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Article
Atomistic Insight into the Correlation among Oxygen Vacancies, Protonic Defects, and the Acceptor Dopants in Sc-Doped BaZrO using First-Principles Calculations 3
Hiroki Takahashi, Itaru Oikawa, and Hitoshi Takamura J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b11742 • Publication Date (Web): 01 Mar 2018 Downloaded from http://pubs.acs.org on March 3, 2018
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The Journal of Physical Chemistry C is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.
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The Journal of Physical Chemistry
1
Atomistic Insight into the Correlation among Oxygen Vacancies, Protonic
2
Defects, and the Acceptor Dopants in Sc-Doped BaZrO3 using First-Principles
3
Calculations
4
Hiroki Takahashi,1,2,* Itaru Oikawa,1 Hitoshi Takamura,1,*
5
1
6
6-6-02 Aramaki Aoba, Sendai 980-8579, Japan
7
2
8
*Corresponding Authors
9
E-mail:
[email protected] 10
Department of Materials Science, Graduate School of Engineering, Tohoku University,
Mitsui Mining & Smelting Co., Ltd., 1333-2 Haraichi, Ageo, Saitama 362-0021, Japan
E-mail:
[email protected] 11 12
Abstract
13
It is necessary to elucidate the correlation between hydration properties and proton
14
distributions in electrolytes as proton conductors to allow for further improvements in
15
solid oxide fuel cells (SOFCs). In this study, the hydration properties of Sc-doped BaZrO3
16
(BZO) were investigated by means of density functional theory calculations capable of
17
taking both the local structural configurations and the hydration levels into account. At a
18
low hydration level, Sc-doped BZOs gained a negatively larger hydration energy, i.e. more
19
exothermic reaction, by incorporating an H2O molecule with unstable oxygen vacancies
20
adjacent to Zr. At a high hydration level, the configuration of ScO4(OH)2, which has a
21
positive net charge as a local structure, was formed with a smaller but negative hydration
22
energy by the reaction of H2O with oxygen vacancies adjacent to Sc. This indicates that the
23
stability of the whole system, and not only the local electrostatic interactions of point
24
defects, needs to be taken into account when considering the hydration energy. The
25
characteristic local structure of ScO4(OH)2 was identified using 1 ACS Paragon Plus Environment
45
Sc nuclear magnetic
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1
resonance (NMR) chemical shift calculations. It is proposed that the resolution of current
2
45
3
Sc-doped BZOs, and that a higher resolution
4
existence of ScO4(OH)2.
Sc NMR spectroscopy techniques does not allow for the detection of ScO4(OH)2 in 45
Sc NMR technique will likely reveal the
5 6
1. Introduction
7
Proton conductors for intermediate temperature solid oxide fuel cell (IT-SOFC) have
8
been attracting much attention as potential electrolytes. An acceptor-doped
9
perovskite-type oxide, ABO3, is one of the candidate materials for proton conductors.1–3
10
Among a number of perovskite-type oxides, BaZrO3 (BZO) exhibits high proton
11
conductivity and is chemically stable in water vapor and CO2.4–6 For BZO, the substitution
12
of the tetravalent Zr4+ cation by a trivalent cation leads to the formation of oxygen
13
vacancies. The subsequent creation of protons proceeds by the reaction of oxygen
14
vacancies with the H2O molecule according to the following equation using the
15
Kröger-Vink notation:
16
•• • Hଶ Oሺgሻ + O× + V ↔ 2OH
(1)
17
In this reaction, the H2O molecule reacts with an oxygen vacancy and a host oxide ion,
18
resulting in the generation of two OH groups, generally referred to as protonic defects.
19
These protonic defects migrate from one oxide ion to the adjacent oxide ion in a process
20
known as protonic conduction. Proton conductivity depends on both dopants and host
21
cations. There have been various studies reported focused on the relationship between
22
the local structural property of dopants and protonic defects, including proton trapping.7–9
23
In these reports, nuclear magnetic resonance (NMR) is used as one of the most powerful
24
techniques for determining the local structures around specific ions.8–17 Meanwhile,
25
computational simulations represented by density functional theory (DFT) calculations are 2 ACS Paragon Plus Environment
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also effective in the investigation the state of protonic defects under ideal conditions. In
2
ref.s 9 and 11, the proton configurations of Y-doped BZO and Y-doped BaSnO3 have been
3
successfully studied by combining NMR measurements with DFT calculations.
4
Oikawa et al. revealed the distribution of oxygen vacancies and protons in Sc-doped 45
Sc NMR.17 Their key finding was that, since
5
BZO for various hydration levels using
6
protonic defects and oxygen vacancies coexist under partially hydrated situations, protonic
7
defects tend to avoid the occupation around the Sc dopant adjacent to the oxygen vacancy
8
due to electrostatic repulsion. It is, however, as yet unclear whether such electrostatic
9
interactions exist in partially hydrated BZOs. In this study, the combination of DFT
10
calculations with the experimental results provides deeper insight into the proton
11
configuration in BZOs, in effect opening a pathway for the design of a better protonic
12
conductor not limited to BZOs. Though many studies on the DFT calculations of hydration
13
in BZOs have been reported,18–33 few studies have taken both the hydration level and
14
configurations of local structures into account because of use of restricted small cell size.
15
In this paper, we focus on the hydration properties of Sc-doped BZO in the change of the
16
hydration level, and investigate the stability of various defect configurations using a large
17
supercell in DFT calculations. Moreover, we consider appropriate defect structures
18
consistent with the previous experimental results of
19
projector augmented wave (GIPAW) methods.
45
Sc NMR by the gauge-including
20 21
2. Methods
22
2.1
23 24 25
DFT Calculations According to the above equation eq 1, the hydration energy (Ehydr) of Sc-doped BZO
can be evaluated by the following equation: ′
•
′
×
••
Ehydr = Et(2ScZr, 2OHO) − Et(2ScZr, OO, V O ) − Et(H2O) 3 ACS Paragon Plus Environment
(2)
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1
where Et denotes the total energy, and the defects and the species in parentheses are
2
taken into account. These values were calculated using the CASTEP code, which is based
3
on the density functional theory (DFT).34 DFT calculations were performed with
4
plane-wave
5
Perdew-Burke-Emzerhof form (GGA-PBE). The ionic cores were represented by on-the-fly
6
generated (OTFG) ultrasoft pseudopotentials.35 The plane-wave cutoff energy was set at
7
630 eV, and a 4×4×4 supercell of a BaZrO3 unit cell was used with a single k-point sampling
8
at Γ-point. Geometry optimizations were performed by relaxing all atom positions and
9
lattice volumes under the following conditions: the total energy convergence for the
10
geometry optimization was 2×10-5 eV/atom and the stress was smaller than 0.1 GPa with
11
an energy convergence of 5×10-7 eV/atom for self-consistent calculations.
12
shielding was calculated using the GIPAW method.36,37 A k-point spacing of 0.03 Å-1 was
13
used, which corresponded to 2×2×2 k-point sampling. To allow for a direct comparison
14
with experimental data, isotropic NMR shielding (σiso) was converted to the isotropic
15
chemical shift (δiso) according to the following equation:38–40
expansions
using
the
generalized
δiso = σref − σiso
16
gradient
approximation
in
45
the
Sc NMR
(3)
17
As can be seen from eq 3, the correlation between experimental NMR chemical shifts and
18
calculated NMR shieldings provides minus unity of the slope. We used a value of σref = 783
19
ppm as the reference of
20
shielding of Ba3Sc4O9, ScPO4 and NaScO2.41,42 Details are provided in Figure S1 in the
21
Supporting Information.
45
Sc NMR shielding which was decided using the isotropic
45
Sc
22 23
2. 2
Modeling of Structures and Procedure of Calculations
24
The initial structure before hydration of Sc-doped BZO was constructed by referring to
25
the local structure experimentally observed by 45Sc NMR in ref 17. The concentration of Sc 4 ACS Paragon Plus Environment
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′
••
1
was set at 12.5 mol%; that is, the simulated model was expressed as (8ScZr, 4V O ), with four
2
oxygen vacancies introduced to maintain overall electroneutrality. Figures 1 a-c show the
3
schematic representation of the local structures of the initial state containing four oxygen
4
vacancies before hydration. Two Zr−VO−Zr pairs (in Figures 1 a and b), one Sc−VO−Zr pair (in
5
Figure 1 a) and one Sc−VO−Sc pair (in Figure 1 c) were considered. In addition to the
6
5-coordinated Sc (ScO5), 6-coordinated Sc (ScO6) (not shown in Figure 1) was also arranged
7
in the calculation model to have a ratio of 1:1.67, which is close to the experimental value
8
(1:1.7) reported in ref 17. Note that even though two Sc−VO−Zr pairs can be adopted
9
instead of one Sc−VO−Sc pair, we adopted the Sc−VO−Sc pair, which is the associated
10
complex defect and is more energetically favored than the isolated configuration (two
11
Sc−VO−Zr pairs).43 These configurations were allocated in the 4×4×4 BZO supercell so that
12
they were the second nearest neighbor (2NN) when close or were even further apart in
13
order to avoid artificial interactions among them due to the limited cell size.
14
Since the calculated model includes four oxygen vacancies, as mentioned above, the
15
hydration level can be increased by 25% with every reaction with an H2O molecule
16
according to eq 1. There appear to be several possible configurations during the hydration
17
reaction, which involves the production of two protons by incorporating an H2O molecule
18
into an oxygen vacancy site. In this study, one of the protons expressed as OH in eq 1 was
19
fixed at the filled oxygen vacancy site; the other proton searches for an appropriate site
20
only within 1NN from the oxygen vacancy site, as shown in Figures 1 d-j. By using the most
21
stable configuration for the 25% hydration level, another H2O molecule was then
22
incorporated into the other oxygen vacancy site to construct a candidate model for a
23
hydration level of 50%. The same procedures of the hydration process were repeated by
24
incorporating an H2O molecule step by step to reproduce the 75% and 100% hydration
25
levels. 5 ACS Paragon Plus Environment
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1 2
3. Results and discussion
3
3.1
Stable Configurations of Protons in Sc-Doped BZO
4
The computationally derived lattice constant of a non-doped BZO unit cell was
5
calculated as a = 4.230 Å, while the experimentally obtained lattice constant was reported
6
as a = 4.194 Å.44 The calculated value is in good agreement with the experimental value
7
within 1% error, indicating that the quality of this calculation method is such that the
8
structure of BZO can be reproduced.
9
First of all, we deal with the model Figure 1 b as a trial case to reveal the effect of
10
proton configurations, and especially the bonding direction of two protons, on stability in
11
the hydration reaction. Figure 2 shows the schematic representation which expresses
12
three configurations (b) on plane, (c) parallel and (d) perpendicular at the 25% hydration
13
level based on the Figure 2 a model before hydration. Among the three configurations (b)
14
to (d), the configuration of (d) perpendicular model was found to be the most energetically
15
stable. The total energies of (b) on plane and (c) parallel are 0.1 eV and 0.2 eV larger than
16
that of (d) perpendicular type, respectively. According to this result, the perpendicular
17
bonding direction of two protons was used as a standard stable hydrated model in the
18
series of calculations.
19 20
3.2
Hydration Energy as a Function of Hydration Level
21
The hydration energies for the seven possible configurations at the 25% hydration
22
level (case 1 to 7) are shown in the 4th column in Table 1. Case 1 is the most stable
23
configuration. No significant difference was found between the hydration energies of cases
24
3 (-1.11 eV), 6 (-1.07 eV) and that of case 1 (-1.13 eV). These three cases 1, 3 and 6 have
25
similar defect configurations, with an oxygen vacancy of the Zr−VO−Zr pair hydrated by an 6 ACS Paragon Plus Environment
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H2O molecule to form OH, and then the remaining H locates the O adjacent to Sc. The
2
reason for the negatively larger hydration energy, i.e. stable configuration, of these three
3
cases is that VO in Zr−VO−Zr pair is less stable than the VO in Sc−VO−Zr and Sc−VO−Sc,
4
allowing energetically unstable oxygen vacancies to be readily hydrated.21,22,43,45,46 The
5
remaining positively charged H (OH O ) then favors the O site adjacent to the negatively
6
charged ScZr site due to the Coulombic attractive interaction. The opposite is true in cases
7
4 and 7. That is, the hydration reaction of the oxygen vacancy adjacent to Sc shows
8
moderate hydration energy because the oxygen vacancy adjacent to Sc is stable as it
9
is.21,22,43 Meanwhile, based on the negatively smaller hydration energy for case 2 (-0.79 eV),
10
it can be assumed that the incorporation of two protons on the O site adjacent to the
11
same Zr without the nearest-neighboring Sc is unstable even when the hydration reaction
12
takes place at the oxygen vacancy in Zr−VO−Zr. A similar tendency can be seen in cases 4
13
and 5.
•
′
14
According to ref. 43, protons are the most stable at 1NN of Sc. This means that case 1
15
at 25% hydration level with two protons located at 1NN (Sc−OH−Zr) and 2NN (Zr−OH−Zr)
16
of Sc is not the global minimum state. More stable proton configurations were then
17
explored based on case 1. In the cases of 8 and 9 shown in Figure S2, two protons diffuse
18
to 1NN of Sc and are located apart from each other; their hydration energies are
19
negatively larger than that of case 1, as shown in Table S1 (a). This implies that protons
20
essentially favor the 1NN of Sc: this is interpreted as proton trapping behavior.7–9
21
Meanwhile, we assume in this study that H2O instantaneously reacts with oxygen
22
vacancies successively without proton diffusion in the process of the hydration reaction.
23
This means that the systems under consideration are not energetically global minimum
24
states. To estimate the effect of neglecting proton diffusion on the hydration energy, the
25
hydration energy was calculated based on the isolated models in ref. 43: in these models 7 ACS Paragon Plus Environment
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1
the dopants are located apart from each other and two protons exist at 1NN and 2NN of
2
the dopants. The results are shown in Table S1 (b). As can be seen, even though the
3
hydration energies of the model which takes proton diffusion into account (H diffusion) is
4
negatively larger, as expected, than those of the original models without proton diffusion
5
(After hydration), the order of hydration energy with respect to the kind of dopants does
6
not change (Al > Ga > Sc). This trend indicates that, even with the assumption that H2O
7
instantaneously reacts with oxygen vacancies successively without proton diffusion, it is
8
possible to discuss their hydration properties, including site preferences. Meanwhile, it
9
should also be noted that because of the assumption, the absolute values of hydration
10
reactions may be further increased by approximately 0.25 eV due to the effect of proton
11
diffusion searching for its global minimum sites. We then constructed candidate models
12
with a hydration level of 50% based on case 1.
13
The 50% hydrated level was prepared by incorporating one more H2O molecule for
14
case 1. The results are summarized in Table 1 (see the 5th column). In case 6, the 50%
15
hydrated level shows the largest negative hydration energy among the three cases, 4, 6,
16
and 7, in Table 1. The structural feature of case 6 for the 50% hydration level is that, like
17
case 1 at the 25% hydration level, an oxygen vacancy of Zr−VO−Zr pair is hydrated by an
18
H2O molecule to form OH and then the remaining H locates at the O site adjacent to Sc.
19
The 75% hydrated models were also prepared by incorporating one more H2O molecule
20
into case 6 for the 50% hydration level. In case 4 for the 75% hydration level by containing
21
the oxygen vacancy adjacent to Sc, the negative hydration energy becomes larger. At 100%
22
hydration, an H2O molecule finally reacts with an Sc−VO−Sc associated complex
23
configuration. In other words, the VO in the Sc−VO−Sc associated configuration is extremely
24
stable; this VO can be hydrated only at the full hydration level.43 Figure 3 includes a
25
summary of the hydration energy with respect to the hydration level. As the hydration 8 ACS Paragon Plus Environment
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reaction progresses, the hydration energy becomes negatively less, that is, unstable
2
oxygen vacancies around Zr readily react with the H2O molecule and gain larger negative
3
hydration energy. On the other hand, more stable oxygen vacancies remain intact at low
4
hydration levels and finally accept H2O molecules at the high hydration level, leading to
5
less negative hydration energy. It should be also noted that the full hydration has been
6
experimentally achieved in 10 mol% Sc-doped BZO even with negatively smaller hydration
7
energy at a high hydration level.17
8 9
3.3
′
••
•
Repulsive Interaction between (ScZr−V O ) and OH O ′
10
Oikawa et. al. concluded there was a Coulombic repulsive interaction between (ScZr
11
−V O ) and OH O adjacent to Sc for partially hydrated Sc-doped BZO.17 To elucidate the
12
Coulombic repulsive interaction between them, a comparison can be made between case
13
1 with Zr−OH−Sc−O and case 3 with Zr−OH−Sc−VO at the 25% hydration level from the data
14
in Table 1. Even though the case 3 with Sc−VO is unstable by 0.02 eV, the difference is
15
significantly smaller than expected. Meanwhile, the proton locating O adjacent to Sc in
16
case 3 shows a peculiar perpendicular bonding with respect to the O−Sc bonding direcƟon:
17
this repulsive interaction affects the geometry of proton site around O−Sc−VO.
••
•
18
Figure 4 b shows the relaxed structure around O−Sc−VO (VO(2)) for case 3 represented
19
in Figure 4 a. To clarify the stable geometry for the proton around O−Sc−VO, the change in
20
the total energy was calculated by moving the initial proton H(2) site in Figure 4 b within
21
the region of the cross sections near the oxygen vacancy shown in Figure 4 c. This is the
22
so-called potential energy surface (PES) of the proton.47 As can be seen from the PES in
23
Figure 4 d, the proton located on the plane of the ScO4 unit which faces the oxygen
24
vacancy is stable with a smaller relative total energy (Erel), in the range of 0 ~ 0.35 eV,
25
which corresponds to the area indicated from cyan to blue in the PES. On the other hand, 9 ACS Paragon Plus Environment
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1
the proton on the plane including Sc−VO−Zr is less stable by Erel = 0.35 ~ 0.45 eV (the blue
2
area in Figure 4 e). The protons bonding with the O located on the opposite side of the
3
oxygen vacancy are the least stable (Erel = 0.75 ~ 0.90 eV, the red area in Figure 4 e). This is
4
because the atomic distance between Sc and the O located on the opposite side of the
5
oxygen vacancy was as short as 1.93 Å (the other Sc−O distances were 2.0 to 2.2 Å as
6
shown in Figure 4 b) due to the repulsive interaction of the facing cations (Sc and Zr) which
7
resulted from the absence of oxide ions at the VO(2) site. It was thus determined that a
8
repulsive interaction between (ScZr−V O ) and OH O does indeed exist and may affect the
9
anisotropy required for proton migration. Even though steric interactions between the two
10
hydrogen atoms may be also involved, given that Figure 4 e indicates that (1) the region of
11
the least stable area around H1 is very limited, and (2) stable areas facing the VO site are
12
basically symmetrical, we can conclude that it is the repulsive interaction which appears to
13
be the main contributor to the defect configurations.
′
••
•
14 15
3.4
Occupation Site of Protons as a Function of Hydration Level
16
According to the data reported in an experimental NMR study on Sc-doped BZO in ref
17
17, protons are distributed not only in the vicinity of Sc but also Zr. The local structure of
18
ZrO5(OH) with a positive net charge is likely to be unstable on the basis of the local
19
electroneutrality. Based on a series of calculated cases, the energetically favored protonic
20
sites are plotted as a function of their hydration levels. Figure 5 shows the ratio of protons
21
located on O adjacent to Sc (blue line) or Zr (red dashed line) as a function of the hydration
22
level. Protons exist not only at 1NN of Sc but also 1NN of Zr even when the hydration
23
levels are a low 25% or at 50%, which has at least 1NN of Sc still available. This is because
24
when the hydration reaction consumes the oxygen vacancy adjacent to Zr, the stability of
25
the whole system is improved, i.e. negatively large hydration energy of ≈ -1 eV (exothermic 10 ACS Paragon Plus Environment
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1
reaction), even though the local instability, which seems to be a minor issue, is the result
2
of the formation of the positive net charge of ZrO5(OH). At high hydration levels, a
3
hydration reaction takes place which utilizes the oxygen vacancies near Sc (case 4:75% and
4
7:100% in Table 1). In these cases, two protons originating from H2O exist at the oxygen
5
adjacent to the identical Sc atom. While the positive net charge of ScO4(OH)2 suggests this
6
configuration is less stable, even such a configuration with a positive net charge shows
7
sufficient hydration energy (-0.78 eV of case 4(75%), -0.71 eV of case 7(100%)). This
8
indicates that besides classical treatments based on the local net charge, quantum
9
treatment based on first-principles calculations which takes the covalency of chemical
10
bonding as well as the total energy of the whole system into account is required to
11
evaluate the stability of protons.48
12 13
3.5
The Relationship between Local Structures and the 45Sc NMR Spectra
14
The atomistic calculations for Sc-doped BZO provide useful information for NMR
15
studies on this material. The chemical shift in 45Sc NMR for various defect configurations
16
can be derived, as shown in Table 2. These chemical shifts in
17
structure around Sc. The 45Sc NMR chemical shifts of ScO6, ScO5(OH) and ScO5 in Sc-doped
18
BZO were calculated at 150 ppm, 158 ppm and 230 ppm, respectively. Figure 6 shows a
19
45
20
chemical shifts calculated in this study. As can be seen, these calculated chemical shifts are
21
in good agreement with the experimental data (dashed lines). This implies that our
22
simulated models are well-suited for the reproduction of experimental results. In the case
23
of ScO5(OH), the chemical shift ranges from 153 ppm to 164 ppm, which is within the
24
range of the experimental value. This also indicates that the
25
sensitive to a slight difference in proton position. As for ScO4(OH)2, though no such
45
Sc NMR reflect the local
Sc NMR spectrum taken for a partially hydrated 10 mol% Sc-doped BZO17 with the
11 ACS Paragon Plus Environment
45
Sc NMR chemical shift is
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1
configuration has yet to be identified experimentally, the chemical shift is estimated to be
2
approximately 160 ppm (red line), which is within the range of the chemical shift of
3
ScO5(OH) mentioned above. While experimentally distinguishing these two local structures
4
when taking the broadness of
5
improved resolution of
6
configurations of ScO5(OH) and ScO4(OH)2 and the distribution of protons around Sc can be
7
interpreted with higher accuracy.
45
45
Sc NMR spectrum into account is clearly difficult, with
Sc NMR spectra, it will be possible to distinguish the two
8 9
4. Conclusion
10
We investigated the hydration properties of Sc-doped BZOs by taking both the
11
hydration level and the local structural configurations into account. At the low hydration
12
level, Sc-doped BZOs gain larger negative hydration energy by incorporating H2O with the
13
oxygen vacancies adjacent to Zr. Protons near ScZr−V O do not show any significant
14
repulsive interaction in terms of the hydration energy; rather, the interaction affects the
15
spatial anisotropic distribution of the protons. At the high hydration level, the protons
16
become finally incorporated with stable oxygen vacancies near Sc resulting in a relatively
17
small hydration energy. Even when the configuration includes two protons at identical Sc
18
(ScO4(OH)2), which will not be favored considering the positive net charge of the local
19
structure, negatively hydration energy is sufficiently high. This implies that the correlation
20
among defects (dopants, oxygen vacancies, and protons) needs to be considered by taking
21
the total energy of the whole system and not just the local electrostatic interactions of
22
those point defects into account. Furthermore, it was found that the NMR peak which has
23
been experimentally assigned to ScO5(OH) may overlap with ScO4(OH)2 at the high
24
hydration level.
′
••
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Supporting Information
2
Relationship between the calculated isotropic 45Sc NMR shielding and the experimental
3
chemical shift of Ba3Sc4O9, ScPO4 and NaScO2 as reference materials (Figure S1), schematic
4
representation of the proton configuration at 25% hydration level after the diffusion of
5
two protons towards the most stable site at the first nearest neighbor of Sc (Figure S2),
6
hydration energy of (a) cases 1, 8 and 9 at the 25% hydration level, and (b) isolated models
7
of M-doped BaZrO3 (M=Al, Sc, Ga) in ref. 43, and H diffusion models calculated in this
8
study (Table S1), and convergence test of cutoff energy for calculations of PES map (Figure
9
S3).
10 11
Acknowledgement
12
This work has been financially supported in part by JSPS KAKENHI Grant Number
13
26249103.
14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35
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System. J. Solid State Chem. 2003, 175 (2), 170–181. Bévillon, É.; Geneste, G. Hydration Properties of BaSn 0.875M0.125O3−δ Substituted by Large Dopants (M=In, Y, Gd, and Sm) from First Principles. Phys. Rev. B 2008, 77 (18), 184113. Bévillon, É.; Geneste, G.; Chesnaud, A.; Wang, Y.; Dezanneau, G. Ab Initio Study of La-Doped BaSnO3 Proton Conductor. Ionics (Kiel). 2008, 14 (4), 293–301. Toyoura, K.; Hatada, N.; Nose, Y.; Tanaka, I.; Matsunaga, K.; Uda, T. Proton-Conducting Network in Lanthanum Orthophosphate. J. Phys. Chem. C 2012, 116 (36), 19117–19124. Liu, Q. J.; Liu, Z. T.; Feng, L. P. Elasticity, Electronic Structure, Chemical Bonding and Optical Properties of Monoclinic ZrO2 from First-Principles. Phys. B Condens. Matter 2011, 406 (3), 345–350. Momma, K.; Izumi, F. VESTA 3 for Three-Dimensional Visualization of Crystal, Volumetric and Morphology Data. J. Appl. Crystallogr. 2011, 44 (6), 1272–1276.
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1
2 3 4
Figure 1 (a)-(c) Schematic representation of the local structures of the initial state
5
containing four oxygen vacancies before hydration. (d)-(j) Representation of hydrated
6
cases by incorporating an H2O molecule with four oxygen vacancies.
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1 2 3
Figure 2 Schematic representation of three configurations of two protons, (b) on plane and
4
face to face, (c) parallel and (d) perpendicular at 25% hydration level. H bonding direction
5
is expressed by the Natta projection way. Depicted triangular in stripe pattern means
6
bonding direction retreating into the paper. Model (a) corresponds to Figure 1 b.
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Table 1 Hydration energy of each reaction cases at 25% to 100% hydration level (unit: eV) Case
OH site(VO)
H site(OO)
Ehydr at 25%
Ehydr at 50%
1
Zr−VO(1)−Zr
Sc−OO−Zr
-1.13
−
−
−
2
Zr−VO(1)−Zr
Zr−OO−Zr
-0.79
−
−
−
3
Zr−VO(1)−Zr
Zr−OO−Sc−VO
-1.11
−
−
−
4
Sc−VO(2)−Zr
Sc−OO−Zr
-0.80
5
Sc−VO(2)−Zr
Zr−OO−Zr
-0.51
6
Zr−VO(3)−Zr
Sc−OO−Zr
-1.07
-0.96
7
Sc−VO(4)−Sc
Sc−OO−Zr
-0.82
-0.79
-0.80 −
2 3
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Ehydr at 75%
-0.78
Ehydr at 100%
−
−
−
−
−
-0.73
-0.71
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1
2 3
Figure 3 Summary of the hydration energy with respect to the hydration level.
4 5
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1 2
Figure 4 (a) Schematic representation of the local structures of 25% hydrated case 3 in
3
Figure 1. The area surrounded by the green dashed line corresponds to (b). (b) Relaxed
4
structure and Sc−O atomic distance around the oxygen vacancy VO(2). (c) Schematic
5
illustration of the cross sections calculated the potential energy surface (PES) of the proton
6
H(2). (d) and (e) PES cross sections corresponding to the orange and blue regions shown in
7
(c), respectively. Cross section (d) includes the ScO4 unit and lies in the yz-plane, and (e)
8
includes Sc−VO−Zr on the xy-plane. Under the condition that the proton H(1) is fixed at the
9
initial stable site, the proton H(2) moves within the region of the cross sections with 0.1 Å
10
grid spacing for the calculation of PES. The cutoff energy was decreased to 380 eV to
11
reduce calculation time. A convergence test of cutoff energy is shown in Figure S3. Ba
12
atoms are omitted for clarity. Structures and PES cross sections are visualized using
13
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1 2 3
Figure 5 Distribution of protons distinguished for each the nearest cations with respect to
4
the hydration level.
5
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1
Table 2
Sc NMR chemical shift classified by the local structure around Sc (unit: ppm).
2
When there were plural identical structures, the chemical shifts were averaged. Local structure Hydration ScO5
ScO6
ScO5(OH)
0 (initial)
232.9
150.2
−
−
25 (case 1)
230.3
151.7
164.2
−
50 (case 6)
228.8
151.5
157.8
−
75 (case 4)
231.0
152.1
152.9
159.5
100 (case 7)
−
152.6
155.6
163.7
ScO4(OH)2
level (%)
3 4
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1 2 45
3
Figure 6 Experimental (10 mol% Sc-doped BZO) and calculated
4 5
with various defect configurations. The 45Sc NMR spectrum is taken from ref. 17.
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Sc NMR chemical shifts
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