14 A Theoretical Study on Proton Conduction Mechanism in BaZrO 3 Perovskite
235
titanium vacancy, and proton conduction mechanism related to O–H defect are still
unknown. In BaZrO 3 perovskite, zirconium vacancy and O–H defects are created
under oxidizing conditions in the same manner.
2H 2 O + 2O
X
O → V
Zr + 4OH
•
O .
(14.3)
In this study, we investigate the effect of a hydrogen defect around zirconium vacancy on proton conductivity, from energetics and bonding.
14.2 Computation
14.2.1 Calculation Method
The calculations presented here were performed using the BHHLYP hybrid KohnSham method [20], which properly reproduces the electronic structure of the
strongly correlated perovskite-type transition metal oxides. In BHHLYP theory, the
total exchange and correlation energy is expressed by 50 % Hartree-Fock (HF) exchange, 50 % Becke exchange and LYP correlation energies. Previously, we demonstrated that bandgap and effective exchange integral depend on HF exchange coefficient [21, 22] because M–O (M = transition metal) bonding character is controlled by localization effect. In this study, HF, B3LYP and BLYP theories with
100 %, 20 % and 0 % HF exchange, respectively, was also used to investigate
the dependence of localization effect on activation energy. We used the TatewakiHuzinaga MINI basis [23] for zirconium, barium, yttrium and scandium, combined
with the 6-31G(d) basis for oxygen and hydrogen. All calculations were performed
with the GAMESS program [24]. The molecular orbitals (MOs) were plotted using
MOLEKEL 4.3 [25].
14.2.2 Calculation Model
BaZrO 3 has a simple cubic structure, with a lattice parameter (the Zr–O–Zr distance) of 4.20 Å [26]. In our previous work, several ionics models were constructed
to investigate an ionic conduction in perovskite-type solids [13–16, 27, 28]. The positions of the atoms in perovskite-type solids were kept fixed while the conductive
ions migrated inside these models. To introduce hydrogen atom in BaZrO 3 perovskite, trivalent cation or trivalent anion is doped at zirconium or oxygen site,
respectively. As the doped concentration is below 10 %, the pseudo-cubic structure
can be adapted to construct cluster models.
Ba 2 Zr 4 O 4 H model was constructed to investigate the energetics and bonding in
three proton conduction paths (see Fig. 14.2). In our ionics models [27], counter
cation (in this case, barium) is included. It is because it participates in O–H and
O–H–O bond formation. Figure 14.3 illustrates four proton conduction paths in
235
titanium vacancy, and proton conduction mechanism related to O–H defect are still
unknown. In BaZrO 3 perovskite, zirconium vacancy and O–H defects are created
under oxidizing conditions in the same manner.
2H 2 O + 2O
X
O → V
Zr + 4OH
•
O .
(14.3)
In this study, we investigate the effect of a hydrogen defect around zirconium vacancy on proton conductivity, from energetics and bonding.
14.2 Computation
14.2.1 Calculation Method
The calculations presented here were performed using the BHHLYP hybrid KohnSham method [20], which properly reproduces the electronic structure of the
strongly correlated perovskite-type transition metal oxides. In BHHLYP theory, the
total exchange and correlation energy is expressed by 50 % Hartree-Fock (HF) exchange, 50 % Becke exchange and LYP correlation energies. Previously, we demonstrated that bandgap and effective exchange integral depend on HF exchange coefficient [21, 22] because M–O (M = transition metal) bonding character is controlled by localization effect. In this study, HF, B3LYP and BLYP theories with
100 %, 20 % and 0 % HF exchange, respectively, was also used to investigate
the dependence of localization effect on activation energy. We used the TatewakiHuzinaga MINI basis [23] for zirconium, barium, yttrium and scandium, combined
with the 6-31G(d) basis for oxygen and hydrogen. All calculations were performed
with the GAMESS program [24]. The molecular orbitals (MOs) were plotted using
MOLEKEL 4.3 [25].
14.2.2 Calculation Model
BaZrO 3 has a simple cubic structure, with a lattice parameter (the Zr–O–Zr distance) of 4.20 Å [26]. In our previous work, several ionics models were constructed
to investigate an ionic conduction in perovskite-type solids [13–16, 27, 28]. The positions of the atoms in perovskite-type solids were kept fixed while the conductive
ions migrated inside these models. To introduce hydrogen atom in BaZrO 3 perovskite, trivalent cation or trivalent anion is doped at zirconium or oxygen site,
respectively. As the doped concentration is below 10 %, the pseudo-cubic structure
can be adapted to construct cluster models.
Ba 2 Zr 4 O 4 H model was constructed to investigate the energetics and bonding in
three proton conduction paths (see Fig. 14.2). In our ionics models [27], counter
cation (in this case, barium) is included. It is because it participates in O–H and
O–H–O bond formation. Figure 14.3 illustrates four proton conduction paths in