oxide ion conduction [19][20][21][22][24][25][26][27]. A high level of occupational disorder at the octahedral O2 and tetrahedral O3 sites yields a high probability density of oxygen atoms between the O2 and O3 sites, leading to a high level of oxide ion conductivity [27]. A possible means of increasing the probability density of oxygen atoms on the O2-O3 pathway is to have a larger amount of excess oxygen. Thus, the oxide ion conductivity of Ba 3 WVO 8.5 can be expected to increase by increasing the amount of oxygen 8.5+x/2 via W/V substitution in Ba 3 W 1+x V 1−x O 8.5+x/2 . Herein, we report new hexagonal perovskite-related oxides Ba 3 W 1+x V 1−x O 8.5+x/2 and their improved oxide ion conductivity compared with the mother material, Ba 3 WVO 8.5 . In the present work, we demonstrate that the bulk conductivity of Ba 3 W 1.6 V 0.4 O 8.8 is 21 times higher than that of mother material Ba 3 WVO 8.5 at 500 • C, which is ascribed to the greater amount of excess oxygen atoms O 0.3 and the lower activation energy for oxide ion conduction in Ba 3 W 1.6 V 0.4 O 8.8 .

Results and Discussion
1, −0.05, 0, 0.05, 0.1, 0.25, 0.4, 0.5, 0.6, and 0.75) oxides were prepared via solid-state reactions. Most of their X-ray powder diffraction (XRD) peaks at room temperature (RT) were indexed to a rhombohedral lattice, indicating that the main phase of Ba 3 W 1+x V 1−x O 8.5+x/2 is rhombohedral (space group: R3m and crystal symmetry: trigonal), which is consistent with the phase identification of Ba 3 WVO 8.5 in the literature [21,22]. Figure S1a is a typical XRD pattern of Ba 3 W 1.6 V 0. 4 O 8.8 , showing the main rhombohedral phase in addition to a small amount of BaWO 4 phase. The lattice volume and lattice parameter c of Ba 3 W 1+x V 1−x O 8.5+x/2 decrease with increasing excess W content x in the compositional range from x = 0.1 to 0.6, (Figure S1b,c), suggesting the formation of rhombohedral Ba 3 W 1+x V 1−x O 8.5+x/2 solid solutions. Figure 1a shows the Arrhenius plots of the direct current (DC) electrical conductivity σ DC of Ba 3 W 1+x V 1−x O 8.5+x/2 (x = −0.1, −0.05, 0, 0.05, 0.1, 0.25, 0.4, 0.5, 0.6, and 0.75) in static air. The σ DC increases with increasing temperature. At any temperature between 600 and 1000 • C, the corrected full-density DC electrical conductivity σ DC/corr increases with an increase in excess W content x in Ba 3 W 1+x V 1−x O 8.5+x/2 from x = −0.1 to 0.6, which can be ascribed to the increase in carrier concentration due to the increase in excess oxygen atoms x/2 in Ba 3 W 1+x V 1−x O 8.5+x/2 (Figure 1b). Meanwhile the σ DC/corr for x = 0.75 is lower than that for x = 0.6, over the entire temperature range, which can be ascribed to overdoping due to defect association and/or a greater amount of BaWO 4 impurity in the x = 0.75 sample. Similar overdoping has been observed in other hexagonal perovskiterelated oxides, such as Ba 7 Ta 4−x Mo 1+x O 20+x/2 [26]. Ba 3 W 1.6 V 0.4 O 8.8 exhibits the highest conductivity σ DC among Ba 3 W 1+x V 1−x O 8.5+x/2 (x = −0.1, −0.05, 0, 0.05, 0.1, 0.25, 0.4, 0.5, 0.6, and 0.75) over the entire temperature range (Figure 1a,b). Therefore, we focus on Ba 3 W 1.6 V 0.4 O 8.8 for further studies. For example, at 600 • C, the σ DC of Ba 3 W 1.6 V 0.4 O 8.8 (3.0 × 10 −4 S cm −1 ) is 86 times higher than that of the mother material, Ba 3 WVO 8.5 (3.5 × 10 −6 S cm −1 ). The σ DC values of Ba 3 W 1.6 V 0.4 O 8.8 at 800 and 1000 • C were as high as 3.7 × 10 −3 and 0.021 S cm −1 , respectively. X-ray photoelectron spectroscopy (XPS) spectra of Ba3W1.6V0.4O8.8 and Ba3WVO8.5 showed that the valences of W and V at RT were +6 and +5, respectively, ( Figure S2 Figure S3), demonstrating no change in oxygen content. Therefore, the chemical compositions at a high temperature of 800 °C are the same as those at RT. Figure 2a shows the oxygen partial pressure P(O2) dependence of the DC electrical conductivity σDC of Ba3W1.6V0.4O8.8 at 820 °C in dry conditions. The σDC increases with a decrease in P(O2) below 10 −18 atm, suggesting electronic conduction due to the reduction in W and/or V cations. Meanwhile the σDC is almost independent of P(O2) between 10 −17 and 0.21 atm at 820 °C, indicating that the influence of the p-type conducting BaWO4 impurity on the σDC is negligible (See the Supplementary Note in the Supporting Information). The UV-vis reflectance spectra of Ba3W1.6V0.4O8.8 indicated a wide optical band gap ( Figure S4), suggesting an electronic insulator. To examine possible proton conduction, the σDC was also measured in wet and dry air. The σDC values in wet air almost agree with those in dry air (Figure 2b). These results suggest oxide ion conduction in Ba3W1.6V0.4O8.8.   8.5 showed that the valences of W and V at RT were +6 and +5, respectively, ( Figure S2), indicating (Ba 2+ ) 3 (W 6+ ) 1.6 (V 5+ ) 0.4 (O 2− ) 8.8 and (Ba 2+ ) 3 (W 6+ )(V 5+ )(O 2− ) 8.5 . The thermogravimetric analyses in dry air indicated no significant weight change in the second and third heating/cooling cycles ( Figure S3), demonstrating no change in oxygen content. Therefore, the chemical compositions at a high temperature of 800 • C are the same as those at RT. Figure 2a shows the oxygen partial pressure P(O 2 ) dependence of the DC electrical conductivity σ DC of Ba 3 W 1.6 V 0.4 O 8.8 at 820 • C in dry conditions. The σ DC increases with a decrease in P(O 2 ) below 10 −18 atm, suggesting electronic conduction due to the reduction in W and/or V cations. Meanwhile the σ DC is almost independent of P(O 2 ) between 10 −17 and 0.21 atm at 820 • C, indicating that the influence of the p-type conducting BaWO 4 impurity on the σ DC is negligible (See the Supplementary Note in the Supporting Information). The UV-vis reflectance spectra of Ba 3 W 1.6 V 0.4 O 8.8 indicated a wide optical band gap ( Figure S4), suggesting an electronic insulator. To examine possible proton conduction, the σ DC was also measured in wet and dry air. The σ DC values in wet air almost agree with those in dry air ( Figure 2b). These results suggest oxide ion conduction in Ba 3 W 1.
Impedance measurements of Ba 3 W 1.6 V 0.4 O 8.8 were carried out in dry air to obtain its bulk conductivity. The impedance data were analyzed using the equivalent circuits shown in Figure S5 to extract the bulk and grain boundary conductivities. Figure 2c shows typical Nyquist plots of Ba 3 W 1.6 V 0.4 O 8.8 , with the bulk and grain boundary components indicated by semicircles. The bulk conductivity in dry air σ b of Ba 3 W 1.6 V 0.4 O 8.8 increases with increasing temperature and is as high as 3.0 × 10 −3 S cm −1 at 794 • C. The activation energy for σ b is lower than the activation energy for grain boundary conductivity ( Figure S6). The σ b of Ba 3 W 1.6 V 0.4 O 8.8 is higher than that of the mother material Ba 3 WVO 8.5 (e.g., it is 21 times higher at 500 • C). The σ b of Ba 3 W 1.6 V 0.4 O 8.8 is higher than that of Ba 3 WNbO 8.5 below 500 • C [20] and is comparable to that of Ba 3 MoNbO 8.5 around 370 • C [24], indicating that Ba 3 W 1.6 V 0.4 O 8.8 is a superior oxide ion conductor. The higher σ b of Ba 3 W 1.6 V 0.4 O 8.8 compared to Ba 3 WVO 8.5 is attributable to both the lower activation energy for σ b and the higher carrier concentration (a larger oxygen content of 8.8) of  8.5 . The structural origins of the lower activation energy and higher carrier concentration will be described below. Impedance measurements of Ba3W1.6V0.4O8.8 were carried out in dry air to obtain its bulk conductivity. The impedance data were analyzed using the equivalent circuits shown in Figure S5 to extract the bulk and grain boundary conductivities. Figure 2c shows typical Nyquist plots of Ba3W1.6V0.4O8.8, with the bulk and grain boundary components indicated by semicircles. The bulk conductivity in dry air σb of Ba3W1.6V0.4O8.8 increases with increasing temperature and is as high as 3.0 × 10 −3 S cm −1 at 794 °C. The activation energy for σb is lower than the activation energy for grain boundary conductivity ( Figure  S6). The σb of Ba3W1.6V0.4O8.8 is higher than that of the mother material Ba3WVO8.5 (e.g., it is 21 times higher at 500 °C). The σb of Ba3W1.6V0.4O8.8 is higher than that of Ba3WNbO8.5  To investigate the origin of its high oxide ion conductivity, the crystal structure was analyzed using neutron diffraction data of Ba 3 W 1.6 V 0.4 O 8.8 and Ba 3 WVO 8.5 taken in situ at 18 and 800 • C (Figure 3). Rietveld analyses of Ba 3 W 1.6 V 0.4 O 8.8 and Ba 3 WVO 8.5 were successfully carried out as a hybrid structure (space group: R3m, Figure 4). Figure 3 shows the Rietveld patterns, indicating satisfactory fits. Preliminary structure analyses indicated no significant occupancy of W/V atoms at the Wyckoff position 3b and full occupancy of W/V atoms at the 6c position (W/V site), indicating the chemical order of W/V atoms and W/V vacancies. Anisotropic atomic displacement parameters (ADPs) provided lower reliability factors than isotropic ADPs for Ba1, Ba2, O1, and O2 atoms. A split-atom model for the apical oxygen O3 at the 36i Wyckoff position yielded lower reliability factors compared with a non-split atom model. Therefore, we used anisotropic ADPs for Ba1, Ba2, O1, and O2 atoms and a split-atom model for the O3 atom in the final refinements. The refined crystal parameters and reliability factors are listed in Tables S1-S4. The bond valence sums of the Ba1, Ba2, W, V, and O1 atoms agree with their valences of +2, +2, +6, +5, and −2, validating the refined crystal structures. The crystal parameters of Ba 3 WVO 8.5 at room temperature and at 800 • C obtained in this work are consistent with those reported in the literature [21,22].
To investigate the origin of its high oxide ion conductivity, the crystal structure was analyzed using neutron diffraction data of Ba3W1.6V0.4O8.8 and Ba3WVO8.5 taken in situ at 18 and 800 °C (Figure 3). Rietveld analyses of Ba3W1.6V0.4O8.8 and Ba3WVO8.5 were successfully carried out as a hybrid structure (space group: R3m, Figure 4). Figure 3 shows the Rietveld patterns, indicating satisfactory fits. Preliminary structure analyses indicated no significant occupancy of W/V atoms at the Wyckoff position 3b and full occupancy of W/V atoms at the 6c position (W/V site), indicating the chemical order of W/V atoms and W/V vacancies. Anisotropic atomic displacement parameters (ADPs) provided lower reliability factors than isotropic ADPs for Ba1, Ba2, O1, and O2 atoms. A split-atom model for the apical oxygen O3 at the 36i Wyckoff position yielded lower reliability factors compared with a non-split atom model. Therefore, we used anisotropic ADPs for Ba1, Ba2, O1, and O2 atoms and a split-atom model for the O3 atom in the final refinements. The refined crystal parameters and reliability factors are listed in Tables S1-S4. The bond valence sums of the Ba1, Ba2, W, V, and O1 atoms agree with their valences of +2, +2, +6, +5, and −2, validating the refined crystal structures. The crystal parameters of Ba3WVO8.5 at room temperature and at 800 °C obtained in this work are consistent with those reported in the literature [21,22].     To discuss the origin of the high oxide ion conductivity of Ba3W1.6V0.4O8.8, neutron scattering length densities (NSLDs) were analyzed via the maximum entropy method (MEM), using the structure factors estimated in the Rietveld analyses of the neutron diffraction data of Ba3W1.6V0.4O8.8 and Ba3WVO8.5 taken in situ at 18 and 800 °C. It is known that MEM enables the visualization of the oxide ion diffusion pathways and structural disorder [18,19,22,27,29]. Figure 5 shows the NSLD distributions and corresponding refined structures of Ba3W1.6V0.4O8.8 at 800 °C. Connected NSLD distributions are clearly observed between the octahedral O2 and tetrahedral O3 atoms, which corresponds to the experimental visualization of the oxide ion O2-O3 diffusion pathways.    To discuss the origin of the high oxide ion conductivity of Ba 3 W 1.6 V 0.4 O 8.8 , neutron scattering length densities (NSLDs) were analyzed via the maximum entropy method (MEM), using the structure factors estimated in the Rietveld analyses of the neutron diffraction data of Ba 3 W 1.6 V 0.4 O 8.8 and Ba 3 WVO 8.5 taken in situ at 18 and 800 • C. It is known that MEM enables the visualization of the oxide ion diffusion pathways and structural disorder [18,19,22,27,29]. Figure 5 shows the NSLD distributions and corresponding refined structures of Ba 3 W 1.6 V 0.4 O 8.8 at 800 • C. Connected NSLD distributions are clearly observed between the octahedral O2 and tetrahedral O3 atoms, which corresponds to the experimental visualization of the oxide ion O2-O3 diffusion pathways. Figure 5b  The NSLD distributions around the O2 and O3 sites are localized at 18 • C (Figure 6a,b), while they are connected between the O2 and O3 sites at 800 • C (Figure 6c,d), which is consistent with the higher conductivity at higher temperature (Figures 1a and 2d). The minimum NSLD between the O2 and O3 sites (Figure 6e,f) can be a measure of oxide ion conductivity [27,29]. The minimum NSLD of Ba 3 WVO 8.5 at 800 • C (0.73 fm Å −3 ) is higher than that at 18 • C (0.08 fm Å −3 ), which is consistent with the higher conductivity observed at 800 • C (Figures 1a and 2d). Similarly, the minimum NSLD of Ba 3 W 1.6 V 0.4 O 8.8 at 800 • C (1.62 fm Å −3 ) is higher than that at 18 • C (0.95 fm Å −3 ), which is also consistent with the higher conductivity observed at 800 • C. We have demonstrated that Ba 3 W 1.6 V 0.4 O 8.8 exhibits higher oxide ion conductivity compared with the mother material Ba 3  The NSLD distributions around the O2 and O3 sites are localized at 18 °C ( Figure  6a,b), while they are connected between the O2 and O3 sites at 800 °C (Figure 6c,d), which is consistent with the higher conductivity at higher temperature (Figures 1a and 2d). The minimum NSLD between the O2 and O3 sites (Figure 6e,f) can be a measure of oxide ion conductivity [27,29]. The minimum NSLD of Ba3WVO8.5 at 800 °C (0.73 fm Å −3 ) is higher than that at 18 °C (0.08 fm Å −3 ), which is consistent with the higher conductivity observed at 800 °C (Figures 1a and 2d). Similarly, the minimum NSLD of Ba3W1.6V0.4O8.8 at 800 °C (1.62 fm Å −3 ) is higher than that at 18 °C (0.95 fm Å −3 ), which is also consistent with the higher conductivity observed at 800 °C. We have demonstrated that Ba3W1.6V0.4O8.8 exhibits higher oxide ion conductivity compared with the mother material Ba3WVO8.5. The minimum NSLD of Ba3W1.6V0.4O8.8 at 800 °C (1.62 fm Å −3 ) is higher than that of Ba3WVO8.5 at 800 °C (0.73 fm Å −3 ), which is consistent with the higher conductivity of Ba3W1.6V0.4O8.8. Ba3W1.6V0.4O8.8 Next, we discuss the origins of the higher conductivity of Ba3W1.6V0.4O8.8 compared with Ba3WVO8.5, based on their NSLD distributions at 800 °C ( Figure 6). Figure 6e,f shows  Next, we discuss the origins of the higher conductivity of Ba 3 W 1.6 V 0.4 O 8.8 compared with Ba 3 WVO 8.5 , based on their NSLD distributions at 800 • C ( Figure 6). Figure 6e,f shows schematic NSLD distributions between the nearest-neighbor O2 and O3 sites of Ba 3 WVO 8.5 (e) and Ba 3 W 1.6 V 0.4 O 8.8 (f) at 800 • C. Ba 3 W 1.6 V 0.4 O 8.8 has 0.3 excess oxygen atoms compared with the mother material Ba 3 WVO 8.5 . The excess oxygen atoms are incorporated at the O2 and O3 sites; therefore, the occupancy factors of the O2 and O3 atoms and oxygen content on the c' layer of Ba 3 W 1.6 V 0.4 O 8.8 are higher than those of Ba 3 WVO 8.5 . Thus, the NSLD and minimum NSLD between the O2 and O3 sites of Ba 3 W 1.6 V 0.4 O 8.8 (e.g., 1.62 fm Å −3 at 800 • C) are higher than those of Ba 3 WVO 8.5 (e.g., 0.73 fm Å −3 at 800 • C), leading to the higher oxide ion conductivity of Ba 3 W 1.6 V 0.4 O 8.8 . It is known that O2/O3 occupational disordering can enhance the oxide ion conductivity in Ba 3 WNbO 8.5 [27]. The disorder parameter DP was calculated using the formulation of Yasui et al. [27] and the refined crystal parameters in Tables S1-S4. The DP of Ba 3 W 1.6 V 0.4 O 8.8 (0.7660 (15) at 800 • C) is slightly lower than the DP of Ba 3 WVO 8.5 (0.860(4) at 800 • C), which cannot explain the conductivity enhancement observed in Ba 3 W 1.6 V 0. 4 O 8.8 . These results indicate the enhancement of the oxide ion conductivity of Ba 3 W 1.6 V 0.4 O 8.8 due to the excess oxygen.

Structural Origins of High Oxide Ion Conductivity in
We have indicated that the activation energy for the bulk conductivity of Ba 3 W 1.6 V 0.4 O 8.8 (0.741(12) eV) is lower than that of the mother material Ba 3 WVO 8.5 (1.13(1) eV) (Figure 2d). The occupancy factor of the larger W 6+ cation at the W/V site in Ba 3 W 1.6 V 0.4 O 8.8 (0.8) is higher than that in Ba 3 WVO 8.5 (0.5). Therefore, the (W/V)-O2 bond length of Ba 3 W 1.6 V 0.4 O 8.8 (2.1567(16) Å at 800 • C) is longer than that of Ba 3 WVO 8.5 (2.123 (4)  The calcined samples were crushed into powders and mixed again as ethanol slurries and dry powders using the agate mortar for 1 h, followed by ball milling processes using 5, 3, and 1 mm diameter zirconia balls at 300 rpm for 30 min at each size with a FRITSCH PULVERISETTE 7. The powders thus obtained were isostatically pressed into pellets at 150 MPa and sintered at 950-1020 • C for 20 h. The phase purity of Ba 3 W 1+x V 1−x O 8.5+x/2 were evaluated by XRD measurements using an X-ray diffractometer (Bruker D8, Cu Kα). The lattice parameters of Ba 3 W 1+x V 1−x O 8.5+x/2 were refined via the Le Bail analyses of the XRD data of the mixture of Ba 3 W 1+x V 1−x O 8.5+x/2 and an internal silicon standard using the software FullProf [30].
The  The total DC electrical conductivities σ DC of the sintered Ba 3 W 1+x V 1−x O 8.5+x/2 (x = −0.1, −0.05, 0, 0.05, 0.1, 0.25, 0.4, 0.5, 0.6, and 0.75) were measured via a DC four-probe method in static air at 600-1000 • C. Pt electrodes with Pt wires were attached to each pellet. The σ DC of Ba 3 W 1.6 V 0.4 O 8.8 was measured in dry and wet (water vapor pressure: P(H 2 O) = 0.023 atm) air. The P(O 2 ) dependence of Ba 3 W 1.6 V 0.4 O 8.8 was measured at 820 • C in a P(O 2 ) between 0.21 and 5.4 × 10 −25 atm, and the P(O 2 ) was controlled using a mixture of O 2 , N 2 , and 5% H 2 /N 2 gases and monitored by a YSZ oxygen sensor downstream of the apparatus. The impedance spectra of the sintered Ba 3 W 1.6 V 0.4 O 8.8 pellet with Pt electrodes were measured using a Solartron 1260 impedance analyzer in the frequency range of 1 MHz to 100 mHz with an AC voltage of 100 mV. The AC impedance measurements were carried out under a dry air flow from 794 to 382 • C. An equivalent circuit analysis was performed using ZView software (Scribner Associates, Inc., Southern Pines, USA) to exact the bulk and grain boundary conductivities. Neutron powder diffraction (ND) patterns of Ba 3 WVO 8.5 and Ba 3 W 1.6 V 0.4 O 8.8 were obtained using a fixed-wavelength neutron diffractometer, Echidna [31], at the OPAL research reactor, ANSTO, Australia. The range of 2θ was 10 • ≤ 2θ ≤ 160 • at 18 and 800 • C. The ND data were analyzed via the Rietveld method using Z-Rietveld [32,33]. The neutron scattering length density distributions were investigated using the maximum entropy method (MEM). The MEM analyses were performed with the structure factors obtained from the Rietveld analyses of Ba 3 WVO 8.5 and Ba 3 W 1.6 V 0.4 O 8.8 using Z-Rietveld [32,33]. The refined crystal structures and NSLD distributions were visualized using VESTA [34].

Conclusions
We have synthesized new hexagonal perovskite-related materials: Ba 3 Figure 1). Electrical properties and a wide optical band gap indicated the oxide ion conduction of Ba 3 W 1.6 V 0.4 O 8.8 (Figures 2 and S4). The bulk conductivity σ b of Ba 3 W 1.6 V 0.4 O 8.8 is higher than that of the mother material Ba 3 WVO 8.5 over the entire temperature range (Figure 2d). The refined crystal structure and MEM NSLD distributions of Ba 3 W 1.6 V 0.4 O 8.8 and Ba 3 WVO 8.5 at 800 • C indicated that the oxide ions migrate via the octahedral O2 and tetrahedral O3 sites (Figures 3-5, Tables S1-S4). The O2-O3 distance is short (e.g., 1.5880(6) Å in Ba 3 W 1.6 V 0.4 O 8.8 at 800 • C), which suggests an interexchange between the octahedral and tetrahedral geometries and an interstitialcy cooperative diffusion mechanism of the oxide ions, as in Ba 7 Nb 3.9 Mo 1.1 O 20.05 [18].
We have demonstrated that the excess amount of W species at the W/V site considerably improves the oxide ion conductivity. A larger excess of W species x produces a larger excess of oxygen x/2 in Ba 3 W 1+x V 1−x O 8.5+x/2 , which leads to more oxygen atoms at the O2 and O3 sites in the oxygen-deficient c' layer. This creates a higher NSLD between the O2 and O3 sites, leading to the higher oxide ion conductivity ( Figure 6). Thus, improvement in the oxide ion conductivity via excess oxygen can be a strategy to search for oxide-ionconducting hexagonal perovskite-related oxides. Another reason for the higher oxide ion conductivity of Ba 3 W 1.6 V 0.4 O 8.8 is the lower activation energy for oxide ion conduction (Figure 2d). We have suggested a size effect of the W/V cation on the activation energy for oxide ion conductivity E a in which the lower E a of Ba 3 W 1.6 V 0.4 O 8.8 can be ascribed to the longer (W/V)-O2 and (W/V)-O3 distances. Therefore, the substitution of the M cation with a larger one in Ba 3 M 2 O 8.5 oxides can be another strategy for improving oxide ion conductivity.
Supplementary Materials: The following supporting information can be downloaded at: https: //www.mdpi.com/article/10.3390/inorganics11060238/s1, Figure S1: X-ray powder diffraction pattern of Ba 3 W 1.6 V 0.4 O 8, lattice parameters and lattice volume of Ba 3 W 1+x V 1−x O 8.5+x/2 as functions of excess W content x; Figure S2: XPS spectra of Ba 3 W 1.6 V 0.4 O 8.8 and Ba 3 WVO 8.5 ; Figure S3: Thermogravimetric curves of Ba 3 W 1.6 V 0.4 O 8.8 ; Figure S4: Diffuse reflectance spectra and Tauc plots of Ba 3 W 1.6 V 0.4 O 8.8 ; Figure S5: Equivalent circuits and complex impedance plots of Ba 3 W 1.6 V 0.4 O 8.8 ; Figure S6: Arrhenius plots of bulk and grain boundary conductivities of Ba 3 W 1.6 V 0.4 O 8.8 ; Table S1: Refined crystallographic parameters and reliability factors of the neutron diffraction data of Ba 3 W 1.6 V 0.4 O 8.8 at 18 • C; Table S2: Refined crystallographic parameters and reliability factors of the neutron diffraction data of Ba 3 WVO 8.5 at 18 • C; Table S3: Refined crystallographic parameters and reliability factors of the neutron diffraction data of Ba 3 W 1.6 V 0.4 O 8.8 at 800 • C; Table S4: Refined crystallographic parameters and reliability factors of the neutron diffraction data of Ba 3 WVO 8.5 at 800 • C; Supplementary Note: Influence of BaWO 4 impurity on the electrical conductivity of Ba 3 W 1.6 V 0.4 O 8.8 . References [35][36][37][38][39] are cited in the supplementary materials.