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E-mails: [email protected]; [email protected]., †. East China University of Science and Technology. , ‡. The Queen's University of Belfast. Cite thi...
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J. Phys. Chem. C 2009, 113, 10229–10232

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A Model to Understand the Oxygen Vacancy Formation in Zr-Doped CeO2: Electrostatic Interaction and Structural Relaxation Hai-Feng Wang,†,‡ Xue-Qing Gong,† Yang-Long Guo,† Yun Guo,† Guan Zhong Lu,*,† and P. Hu*,‡ Laboratories for AdVanced Materials, Research Institute of Industrial Catalysis, East China UniVersity of Science and Technology, 130 Meilong Road, Shanghai 200237, P. R. China, School of Chemistry and Chemical Engineering, The Queen’s UniVersity of Belfast, Belfast, BT9 5AG, U.K. ReceiVed: February 2, 2009; ReVised Manuscript ReceiVed: April 18, 2009

Using density functional theory with the inclusion of on-site Coulomb correction, the O vacancy formation energies of CexZr1-xO2 solid solutions with a series of Ce/Zr ratios are calculated, and a model to understand the results is proposed. It consists of electrostatic and structural relaxation terms, and the latter is found to play a vital role in affecting the O vacancy formation energies. Using this model, several long-standing questions in the field, such as why ceria with 50% ZrO2 usually exhibit the best oxygen storage capacity, can be explained. Some implications of the new interpretation are also discussed. 1. Introduction O vacancy is one of the most important defects in metal oxides, and tuning its formation energy by forming composite oxides is a very common practice in chemistry to achieve desired oxide properties.1-4 In particular, the O vacancy formation in ceria (CeO2) has been extensively studied, since it is closely related to ceria’s wide applications spanning from heterogeneous catalysis to solid oxide fuel cells.5-7 Doping Zr to form Ce1-xZrxO2 solid solutions, an indispensable component in three-way automotive catalysts as an oxygen buffer, has been found to dramatically facilitate the formation of the oxygen vacancies.5,8 Despite a large effort spent on the subject in the last few decades, a fundamental issue in the field (i.e., what are the key factors that affect the O vacancy formation of Ce1-xZrxO2?) still remains elusive. In this paper, we propose a general model to shed light on this issue, which may also possess some significant implications for other materials. Ce1-xZrxO2 solid solutions exhibit unique oxygen storage capacity (OSC) (i.e., releasing/storing oxygen by forming/filling oxygen vacancies under reducing/oxidizing conditions), which is quantitatively related to the formation energy of the O vacancy. Because of this unique property, they become an important material in many catalytic systems, such as car exhaust emission control. In the last few decades, they have been extensively investigated, and a large number of experimental observations have been accumulated: (i) The addition of Zr to ceria significantly increases the ceria OSC.9-11 (ii) The OSC of Ce1-xZrxO2 is closely related to the ratio of Ce/Zr, and x at 0.5 (normally assigned as Ce0.5Zr0.5O2) generally gives higher OSC than others.8,9,12 Specifically, high OSC efficiency (89% with respect to the theoretical OSC value), has been achieved from the well-ordered Ce0.5Zr0.5O2 solid solution phase.12 To understand these findings, a wide range of experimental and theoretical work has been carried out. Yang et al.13 found that the introduction of Zr lowers the formation energy of O vacancy by ∼0.6 eV in a 96-atom bulk CeO2 structure. Balducci * Corresponding authors. E-mails: [email protected]; [email protected]. † East China University of Science and Technology. ‡ The Queen’s University of Belfast.

et al.14 proposed that the small ionic size of Zr4+ can reduce the strain caused by the increase in the ionic size of Ceδ+ when δ changes from 4 to 3. Kasˇpar and co-workers15 and Dutta et al.16 suggested that the distortion of the oxygen sublattice due to the introduction of Zr4+ generates some mobile or weakly bonded oxygens, which are responsible for the improved redox properties of CexZr1-xO2. In addition, interatomic potential studies for cubic ZrO2-CeO2 solid solutions in the whole composition range have indicated that the Ce4+/Ce3+ reduction energy can be substantially lowered by the introduction of 10% of ZrO2, while it remains approximately constant for higher ZrO2 contents,15 being inconsistent with the experimental results. Despite this progress made in the field, there is no general model that can be used to rationalize the experimental observations. The following fundamental questions still remain to be answered: (i) Why does Ce1-xZrxO2 at x ) 0.5 exhibit the best OSC performance? (ii) What is the physical origin of the Zr doping effect? To tackle these questions, in this study, we carry out density functional theory (DFT) calculations to systematically investigate formation energies of O vacancy in Ce1-xZrxO2 with x ) 0, 0.25, 0.50, 0.75, and 1. We propose a simple model to understand the oxygen vacancy formation energy based on detailed analyses of DFT results. 2. Model and Calculation Method CeO2 exists in the cubic fluorite structure, which consists of a cubic array of 4-fold-coordinated oxygen ions and metal ions occupying half of the 8-fold-coordinated cationic sites (see Figure 1a). To be consistent with the work in the literature,17 the lattice substituting model was used to model the Ce1-xZrxO2: In the primitive cell containing four CeO2 units, one to three of the four Ce4+ were substituted with Zr4+ to represent Ce0.75Zr0.25O2, Ce0.5Zr0.5O2, and Ce0.25Zr0.75O2, respectively (Figure 1b-d), in which the oxygen is coordinated by 4(1 - x) Ce4+ and 4x Zr4+. For ZrO2, the cubic fluorite was utilized. Lattice constants for each of these structures were optimized. The formation energy of the O vacancy was calculated as follows: EVf )(1)/(N)(E[Ce1-xZrxO2-δ] - E[Ce1-xZrxO2] +(N)/ (2)E[O2]), in which E[Ce1-xZrxO2-δ], E[Ce1-xZrxO2], and E[O2] are the energies of Ce1-xZrxO2-δ (defective Ce1-xZrxO2), bulk

10.1021/jp900942a CCC: $40.75  2009 American Chemical Society Published on Web 05/18/2009

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Figure 1. Bulk structures of optimized stoichiometric (a) CeO2, (b) Ce0.75Zr0.25O2, (c) Ce0.5Zr0.5O2, and (d) Ce0.25Zr0.75O2 and corresponding reduced ones (e-h), respectively) viewed along [001]. The gray, red, and green balls are Ce, O, and Zr ions, respectively. The big brown ball represents the oxygen vacancy and the yellow balls are oxygen ions hidden by the top-layer ones. This notation is used throughout the paper. Isosurfaces of the spin densities that are localized are also shown (in gray). Local topological structures are labeled as Ti (i ) 1-4), which are explained in the text.

Ce1-xZrxO2, and gas-phase O2, respectively; and N is the number of removed oxygens. The calculations were performed with the GGA-PW91 functional using the VASP code.18 The project-augmented wave method was used to describe the core-valence interaction, with [He] and [Xe] cores for oxygen and cerium (zirconium), respectively. Regarding the failure of common DFT in describing the electronic and geometric structure of defective ceriabased materials, the on-site Coulomb correction was used to describe the localization of the 4f electron of Ce; that is, the so-called DFT + U19,20 in which the value of U was set to 5 eV, as suggested in other theoretical work.20 For the systems with substoichiometric oxygen, the spin-polarized calculations were carried out. We used a plane-wave cutoff energy of 500 eV and applied a 6 × 6 × 6 Monkhorst-Pack k-point mesh for the unit cell of (1 × 1 × 1) with Gaussian smearing of 0.20 eV. All internal structural parameters were relaxed until the Hellman-Feynman forces on each ion were less than 0.02 eV/ Å. Using the above setting, the lattice constant of pure ceria is calculated to be 5.49 Å, and the electronic analysis shows that, for the defective ceria with an O vacancy, a new occupied Ce 4f state that is 1.4 eV above the O 2p band edge appears between the O 2p band and unoccupied Ce 4f band, and the occupied 4f electrons are localized on two of the Ce ions around the O vacancy, agreeing well with the experimental and other theoretical results.20,21 3. Results and Discussion We first calculated the O vacancy formation energy (EVf) as a function of ZrO2 content; the results are shown in Figure 2 (red curve). It can be seen that EVf first decreases and then increases when x changes from 0 to 1.0; at x ) 0.5, Ce1-xZrxO2 exhibits the lowest formation energy of O vacancy, 0.54 eV lower compared to pure CeO2, in agreement with experimental results. To understand these results, we propose the following model; the formation of an O vacancy is decomposed into two steps: (i) removing an O while the structure is fixed; and (ii) relaxing the structure in the presence of the O vacancy. Accordingly, EVf can be written as the sum of two terms:EVf ) Ebond + Erelax, in which Ebond is the energy required to remove the oxygen atom with fixed structure of Ce1-xZrxO2-δ, and Erelax is the energy gained from the structural relaxation in the presence of the O vacancy. The variations of Ebond and Erelax as a function of ZrO2 content are shown in Figure 2 (black and

Figure 2. Variations of O vacancy formation energies,EVf, and related electrostatic (Ebond) and structural relaxation (Erelax) terms with respect to ZrO2 molar content in Ce1-xZrxO2.

blue curves, respectively). The following striking features can be seen from the figure: (i) Ebond increases approximately linearly with the ZrO2 content, indicating that doping Zr does not weaken the bond strength of O in the system; and (ii) Erelax changes according to a parabola-like curve with the minimum at x ) 0.5. These features clearly suggest that Erelax is a more dominating term than Ebond in determining the overall trends of O vacancy formation energy, since EfV possesses a shape similar to Erelax. More importantly, it shows that the distinguishing OSC of Ce0.5Zr0.5O2, in fact, results from its largest structural relaxation. It is also worth mentioning that one may combine the curves of Ebond and Erelax to estimate the variations of O vacancy formation energies around 50%: (i) in the range of 25-50%, ZrO2 molar contents, the variation of O vacancy formation energy is small, and (ii) above 50%, the O vacancy formation energy increases considerably. This is consistent with the experimental results in which Ce1-xZrxO2 with x ) ∼0.3-0.5 exhibited high OSC and was typically used. To understand features i and ii, we first calculated the Madelung potentials at the oxygen site in the Ce1-xZrxO2 solids using Ewald summation with formal charges (V formal, +4 for Zr and Ce, -2 for O) as well as Bader charges22 from selfconsistent PW91 + U calculations (V PW91); see Table 1. It is

Oxygen Vacancy Formation in Zr-Doped CeO2

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TABLE 1: The Bader Charges (e) of O, Ce, and Zr and Madelung Potentials (V PW91 and V formal) (V) at the Oxygen Site in Various Ce1-xZrxO2 Bulk Structures, and Calculated Ebond Terms X

O

Ce

0 0.25 0.50 0.75 1

-1.14 -1.22 -1.23 -1.24 -1.30

+2.28 +2.40 +2.38 +2.30

Zr

V PW91

V formal

Ebond (eV)

+2.56 +2.52 +2.54 +2.61

12.15 13.22 13.48 13.86 14.84

21.36 21.62 21.94 22.34 22.78

4.39 4.59 4.98 5.45 5.87

clear from the table that both V formal and V PW91 monotonically increase as ZrO2 content changes from 0 to 1. In fact, there are good linear correlations between Ebond and the two Madelung potentials (see Figure 3a), indicating that the first term, Ebond, is electrostatic in nature. Table 1 also shows that Zr always has higher effective charges compared to Ce in Ce1-xZrxO2 and, consequently, exhibits stronger electrostatic interaction toward O2-. Thus, in the composite oxides with increasing ZrO2 content, more Zr4+-O2- bonds need to be broken to remove an O anion, giving rise to larger Ebond terms. After an O atom is removed from the oxide matrix, the surrounding atoms near the vacancy will relax to compensate for the missing bonds. The energy gain in this process is reflected in the second term in our model, the relaxation energy (Erelax). It was found from calculations that the relaxation of Ce and Zr cations is much smaller than that of O ions. Thus, to shed light on the dependence of Erelax, we calculated the relaxation of the six nearest O ions near the O vacancy in Ce1-xZrxO2-δ by measuring the root-mean-square (rms) of displacements:

∑ 6

rRMS )

1 (r - ri0)2 6 i)1 i

(1)

where ri0and ri are the positions of the surrounding O ions before and after relaxation, respectively. It was found that Erelax linearly correlates with rrms (R2 ) 0.98), as shown in Figure 3b, indicating that the structural relaxation can be quantitatively measured by rrms, which will allow us to further understand the structural relaxation. Careful examination of O2- displacements reveals that rrms is determined mainly by the local topological structures, as described as follows: (i) In CeO2, O2- is bonded to four Ce cations (labeled as T1 in Figure 1e). As an O vacancy is formed beside T1, the two excess electrons in the presence of an O vacancy will localize in the 4f orbitals of two of the

four Ce cations around the O vacancy (the isosurface of the corresponding spin density is shown in Figure 1e); hence, forming two Ce3+. Ce3+ has a larger radius and weaker electrostatic interaction with O2- compared to Ce4+. Consequently, the asymmetric interaction facilitates the nearest O2in T1 to move toward the O vacancy and gain the relaxation energy. (ii) For Ce0.75Zr0.25O2 (T2 in Figure 1f), the presence of one Zr4+ induces a larger displacement of the surrounding O2to compensate for the missing bonds as the result of the stronger electrostatic interaction between the Zr4+ and O2-. (iii) In Ce0.5Zr0.5O2 (T3 in Figure 1g), there are two Zr4+ near the O vacancy. The neighboring O2- then moves considerably toward the two Zr4+, leading to an even larger displacement than that in T2. (iv) For Ce0.25Zr0.75O2 (T4 in Figure 1h), one O2- is surrounded by three Zr4+ and one Ce4+. Compared to that of Ce0.5Zr0.5O2, O2- in T4 also moves toward the two Zr4+ but with a smaller displacement. This is because the third Zr4+ is also pulling the O2- but in the opposite direction. (v) In ZrO2, O2is symmetrically surrounded by four Zr4+ (T5, not shown), and naturally, the displacement in this structure is even smaller than that in Ce0.25Zr0.75O2. From the above discussion, we can see that at low Zr concentrations, the movement of neighboring O2- around the O vacancy is enhanced with the increasing number of stronger Zr4+-O2- bonds. In contrast, as the content of Zr4+ further increases, extra Zr4+ will pull O2- in the opposite direction, leading to smaller O2- displacements. Specifically, O2- in T3 structure (surrounded by two Ce and two Zr cations) possesses the largest displacement, and it can be expected that a good OSC material should contain as many T3 structures as possible. The determination of the crucial role of relaxation energy in our model can help us to understand a broader doping effect. Using GGA + U calculations, Andersson et al.21 found that for dopants of M (M ) Zr, Hf, Ti, and Th), there is a linear correlation between the formation energies of the O vacancy in doped ceria and the ionic radii of M4+. We may use our model to quantitatively elucidate the physical origin of the existence of the linear correlation. We calculated the O vacancy formation energies and the corresponding relaxation energies for Ce0.75M0.25O2 (M ) Zr, Hf, Ti, Th). It was found that the formation energies of O vacancies are, indeed, largely determined by the structural relaxation. More interestingly, the relaxation energies were found to correlate linearly with the ionic radius of the metal cation doped (R2 ) 0.97), as shown in Figure 3c. This result can be understood as follows. They are irreducible M4+ and are accommodated in the same local geometries. Thus, the ionic radii of these M4+ may affect the O vacancy formation in a similar way: the smaller the ionic radius, the larger the

Figure 3. (a) Correlations between Madelung potentials at the oxygen site and the bond energy terms, Ebond, and (b) the dependence of relaxation energies after the oxygen removal on the displacements of the nearest O2- around the oxygen vacancy for Ce1-xZrxO2 (x ) 0, 0,25, 0.50, 0.75, and 1). (c) Correlation between relaxation energies and ionic radius of dopants Hf4+, Zr4+, Ti4+, and Th4+.

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space in which O can move, leading to an increase in O displacement and structural relaxation. Therefore, the effect of ionic radii of different dopants may be understood from the structural relaxation proposed in our model. It should be noted that there are many different types of solids, and our model may be only applicable to some of them. However, considering that CeO2-ZrO2 solid solutions are the most important ceriabased materials, we believe that the decomposition model proposed to understand O vacancy formation energies in this work may be of general interest in the field.

Wang et al.

References and Notes

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JP900942A

4. Conclusions In summary, by calculating, for the first time, the formation energies of O vacancy in a series of Ce1-xZrxO2 materials using DFT within the GGA + U framework, we found that the oxides with a content of 50% ZrO2 possess the lowest formation energy of the O vacancy. On the basis of comprehensive analyses, we proposed a model to understand the O vacancy formation by decomposing it into two terms: the bond energy (Ebond) and relaxation energy (Erelax). The physical origins of the two terms are discussed. It is shown that Erelax is the dominating term and is determined by the local topological structures around the O vacancy. Using this model, we are able to explain why ceria with 50% ZrO2 exhibits the best OSC performance. This novel interpretation sheds new light on our basic understanding of doping effects on ceria, and it may also have some significant implications for other systems. Acknowledgment. This work is financially supported by the National Basic Research Program (2004CB719500), International Science and Technology Cooperation Program (2006DFA42740), the 111 Project (B08021), and National Natural Science Foundation (20703017, 20601008) of China. H.-F.W. also gratefully thanks the China Scholarship Council for a Joint Ph.D. studentship with QUB.