Comparison of Space-Charge Formation at Grain Boundaries in

Article pubs.acs.org/cm

Comparison of Space-Charge Formation at Grain Boundaries in Proton-Conducting BaZrO3 and BaCeO3 Anders Lindman,* Edit E. Helgee,* and Göran Wahnström* Department of Physics, Chalmers University of Technology, SE-412 96 Gothenburg, Sweden S Supporting Information *

ABSTRACT: Acceptor-doped BaZrO3 (BZO) and BaCeO3 (BCO) both exhibit considerable bulk proton conductivity, which makes them suitable as electrolytes in electrochemical devices. However, these materials display high grain-boundary (GB) resistance that severely limits the overall proton transport in polycrystalline samples. This effect has been attributed to the presence of space charges at the GBs, which form because of segregation of protons and charged oxygen vacancies. This blocking behavior is less prominent in BCO, but in contrast to BZO, BCO suffers from poor chemical stability. The aim with the present work is to elucidate why GBs in BZO are more resistive than GBs in BCO. We use density-functional theory (DFT) calculations to study proton and oxygen vacancy segregation to several GBs and find that the oxygen vacancy segregation energy is quite similar in both materials while the tendency for proton segregation is larger in BZO compared with that in BCO. This is not related to the GBs, which display similar proton formation energies in both materials, but because of different formation energies for protons in the bulk regions. This can be understood from a stronger hydrogen bond formation in bulk BCO compared with that in bulk BZO. Furthermore, segregation energies are evaluated in a space-charge model, and the resulting space-charge potentials provide a consistent explanation of the experimentally observed difference in GB conductivity.

1. INTRODUCTION Solid-state proton conductors are considered interesting for use in applications such as solid oxide fuel cells, electrolyzers, and chemical reactors because of their ability to conduct protons at intermediate temperatures.1 Two of the most promising materials are acceptor-doped BaZrO3 (BZO) and BaCeO3 (BCO), two perovskite oxides that display considerable bulk proton conductivity, in particular when doped with yttrium.2−4 The main interest for these compounds lies in applications where they act as pure ionic conductors,5−12 but mixedconducting derivatives of BZO have also been considered as cathode materials.5,8,13 Upon sintering, these materials form dense polycrystalline structures, and while bulk conductivities are high, grain boundaries (GBs) display significant resistance; the net effect is a reduced total proton conductivity in these samples (see Figure 1). While this problem is considerably more severe for BZO,14 BCO suffers from poor chemical stability toward CO2,2 which deteriorates its long-term stability and prohibits the use of carbon-based fuels and reactants. BZO, on the other hand, exhibits excellent chemical stability. For a capture of the beneficial properties of both materials, a lot of attention has been directed toward BZO−BCO solid solutions where some amounts of Zr in BZO are substituted with Ce to improve on the low GB conductivity while maintaining chemical stability, such as BaZr0.7Ce0.2Y0.1O3−δ (BZCY).2,8−11,17 In spite of the success of BZCY, the reason for the different GB conductivities in the two materials is still © 2017 American Chemical Society

unknown, and the development of the mixed Zr/Ce systems is based on a trial-and-error procedure. The aim with the present communication is to elucidate the underlying mechanisms that lead to this difference in GB behavior. It is now well-established that the main reason for the low GB conductivity in acceptor-doped BZO is the formation of space-charge regions in the vicinity of GBs.14 These regions form because of segregation of positively charged defects (protons and oxygen vacancies) to the GB cores and become depleted of protons, which reduces the conductivity across the GB. Many experimental18−22 and theoretical23−31 studies of BZO have been conducted where space-charge potentials between 0.3 and 0.9 V have been found depending on doping and sintering conditions. While the space-charge model also has been used to explain GB effects in BCO,32 fewer in-depth studies of this phenomenon exist for this material. Although the GB conductivity in different samples can vary depending on the ceramic fabrication processes,22,33 GBs in BZO are more blocking under similar conditions14 (e.g., Figure 1), and it is not clear why the GB resistance is less pronounced in BCO. In this work, we investigate the different GB behavior of BZO and BCO by studying both bulk and GB properties of these two materials by the means of first-principles calculations Received: July 7, 2017 Revised: August 24, 2017 Published: August 25, 2017 7931

DOI: 10.1021/acs.chemmater.7b02829 Chem. Mater. 2017, 29, 7931−7941

Article

Chemistry of Materials

All calculations were performed nonspin polarized using a cutoff energy of 500 eV. k-point sampling was carried out using the Monkhorst−Pack scheme with 6 × 6 × 6 and 4 × 3 × 4 grids for the cubic BZO (5 atoms) and orthorhombic BCO (20 atoms) unit cells, respectively. For the defect calculations, which were performed with 3 × 3 × 3 (BZO) and 2 × 2 × 2 (BCO) supercells, these k-point densities lead to 2 × 2 × 2 grids for both system sizes, while for the GB supercells (see Section 2.4 and Table 2) the resulting grids were 1 × 4 × 2 (BZO) and 1 × 1 × 2 (BCO). Ionic positions were relaxed until residual forces were smaller than 10 meV Å−1 for bulk calculations while the less strict criterion of 50 meV Å−1 was used for GB calculations. Complete volume relaxations were performed for bulk unit cells while GB supercells were allowed to relax only in the direction perpendicular to the GB interface. 2.3. Bulk Properties. Calculated and experimental bulk properties are compiled in Table 1, and there is a reasonable agreement. Lattice constants and band gaps are also in agreement with previous DFT results.45−47 A noticeable difference between the two materials is the elastic and dielectric properties. The shear and Young’s modulus of BCO are nearly half of those for BZO, and BCO thus exhibits a much softer lattice compared with BZO. Furthermore, the ionic contribution to the dielectric constant (εion) is more than twice as large in BZO, which influences the space-charge formation. 2.4. Grain-Boundary Structures. To our knowledge, there have not been any experimental studies of GBs with atomic resolution in either BZO or BCO, and specific GBs that may be present in these materials are not known. GBs in BZO have been studied quite extensively by theoretical modeling, and several different GB structures exist with high symmetry that are possible to study with DFT.25,53 Such GBs have been seen in cubic SrTiO3 with high-resolution experimental techniques,54−56 and most likely these GBs will also be present in BZO and BCO. In BZO, we have chosen to study two of these: the symmetric (111)[11̅ 0] and (112)[11̅ 0] tilt GBs, which here are denoted BZO-G1 and BZO-G2, respectively. These have been considered previously in several theoretical studies23−26,29,31 and are suitable in the sense that they cover two different scenarios concerning 25 seg < ΔEseg > ΔEseg segregation energies, namely, ΔEseg v•• OH•O and ΔEv•• OH•O. O O For a comparison of GBs to be relevant, it is important that the same types of GBs are considered in BCO. The lower symmetry of the orthorhombic structure leads to several distinct but structurally similar configurations for the two chosen GB orientations. All of these have

Figure 1. Experimental bulk and GB proton conductivity of BaCe0.9Y0.1O3−δ (BCO)15 and BaZr0.94Y0.06O3−δ (BZO).16

and thermodynamic space-charge modeling. For a systematic comparison, we consider GBs that are structurally similar, and we have constructed four BCO GBs that are analogous to the (111)[1̅10] and (112)[1̅10] symmetric tilt GBs in BZO, which have been investigated in several previous studies.23−26,29,31 We study proton (OH•O) and oxygen vacancy (v•• O ) segregation to the GB core using density-functional theory (DFT) calculations and find that the oxygen vacancy segregation energy is quite similar in both materials while the tendency for proton segregation is larger in BZO compared with that in BCO. This is not directly related to the GBs, however, which display similar proton formation energies in both materials, but is due to different formation energies for protons in the bulk region. This can be understood from a stronger hydrogen bond formation in bulk BCO compared with that in bulk BZO. Segregation energies are evaluated in a space-charge model, and the resulting space-charge potentials provide a consistent explanation for the experimental conductivity data (see, e.g., Figure 1).

Table 1. Calculated and Experimental Bulk Properties of BZO and BCO

2. METHODOLOGY

BZO

2.1. Space-Charge Modeling. Several different space-charge models exist in the literature with varying levels of complexity.25,34−38 We employ the model introduced in ref 25, although only a single layer is considered here as opposed to several layers in the previous study. The single layer will be referred to as the core, and we make this simplification since we only calculate segregation energies for sites in one specific layer for each considered GB (see Sections 3.2 and 3.3). We make use of the Mott−Schottky approximation and only consider immobile dopants. The considered space-charge model is outlined in more detail in the Supporting Information (SI). 2.2. Computational Details. Density-functional theory (DFT) calculations have been performed using VASP (Vienna ab initio simulation package)39 with the semilocal exchange-correlation functional PBE (Perdew−Burke−Ernzerhof).40 The projector-augmented wave method41,42 has been used for the description of the core regions, while the explicitly treated valence states are 5s, 5p, and 6s for Ba; 5s, 5p, 4f, 5d, and 6s for Ce; 2s and 2p for O; and 4s, 4p, 5s, and 4d for Zr. Although the localized nature of the Ce 4f state is not well-described with semilocal approximations, this is not an issue here since this orbital will be empty as we only consider the proton and the vacancy in their fully ionized charge states (+1 and +2, respectively). The band gap problem43 has been addressed using the range-separated hybrid functional HSE06,44 from which band edge shifts are determined by following the procedure in ref 45.

DFT

BCO

experimental

a (Å)a b (Å)a c (Å)a K (GPa)b E (GPa)c G (GPa)d Eg (eV)e ΔϵVBM (eV)f ΔϵCBM (eV)f ε∞g

4.236

4.19248

151.4 234.4 94.3 3.12/4.61 −1.04 0.45 4.86

127.2,48 18949 24348 10348 4.8,50 5.351

εiong

60.52

DFT

experimental

6.291 8.868 6.282 112.5 130.5 49.9 2.16/4.06 −1.08 0.83 5.39 5.39 5.47 25.97 24.70 21.98

6.25148 8.78648 6.22048 138.348 15448 58.748 4.2352

a

a, b, c: lattice constants. bK: bulk modulus. cE: Young’s modulus. dG: shear modulus. eEg: band gap, which has been calculated with both PBE and HSE06 (PBE/HSE06). fΔϵVBM, ΔϵCBM: band edge shifts. g ε∞, εion: dielectric constants. 7932


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Chemistry of Materials been taken into consideration, and we have arrived at the selection of two configurations for each GB type for further study (for more details on the selection of BCO GBs, see the SI). The (011)[100] and (01̅1) [111] GBs are structurally similar to BZO-G1, and they will be denoted BCO-G1a and BCO-G1b, respectively. The (120)[001] and (3̅21)[111] GBs, on the other hand, are structurally similar to BZOG2 and will be denoted BCO-G2a and BCO-G2b, respectively. The planes and vectors in the BCO GB notations refer to the lattice vectors of the orthorhombic unit cell. The atomic structures of the GBs are shown in Figures 2 and 3, and a summary of the GB supercell properties (lattice vectors, number of atoms, and cell dimensions) is given in Table 2. The GBs are characterized by their formation energy and expansion, SC which are defined as γGB = (ESC GB − nEbulk)/2A and ΔGB = (VGB − SC (V nVbulk)/2A, respectively, where the terms are as follows: ESC GB GB) is the energy (volume) of the GB supercell, n is the number of formula units in the GB supercell, Ebulk (Vbulk) is the energy (volume) per formula unit in bulk, and A is the area of the GB in the supercell. The factor of 1/2 is included because each supercell contains two GBs. All BCO GBs expand by approximately 0.2 Å and have formation energies close to 0.04 eV Å−2 (0.64 J m−2), which is slightly higher than the value of 0.033 eV Å−2 (0.53 J m−2) reported for a similar G1-type GB in BCO.32 The BCO GBs are thus more similar in terms of GB formation energy than the corresponding GBs in BZO (see Table 2).

Figure 3. Atomic structure of the Group 2 GBs, where the top, middle, and bottom panels depict the BZO-G2, BCO-G2a, and BCO-G2b GBs, respectively. Colors are as in Figure 2.

3. RESULTS AND DISCUSSION

f tot q ΔEdef = (Edef + Ecorr ) − Eidtot −

3.1. Defects in Bulk. Following the standard first-principles treatment of point defects,57 formation energies have been calculated according to the following:

∑ Δniμi i

+ q[(ϵVBM + ΔϵVBM) + μe + Δvq]

(1)

tot Here, the terms are as follows: Etot def and Eid are the total energies of the defective and ideal systems, respectively, Δni is the change in atomic species i, μi is the associated chemical potential, and q is the defect charge. The electron chemical potential μe is given with respect to the position of the valence band maximum (VBM), ϵVBM. To account for spurious contributions to ΔEfdef that arise for charge defects in periodic calculations, we apply the correction scheme of Lany and Zunger,58,59 which includes both image charge (Eqcorr) and potential alignment (Δvq) corrections. For the latter, we consider the difference in the electrostatic potential between the defective and ideal supercell far from the defect center. Eqcorr amounts to 16 meV (66 meV) and 31 meV (123 meV) for protons (oxygen vacancies) in BZO and BCO, respectively, while Δvq was found to be zero for BZO and 25 meV for both defects in BCO. Finally, the band gap problem is corrected by using a scissor shift (ΔϵVBM), a scheme which has been shown to work well in this context45 (see Table 1 for band edge shifts). As formation energies of charged defects depend on the electron chemical potential, it is crucial that the band structures are aligned on a common scale if these quantities are to be compared between different materials. The position of the VBM can differ by more than 1 eV for some oxides,60 which could have serious implications if not properly addressed. To this end, we align the band structures using the oxygen 1s states,61 which puts the VBM of BCO 16 meV below that of BZO (see Figure 4). Furthermore, μe can be different in the two materials, and its respective positions under relevant conditions are needed for a proper comparison of formation energies. In the present case (acceptor-doped materials), it is reasonable to assume that the electron chemical potential will be the same in BZO and BCO

Figure 2. Atomic structure of the group 1 GBs, where the top, middle, and bottom panels depict the BZO-G1, BCO-G1a, and BCO-G1b GBs, respectively. Green, red, blue, and yellow represent Ba, O, Zr, and Ce, respectively. 7933


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Table 2. Calculated GB Energies γGB’s, GB Expansions ΔGB’s, and Supercell Characteristics for the Selected GBs in BZO and BCO BZO BCO

GB

notation

(111)[1̅10] (112)[1̅10] (011)[100] (01̅1)[111] (120)[001] (32̅ 1)[111]

BZO-G1 BZO-G2 BCO-G1a BCO-G1b BCO-G2a BCO-G2b

axes [111], [112], [012], [012̅], [110], [311̅ ]̅ ,

[112]̅ , [111̅], [01̅0], [3̅11], [2̅10], [012]̅ ,

atoms [1̅10] [1̅10] [001] [111] [001] [111]

240 180 480 480 480 480

29.74 31.41 30.76 30.76 43.49 43.56

× × × × × ×

10.38 × 11.98 7.34 × 11.98 21.73 × 12.58 21.78 × 12.56 15.39 × 12.56 15.38 × 12.56

γGB (eV Å−2)

ΔGB (Å)

0.032 0.049 0.040 0.040 0.038 0.037

0.20 0.14 0.23 0.23 0.22 0.22

in the orthorhombic phase of BCO, which correspond to the Wyckoff positions 4c and 8d, where the former is slightly more favorable for both defects. These formation energies yield hydration energies of −0.82 and −1.41 eV for BZO and BCO, respectively, which are in agreement with previous results in the literature.2,45,47,63 The aligned formation energies indicate that the more negative hydration energy for BCO is mainly due to the fact that protons are more stable in this material. To understand the higher stability for the proton in BCO, we consider the local environment and the hydrogen bond configuration (see Figure 5 and Table 3). The hydrogen bond is characterized by its bond length and bond angle, the angle between the covalent O−H bond direction and the O···H hydrogen bond direction. When the angle is closer to 180°, the hydrogen bond is stronger, and the hydrogen bond distance is shorter.64 In BCO, the proton forms an almost linear hydrogen bond with bond length 1.95 Å and bond angle 176°. It is an interoctahedral hydrogen bond formation; i.e., the two oxygen ions involved are located in different octahedra. The O−H bond is also slightly larger in BCO compared with that in BZO (cf. 0.995 with 0.979 Å). In BZO, the proton establishes a configuration with two symmetric nonlinear hydrogen bonds, where both bonds correspond to intraoctahedral configurations. For each bond, the bond angle is 120° (see Figure 5), and the hydrogen bond distance is 2.25 Å, significantly larger compared with the bond distance in BCO. We therefore assign the more negative protonic formation energy in BCO, i.e., the higher stability for the proton, to a stronger hydrogen bond formation in BCO.

• Figure 4. Oxygen vacancy (v•• O ) and proton (OHO) formation energies in BZO and BCO as functions of electron chemical potential, where the band structures have been aligned using the oxygen 1s states.

on a common scale as their respective valence band structures derive from oxygen 2p orbitals,45,46 and yttrium dopants act as shallow acceptors in both materials.46,62 The chemical potentials of O and H are given by μO = μO2/2 and μH = (μH2O − μO)/2, where atomic PBE energies are together considered experimental cohesive energies as described in ref 45. With this choice of chemical potentials (H2O and O2), the energy of the hydration reaction (eq S4) is directly given by the following: f f • − ΔE •• ΔE hydr = 2ΔEOH vO O

supercell dimensions (Å)

(2)

With the methodology described above, we can now compute aligned formation energies that can be compared between the two materials. We find that the vacancy formation energies are quite similar in the two materials, while the protonic counterparts are about 0.35 eV lower in BCO (see Table 3 and Figure 4). In contrast to cubic BZO where all oxygen ions are equivalent, there are two distinct oxygen sites Table 3. Oxygen Vacancy and Proton Formation Energiesa in Bulk Together with the Associated Proton Bond Lengths to the Nearest (O−H) and Next Nearest (O···H) Neighboring Oxygen Ion with the Corresponding Bond Angle α BZO BCO (4c) BCO (8d)

ΔEfv••O (eV)

ΔEfOH•O (eV)

O−H (Å)

O···H (Å)

α

−0.69 −0.82 −0.75

−0.76b −1.12b −1.07

0.979b 0.995b 1.002

2.25b 1.95b 1.84

120b 176b 175

Figure 5. Local environment (Zr/Ce−O network) of protons in bulk and GBs of BZO (top panels) and BCO (bottom panels), where each figure represents the low energy configuration for that system. The dashed lines denote the hydrogen bond to the next nearest oxygen ion (ions). Bond lengths and angles are listed in Tables 3 (bulk) and 4 (GBs), where the relevant data are indicated with a footnote. Colors are as in Figure 2.

a

Formation energies are given for a common electron chemical = 0, μBCO = 16 meV). bProton configurations that are potential (μBZO e e depicted in Figure 5. 7934


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Chemistry of Materials The hydrogen bond formation in BCO is accomplished by large structural relaxation of the surrounding lattice, which is facilitated by the orthorhombic structure as well as the flexibility (softness) of BCO (see Section 2.3 and Table 1). The cubic BZO lattice is more rigid, and the interoctahedral hydrogen bond configuration, as found in BCO, cannot be formed. The distance between the two oxygen ions that are involved in the formation of the O−H bond and the hydrogen bond is substantially reduced in BCO, from 3.83 Å (3.71 Å) to 2.94 Å (2.84 Å) for the 4c (8d) configuration. In BZO, the displacements of the oxygen ions are considerably lower.65 However, the magnitude of the induced strain energy, when the proton configuration is formed, is similar in the two materials. In BZO it is 1.06 eV while it is only slightly larger in BCO, 1.24 eV (1.28 eV) for the 4c (8d) configuration. The induced strain energy is obtained from the difference in energy between a distorted configuration, where the ionic positions are the same as if the proton was present, and the ideal bulk structure. These energies imply that the higher stability for the proton in BCO is not due to different induced strain energies in the two different materials, but directly related to stronger hydrogen bonding in BCO. A strong hydrogen bond should also be visible as a large red shift of the O−H stretch mode. Indeed, infrared spectra for Y-doped BCO show a clear peak around 2350 cm−1, which is absent in Y-doped BZO.66 3.2. Segregation Tendency: Electrostatic Potential and Strain. The lower symmetry of the BCO lattice leads to a much larger set of unique oxygen sites at the GBs compared to those at the corresponding BZO GBs and hence to a larger number of possible segregation sites, especially for the proton. Within the concept of space-charge formation, however, the most relevant sites are those with the most negative segregation energies as these will be the determining factor for the height of the space-charge potential. To find these low-energy sites without considering all oxygen sites explicitly, which is cumbersome for the BCO GBs, we resort to two properties that are expected to influence the segregation energies: the average electrostatic potential and the strain. The former is determined by placing a test charge at the center of the ion while the latter is defined as the sum of all nearest neighbor (NN) strain contributions, where compressive and tensile components are treated separately. The individual strain component between the oxygen ion i and the neighboring ion j of species X, which are separated by the distance rij, is defined as follows:

εij =

Figure 6. Average electrostatic potential as well as compressive and tensile strain with respect to oxygen vacancy segregation energy for different oxygen sites in the two BZO GB supercells. The electrostatic potential has been shifted such that it is zero at the site in the bulk region.

For the tensile contribution, however, there is no clear correlation. The fact that compressive strain favors segregation is reasonable since the oxygen vacancy, as well as the hydroxide ion (proton), is smaller than the oxygen ion in acceptor-doped BZO.68 We can now turn to the BCO GBs and determine at which oxygen sites segregation is most favorable by studying the electrostatic potential and the compressive strain. As there are two distinct oxygen sites in the orthorhombic phase of BCO, there are multiple values of rO−X for each species X. Close to the GB, however, the bulk lattice symmetry breaks down, and it becomes difficult to distinguish which value of rO−X should be considered for each neighbor pair. We therefore use the average interatomic distance for each pair, which for BCO are rO−Ba = 3.17, rO−Ce = 2.27, and rO−O = 3.21 Å. The two BCO-G1 GBs show an almost identical behavior, where both the largest potentials and the most significant strains are found at the GB core (left panels in Figure 7). These sites are analogous to the low-energy sites at the core in the BZO-G1 GB, and it is thus very likely that the most negative segregation energies in the BCO-G1 GBs are found among them. Compared to the BCO-G1 GBs, the potential and strain display larger variations between the two BCO-G2 GBs, but they still follow a common trend (right panels in Figure 7). The sites with the largest potentials and compressive strain are found within the first atomic layer next to the GB core, which is also where the low-energy site in the BZO-G2 GB resides. The same analysis for the BZO GBs (see Figure S3) yields similar trends for the respective GB types. 3.3. Defects at Grain Boundaries. Since the strain and potential analysis in the previous section lead to almost

rij − rObulk −X rObulk −X

(3)

where rbulk O−X is the nearest neighbor distance between the two ions in the ideal lattice. This definition is similar to the approach in ref 67. To verify that the potential and strain can indeed serve as predictors for the segregation energy, we first consider oxygen vacancy segregation in the two BZO GBs, where all unique segregation sites have been considered in our previous work.25 The electrostatic potential is found to correlate with the segregation energy in a close-to-linear behavior for both GBs, where an increase in the potential results in a more negative energy, although the slope is different for the two structures (see Figure 6). A linear trend also emerges for the compressive strain, which is similar for both GBs and where a larger (in magnitude) strain yields a more negative segregation energy. 7935


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Figure 7. Average electrostatic potential (top panels) and the compressive strain (bottom panels) with respect to the distance to the GB core for oxygen sites in the G1- and G2-type (left and right panels, respectively) GBs in BCO. The shaded regions highlight the selected oxygen sites for computing segregation energies. The electrostatic potential has been shifted so that it is zero at the site in the bulk region.

Table 4. Segregation Energies (in eV) of Oxygen Vacancies and Protons at Different Oxygen Sites in the G1- and G2-Type GBs in BCO and BZO, Proton Bond Lengths (Å) to the Nearest (O−H) and Next Nearest (O···H) Neighboring Oxygen Ion with the Corresponding Bond Angle α, and, in the Lower Part, Average Segregation Energies for Both Defects at Each GB G1 ΔEseg vO•• −0.66 −0.67 −0.31 −0.42 −0.61 −0.32 −0.43 −0.62

BZO BCO

ΔEseg OHO• a

−0.84 −0.83 −0.35 −0.47a −0.42 −0.35 −0.47 −0.41

BZO BCO a

G2

O−H

O···H

0.996a 0.994 1.007 0.994a 0.995 1.006 0.994 0.994

1.89a 1.93 1.78 1.98a 1.93 1.80 1.98 1.94 G1

α

ΔEseg vO••

ΔEseg OHO• a

O−H

O···H

α

173a 172 169 175a 175 169 175 175

−1.51

−0.79

1.046a

1.44a

150a

−1.11 −1.74 −1.57 −1.10

−0.49 −0.39 −0.46 −0.51a

1.014 1.030 1.034 1.020a

1.66 1.54 1.52 1.61a

154 156 157 155a

G2

⟨ΔEseg ⟩ v•• O

⟨ΔEseg OH•O⟩

⟨ΔEseg ⟩ v•• O

⟨ΔEseg OH•O⟩

−0.66 −0.45

−0.83 −0.41

−1.51 −1.38

−0.79 −0.47

Proton configurations that are depicted in Figure 5.

from the GB, the one that yields the lowest defect formation energy is chosen as the bulk reference. The expression in eq 4 can be simplified using the fact that in equilibrium both the atomic and electron chemical potentials should be constant. If one further assumes that the electrostatic correction terms (see Section 3.1) are spatially invariant, then eq 4 reduces to the following:

identical behavior for the BCO GBs within each group, we only consider one GB from each group for calculating segregation energies. We choose the BCO-G1a and BCO-G2a GBs, which will simply be referred to as BCO-G1 and BCO-G2 from now on. We make the restriction to only study segregation to the atomic layer with the largest segregation tendency, although we consider all unique sites within this layer. In the BCO-G1 GB, there are six unique sites, which are reduced to two different sites in the BZO-G1 GB where one is doubly degenerate. In the BCO-G2 GB, there are four unique sites while there is only one in the BZO-G2 GB. The defect segregation energy is defined as follows: seg f f ΔEdef = ΔEdef,GB − ΔEdef,bulk

seg tot tot ΔEdef = Edef,GB − Edef,bulk

(5)

tot where Etot def,GB and Edef,bulk are the total energies of the defective GB and bulk systems, respectively. We find that the oxygen vacancy segregation energies are fairly similar in both materials within each GB group, although there is some spread in the energies at the different sites in BCO (see Table 4). The segregation is more pronounced in G2, and the average segregation energies are −0.5 eV (−0.7 eV) and −1.4 eV (−1.5 eV) for BCO (BZO) in G1 and G2, respectively. The stronger segregation in G2 is due to significant structural relaxation at the GB upon vacancy

(4)

where ΔEfdef,GB is the formation energy at the GB while ΔEfdef,bulk represents the formation energy in the bulk. In practice, the bulk system is represented by the site in the GB supercell that is as far away from both GBs as possible. In the presence of several sites at approximately the same distance 7936


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tendency for proton segregation in BCO is due to the higher stability of protons in the BCO bulk phase. The G1 and G2 GBs have been studied previously in cubic SrTiO3,69 where the local GB structures were very similar to those found here for BZO and BCO. Additionally, the structure of the Σ5 (310)[001] GB in cubic SrTiO3 and BaTiO3 has been shown to be almost the same in both materials.67 These results give an indication that a specific GB orientation displays quite similar structures in different perovskite oxides. On the basis of the present results, it is thus possible that GBs in different perovskites exhibit similar proton formation energies and that the bulk structure is the determining factor for proton segregation in these materials. 3.4. Space-Charge Formation. With the calculated defect formation and segregation energies, we can study space-charge formation using the model outlined in Section 2.1 and in the SI. We consider a dopant concentration of 10% and a water partial pressure of pH2O = 0.025 atm. For the bulk hydration thermodynamics, we consider the hydration energies calculated here together with the hydration entropies −93 (BZO) and −177 (BCO) meV K−1, which were calculated using DFT by Bjørheim and co-workers.47,70 With the corresponding free energies, the bulk starts to dehydrate at around 700 K in both materials (see Figure 9). For the dielectric constants, we consider the calculated values (see Table 1), εr = ε∞ + εion, where for BCO we take the average of the diagonal components. In the G1 GBs, there are three available segregation sites per formula unit in the core while there are only two sites considered for the G2 GBs, because defect formation is not limited to a single site in these GBs. Such a site distribution was also considered for this BZO GB in ref 31, but not in ref 25. From the spacing between layers in these GBs, it follows that

formation (see discussions in refs 23 and31). The spread in oxygen vacancy segregation energy implies that the effective (or relevant) segregation energy will depend on the scenario under consideration. For the cases that we consider for space-charge formation (see Section 3.4), we find that in the BCO-G1 GB only a small fraction of the sites become occupied. This implies an effective segregation energy of about 0.6 eV, which is close to the BZO-G1 segregation energy. For the BCO-G2 GB, up to a third of the sites become occupied, and also in this case the relevant segregation energy is quite similar to that of BZO-G2. Indeed, we find a similar space-charge behavior for BZO and BCO under dry conditions (see Figure 10). A different behavior is found for the proton, where similar segregation energies are obtained for the two GB types, but they differ significantly between the two materials. For BZO, the energies are about −0.8 eV in both GBs while they are only −0.4 and −0.5 eV in BCO-G1 and BCO-G2, respectively. Our result for BCO-G1 is in agreement with previous calculations of a similar G1-type GB in BCO.32 To understand the different proton segregation behavior, we again turn to the local environment of the proton as in the bulk case. The GBs within each group show very similar local structures (see Figure 5), and it is evident that the strained GBs facilitate environments where favorable hydrogen bond formation is possible without the need for major structural relaxations. Hence, the larger flexibility of the BCO lattice is less important here. The hydrogen bond lengths and bond angles are significantly altered compared to those in the bulk, especially for BZO (see Table 4). For G1, the hydrogen bond varies between 1.8 and 2.0 Å, and is associated with angles close to 180°. In G2, both of these quantities are reduced to 1.4−1.7 Å and 150°. The fact that the GBs in the two materials display such similar proton configurations but different segregation energies leads to the conclusion that the different proton segregation behavior stems from the stability of protonic defects in the bulk phase. Further evidence for this explanation is given by the aligned defect formation energies at the GBs, which are obtained by combining the bulk formation energies (eq 1) and the segregation energies (eq 4) according to the following: seg f f ΔEdef,GB = ΔEdef + ΔEdef

(6)

The results (Figure 8) show that the proton formation energies are similar at the GBs in the two materials but differ more in the bulk regions. It can thus be concluded that the smaller

Figure 8. Formation energies of protons (left panel) and oxygen vacancies (right panel) in bulk and at the G1- and G2-type GBs in BZO and BCO at a common absolute electron chemical potential = 0, μBCO = 16 meV). (μBZO e e

Figure 9. Concentration of oxygen vacancies (v•• O ) and protons (OH•O) in bulk as well as the G1- and G2-type GBs for both BZO and BCO. 7937


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Chemistry of Materials the GB core widths are a0/√3 and a0/√6 for G1 and G2, respectively, where we use an average pseudocubic lattice spacing (a0) for BCO. While the considered segregation layer for G2 is the one next to the GB core, the defects in this layer relax into the GB core, and we therefore treat them as being located in the middle of core in the space-charge model. For the G1 GBs, the more negative segregation energies in BZO lead to hydration of the GB core at a much higher temperature and to a twice-as-large proton concentration in the hydrated regime at low temperatures (Figure 9). The resulting space-charge potentials (Figure 10) are about 0.6−0.7 and 0.3− 0.4 V for BZO and BCO, respectively, which are in agreement with previous results for this GB type in both BZO25 and BCO.32 The potential under dry conditions is also determined and is found to be around 0.2−0.3 V in both materials (Figure 10). In the G2 GBs, the hydration of the GBs occurs at much lower temperatures because of the strong vacancy segregation. For BCO, the hydration begins at 500 K, a temperature at which the BZO-G2 GB is almost saturated with protons (Figure 9). At higher temperatures, the GBs are dominated by oxygen vacancies, and the potential is slightly larger in BCO. The transition from vacancies to protons in the core leads to a reduction in the space-charge potential, which follows from the large difference in the segregation energies (Figure 10). This is most prominent for BCO where the potential decreases from more than 0.6 V at 800 K to 0.4 V at 300 K. In BZO, the reduction is smaller, about 0.05 V, and the space-charge potential therefore becomes larger in BZO at lower temperatures where the material is protonated. The BZO-G2 GB was considered recently31 using free segregation energies as input to the space-charge model, and in that study, the potential decreased more at lower temperatures than that found here. This different behavior is related to the fact that we have a finite core width here, in contrast to the more simple abrupt core model used in that study, which leads to an increase in the potential. Additionally, the same GB was also considered in ref 25, where the potential instead increased and reached a value above 0.6 V at a low temperature. In that study, more segregation sites were available in the GB, both more of the low-energy sites considered here as well as sites

further out from the core with weaker yet negative segregation energies. Saturation was therefore not reached, in contrast to the present case (Figure 9), which explains the higher potential barrier. We expect that, by including more layers with proton segregation for the BZO-G2 GB in the present modeling, the space-charge potential for hydrated BZO would increase, and the difference between BZO and BCO would become larger. The space-charge potentials are found to be larger in BZO by 0.3−0.4 V for G1 and 0.1−0.2 V for G2. These potentials correspond to energies that are similar to the difference in the activation energy for grain-boundary proton conductivity between BZO and BCO found experimentally (see Figure 1), which suggests that the different GB resistances can be explained by the differences in space-charge formation in the two materials. As demonstrated above, the larger tendency for proton segregation in BZO leads to larger space-charge potentials in the hydrated regime. There are, however, other material properties that are different for BZO and BCO that could influence space-charge formation, where the most notable difference is found in the dielectric constant, which is more than twice as large for BZO. We have therefore studied how four different parameters in the space-charge model affect the core concentrations and space-charge potential (Figure 11): the lattice constant, the dielectric constant, and the proton and vacancy segregation energies. We consider a G2-type GB with two equivalent sites in the core that are associated with a single segregation energy for each defect species. The modeling is performed at 300 K where BCO and BZO display similar bulk hydration (see Figure 9). All four parameters are varied

Figure 11. Core concentrations of oxygen vacancies (v•• O ) and protons (OH•O) and the corresponding space-charge potential at 300 K as a function of lattice constant (top left panel), dielectric constant (top right panel), OH•O segregation energy (bottom left panel), and v•• O segregation energy (bottom right panel). The model GB used here corresponds to a G2-type GB with two equivalent segregation sites in the core. The reference values of the four different parameters are a0 = seg 4.236 Å, εr = 60, ΔEseg = −1.0 eV. OH•O = −0.6 eV, and ΔEv•• O

Figure 10. Space-charge potentials under hydrated (solid lines) and dry (dashed lines) conditions for the G1 (top panel) and G2 (bottom panel) GBs in BZO and BCO. 7938


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Chemistry of Materials individually using a reference state with a0 = 4.236 Å, εr = 60, seg = −1.0 eV. ΔEseg OH•O = −0.6 eV, and ΔEv•• O We find that a change in the lattice constant has little effect on space-charge formation. The dielectric constant, on the other hand, has a larger influence where an increased screening reduces the potential and allows for more protons in the core. The different dielectric constants for BCO and BZO (cf. 30 to 65) result in a potential difference of about 0.05 V. The largest effect in the space-charge potential is seen for the proton segregation energy, where a change from −0.3 to −0.8 eV increases the potential by 0.4 V. For the vacancy segregation, the effect is much smaller, and the difference between the segregation energies in BZO and BCO has no impact here. These results thus show that the major contribution to the difference in the space-charge potentials stems from proton segregation. There are several simplifications done in the present modeling that could have an impact on the results. Defect formation energies are computed for individual defects, and defect−defect interactions beyond the mean-field electrostatic interaction in the space-charge model are thus neglected. It is difficult to assess the effect of such interactions, but they should under hydrated conditions be more important for BZO since the proton core concentration in this material is much larger. Although not considered here, dopant segregation can also occur,22,31,71 and dopant−proton interactions could thus be of importance. In bulk, however, BZO and BCO display similar dopant−proton association energies,65,72 and it is thus reasonable to assume that these interactions would lead to similar changes in both materials. Finally, we only consider total segregation energies at 0 K and not free segregation energies, thus neglecting temperature effects. Free energies are dominated by vibrational contributions, which were recently calculated for the BZO-G2 GB.31 This study showed that the segregation entropy is of minor importance for protons, and the results obtained here at lower temperatures where protons dominate should therefore not be affected much if the phonon contribution is taken into account.

configurations with hydrogen bond lengths of less than 2 Å. These configurations can be formed without major structural relaxations, and the influence of the material’s different elastic properties therefore becomes less important; the resulting proton segregation energies become more negative in BZO compared with those in BCO. The segregation energies are further evaluated in a thermodynamic space-charge model. Similar space-charge potentials are obtained for the two materials at high temperatures and under dry conditions. In humid atmospheres at lower temperatures, however, the BZO GBs take up significantly more protons, which results in space-charge potentials that are 0.1−0.3 V higher compared to those found for BCO. The corresponding energy difference (0.1−0.3 eV) is observed for the GB proton activation energies (see Figure 1), and it is thus reasonable to conclude that the more resistive character of the BZO GBs compared that of BCO stems from the less favorable hydration energetics of the cubic BZO bulk phase.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.chemmater.7b02829. Detailed description of the space-charge model considered in this study as well as further information on the procedure for constructing and selecting the grain boundaries in orthorhombic BaCeO3 (PDF)

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. *E-mail: [email protected]. ORCID

Anders Lindman: 0000-0002-1712-008X Notes

The authors declare no competing financial interest.

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4. CONCLUSIONS In this Article, we have studied the origin of the different resistive nature of grain boundaries (GBs) in BaZrO3 (BZO) and BaCeO3 (BCO) within the framework of densityfunctional theory and space-charge modeling. We have studied both bulk and GB properties, where structurally similar symmetric tilt GBs in the two materials have been considered. In the bulk phases, we find that oxygen vacancies exhibit quite similar formation energies despite the different chemical and structural properties of cubic BZO and orthorhombic BCO. Protons, however, are more stable in BCO with a formation energy that is almost 0.4 eV lower than that in BZO. This explains the more exothermic hydration enthalpies that have been observed experimentally. In BCO, protons form almost linear interoctahedral hydrogen bonds with bond length 1.95 Å, which is accomplished by the flexibility (the softness) of the surrounding lattice. This is not possible in the more rigid cubic lattice of BZO, and protons therefore form a configuration with two symmetric weaker nonlinear intraoctahedral hydrogen bonds with larger bond lengths of 2.25 Å. In the GBs, however, protons display similar formation energies in both materials in contrast to the bulk case. In the GBs of both materials, the proton can establish favorable

ACKNOWLEDGMENTS We would like to acknowledge the Swedish Energy Agency (Project 36645-1) for financial support. Computational resources have been provided by the Swedish National Infrastructure for Computing (SNIC) at PDC (Stockholm), C3SE (Gothenburg), and NSC (Linköping).

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REFERENCES

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Comparison of Space-Charge Formation at Grain Boundaries in

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