Solid State Ionics 188 (2011) 1 5. Contents lists available at ScienceDirect. Solid State Ionics. journal homepage:

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1 Solid State Ionics 188 (11) 1 5 Contents lists available at ScienceDirect Solid State Ionics journal homepage: First principles calculations of oxygen vacancy formation and migration in mixed conducting Ba.5 Sr.5 Co 1 y y O δ perovskites E.A. Kotomin a,b,, Yu. A. Mastrikov a,c, M.M. Kuklja c, R. Merkle a, A. Roytburd c, J. Maier a a Max Planck Institute for Solid State Research, Heisenbergstr.1, Stuttgart, Germany b Institute of Solid State Physics, University of Latvia, Kengaraga str. 8, Riga. Latvia c Materials Science and Engineering Department, University of Maryland, College Park, MD, USA article info abstract Article history: Received 8 July Received in revised form 4 October Accepted October Available online 26 November Keywords: Solid oxide fuel cell SOFC Oxygen permeation Oxygen diffusion Ionic conductivity Density of states (DOS) Defect model First-principles supercell calculations of oxygen vacancies in the Ba.5 Sr.5 Co 1 y y O δ (BSCF) perovskites are presented. The density of states is determined for different iron content and oxygen vacancy concentrations, and the characteristic differences for Co and are discussed. We analyze the dependences of the defect (oxygen vacancy) formation and migration energies on the content and compare the calculated properties with those of related LaCoO and LaO perovskites. Elsevier B.V. All rights reserved. 1. Introduction Mixed conducting perovskites have been used as cathode materials in solid oxide fuel cells (SOFC) since early 198s, and La 1 x Sr x MnO ±δ (LSM) was the first widely applied oxide cathode material. Currently, Ba.5 Sr.5 Co O δ (BSCF) shows the best oxygen exchange performance [1,2]. Despite having drawbacks for application as a SOFC cathode (e.g. reactivity with electrolyte materials, CO 2 poisoning and a phase transformation at T b9 C, see [] and references therein), it is still a promising material for oxygen permeation membranes [4]. Asitiswellunderstoodbynow [,5], both the high oxygen vacancy concentration at the cathode surface and high vacancy mobility are key factors for the fast oxygen reduction at SOFC cathodes and at the surface of permeation membranes. While bulk oxygen vacancy concentrations and mobilities are available from experiments, the respective quantities for the surface layer, which are decisive for the surface reaction, are almost impossible to be measured. Hence, an extensive set of large-scale first principles DFT calculations was carried out for LaMnO and LSM [6 9]. Thefirst ab initio study for complex BSCF perovskites has been performed only recently []. Here, we analyze the atomic and electronic structure of bulk oxygen vacancies, their formation and migration energies, and how these Corresponding author. Max Planck Institute for Solid State Research, Heisenbergstr.1, Stuttgart, Germany. addresses: kotomin@fkf.mpg.de, kotomin@latnet.lv (E.A. Kotomin). properties depend on the chemical composition of the BSCF perovskite. 2. Computational details We employed the ab initio DFT computer code VASP 4.6 in conjunction with the projector-augmented method (PAW) and plane wave basis set [11]. The exchange-correlation GGA functional was of PBE-type. In the library of potentials supplied with the VASP code there are a single PAW PBE potential for Ba, Sr and Co and several potentials for and O, which differ by the number of valence electrons and the basis set cut-off energy, respectively. Test calculations showed that there is practically no dependence of the lattice constant (b.5%) as well as the binding energy (b.4%) of BSCF upon the choice of PAW PBE potentials, thus we used the (d 7 4s 1 ) and Co (d 8 4s 1 ) potentials. For oxygen, we used the soft PAW PBE potential, which gives an O 2 molecule binding energy very close to the experimental values and a reasonable bond length (5.24 ev and 1.29 Å, cf. experimental 5.12 ev and 1.21 Å [12]). The k-point mesh in the Brillouin zone was created by the Monkhorst-Pack scheme [1] for the Ba 4 Sr 4 Co 8 8y 8y O 24 supercells. Ion charges were calculated by the Bader method [14]. The kinetic energy cut-off for the plane wave basis set was 5 ev. Basic properties of defect-free BSCF are discussed in ref. []. The spin states of, Co ions are obtained self-consistently from the calculations. We use 4-atom supercells (cubic ABO unit cell expanded twice along all three translation vectors) with oxygen vacancies (V O ). We calculate several cation /$ see front matter Elsevier B.V. All rights reserved. doi:.16/j.ssi.11

2 2 E.A. Kotomin et al. / Solid State Ionics 188 (11) 1 5 arrangements in Ba.5 Sr.5 Co 1 y y O δ (Ba and Sr are placed in a regularly alternating arrangement) with varying concentration y 1. Typical structures are shown in Fig. 1 along with different positions and surroundings of oxygen vacancies. These structures remain cubic, and we optimised all atomic positions in the supercells. For Ba.5 Sr.5 Co O δ we compared the defect formation energies for relaxed and fixed lattice parameters; they typically differ no more than.5 ev. All data given in this paper refer to the lattice parameter being fixed at the value of the defect-free (δ=) material.. Results and discussion We start with calculations for Ba.5 Sr.5 Co O without O deficiency. The optimized lattice constant is.92 Å. From the calculations, iron is found to be in the high spin state ( 4+ :t 2g e 1 g, + :t 2g e 2 g ), and Co in intermediate spin state (Co 4+ :t 4 2g e 1 g,co + : t 5 2g e 1 g ). The Bader (topological) atomic charges indicate a considerable covalent contribution in the Co-O and -O bonds: Co+1.61 e, e, O -1.7 e, whereas Ba and Sr charges are closer to the formal charges (+1.59 e and e ). Fig. 2 shows the projected electronic densities of states (DOS). For the same δ but different V O locations (CoV O Co versus CoV O ) the DOS look very similar (thus only the CoV O Co configuration is depicted), which emphasizes a significant degree of electron delocalization. Since the computational method generates absolute energies for each particular system which are hard to compare due to the difference in stoichiometries, the energy scale is aligned to match the O2s core states coincide (this also yields a good coincidence of the O2p states). The electrons left behind upon oxygen removal force the rmi energy upward. The shift is.17 ev /.42 ev for Ba.5 Sr.5- Co O δ (δ=.125/.75), and stronger by.25 ev/.6 ev for Ba.5 Sr.5 O δ, which could be understood from the DOS region close to. The DOS is very small close to and exhibits a gap of 2 ev. In contrast, the Co DOS directly above is much larger, thus the electron allocation upon the oxygen removal requires a smaller increase of. These characteristic differences of and Co DOS are also consistent with the experimental finding of a significantly lower electronic conductivity for -rich materials compared to Co-rich compositions [15,16], and with the observation of a + plateau in LSF [17] while Co smoothly changes the oxidation state from 4+ through + to 2+ in related LSC perovskites [18]. A comparison with qualitative BSCF and LSCF band schemes deduced from defect chemical studies reveals that they correctly cover some key features (the narrow empty band above empty Co states [2]; considerable fraction of empty Co DOS directly above [26]) but are less reliable for other aspects (extension of O 2p states above [26])..1. Defect formation energies The bulk oxygen vacancy formation energies, E V,forBa.5 Sr.5- Co 1-y y O as final states are shown in Fig. and Table 1: E V increases with content almost linearly from 1.2 ev up to 2.2 ev. The similar E V values of different local vacancy configurations (CoV O and CoV O Co, V O ) but same iron content and δ reflect the delocalized character of the electronic density. The increase of E V with increasing content can be related to the DOS and the stronger increase of the rmi energy for -rich materials. The calculated vacancy formation energies for BSCF (formally reducing (,Co) 4+ to (,Co) + ) are smaller than for SrTiO (ca. 6 ev, formally Ti 4+ Ti + [19]) and La.75 Sr.25 MnO (2.7 ev, formally Mn 4+ Mn + [9,]), in particular for Co-rich materials owing to the easy reduction of Co ions. The trend that cobalt-rich systems exhibit a lower E V is in qualitative agreement with the fact that the vacancy concentration for given temperature and oxygen partial pressure increases from Ba.5 Sr.5 O δ to Ba.5 Sr.5 Co.8.2 O δ [,21,22] (for higher Co content the cubic perovskite structure is unstable), as well as from La.6 Sr.4 O δ and La.6 Sr.4 Co.6.4 O δ [2]. Comparing the calculated E V to experimental data we have to account for the much higher vacancy concentrations in the real samples. While the vacancy formation energy in Ba.5 Sr.5 O δ shows only a small variation with oxygen deficiency δ, the dependence is very strong in Ba.5 Sr.5 Co.8.2 O δ [24]. Extrapolating these experimental data to low vacancy concentrations, the same trend is obtained as in the DFT calculations, i.e. lower E V values for Co-rich compositions, although the absolute E V values differ. The charge redistribution (column 4 in Table 1) shows that when an O atom is removed, the largest part of its negative charge is distributed over the nearest transition metal ions in the first coordination sphere, whereas the eight oxygen atoms in the second coordination sphere receive.6 e each. That is,.7 e are localized on ions surrounding the V O. Depending on the actual cation A y=1/8 B X: δ = /8 Co C y=1/2 E y=/8 Y: δ =1/2 1 Fig. 1. and Co arrangements in Ba.5 Sr.5 Co 1 y y O δ in the supercell (Ba and Sr not shown for clarity; for yn.5 and Co have to be interchanged). Oxygen vacancy positions are indicated by numbers (see Table 1, only one of equivalent V O configurations is shown). X: vacancy configuration for δ=/8 ( V O per supercell), Y: an example of the BSCF configuration with δ=.5 is shown.

3 E.A. Kotomin et al. / Solid State Ionics 188 (11) 1 5 a Ba.5 Sr.5 Co O -δ Co 4 O δ = δ = 1/8 CoV O Co δ = /8 CoV O Co energy / ev 4 b Ba.5 Sr.5 O -δ 4 O δ = δ = 1/8 V O δ = /8 V O energy / ev Fig. 2. Projected Co, and O density of states of a) Ba.5 Sr.5 Co O δ and b) Ba.5 Sr.5 O δ for various δ. The energy scale is adjusted to align the O2s states (solid vertical line), dashed lines indicate the relevant rmi energies. and vacancy configuration and on the region of averaging (only /Co directly neighboring the V Ö, or whole supercell), either or Co receive the larger share of the transferred electrons. This is in qualitative agreement with in-situ XAS experiments, indicating that it depends delicately on T, po 2, which of the two transition metals (or even the oxygen ions) experiences the larger electron transfer [26]. The absolute effective charge is generally smaller for Co, e.g. q Co = e and q =+1.66 e in Ba.5 Sr.5 Co O, in qualitative agreement with EELS results for Ba.5 Sr.5 Co.8.2 O δ [25] and XAS on Ba.1 Sr.9 Co.8.2 O δ [26]. Fig. 4 shows the calculated vacancy formation energies for Ba.5 Sr.5 Co O δ and Ba.5 Sr.5 O δ. The vacancy formation energies in Fig. 4 increase approximately linearly with an increase of vacancy concentration. This holds even for δn.5 (i.e. for the average and Co oxidation state decreasing below +) for Ba.5 Sr.5 Co O δ, in accord with the experimental data showing no phase transition or discontinuity in other properties. While an increase of the oxidation enthalpy with increasing δ is found experimentally [24], the more pronounced increase for the cobalt-rich materials is not obtained in the present calculations. This might be related to Co + disproportionation occurring at elevated temperatures, which is neglected in the DFT calculations performed for K [27]. Fig. 4 also indicates that a simple defect-chemical model (a single mass action law) for Ba 1 x Sr x Co 1 y y O δ will not be applicable. Since even for a fixed cation composition, E V varies strongly with V O concentration, a single mass-action law cannot be expected to correctly reproduce the vacancy formation reaction. Instead, elastic and electrostatic defect interactions as well as the energy distribution of Co and states and the involvement of the oxygen vacancy formation energy / ev Co-V O -Co Co-V O - -V O - Ba.5 Sr.5 Co 1-y y O fraction y Fig.. Oxygen vacancy formation energy E V as function of iron content y in Ba.5 Sr.5 Co 1 y y O

4 4 E.A. Kotomin et al. / Solid State Ionics 188 (11) 1 5 Table 1 Oxygen vacancy formation energies E V (with respect to 1/2 free O 2 molecule in triplet state, 5.24 ev) for selected Ba.5 Sr.5 Co 1-y y O compositions, change of ion charge Δq for neighbouring Co,, O (in second coordination sphere); and vacancy migration barriers E m (initial state =column 2, final state indicated in last column). For definition of cation and vacancy configurations see Fig. 1. y cation and vacancy configuration E V /ev Δq Co /e Δq /e Δq O /e V O migration barrier E m /ev final configuration: CoV O Co CoV O V O CoV O Co 1.2. (.1) 8. (.6) B2 CoV O Co (.12) 8. (.6) B1 CoV O (.6) C1 CoV O (.6) B1 CoV O (.6).59.6 B2 V O (.12) 8. (.6) V O (.1) 8. (.5).72 states in the redox reaction to varying degree [26] would have to be included..2. Defect migration energies Anion migration occurs by a jump of an oxygen ion into a V O along the edge of the BO 6 octahedron on a path slightly curved away from the B cation (nevertheless, the B O distance in the transition state is shorter than in the initial state). In the transition state, the migrating oxygen ion passes through a triangle set up by two A- and one B-cations. Table 1 summarizes the bulk V O migration barriers for Ba 1 x Sr x Co 1 y y O (for asymmetric jumps, e.g. between CoV O Co and CoV O configurations, the difference in the forward and backward barrier corresponds to the difference in the respective E V,typically.1eV). The DFT-derived V O migration barriers in LaMnO δ [6], LaO δ and LaCoO δ [28] perovskites all amount to.8.9 ev; this is in good agreement with the essentially materials-independent vacancy diffusion coefficient in (La,Sr)(Mn,,Co)O δ perovskites [29,]. Incontrast, Fig. 5 shows a strong variation within the Ba 1 x Sr x Co 1 y y O family with the migration barriers E m ranging from.4 ev to over.7 ev. A pronounced, roughly linear increase is found if the barrier is plotted either versus the sum of direct neighbours of the V O in the initial and final state (a local property), or content (a long-range averaged quantity, giving a slightly better correlation), indicating that both shortand long-range environments affect E m. The migration barriers fall into the same range as obtained from experimental vacancy diffusion coefficients for Ba.5 Sr.5 Co.8.2 O δ (.5 ev), Ba.5 Sr.5 O δ and SrO δ (.9 ev) [,1]. While the concept of the critical radius r c [2] is useful for perovskites with a Goldschmidt tolerance factor t b1, an estimate of r c based on ionic radii predicts smaller values for Ba.5 Sr.5 Co 1 y y O δ than for LaO δ and LaCoO δ, i.e. V O migration should be more energetically costly in BSCF. One reason for this wrong prediction, which is based on the cation geometry while the oxygen ion is still in the initial state, can be seen from Table 2 by looking at the displacements within the triangle of two A-site and one B-site cations through which the O jumps. For both materials the A1 A2 distance increases by.2 Å, but in BSCF (represented by BSF and BSC in Table 2) the outward displacement of the B cation is three times larger than in LaCo 1 y y O δ, which is possible due to tn1 (i.e. in a perovskite where the B cation is too small ). Together with the higher cation polarizability, in particular of Ba 2+, this higher flexibility of the lattice seems to decrease migration barrier. The increase of E m with content for Ba.5 Sr.5 Co 1 y y O δ may be related to the A1 A2 B triangle in the transition state having almost the same size for BSC and BSF (Table 2), but (high spin state) being larger than Co (intermediate spin) decreases the available open space for the migrating O. Since the (Co,) O distance is shorter in BSCF compared to LaCo 1 y y O δ, this size difference (and maybe also a higher polarizability of Co compared to ) seems to affect E m in BSCF while it appears to be less important in LaCo 1 y y O δ. In principle, also a reduction of the oxygen ion charge in the transition state (decreasing its effective ion size) could affect the migration barriers, but such a charge redistribution was found to be small in LaNiO 4+δ []. In contrast to our DFT calculations, the increased V O mobility in BSC compared to BSF (agreeing well with higher diffusion coefficients for Ba.5 Sr.5 Co.8.2 O δ than for Ba.5 Sr.5 O δ [,1]) is not reproduced in semi-empirical pairpotential molecular dynamics simulations [4], yielding similar diffusivities for Ba.8 Sr.2 CoO 2.5 and Ba.8 Sr.2 O 2.5. vacancy formation energy / ev open symbols: Ba.5 Sr.5 O -δ -V O - Co-V O - Co-V O -Co solid symbols: Ba.5 Sr.5 Co O -δ oxygen deficiency δ Fig. 4. Oxygen vacancy formation energy E V as function of oxygen deficiency δ in Ba.5 Sr.5 Co O δ (solid symbols; for δ.5 denotes a combination of Co V O Co and Co V O ) and Ba.5 Sr.5 O δ (open symbols). vacancy migration barrier / ev Ba.5 Sr.5 Co 1-y y O fraction y V O CoV O CoV O Co V O CoV O CoV O CoV O Co CoV O Co V O CoV O 4 # involved Fig. 5. Variation of oxygen vacancy migration barrier E m in Ba.5 Sr.5 Co 1 y y O with fraction y and number of surrounding ions

5 E.A. Kotomin et al. / Solid State Ionics 188 (11) Table 2 Distances (in Å) in the transition state between the migrating O and cations, and between the corners of the A1 A2 B cation triangle. Italic numbers give the change (in Å) relative to the initial state; the last column gives the outward displacement of the B cation away from the migrating O. BSF=Ba.5 Sr.5 O, BSC=Ba.5 Sr.5 CoO (here, cubic BSC stands for the Co-rich cubic BSCF compositions, while experimentally it transforms to a hexagonal phase). Lattice constant O to A1=La or Ba O to A2=La or Sr O to B=Co or A1 A2 A1 B A2 B B displacement LaO LaCoO BSF BSC Conclusions The trends in vacancy formation energy E V and migration barriers E m in Ba.5 Sr.5 Co 1 y y O δ obtained from our DFT calculations are in good agreement with experimental data as far as available, although the absolute E V values are moderately overestimated. The gradual increase of E V with increasing iron content and also with increasing oxygen deficiency can be rationalized based on the calculated electronic density of states with unoccupied iron states located higher in energy than cobalt states (and having a smaller band width). For the calculated low oxygen vacancy migration barriers in BSCF, the fact that Ba-containing materials allow for larger B cation displacements in the transition state appears to be important. Our calculations confirm that the compositions with the highest cobalt content which still form the cubic perovskite phase (i.e. content y.2) are most suitable for oxygen permeation membranes since they combine the lowest vacancy formation energy E V with the lowest V O migration barrier. A further detailed analysis of the lattice polarization effects in defect formation and migration processes is in progress. Acknowledgments The research leading to these results has received funding from the European Union's Seventh Framework Programme FP7/7-1 (NASA-OTM) under grant agreement no and the US National Science Foundation (NSF) grant no Authors thank NSF for its support through TeraGrid resources provided by Texas Advanced Computing Center (TACC) and The National Center for Supercomputing Applications (NCSA) under grant number TG-DMR21. MMK is grateful to the Office of the Director of NSF for support under the IRD Program. Any appearance of findings, conclusions, or recommendations, expressed in this material are those of the authors and do not necessarily reflect views of NSF. Fruitful discussions with D. Gryaznov, E. Heifets, D. Samuelis and L. Wang are greatly appreciated. References [1] Z. Shao, S.M. Haile, Nature 41 (4) 17. [2] F.S. Baumann, J. Fleig, H.-U. Habermeier, J. Maier, Solid State Ionics 177 (6) 71. [] L. Wang, R. Merkle, J. Maier, J. Electrochem. Soc. 157 () B182. [4] Z.P. 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[16] Please note that since overlap between the transition metal and oxygen orbitals is required for electronic conductivity, the nonzero density of Co states at does not necessarily imply metallic conductivity. [17] J. Mizusaki, M. Yoshihiro, S. Yamaguchi, K. Fueki, J. Solid State Chem. 58 (1985) 257. [18] M.H.R. Lankhorst, H.J.M. Bouwmeester, H. Verweij, J. Solid State Chem. 1 (1997) 555. [19] Y.F. Zhukovskii, E.A. Kotomin, S. Piskunov, D.E. Ellis, Solid State Comm. 149 (9) 159. [] It is important to choose the same change of the formal oxidation states for a proper comparison of vacancy formation energies: while E V =2.7 ev for (Mn 4+ Mn + [9]) for La.75 Sr.25 MnO, E V amounts to more than 4 ev in LaMnO where Mn + Mn 2+ [8]. For the inverse reaction (oxidation) one has to consider if it is formulated for O 2 or 1/2 O 2. [21] L. Wang, PhD thesis, University of Stuttgart (9). [22] A.S. Harvey, F.J. Litterst, Z. Yang, J.L.M. Rupp, A. Infortuna, L.J. Gauckler, Phys. Chem. Chem. 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