Defect Chemistry and Electrical Conductivity of Sm-Doped La1

Article pubs.acs.org/JPCC

Defect Chemistry and Electrical Conductivity of Sm-Doped La1−xSrxCoO3−δ for Solid Oxide Fuel Cells

Mårten E. Björketun,† Ivano E. Castelli,*,†,‡ Jan Rossmeisl,‡,† Thomas Olsen,† Kenji Ukai,§ Michiaki Kato,§ Gilles Dennler,⊥ and Karsten W. Jacobsen† †

Center for Atomic-scale Materials Design,Department of Physics, Technical University of Denmark, DK-2800, Kongens Lyngby, Denmark ‡ Nano-Science Center, Department of Chemistry, University of Copenhagen, DK-2100, Copenhagen, Denmark § Aisin Seiki Co., Ltd. 918-11, Sakashita, Mitsukuri-cho, Toyota, Aichi, 470-0424 Japan ⊥ IMRA Europe S.A.S., 06904 Sophia Antipolis, France ABSTRACT: We have calculated the electrical conductivity of the solid oxide fuel cell (SOFC) cathode contact material La1−xSrxCoO3−δ at 900 K. Experimental trends in conductivity against x, and against δ for fixed x, are correctly reproduced for x ≲ 0.8. Furthermore, we have studied the chemistry of neutral and charged intrinsic and extrinsic defects (dopants) in La0.5Sr0.5CoO3 and have calculated the conductivity of the doped systems. In particular, we find that doping with Sm on the La site should enhance the conductivity, a prediction that is subsequently confirmed by electrical conductivity measurements.

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INTRODUCTION Fuel cells, which consume hydrogen and oxygen to produce electricity, water, and heat, are forecast to become a significant part of the future worldwide energy production.1 As a matter of fact, the interest for fuel cell technologies is becoming increasingly important in the industrial sector, as these renewable energy devices have been significantly penetrating the marketplace for several years now: In 2014, the worldwide sales of fuel cells reached 2.2 billion U.S. dollars, experiencing a growth of more than 50% in average since 2010.2 In spite of the fact that proton exchange membrane fuel cells (PEMFCs) largely dominate the market with about 180 megawatt (MW) shipped in 2015, solid oxide fuel cells (SOFCs) are likely to soon become the second most important technology in terms of power sold (63 MW shipped in 2015).3 This trend is mainly explained by the significant growth of stationary applications that can be illustrated by the 700 W residential Ene-Farm, which counted more than 110 000 units installed in Japan in early 2015.4 To enhance the market penetration of this technology, further cost reduction and performance improvement are necessary. In the case of anode supported tubular structures, increasing the power and thereby the size of SOFC devices tends to induce some performance losses because of the too large electrical resistivity of the cathode material (CM). One countermeasure to this issue consists in coating the cathode with a layer called the cathode current collecting material (CCCM) which should both have a large conductivity at © XXXX American Chemical Society

operating temperature and a coefficient of thermal expansion close to that of the CM. Strontium doped lanthanum cobaltite (La1−xSrxCoO3−δ, LSC) is commonly used as CM and has been the focus of intensive research during recent decades (see refs 5 and 6 and references therein) because of its high oxygen ionic and electronic conductivities at high temperatures.7 Therefore, developing an LSC based CCCM would be highly beneficial as it would ensure a proper matching of the thermal expansion between the cathode and the CCCM. For that matter, our study focused on identifying, by ab initio calculations, extrinsic dopants that could increase the conductivity of LSC and make it usable as CCCM. Apart from its importance for direct applications, LSC has also attracted attention for more fundamental reasons. Its rich electronic and magnetic properties and crystal structure, which all change with composition and temperature,8−13 have inspired both experimental and theoretical studies.8−21 Many of the theoretical works have employed density functional theory (DFT) and have concentrated mainly on obtaining an accurate description of the electronic and magnetic structures.16,19−21 These are highly complex and typically require theory that goes beyond traditional implementations of DFT. In this paper, we evaluate the electronic conductivity of LSC, on the basis of its electronic band structure calculated with Received: March 20, 2017 Revised: May 23, 2017 Published: June 22, 2017 A

DOI: 10.1021/acs.jpcc.7b02608 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C

properties of all systems included in the current study can be retrieved from a database in ref 24. The DFT calculations were performed spin-paired (except for a few test calculations on LaCoO3 and oxygen deficient La0.5Sr0.5CoO3 as well as total energy calculations of elemental Co and CoxOy oxides for which spin-polarization was turned on) using GPAW,25,26 a real-space projector-augmented wave (PAW)27 code, and the atomic simulation environment (ASE)28 to set up and analyze the simulations. All calculations were carried out in finite difference (FD) mode. The density, effective potential, and wave functions were evaluated on a realspace grid with a grid spacing of ∼0.16 Å. The exchangecorrelation energy was evaluated with a PBE-SOL 29,30 generalized gradient approximation (GGA) functional. In addition, an HSE0631,32 hybrid functional was used in a few cases to provide benchmarks for band gap calculations. The Brillouin zone (BZ) of the 40-atom La1−xSrxCoO3 cell was sampled with a 4 × 4 × 4 Monkhorst−Pack k-point grid during geometrical optimizations and with a 6 × 6 × 6 k-point grid during conductivity calculations. A k-point density given by ki × ai ≈ 30, where ai is the ith lattice vector, was used to sample the BZs of the reference metals and oxides. For O2(g), we used a 12 × 12 × 12 Å3 box and only Γ-point Bloch functions. We further added 1 eV to the calculated O2 energy to correct for the known overbinding of O2 by DFT-GGA.33 The lattice constants of La1−xSrxCoO3 were determined by fitting to the Murnaghan equation of state. This resulted in lattice constants ranging from 3.765 Å for SrCoO3 to 3.779 Å for LaCoO3 (for comparison, the experimental lattice constant of cubic SrCoO 3 is 3.829 Å). 18,34 During structural optimization, the atomic positions were relaxed until all residual forces were less than 0.02 eV/Å. The DFT+U methodology35 was applied to all calculations reported in the present paper to improve the electronic description of the various LSC compositions. We applied a Ueff = U − J = 2 eV correction to the f-orbitals of the lanthanides, the d-orbitals of Co, and the p-orbitals of O. The Ueff value was chosen so as to give sufficient agreement with HSE06 and/or experimental band gaps over the entire range of x values. More specifically, we obtain the following band gaps (HSE06 data within parentheses): LaCoO3, 0.70(1.03) eV; La0.5Sr0.5CoO3, 0.51(0.61) eV; and SrCoO3, 0.30(0.28) eV. Chainani et al. estimated a band gap of 0.6 eV for LaCoO3 from ultraviolet photoemission spectroscopy measurements.36 In addition, the resulting density of states (DOS) for LaCoO3 compares well with the DOS calculated by He and Franchini with an HSE-10 functional.19

DFT, for a large set of compositions, ranging from LaCoO3 to SrCoO3. We further calculate the formation energy and concentration of various intrinsic and extrinsic point defects and investigate how oxygen vacancies and dopants affect the conductivity. Our main objective has been to identify trends in the electronic conductivity and to use that understanding to screen for new competitive CCCMs rather than to correctly reproduce all features of the electronic structure for each and every composition. However, as we will see later, to accurately capture the trends, we still need a relatively good description of the electronic structure, especially of the LSC’s small band gap. Consequently, we have benchmarked our electronic structure calculations against published high-precision DFT data and relevant experimental studies. More precisely, we use semiclassical Boltzmann theory to describe the conductivity. This theory admittedly has its limitations as it neglects, for example, contributions to the conductivity from polaron hopping. However, since most of the investigated compounds exhibit metallic type conductivity at the considered temperature of 900 K (partly because of significant Fermi smearing), we neglect this contribution, which is much smaller than the contribution from conductive electrons. We further assume that the calculated band structures are representative also of the band structures at high temperatures, above reported metal−insulator transition temperatures, that is, we implicitly assume that no dramatic, abrupt change in the electronic structure takes place as the temperature increases, but rather more and more electrons are excited across the small band gap. Last, we ignore any potential energy dependence in the scattering time, and we assume that it is the same and that it exhibits the same temperature dependence in all investigated oxides (cf. eq 1). This is another relatively crude assumption to which room-temperature measurements on La1−xSrxCoO3, x ∈ [0, 0.3], by Wang et al.22 attest. In these experiments, the relaxation time first increases 10 times from x = 0 to x = 0.2 because of an increase of the Co−O−Co bond angle and relaxation of distortions upon increased Sr doping according to the authors, whereafter it reduces somewhat supposedly because of enhanced point defect scattering. However, these are still relatively modest variations compared to the most important contribution to the conductivity, the number of electronic bands crossing the Fermi surface and their gradient in k-space at the crossing, which we capture with the semiclassical Boltzmann eq (eq 1). For example, while the difference in scattering time between the x = 0 and x = 0.3 systems is less than 10 in the quoted experiments, the difference in electrical conductivity is larger than 18 000. Consequently, by using an arguably crude approximation, we are able to capture the most important contribution to the conductivity and quickly establish the relative conductivity of a large set of oxides.

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EXPERIMENT Sample Preparation. Powders of La0.5 Sr0.5 O 3 and La0.5−ySmySr0.5CoO3 (y ∈ {0.0005, 0.005, 0.04, 0.08, 0.12, 0.24, 0.36}) were prepared by the solid state reaction method. The average crystals thus obtained measured 0.5 μm across. Powder samples of 50 g were put into 50 × 60 mm dyes. Molded bodies were then obtained by subjecting the samples to 10.8 MPa uniaxial pressure for 2 min with a TG-62101 (RIKENKIKI Co., Ltd.) hydraulic press. To improve the packing density, the samples were subsequently exposed to cold isostatic pressing (CIP) at 245 MPa for 1 min in a 3kB (Kobe Steel. Ltd.) wet isostatic press. The molded bodies were finally sintered for 2 h at 1273 K in an electric furnace. Conductivity and Thermal Expansion Measurements. The sintered bodies were cut into rectangular bars (5 × 5 × 20

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COMPUTATIONAL DETAILS Cubic La1−xSrxCoO3, x ∈ [0, 1], was modeled by a 40-atom supercell, obtained by repeating a primitive LaCoO3 cell twice in each direction and replacing 8x La ions with Sr in all their inequivalent positions. This allowed us to change the La/Sr concentration in steps of 0.125. For test purposes, we also used a rhombohedral 10-atom LaCoO3 cell. For other oxides and metals, used to evaluate the reference chemical potentials of various defects, we used the experimental structure and stoichiometry23 that resulted in the lowest DFT reference energy. The geometry, electronic energy, and assorted physical B


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Figure 1. (a) Normalized theoretical and experimental electrical conductivity of La1−xSrxCoO3, x ∈ [0, 1]. The conductivities labeled Theory and Experiment have been calculated and measured in this work, and the other data points have been obtained from experimental literature. The experimental conductivities at 923 K have been plotted relative to the room temperature x = 0.4 value of ref 38. (b) Normalized theoretical electrical conductivity of La1−xSrxCoO3−δ for x = 0, 0.5, and 1. (c−e) Supercells used to model the x = 0.625 system. The corresponding normalized conductivities are indicated in a.

Figure 2. (a) Electronic band structure and atom-projected DOS of cubic La1−xSrxCoO3 as a function of x, obtained with Ueff = 2 eV. La and Sr pstates contribute mainly to a peak at −13.5 eV, and La d-, f-states contribute to a peak at 5.5 eV, thus falling outside the displayed energy window. (b) DOS for cubic LaCoO3, calculated with Ueff = 0 eV (solid line) and Ueff = 2 eV (dashed line). (c) DOS for cubic (dashed line) and rhombohedral (dash-dotted line) LaCoO3, calculated with Ueff = 2 eV.

mm) using a diamond cutter. Platinum wires were wound around the bars, and platinum paste was applied around the wires to reduce contact resistance. The samples were then

placed in the electric furnace, and four-probe electrical resistance measurements were performed at temperatures ranging from 873 to 1073 K. C


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DFT with (semi)local approximations to exchange and correlation fails to reproduce the gap and predicts LaCoO3 to be metallic.19 However, by applying a moderate Hubbard U (Ueff = 2 eV) to the f-states of La, the d-states of Co, and the pstates of O, we manage to open a small gap (cf. Figure 2b) that is in good agreement with the experimental LaCoO3 gap and with HSE06 gaps over the entire x-range (see Computational Details for further information). To create a gap is crucial for reproducing and understanding the experimentally observed trend in conductivity. If we compare the band structure of LaCoO3 with the systems with finite Sr contents (Figure 2a), we see that Sr behaves as an acceptor dopant that transforms the material into a p-type semiconductor and hence shifts the Fermi level down toward the valence band. For small x, there are only a few or even no bands crossing the Fermi surface (level), but for larger x (x ≥ 0.25), many bands cross the Fermi surface, and the material changes to a conductor. The observed change in electron density around the Fermi surface is consistent with ultraviolet photoelectron spectra of La1−xSrxCoO3 (x ≤ 0.4) measured by Chainani et al.36 and Saitoh et al.9 After x ≈ 0.25, continued doping has much less impact on the conductivity. The prediction that La1−xSrxCoO3 is a (p-type) conductor at higher Sr contents is consistent with the experimental finding by Tucker et al. that La0.7Sr0.3CoO3 exhibits nearly temperatureindependent conductivity.43 The calculated change in electronic structure and conductivity is also consistent with other experimental reports of a gradual transition from semiconductor to metal type conduction between x ≈ 0.125 and x ≈ 0.3.9,14,44,45 Structural analysis has shown that SrCoO3 assumes cubic symmetry18,34 while La1−xSrxCoO3 with lower Sr contents is rhombohedrally distorted. The rhombohedral-to-cubic transition is further known to take place at x ≳ 0.4.13,16,46 This casts some doubt on the use of cubic symmetry when simulating the conductivity of small x systems, in particular when x = 0. However, test calculations show that the density of states (DOS) around the gap of LaCoO3 is very similar if a rhombohedral cell is employed (cf. Figure 2c), and as a result, the conductivity, at 900 K, also turns out to be similar, σ̅ rhomb. = 0. 85 × σ̅ cubic. We therefore conclude that the calculated relative conductivities are reliable nevertheless. Also, even though we employ cubic cells in the simulations, the individual atoms are allowed to move according to the interatomic forces to their fully relaxed positions. This internal flexibility makes it possible to capture some of the rhombohedral distortion of the oxygen octahedra. For example, the average Co−O−Co angle decreases steadily from 169.1° in SrCoO3 to 166.0° in LaCoO3. We have further investigated how oxygen vacancy, VO, formation affects σ̅ in LaCoO3, La0.5Sr0.5CoO3, and SrCoO3 (cf. Figure 1b). In LaCoO3, which is an intrinsic semiconductor, VO acts as a donor defect, donating electrons to the conduction band, thus significantly increasing the conductivity. In the ptype conductors La0.5Sr0.5CoO3 and SrCoO3, creation of VO reduces the number of holes in the valence band, which lowers the conductivity. At some point, all the holes in the host material have been compensated, and the conductivity reaches a minimum. Upon further VO formation, electrons are donated to the conduction band, and the conductivity starts to increase. The observed initial decrease in conductivity for La0.5Sr0.5CoO3 is fully consistent with the σ-versus-[VO] dependence measured by Søgaard et al.7 in La0.6Sr0.4CoO3.

The thermal expansion at 923 K was measured with a TMA8310 (Rigaku Co.) thermomechanical analyzer. The measurements were carried out in air atmosphere, that is, at 21% of O2 and 1 atm, the heating rate was 5 K/min, and Al2O3 was used as reference material.

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RESULTS AND DISCUSSION La1−xSrxCoO3−δ: Electronic Structure, Electrical Conductivity, and Stability. From a semiclassical Boltzmann equation, the directionally averaged longitudinal electrical conductivity can be calculated according to σ=τ

e2 4π 3

∑∫ n

BZ

dkvnk

−∂f 0 (εnk ) ∂εnk

(1)

where f 0 is the Fermi−Dirac distribution function and τ is the scattering time.37 τ depends on lattice vibrations and impurities which makes it difficult to evaluate from first principles. A small τ may destroy the conductivity, but a minimum requirement for a good conductor is a nonvanishing σ̅ = σ/τ. In the present study, we will therefore use σ̅ as a descriptor of the electrical conductivity and assume, as mentioned earlier, that τ is similar in all investigated systems. The size of σ, and hence σ̅, is proportional to the density of states at the Fermi level weighted by the Fermi velocity at the individual k-points. We have calculated σ̅ for cubic La1−xSrxCoO3, x ∈ [0, 1], at an electronic temperature Te = 900 K, and the resulting relative conductivity σ̅/σ̅ LaCoO3 is indicated by black circles in Figure 1a. We find that starting from pure LaCoO3, the conductivity increases rapidly with increasing Sr contents up to x ≈ 0.25. Thereafter, the increase is much more moderate. Qualitatively, the calculated x-dependence agrees well with measured room temperature conductivities for x ≤ 0.8, cf. Figure 1a.22,38−40 However, the relative difference between x = 0.25 and x = 0 is 2 orders of magnitude larger in the measured data. This can be explained as a temperature effect; later, we will see that LaCoO3 is an intrinsic semiconductor, thus exhibiting strongly temperature dependent conductivity, while the oxides with x ≠ 0 become increasingly p-type in character with increasing x, which drastically reduces the effect of temperature. For x > 0.8, the measured conductivity displays a sudden drop.38,40 It has been attributed to the onset of formation of a brownmillerite impurity phase,38 which would explain why we fail to reproduce this feature. For x = 0.25, 0.375, 0.625, and 0.75, we report three different data points since the 8(La1−xSrxCoO3) cell used in the simulations allows La and Sr to be distributed in three symmetrically inequivalent configurations that could be associated with different conductivities as shown in Figure 1c−e for x = 0.625. (A special quasirandom structure approach could be used to investigate the different possible configurations of La and Sr in the unit cell.41) In the case of x = 0.625, where we find the largest variation, the energetically most stable system shows the highest resistance and smallest shift of the Sr ions away from their ideal cubic positions (Figure 1c), whereas the least stable system is the most conductive (Figure 1d). However, the energy differences between the three systems are small (see database in ref 24), and the thermally averaged conductivity is therefore as high as ∼40% of the maximum x = 0.625 value. The x-dependence of σ̅ can be straightforwardly understood from the electronic band structure of the material, cf. Figure 2a. Experimentally, LaCoO3 is known to be a small band gap (Eg = 0.6 eV36) semiconductor at low temperatures.9,42 Standard D


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Table 1. Formation Free Energies ΔGf, Given in Units of eV, of Select Intrinsic Defects D in La0.5Sr0.5CoO3a

Finally, using linear programming,47 we have calculated the stability of cubic La1−xSrxCoO3, x ∈ [0, 1], relative to the most stable linear combination of 17 reference systems: La, Sr, Co, O2, La2O3, SrO2, SrO, CoO, CoO2, Co3O4, La3Co, LaCo13, La2Co3, LaCoO3, Sr2Co2O5, Sr6(CoO3)5, and SrCo6O11. The heat of formation has been evaluated at 900 K and standard pressure and is reported in Figure 3.

defect VO

VCo

VLa

VSr

Oi

Figure 3. Stability, per atom, of La1−xSrxCoO3 relative to a set of 17 reference systems at 900 K and standard pressure.

Coi

In this analysis, we have included the translational and vibrational entropy of the O2 molecule but have ignored vibrational contributions from La1−xSrxCoO3 and the other reference systems. When O2 is one of the decomposition products, this introduces a small error associated with unaccounted oxygen ion modes lost during decomposition of La1−xSrxCoO3. Accounting for this effect would destabilize SrCoO3 (x = 1), the system that produces the most O2 upon decomposition, with ∼4 meV compared to the value shown in Figure 3 if we assume that the vibrational entropy of each lost oxygen mode contributes ∼0.1 eV to the formation free energy at 900 K.48 For the smaller x, La1−xSrxCoO3 decomposes into binary and tertiary oxides. In this case, the vibrational frequencies are more or less preserved, and the error introduced is negligible. Other effects we have disregarded when assessing the stability are entropy of mixing, the oxygen nonstoichiometry, found predominantly in the higher-x systems,49 and the experimentally observed transition from cubic to rhombohedral crystal structure for x ≲ 0.4. If mixing entropy had been included, it would have stabilized the x = 0.5 system with ∼10 meV per atom,50 while the effect would have been smaller for other compositions. The error associated with the nonstoichiometry affects basically the same systems as the vibrational effect discussed earlier. It is also of similar magnitude but opposite sign, for instance, the energy gained by formation of one-eighth VO in La0.5Sr0.5CoO3, a rather typical vacancy concentration at 900 K,49 is ∼5 meV per atom, cf. Table 1. The two errors will, therefore, to a large extent, cancel out. The error introduced by studying a higher-energy (cubic) structure for small x is larger, but correcting for it would only further stabilize those systems that are already predicted to be stable. In relation to this, other theoretical works have reported higher stability for cubic La1−xSrxCoO3, but the decomposition products, that is, reference systems, have been different in these cases.51,52 As in Figure 1a, we report more than one data point for some x-values because the 8(La1−xSrxCoO3) cell used in the simulations allows La and Sr to be distributed in symmetrically and energetically inequivalent configurations. The variation in

CoLa CoSr

{CoLa, LaCo} {CoSr, SrCo}

q

b ΔGfμlow /ΔGfμhigh D D

0 +1 +2 0 −1 −2 −3 0 −1 −2 −3 0 −1 −2

0.68 0.19 −0.19 0.88/4.08 1.20/4.40 1.33/4.53 1.24/4.44 1.23/11.68 1.66/12.11 1.87/12.31 1.85/12.30 2.03/8.89 2.29/9.16 2.33/9.20

3.5 4.4 1.3 8.0 6.1 5.9 1.1 7.5 1.3 4.4 3.2 1.8 3.0 9.6

× × × × × × × × × × × × × ×

10−4 10−3 10−2 10−6 10−6 10−5 10−2 10−8 10−8 10−8 10−6 10−12 10−12 10−11

0 −1 −2 0 +1 +2 +3

2.33 2.38 2.21 6.38/3.18 6.14/2.94 5.81/2.61 5.27/2.07

9.7 2.7 1.4 3.4 1.5 2.3 5.6

× × × × × × ×

10−14 10−12 10−9 10−37 10−37 10−37 10−36

0 0 +1

2.12/9.38 3.35/7.02 2.94/6.61

2.6 × 10−13 2.0 × 10−20 8.7 × 10−20

5.68 6.79

5.1 × 10−33 1.9 × 10−39

0 0

c

For charged defects (q ≠ 0), the Fermi energy is taken as the energy of the top of the valence band (EF = εVBM = 0) of the defect-free host oxide. The free energies are calculated at T = 900 K and pO2 = 1 atm. Defect concentrations c (given in units of a−3 0 , where a0 is the lattice parameter of one La0.5Sr0.5CoO3 unit) have been calculated for μlow D and a Fermi energy corresponding to overall charge neutrality in the 1 c e l l . b μ Dl o w : μO = 2 E[O2 ], μ C o = E [ C o O 2 ] − E [ O 2 ] , a

μLa = μO =

1 3 E[La 2O3] − 2 E[O2 ] 2 1 E[O2 ], μM = Ebulk M . 2

(

),

μSr = E[SrO2] − E[O2]. μDhigh:

stability is, however, small, and it is clear that La1−xSrxCoO3 is thermodynamically unstable for x ≳ 0.30. More precisely, the thermodynamic modeling suggests that La1−xSrxCoO3 would decompose into a combination of Sr6(CoO3)5, SrCo6O11, LaCoO3, and La2O3 for 0 < x < 0.5 and into a combination of Sr6(CoO3)5, SrCo6O11, La2O3, and O2 for x ≥ 0.5. Still, many of the x ≳ 0.30 compositions are likely to be metastable, that is, there might be considerable barriers for decomposition into the reference systems. The many experimental studies performed on midrange-x systems, also at high temperatures, suggest that this is in fact the case.7,22,38−40 La0.5Sr0.5CoO3: Point Defects and Their Influence on the Conductivity. We have chosen to study the x = 0.50 composition in further detail. It is a system that offers a reasonable compromise between conductivity and stability (assuming a metastable region of a few hundreds of an electronvolt in Figure 3) and lends itself to computational studies because of its high symmetry. More specifically, we have E


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are present only in low concentrations. An EF > 0 would stabilize negatively charged defects. However, all negative defects, apart from Co vacancies in the highest charge state, will remain unstable for all positions of EF within the small band gap of La0.5Sr0.5CoO3 (cf. Figure 2a). That this is the case can be clearly seen from the defect-energy diagrams presented in ref 24. To quantify the earlier observations, we have solved for the concentrations of all investigated defects under the condition of overall charge neutrality in the system. The charge neutrality condition can be expressed as64

calculated the formation free energy of various neutral and charged point defects under normal operating conditions and have investigated how they affect the conductivity. The next section reports on intrinsic defects while the subsequent section focuses on extrinsic defects. A similar rigid band model used here to calculate formation energies and concentrations of defects has already been described in the literature.53−56 The formation energy of an isolated defect or set of defects of charge q can be calculated according to57 f ΔE D, q = E D, q − E H +

∑ nαμα + q·EF + q·ΔVpa + ΔEi α

∑ qicD(qi) + pVB − nCB = 0

(2)

(3)

D,i

where ED,q is the energy of a supercell containing the defects and with the number of electrons adjusted to create a defect with effective charge q, EH is the energy of the corresponding host supercell, nα is the number of atoms α that have been removed from (nα ≥ 1) or added to (nα ≤ −1) the system to form the defects, μα is the reference energy (chemical potential) of α, EF is the Fermi energy, ΔVpa is a potential shift applied to align the average electrostatic potential of the defective cell with that of the host cell, and ΔEi is a correction for the electrostatic interaction between the images of charged supercells (see ref 57). The first-order correction to ΔEi is

where cD(qi) is the concentration of a specific point defect D in charge state q i and where p VB and n CB denote the concentrations of holes in the valence band and electrons in the conduction band, respectively. We have obtained the hole and electron concentrations by integrating over the density of states g(ε) of La0.5Sr0.5CoO3 according to65 pVB =

2

qα

given by ΔE i1 = 2εLM , where αM is the Madelung constant of the given supercell geometry, L = V−1/3 supercell, and ε is the dielectric constant.57 Experimental studies indicate that ε ≫ 1 × 103 for La0.5Sr0.5CoO3.58,59 Hence, because of the good screening, ΔEi is not expected to exceed ∼1 meV and has been neglected in the present work. Intrinsic Point Defects. In Table 1, we report formation free energies, ΔGf = ΔEf − TΔSf, of potential intrinsic defects mentioned in the literature60−62 (vacancies VX, interstitials Xi,63 antisites AB, and antisite pairs {AB, BA}) in various charge states q at T = 900 K and pO2 = 1 atm. When calculating the formation energies, ΔEf, we have assumed that the chemical potential of the electrons equals the energy of the valence band maximum εVBM = 0. If the Fermi level is higher in energy, a term q·EF must be added to the ΔGf reported in Table 1. The change of ΔGf with EF within the theoretical band gap is reported, in the form of defect energy diagrams, in ref 24. Moreover, for each metal species M, we have considered two different reference energies: μlow M , its chemical potential in the most stable MxOy oxide, and μhigh M , its chemical potential in the corresponding elemental metal. For the application considered here (an oxygen-rich atmosphere), however, only the binary oxide reference should be relevant. Finally, we have assumed that oxygen vacancies/interstitials are created by exchange of oxygen molecules with the surrounding atmosphere. Consequently, these processes are associated with large gains/losses of translational and to a lesser extent vibrational entropy. In the same way as for the stability of La1−xSrxCoO3, discussed in conjunction with Figure 3, there is an uncertainty of ∼0.1 eV in the calculated oxygen defect formation energies associated with unaccounted oxygen ion modes in La0.5Sr0.5CoO3, lost/gained during formation of vacancies/interstitials. Other defects, on the other hand, are created by exchanging metal species with another solid phase. In this case, the change in entropy, ΔSf, is small, and we have assumed that ΔGf is similar to ΔEf. The data collected in Table 1 suggest that all investigated defects, except for oxygen vacancies in higher charge states, are energetically unfavorable when EF = εVBM = 0 and, therefore,

nCB =

εVBM

∫−∞ ∫ε

g (ε)[1 − f (ε , E F)]dε

(4)

∞

g (ε)f (ε , E F)dε

CBM

(5)

where εVBM and εCBM are the energies of the valence band maximum and conduction band minimum and where f(ε, EF) is the Fermi−Dirac distribution function. Furthermore, we have calculated the concentration of a point defect D in charge state qi according to 1 cD(qi) = ND 1 + exp[(ΔG μf low + qi ·E F)/kBT ] D

(6)

where ND is the number of available sites for the defect in the primitive La0.5Sr0.5CoO3 cell and ΔGfμlow is the formation free D energy when EF = εVBM = 0. By using the expressions for the concentrations of point defects, holes and electrons (eqs 4− 6), values for ΔGfμlow from D Table 1, and Eg = εCBM − εVBM = 0.51 eV, deduced from Figure 2a, we obtain EF = 0.30 eV at overall charge neutrality from eq 3. This value plugged back into eq 6 finally gives the defect concentrations (average number of defects per La0.5Sr0.5CoO3 2 unit) reported in Table 1. As expected, Vq=+ and Vq=−3 O Co are the most abundant point defects at equilibrium. According to measurements by Mizusaki et al.,49 La0.5Sr0.5CoO3−δ has a nonstoichiometry parameter δ of ∼0.09 after equilibration of the solid solution at 900 K in 1 atm O2. This is significantly higher than our estimated equilibrium concentration of ∼0.013. It should be stressed, however, that the energies in Table 1 were obtained by spin-paired calculations on relatively small (40 atoms) supercells. The usage of spin-polarization and larger supercells, which would allow for better convergence of electrostatic and elastic effects, could potentially stabilize the vacancy. Test calculations show that spin-polarization stabilizes VO with 0.05 eV, resulting in an equilibrium concentration of ∼0.019, closer to but still far from 0.09. Likewise, test calculations on 135 atoms and 320 atoms supercells suggest that the uncertainties in electrostatic and elastic effects are both ≤0.1 eV, but the combined effect seems to somewhat destabilize rather than stabilize the vacancy in the larger cells. F


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The Journal of Physical Chemistry C Table 2. Formation Free Energies ΔGf, Given in Units of eV, of Select Extrinsic Defects D in La0.5Sr0.5CoO3a defect

ΔG f high

q

μD

b

ΔG f high

ΔG f low

low μD , μLa/Sr

low , μLa/Sr

μD

high

, μLa/Sr

ΔG f low

0 −1 0 0 0 0

−6.72 −6.46 −11.59 −9.36 −10.55 −7.74

0.07 0.33 1.10 −0.36 0.81 −0.07

3.73 3.99 −1.15 1.09 −0.10 2.71

10.52 10.78 11.55 10.09 11.26 10.38

BaSr CaSr CdSr EuSr NaSr

0 0 0 0 0 −1

−5.98 −7.01 −2.41 −7.98 −2.31 −2.15

0.81 −0.45 0.31 0.14 1.58 1.74

0.89 −0.14 4.45 −1.11 4.55 4.71

7.67 6.42 7.17 7.00 8.45 8.61

Vo in SmLa

0 +1 +2

BaLa CeLa NdLa PrLa SmLa

high

μD , μLa/Sr

0.29 0.01 −0.51

a For charged defects (q ≠ 0), the Fermi energy is taken as the energy of the top of the valence band (EF = εVBM = 0) of the defect-free host oxide. The free energies are calculated at T = 900 K and pO2 = 1 atm. In addition, the unit cells for three different numbers of VO, i.e., nonstoichiometry

parameters δ, in SmLa are shown. μPr = E[PrO2 ] − E[O2 ],

μEu =

1 2

b low μD :

μSm =

1 2

1

1

μO = 2 E[O2 ], μBa = E[BaO] − 2 E[O2 ], μCe = E[CeO2 ] − E[O2 ], μ Nd = E[NdO2 ] − E[O2 ],

(E[Sm2O3] − 23 E[O2]),

(E[Eu2O3] − 23 E[O2]), μNa = E[NaO3] − 23 E[O2]

66,67

1

μCa = E[CaO] − 2 E[O2 ],

1

μCd = E[CdO] − 2 E[O2 ],

1

bulk , μhigh D : μO = 2 E[O2 ], μM = EM .

Figure 4. Calculated change in conductivity with dopant M at 900 K for (a) La0.5Sr0.375M0.125CoO3 and (b) La0.375M0.125Sr0.5CoO3. Three different configurations are considered: structure relaxed for the doped stoichiometry (full conductivity, solid black line); La4Sr4Co8O24 stoichiometry at the relaxed doped geometry (dashed red line); composition adjusted to include the dopant, but structure fixed at La4Sr4Co8O24 geometry (dotted green line). (c) DOS and projected-density of states (PDOS) for the three different configurations at the La0.375Sm0.125Sr0.5CoO3 stoichiometry and/or geometry. 2 reduction of this parameter with 0.4 eV would stabilize Vq=+ O with 0.2 eV and would result in δ = 0.06. Finally, we note that 2 the formation of Vq=+ will cause a slight reduction in the O

Another source of uncertainty is the 1 eV correction we have added to the O2 energy to compensate for the overbinding of O2 (see Computational Details). For example, we note that a G


Article

The Journal of Physical Chemistry C electrical conductivity of La0.5Sr0.5CoO3 (cf. Figure 1), but this is expected to be partly offset by the simultaneous formation of Vq=−3 Co . Extrinsic Point Defects. We have further investigated doped systems in which a quarter of either the La or the Sr ions have been replaced by alkali, alkaline earth, lanthanide, and actinide metals. First of all, we have calculated the formation energies52 of the various substitutional defects, and the result is reported in Table 2. In the same way as for the intrinsic defects, we have considered two different chemical potentials for the extrinsic metals and La/Sr exchanged in the defect formation process. Again, the binary oxide reference μlow M (column 4) is the most relevant under typical operating conditions. However, Table 2 indicates that a wide range of defect stabilities can be obtained during synthesis depending on which pure metals and/or oxides are in excess. Unlike the majority of the intrinsic defects, several of the extrinsic defects are quite easily formed. In particular, BaLa, NdLa, SmLa, CaSr, and EuSr exhibit small or negative formation energies. Second, we have calculated the electrical conductivity of the various La- and Sr-site doped systems at 900 K; see Figure 4 where undoped La0.5Sr0.5CoO3 has been included as reference. Figure 4a, b (solid black lines) suggests that it might be possible to obtain about 40% enhancement in conductivity, compared to pure La0.5Sr0.5CoO3, with SmLa (37% increase) at the current level of doping because of favorable changes in the electronic band structure. However, we have previously seen that formation of oxygen vacancies would reduce the conductivity of La0.5Sr0.5CoO3 (cf. Figure 1) and, given its susceptibility to vacancy formation (cf. Table 2), a similar or larger counteracting effect might be anticipated for SmLa. Figure 4a, b shows how the enhanced conductivity in the Sm doped system can be ascribed to a combined effect of structural and compositional changes. In fact, the conductivity of the Sm doped system becomes lower than that of the undoped system if the geometry is kept frozen at the La0.5Sr0.5CoO3 crystal structure (see stoichiometric change, dotted green line). On the other hand, the conductivity of La0.5Sr0.5CoO3 hardly changes when it adopts the La0.375Sm0.125Sr0.5CoO3 structure (geometric change, dashed red line). This observation can be explained by studying the (P)DOS, see Figure 4c. Considered alone, a change in the geometry or stoichiometry has little influence on the density of states at the Fermi level. However, when the two effects are combined, the distortions in the oxygen octahedra result in an upshift of the occupied Sm levels, causing them to cross the Fermi level. A similar behavior can also be seen for BaLa. The earlier prediction has been tested experimentally by electrical conductivity measurements (see Experiment section for experimental details). Figure 5, upper pane, reports the results of conductivity measurements performed on La0.5−ySmySr0.5CoO3 (LSSC), where y = 0 thus corresponds to La0.5Sr0.5CoO3 (LSC), at temperatures ranging from 873 to 1073 K. We first note that the measurements confirm the theoretical prediction σLSSC > σLSC. If we interpolate the experimental conductivities at 923 K to the theoretical condition y = 0.125, we find that σLSSC(y = 0.125) = 1104 S cm−1, which is an 11% enhancement compared to σLSC ≈ 999 S cm−1. The improvement is thus somewhat smaller than predicted. This could be a reflection of the anticipated reduction in conductivity because of oxygen vacancy formation. Also, the conductivity of LSSC reaches a maximum at

Figure 5. Conductivity (upper pane) and thermal expansion coefficient (lower pane) of La0.5−ySmySr0.5CoO3 measured at temperatures ranging from 873 to 1073 K. The star in the upper pane indicates the calculated conductivity of La0.375Sm0.125Sr0.5CoO3 relative to La0.5Sr0.5CoO3 (y = 0) at 900≈923 K.

somewhat smaller dopant concentrations, y ≈ 0.04. For this composition, the increase in conductivity is roughly 20%. To assess the impact of the increased conductivity on the performance of tubular devices, we have estimated the output voltages, Vcell, of fuel cells with LSC and LSSC (y = 0.04) as CCCM, using the equivalent circuit illustrated in Figure 6. Our calculations show that Vcell should increase from 0.7 V with LSC as CCCM to 0.73 with LSSC (y = 0.04), which represents an enhancement of about 4%.

Figure 6. Equivalent circuit of a tubular SOFC where Vcell is the output voltage of the cell, I0 is the current flowing in the devices, E0 is the open-circuit voltage, Rcea is the internal circuit of the devices, rc is the resistance of the CCCM, ra is the resistance of the anode current collector, rc,terminal is the resistance of the cathode terminal, and ra,terminal is the resistance of the anode terminal.

Finally, the experimental investigation further reveals that LSSC exhibits metallic type conductivity as predicted by the calculations (see the moderate reduction in conductivity with increasing temperature reported in the upper pane of Figure 5). It also shows that LSSC’s thermal expansion coefficient is superior to that of LSC, especially for y ≈ 0.04, as it falls closer to the target area of ≤15 × 10−6/K for good matching with other cell components (cf. Figure 5, lower pane). This advantageous thermal matching, combined with the high electronic conductivity, renders LSSC a highly interesting candidate as CCCM in solid oxide fuel cells. To protect this discovery, a patent application (application number JP,2016037201) has been filed. H


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(9) Saitoh, T.; Mizokawa, T.; Fujimori, A.; Abbate, M.; Takeda, Y.; Takano, M. Electronic Structure and Magnetic States in La1−xSrxCoO3 Studied by Photoemission and X-ray-absorption Spectroscopy. Phys. Rev. B: Condens. Matter Mater. Phys. 1997, 56, 1290−1295. (10) Tokura, Y.; Okimoto, Y.; Yamaguchi, S.; Taniguchi, H.; Kimura, T.; Takagi, H. Thermally Induced Insulator-metal Transition in LaCoO3 A View Based on the Mott Transition. Phys. Rev. B: Condens. Matter Mater. Phys. 1998, 58, R1699−R1702. (11) Kriener, M.; Zobel, C.; Reichl, A.; Baier, J.; Cwik, M.; Berggold, K.; Kierspel, H.; Zabara, O.; Freimuth, A.; Lorenz, T. Structure, Magnetization, and Resistivity of La1−xMxCoO3 (M = Ca, Sr, and Ba. Phys. Rev. B: Condens. Matter Mater. Phys. 2004, 69, 094417. (12) Kriener, M.; Braden, M.; Kierspel, H.; Senff, D.; Zabara, O.; Zobel, C.; Lorenz, T. Magnetic and Structural Transitions in La1−xAxCoO3 (A = Ca, Sr, and Ba). Phys. Rev. B: Condens. Matter Mater. Phys. 2009, 79, 224104. (13) Mastin, J.; Einarsrud, M.-A.; Grande, T. Structural and Thermal Properties of La1−xSrxCoO3−δ. Chem. Mater. 2006, 18, 6047−6053. (14) Raccah, P. M.; Goodenough, J. B. A Localized Electron to Collective Electron Transition in the System (La, Sr)CoO3. J. Appl. Phys. 1968, 39, 1209−1210. (15) Yamaguchi, S.; Okimoto, Y.; Taniguchi, H.; Tokura, Y. Spinstate Transition and High-spin Polarons in LaCoO3. Phys. Rev. B: Condens. Matter Mater. Phys. 1996, 53, R2926−R2929. (16) Ravindran, P.; Korzhavyi, P. A.; Fjellvåg, H.; Kjekshus, A. Electronic Structure, Phase Stability, and Magnetic Properties of La1−xSrxCoO3 from First-principles Full-potential Calculations. Phys. Rev. B: Condens. Matter Mater. Phys. 1999, 60, 16423−16434. (17) Samal, D.; Kumar, P. S. A. A Critical Re-examination and a Revised Phase Diagram of La1−xSrxCoO3. J. Phys.: Condens. Matter 2011, 23, 016001. (18) Long, Y.; Kaneko, Y.; Ishiwata, S.; Taguchi, Y.; Tokura, Y. Synthesis of Cubic SrCoO3 Single Crystal and its Anisotropic Magnetic and Transport Properties. J. Phys.: Condens. Matter 2011, 23, 245601. (19) He, J.; Franchini, C. Screened Hybrid Functional Applied to 3d0 →3d8 Transition-metal Perovskites LaMO3 (M = Sc-Cu): Influence of the Exchange Mixing Parameter on the Structural, Electronic, and Magnetic Properties. Phys. Rev. B: Condens. Matter Mater. Phys. 2012, 86, 235117. (20) Ali, Z.; Ahmad, I. Band Profile Comparison of the Cubic Perovskites CaCoO3 and SrCoO3. J. Electron. Mater. 2013, 42, 438− 444. (21) Aliabad, H. A. R.; Hesam, V.; Ahmad, I.; Khan, I. Electronic Band Structure of LaCoO3/Y/Mn Compounds. Phys. B 2013, 410, 112−119. (22) Wang, Y.; Sui, Y.; Ren, P.; Wang, L.; Wang, X.; Su, W.; Fan, H. J. Correlation between the Structural Distortions and Thermoelectric Characteristics in La1−xAxCoO3 (A = Ca and Sr). Inorg. Chem. 2010, 49, 3216. (23) The Inorganic Crystal Structure Database. https://icsd.fizkarlsruhe.de (accessed June 2017). (24) Online Supplementary Information, KatlaDB - Theoretical Catalysis Database, Nano-Science Center, Department of Chemistry, University of Copenhagen. http://nano.ku.dk/english/research/ theoretical-electrocatalysis/katladb (accessed June 2017). (25) Mortensen, J. J.; Hansen, L. B.; Jacobsen, K. W. Real-space Grid Implementation of the Projector Augmented Wave Method. Phys. Rev. B: Condens. Matter Mater. Phys. 2005, 71, 035109. (26) Enkovaara, J.; Rostgaard, C.; Mortensen, J. J.; Chen, J.; M. Dułak, L. F.; Gavnholt, J.; Glinsvad, C.; Haikola, V.; Hansen, H. A.; Kristoffersen, H. H.; et al. Electronic Structure Calculations with GPAW: a Real-space Implementation of the Projector Augmentedwave Method. J. Phys.: Condens. Matter 2010, 22, 253202. (27) Blöchl, P. E. Projector Augmented-wave Method. Phys. Rev. B: Condens. Matter Mater. Phys. 1994, 50, 17953. (28) Larsen, A. H.; Mortensen, J. J.; Blomqvist, J.; Castelli, I. E.; Christensen, R.; Dulak, M.; Friis, J.; Groves, M. N.; Hammer, B.;

CONCLUSIONS We have investigated the electrical conductivity of the prospective cathode current collecting material (CCCM) La1−xSrxCoO3−δ (x ∈ [0, 1], δ ∈ [0, 1/4]) from first principles, using σ ̅ =

e2 4π 3

∑n ∫ dkvnk BZ

−∂f 0 (εnk ) ∂εnk

as a descriptor. The

experimental trends in conductivity as a function of x and δ are reproduced. However, it should be stressed that unless the electronic structure of the material is adequately described, in particular its band gap, the descriptor will lose its predictive power. Additionally, we have performed an in-depth analysis of one of the compositions, La0.5Sr0.5CoO3 (LSC). We have studied the chemistry of intrinsic and extrinsic defects in various charge states, solved for the full intrinsic defect equilibrium, and calculated the electrical conductivity of a set of doped systems. In particular, we predicted that La0.5−ySmySr0.5CoO3 (LSSC) should exhibit enhanced conductivity compared to LSC, a common cathode material. This was subsequently confirmed by electrical conductivity measurements; for y ≈ 0.04, the increase in conductivity was found to be 20%, and an equivalent circuit analysis showed that this corresponds to a 4% enhancement of the output cell voltage. In spite of the fact that this increase may appear limited, we believe that it confirms the integrated approach of material optimization that we have employed in this study. Besides the cost of a fuel cell system being mainly driven by the cost of the fuel cell themselves, this increase in performance may directly impact the cost of the final product and thereby may enlarge its market acceptance. Finally, experimental measurements also showed LSSC’s thermal expansion coefficient to be favorable for matching with other cell components, which further establishes it as a promising CCCM.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Ivano E. Castelli: 0000-0001-5880-5045 Notes

The authors declare no competing financial interest.

■

REFERENCES

(1) International Energy Agency. Technology Roadmap: Hydrogen and Fuel Cells; Paris, 2015. (2) U.S. Department of Energy. Fuel Cell Technology Market Report 2014; Washington, DC, 2014. (3) E4Tech. The Fuel Cell Industry Review 2015; 2015. (4) www.nedo.go.jp (accessed June 2017). (5) Adler, S. B. Factors Governing Oxygen Reduction in Solid Oxide Fuel Cell Cathodes. Chem. Rev. 2004, 104, 4791. (6) Lee, K. T.; Manthiram, A. Comparison of Ln0.6Sr0.4CoO3−δ (Ln = La, Pr, Nd, Sm, and Gd) as Cathode Materials for Intermediate Temperature Solid Oxide Fuel Cells. J. Electrochem. Soc. 2006, 153, A794. (7) Søgaard, M.; Hendriksen, P. V.; Mogensen, M.; Poulsen, F. W.; Skou, E. Oxygen Nonstoichiometry and Transport Properties of Strontium SuInformation,bstituted Lanthanum Cobaltite. Solid State Ionics 2006, 177, 3285. (8) Saitoh, T.; Mizokawa, T.; Fujimori, A.; Abbate, M.; Takeda, Y.; Takano, M. Electronic Structure and Temperature-induced Paramagnetism in LaCoO3. Phys. Rev. B: Condens. Matter Mater. Phys. 1997, 55, 4257−4266. I


Article

The Journal of Physical Chemistry C Hargus, C.; et al. The atomic simulation environmenta Python library for working with atoms. J. Phys.: Condens. Matter 2017, 29, 273002. (29) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1996, 77, 3865. (30) Perdew, J. P.; Ruzsinszky, A.; Csonka, G. I.; Vydrov, O. A.; Scuseria, G. E.; Constantin, L. A.; Zhou, X.; Burke, K. Restoring the Density-Gradient Expansion for Exchange in Solids and Surfaces. Phys. Rev. Lett. 2008, 100, 136406. (31) Heyd, J.; Scuseria, G. E.; Ernzerhof, M. Hybrid Functionals Based on a Screened Coulomb Potential. J. Chem. Phys. 2003, 118, 8207. (32) Krukau, A. V.; Vydrov, O. A.; Izmaylov, A. F.; Scuseria, G. E. Influence of the Exchange Screening Parameter on the Performance of Screened Hybrid Functionals. J. Chem. Phys. 2006, 125, 224106. (33) Kurth, S.; Perdew, J. P.; Blaha, P. Molecular and Solid-State Tests of Density Functional Approximations: LSD, GGAs, and MetaGGAs. Int. J. Quantum Chem. 1999, 75, 889. (34) Balamurugan, S.; Takayama-Muromachi, E. Structural and Magnetic Properties of High-pressure/High-temperature Synthesized (Sr1−xRx)CoO3 (R = Y and Ho) Perovskites. J. Solid State Chem. 2006, 179, 2231−2236. (35) Anisimov, V. I.; Aryasetiawan, F.; Lichtenstein, A. I. First Principles Calculations of the Electronic Structure and Spectra of Strongly Correlated Systems: the LDA + U Method. J. Phys.: Condens. Matter 1997, 9, 767. (36) Chainani, A.; Matthew, M.; Sharma, D. D. Electron-spectroscopy Study of the Semiconductor-metal Transition in La1−xSrxCoO3. Phys. Rev. B: Condens. Matter Mater. Phys. 1992, 46, 9976. (37) Grosso, G.; Pastori Parravicini, G. Solid state physics; Academic Press: San Diego, CA, 2000. (38) Kozuka, H.; Yamada, H.; Hishida, T.; Yamagiwa, K.; Ohbayashi, K.; Koumoto, K. Electronic Transport Properties of the Perovskitetype Oxides La1−xSrxCoO3±δ. J. Mater. Chem. 2012, 22, 20217. (39) Kozuka, H.; Yamagiwa, K.; Ohbayashi, K.; Koumoto, K. Origin of High Electrical Conductivity in Alkaline-earth Doped LaCoO3. J. Mater. Chem. 2012, 22, 11003. (40) Cheng, X.; Fabbri, E.; Nachtegaal, M.; Castelli, I. E.; El-Kazzi, M.; Haumont, R.; Marzari, N.; Schmidt, T. J. Oxygen Evolution Reaction on La1−xSrxCoO3 Perovskites: A Combined Experimental and Theoretical Study of Their Structural, Electronic, and Electrochemical Properties. Chem. Mater. 2015, 27, 7662. (41) Zunger, A.; Wei, S.-H.; Ferreira, L. G.; Bernard, J. E. Special Quasirandom Structures. Phys. Rev. Lett. 1990, 65, 353−356. (42) Bhide, V. G.; Rajoria, D. S.; Rao, G. R.; Rao, C. N. R. Mössbauer Studies of the High-Spin-Low-Spin Equilibria and the LocalizedCollective Electron Transition in LaCoO3. Phys. Rev. B 1972, 6, 1021−1032. (43) Tucker, M. C.; Cheng, L.; DeJonghe, L. C. Selection of Cathode Contact Materials for Solid Oxide Fuel Cells. J. Power Sources 2011, 196, 8313. (44) Bhide, V. G.; Rajoria, D. S.; Rao, C. N. R.; Rao, G. R.; Jadhao, V. G. Itinerant-electron Ferromagnetism in La1−xSrxCoO3: A Mössbauer Study. Phys. Rev. B 1975, 12, 2832−2843. (45) Mineshige, A.; Inaba, M.; Yao, T.; Ogumi, Z.; Kikuchi, K.; Kawase, M. Crystal Structure and Metal-Insulator Transition of La1−xSrxCoO3. J. Solid State Chem. 1996, 121, 423−429. (46) Anjana, P. S.; George, S.; Sebastian, M. T. CeO2 − La0.5Sr0.5CoO3−δ Composites for Giant Permittivity Applications. J. Phys. D: Appl. Phys. 2009, 42, 225502. (47) Castelli, I. E.; Landis, D. D.; Thygesen, K. S.; Dahl, S.; Chorkendorff, I.; Jaramillo, T. J.; Jacobsen, K. W. New Cubic Perovskites for One- and Two-photon Water Splitting Using the Computational Materials Repository. Energy Environ. Sci. 2012, 5, 9034. (48) Sundell, P. G.; Björketun, M. E.; Wahnström, G. Thermodynamics of Doping and Vacancy Formation in BaZrO3 Perovskite Oxide from Density Functional Calculations. Phys. Rev. B: Condens. Matter Mater. Phys. 2006, 73, 104112.

(49) Mizusaki, J.; Mima, Y.; Yamauchi, S.; Fueki, K. Nonstoichiometry of the Perovskite-Type Oxides La1−xSrxCoO3−δ. J. Solid State Chem. 1989, 80, 102. (50) Alling, B.; Högberg, H.; Armiento, R.; Rosen, J.; Hultman, L. A Theoretical Investigation of Mixing Thermodynamics, Age-hardening Potential, and Electronic Structure of Ternary M1−x1Mx2B2 Alloys with AlB2 Type Structure. Sci. Rep. 2015, 5, 9888. (51) Lee, Y.-L.; Kleis, J.; Rossmeisl, J.; Morgan, D. Ab-initio Energetics of LaBO3(001) (B = Mn, Fe, Co, and Ni) for Solid Oxide Fuel Cell Cathodes. Phys. Rev. B: Condens. Matter Mater. Phys. 2009, 80, 224101. (52) Lee, D.; Lee, Y.-L.; Hong, W. T.; Biegalski, M. D.; Morgan, D.; Shao-Horn, Y. Oxygen Surface Exchange Kinetics and Stability of (La,Sr)2CoO4±−δ/La1−xSrxMO3−δ (M = Co and Fe) Hetero-interfaces at Intermediate Temperatures. J. Mater. Chem. A 2015, 3, 2144−2157. (53) Zhang, S. B.; Northrup, J. E. Chemical Potential Dependence of Defect Formation Energies in GaAs: Application to Ga Self-diffusion. Phys. Rev. Lett. 1991, 67, 2339−2342. (54) Lankhorst, M. H. R.; Bouwmeester, H. J. M.; Verweij, H. Use of the Rigid Band Formalism to Interpret the Relationship between O Chemical Potential and Electron Concentration in La1−xSrxCoO3−δ. Phys. Rev. Lett. 1996, 77, 2989−2992. (55) Lee, Y.-L.; Kleis, J.; Rossmeisl, J.; Shao-Horn, Y.; Morgan, D. Prediction of Solid Oxide Fuel Cell Cathode Activity with Firstprinciples Descriptors. Energy Environ. Sci. 2011, 4, 3966−3970. (56) Freysoldt, C.; Grabowski, B.; Hickel, T.; Neugebauer, J.; Kresse, G.; Janotti, A.; Van de Walle, C. G. First-principles Calculations for Point Defects in Solids. Rev. Mod. Phys. 2014, 86, 253−305. (57) Lany, S.; Zunger, A. Accurate Prediction of Defect Properties in Density Functional Supercell Calculations. Modell. Simul. Mater. Sci. Eng. 2009, 17, 084002. (58) Huang, T.-W.; Chang, Y.-S.; Chen, G.-J.; Chung, C.-C.; Chang, Y.-H. The Structural Characterization and Dielectric Properties of the La1−xKxCo1−xNbxO3 (x = 0−1) System. J. Electrochem. Soc. 2007, 154, G244. (59) Deepa, K. S.; Shaiju, P.; Sebastian, M. T.; Bhoje-Gowd, E.; James, J. Poly(Vinylidene Fluoride)La0.5Sr0.5CoO3−δ Composites: the Influence of Particle Size on the Structure and Dielectric Properties. Phys. Chem. Chem. Phys. 2014, 16, 17008. (60) Glöckner, R.; Islam, M. S.; Norby, T. Protons and Other Defects in BaCeO3: a Computational Study. Solid State Ionics 1999, 122, 145− 156. (61) Davies, R. A.; Islam, M. S.; Gale, J. D. Dopant and Proton Incorporation in Perovskite-type Zirconates. Solid State Ionics 1999, 126, 323−335. (62) Skjærvø, S. H.; Wefring, E. T.; Nesdal, S. K.; Gaukås, N. H.; Olsen, G. H.; Glaum, J.; Tybell, T.; Selbach, S. M. Interstitial Oxygen as a Source of p-type Conductivity in Hexagonal Manganites. Nat. Commun. 2016, 7, 13745. (63) In the highly symmetric La0.5Sr0.5CoO3 cell, the Co and O interstitials were placed halfway between La and Sr, a position that maximizes the distance to surrounding atoms. Upon relaxation, Co stays more or less in the same position, while the surrounding lattice undergoes rather substantial deformation. The O interstitial, on the other hand, coordinates to a neighboring lattice oxygen with a bond length of 137 pm when the internal coordinates are optimized. (64) Nyman, B. J.; Björketun, M. E.; Wahnström, G. Substitutional Doping and Oxygen Vacancies in La2Zr2O7 Pyrochlore Oxide. Solid State Ionics 2011, 189, 19−28. (65) Lindman, A.; Erhart, P.; Wahnström, G. Implications of the Band Gap Problem on Oxidation and Hydration in Acceptor-doped Barium Zirconate. Phys. Rev. B: Condens. Matter Mater. Phys. 2015, 91, 245114. (66) The references used here are the ones that have been predicted by DFT to be most stable at 0 K among several investigated stoichiometries. The dopant in La0.5Sr0.5CoO3 would be stabilized with respect to the reported energies if other, less stable, stoichiometries were to be used as reference. J


Article

The Journal of Physical Chemistry C (67) Konings, R. J. M.; Benes, O.; Kovacs, A.; Manara, D.; Sedmidubsky, D.; Gorokhov, L.; Iorish, V. S.; Yungman, V.; Shenyavskaya, E.; Osina, E. The Thermodynamic Properties of the f-Elements and their Compounds. Part 2. The Lanthanide and Actinide Oxides. J. Phys. Chem. Ref. Data 2014, 43, 013101.

K


Defect Chemistry and Electrical Conductivity of Sm-Doped La1

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