The Intrinsic Defects, Disordering, and Structural Stability of BaxSr1

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The Intrinsic Defects, Disordering, and Structural Stability of BaxSr1-xCoyFe1-yO3-# Perovskite Solid Solutions Maija M. Kuklja, Yuri A. Mastrikov, Bavornpon Jansang, and Eugene Kotomin J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/jp304055s • Publication Date (Web): 14 Aug 2012 Downloaded from http://pubs.acs.org on August 26, 2012

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The Journal of Physical Chemistry

The Intrinsic Defects, Disordering, and Structural Stability of BaxSr1-xCoyFe1-yO3-δ Perovskite Solid Solutions Maija M. Kuklja,*a Yuri A. Mastrikov,b Bavornpon Jansanga and Eugene A. Kotominb,c a

Department of Materials Science and Engineering, University of Maryland College Park, College Park, MD 20742 USA, Fax: (301)-314-2029; Tel: (301)-405-4646; E--mail: [email protected] or [email protected] b Institute of Solid State Physics, University of Latvia, Kengaraga iela, Riga, LV 1063, Latvia. Fax: +371-71- 2778; Tel: +371-718-7480, E-mail: [email protected] c Max Planck Institute for Solid State Research, Heisenbergstr. 1, D-70569, Stuttgart, Germany, Fax: +49-711-6891722, Tel: +49 (0)711-689-1773, E-mail: [email protected]

Abstract First principles DFT modeling of point defects and structural disordering in BaxSr1-xCoyFe1-yO3-δ (BSCF) perovskites reveals that the material tends to decompose at low temperatures into a mixture of cubic and hexagonal perovskite and/or oxide phases. Special attention is paid to elucidating the effects of oxygen nonstoichiometry on cubic and hexagonal phase stability, decomposition energies, and oxygen vacancy formation energies. The observed lattice instability is likely to negate the advantages of the fast oxygen transport chemistry and impede the applicability of BSCF in solid oxide fuel cells and oxygen separation ceramic membranes. The general methodology presented here can be applied to analyze other candidate materials for many energy conversion applications.

Key words: density functional theory, phase decomposition, solid oxide fuel cells, oxygen permeation membranes, energy conversion, cubic-hexagonal phase transition

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I.

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INTRODUCTION

Among the many novel advanced materials for ecologically clean energy, ABO3-type cubic perovskite solid solutions, e.g. BaxSr1−xCo1−yFeyO3−δ (BSCF), are currently considered to be one of the most promising for applications as cathodes in solid oxide fuel cells (SOFC), oxygen permeation membranes,1,2,3,4 and oxygen evolution catalysis5. These perovskites exhibit good oxygen exchange performance, the highest oxygen permeation rates known for a solid oxide,1 ,6 and mixed ionic and electronic conductivity. The low oxygen vacancy formation energy that is characteristic in these perovskites leads to the high oxygen vacancy concentration, and the relatively low activation barrier for the vacancy diffusion causes the high ionic mobility7. These factors largely define the fast oxygen reduction chemistry of these materials8,9,10, which makes them such good candidates for energy conversion. However, a serious disadvantage of BSCF is its slow transformation at intermediate temperatures into a mixture of several phases, including a hexagonal phase with strongly reduced performance.11,12,13,14,15 The basic properties of these perovskites and their stability with respect to decomposition into several phases are governed by structural defects and disordering. Detailed information regarding defect-induced effects, even in “simple” parent ABO3 perovskites, with the sole exception of oxygen vacancies, is largely lacking thus far because these materials are extraordinarily complex and especially difficult to tackle experimentally. Hence, our understanding of the structure-property-function relationship in BSCF and similar materials is still far from comprehensive, which significantly hampers the progress in energy research and limits prospects to enhance existing materials or design new materials to improve efficiency of energy conversion devices.

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In this research, a set of point defects: all types of single vacancies, Frenkel and Schottky disorder, and cation exchange, is explored in BSCF by means of first principles density functional theory (DFT) calculations. Configurations and energies of those defects are carefully characterized and discussed in the context of available experimental data. Previously, the electronic structure and density of states for perfect and defective BSCF were discussed.9 Now, we focus on the defect energetics. It is confirmed that an oxygen vacancy has the lowest formation energy among all single vacancies probed. It is also established that oxygen Frenkel defects, full Schottky disorder and partial Schottky disorder accompanied by the growth of a new phase (e.g. a binary oxide) all have relatively low formation energies and are favorable. The obtained cation exchange energies are very low on both the A- and B- sublattices of the perovskite structure, which carries implications as to the stability of the materials and ultimately to the efficiency of energy conversion.

II.

DETAILS OF CALCULATIONS

The results were obtained by means of density functional theory (DFT) as implemented in the computer code VASP 4.616 with Projector Augmented Wave (PAW) pseudopotentials and the exchange-correlation GGA functional of the PBE-type. We used the soft PAW PBE potential for O ions, which yields a binding energy for a free O2 molecule very close to the experimental value and a reasonable O-O bond length (5.24 eV and 1.29 Å, cf. the experimental values of 5.12 eV and 1.21Å, respectively17). Periodically distributed defects were simulated using large periodic supercells that were constructed by expanding the five-atom ABO3-type cubic primitive unit cell by 2x2x2 (40 atoms) and by 4x4x4 (320 atoms). The 8x8x8 k-point mesh was created using the Monkhorst-Pack scheme18 for the ABO3 unit cell, 4x4x4 mesh used for 40 atom supercells and 2x2x2 for 320 atom supercells. The largest, 320 atom supercells were used for 2 ACS Paragon Plus Environment


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modeling pairs of Frenkel defects as they allow to accommodate both the close and the distant pairs in the same supercells, and for modeling of the cation exchange. Ionic charges were calculated by the Bader method19. The kinetic energy cut-off for the plane wave basis set was set to 520 eV. The basic properties of defect-free BSCF and of oxygen vacancies therein are detailed in our previous publications8,9,20. In the calculations, the most common in experiments material composition Ba0.5Sr0.5Co0.75Fe0.25O3 is modeled, unless indicated otherwise.

Note that in

vacancy calculations, a whole supercell is neutral, the charge redistribution around a vacancy is calculated self-consistently according to the minimum of the total energy9,20. Thus, there is no need to take into account interactions of the charged defects in periodic cells.

III.

DISCUSSION OF THE OBTAINED RESULTS 1.

Modeling single vacancies

A schematic view of basic defects studied is shown in Fig.1. The cation vacancy formation energy EV correspond to the reaction

→

(1),

where Me=Ba, Sr, Co, or Fe, and y=2 for A-site cations, Ba and Sr, and y=4 for B-site cations, Co and Fe, and an index (g) indicates that the metal left the crystal as an isolated atom. The oxygen vacancy formation energy EV was calculated from the equation

→ 2 2

(2)

and includes a decrease of the oxidation state of two transition metal atoms due to the electrons left behind by the removed oxygen20. Table 1 shows that the oxygen vacancy formation requires a considerably smaller energy EV (~4 eV) than cation vacancies (8.6-9.3 eV), all obtained with respect to isolated atoms. The oxygen vacancy formation energy calculated with respect to 1/2 3 ACS Paragon Plus Environment

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free O2 molecule in the triplet state yields 1.34 eV for the oxygen vacancy placed between two Co atoms (Co-O-Co) and 1.40 eV between one Co and one Fe atom (Co-O-Fe)9. These energies are significantly smaller than those for a wide-gap perovskite SrTiO3 (ca. 6 eV) 21 and even for La0.75Sr0.25MnO3 used in SOFC applications (2.7 eV) 22,23. Under normal, oxygen-rich conditions, the oxygen vacancy formation energy shows a strong temperature- and gas-pressure dependence as recently analyzed23. 2.

Frenkel and Schottky disorder

Among the Frenkel defects, the oxygen vacancy-interstitial pairs have the lowest energy of ~0.75-0.89 eV per defect (Table 1)24 with some preference given again to the oxygen vacancy placed between two Co atoms in the BSCF lattice rather than between one Co and one Fe atom. This is in agreement with the low formation energies of the respective single oxygen vacancies. Note that the formation energies for oxygen Frenkel defects in BSCF turn out to be much smaller than in other perovskites, e.g. SrTiO3 (~10 eV)25, which translates into a much higher equilibrium concentration of defects. Both the split and hollow configurations were probed for interstitial atoms (Fig. 1) for close (~5 Å) and distant (>15 Å) interstitial-vacancy pairs calculated within the same supercell. Only a very minor difference in energy was observed for the corresponding close and distant pairs, hence, only energies of well-separated defects are listed in Table 1. In the split oxygen interstitial defect, a displaced atom forms a dumbbell with a regular atom in such a way that neither atom is on the ideal crystalline site but the two are symmetrically displaced from it. In the hollow interstitial configuration, the displaced atom is located in an available interstitial position. Interstitial defects cause a significant lattice distortion and redistribution of the electronic density, as illustrated in Fig. 2.



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The energy of Schottky defects is derived from equations presented in Table 2, showing the canonical Schottky disorder (Eq. 2) and examples of a possible change in the chemical composition of the material. The left-hand side in each equation represents the total energy of an ideal 40 atom (8 formula units) BSCF supercell. The right-hand side describes a particular vacancy disorder (a set of vacancies, with each individual vacancy placed in a separate 40 atom BSCF supercell) or a combination of a partial vacancy disorder and a new material phase formation. The energy of the right-hand side is then normalized per defect to make it comparable to different equations in Tables 1 and 2. The first equation describes a BSCF crystal that is built out of supercells containing a single vacancy each; the vacating atoms are assumed to go to the gas phase. Thus, the energy of such a vacancy disorder should be relevant to the crystal binding energy per atom and to the formation energy of single isolated vacancies. Indeed, Eq. (1) yields the energy of 6.02 eV (average per vacancy) which is close to the cohesive energy of 5.13 eV per atom and with the range of formation energies of single vacancies in BSCF (3.96 eV for oxygen and 8.63-9.76 eV for cations, Table 1). Realistically, the bulk atoms, after creating vacancies and diffusing outward, may randomly distribute on a surface, form a surface layer of BSCF described in Eq. (2), or serve as nuclei to grow grains of a new phase of other relevant oxides illustrated in Eqs. (3)-(6). There is a simple difference in calculating equations (1) and (2). In Eq. (1), the energies of the vacating atoms are represented by a sum of energies of isolated atoms (Ba, Sr, Co, Fe, and 1/2O2), which implies that the atoms go to the gas phase. In Eq. (2), the energies of the vacating atoms are represented by a total energy of the corresponding amount of the BSCF crystal, implying that the atoms are used to build a new BSCF fragment on a crystal’s surface.


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An analysis of the calculated reaction energies reveals that full Schottky disorder, Eq. (2), and all probed segregation mechanisms, Eqs. (3)-(6), require rather low energies (0.73-1.48 eV). Although the partial Schottky defects accompanied by the formation of binary oxides (Eqs. (5),(6)) require larger energies, 1.40-1.48 eV, than the formation of perovskites (Eqs. (3), (4), 0.73-0.86 eV), these energies are low enough to expect an efficient formation of binary oxides also at grain boundaries. We note that despite the fairly high cation vacancy formation energies (Table 1), full Schottky and Schottky-like disorders as well as Frenkel disorder are favorable. Segregation into oxides is comparable in energy with the oxygen Frenkel disorder, and the growth of perovskites may become even more favorable than oxygen defect pairs. The explanation is owned to the high binding energy of perovskites, which plays a crucial role in the energy balance in the equations. Note that oxygen vacancies also show very low formation energies (1.34 eV with respect to atoms in O2 gas phase molecule, Table 1). This implies that the presence of cation vacancies in BSCF, which results in an appearance of mobile atoms, will lead to the nucleation and growth of new perovskites or oxides, also meaning that grain boundaries and BSCF surfaces should favor parent ABO3 compositions. This notion is convincingly verified by recent Scanning Electron Microscopy (SEM) and Transmission Electron Microscopy (TEM) measurements, revealing that the new hexagonal phase grows predominantly at the grain boundaries of BSCF ceramics and that the cation composition of the newly formed hexagonal phase differs from that of the starting material11,12. It is clear that the efficiency of crystallization into a new phase will depend not only upon the favorable thermodynamics – the reaction energy (which is low, as demonstrated above), but also upon the kinetics - the reaction rate, which, in turn, is a strong function of the activation barriers for the cation diffusion and their rates. Cations in perovskites tend to migrate much slower than



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oxygen26. Hence, we expect that the process of a new phase transformation is fairly slow compared to the oxygen chemistry. 3.

Cation exchange

Further, motivated by the predicted self-segregation, we explored the cation exchange. The calculations were additionally inspired by some earlier work in which it was discovered that antisite defects induce the most favorable disorder in yttrium aluminum perovskite and largely define the properties and stability of the material27. Energies describing the disorder on the cation sublattice of BSCF are summarized in Table 3. We found that the cation exchange on either the A- or B- sublattices of the ABO3 perovskite lattice (Eq. (1) and (6)) does not require a significant additional energy. From the energetic point of view, this indicates that both the A metals (Ba and Sr) and the B metals (Co and Fe) can be almost randomly dissolved on the respective sublattices; this is in agreement with earlier calculations28. This conclusion lends strong support to the high tolerance of the cubic polymorph towards the A-site and B-site compositions suggested based on TEM images and Selected Area Electron Diffraction (SAED) patterns of cubic and hexagonal BSCF12. Exchanging one Ba with one Sr in the supercell results in the aggregation of the Sr and Ba perovskite phases, hereafter referred to as the cation clustering effect. In a sense, this is another manifestation of the self-segregation process on the cation sublattices. Furthermore, we established that antisite substitutions, or a pair of defects in which an A metal occupies a B position of the ABO3 lattice and the corresponding B metal fills the A position, (for example, Sr↔Co) are also possible (Eq. (2)-(5)). However, as expected, they require a significantly higher energy than the clustering of cations within the same sublattice due to the need for charge compensation, the difference in ionic radii of the A and B atoms, and the different coordination numbers in the ideal crystalline lattice. Table 3 illustrates the process of 7 ACS Paragon Plus Environment

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introducing a small concentration of such antisite defects in otherwise ideal BSCF, showing that a single A↔B cation exchange in a large 320 atom model supercell (64 BSCF formula units) requires 3.79-7.87 eV. Bearing in mind that the cation diffusion is relatively slow, the antisite defects can be hardly considered as a favorable disorder in BSCF. 4.

Phase decomposition reactions

Our DFT calculations of ideal, stoichiometric in oxygen BSCF structures at 0K predict that the hexagonal BSCF crystal phase is 0.66 eV per formula lower in energy than the cubic phase (Fig. 3a). It is established that practical nonstoichiometric BSCF samples rest on the cubichexagonal stability border, but at high temperatures the crystal maintains its cubic structure, see for example.12 To relate our modeling to real crystals and experimental observations, we simulated oxygen nonstoichiometry in the model BaxSr1-xCo0.75Fe0.25O3-δ composition in both cubic and hexagonal (2H) phases by varying the δ parameter in a wide range, from 0 to 1 (0 30% of oxygen sites are vacant), as illustrated in Fig. 3. Several important conclusions are drawn from this modeling. First, Fig. 3c demonstrates that the presence of oxygen vacancies stabilizes the cubic phase, which becomes energetically more favorable than the hexagonal phase at δ>0.75. We note here that the close matching between theoretical and experimental results of the BSCF lattice parameters were also obtained only with the oxygen vacancies and the corresponding lattice expansions included in the calculations.8, 20 Second, the formation energy of oxygen vacancies in the cubic phase is considerably smaller than in the hexagonal phase (Fig. 3d), which translates into a significantly higher defect concentration expected in the cubic BSCF. Third, the defect formation energy in the cubic phase strongly increases with the defect



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concentration, which limits vacancy accumulation, while in the hexagonal phase, the formation energy changes only slightly. Next, two imperative observations obtained from our modeling, the low energy of the new phase growth (or self-segregation) coupled with the low energy of the cation substitutions within the A or B sublattice (or high cation miscibility), evidently point to the possible decomposition of BSCF into other solid solutions or parent perovskites. Hence, we explored a few select decomposition reactions shown in Table 4 for both cubic and hexagonal phases and two extreme stoichiometry parameters, δ=0 and δ=1. The calculations were performed by comparing the total energy of ideal or vacancy-containing BSCF (left-hand side of the equation) with the combined total energy two new perovskite phases (right-hand side). Thus, Eq. (1) describes a decomposition of BaxSr1-xCo0.75Fe0.25O3-δ (x=0.5) into

Ba- and

Sr-rich perovskites,

BaCo0.75Fe0.25O3 and SrCo0.75Fe0.25O3 (x=1,0). The energy of this reaction that imitates the ultimate separation of A cations (or the maximum extent of Ba and Sr clustering) in BSCF is close to zero or negative. In the same way, Eq. (2) describes a full partition of Ba0.5Sr0.5Co1yFeyO3-δ

(y=0.25) into hexagonal Ba0.5Sr0.5CoO3 cobaltite and cubic Ba0.5Sr0.5FeO3 ferrate

(y=0,1) perovskite phases, which yields an energy gain of -0.56 eV for the cubic BSCF phase and a small reaction energy of 0.09 for the hexagonal phase. This indicates that in both stoichiometric phases, the BSCF material at low temperatures is unstable. An incorporation of high concentration of oxygen vacancies (δ=1) makes the reaction even more exothermic as the initial defective BSCF crystal is higher in energy if compared to the ideal material. We stress here that in the nonstoichiometric case, the reaction energetics is a function of temperature. The oxygen formation energy of BSCF containing defects decreases with the temperature increase due to entropy effects,23,29 and therefore the reaction energy would increase


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by the same amount. For example, taking into account a reduction in energy of ~1 eV caused by heating the material from room temperature to 1200K (see

17,23,29

), increases the decomposition

reaction energy of cubic BSCF from -2.9 eV to -1.9 eV (Eq. (2), δ=1 in Table 4), that is the material becomes more stable. Lastly, decomposition into three parent perovskites is also energetically favorable (Eq. (3) in Table 4). The separation into the respective phases is in qualitative agreement with SEM, TEM, SAED, and XRD experimental observations12 and consistent with the observed slow phase transition or decomposition of BSCF13 into Ba-substituted Sr6Co5O15 (ICSD 81312) with enlarged lattice constants, an iron-substituted Co3O4 (ICSD 63165), and a hexagonal perovskite with a 2H stacking sequence (see also4,15). Note that our calculations are inavoidably simplified as the relative stability of possible phases strongly depends not only on defect content, but also on their cation compositions.12,13 Nevertheless, qualitative agreement between our theoretical predictions and experimental observations remains valid, and, most importantly, we can foresee the behavior of complex perovskite solid solutions based on ab initio modeling with no a priori assumptions, and therefore, our calculations can aid in the interpretation of experiments and the design of further studies.

IV.

SUMMARY AND CONCLUSIONS

A range of point defects and select relevant solid-solution chemical reactions were explored by means of ab initio DFT calculations performed by using large supercells and a variety of ideal and defective BSCF related crystalline structures. We established that the complexity of the BSCF crystalline arrangement leads to a possibility of accommodating many variations of point defects in the lattice and determines its chemical instability. Cation clustering in the A-sublattice 10 ACS Paragon Plus Environment


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(exchange of Sr and Ba positions) or B-sublattice (exchange of Co and Fe positions) requires a low energy, implying that the distribution of metals in the BSCF lattice is not necessarily highly ordered. This behavior considerably differs from dopant ordering predicted theoretically for Sr in LaMnO329 and observed experimentally for Sr in LaCoO330. Unlike cation clustering, the formation of A↔B antisite (Ba↔Fe) defects is energetically costly and hardly contributes to disorder. Oxygen Frenkel defects, Schottky defects, partial Schottky-like disorder coupled with the growth of new materials phases and oxygen vacancies all exhibit unusually low formation energies. However, due to entropy effects the oxygen vacancy formation energy strongly decreases with the temperature, which makes oxygen vacancies the predominant defects in BSCF at the SOFC operational temperatures, in agreement with experiment. We have demonstrated that a high concentration of oxygen vacancies serves to stabilize the BSCF cubic phase in which their formation energies are considerably smaller than those in the hexagonal phase. However, vacancy formation energies in both phases appreciably increase with the material non-stoichiometry. Based on energetic considerations, both oxygen-stoichiometric and vacancy containing BSCF are thermodynamically unstable and hence are expected to decompose at relatively low temperatures into a mixture of several cubic and hexagonal perovskite phases via several alternative routes. This process depends on a delicate balance between a thermodynamical trend for segregation with a decrease of temperature and a sharp slowdown of the kinetics of this process in BSCF12. This translates into the narrow temperature window (~800-1000 C for BSCF) where the hexagonal phase is indeed experimentally observed. The new perovskite phases are predicted to nucleate and grow, most likely, on grain boundaries or surfaces of BSCF, which will significantly impede the efficiency of BSCF based fuel cell cathodes, separation membranes, and


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catalysts largely due to the less advantageous oxygen chemistry in those resultant materials. The obtained conclusions are consistent with available experimental observations and could help for future reliable predictions of the behavior of other relevant candidate materials (e.g. LSCF) under realistic operational conditions.

Acknowledgement Authors are greatly indebted to R. Merkle, J. Maier, D. Fuks, R. A. De Souza, J. Caro, D. Gryaznov, and A. Roytburd for many stimulating discussions. This research was supported in part by the German-Israeli Foundation grant no. 1025-5.10/2009, National Science Foundation (NSF) grant CMMI-1132451, and DOE Contract DE-AC02-05CH11231, supporting NERSC resources. 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 the views of NSF.



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References and notes 1

Shao, Z.; Haile, S. M. Nature, 2004, 431, 170-173. Wang, L.; Merkle, R.; Maier, J.J. Electrochem. Soc., 2010, 157, B1802-B1808. 3 Zhou, W.; Ran, R.; Shao, Z.J.Power Sources, 2009, 192, 231-246. 4 Liang, F.; Jiang, H.; Luo, H.; Caro, J. ; Feldhoff, A. Chemistry of Materials, 2011, 23, 47654772. 5 Suntivich, J.; May, K.J.; Gasteiger, H.A.; Goodenough, J.B.; Shao-Horn, Y. Science, 2011, 334 (6061),1383-1385. 6 Shao, Z.; Yang, W.; Cong, Y.; Dong, H.; Tong, J.; Xiong, G. J. Membr. Sci., 2000, 172, 177188. 7 Wang, L.; Merkle, R.; Maier, J. ECS Trans, 2009, 25, 2497-2505. 8 Mastrikov, Yu. A.; Kuklja, M.M.; Kotomin, E.A.; Maier, J. En. Env. Sci., 2010, 3, 1544-1550. 9 Kotomin, E.A.; Mastrikov, Yu. A.; Kuklja, M.M.; Merkle, R.; Roytburd, A.; Maier, J. Solid State Ionics, 2011, 188, 1-5. 10 Baumann, F. S.; Fleig, J.; Habermeier, H. -U.; Maier, J. Solid State Ionics, 2006 , 177, 31873191. 11 Švarcova, S.; Wiik, K.; Tolchard, J.; Bouwmeester, H. J. M.; Grande, T. Solid State Ionics, 2008, 178, 1787-1791. 12 Mueller, D. N.; De Souza, R. A.; Weirich, T. E.; Roehrens, D.; Mayer, J.; Martin, M. Phys. Chem. Chem. Phys., 2010, 12, 10320–10328. 13 Kriegel, R.; Kircheisen, R.; Töpfer, J. Solid State Ionics, 2010, 181, 64-70. 14 Efimov, K.; Xu, Q.; Feldhoff, A. Chemistry of Materials, 2010, 22, 5866-5875. 15 Mueller, D.; De Souza, R.A.; Yoo, H.I.; Martin, M. Chemistry of Materials, 2012, 24, 269274. 16 Kresse, G.; Furthmueller, J. VASP the Guide: Univ. Vienna, 2003. 17 NIST Computational Chemistry Comparison and Benchmark Database, 14th ed., Am. Chem. Soc., Washington (2006). 18 Monkhorst, H.J.; Pack, J.D. Phys. Rev. B, 1976, 13, 5188-5192. 19 Henkelman, G.; Arnaldsson, A.; Jónsson, H. Comp. Mater. Sci., 2006, 36, 254-360. 20 Merkle, R.; Mastrikov, Yu. A.; Kotomin, E.; Kuklja, M. M.; Maier, J. J. Electrochem. Soc., 2012, 159, B212-226. 21 Zhukovskii, Y.F.; Kotomin, E.A.; Evarestov, R.A.; Ellis, D.E. Int. J Quant Chem, 2007, 107 (14), 2956-2985. 22 S. Piskunov, E. Heifets, T. Jacob, E.A. Kotomin, D.E. Ellis, E. Spohr, Phys. Rev. B, 2008, 78, 121406 (4 pages). 23 Mastrikov, Y. A.; Merkle, R.; Heifets, E.; Kotomin, E. A.; Maier, J. J. Phys. Chem. C, 2010, 114 (7), 3017–3027. 24 We note that our preliminary calculations reported in M.M. Kuklja, Yu. A. Mastrikov, S.N. Rashkeev, E.A. Kotomin, ECS Transactions, 2011, 35, Solid Oxide Fuel Cells 12 (SOFC-XII), 2077-2084, demonstrated the similar trends and achieved the same conclusions regarding Frenkel disorder. However, Frenkel defect energies were probed in simplified models in which a distant pair of defects was represented as a superposition of two isolated vacancy and interstitial defects, each calculated in a 40-atom supercell. The current study presents refined, more sophisticated modeling of vacancy-interstitial pairs that are placed in a 320-atom supercell at a 2


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short (close pair) and a long (distant pair) distances, which allows for unambiguous interpretation of the obtained results. 25 Thomas, B.S.; Marks, N.A.; Begg, B.D. Nucl. Inst. Meth. B, 2007, 254, 211-218. 26 Yi, J X; Lein, H L; Grande, T; Yakovlev, S; M Bouwmeester, H J Solid State Ionics, 2009, 180, 1-5 27 Kuklja, M.M. Journal of Physics: Condensed Matter, 2000, 12(13), 2953-2967. 28 Gangopadhayay, S.; Inerbaev, T.; Mansurov, A.E.; Altilio, D.; Orlovskaya, N. Appl. Mat. And Interf. 2009, 1, 1512-1519. 29 Evarestov, R.; Blokhin, E.; Gryaznov, D.; Kotomin, E. A.; Merkle, R.; Maier, J. Phys. Rev. B, 2012, 85, 174303 (5 pages). 30 Wang, Z.L.; Zhang, J.Phys Rev B, 1996, 54, 1153-1158.



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Tables Table 1. Single vacancy and vacancy-interstitial pair (Frenkel disorder) formation energies are described in standard Kröger and Vink notations and calculated per defect. Vacancy formation energies in the Ba0.5Sr0.5Co0.75Fe0.25O3 lattice are calculated with respect to the corresponding isolated atoms, as indicated by (g) symbol. VMe stands for the metal vacancy (Me=Ba, Sr, Co, and Fe). Two possible oxygen vacancy configurations were probed, the vacancy placed between two Co atoms, VCo-O-Co, and the vacancy placed between one Co and one Fe atom9,20.

Vacancy (1) VBa+Ba(g) (2) VSr+Sr(g) (3) VCo+Co(g) (4) VFe+Fe(g)

a

Formation energy [eV] 9.19 9.32 8.63 9.76

Frenkel pairs V″Ba+Bai⋅⋅ V″Sr+Sri⋅⋅ V″″Co+Coi⋅⋅⋅⋅ V″″Fe+Fei⋅⋅⋅⋅

(5) VCo-O-Co+O(g)

3.96/1.34a

V⋅⋅Co-O-Co +Oi″

(6) VCo-O-Fe+O(g)

4.02/1.40a

V⋅⋅Co-O-Fe +Oi″

Interstitial configuration Split Split Hollow Hollow Split Hollow Split Hollow

Formation energy [eV] 6.02 4.49 1.76 2.41 0.75 1.85 0.89 1.88

The second energy is calculated with respect to 1/2 free O2 molecule in the triplet state.

Table 2. Schottky and Schottky-like structural disorder in the cubic Ba0.5Sr0.5Co0.75Fe0.25O3 lattice. Energies are given per defect, with each individual vacancy simulated in a 40 atom supercell (8 formula units). The ground state energy of BSF is taken in the cubic phase and BSC in the hexagonal phase.

(1) (2) (3) (4) (5) (6)

Reaction 0 (bulk→gas) ↔ 2V″Ba+2V″Sr+3V″″Co+V″″Fe+12V⋅⋅O 0 (bulk→surface) ↔ 2V″Ba+2V″Sr+3V″″Co+V″″Fe+12V⋅⋅O BaBa+ SrSr+ FeFe +3OO ↔ Ba0.5Sr0.5FeO3 (cub) +1/2V″Ba+1/2V″Sr+ V″″Fe +3V⋅⋅O BaBa+ SrSr+ CoCo+3OO ↔ Ba0.5Sr0.5CoO3 (hex)+1/2V″Ba+1/2V″Sr+ V″″Co +3V⋅⋅O BaBa+OO ↔ BaO +V″Ba+ V⋅⋅O SrSr+ OO ↔ SrO +V″Sr+ V⋅⋅O

Energy [eV] 6.02 0.90 0.86 0.73 1.48 1.40


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Table 3. Energies of the cation structural disorder on the BSCF lattice. Calculations are performed for a single exchange pair of cations placed in a large 320 atom model supercell, which consists of 64 BSCF formula units. Reactions (1) and (6) represent the clustering effect on the A- and B- sublattices, respectively; reactions (2)-(5) describe the formation of antisite defects.

N (1) (2) (3) (4) (5) (6)

Cation Exchange Ba ↔ Sr Ba ↔ Co Ba ↔ Fe Sr ↔ Co Sr ↔ Fe Co ↔ Fe

Energy [eV] -0.20 6.16 7.87 3.79 5.70 0.08

Table 4. Energies of three select decomposition reactions of cubic and hexagonal stoichiometric BSCF (Ba0.5Sr0.5Co0.75Fe0.25O3-δ with δ=0) and the material containing oxygen vacancies (Ba0.5Sr0.5Co0.75Fe0.25O3-δ +1/2O2 with δ=1) are calculated at 0 K and normalized per formula unit. An entropy contribution is neglected in calculations. A negative energy indicates an exothernic reaction.

N

Phase Decomposition

(1) BSCF ↔ 1/2BaCo0.75Fe0.25O3 + 1/2SrCo0.75Fe0.25O3 (2) BSCF ↔ 3/4Ba0.5Sr0.5CoO3(hex)+ 1/4Ba0.5Sr0.5FeO3(cub) (3) BSCF ↔ 1/2BaCoO3 (hex) + 1/4SrCoO3+1/4SrFeO3

Energy per formula unit [eV] Cubic Hexagonal δ=0 δ=1 δ=0 δ=1 0.65 -2.49 -0.01 -2.34 -0.56 -2.90 0.09 -3.04 0.48 -2.65 -0.18 -2.51



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Figures Fig.1. A schematic view of the BSCF crystal structure and basic defects under study: a) the crystalline cubic arrangement, b) a local perfect arrangement centered on a B-sublattice site, c) an oxygen hollow interstitial defect, d) an oxygen vacancy, e) an oxygen split interstitial defect, f) Ba clustering (in an ideal BSCF crystal, the center of the tetrahedron would be occupied by Sr), and g) Sr clustering (in an ideal BSCF crystal, the center of the tetrahedron would be occupied by Ba).

a)

b) A-site cation (Ba,Sr) B-site cation (Co, Fe) Oxygen

e)

d)

c)

f)

g)


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Fig. 2 Co-O-Co oxygen hollow (a) and split (b) interstitial configurations, their atomic charges, and inter-atomic distances.

a)

b)



Fig. 3 a) The cubic and b) the hexagonal (2H) BSCF structures are presented. c) The total energy and d) the single vacancy formation energy of the cubic and hexagonal phases of BSCF are shown as a function of oxygen non-stoichiometry parameter δ. The total energies are given with respect to the stoichiometric hexagonal phase BSCF unit cell, which is 0.66 eV lower than the cubic phase unit cell. Five points shown for δ=0.5 demonstrate the energy dispersion depending upon a distribution of vacancies in the crystal.

a)

3.5

c)

3.0

2.5

DE, eV

2.0

1.5

1.0

, ,

, , cubic phase

0.5

hexagonal phase (2H)

b)

0.0

d)

single O vacancy formation energy, eV

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3.5

3.0

2.5

2.0

1.5

1.0

0.5 0.0

0.2

0.4

0.6

0.8

1.0

d


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TOC entry TOC entry is given here in two different formats. Both images can be downsized without loss of quality.



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Oxygen Vacancy Hollow Interstitial

Split Interstitial

Cation Clustering


The Intrinsic Defects, Disordering, and Structural Stability of BaxSr1

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