Surface reduction properties of ceria–zirconia solid solutions: a first-principles study

Abstract

Based on the density functional theory (DFT), the reduction properties of Ce_1−xZr_xO₂ (110) surfaces were systematically calculated using CO as a probe for thermodynamic study, and a large supercell was applied to build the whole composition range (x = 0.125, 0.250, 0.375, 0.500, 0.625, 0.750, 0.875). From the calculated energy barriers of CO oxidation by lattice oxygen, we found that composition Ce_0.875Zr_0.125O₂ exhibited the most promising catalytic effectiveness with the lowest activation energy of 0.899 eV. Moreover, the active surface O_3c ions coordinated by two Zr ions and one Ce ion were facilely released from their bulk positions than the O_3c ions surrounded by two Ce ions and one Zr ion on Ce_0.625Zr_0.375O₂, Ce_0.500Zr_0.500O₂, and Ce_0.375Zr_0.625O₂ (110) surfaces. This difference could be explained by the binding strength of O_3c with different neighboring cations.

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1. Introduction

Ceria–zirconia (Ce_1−xZr_xO₂) solid solutions exhibit superior performance as heterogeneous catalytic materials due to its good thermal stability,^1,2 excellent oxygen storage/release capacity and reducibility.^3–5 In the last few decades, Ce_1−xZr_xO₂ has been extensively used as an active component in three-way catalysts (TWCs) to expand the air-to-fuel ratio operating window, ensuring the effective elimination of carbon monoxide (CO), nitrogen oxides (NO_x), and hydrocarbons (HCs) during engine operation.⁶ Besides, water gas shift reaction,⁷ NH₃ selective catalytic reduction,⁸ catalytic oxidation of volatile organic compounds (VOCs)⁹ and various catalytic reactions also can be promoted by Ce_1−xZr_xO₂.

Ce_1−xZr_xO₂ solid solutions with different compositions result in different catalytic performance and surface properties. Great efforts have been made to investigate the most promising Ce_1−xZr_xO₂ compositions for OSC,^10–13 which is closely related to the reduction behavior. Madier et al.¹⁰ observed that Ce_0.63Zr_0.37O₂ had the maximum CO uptake across the whole composition range, with a dynamic OSC of 219 μmol O per g at 400 °C. Boaro et al.¹¹ proposed that Ce_1−xZr_xO₂ with 0.2 < x < 0.5 showed an increased CO oxidation activity under cycling feed-stream conditions. For heterogeneous catalytic reactions, the most important is the surface redox properties.¹⁴ To obtain the optimum composition (Ce/Zr ratio), evaluation of the surface reducibility of Ce_1−xZr_xO₂, especially the Ce⁴⁺/Ce³⁺ redox behavior is necessary.

Oxygen vacancy formation energies at surfaces have been calculated using the DFT + U (U = 5.0 eV) method, by comparing the formation energies of CeO₂ (110) surface (2.30 eV) and Ce_0.75Zr_0.25O₂ (110) surface (0.94 eV);¹⁵ Zr-doping (25% in this work) dramatically improved the reduction properties of ceria. In contrast, Zr-doping in CeO₂ (111) surface and ceria bulk only lowered the formation energies by 0.52 eV (ref. 16) and 0.62 eV,¹⁷ respectively. To explain the lowering of the surface reduction energy, the electronic structure was obtained via the density of states (DOS) and partial charge density distribution. Yang et al.¹⁵ found that for the Ce_0.75Zr_0.25O_2−x (110) slab, the excess electrons localized on a surface of Ce-ion and on a subsurface of Ce-ion were stabilized by the crystal potential and occupied the gap states lower in energy compared to the CeO_2−x (110) surface. Balducci et al.¹⁸ suggested that the smaller Zr dopants removed the strain caused by the increase in the ionic size when Ce⁴⁺ changed to Ce³⁺, which is responsible for the improvement in the reducibility.

In the present work, we explored the CO oxidation mechanisms and energetics on Ce_1−xZr_xO₂ (110) surfaces, using periodic DFT computation. The catalytic models were built from a 2 × 2 × 2 supercell to cover the whole composition range (x = 0.125, 0.250, 0.375, 0.500, 0.625, 0.750, 0.875). The main focus of this paper is to determine how the Ce/Zr ratio affects the surface reducibility of Ce_1−xZr_xO₂, which has not been systematically calculated. Furthermore, low-temperature oxidation of CO is of practical importance for pollution control in many industrial processes, such as lowering automotive emissions.^19,20 Our investigation provides an atomic-scale insight for the design of efficient and economical heterogeneous catalysts.

2. Computational details

2.1. Computational methods

In this study, all geometric optimization and calculations were performed by using the DMol³ software package in Material Studio,^21,22 based on the periodic DFT method. The generalized gradient approximation (GGA) with Perdew–Burke–Ernzerhof (PBE)²³ was implemented as the exchange–correlation functional. The double numerical plus d-function (DND) basis set was used to optimize all spin unrestricted structures. The Ce (4f¹, 5s², 5p⁶, 5d¹, 6s²) and Zr (4s², 4p⁶, 4d², 5s²) electrons were treated as valence electrons using the effective core potential (ECP) method.²⁴ The electrons of O, C and N atoms were treated using the all electron method. Specifically, a Fermi smearing of 0.005 Ha and an orbital cutoff of 5.0 Å were used to improve the computational performance. A grid of 1 × 1 × 1 Monkhorst–Pack k-points was applied to perform integration in the first Brillouin zone.²⁵ The SCF tolerance was employed to 1.0 × 10⁻⁵ Ha, and then the convergence criteria of maximum energy change, maximum force, and maximum displacement were set as 2.0 × 10⁻⁵ Ha, 0.004 Ha Å⁻¹, and 0.005 Å, respectively.

The adsorption energy (E_ads) of the adsorbate was defined as follows:

E_ads = E_{(substrate+adsorbate)} − E_(substrate) − E_(adsorbate) (1)

where E_{(substrate+adsorbate)}, E_(substrate) and E_(adsorbate) represent the total energies of the substrate–adsorbate system, the substrate and adsorbate, respectively. The more negative E_ads, the more strongly the adsorbate binds with the substrate. Linear synchronous transit and quadratic synchronous transit (LST/QST) method^26,27 was applied to isolate the transition states (TS) and calculated the corresponding activation barriers (E_a). The transition state configurations were identified by the vibrational analysis to confirm a single imaginary frequency corresponding to the reaction mode. The reaction energy (ΔE) and activation barrier energy (E_a) were defined as follows:

ΔE = E_FS − E_IS (2)

E_a = E_TS − E_IS (3)

where E_IS, E_TS and E_FS represent the total energies of initial state (IS), transition state (TS), and final state (FS), respectively.

2.2. Computational models

Ceria is a cubic fluorite structure with a space group Fm3̄m; the optimized lattice parameter was 5.478 Å, which is in good agreement with the experimental result of 5.411 Å.²⁸ Moreover, cubic zirconia (c-ZrO₂, the Fm3̄m space group) is also attributed to fluorite oxides. CeO₂ and c-ZrO₂ are interesting as the limiting forms of ceria–zirconia. Our calculated lattice constant for c-ZrO₂ was 5.112 Å, the corresponding experimental value was 5.090 Å.²⁹

The computational model in this study was a 2 × 2 × 2 supercell with 96-atom built from a conventional 12-atom unit cell of bulk CeO₂. To be consistent with the models studied by Wang et al.,^12,30 the lattice substituting model was used to model Ce_1−xZr_xO₂. In the supercell, 4, 8, 12, 16, 20, 24 and 28 Zr-doping atoms were introduced to replace Ce atoms to represent stoichiometric Ce_0.875Zr_0.125O₂, Ce_0.750Zr_0.250O₂, Ce_0.625Zr_0.375O₂, Ce_0.500Zr_0.500O₂, Ce_0.375Zr_0.625O₂, Ce_0.250Zr_0.750O₂, and Ce_0.125Zr_0.875O₂ bulk (see Fig. 1), respectively. Besides, Ce_1−xZr_xO₂ (110) surfaces were cleaved due to its lower surface energy and Ce⁴⁺/Ce³⁺ reduction energy.³¹ A 15 Å vacuum thickness was applied to eliminate slab–slab interactions. The Ce_1−xZr_xO₂ (110) slabs consist of four atomic layers with the bottom two layers kept fixed in their bulk positions and the others were relaxed.

Fig. 1 The 96-atom 2 × 2 × 2 supercell models of stoichiometric (a) Ce_0.875Zr_0.125O₂, (b) Ce_0.750Zr_0.250O₂, (c) Ce_0.625Zr_0.375O₂, (d) Ce_0.500Zr_0.500O₂, (e) Ce_0.375Zr_0.625O₂, (f) Ce_0.250Zr_0.750O₂ and (g) Ce_0.125Zr_0.875O₂. Red, ivory and cyan spheres represent the O, Ce and Zr atoms, respectively.

The DFT calculation with a Hubbard U correction (DFT + U) was applied to describe the electronic properties of CeO₂ and ZrO₂, where U = 5 eV was suggested to be proper for modeling on stoichiometric and reduced CeO₂ and ZrO₂ surfaces.^15,32 However, previous researches indicated that plain DFT calculations could provide a reasonable prediction of reduction energies, even better than that from DFT + U.^33,34 To ascertain the importance of the U parameter, we have calculated the oxygen vacancy formation energies on Ce_0.875Zr_0.125O₂ (110) surface with U = 5 eV (0.472 eV) and without incorporating U (0.476 eV). The vacancy formation energy without incorporating U was within 1% of U = 5 eV ones. Hence, the DFT + U method was not considered in the current work.

3. Results

3.1. CO oxidation on Ce_0.875Zr_0.125O₂ (110) surface

Conserving Ce_0.875Zr_0.125O₂ (110) surface stoichiometry with bulk, top surface layer and the subsurface layer of the slab contained sixteen Ce⁴⁺, two of the top surface layer Ce⁴⁺ were replaced with Zr⁴⁺. To better understand the catalytic mechanism, the adsorption behaviors of CO gas molecules on Ce_0.875Zr_0.125O₂ (110) surface were carefully discussed. We identified nine adsorption sites (Fig. S1(a)†): (1) the top site of Zr (Zr_T); (2) the top site of Ce (Ce_T); (3) the top site of O (O_T1, O_T2); (4) the 4-fold O-hollow site (O_H1, O_H2); (5) the bridge site between two O atoms (O_b1, O_b2, O_b3). All the optimized configurations were illustrated in Fig. S1† and the calculated adsorption energies of CO on Ce_0.875Zr_0.125O₂ (110) surface were summarized in Table S1.† We found that the adsorption of CO on the top site of Zr (Fig. S1(b)†) was the most stable configuration with an adsorption energy of −0.569 eV. Moreover, Zr-doping could increase the binding energy of CO with an interface, by comparing the calculated binding energy of Zr-doped ceria (≈−0.4 eV) and ceria (≈−0.2 eV).^34,35

It is widely believed^36,37 that the detailed mechanism of CO oxidation on CeO₂ surface through the Mars–van Krevelen (MvK) mechanism,³⁸ in which CO extracts a surface lattice oxygen to form CO₂ and leaves behind an oxygen vacancy (O_V), and then gas phase O₂ replenishes the oxygen vacancy site to complete the catalytic cycle. For the reaction mechanism of a single CO interacting with one lattice O of Ce_0.875Zr_0.125O₂ (110) surface, the calculated energy profile and structure models of the reactant, transition state and product were presented in Fig. 2.

Fig. 2 Calculated energy profile and structures of key states of CO oxidation by lattice oxygen on Ce_0.875Zr_0.125O₂ (110) surface. Gray spheres represent the C atoms.

We took the state with CO gas molecule adsorbed at Zr_T site (E_ads = −0.569 eV) as the initial state (IS), the distance between C atom and surface lattice O was 2.559 Å. Subsequently, the CO molecule directly incorporated a surface O from the gas phase following the so-called Eley–Rideal (ER) mechanism. The energy barrier for this process was 0.899 eV, this result was a little lower than that of CO oxidation on the Pd₁/CeO₂ (110) surface (0.954 eV),³⁹ indicating that the catalytic activity of ceria–zirconia solid solutions was comparable with traditional ceria-based single-atom catalyst. In the final state (FS), gas phase CO₂ formed above the Ce_0.875Zr_0.125O₂ (110) surface containing an oxygen vacancy, meanwhile, the surface oxygen anion neighboring the vacancy moved toward the Ce–Zr bridge site by about 1.281 Å.

3.2. CO oxidation on Ce_0.750Zr_0.250O₂ (110) surface

On the Ce_0.750Zr_0.250O₂ (110) surface, four of the top surface layer Ce atoms were replaced with Zr (Ce_0.750Zr_0.250O₂, see Fig. 3). Based on the adsorption behaviors of CO on Ce_0.875Zr_0.125O₂ (110) surface as discussed above, we also considered CO adsorbtion at the Zr_T site as the initial state for CO oxidation on Ce_1−xZr_xO₂ (x = 0.250, 0.375, 0.500, 0.625, 0.750, 0.875) (110) surfaces. As shown in Fig. 3 (IS), CO combined with a Zr atom, the distance was determined to be 2.562 Å and the binding energy was −0.600 eV. In the transition state (TS, Fig. 3), adsorbed CO molecule migrated to a lattice O and the distance decreased to 2.103 Å. This process needed to overcome an activation barrier of 1.555 eV and was exothermic by 2.367 eV. With the formation of CO₂ (FS, Fig. 3), the neighboring lattice O moved to the Ce–Zr bridge site, the bond of Ce–O, and Zr–O were 2.485 Å and 2.048 Å, respectively.

Fig. 3 Calculated energy profile and structures of key states of CO oxidation by lattice oxygen on Ce_0.750Zr_0.250O₂ (110) surface.

3.3. CO oxidation on Ce_0.625Zr_0.375O₂ and Ce_0.500Zr_0.500O₂ (110) surfaces

On the Ce_0.625Zr_0.375O₂ (110) surface, four of the top surface layer Ce atoms and two of the subsurface layer Ce atoms were replaced with Zr (Ce_0.625Zr_0.375O₂, see Fig. 4). In this case, four surface lattice oxygen neighboring Zr_T sites were not all equivalent: three of these oxygen (O_A) bonded with two Ce⁴⁺ and one Zr⁴⁺, while one of the oxygen (O_B) bonded with two Zr⁴⁺ and one Ce⁴⁺. There are two pathways for CO oxidation with different surface lattice oxygen; the corresponding energy profile and structure models are illustrated in Fig. 4. From the initial state (IS), CO adsorbed at the Zr_T site of Ce_0.625Zr_0.375O₂ (110) surface, the adsorption energy was calculated to be −0.607 eV. Then, CO extracted O_A via TS1; this process needed a higher energy barrier of 2.239 eV and the reaction energy was −2.216 eV. Alternatively, CO might combine with O_B, going through another transition state (TS2) with a smaller energy barrier of 1.175 eV.

Fig. 4 Calculated energy profile and structures of key states of CO oxidation by lattice oxygen on Ce_0.625Zr_0.375O₂ (110) surface.

On the Ce_0.500Zr_0.500O₂ (110) surface, four of the top surface layer Ce atoms and four of the subsurface layer Ce atoms were replaced with Zr (Ce_0.500Zr_0.500O₂, see Fig. S2†). According to our calculations, the detailed mechanisms of CO oxidation on the Ce_0.500Zr_0.500O₂ (110) surface were similar to that on the Ce_0.625Zr_0.375O₂ (110) surface, as shown in Fig. S2.†

3.4. CO oxidation on Ce_0.375Zr_0.625O₂, Ce_0.250Zr_0.750O₂ and Ce_0.125Zr_0.875O₂ (110) surfaces

On the Ce_0.375Zr_0.625O₂ (110) surface, four of the top surface layer Ce atoms and six of the subsurface layer Ce atoms were replaced with Zr (Ce_0.375Zr_0.625O₂, see Fig. 5). Two possible reaction routes were estimated based on the two types of surface lattice oxygens (O_A and O_B) as mentioned above. For the first route, the migration of adsorbed CO species (−0.521 eV, IS, Fig. 5) toward O_A led to the formation of a bent CO₂ species (IM1, Fig. 5) via TS1 (E_a = 1.602 eV, Fig. 5); IM1 was calculated to be 0.301 eV, more stable than the IS. Then IM1 evolved to the final state (FS1, Fig. 5) through an almost barrierless process. The second route was determined to be the same as that of the first route.

Fig. 5 Calculated energy profile and structures of key states of CO oxidation by lattice oxygen on Ce_0.375Zr_0.625O₂ (110) surface.

On the Ce_0.250Zr_0.750O₂ (110) surface, four of the top surface layer Ce atoms and eight of the subsurface layer Ce atoms were replaced with Zr (Ce_0.250Zr_0.750O₂, see Fig. S3†). On the Ce_0.125Zr_0.875O₂ (110) surface, six of the top surface layer Ce atoms and eight of the subsurface layer Ce atoms were replaced with Zr (Ce_0.125Zr_0.875O₂, see Fig. S4†). Calculated energy profile and structure models were presented in Fig. S3 and S4† for CO oxidation on Ce_0.250Zr_0.750O₂ and Ce_0.125Zr_0.875O₂ (110) surfaces, respectively.

4. Discussion

In this work, the adsorption energies and barrier energies of CO oxidation on various Ce_1−xZr_xO₂ (110) surfaces were systematically studied using the DFT method. These calculation results provide some insights into the surface reducibility of Ce_1−xZr_xO₂ toward CO oxidation. From the adsorption behaviors of CO on the Ce_0.875Zr_0.125O₂ (110) surface, we found that Zr_T was the most favorable active site owing to the maximum adsorption energy. Besides, according to the adsorption energies of CO on the CeO₂ (110) surface (E_ads ≈ −0.2 eV)^34,35 and ZrO₂ (110) surface (E_ads ≈ −0.6 eV),⁴⁰ it also could be concluded that CO preferred to interact with Zr atoms and adsorb on the top site of Zr on Ce_1−xZr_xO₂ (110) surfaces. However, it is noteworthy that CO adsorption on Ce_1−xZr_xO₂ (110) surfaces were still rather weak (E_ads ≈ −0.6 eV), indicating that the feasible CO oxidation mechanism was gas-phase CO molecule directly extracting surface lattice oxygen following the so-called Eley–Rideal (ER) mechanism,^36,37 exactly as CO oxidation on the CeO₂ (110) and (111) surfaces.³⁵

As shown in Fig. 4, S2,† and 5, Ce_0.625Zr_0.375O₂, Ce_0.500Zr_0.500O₂, and Ce_0.375Zr_0.625O₂ (110) surfaces contained two types of lattice oxygens, the CO oxidation activity of these oxygens were quite different. In particular, the activation barriers of CO reacted with O_3c ions coordinated by two Zr ions and one Ce ion were relatively lower than O_3c ions surrounded by two Ce ions and one Zr ion. In the previous work, different types of surface O ions were also found on the Ce_0.75Zr_0.25O₂ (111) surface, and the vacancy formation energy for the surface O_3c surrounded by three Ce neighbors was higher than the surface O_3c coordinated by two Ce ions and one Zr ion.¹⁶ We interpreted that the binding strength of O_3c with neighboring cations caused the difference of O_3c reactivity. Considering that the size of Ce ion would increase when Ce⁴⁺ changed to Ce³⁺, O_3c ions coordinated by smaller Zr ion might promote the reduction process.¹⁸

We presented the activation barrier energies of CO oxidation on various Ce_1−xZr_xO₂ (110) surfaces in Fig. 6. As we all know, the occurrence of redox reaction through a low energy barrier process was thermodynamically favorable. Therefore, energy barriers of 1.175 eV, 1.281 eV and 1.340 eV for CO oxidation on Ce_0.625Zr_0.375O₂, Ce_0.500Zr_0.500O₂ and Ce_0.375Zr_0.625O₂ (110) surfaces were used to compare with others. Among all the compositions, the Ce_0.875Zr_0.125O₂ (110) surface exhibited the most remarkable catalytic effectiveness, with the lowest energy barrier of 0.899 eV. This result was consistent with the experimental value reported by Piumetti et al.⁴¹ that the Ce_0.9Zr_0.1O₂ catalyst shown the highest CO oxidation activity (Zr-content was in the range of 10–30%). Trovarelli et al.³ observed that dynamic OSC of Ce_1−xZr_xO₂ showed a monotonic increase with increasing Ce-content and the optimum composition was Ce_0.9Zr_0.1O₂. However, these results were at odds with we mentioned above, composition of Ce_1−xZr_xO₂ with 0.2 < x < 0.5 possessed an increased catalytic activity.^10,11,42,43 There is still an intense scientific debate on the optimum Ce/Zr composition for catalytic materials.

Fig. 6 Activation energies for CO oxidation by lattice oxygen on Ce_1−xZr_xO₂ (x = 0.125, 0.250, 0.375, 0.500, 0.625, 0.750, 0.875) (110) surfaces.

Finally, we completed the overall catalytic cycle of CO oxidation on the optimum Ce_0.875Zr_0.125O₂ (110) surface, which focused on the explanation of the gas-phase O₂ diffusion through the catalyst instead of oxygen-ion diffusion within the lattice. As shown in Fig. 7, following the first gas-phase CO₂ and one O_V formation (IM1, Fig. 7) via TS1 (Fig. 7, the same as in Fig. 2), the CO₂ desorbed from the surface (IM2, Fig. 7) overcoming 0.480 eV energy. Subsequently, O₂ adsorbed on the O_V site (IM3, Fig. 7), and then, the second CO molecule bound with the adsorbed O₂ to form a coadsorption configuration IM4 (Fig. 7), with the binding energy of −0.819 eV, followed by CO approaching the upper O of the adsorbed O₂ to form the second CO₂ molecule (IM5, Fig. 7) via TS2 (Fig. 7). The energy barrier for the second CO₂ formation was 0.672 eV, dramatically lower than that of the first CO₂ formation (0.899 eV). It is obvious that CO oxidation by surface oxygen was the elementary step in the overall catalytic cycle.

Fig. 7 Calculated energy profile and structures of key states for the catalytic cycle of CO oxidation on Ce_0.875Zr_0.125O₂ (110) surface.

5. Conclusions

In the current work, DFT method was performed to investigate the reduction properties of Ce_1−xZr_xO₂ (x = 0.125, 0.250, 0.375, 0.500, 0.625, 0.750, 0.875) (110) surfaces, using CO as a probe for the thermodynamic study. For the details of the reaction mechanism, CO preferred to adsorb on the Zr_T site with rather weak binding energies (≈−0.6 eV), thus gas-phase CO directly extracted surface lattice O to form CO₂ and surface O_V following the Eley–Rideal (ER) mechanism. From the calculated energy barriers, we proposed that Ce_0.875Zr_0.125O₂ was the optimum composition to efficiently release surface lattice O. In addition, the occurrence of surface O_V had significant effects on catalytic processes.^44,45 Especially, two different types of active O_3c (O_A and O_B) existed on Ce_0.625Zr_0.375O₂, Ce_0.500Zr_0.500O₂ and Ce_0.375Zr_0.625O₂ (110) surface, the CO oxidation activity of O_B was significantly higher than that of O_A with the energy barriers of 1.175 < 2.239 eV, 1.281 < 2.224 eV and 1.340 < 1.602 eV on Ce_0.625Zr_0.375O₂, Ce_0.500Zr_0.500O₂ and Ce_0.375Zr_0.625O₂ (110) surface, respectively. We explained that the binding strength of active O_3c with neighboring cations causes the difference, and since the ionic size increased when Ce⁴⁺ changed to Ce³⁺ and O_3c ions coordinated by smaller Zr ions may facilitate the reduction process.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

This work is supported by National Natural Science Foundation of China (21607011, 21976109), Key Research and Development Project of Shandong Province (2019GSF109021, 2019GSF109037), Natural Science Foundation of Shandong Province (ZR2018MB043), the Fundamental Research Funds of Shandong University (2018JC027).

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c9ra09550k

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