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Computational studies of proton migration in perovskite oxides
SWD
STATE ioms
Solid State Ionics 77 ( 1995) 207-209
Computational
studies of proton migration in perovskite oxides
M. Cherry a-b,MS. Islam b*L,J.D. Gale ‘, C.R.A. Catlow a a The Royal Institution of GreatBritain, 21 Albemarle St, London, WIX 4BS. UK ’ Department of Chemistry, University ofsurrey, Guildford, Surrey GU2 5XH, UK ’ Department ofchemistry, Imperial College, London SW7 2BP, UK
Abstract The mechanism and energetics of proton migration in perovskite oxides are investigated by ab-initio quantum mechanical cluster calculations. We calculate the energy barrier to proton transfer between two adjacent oxygen ions. The charge distribution and relaxation effects are also discussed. Keywords: Proton migration; Perovskite oxides; Relaxation; Ionic conductivity
1. Introduction
High temperature proton conductors have a large potential for use in electrochemical processes such as fuel cells, steam electrolysis and hydrogen gas sensors [ l-31. Iwahara [ 21 first demonstrated the existence of proton conduction in ABO, perovskites, and several studies [2-l 1 ] have since shown that many ABOJ perovskite type oxides, in particular those based upon cerates and zirconates (A’+ = Sr, Ba, Ca and B4+ = Ce, Zr), can possess appreciable levels of protonic conductivity. However, work investigating proton conduction in perovskites in which both cations are trivalent has so far been limited. For example, Iwahara [ 121 investigated Ca-doped LaYO,, whilst recently Larring and Norby [ 13 ] have shown that under certain conditions LaEr03 is a proton conductor. In this paper we study the fundamental mechanism of proton migration in LaB03 perov’ Corresponding author. Tel: (+44) 01483 300800 x2596. Fax: ( +44) 01483 300803. E-mail: [email protected]. 0167-2738/95/$09.50
skites, although the conclusions apply to all perovskite structured materials. For LaBO, systems the La3+ ion is commonly substituted by ST*+, resulting in charge compensating oxygen vacancies, represented by the defect equation: LaL,+SrO-*Sr;,+$V,+jLa,03.
In the presence of water vapour these vacancies are readily occupied by hydroxyl ions, which are created by the following defect reaction: H,O(g)
+V,
+O,“o20H..
(2)
Improving our understanding of transport properties and the nature of proton migration have been the impetus behind many investigations. This includes the study of the EMF in electrochemical cells and IR absorption measurements investigating isotope effects between proton and deuteron migration. The results support the proposal that the migration takes place via tunnelling of the proton from one oxide ion to the next, although the exact mechanism is still uncertain [ 14,15 1. In this work we will investigate the energet-
0 1995 Elsevier Science B.V. All rights reserved
SSDIO167-2738(94)00234-7
(1)
208
h4. Chetty et al. /Solid State Ionics 77 (1995) 207-209
its of proton migration by Quantum Mechanical cluster calculations.
2. QM cluster calculations Quantum mechanical techniques are used to investigate the energy barrier to the transfer of a proton between two neighbouring 02- ions. Gale [ 161 calculated the activation energy for this process for two O*- ions at different spacings, embedded in an array of point charges simulating the remainder of the lattice. We now extend this treatment to a cluster of 13 lattice ions (Fig. I), and again the remainder of the lattice is represented using an array of point charges, which reproduce the correct electrostatic potential. All calculations are performed using the CADPAC code [171. The calculations were based upon the LaA103 system, with high quality basis sets; Al 8-5 1lG, 0 841 lG, and H 6-3 11G. The Al and 0 basis sets were optimised for Alz03 and therefore particularly applicable to this material, La is represented by an Y-pseudopotential. The calculations were performed at the SCF Hartree-Fock level, allowing the ions Al 1, 04 and 05 (see Fig. 1) to relax. Then single point correlation effects were included by the addition of Moller-Plesset perturbation theory to the second order (MP2 technique). The energy barrier (E,,) for the proton transfer is calculated as the difference in energy between the following states: (i) the ground state in which the hydrogen is effectively bound to an oxide ion, and (ii) the barrier state in which the hydrogen is equidistant between the two adjacent oxide ions.
Fig. 1. QM cluster, La ions lie (IL l/2 lattice units) above and below plane of diagram.
3. Results and discussion The energy barrier to the transfer of the proton between two adjacent oxide ions was calculated for a series of O...O spacings using ab-initio QM calculations, based on LaAIOs as discussed above. The resulting energies are given in Table 1. The energy barrier increases with increasing separation between the two oxygens at the SCF HartreeFock level of calculation. However, inclusion of correlation effects in each case reduces E,, considerably; the lowest of -0.02 eV is comparable to thermal energies. The low energy barrier is consistent with the tunnelling mechanism and shows the importance of electronic interactions across the O-H-O bridge. The energy required to break the O-H bond is _ 4 eV, so the proton transfer takes place through a mechanism in which there is no significant bond breaking. The very low energy barrier for this process is a result of the strong interactions of the proton with both oxygen configurations. The QM calculations can also probe the preferred geometry of the ions, shown in Fig. 2. In the ground state the O-H group moves away from the Al ion, and the neighbouring oxide ion is drawn towards the hydroxyl. In the barrier state both oxide ions are drawn towards the proton. Table 1 Variation in E,, with O...O spacing Separation o...o (A)
2.67 2.76 2.90
Eb (eV)
SCF H-F
+ MP2
0.29 0.40 0.66
0.02 0.04 0.16
Fig. 2. Schematic of calculated geometries for the ground and barrier states, dashed lines indicate perfect lattice geometries.
M. Cherry et al. /Solid State Ionics 77 (1995) 207-209
Analysis of the Mulliken populations is consistent with the above discussion. The calculated charges for the atoms in the cluster are presented in Table 2. They indicate electronic interaction between the proton and both neighbouring oxide ions. As expected, in the ground state the proton and nearest oxide ion (labelled as 04) adopt a charge distribution comparable to a hydroxyl group. We note that there is also a reduction of the effective charge of the next nearest oxide ion (05 ), suggesting electronic interaction with the proton. Upon displacement to the barrier state, both neighbouring oxide ions (04 and 05 ) are drawn towards the proton position, and the charge becomes evenly distributed over the ions. This is consistent with the proposal that bond breaking is unnecessary in this proton transfer process. Experimental values for the activation energy for proton migration in AB03 perovskites are in the range 0.35-1.1 eV [3,9-131. The calculated energies are obviously well below any of these values. However our result simply represents the energy barrier for the proton transfer between oxide ions. The activation energy for proton migration will depend on other energy terms. For tunnelling to take place the corresponding anions must be in equivalent environments. The activation energy for proton migration will thus be associated with lattice relaxation needed to generate such an environment about the two oxide ions. The overall proton migration would occur via the process shown in Fig. 3. The energy required to obtain this intermediate state could form the major constituent of the proton migration activation energy. Atomistic simulation calculations are currently in progress to obtain a value for this energy. Table 2 Calculated charges for atoms in cluster Atom
Al(l) Al(2,3) Q(4) O(5) ‘X6,7) H
Configuration ground state
barrier state
2.12 2.96 - 1.34 - 1.85 -1.97 0.50
2.71 2.96 -1.62 - 1.62 -1.97 0.57
209
Fig. 3. Schematic of the tunnelling process, showing equalisation of energy levels about the two sites.
4. Conclusion QM cluster calculations have been used to investigate the mechanism and energetics for proton migration. The results indicate very low energy barriers for proton transfer between neighbouring oxide ions, This supports the postulate that proton migration occurs by tunnelling. Acknowledgements We thank Dr. S. Ramdas (BP) for helpful discussions. This work is supported by the EPSRC and BP Research and Engineering.
[ 1] H. Iwahara, Solid State Ionics 53-56 ( 1992) 575.
[ 21 H. Iwahara, T. Esaka, H. Uchida and N. Mae&, Solid State Ionics 3/4 (1981) 359. [3] R.C.T. Slade and N. Singh, Solid State Ionics 61 ( 1993) 111. [4] T. Hibino, K. Mizutani, T. Yajima and H. Iwahara, Solid State Ionics 57 ( 1992) 303. [ 51 H. Iwahara, T. Yajima, T. Hibino, K. Ozaki and H. Suzuki, Solid State Ionics 61 (1993) 65. [ 61 T. Yajima and H. Iwahara, Solid State Ionics 53-56 ( 1992) 983. [ 7) I. Kosacki, J. Schooman and M. Balkanski, Solid State Ionics 57 (1992) 345. [8] R.C.T. Slade, S.D. Flint andN. Singh, JMater. Chem. 4(4) (1994) 509. [9] W.-K. Lee, A.S. Nowick and L.A. Boatner, Adv. Ceramics 23 (1987) 387. [lo] S.Q. Fu, W.-K. Lee, A.S. Nowick, L.A. Boatner and M.M. Abraham, J Solid State Chem. 83 ( 1989) 221. [ 111 T. Scherban and AS. Nowick, Solid State Ionics 53-56 (1992) 1004. [ 121 T. Takahashi and H. Iwahara, Rev. Chim. Miner. 17 ( 1980) 243. [ 131 Y. Larring and T. Norby, Solid State Ionics 70/7l ( 1994) 305. [ 141 T. Norby, Solid State Ionics 40/41 (1991) 857. [ 151 N. Bonanos, Solid State Ionics 53-56 (1992) 967. [ 161 C.R.A. Catlow, Solid State Ionics 53-56 (1992) 955. [ 17 ] R.D. Amos, CADPAC VS.1 (Cambridge Analytic Derivatives Package) 1992.
STATE ioms
Solid State Ionics 77 ( 1995) 207-209
Computational
studies of proton migration in perovskite oxides
M. Cherry a-b,MS. Islam b*L,J.D. Gale ‘, C.R.A. Catlow a a The Royal Institution of GreatBritain, 21 Albemarle St, London, WIX 4BS. UK ’ Department of Chemistry, University ofsurrey, Guildford, Surrey GU2 5XH, UK ’ Department ofchemistry, Imperial College, London SW7 2BP, UK
Abstract The mechanism and energetics of proton migration in perovskite oxides are investigated by ab-initio quantum mechanical cluster calculations. We calculate the energy barrier to proton transfer between two adjacent oxygen ions. The charge distribution and relaxation effects are also discussed. Keywords: Proton migration; Perovskite oxides; Relaxation; Ionic conductivity
1. Introduction
High temperature proton conductors have a large potential for use in electrochemical processes such as fuel cells, steam electrolysis and hydrogen gas sensors [ l-31. Iwahara [ 21 first demonstrated the existence of proton conduction in ABO, perovskites, and several studies [2-l 1 ] have since shown that many ABOJ perovskite type oxides, in particular those based upon cerates and zirconates (A’+ = Sr, Ba, Ca and B4+ = Ce, Zr), can possess appreciable levels of protonic conductivity. However, work investigating proton conduction in perovskites in which both cations are trivalent has so far been limited. For example, Iwahara [ 121 investigated Ca-doped LaYO,, whilst recently Larring and Norby [ 13 ] have shown that under certain conditions LaEr03 is a proton conductor. In this paper we study the fundamental mechanism of proton migration in LaB03 perov’ Corresponding author. Tel: (+44) 01483 300800 x2596. Fax: ( +44) 01483 300803. E-mail: [email protected]. 0167-2738/95/$09.50
skites, although the conclusions apply to all perovskite structured materials. For LaBO, systems the La3+ ion is commonly substituted by ST*+, resulting in charge compensating oxygen vacancies, represented by the defect equation: LaL,+SrO-*Sr;,+$V,+jLa,03.
In the presence of water vapour these vacancies are readily occupied by hydroxyl ions, which are created by the following defect reaction: H,O(g)
+V,
+O,“o20H..
(2)
Improving our understanding of transport properties and the nature of proton migration have been the impetus behind many investigations. This includes the study of the EMF in electrochemical cells and IR absorption measurements investigating isotope effects between proton and deuteron migration. The results support the proposal that the migration takes place via tunnelling of the proton from one oxide ion to the next, although the exact mechanism is still uncertain [ 14,15 1. In this work we will investigate the energet-
0 1995 Elsevier Science B.V. All rights reserved
SSDIO167-2738(94)00234-7
(1)
208
h4. Chetty et al. /Solid State Ionics 77 (1995) 207-209
its of proton migration by Quantum Mechanical cluster calculations.
2. QM cluster calculations Quantum mechanical techniques are used to investigate the energy barrier to the transfer of a proton between two neighbouring 02- ions. Gale [ 161 calculated the activation energy for this process for two O*- ions at different spacings, embedded in an array of point charges simulating the remainder of the lattice. We now extend this treatment to a cluster of 13 lattice ions (Fig. I), and again the remainder of the lattice is represented using an array of point charges, which reproduce the correct electrostatic potential. All calculations are performed using the CADPAC code [171. The calculations were based upon the LaA103 system, with high quality basis sets; Al 8-5 1lG, 0 841 lG, and H 6-3 11G. The Al and 0 basis sets were optimised for Alz03 and therefore particularly applicable to this material, La is represented by an Y-pseudopotential. The calculations were performed at the SCF Hartree-Fock level, allowing the ions Al 1, 04 and 05 (see Fig. 1) to relax. Then single point correlation effects were included by the addition of Moller-Plesset perturbation theory to the second order (MP2 technique). The energy barrier (E,,) for the proton transfer is calculated as the difference in energy between the following states: (i) the ground state in which the hydrogen is effectively bound to an oxide ion, and (ii) the barrier state in which the hydrogen is equidistant between the two adjacent oxide ions.
Fig. 1. QM cluster, La ions lie (IL l/2 lattice units) above and below plane of diagram.
3. Results and discussion The energy barrier to the transfer of the proton between two adjacent oxide ions was calculated for a series of O...O spacings using ab-initio QM calculations, based on LaAIOs as discussed above. The resulting energies are given in Table 1. The energy barrier increases with increasing separation between the two oxygens at the SCF HartreeFock level of calculation. However, inclusion of correlation effects in each case reduces E,, considerably; the lowest of -0.02 eV is comparable to thermal energies. The low energy barrier is consistent with the tunnelling mechanism and shows the importance of electronic interactions across the O-H-O bridge. The energy required to break the O-H bond is _ 4 eV, so the proton transfer takes place through a mechanism in which there is no significant bond breaking. The very low energy barrier for this process is a result of the strong interactions of the proton with both oxygen configurations. The QM calculations can also probe the preferred geometry of the ions, shown in Fig. 2. In the ground state the O-H group moves away from the Al ion, and the neighbouring oxide ion is drawn towards the hydroxyl. In the barrier state both oxide ions are drawn towards the proton. Table 1 Variation in E,, with O...O spacing Separation o...o (A)
2.67 2.76 2.90
Eb (eV)
SCF H-F
+ MP2
0.29 0.40 0.66
0.02 0.04 0.16
Fig. 2. Schematic of calculated geometries for the ground and barrier states, dashed lines indicate perfect lattice geometries.
M. Cherry et al. /Solid State Ionics 77 (1995) 207-209
Analysis of the Mulliken populations is consistent with the above discussion. The calculated charges for the atoms in the cluster are presented in Table 2. They indicate electronic interaction between the proton and both neighbouring oxide ions. As expected, in the ground state the proton and nearest oxide ion (labelled as 04) adopt a charge distribution comparable to a hydroxyl group. We note that there is also a reduction of the effective charge of the next nearest oxide ion (05 ), suggesting electronic interaction with the proton. Upon displacement to the barrier state, both neighbouring oxide ions (04 and 05 ) are drawn towards the proton position, and the charge becomes evenly distributed over the ions. This is consistent with the proposal that bond breaking is unnecessary in this proton transfer process. Experimental values for the activation energy for proton migration in AB03 perovskites are in the range 0.35-1.1 eV [3,9-131. The calculated energies are obviously well below any of these values. However our result simply represents the energy barrier for the proton transfer between oxide ions. The activation energy for proton migration will depend on other energy terms. For tunnelling to take place the corresponding anions must be in equivalent environments. The activation energy for proton migration will thus be associated with lattice relaxation needed to generate such an environment about the two oxide ions. The overall proton migration would occur via the process shown in Fig. 3. The energy required to obtain this intermediate state could form the major constituent of the proton migration activation energy. Atomistic simulation calculations are currently in progress to obtain a value for this energy. Table 2 Calculated charges for atoms in cluster Atom
Al(l) Al(2,3) Q(4) O(5) ‘X6,7) H
Configuration ground state
barrier state
2.12 2.96 - 1.34 - 1.85 -1.97 0.50
2.71 2.96 -1.62 - 1.62 -1.97 0.57
209
Fig. 3. Schematic of the tunnelling process, showing equalisation of energy levels about the two sites.
4. Conclusion QM cluster calculations have been used to investigate the mechanism and energetics for proton migration. The results indicate very low energy barriers for proton transfer between neighbouring oxide ions, This supports the postulate that proton migration occurs by tunnelling. Acknowledgements We thank Dr. S. Ramdas (BP) for helpful discussions. This work is supported by the EPSRC and BP Research and Engineering.
[ 1] H. Iwahara, Solid State Ionics 53-56 ( 1992) 575.
[ 21 H. Iwahara, T. Esaka, H. Uchida and N. Mae&, Solid State Ionics 3/4 (1981) 359. [3] R.C.T. Slade and N. Singh, Solid State Ionics 61 ( 1993) 111. [4] T. Hibino, K. Mizutani, T. Yajima and H. Iwahara, Solid State Ionics 57 ( 1992) 303. [ 51 H. Iwahara, T. Yajima, T. Hibino, K. Ozaki and H. Suzuki, Solid State Ionics 61 (1993) 65. [ 61 T. Yajima and H. Iwahara, Solid State Ionics 53-56 ( 1992) 983. [ 7) I. Kosacki, J. Schooman and M. Balkanski, Solid State Ionics 57 (1992) 345. [8] R.C.T. Slade, S.D. Flint andN. Singh, JMater. Chem. 4(4) (1994) 509. [9] W.-K. Lee, A.S. Nowick and L.A. Boatner, Adv. Ceramics 23 (1987) 387. [lo] S.Q. Fu, W.-K. Lee, A.S. Nowick, L.A. Boatner and M.M. Abraham, J Solid State Chem. 83 ( 1989) 221. [ 111 T. Scherban and AS. Nowick, Solid State Ionics 53-56 (1992) 1004. [ 121 T. Takahashi and H. Iwahara, Rev. Chim. Miner. 17 ( 1980) 243. [ 131 Y. Larring and T. Norby, Solid State Ionics 70/7l ( 1994) 305. [ 141 T. Norby, Solid State Ionics 40/41 (1991) 857. [ 151 N. Bonanos, Solid State Ionics 53-56 (1992) 967. [ 161 C.R.A. Catlow, Solid State Ionics 53-56 (1992) 955. [ 17 ] R.D. Amos, CADPAC VS.1 (Cambridge Analytic Derivatives Package) 1992.