Understanding Oxygen-Vacancy Migration in the Fluorite Oxide CeO2

Article pubs.acs.org/JPCC

Understanding Oxygen-Vacancy Migration in the Fluorite Oxide CeO2: An Ab Initio Study of Impurity-Anion Migration Annalena R. Genreith-Schriever, Pascal Hebbeker, Judith Hinterberg, Tobias Zacherle, and Roger A. De Souza* Institute of Physical Chemistry, RWTH Aachen University, Aachen, Germany 52056 ABSTRACT: The site exchange of an anion moiety (O, N, F, Ne, P, S, Cl, and Ar) with an oxygen vacancy in fluorite-structured CeO2 was studied by means of density functional theory (DFT) calculations. The obtained activation energies of migration vary between 0.2 and 0.9 eV, and increase with the formal valence of the migrating ion; the size of the migrating ion appears to play a minor role. An analysis of ion displacements suggests that repulsive Coulombic interactions between the migrating anion and oxygen ions as the next-nearest neighbors in the saddle-point configuration provide the dominant contribution to the activation energy of migration. As well as emphasizing the ease with which anion moieties are mobile in AO2 fluorite materials, these results suggest a new paradigm for understanding fast oxygen-ion conducting materials.

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INTRODUCTION Oxides that display high oxygen-ion conductivity crystallize, with a few notable exceptions, in the AO2 fluorite structure, the ABO3 perovskite structure, or derivatives thereof.1−5 Understanding why high conductivity arises in these oxides is not only of fundamental interest; it would also allow optimization of such materials for a wide variety of applications, such as electrolytes for solid oxide fuel cells (SOFC) and solid oxide electrolyzer cells (SOEC), sensors, catalysts, and resistively switching memory devices. High ionic conductivity in an AO2 fluorite oxide is achieved by partially substituting the host lattice with an M2O3 oxide, in order to produce high concentrations of charge carriers (oxygen vacancies). The introduction of the M2O3 oxide, however, affects not only the concentration of the charge carriers, but also their mobility. The oxygen-ion conductivity of a given AO2 host can be optimized by selecting the optimal amount of an optimal M2O3 oxide.6,7 Empirically, optimal M3+ cations have been found to be those whose radii closely match those of the host A4+ cation. Theoretical investigations provide support for this empirical rule, that the ionic radius is a crucial factor in determining the mobility of oxygen vacancies in the host lattice.8,9 In this paper, we study the migration process at the atomic level using ab initio computational methods. Previous work examined oxygen-ion migration in a specific AO2 oxide with various M2O3 substituents,10−12 in various AO2 oxides (including solid solutions such as (Ce, Zr)O213), or in various related oxide structures.14 Here, we want to obtain a deeper understanding of oxygen-ion migration in AO2 oxides by using the type of migrating anion as the variable. That is, we examine the migration of N, O, F, Ne, P, S, Cl, and Ar by a vacancy mechanism in the cubic fluorite lattice of CeO2 by means of density functional theory (DFT) calculations. The advantage © 2015 American Chemical Society

over previous studies is that the host structure and composition of the material remain unchanged. We emphasize that the focus of this study is on defect kinetics and not on defect thermodynamics. That is, we consider exclusively the activation energies of migration of the anion substituents; we do not consider their equilibrium concentrations, nor do we consider the equilibrium concentration of the oxygen vacancies required for anion migration.15−19 In addition, we do not consider defect−defect interactions that may affect the migration process. These interactions may arise between the migrating anion moiety and either substituent M3+ cations or small polarons (Ce3+) formed on reduction of the oxide.15,18−22 We leave these topics for future study, because, already in the case of oxygen-ion migration in CeO2, previous studies have revealed that defect− defect interactions lead to complex migration behavior.11,16 In this study we use a variety of anion moieties simply to have a new method with which to probe the anion migration process in CeO2 at the most basic level of dilute, noninteracting defects.

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COMPUTATIONAL METHODOLOGY All density functional theory (DFT) calculations were performed according to the generalized gradient approximation (GGA) proposed by Perdew, Burke, and Ernzerhof23 and the projector augmented wave method (PAW),24 as implemented in the Vienna ab initio simulation package (VASP).25,26 The electronic wave functions were expanded with a basis set of plane waves with kinetic energies of up to 500 eV. Convergence tests up to 800 eV indicated no significant changes in total energies and bulk modulus. A 2 × 2 × 2 super Received: August 11, 2015 Revised: November 10, 2015 Published: November 23, 2015 28269

DOI: 10.1021/acs.jpcc.5b07813 J. Phys. Chem. C 2015, 119, 28269−28275

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The Journal of Physical Chemistry C cell with 96 atoms (768 electrons) was employed. For the kpoint sampling, a 2 × 2 × 2 Monkhorst−Pack mesh was used. The convergence criteria for the electronic and ionic relaxations were set to 10−6 eV and 5 × 10−3 eV, respectively. For cerium the 5s2 5p6 6s2 5d1 4f1 electrons were treated as valence electrons. To account for the strongly correlated f electrons of ceria, a Hubbard U parameter was employed. A rotationally invariant approach27 with an effective U parameter of U = 5 eV was used, as recommended in the literature.17 For oxygen the 2s2 2p4 electrons were considered. This set of parameters, it is emphasized, were able to successfully predict the point-defect behavior of CeO2,15 formation entropies,28 and also migration enthalpies in cation doped CeO2.29 For the migration calculations, we introduced a doubly charged oxygen vacancy into the simulation cell, by removing an oxygen ion. At a neighboring anion site we placed an anion moiety in its nominal valence state, resulting in no net excess of electrons or holes in the super cell. That is, to substitute an oxygen ion with a nitrogen ion, we removed an oxygen atom and two electrons from the cell, and then added an N atom and three electrons. We have attempted to also investigate defects in charge states other than their formal valence state, e.g., N2−, but so far we have not been successful in localizing the corresponding electron hole at the defect site. For the impurity anion species the corresponding s and p orbital electrons were included, e.g., 2s2 2p3 for N, and 3s2 3p6 for Ar. The minimum-energy paths for the migration processes were determined by means of climbing image NEB calculations.30,31 After relaxing the configuration of the perfect ceria lattice at zero pressure, the initial, saddle-point, and final configurations of a migration process were relaxed at constant volume. The activation energy of migration, ΔEmig, is given by the difference in cell energy between the saddle-point configuration (spc) and initial configuration (ic).

Figure 1. Energy profile for the migration of an oxygen ion by a vacancy mechanism along the ⟨100⟩ direction in CeO2. The line is a guide to the eye and is a natural cubic spline fit.

Table 1. Comparison of the Oxygen Migration Energy Determined in This Work with Literature Data

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RESULTS Oxygen-vacancy migration in an AO2 fluorite oxide can in principle occur along the ⟨100⟩, ⟨110⟩, and ⟨111⟩ directions. The first possibility is expected to exhibit the lowest activation energy of migration because it is the shortest path. Indeed, Nakayama et al. found through DFT calculations that the migration of an oxygen ion along the ⟨100⟩ direction is by far the most favorable.10 In this study we focused, therefore, on anion migration along this path. In Figure 1 we show the energy calculated for an oxygen ion at various positions along the relaxed NEB path. As expected from the symmetry of the cubic fluorite lattice and the crystallographic equivalence of all regular oxygen-ion positions, the energy profile for oxygen-ion migration is symmetrical. The calculated activation energy for oxygen-ion migration is ΔEOmig = 0.51 eV, which is in very good agreement with literature data from both experimental and other computational studies, as can be seen in Table 1. A Bader analysis32 of the initial and saddlepoint configurations indicated that the migrating oxygen ion did neither lose nor gain charge during the migration jump (see Table 2). In Figure 2 we plot the calculated energy profiles for the migration of various impurity anions between two oxygen-ion sites along the ⟨100⟩ direction. For both periods, N3− to Ne0 and P3− to Ar0, there is a clear trend of decreasing activation energy of migration with increasing atomic number. Again, a Bader analysis of the respective initial and saddle-point

reference

method

ΔEOmig/ eV

This study Nakayama et al.(2009)10 Nakayama et al.(2012)11 Dholabhai et al.33 Hinterberg et al.34 De Souza et al.35 Burbano et al.36 Gotte et al.37 Steele et al.38 Wang et al.39 Adler et al.40 Faber et al.6

DFT-GGA+U DFT-GGA DFT-GGA+U DFT-GGA+U DFT-GGA+U S-EPP S-EPP MD-EPP expt. (conductivity) expt. (conductivity) expt. (NMR) expt. (NMR)

0.51 0.5 0.62 0.47 0.51 0.6 0.47 0.57 0.52 0.6 0.49 0.6

Table 2. Bader Analysis for the Charge of the Migrating Anion in the Initial and Saddle-Point Configuration Based on the Full Electron Densities N O F Ne P S Cl Ar

qBader,ic/e

qBader,spc/e

−1.41 −1.22 −0.79 −0.05 −0.96 −0.96 −0.64 −0.02

−1.37 −1.15 −0.76 −0.05 −1.01 −0.98 −0.64 −0.03

configurations indicated no significant change in the charge of the migrating anion (see Table 2).

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DISCUSSION Over 30 years ago, Kilner and Brook41 conducted a geometrical analysis of the migration process of oxygen ions in various oxides. In the case of fluorite-structured oxides, for instance, they pointed out (i) that the saddle-point configuration consists of the migrating anion pushing past two cations; (ii) that the distance between the two cations is smaller than the diameter of the migrating anion; and (iii) that, as a consequence, energy has to be expended in the migration process in pushing the cations apart (see Figure 3). For CeO2 substituted with M3+ 28270

DOI: 10.1021/acs.jpcc.5b07813 J. Phys. Chem. C 2015, 119, 28269−28275

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The Journal of Physical Chemistry C

Figure 4. Calculated migration energies as a function of the ionic radii as determined by Shannon43 (and according to Pauling44 in the case where no Shannon data are available for the specific charge states). Ions of the same nominal charge are shaded in the same color.

Figure 2. Energy profiles for the migration of impurity anions by a vacancy mechanism along the ⟨100⟩ direction in CeO2. The lines are a guide to the eye and are natural cubic spline fits. For comparison the migration profile of oxygen is also depicted.

Table 3. Nominal Charges, Ionic Radii, and Migration Energies of Various Impuritiesa N O F Ne P S Cl Ar

Figure 3. Saddle-point configuration of the migration of O with the two closest Ce cations highlighted in blue and the eight closest O anions highlighted in yellow.

qanion/e

ranion43,44/Å

ΔEmig/eV

−3 −2 −1 0 −3 −2 −1 0

1.46 1.38 1.31 1.12 2.12 1.84 1.81 1.54

0.90 0.51 0.29 0.18 0.56 0.55 0.39 0.18

a

Ionic radii as tabulated by Shannon43 and, where no data is available, by Pauling.44

If the dominant factor is not ranion, is it qanion? In Figure 5 we plot ΔEmig as a function of qanion and we find a clear correlation,

cations, Nakayama and Martin10 employed DFT calculations to determine ΔEOmig for Ce−Ce, Ce−M, and M−M migration edges,42 and found that ΔEOmig increases, as expected, with rM3+. Kilner and Brook’s critical radius model is thus the standard model for rationalizing anion migration in fluorite oxides. In our casevarying anion moietiesthe same trend is expected. As the ionic radius of the migrating anion increases, the degree of lattice perturbation is expected to rise, and thus the migration barrier should increase. In Figure 4 we plot the migration energies as a function of ionic radius.43,44 Although one perceives an increase in ΔEmig with radius within a period, this comparison is deceiving because the formal ionic charge is also changing. One must, therefore, restrict the comparison to ions of the same formal charge, i.e., to the pairs Ne0/Ar0, F−/Cl−, O2−/S2−, and N3−/P3−. In this case one hardly sees any increase in the migration energy with increasing radius with the exception of the N3−/P3− pair (for which the larger ion, P3−, even has a lower ΔEmig). We return to this exception later. This strongly suggests that ranion plays only a minor role in determining ΔEmig. The migration energy varies more strongly within each period, where small changes in radius are accompanied by considerable changes in the formal charge, than between isovalent ions of different radii. Possibly, one could claim that the ionic radii32,44 are inaccurate, but it is extremely unlikely that they are qualitatively incorrect. Indeed, N, P, S, Cl, and Ar are all significantly larger than O, but only N exhibits a significantly higher migration energy.

Figure 5. Plot of the migration energies as a function of the nominal charges of the migrating species.

with only P (again) deviating significantly from the trend. We can also rationalize this behavior. Since the migration energy increases with increasing negative charge, it appears that repulsive Coulombic interactions play a crucial role in the migration process. The immediate candidates for repulsive interactions with the migrating anion are the oxygen ions that 28271

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The Journal of Physical Chemistry C are next-nearest neighbors (NNN) [the nearest-neighbors (NN) are cerium ions]. While steric considerations regard only the first coordination sphere, Coulomb interactions extend obviously much, much further. We therefore propose that Coulombic interactions with the next-nearest neighbors largely determine the height of the migration barrier. Finally in this section we examine the geometry of the saddle-point configuration. From the DFT calculations, we extracted the separation of the migrating anion to the NN Ce ions and the NNN O ions for each migrating anion. These two distances are plotted against each other in Figure 6. The

Figure 7. Migration energy ΔEmig as a function of the difference in electrostatic energy between the starting and saddle-point configuration, ΔEes,mig, considering the first two coordination shells of the migrating anion.

that Coulombic interactions provide the main contribution to the energetic barrier of the migration process. If ΔEmig can be explained in terms of Coulomb interactions, the data obtained in previous studies, e.g., by Nakayama and Martin,10 should also be explicable in these terms. Nakayama and Martin, on the one hand, report an increase in the migration energy with increasing ionic radius. On the other hand, they find a drastic increase in the migration energy when successively substituting the two closest cerium ions with rareearth dopants.10 We re-examined, therefore, oxygen-ion migration across Ce−Sm and Sm−Sm edges and across Ce− Y and Y−Y edges. In addition to determining ΔEmig, we also analyzed the initial and saddle-point configurations to obtain ΔEes,mig. These data are plotted in Figure 8 together with data

Figure 6. Distance between the closest oxygen ions and the migrating ion in the saddle-point configuration as a function of the distance between the closest cerium ions and the migrating ion.

behavior is entirely consistent with Coulomb interactions dominating the migration energetics. The more negatively charged the migrating anion is, the more strongly it will attract the NN Ce ions, and the more strongly it will repel the NNN oxygen ions. That is, one sees an inverse correlation between dmig−O and dmig−Ce. The behavior is also inconsistent with the critical-radius model41 (for which Coulomb interactions are negligible). In such a case, a larger anion, say, that pushes the Ce ions apart is expected to push the nearest O ions away, too. That is, one expects a positive correlation between dmig−O and dmig−Ce, in constrast to the behavior seen in Figure 6. New Model of Migration Energetics. If the migration energy is essentially determined by Coulomb interactions, we expect to see a correlation between ΔEmig and the difference in the electrostatic energy of the starting and the saddle-point configuration ΔEes,mig. We are interested in a simple model to determine the electrostatic energy, preferably one that allows us to probe the immediate environment of the migrating anion. For this reason we calculate the Coulomb energy of the first two coordination shells of the migrating anion.45 To be specific, we calculate ΔEes,mig according to ΔEes,mig

Figure 8. Migration energy ΔEmig as a function of the difference in electrostatic energy between the starting and saddle-point configuration ΔEes,mig considering the first two coordination shells of the migrating anion.

⎡⎛ M ⎛ N qq ⎞ ⎤ qk ql ⎞ 1 ⎢⎜ ⎟ − ⎜ ∑ i j⎟ ⎥ = ∑ ⎢ ⎜ ⎟ ⎥ ⎜ 4π ϵ0 ⎢⎝ k = 0; l > k dk , l ⎟⎠ ⎝ i = 0; j > i di , j ⎠ic ⎥⎦ ⎣ spc

from Figure 7. We find that these data are indeed broadly consistent with our hypothesis. Figure 8 shows a clear correlation between ΔEmig and ΔEes,mig for oxygen-ion migration in the presence of Y and Sm, as predicted from our model. We suggest that our model could further explain the increase in migration energy observed by Nakayama and Martin when successively substituting the cerium ions with rare-earth

(1)

where i,j and k,l here denote the ions in the starting and saddlepoint configurations, respectively, and ϵ0 is the vacuum permittivity. The results are compared in Figure 7. The migration energy clearly correlates with the difference in the electrostatic Coulomb energy. This supports our hypothesis 28272

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Coulomb interactions essentially facilitate fast oxygen-ion conduction.

dopants. With the repulsive Coulomb interactions between the migrating anion and the oxygen ions largely determining the activation energy of migration, we suggest that the two closest cerium ions with their 4-fold positive charge help stabilize the saddle-point configuration. Any replacement of the cerium ions with an M3+ cation will increase the Coulomb energy of the saddle-point configuration and will thus increase the migration barrier. A migrating anion apparently has the greatest energetic expenses if it bears a high negative charge (and exhibits a large ionic radius), as is the case for example for N3−. While based on these considerations P3− is also expected to exhibit a high migration barrier, the calculations yield a surprisingly low migration barrier. We suggest that this is due to covalent contributions to the P bonds, which do not follow our model of Coulombic point charge interactions. Covalency, in general, may therefore be beneficial in reducing the migration barrier. Although the size according to Figure 4 has some impact on the migration process, the scope of this influence must be deemed rather limited. The main contribution to the migration barrier of oxygen ion migration in ceria stems from electrostatic interactions. To some, this conclusion may appear unsurprising: Coulomb interactions are the dominant interactions in an ionic solid. There are, however, no studies of oxygen-ion migration in the literature in which this conclusion has been reached on the basis of a quantitative model. When studying the migration processes and energy barriers in oxides, we therefore recommend to investigate electrostatic contributions. Any optimization of fast oxygen conducting materials must be aimed at reducing the repulsive Coulombic interactions in the migration process. Extension to Other Oxygen-Ion Conductors. Various criteria have been proposed to explain and predict high oxygenion conductivity in oxides.46−49 The oxide’s structure should be highly symmetrical and it should be able to tolerate a high concentration of oxygen defects (vacancies or interstitials). It should possess open paths between oxygen-ion sites that are of equal energy for oxygen defects. We suggest that besides these conventional criteria new factors have to be listed reducing repulsive Coulomb interactions, such as a low negative charge of the migrating anion, a high positive charge of the neighboring cations, and, possibly, significant covalency. We propose that these new criteria are not restricted to ceria or even to fluorite oxides, but that they apply to all oxygen-ion conductors, independent of the structure of the material. Our findings could, for example, explain the high oxygen conductivity of δ-Bi2O3 (with its low activation enthalpy of migration of 0.4 eV).50,51 The latter crystallizes in the fluorite structure, too, but with 25% of the oxygen sites remaining vacant. Compared with the AO2 fluorite oxides, δ-Bi2O3 exhibits a very high oxygen conductivity.50,52,53 As the repulsive Coulombic interactions between the migrating anion and the nearest oxygen ions in the saddle-point configuration seem to form the main contribution to the migration barrier, we suggest that the missing oxygen ions drastically reduce the migration barrier, thereby facilitating the oxygen-ion migration in δ-Bi2O3. Schie et al. have suggested that the oxygen migration in SrTiO3 is influenced by Coulombic interactions.54 Skinner et al. report high oxygen mobilites in complex noncubic systems,55 such as LAMOX,56 BIMEVOX,57,58 or apatite-structured materials.59 We suggest that in these materials, too, favorable

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CONCLUSIONS We have studied the migration of oxygen in ceria by means of investigating impurity ions migrating on the oxygen site. In determining the migration energies for all O2− substituents and analyzing them in terms of ionic radius and charge, we observe three aspects of interest. First, little influence of the ionic radius on the height of the migration barrier is seen. While studies of the anion migration in fluorite oxides have so far focused mainly on steric considerations, pointing out the difficulty of the migrating anion pushing past the two closest cerium ions in the saddlepoint configuration, we suggest that the radius of the migrating anion plays a minor role. Second, the migration energy strongly depends on the charge of the migrating ion. Ions with a higher negative charge exhibit a higher migration energy. We therefore propose that repulsive Coulombic interactions are the decisive factor determining the activation energy of migration, specifically repulsive Coulomb interactions between the migrating anion and the nearest oxygen ions in next-nearest neighbor positions. Third, a strong correlation between the migration energy and the difference in the Coulomb energy between the starting and saddle-point configuration is observed. This correlation holds not only for the data determined in this work, but also for data from previous studies. We therefore propose a new model of fast oxygen-ion conduction, based on the Coulomb interactions as the central influence on the migration process. Further investigations of fast ionic conduction in fluorite-oxide materials should pay heed to the strong Coulombic interactions in these materials. Any approach to tailoring materials’ properties to their applications will have to be aimed at reducing these Coulombic repulsive components of the migration energy barrier.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +49 (0)241 8094739. Fax: +49 (0)241 8092128. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We gratefully acknowledge support for A.R. Genreith-Schriever from the Fonds der Chemischen Industrie, Germany. This work was supported in part by the German Science Foundation (DFG) within the framework of the collaborative research centre ”Nanoswitches” (SFB 917). Simulations were performed with computing resources granted by JARA-HPC from RWTH Aachen University under project jara0100.

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DOI: 10.1021/acs.jpcc.5b07813 J. Phys. Chem. C 2015, 119, 28269−28275

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DOI: 10.1021/acs.jpcc.5b07813 J. Phys. Chem. C 2015, 119, 28269−28275