Defect Interactions in the CeO2âZrO2âY2O3 Solid Solution - The

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Defect Interactions in the CeO-ZrO-YO Solid Solution Steffen Grieshammer J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b03507 • Publication Date (Web): 15 Jun 2017 Downloaded from http://pubs.acs.org on June 30, 2017

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The Journal of Physical Chemistry

Defect Interactions in the CeO2-ZrO2-Y2O3 Solid Solution Steffen Grieshammer Helmholtz-Institut Münster (IEK-12), Forschungszentrum Jülich GmbH, Corrensstraße 46, 48149 Münster, Germany

Institute of Physical Chemistry, RWTH Aachen University and JARA-HPC, Landoltweg 2, 52056 Aachen, Germany

JARA-HPC, RWTH Aachen University and Forschungszentrum Jülich GmbH, Landoltweg 2, 52056 Aachen, Germany

ABSTRACT The solid solutions CeO2-ZrO2 and CeO2-ZrO2-Y2O3 are of interest for applications in industrial catalysis and automotive exhaust purification and possess high oxygen storage capacity. The reduction properties are greatly influenced by the interaction of defects in the ceria host lattice. The large number of different defects complicates the description of these materials. In this study, the interactions of defects in cerium oxide substituted with zirconium oxide and yttrium oxide were investigated, both for stoichiometric and non-stoichiometric composition, by means of density functional theory and Monte Carlo simulations. From the simulations, the impact of defect interactions on the energy of reduction was obtained. In agreement with experimental data, substitution with zirconium oxide leads to a strong decrease of the energy of reduction, which originated from the association between oxygen vacancies and zirconium ions. Detailed analysis of the calculated structures reveals pronounced local relaxation as the origin of the strong association.

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INTRODUCTION Doped ceria is of major technological interest due to its versatile applicability in industry and for future technology. Doping with rare-earth oxides leads to the formation of oxygen vacancies resulting in high oxygen ion conductivity, which makes the material a promising candidate as electrolyte in solid oxide fuel cells (SOFC) and high temperature batteries.1 In industry, ceria is well known as an important catalytic material especially due to its high oxygen storage capacity (OSC), which is crucial in automotive three way catalysts.2,3 The OSC is based on the endothermic reduction of ceria, which leads to the formation of oxygen vacancies (VO∙∙ in Kröger-Vink-notation)

and polarons (Ce′Ce ):

2 CexCe + OxO ⇌ 2 Ce′Ce +

1 O + VO∙∙ 2 2(g)

(1)

In particular, the ceria-zirconia solid solution exhibits an extraordinary high OSC.2,4–6 Doping

ceria-zirconia with trivalent oxides, e.g. Y2O3, attracted additional interest due to the stabilization of the cubic structure and suppression of degradation effects.7,8 More recently, pure and doped ceria were identified as candidates for utilization in the thermochemical production of solar fuel with Zr-doped ceria exhibiting best performances.9–11 In several studies, zirconia doping of ceria was investigated by means of density functional theory (DFT) to clarify the influence on the energy of reduction for reaction (1). Yang et al.12 performed GGA+U calculations for ceria supercells containing a single zirconium ion and observed an asymmetric perturbation of the oxygen ions adjacent to the dopant ion. In comparison to pure ceria, they found a decrease of the energy of reduction by 0.65 eV if the oxygen vacancy is created in the nearest neighbor (1NN) position of the Zr4+ ion. A similar value of 0.6 eV was obtained by Andersson et al.13 who explained this observation by a balancing of the formation of large Ce3+ ions, which accompany the vacancy formation, by the small zirconium cation. Chen et


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al.14 calculated the energy of reduction for ceria supercells with different fractions of zirconium ions and found a minimum for the composition Ce0.5Zr0.5O2. In this case, the energy of reduction was approximately 2.22 eV lower than in pure ceria. The same authors also describe an increase of the distortion of the oxygen polyhedra around an oxygen vacancy if a zirconium ion is adjacent. Wang et al.15 investigated the κ-Ce2Zr2O8 phase and calculated the energy of formation of oxygen vacancies. They explained the low energy of formation for an oxygen vacancy surrounded only by Zr4+ ions by a weaker Zr4+-O2- bond compared to the Ce4+-O2- bond and a strong local relaxation effect. Plata et al.16 investigated a zirconia/ceria heterostructure and found the lowest energy of formation for an oxygen vacancy that is directly at the interface. Those first principles findings illustrate that doping with zirconia leads to a lowering of the energy of reduction if the oxygen vacancy is adjacent to the dopant and thus an enhanced reducibility compared to pure ceria, which is in agreement with experimental findings. However, in the DFT calculations, energies are only determined for a limited number of dopant concentrations and specific defect arrangements, whereas in real materials various defect configurations will emerge depending on dopant fraction and temperature. In order to predict the defect distribution, the interactions between the defects have to be known. In the CeO2-ZrO2-Y2O3 solid solution under reducing conditions the description of defect interactions becomes sophisticated due to the existence of four different defects, namely oxygen vacancies (V), yttrium ions (Y), zirconium ions (Zr), and polarons (Ce’), and their mutual interactions.

In this study, the pair interactions between zirconium ions and other defects in ceria are calculated by means of DFT+U according to previous studies on rare-earth doped ceria.17,18 The structural distortions around the defects are analyzed to identify the origin of the strong association


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between oxygen vacancy and zirconium ions. The pair interaction energies are applied in the Metropolis Monte Carlo19 algorithm to simulate the defect distributions in thermodynamic equilibrium for various dopant fractions at finite temperature. From the simulations the influence of defect interactions on the energy of reduction is estimated and the contributions of different pair interactions are separated.

COMPUTATIONAL DETAILS DFT Calculations Pair interactions of defects were calculated by means of DFT+U within the generalized gradient approximation (GGA) according to Perdew, Burke and Ernzerhof20 (PBE) and the projector augmented wave21 (PAW) method as implemented in the Vienna Ab initio Simulation Package (VASP).22,23 The wave functions were expanded in a set of plane waves with an energy cutoff of 500 eV. For the 2 × 2 × 2 supercells of the ceria fluorite structure a 3 × 3 × 3 Monkhorst-Pack24 kpoint mesh was applied. The convergence parameters for electronic and ionic relaxation were set to 10-4 eV and 0.01 eV/Å, respectively. The 2s22p4, 5s25p66s25d14f1, 4s24p65s24d1, and 4s24p65s24d2 electrons of oxygen, cerium, yttrium and zirconium atoms were treated as valence electrons, respectively. A Hubbard U-parameter was introduced to account for the localization of strongly correlated electrons by the simplified rotational invariant approach25 with U = 5 eV for the 4f-orbitals of cerium. The lattice parameter of the unit cell was fixed at the value of bulk ceria (5.49 Å) according to previous calculations.18 For all defective cells, the total number of electrons in the cell was adapted to reproduce the actual charge state of the different defects, e.g. (Ce32O63)+ for a 2 × 2 × 2 supercell containing an oxygen vacancy (VO∙∙ ) and a polaron (Ce′Ce ). The ‘ramping’

method introduced by Meredig et al.26 was applied to ensure the convergence to the true electronic


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ground state for calculations involving polarons. Reduction of Zr4+ to Zr3+ was not considered as the required oxygen partial pressure would be very low. The interaction energies were determined as described before from the energy difference of two cells.18 Here, one cell contained two defects in neighboring positions, while the other cell contained the two defects in separate positions. Energies were calculated for differently sized supercells and extrapolated to infinite dilution to correct finite-size errors. For some extrapolations, only two supercells were included in the fit as the inverse linear dependence on the number of atoms was shown in a previous paper.18

Monte Carlo Simulations The distribution of the defects was simulated by the Metropolis Monte Carlo algorithm19 as described in previous studies (see references for more details).17,18 The lattices were constructed from 12 × 12 × 12 ceria unit cells and the defect distributions were equilibrated until the averaged energy was constant. Since the cations in the fluorite structure are only mobile at high temperature, they were pre-equilibrated at 1500 K and fixed for lower temperatures, where only oxygen vacancies and polarons are mobile. The interaction energy for every distribution was calculated from the number of defect pairs 𝑁𝑁𝑖𝑖𝑖𝑖𝑑𝑑 for defects of type i and j in distance d and the corresponding

𝑑𝑑 obtained from DFT calculations. pair interaction energy 𝜀𝜀𝑖𝑖𝑖𝑖 𝑑𝑑 𝐸𝐸inter = � 𝑁𝑁𝑖𝑖𝑖𝑖𝑑𝑑 𝜀𝜀𝑖𝑖𝑖𝑖

(2)

𝑑𝑑,𝑖𝑖,𝑗𝑗≤𝑖𝑖

The interaction range was cut off at 5.5 Å as all interaction energies are small (< 0.1 eV) beyond this distance.


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After the equilibration, the energy and coordination numbers were sampled over 105 subsequent steps. For every data point, 10 or 20 independent simulations were performed for the stoichiometric and non-stoichiometric composition, respectively, to obtain the total interaction energy 𝐸𝐸�inter of the lattice. This energy reflects the difference between a system of non-interacting defects and a system of interacting defects.

For non-interacting defects the energy of reduction corresponds to the formation of isolated defects in reaction (1). In the case of interacting defects, the interaction energy contributes to the energy of reduction with ∆𝐸𝐸inter , defined as the difference between 𝐸𝐸�inter for the nonstoichiometric (δ ≠ 0) lattice and the stoichiometric (δ = 0) lattice as described before:17 ∆𝐸𝐸inter = 𝐸𝐸�inter (𝛿𝛿 ≠ 0) − 𝐸𝐸�inter (𝛿𝛿 = 0)

(3)

It is noted that in this paper only the internal energy of defect interaction is considered, without

entropic contributions. The association of defects will influence the local vibrational modes and thus lead to vibrational entropies of association. However, these are time consuming to calculate accurately by ab-initio methods and are neglected here. The change of the configurational entropy due to defect interaction has been discussed in a previous paper.27

RESULTS & DISCUSSION Interaction energies The calculated interaction energies for a pair of one zirconium ion and another Zr4+ ion, a Ce3+ ion, a Y3+ ion or an oxygen vacancy are given in Table 1 together with previously calculated interactions used in this study.17 The interaction of the zirconium ion with a trivalent cation or another zirconium ion is negligible with absolute values not exceeding 0.01 eV. This could be


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expected as there is no coulombic attraction or repulsion of the defects and all pair interactions are dedicated to elastic effects and relaxation. However, impurity cations only induce a small distortion in the lattice (see below in the text), which is associated with small interaction energy. In contrast, a strong attraction is found for the Zr-V pair in 1 NN position, whereas its absolute value rapidly decreases at the next nearest neighbor (2NN) position. This strong association is attributed to the small size of the zirconium ion, which favors a lower coordination number than the 8-fold coordination found in ceria. Andersson et al.13 explained the decrease of the energy of formation for an oxygen vacancy in the vicinity of a zirconium ion by the balancing of the large Ce3+ cations, which accompany the reduction, by the small Zr4+ cation. In contrast, this study shows that the interaction between the oxygen vacancy and the Zr4+ ion has the largest influence, while the interaction between polaron and Zr4+ is zero.

Table 1. Pair Interaction Energies Used in the Study in eV.a Distance

Zr-Zr

Zr-Ce‘

Zr-Y

Zr-V

Y-Y

Ce‘-Ce‘ Ce‘-Y

Y-V

Ce‘-V

1NN

-0.01

0.00

-0.01

-0.60

0.11

0.1

0.1

-0.35

-0.14

2NN

-

-

-

-0.05

-

-

-

-0.14

-0.19

a

Energies for pairs containing Zr4+ were calculated in this study; others are taken from the reference 17. V-V pair interactions used in this study are not stated.

In Figure 1, the interaction energy for the Zr-V pair is compared with the previously calculated interaction energies for pairs of an oxygen vacancy and a trivalent cation. The values in 1NN position can be well described by a second order polynomial depending on the ionic radius 𝑟𝑟 of the cation in Å:28


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1NN 𝜀𝜀𝑋𝑋−V /eV = −6.05 + 9.02 𝑟𝑟 − 3.37 𝑟𝑟 2

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(4)

Extrapolating this equation, a value of -0.85 eV for the 1NN interaction would be expected for

a trivalent ion with the size of Zr4+.

Figure 1. Pair interaction energies of different impurities in ceria with oxygen vacancies in the nearest neighbor (1NN) and next nearest neighbor (2NN) position. Values for trivalent cations are taken from the reference.17 Ionic radii according to Shannon.28 However, for trivalent ions the coulombic attraction between oxygen vacancy and cation due to opposite relative charges has to be considered. This is not the case for the tetravalent zirconium ion. For the calculated relative dielectric constant of 25 for ceria, the coulombic interaction energy ′ for a pair of a trivalent cation (𝑋𝑋Ce ) and an oxygen vacancy (VO∙∙ ) in 1NN position is -0.48 eV.18 It

could be assumed that the pair interaction energy is the sum of the electrostatic and elastic

interaction, the latter including the lattice relaxation. For the Zr-V pair, the subtraction of the electrostatic part from the extrapolated value, according to eq (4), would lead to an interaction energy of -0.37 eV. Consequently, the attraction between vacancy and zirconium ion is even stronger than expected from the analysis of the trivalent ions.


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For a detailed study of the pair interaction energies, the distortions of the lattice around single defects and defect pairs are examined. In Figure 2, the lattice distortions around a zirconium ion, yttrium ion, a polaron, and an oxygen vacancy are shown for the closest anion and cation shell in ceria. In the case of the Zr4+ ion, the nearest anions and cations are drawn towards the dopant by 0.09 Å and 0.03 Å, respectively. This displacement is due to the small size of the Zr4+ ion leading to a shortening of the Zr4+-O2- bond. The displacement around the Y3+ ion is considerably smaller, where the Y3+-O2- distance is elongated and the Y3+-Ce4+ distance is shortened by 0.02 Å. This effect can be attributed to the increased negative charge due to the aliovalent dopant. In contrast to Zr4+ and Y3+, the distortion around the Ce3+ ion is not fully symmetric. This could be explained by the localization of the excess electron in the cerium f-orbital that is not spherically symmetric. The elongation of the Ce3+-O2- bonds is about 0.06 Å while the shortening of the Ce3+-Ce4+ distances is up to 0.02 Å. The trends for Y3+ and Ce3+ are similar as can be expected from electrostatic considerations. However, the bonds Ce3+-O2- and Ce3+-Ce4+ are longer due to the larger radius of the Ce3+ compared to the Y3+ ion.


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Figure 2. Lattice distortions around point defects. a) zirconium (green), b) yttrium (blue), c) polaron (orange), d) vacancy (black). Oxygen ions and cerium ions in relaxed position are given in red and yellow, respectively. Undistorted positions of the perfect fluorite structure are given in grey. The position of the vacancy is indicated at the original position of the removed oxygen ion. Structures were obtained from constant volume calculations in a 3×3×3 supercell. The most distinct distortion is found for the oxygen vacancy with a displacement of the oxygen ions by 0.24 Å towards the vacancy and of the cerium ions by 0.17 Å away from the vacancy due to the missing negative charge of the O2- ion. In Figure 3, the same distortions are shown for Y3+, Ce3+, and Zr4+ in 1NN position to an oxygen vacancy. In the case of Y-V, the Y3+-O2- distances are shortened by 0.02 to 0.13 Å compared to the perfect fluorite lattice, while it was 0.02 Å for the single yttrium ion in Figure 2. The main reason for this distortion is the repulsion of the dopant ion and the simultaneous attraction of the oxygen ions by the vacancy. The distortions of the oxygen ions in nearest neighbor position to the vacancy (0.22 Å to 0.23 Å shortening) are similar to the case of the single vacancy. The same


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holds true for the cerium ions around the vacancy, whereas the repulsion of the yttrium ion is slightly stronger. Overall, the distortion of the lattice is dominated by the vacancy as could already be expected by comparison of the single defects in Figure 2. In the Ce’-V case, the Ce3+ ion possesses the same charge as the yttrium ion but has a larger ionic radius. The Ce3+-O2- distances are similar as in the case of the single polaron. The cerium ions are mainly repelled from the polaron and the distances of all ions around the vacancy are similar to the single vacancy. For Zr-V the most prominent feature is the shortening of the distance by 0.37 Å between the vacancy and the oxygen ions, which are in 1NN position of both, vacancy and Zr4+ ion, compared to 0.24 Å in the case of the single vacancy. In addition, the zirconium ion shows the largest repulsion from the oxygen vacancy (0.22 Å) of all cations, possibly due to high flexibility of the cation associated with its small size. Furthermore, the distances Zr4+-O2- are shorter than in the case of the single zirconium dopant due to the displacement of the zirconium ion and the attraction of the oxygen ions by the vacancy.


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Figure 3. Lattice distortions around cation defects with a vacancy in 1NN position. a) yttrium (blue), b) polaron (orange), c) zirconium (green). Oxygen ions and cerium ions in relaxed position are given in red and yellow, respectively. Undistorted positions are given in grey and the oxygen vacancy is indicated as black sphere at the original position of the removed vacancy. Structures were obtained from constant volume calculations in a 3 x 3 x 3 supercell. From the comparison of the structural data, it seems apparent that the extraordinary strong association of zirconium dopant and oxygen vacancy could be explained by the pronounced relaxation around the oxygen vacancy, which is facilitated by the small size of the Zr4+ ion. In addition, the relaxation of oxygen ions towards the vacancy further benefits from the higher positive charge of the Zr4+ ion compared to trivalent dopants. Similar conclusions were drawn by Wang et al.15 for the κ-Ce2Zr2O8 phase, explaining the low energy of formation for oxygen vacancies by local relaxation.


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Stoichiometric Ceria Defect distribution in stoichiometric ceria was simulated at 300 K for zirconium fractions 𝑥𝑥Zr

between 0 and 0.5 with a constant yttrium fraction of 𝑥𝑥Y = 0.2. The resulting coordination

numbers of the cations are given in Figure 4. The dashed line indicates the average coordination

number of 7.6 for all cations in a random distribution. The deviation from this value for the individual cations is caused by the interactions of the dopant cations with the oxygen vacancies. Both dopants attract the oxygen vacancies, which leads to lower coordination numbers, especially for Zr4+. Maekawa et al.29 investigated the local structure and coordination numbers in Ce0.8-xZrxY0.2O1.9 by 89Y MAS-NMR spectroscopy and found the same order for the degree of localization of the oxygen vacancies around the cations, i.e. Zr4+ > Y3+ > Ce4+. The averaged experimental coordination numbers for yttrium are given in Figure 4 and match perfectly with the simulated values. For increasing zirconium content, all coordination numbers increase. Although counterintuitive on first sight, this behavior can be explained by the strong association of zirconium ions and oxygen vacancies. With increasing zirconium fraction, the coordination numbers of Ce4+ and Y3+ increase as more Zr4+ ions trap the vacancies. Likewise, the coordination number of zirconium increases as more of these dopants compete for the constant number of vacancies.


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Figure 4. Simulated coordination numbers of cations in Ce0.8-xZrxY0.2O1.9 at 300 K (spheres) and experimental values for Y from Maekawa et al.29 (diamonds). The dashed line indicates the coordination number in a random distribution. Maekawa et al.29 also reported the fraction of yttrium ions with a specific number of oxygen ions in 1NN position. The experimental and simulated values are shown in Figure 5. The values exhibit a good agreement with a slight underestimation/overestimation of the 7-fold/6-fold coordinated yttrium ions by the simulations at low zirconium content. This difference might be attributed to the limitations of the pair interaction model, which includes no many-body contributions. Nevertheless, these effects average out for the coordination numbers as seen in Figure 4.


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Figure 5. Fraction of yttrium ions coordinated by six (blue), seven (red) or eight (black) oxygen ions. Simulated values are depicted as spheres, experimental values from Maekawa et al.29 as diamonds. The dashed lines indicate the fractions in a random distribution.

Non-stoichiometric Ceria The defect distribution in non-stoichiometric ceria was simulated at 1000 K for various zirconium (𝑥𝑥Zr = 0, 0.1, 0.2, 0.3) and yttrium (𝑥𝑥Y = 0, 0.2) fractions with non-stoichiometry 𝛿𝛿

between 0 and 0.15. The change in the energy of defect interactions (∆𝐸𝐸inter ) was calculated according to eq (3) and divided by the number of oxygen vacancies created by reduction 𝑁𝑁V,δ

(Figure 6). Negative values imply a decrease of the energy and thus facilitation of the reduction due to defect interactions. With increasing zirconium fraction, this effect gets stronger as seen in experiments.9 Likewise, the doping of pure ceria with yttria leads to a decrease of the energy. However, in the case of zirconia doped ceria, additional doping with yttria increases the energy again (compare 𝑥𝑥Zr = 0.2, 𝑥𝑥Y = 0 and 𝑥𝑥Zr = 0.2, 𝑥𝑥Y = 0.2). This is in agreement with the finding by Call et al.10 who report that additional doping of zirconia-ceria with lanthanides decreases the yield

in the thermochemical production of solar fuel. The authors explain this finding by the decrease of available Ce4+ sites and an additional strain due to large trivalent dopants. In addition, Kuhn et al.30 stated that oxygen vacancies from acceptor doping counteract the effect of Zr-doping leading to an increase of the energy of reduction in experiments.


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Figure 6. Change in the energy of defect interaction per oxygen vacancy introduced by reduction simulated at 1000 K for different compositions. For a detailed analysis of the observed behavior, the most important contributions to ∆𝐸𝐸inter are

shown in Figure 7 for pure ceria and zirconia-ceria with and without yttrium for 𝛿𝛿 = 0.05. Interactions not shown here are either small or similar for the different compositions. In pure ceria, the decrease of the energy is mainly driven by the formation of energetically favorable Ce’-V pairs in 2NN position. In Zr-doped ceria, this contribution remains nearly constant, but ∆𝐸𝐸inter is strongly decreased by the formation of Zr-V pairs in 1NN position. The situation gets more complicated for Zr/Y-codoped ceria. Here, the energy is further decreased by additional Ce’-V pairs in 2NN position due to the existence of more oxygen vacancies in the lattice. Furthermore, the contributions from Y-V pairs in 1NN position lead to a decrease of the energy, which is counteracted by the positive energy of V-V pairs in 2NN and Ce’-Y pairs in 1NN. Albeit, the most pronounced difference between Zr-doped ceria and Zr/Y-codoped ceria is the smaller contribution of the Zr-V pairs in 1NN in the latter case. This is due to the fact, that the Zr4+ ions are already bound to oxygen vacancies introduced by Y-doping. Therefore, the existence of oxygen vacancies in the oxidized state seems to be the main reason for the detrimental effect of trivalent doping on the reducibility of ceria-zirconia solid solution as previously suggested by Kuhn et al.30


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Figure 7. Most important energy contributions from pair interactions for pure ceria (left), Zr-doped ceria (middle) and Zr/Y-codoped ceria (right) with δ=0.05. All interactions not shown here are either small or do not change significantly between the compositions. The quantity comparable to the experimental enthalpy of reduction is the change of the energy of interaction with each additional oxygen vacancy given by 𝑑𝑑(∆𝐸𝐸inter )/𝑑𝑑𝑁𝑁V,𝛿𝛿 . At low nonstoichiometry, i.e. 𝛿𝛿 → 0, in pure ceria, the defects can be seen as non-interacting and the

corresponding enthalpy of reduction per oxygen vacancy is reported to be about 5 eV in experiments.31–33 For higher defect concentrations, the interactions lead to a change of the enthalpy of reduction and this change is reflects by the simulated 𝑑𝑑(∆𝐸𝐸inter )/𝑑𝑑𝑁𝑁V,𝛿𝛿 values.

Values for 𝑑𝑑(∆𝐸𝐸inter )/𝑑𝑑𝑁𝑁V,𝛿𝛿 are given in Figure 8. Compared to ∆𝐸𝐸inter /𝑁𝑁V,𝛿𝛿 , the values are

slightly shifted, whereas the ordering and curve shapes are essentially the same. It is apparent that for increasing non-stoichiometry the energy decreases for pure ceria but increases for doped ceria.

This means that introduction of additional defects by reduction has a decreasing effect and the spread in the energy for the different compositions is getting smaller. It should be noted that the energies might not be directly comparable to the experimental values since the experimental enthalpies of reduction are not measured directly but are extracted from


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experimental equilibrium constants by an Arrhenius-type fit. Therefore, the enthalpies of reduction are assumed to be temperature independent,9 while the simulated ∆𝐸𝐸inter values are temperature dependent. However, the simulations reveal that the temperature dependence is linear, which again

leads to an Arrhenius-type behavior. In addition, experimental data scatter for different sources due to differences in the experimental setup and data analysis.

Figure 8. Derivative of the change in energy of defect interaction with respect to the number of oxygen vacancies depending on non-stoichiometry. Extracted from the simulations at 1000 K for different compositions. Experimental values of the enthalpy of reduction for Zr-doped and Zr/Y-codoped ceria are given in Figure 9. On the right axis, the difference to the reference value of 5 eV for pure ceria with δ →

0 is given. The following features can be found: The experimental data exhibits severe scattering

for 𝑥𝑥Zr ≈ 0.2. Especially the values by Zhou et al.34 for 𝑥𝑥Zr ≈ 0.19 are comparatively small and

show a different trend than the other values. For small non-stoichiometry the simulated values are similar to the experimental energy differences by Hao et al.9 and Kuhn et al.30 for 𝑥𝑥Zr = 0.1 and

𝑥𝑥Zr = 0.2 and exhibit the same trends. The energy decreases with increasing zirconium content and

decreasing non-stoichiometry. For Zr/Y-codoped ceria the experimental energy values35 (for


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𝑥𝑥Zr = 0.16, 𝑦𝑦Y = 0.18) are higher compared to the simulations (for 𝑥𝑥Zr = 0.2, 𝑦𝑦Y = 0.2) and exhibit a different curve shape. Nevertheless, a higher energy compared to 𝑥𝑥Zr = 0.2 without yttrium is

found in both, experiment and simulation.

The simulated results show that defect interaction has a considerable impact on defect distribution and the energy of reduction of the investigated materials. Other contributions like vibrational energy or the variation of the lattice parameter might have an additional effect on the energy of reduction, however, these are beyond the scope of this study. The vibrational contributions are computationally demanding to estimate and are expected to be small compared to the energy contributions.36 The changes of the lattice parameter are expected to have a lesser influence compared to the local relaxation around the defects.

Figure 9. Experimental values of the enthalpie of reduction for Zr-doped and Zr/Y-codoped ceria according to Hao et al.,9 Kuhn et al.,30 Zhou et al.,34 and Otake et al.35 Right axis: Difference to the reference value of 5 eV. CONCLUSIONS


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The defect interactions in zirconia- and yttria-doped ceria were investigated by means of DFT calculations and Monte Carlo simulations. The interactions between point defects, i.e. dopants, polarons, and oxygen vacancies, are expressed by the corresponding pair interaction energies. Pairs of zirconium ions and oxygen vacancies show strong association. This is due to the small size of the zirconium ion, which allows favorable relaxation around the oxygen vacancy and is even enhanced by the higher charge compared to trivalent dopants. In contrast, zirconium ions show only weak interactions with trivalent cations such as the small polaron. The pair interactions were applied in Monte Carlo simulations to obtain the defect distribution for various dopant fractions at finite temperature and the following main results were obtained: The simulated coordination numbers of cations in the solid solution Ce0.8-xZrxY0.2O1.9 agree well with experimental data from

89

Y MAS-NMR measurements. Oxygen vacancies are preferably

located next to the zirconium ions due to their attractive interaction. The strong interaction between zirconium ions and oxygen vacancies leads to a decrease of the interaction energy for zirconia doped ceria thus facilitating reduction of the material in agreement with the experimental findings. Additional doping with yttria counteracts the effect of zirconia doping due to the binding of zirconium ions to oxygen vacancies, which accompany the trivalent doping. This explains the higher energy of reduction for Zr/Y-codoped ceria compared to Zr-doped ceria.

AUTHOR INFORMATION E-mail: [email protected]. Phone: +49-241-8094840. Fax: +49-241-8092128.


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ACKNOWLEDGEMENT The author thanks M. Martin from RWTH Aachen University for valuable discussions and S. Eisele from RWTH Aachen University for support with the simulations and graphical representations. Calculations were performed with computing resources granted by JARA-HPC at RWTH Aachen University under project jara0035. Figures 2 and 3 were created with the program VESTA.37

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Defect Interactions in the CeO2âZrO2âY2O3 Solid Solution - The

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