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Intra-octahedral proton transfer in bulk orthorhombic perovskite barium cerate
Solid State Ionics 226 (2012) 71–75
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Solid State Ionics journal homepage: www.elsevier.com/locate/ssi
Intra-octahedral proton transfer in bulk orthorhombic perovskite barium cerate Yong-Chan Jeong a, Dae-Hee Kim a, Byung-Kook Kim b, Yeong-Cheol Kim a,⁎ a b
School of Energy, Materials & Chemical Engineering, Korea University of Technology and Education, Cheonan 330–708, Republic of Korea High Temperature Energy Materials Research Center, Korea Institute of Science and Technology (KIST), Seoul 136–791, Republic of Korea
a r t i c l e
i n f o
Article history: Received 16 February 2012 Received in revised form 10 July 2012 Accepted 22 August 2012 Available online 29 September 2012 Keywords: Barium cerate Proton transfer Orthorhombic perovskite structure Density functional theory
a b s t r a c t Intra-octahedral proton transfer in bulk orthorhombic perovskite barium cerate was investigated in order to understand the proton transfer mechanism using density functional theory. Since Ce-centered octahedrons tilt in the orthorhombic perovskite structure to accommodate the tensile strain between Ba and O ions, the Ce\O\Ce unit is bent. A proton attached to an O ion can transfer intra-octahedrally to a neighboring O ion in the structure. An energy barrier of 1.06 eV is required as the bent Ce\O\Ce unit is straightened and bent in the opposite direction during proton transfer. When the bent Ce\O\Ce unit rotates without being straightened during proton transfer, a much lower energy barrier of 0.26 eV is required. The energy barrier for proton transfer by rotating the bent Ce\O\Ce unit increases to 0.45 eV, when the proton transfers near a Y ion that is substituted for a Zr ion as a dopant. Therefore, the proton transfers by rotating the bent Ce\O\Ce unit in bulk orthorhombic barium cerate, resulting in better agreement with experimentally measured energy barriers (0.5–0.54 eV). © 2012 Elsevier B.V. All rights reserved.
1. Introduction Some ABO3 perovskite oxides exhibit proton conductivity at high temperature regimes [1–4]. In perovskite oxides, O ions form interconnected octahedrons with B ions positioned in the center of each octahedron and A ions positioned in the center of eight neighboring octahedrons. When a proton is added to perovskite oxides, the proton is attached to an O ion because of the Coulombic attraction between them. The attached proton can migrate via a combination of rotation around the O ion and transfer to a neighboring O ion. Proton transfers are divided into intra-octahedral transfer in an octahedron and inter-octahedral transfer between two neighboring octahedrons. Energy barriers for proton migration in perovskite oxides have been actively studied using density functional theory (DFT). The calculation results have shown that intra-octahedral proton transfer is the rate-limiting step for proton migration [5–9]. However, the calculated energy barriers for intra-octahedral proton transfer in undoped perovskite oxides (BaZrO3: 0.22–0.25 eV [5,6], CaZrO3: 0.53 eV [5], SrZrO3: 0.32–0.35 eV [7–9]) were lower than the experimentally measured ones in doped perovskite oxides (Y-doped BaZrO3: 0.43–0.47 eV [10–12], In-doped CaZrO3: 0.7 eV [13], Y-doped SrZrO3: 0.43–0.57 eV [14,15]). Islam et al. [16] found an energy barrier for proton transfer of 0.74 eV in an undoped CaZrO3, but Gomez et al. [5] mentioned that the path did not show up in their minimum energy path. The lower calculated energy barriers in undoped perovskite oxides, compared with ⁎ Corresponding author at: 1600 Chungjeolno Byeongchunmyeon Cheonan Chungnam 330–708, Republic of Korea. Tel.: +82 41 560 1326; fax: +82 41 560 1360. E-mail address: [email protected] (Y.-C. Kim). 0167-2738/$ – see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.ssi.2012.08.018
the experimental ones in doped oxides, were acceptable because the attraction between the proton and dopant in perovskite oxides should increase the energy barrier further [7,8,17–22]. However, BaCeO3 has not followed this trend in literature. There were a few reports on the calculated energy barriers (0.64 and 3.42 eV [23,24]) in undoped BaCeO3, and these values were higher than the experimentally measured energy barriers in Y-doped BaCeO3 (0.5–0.54 eV [25,26]). We reconsidered the crystal structure of perovskite oxides in order to understand the discrepancy between the calculated and experimental energy barriers in BaCeO3. The crystal structure of ABO3 perovskite oxides is typically determined by the tolerance factor (t), r þ ro t ¼ pffiffiffi A 2ðr B þ r o Þ
, where rA, rB, and rO are the A, B, and O ionic radii, respectively. The t = 1 condition indicates all A, B, and O ions are closely packed, showing the ideal cubic perovskite structure, while the t b 1 condition indicates the ions are less closely packed, allowing tilting of octahedrons in order to increase the packing density. Therefore, BaCeO3 (t ≈ 0.94) has tilted octahedrons and becomes orthorhombic. The tolerance factor of BaCeO3 is calculated using Shannon ionic radii [27]. The tilted octahedrons are expected to affect the proton migration mechanism because they are distorted during proton transfer. In this study, we focused on intra-octahedral proton transfer in BaCeO3 in order to understand the effect of octahedron tilting on the proton transfer mechanism.
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Fig. 1. Change of perovskite crystal structure from cubic to orthorhombic. (a) Octahedron tilting from the cubic structure when the tolerance factor (t) becomes less than 1, and (b) perspective views of a 2×2×2 super cell with tilted octahedrons, and orthorhombic unit cell. The red-lined structure indicates the orthorhombic unit cell.
2. Calculation details All calculations were performed using the Vienna ab-initio simulation package (VASP) code [28–30] based on DFT. We used Blöchl's projector augmented wave (PAW) method [31] that was implemented into the VASP code by Kresse and Joubert [32]. The exchange correlation energy was described using the generalized-gradient approximation (GGA) of Perdew, Burke, and Ernzerhof (PBE) [33]. The cutoff energy of 500 eV was used, and 4 × 4 × 4 k-points mesh was employed to generate the plane wave basis set using the Monkhorst-Pack grid method [34]. Partial wave occupancies were calculated using the Gaussian smearing method, and its factor was 0.05 eV. Electronic and geometry optimizations were converged when the total energy difference between successive calculation steps was less than 10−3 and 10 −2 eV, respectively. All ions were allowed to relax until the force on each ion was below 0.02 eV/Å. The energy barriers for proton transfer were calculated using the climbing nudged elastic band (CI-NEB) tool [35]. The calculated lattice parameters of a BaCeO3 unit cell were a = 6.32, b = 6.27, and c = 8.84 Å, respectively, and were in good agreement with the experimentally measured ones (a = 6.24, b = 6.21, and c = 8.78 Å [36]) within 1.3% error; more details will be discussed the pffiffiffi in p ffiffiffi next section. The orthorhombic unit cell was extended to a 2 pffiffiffi2 1psuper ffiffiffi cell that contains 40 ions. Bigger super cell of 2 2 2 2 2 containing 160 ions was partially tested to evaluate the size effect of super cells on energy barriers for proton transfer. One proton was added to the super cells to calculate the energy barrier for proton transfer to a neighboring O ion in an octahedron. One Y ion was substituted for a Ce ion to investigate its effect on the energy barrier for proton migration.
3. Results and discussion Fig. 1 shows how the orthorhombic ABO3 perovskite structure is obtained from the cubic structure when the tolerance factor (t) becomes less than 1. In the cubic ABO3 perovskite structure at t=1, both the A and B ions are in contact with the neighboring O ions. As the B ion size in the
cubic ABO3 perovskite structure increases so that t becomes less than 1, the bigger B ion pushes the O and A ions away, producing a gap between the A and O ions, as shown in Fig. 1(a). The gap can be reduced by tilting the octahedron that is composed of six O ions with a B ion positioned at the center. Table 1 shows average interionic distances and lattice parameters of a BaCeO3 unit cell with several different tilting directions; no tilting, tilting to [100] and [110] directions. Tilting to [100] and [110] directions reduced the total energy compared to no tilting, and the tilting to the [110] direction reduced the energy further than that to the [100] direction. This trend of energy decrease follows with the reduction of the Ba\O distance. The calculated orthorhombic lattice parameters are also in good agreement with the experimental one within 1.3% error. In case of the tilting to the [110] direction, the octahedrons tilt toward the A ions. The two neighboring octahedrons are tilted in opposite directions due to the interconnection of the octahedrons via an O ion in a 2×2×2 cubic super cell, as shown in Fig. 1(b). From the super cell with the tilted octahedrons, the red-lined structure becomes a new unit cell. In the new unit cell, the B\O\B units are bent by the octahedron tilting along the newly defined a-axis direction, and its bending directions are opposite to the neighboring B\O\B units. Therefore, a- and b-lattice
Table 1 Average distances of Ba\O, Ce\O, and O\O, and lattice parameters of a BaCeO3 unit cell with different tilting direction of octahedrons. Average interatomic distance [Å]
Lattice parameter [Å]
Ba\O Ce\O O\O A No tilting Tilting to [100] directionb Tilting to [110] directionb Exp. [36] a b
b
c
Total energy [eV]a
Crystal system
3.19 3.18
2.25 2.27
3.19 3.21
4.51 4.51 4.51 0 6.33 6.33 8.89 −1.43
Cubic Tetragonal
3.16
2.26
3.20
6.32 6.24 8.84 −1.63
Orthorhombic
3.13
2.24
3.17
6.24 6.21 8.78 –
Orthorhombic
The super cell contains 40 atoms. The tilting direction is based on the cubic structure.
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Fig. 2. Perspectivepviews ffiffiffi pof ffiffiffi the initial and final state structures for the intra-octahedral proton transfer in 2 2 1 BaCeO3 super cell. The Ol and Oa ions indicate the O ions which the proton leaves and at which the proton arrives during proton transfer, respectively.
parameters become different due to the bending of the B\O\B units along the a-axis only. The c-lattice parameter becomes almost twice that of the cubic unit cell because the neighboring two B\O\B units along the c-axis are oppositely bent. Therefore, the obtained unit cell (red-lined structure) of BaCeO3 becomes an orthorhombic perovskite structure (t≈0.94 [27]) with bent Ce\O\Ce units. Fig. 2 shows the initial and final state structures for the intra-octahedral proton transfer between the neighboring O ions pffiffiffi pffiffiffi in a 2 2 1 BaCeO3 super cell. The Ol and O a ions indicate the O ions which the proton leaves and at which the proton arrives during proton transfer, respectively. When a proton is bonded to an O l ion, the Ce\Ol\Ce angle (155°) is similar to that of the Ce\O\Ce angle without a proton (154°). The smaller angle is chosen to define the Ce\O\Ce angle from the two angles on the plane formed by the bent Ce\O\Ce unit. When the angle changes during proton transfer, this rule for the initial angle is maintained to describe the final angle. The Ce\Oa\Ce unit is bent more (149°) to move the O a ion towards the proton due to their attraction. The proton transfer changes the bending direction of the Ce\O\Ce units in the ac-plane to its opposite direction. Fig. 3(a) shows the bending mechanism of the bent Ce\O\Ce unit and the transition state structure for proton transfer; the Ce\O\Ce unit is straightened and oppositely bent during proton transfer. Its transfer required an energy barrier of 1.06 eV, as shown in Fig. 3(b).
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This value is higher than the measured energy barriers in Y-doped BaCeO3 (0.5–0.54 eV) [25,26]. At the transition state where the energy is the highest, the Ce\Ol\Ce angle changed from 155° to 208°, indicating the Ce\Ol\Ce unit was bent in the opposite direction. The Ce\Oa\Ce unit was less bent (159°) than in the initial state (149°). The average Ce\O\Ce angle, however, excluding those containing Ol and Oa ions, changed from 156 to 171°, indicating the bending was less severe than those containing O l and O a ions. The bending mechanism of the bent Ce\O\Ce units in the super cell without the proton was estimated, and an energy barrier of 0.88 eV was required (Fig. 3(b)). Therefore, the straightening of the bent Ce\O\Ce unit induces a high strain energy in the structure and contributes to the increase of the energy barrier for intra-octahedral proton transfer. Based on this result, a less structural distortion was considered to determine a smaller energy barrier for proton transfer. Fig. 4(a) shows a rotation of the bent Ce\O\Ce unit and the transition state structure for proton transfer; the Ce\O\Ce unit is rotated during proton transfer. The average Ce\O\Ce angle during proton transfer was in the range of 153–160°, indicating that Ce\O\Ce units were always kept bent. Its transfer required an energy barrier of 0.26 eV, as shown in Fig. 4(b). This value is lower than the experimentally measured energy barriers in Y-doped BaCeO3 (0.5–0.54 eV) [25,26]. The rotation of the bent Ce\O\Ce units in the super cell without the proton required an energy barrier of 0.06 eV (Fig. 4(b)). Therefore, the rotation of the bent Ce\O\Ce unit for proton transfer avoids a steep increase of the strain energy and facilitates the intra-octahedral proton transfer between O pffiffiffi pffiffiffi ions. Bigger super cell of 2 2 2 2 2 containing 160 ions was also tested to evaluate the size effect of super cells, and no difference was found in energy barriers for proton transfer. We calculated the energy barriers for proton transfer by rotating the bent Ce\O\Ce unit in Y-doped BaCeO3 to resolve the discrepancy between calculated and experimental energy barriers. Fig. 5(a) shows pffiffiffi the pffiffiffi a 2 2 1 Y-doped BaCeO3 super cell and two slabs that are obtained by cutting the super cell into halves along the dotted square. The front slab contains one Y- and three Ce-centered octahedrons, and the back slab contains four Ce-centered octahedrons. The On ion is the n-th nearest O ion from the Y ion. The bending of M\O\Ce units (M=Y and Ce) in the two slabs was omitted to decrease the complexity of the figures. Fig. 5(b) shows the variation of energy barriers for proton migration when a proton migrates along the a-axis shown by arrows in the two slabs in Fig. 5(a). T and R represent intra-octahedral transfer and rotation of the proton, respectively. The energy is set to 0 eV as a reference when the proton resides near the dopant ion. In the slab
Fig. 3. Intra-octahedral proton transfer by bending mechanism. (a) The bending of the Ce\O\Ce unit and top and perspective views of the transition state structure and (b) energy barriers for proton transfer and structural change. The bending mechanism for proton transfer indicates straightening of the bent Ce\O\Ce unit and bending it in the opposite direction.
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Fig. 4. Intra-octahedral proton transfer by rotating mechanism. (a) The rotation of the Ce\O\Ce unit and top and perspective views of the transition state structure and (b) energy barriers for proton transfer and structural change. The rotating mechanism for proton transfer indicates the rotating of the bent Ce\O\Ce unit.
containing four Ce-centered octahedrons, the highest energy barrier was 0.3 eV among several energy barriers for proton transfer and rotation, when a proton transferred from the O3 to O2 ion. This value is similar to the energy barrier for proton transfer (0.26 eV) in undoped BaCeO3. In the slab containing one Y- and three Ce-centered octahedrons, the highest energy barrier was 0.45 eV, when a proton transfers from the O1 to O2 ion. This increase of the energy barrier is mainly due to the attractive binding energy between the proton and dopant ion. Since the highest calculational energy barrier contributes the most to the experimentally measured energy barrier [37], this result explains the experimentally measured ones in Y-doped BaCeO3 (0.5–0.54) [25,26].
the neighboring O ions within the octahedron by straightening the bent Ce\O\Ce unit and bending it in the opposite direction increased the strain energy, resulting in an energy barrier of 1.06 eV. The proton transfer between the neighboring O ions within the octahedron by rotating the bent Ce\O\Ce unit decreased the strain energy, reducing the energy barrier to 0.26 eV. The energy barrier for proton transfer by rotating the bent Ce\O\Ce unit increases to 0.45 eV, when the proton transfers near an Y ion that is substituted for a Zr ion as a dopant. Therefore, the intra-octahedral proton transfer in BaCeO3 is facilitated by the rotation of the bent Ce\O\Ce unit. Acknowledgements
4. Conclusions We studied the intra-octahedral proton transfer mechanism in bulk orthorhombic BaCeO3 using DFT. The proton transfer between
This research was supported by the Fusion Research Program for Green Technologies through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology
pffiffiffi pffiffiffi Fig. 5. (a) Perspective views of a 2 2 1 Y-doped BaCeO3 super cell and two slabs that are obtained by cutting the super cell into halves along dotted square, and (b) the variation of energy barriers for proton migration when a proton migrates along the a-axis shown by arrows in the two slabs in Fig. 5(a). The On ion is the n-th nearest O ion from Y ion, and T and R represent intra-octahedral transfer and rotation of the proton, respectively.
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(2011–0019304), and by the Education and Research Promotion Program of Korea University of Technology and Education. References [1] T. Norby, Solid State Ionics 125 (1999) 1–11. [2] K.D. Kreuer, Annu. Rev. Mater. Res. 33 (2003) 333–359. [3] H. Iwahara, Y. Asakura, K. Katahira, M. Tanaka, Solid State Ionics 168 (2004) 299–310. [4] L. Malavasi, C.A.J. Fisher, M.S. Islam, Chem. Soc. Rev. 39 (2010) 4370–4387. [5] M.A. Gomez, M.A. Griffin, S. Jindal, K.D. Rule, V.R. Cooper, J. Chem. Phys. 123 (2005) 094703–094712. [6] P.G. Sundell, M.E. Björketun, G. Wahnström, Phys. Rev. B 76 (2007) 094301–094307. [7] Y. Liu, M. Yoshino, K. Tatsumi, I. Tanaka, M. Morinaga, H. Adachi, Mater. Trans. 46 (2005) 1106–1111. [8] C.S. Shi, M. Morinaga, J. Comput. Chem. 27 (2006) 711–718. [9] M.A. Gomez, S. Jindal, K.M. Fletcher, L.S. Foster, N.D.A. Addo, D. Valentin, C. Ghenoiu, A. Hamilton, J. Chem. Phys. 126 (2007) 194701–194706. [10] H.G. Bohn, T. Schober, J. Am. Ceram. Soc. 83 (2000) 768–772. [11] P. Babilo, S.M. Haile, J. Am. Ceram. Soc. 88 (2005) 2362–2368. [12] P. Babilo, T. Uda, S.M. Haile, J. Mater. Res. 22 (2007) 1322–1330. [13] N. Kurita, N. Fukatsu, K. Ito, T. Ohashi, J. Electrochem. Soc. 142 (1995) 1552–1559. [14] T. Yajima, H. Suzuki, T. Yogo, H. Iwahara, Solid State Ionics 51 (1992) 101–107. [15] T. Higuchi, T. Tsukamoto, N. Sata, K. Hiramoto, M. Ishigame, S. Shin, Jpn. J. Appl. Phys. 40 (2001) 4162–4163. [16] M.S. Islam, R.A. Davies, J.D. Gale, Chem. Mater. 13 (2001) 2049–2055. [17] R. Hempelmann, M. Soetratmo, O. Hartmann, R. W ppling, Solid State Ionics 107 (1998) 269–280.
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Contents lists available at SciVerse ScienceDirect
Solid State Ionics journal homepage: www.elsevier.com/locate/ssi
Intra-octahedral proton transfer in bulk orthorhombic perovskite barium cerate Yong-Chan Jeong a, Dae-Hee Kim a, Byung-Kook Kim b, Yeong-Cheol Kim a,⁎ a b
School of Energy, Materials & Chemical Engineering, Korea University of Technology and Education, Cheonan 330–708, Republic of Korea High Temperature Energy Materials Research Center, Korea Institute of Science and Technology (KIST), Seoul 136–791, Republic of Korea
a r t i c l e
i n f o
Article history: Received 16 February 2012 Received in revised form 10 July 2012 Accepted 22 August 2012 Available online 29 September 2012 Keywords: Barium cerate Proton transfer Orthorhombic perovskite structure Density functional theory
a b s t r a c t Intra-octahedral proton transfer in bulk orthorhombic perovskite barium cerate was investigated in order to understand the proton transfer mechanism using density functional theory. Since Ce-centered octahedrons tilt in the orthorhombic perovskite structure to accommodate the tensile strain between Ba and O ions, the Ce\O\Ce unit is bent. A proton attached to an O ion can transfer intra-octahedrally to a neighboring O ion in the structure. An energy barrier of 1.06 eV is required as the bent Ce\O\Ce unit is straightened and bent in the opposite direction during proton transfer. When the bent Ce\O\Ce unit rotates without being straightened during proton transfer, a much lower energy barrier of 0.26 eV is required. The energy barrier for proton transfer by rotating the bent Ce\O\Ce unit increases to 0.45 eV, when the proton transfers near a Y ion that is substituted for a Zr ion as a dopant. Therefore, the proton transfers by rotating the bent Ce\O\Ce unit in bulk orthorhombic barium cerate, resulting in better agreement with experimentally measured energy barriers (0.5–0.54 eV). © 2012 Elsevier B.V. All rights reserved.
1. Introduction Some ABO3 perovskite oxides exhibit proton conductivity at high temperature regimes [1–4]. In perovskite oxides, O ions form interconnected octahedrons with B ions positioned in the center of each octahedron and A ions positioned in the center of eight neighboring octahedrons. When a proton is added to perovskite oxides, the proton is attached to an O ion because of the Coulombic attraction between them. The attached proton can migrate via a combination of rotation around the O ion and transfer to a neighboring O ion. Proton transfers are divided into intra-octahedral transfer in an octahedron and inter-octahedral transfer between two neighboring octahedrons. Energy barriers for proton migration in perovskite oxides have been actively studied using density functional theory (DFT). The calculation results have shown that intra-octahedral proton transfer is the rate-limiting step for proton migration [5–9]. However, the calculated energy barriers for intra-octahedral proton transfer in undoped perovskite oxides (BaZrO3: 0.22–0.25 eV [5,6], CaZrO3: 0.53 eV [5], SrZrO3: 0.32–0.35 eV [7–9]) were lower than the experimentally measured ones in doped perovskite oxides (Y-doped BaZrO3: 0.43–0.47 eV [10–12], In-doped CaZrO3: 0.7 eV [13], Y-doped SrZrO3: 0.43–0.57 eV [14,15]). Islam et al. [16] found an energy barrier for proton transfer of 0.74 eV in an undoped CaZrO3, but Gomez et al. [5] mentioned that the path did not show up in their minimum energy path. The lower calculated energy barriers in undoped perovskite oxides, compared with ⁎ Corresponding author at: 1600 Chungjeolno Byeongchunmyeon Cheonan Chungnam 330–708, Republic of Korea. Tel.: +82 41 560 1326; fax: +82 41 560 1360. E-mail address: [email protected] (Y.-C. Kim). 0167-2738/$ – see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.ssi.2012.08.018
the experimental ones in doped oxides, were acceptable because the attraction between the proton and dopant in perovskite oxides should increase the energy barrier further [7,8,17–22]. However, BaCeO3 has not followed this trend in literature. There were a few reports on the calculated energy barriers (0.64 and 3.42 eV [23,24]) in undoped BaCeO3, and these values were higher than the experimentally measured energy barriers in Y-doped BaCeO3 (0.5–0.54 eV [25,26]). We reconsidered the crystal structure of perovskite oxides in order to understand the discrepancy between the calculated and experimental energy barriers in BaCeO3. The crystal structure of ABO3 perovskite oxides is typically determined by the tolerance factor (t), r þ ro t ¼ pffiffiffi A 2ðr B þ r o Þ
, where rA, rB, and rO are the A, B, and O ionic radii, respectively. The t = 1 condition indicates all A, B, and O ions are closely packed, showing the ideal cubic perovskite structure, while the t b 1 condition indicates the ions are less closely packed, allowing tilting of octahedrons in order to increase the packing density. Therefore, BaCeO3 (t ≈ 0.94) has tilted octahedrons and becomes orthorhombic. The tolerance factor of BaCeO3 is calculated using Shannon ionic radii [27]. The tilted octahedrons are expected to affect the proton migration mechanism because they are distorted during proton transfer. In this study, we focused on intra-octahedral proton transfer in BaCeO3 in order to understand the effect of octahedron tilting on the proton transfer mechanism.
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Y.-C. Jeong et al. / Solid State Ionics 226 (2012) 71–75
Fig. 1. Change of perovskite crystal structure from cubic to orthorhombic. (a) Octahedron tilting from the cubic structure when the tolerance factor (t) becomes less than 1, and (b) perspective views of a 2×2×2 super cell with tilted octahedrons, and orthorhombic unit cell. The red-lined structure indicates the orthorhombic unit cell.
2. Calculation details All calculations were performed using the Vienna ab-initio simulation package (VASP) code [28–30] based on DFT. We used Blöchl's projector augmented wave (PAW) method [31] that was implemented into the VASP code by Kresse and Joubert [32]. The exchange correlation energy was described using the generalized-gradient approximation (GGA) of Perdew, Burke, and Ernzerhof (PBE) [33]. The cutoff energy of 500 eV was used, and 4 × 4 × 4 k-points mesh was employed to generate the plane wave basis set using the Monkhorst-Pack grid method [34]. Partial wave occupancies were calculated using the Gaussian smearing method, and its factor was 0.05 eV. Electronic and geometry optimizations were converged when the total energy difference between successive calculation steps was less than 10−3 and 10 −2 eV, respectively. All ions were allowed to relax until the force on each ion was below 0.02 eV/Å. The energy barriers for proton transfer were calculated using the climbing nudged elastic band (CI-NEB) tool [35]. The calculated lattice parameters of a BaCeO3 unit cell were a = 6.32, b = 6.27, and c = 8.84 Å, respectively, and were in good agreement with the experimentally measured ones (a = 6.24, b = 6.21, and c = 8.78 Å [36]) within 1.3% error; more details will be discussed the pffiffiffi in p ffiffiffi next section. The orthorhombic unit cell was extended to a 2 pffiffiffi2 1psuper ffiffiffi cell that contains 40 ions. Bigger super cell of 2 2 2 2 2 containing 160 ions was partially tested to evaluate the size effect of super cells on energy barriers for proton transfer. One proton was added to the super cells to calculate the energy barrier for proton transfer to a neighboring O ion in an octahedron. One Y ion was substituted for a Ce ion to investigate its effect on the energy barrier for proton migration.
3. Results and discussion Fig. 1 shows how the orthorhombic ABO3 perovskite structure is obtained from the cubic structure when the tolerance factor (t) becomes less than 1. In the cubic ABO3 perovskite structure at t=1, both the A and B ions are in contact with the neighboring O ions. As the B ion size in the
cubic ABO3 perovskite structure increases so that t becomes less than 1, the bigger B ion pushes the O and A ions away, producing a gap between the A and O ions, as shown in Fig. 1(a). The gap can be reduced by tilting the octahedron that is composed of six O ions with a B ion positioned at the center. Table 1 shows average interionic distances and lattice parameters of a BaCeO3 unit cell with several different tilting directions; no tilting, tilting to [100] and [110] directions. Tilting to [100] and [110] directions reduced the total energy compared to no tilting, and the tilting to the [110] direction reduced the energy further than that to the [100] direction. This trend of energy decrease follows with the reduction of the Ba\O distance. The calculated orthorhombic lattice parameters are also in good agreement with the experimental one within 1.3% error. In case of the tilting to the [110] direction, the octahedrons tilt toward the A ions. The two neighboring octahedrons are tilted in opposite directions due to the interconnection of the octahedrons via an O ion in a 2×2×2 cubic super cell, as shown in Fig. 1(b). From the super cell with the tilted octahedrons, the red-lined structure becomes a new unit cell. In the new unit cell, the B\O\B units are bent by the octahedron tilting along the newly defined a-axis direction, and its bending directions are opposite to the neighboring B\O\B units. Therefore, a- and b-lattice
Table 1 Average distances of Ba\O, Ce\O, and O\O, and lattice parameters of a BaCeO3 unit cell with different tilting direction of octahedrons. Average interatomic distance [Å]
Lattice parameter [Å]
Ba\O Ce\O O\O A No tilting Tilting to [100] directionb Tilting to [110] directionb Exp. [36] a b
b
c
Total energy [eV]a
Crystal system
3.19 3.18
2.25 2.27
3.19 3.21
4.51 4.51 4.51 0 6.33 6.33 8.89 −1.43
Cubic Tetragonal
3.16
2.26
3.20
6.32 6.24 8.84 −1.63
Orthorhombic
3.13
2.24
3.17
6.24 6.21 8.78 –
Orthorhombic
The super cell contains 40 atoms. The tilting direction is based on the cubic structure.
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Fig. 2. Perspectivepviews ffiffiffi pof ffiffiffi the initial and final state structures for the intra-octahedral proton transfer in 2 2 1 BaCeO3 super cell. The Ol and Oa ions indicate the O ions which the proton leaves and at which the proton arrives during proton transfer, respectively.
parameters become different due to the bending of the B\O\B units along the a-axis only. The c-lattice parameter becomes almost twice that of the cubic unit cell because the neighboring two B\O\B units along the c-axis are oppositely bent. Therefore, the obtained unit cell (red-lined structure) of BaCeO3 becomes an orthorhombic perovskite structure (t≈0.94 [27]) with bent Ce\O\Ce units. Fig. 2 shows the initial and final state structures for the intra-octahedral proton transfer between the neighboring O ions pffiffiffi pffiffiffi in a 2 2 1 BaCeO3 super cell. The Ol and O a ions indicate the O ions which the proton leaves and at which the proton arrives during proton transfer, respectively. When a proton is bonded to an O l ion, the Ce\Ol\Ce angle (155°) is similar to that of the Ce\O\Ce angle without a proton (154°). The smaller angle is chosen to define the Ce\O\Ce angle from the two angles on the plane formed by the bent Ce\O\Ce unit. When the angle changes during proton transfer, this rule for the initial angle is maintained to describe the final angle. The Ce\Oa\Ce unit is bent more (149°) to move the O a ion towards the proton due to their attraction. The proton transfer changes the bending direction of the Ce\O\Ce units in the ac-plane to its opposite direction. Fig. 3(a) shows the bending mechanism of the bent Ce\O\Ce unit and the transition state structure for proton transfer; the Ce\O\Ce unit is straightened and oppositely bent during proton transfer. Its transfer required an energy barrier of 1.06 eV, as shown in Fig. 3(b).
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This value is higher than the measured energy barriers in Y-doped BaCeO3 (0.5–0.54 eV) [25,26]. At the transition state where the energy is the highest, the Ce\Ol\Ce angle changed from 155° to 208°, indicating the Ce\Ol\Ce unit was bent in the opposite direction. The Ce\Oa\Ce unit was less bent (159°) than in the initial state (149°). The average Ce\O\Ce angle, however, excluding those containing Ol and Oa ions, changed from 156 to 171°, indicating the bending was less severe than those containing O l and O a ions. The bending mechanism of the bent Ce\O\Ce units in the super cell without the proton was estimated, and an energy barrier of 0.88 eV was required (Fig. 3(b)). Therefore, the straightening of the bent Ce\O\Ce unit induces a high strain energy in the structure and contributes to the increase of the energy barrier for intra-octahedral proton transfer. Based on this result, a less structural distortion was considered to determine a smaller energy barrier for proton transfer. Fig. 4(a) shows a rotation of the bent Ce\O\Ce unit and the transition state structure for proton transfer; the Ce\O\Ce unit is rotated during proton transfer. The average Ce\O\Ce angle during proton transfer was in the range of 153–160°, indicating that Ce\O\Ce units were always kept bent. Its transfer required an energy barrier of 0.26 eV, as shown in Fig. 4(b). This value is lower than the experimentally measured energy barriers in Y-doped BaCeO3 (0.5–0.54 eV) [25,26]. The rotation of the bent Ce\O\Ce units in the super cell without the proton required an energy barrier of 0.06 eV (Fig. 4(b)). Therefore, the rotation of the bent Ce\O\Ce unit for proton transfer avoids a steep increase of the strain energy and facilitates the intra-octahedral proton transfer between O pffiffiffi pffiffiffi ions. Bigger super cell of 2 2 2 2 2 containing 160 ions was also tested to evaluate the size effect of super cells, and no difference was found in energy barriers for proton transfer. We calculated the energy barriers for proton transfer by rotating the bent Ce\O\Ce unit in Y-doped BaCeO3 to resolve the discrepancy between calculated and experimental energy barriers. Fig. 5(a) shows pffiffiffi the pffiffiffi a 2 2 1 Y-doped BaCeO3 super cell and two slabs that are obtained by cutting the super cell into halves along the dotted square. The front slab contains one Y- and three Ce-centered octahedrons, and the back slab contains four Ce-centered octahedrons. The On ion is the n-th nearest O ion from the Y ion. The bending of M\O\Ce units (M=Y and Ce) in the two slabs was omitted to decrease the complexity of the figures. Fig. 5(b) shows the variation of energy barriers for proton migration when a proton migrates along the a-axis shown by arrows in the two slabs in Fig. 5(a). T and R represent intra-octahedral transfer and rotation of the proton, respectively. The energy is set to 0 eV as a reference when the proton resides near the dopant ion. In the slab
Fig. 3. Intra-octahedral proton transfer by bending mechanism. (a) The bending of the Ce\O\Ce unit and top and perspective views of the transition state structure and (b) energy barriers for proton transfer and structural change. The bending mechanism for proton transfer indicates straightening of the bent Ce\O\Ce unit and bending it in the opposite direction.
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Y.-C. Jeong et al. / Solid State Ionics 226 (2012) 71–75
Fig. 4. Intra-octahedral proton transfer by rotating mechanism. (a) The rotation of the Ce\O\Ce unit and top and perspective views of the transition state structure and (b) energy barriers for proton transfer and structural change. The rotating mechanism for proton transfer indicates the rotating of the bent Ce\O\Ce unit.
containing four Ce-centered octahedrons, the highest energy barrier was 0.3 eV among several energy barriers for proton transfer and rotation, when a proton transferred from the O3 to O2 ion. This value is similar to the energy barrier for proton transfer (0.26 eV) in undoped BaCeO3. In the slab containing one Y- and three Ce-centered octahedrons, the highest energy barrier was 0.45 eV, when a proton transfers from the O1 to O2 ion. This increase of the energy barrier is mainly due to the attractive binding energy between the proton and dopant ion. Since the highest calculational energy barrier contributes the most to the experimentally measured energy barrier [37], this result explains the experimentally measured ones in Y-doped BaCeO3 (0.5–0.54) [25,26].
the neighboring O ions within the octahedron by straightening the bent Ce\O\Ce unit and bending it in the opposite direction increased the strain energy, resulting in an energy barrier of 1.06 eV. The proton transfer between the neighboring O ions within the octahedron by rotating the bent Ce\O\Ce unit decreased the strain energy, reducing the energy barrier to 0.26 eV. The energy barrier for proton transfer by rotating the bent Ce\O\Ce unit increases to 0.45 eV, when the proton transfers near an Y ion that is substituted for a Zr ion as a dopant. Therefore, the intra-octahedral proton transfer in BaCeO3 is facilitated by the rotation of the bent Ce\O\Ce unit. Acknowledgements
4. Conclusions We studied the intra-octahedral proton transfer mechanism in bulk orthorhombic BaCeO3 using DFT. The proton transfer between
This research was supported by the Fusion Research Program for Green Technologies through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology
pffiffiffi pffiffiffi Fig. 5. (a) Perspective views of a 2 2 1 Y-doped BaCeO3 super cell and two slabs that are obtained by cutting the super cell into halves along dotted square, and (b) the variation of energy barriers for proton migration when a proton migrates along the a-axis shown by arrows in the two slabs in Fig. 5(a). The On ion is the n-th nearest O ion from Y ion, and T and R represent intra-octahedral transfer and rotation of the proton, respectively.
Y.-C. Jeong et al. / Solid State Ionics 226 (2012) 71–75
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