246
T. Onishi and T. Helgaker
Fig. 14.17 A schematic
picture of hydrogen defects
around zirconium vacancy in
BaZrO 3 perovskite
14.4 Concluding Remarks
14.4.1 General Conclusions
In this study, hybrid Kohn-Sham calculations were performed for ionics models to
investigate the proton conduction mechanism in BaZrO 3 perovskite. We concluded
as follows.
1. The activation energies were 2.26, 1.65 and 1.30 eV for O–H rotation within
Zr 4 O 4 square, O–O diagonal path and 3D O–H rotation across Zr 4 O 4 square,
respectively. The total activation energy was 3.91 eV, which is calculated from
the energy difference between the minimum in O–H rotation and maximum in
O–O diagonal path.
2. The activation energy changes, depending on Hartree-Fock coefficient in hybrid
Kohn-Sham method. Pure Kohn-Sham underestimates the activation energy.
3. The strong O–H covalent bonding is formed within Zr 4 O 4 square. O–H–O covalent bonding is in O–H dissociation region, from the energy difference between
bonding and antibonding molecular orbitals. It is considered that hydrogen as a
part of O–H covalent bonding is not recognized in the low-frequency real part of
AC impedance spectra.
4. Proton pumping effect is responsible for high proton conductivity. It is because
the short O–O distance blocks O–H dissociation.
5. Sc-doping is superior to Y-doping at titanium site.
6. N-doping at oxygen site enhances proton conductivity, the same as in SrTiO 3
perovskite.
7. Hydrogen defect is located toward zirconium vacancy, to avoid the ionic repulsion with barium. Proton conduction occurs between oxygen atoms around zirconium vacancy. However, hydrogen atom is trapped around zirconium vacancy,
due to the higher energy barrier.
14.4.2 Future Prospects
Very recently, we concluded that the defect of hydrogen-molecule (H 2 ) exists at
strontium vacancy at the cubic centre, and H 2 conduction occurs through strontium vacancy and Ti 4 O 4 bottleneck in SrTiO 3 perovskite [29]. The activation energy (1.4–1.5 eV) was calculated by BHHLYP hybrid Kohn-Sham method. The
T. Onishi and T. Helgaker
Fig. 14.17 A schematic
picture of hydrogen defects
around zirconium vacancy in
BaZrO 3 perovskite
14.4 Concluding Remarks
14.4.1 General Conclusions
In this study, hybrid Kohn-Sham calculations were performed for ionics models to
investigate the proton conduction mechanism in BaZrO 3 perovskite. We concluded
as follows.
1. The activation energies were 2.26, 1.65 and 1.30 eV for O–H rotation within
Zr 4 O 4 square, O–O diagonal path and 3D O–H rotation across Zr 4 O 4 square,
respectively. The total activation energy was 3.91 eV, which is calculated from
the energy difference between the minimum in O–H rotation and maximum in
O–O diagonal path.
2. The activation energy changes, depending on Hartree-Fock coefficient in hybrid
Kohn-Sham method. Pure Kohn-Sham underestimates the activation energy.
3. The strong O–H covalent bonding is formed within Zr 4 O 4 square. O–H–O covalent bonding is in O–H dissociation region, from the energy difference between
bonding and antibonding molecular orbitals. It is considered that hydrogen as a
part of O–H covalent bonding is not recognized in the low-frequency real part of
AC impedance spectra.
4. Proton pumping effect is responsible for high proton conductivity. It is because
the short O–O distance blocks O–H dissociation.
5. Sc-doping is superior to Y-doping at titanium site.
6. N-doping at oxygen site enhances proton conductivity, the same as in SrTiO 3
perovskite.
7. Hydrogen defect is located toward zirconium vacancy, to avoid the ionic repulsion with barium. Proton conduction occurs between oxygen atoms around zirconium vacancy. However, hydrogen atom is trapped around zirconium vacancy,
due to the higher energy barrier.
14.4.2 Future Prospects
Very recently, we concluded that the defect of hydrogen-molecule (H 2 ) exists at
strontium vacancy at the cubic centre, and H 2 conduction occurs through strontium vacancy and Ti 4 O 4 bottleneck in SrTiO 3 perovskite [29]. The activation energy (1.4–1.5 eV) was calculated by BHHLYP hybrid Kohn-Sham method. The