Fig. 1. Schematic view of the experimental apparatus for the electrical conductivity.

Fig. 2. IR absorption spectra of 0.1 mol% Ba-doped α-alumina annealed in a water and a heavy water vapor atmosphere.

Fig. 3. Absorbance vs. activity of water vapor in the atmosphere.

Fig. 4. Absorbance vs. activity of hydrogen in an oxidizing atmosphere. The line (- - -): fitting curve by Eq. (16).

Fig. 5. Absorbance or concentration of hydrogen vs. activity of hydrogen in the atmosphere. The lines (- - -): fitting curves by Eq. (16).

Fig. 6. Polarization angle dependence of the integral absorption. (a) , (b) and (c) .

Fig. 7. Observed and calculated total amount of change in protons upon substitution of a proton for a deuteron at 1073 K. The lines (—): fitting curves by Eq. (1).

Fig. 8. H⁺/D⁺ isotope effect on electrical conductivity.

Fig. 9. Relaxation of the ohmic resistance of 0.1 mol% Ba-doped α-alumina when the measuring atmosphere was changed from 1%H₂O-1%H₂-Ar to 1%D₂O-1%D₂-Ar. . Fitting curves by Eqs. (6) and (7): (—) cm² s^− 1, (- - -) cm² s^− 1, (– –) cm² s^− 1, (– · –) cm² s^− 1.

Fig. 10. Calculated polarization angle dependence of the integral absorption on the assumption that hydrogen preferentially enters into the OO bond with a specified spacing. a) , (b) and (c) .

Fig. 11. Arrhenius-type plots of the self-diffusion coefficient in α-alumina. 1. Single crystal α-Al₂O₃ (250 ppm V): El-Aiat and Kröger [20]. 2. 0.1 mol% Ba-doped α-Al₂O₃ (10—1̅0): this work. 3. Polycrystalline α-Al₂O₃: Paladino and Kingery [19]. 4. Single crystal α-Al₂O₃: Oishi and Kingery [17]. 5. Single crystal α-Al₂O₃: Reddy and Cooper [18].

Fig. 12. Kröger–Vink diagram for barium-doped α-alumina.

Chemical diffusion coefficient of the D⁺/H⁺ diffusion pair

Drift mobility, conductivity and solubility of protons in 0.1 mol% Ba-doped α-alumina (101–̅0)