Mechanisms of temperature-dependent oxygen absorption/release and appearance of intermediate phase in κ-Ce2Zr2O8: study based on oxygen vacancy formation energy computations

This study clarified the mechanisms of the temperature-dependent oxygen absorption/release properties and appearance of the intermediate phase for κ-Ce2Zr2O8, which is known to have a high oxygen storage/release capacity (OSC). First-principle computations revealed that the vacancy formation energies depend on the number of vacancies and can be categorized into two groups: low-energy and high-energy. The intermediate phase observed experimentally was assigned to the state after all the oxygen vacancies in the low-energy group were formed. We also found that the mechanism of the improved OSC performance by Ti substitution could be explained in terms of the vacancy formation energies.


Introduction
Oxygen storage/release materials have been actively investigated in a wide variety of elds, including environmental protection 1 and energy conversion. 2 In these elds, ceria (CeO 2 )-based materials are known to have high oxygen storage/release capacities (OSCs) and are used in industrial applications such as automobile three-way catalysts, [3][4][5] water-gas shi reactions, 6 and solid oxide fuel cells. 7 In automobile three-way catalysts, ceria-based materials are used as oxygen storage/release materials to adequately control the oxygen concentration on the catalyst surfaces by storing oxygen in an oxidized atmosphere and releasing it under a reduced atmosphere. 3,5,8 Among the ceria-based materials, cation-ordered Ce 2 Zr 2 O 8 (k-Ce 2 Zr 2 O 8 ) has been reported to have an outstanding OSC, where almost all the Ce atoms contribute to the redox conversion. [9][10][11] The mechanism of the high OSC performance of k-Ce 2 Zr 2 O 8 has been studied both experimentally 12,13 and theoretically. 14,15 These studies have claried that oxygen vacancies are formed at oxygen sites coordinated only with Zr atoms, even though the binding strength of Zr 4+ -O 2À is usually stronger than that of Ce 4+ -O 2À . The oxygen vacancy formation energy is known to be dominated by the structural relaxations that occur aer the formation of oxygen vacancies. In k-Ce 2 Zr 2 O 8 , when the Zr 4+ -O 2À bond is broken and an oxygen vacancy is formed, the remaining oxygen atoms move toward the vacancy sites as a result of the driving force caused by the differences in the electrostatic forces and ionic radii of Zr and Ce. The oxygen vacancies at the Zr sites are stabilized by this relaxation. Simultaneously, the valency of Zr is retained at 4+ by electron transfer via the redox reaction of Ce from 4+ to 3+. This electron transfer prevents the signicant movement of Zr atoms, and therefore, the energetically unfavorable lattice distortion is minimized. This latter feature enables the topotactic transformation of k-Ce 2 Zr 2 O 8 into Ce 2 Zr 2 O 7 pyrochlore by maximizing the locality of the structural relaxation. 14 In theoretical studies, the oxygen vacancy formation energies were examined using density functional theory (DFT) calculations and used to understand the atomic-scale structural changes and oxygen vacancy formation properties. 14 18,19 showed that this OSC enhancement could be explained by the formation of weakly bound oxygen atoms. 17 However, despite the efforts made in this eld, the mechanisms of the appearance of the intermediate phase and the two-step oxygen absorption/release behavior have not yet been fully explained. The mechanism of the OSC enhancement by Ti substitution is also unclear.
In this study, we systematically investigated the formation of oxygen vacancies from a fully oxidized state (k-Ce 2 Zr 2 O 8 ) to a fully reduced state (Ce 2 Zr 2 O 7 pyrochlore) using DFT, including the Hubbard-U term (DFT+U). 20,21 The same method was applied to Ti-substituted systems.
The systematic computations of the oxygen vacancy formation energies revealed that they depended on the number of vacancies and could be categorized into two groups: low-and high-energy. The intermediate phase obtained experimentally was assigned to the state aer all the oxygen vacancies in the low-energy group were formed. The theoretical conclusion was veried by comparing the simulated X-ray diffraction (XRD) spectra with the experimental results. This new nding reasonably explained the two-step oxygen absorption/release behavior observed in the experiments. The OSC enhancement at low temperatures by Ti substitution was also reasonably explained by the oxygen vacancy formation energy computations.

First-principle computations
The periodic DFT method was used for the electronic structure computations. The computations were performed using the vienna ab initio simulation package (VASP). 22,23 The generalized gradient approximation (GGA) of the Perdew-Burke-Ernzerhof (PBE) functional 24 was used to describe the exchange-correlation interaction of electrons. The projector-augmented wave (PAW) method 25 was used to describe the core-valence interaction. GGA cannot accurately describe the electronic structure of reduced ceria-based materials because of the presence of the selfinteraction error. 20,26-28 Therefore, an on-site Coulomb correction was included using the DFT+U method 29 to properly incorporate the behavior of Ce 4f electrons. The previous study showed that signicant delocalisation because of the self-interaction error that remained for U < 5 eV, while the results were converged for U $ 5 eV where the localisation was found to be independent of the choice of U. 20,26 The similar oxygen vacancy formation energies of CeO 2 have been reported for U greater than 5 eV (3.15, 3.19, 3.20 eV for U ¼ 5, 6.1, 6.3 eV, respectively). 15,20,26 Therefore, the value of U was set to 5 eV in this study. Spinpolarized calculations were performed to correctly treat the sub-stoichiometric oxygen. The cut-off energy of the plane wave was set to 400 eV, which has been validated for the CeZrO 2 system. 15 The k-point sampling was performed using a 2 Â 2 Â 2 Monkhorst-Pack mesh, except for the calculation of gas-phase oxygen molecules, which was performed using the G point and a cubic unit cell with 10Å per side. Both the lattice and atomic positions were fully relaxed to obtain a stable structure. No symmetries were applied to the structural optimization. To investigate the OSC mechanism in detail, Bader charge analysis was performed using the code of Henkelman et al. 30

Model systems
The 96 atom super cell (Ce 16  To model the Ti-substituted system, we selected a Ce 16 Ti 2 -Zr 14 O 64 system. The Ti cation ratio of this system (6.25 mol%) was close to the composition that exhibited a signicant OSC improvement in an experiment (9.7 mol%). 17 A Ti-substituted system was experimentally conrmed to have a cation-ordered structure. 17 The preferential vacancy formation sites were considered to be the same as those in the k-Ce 2 Zr 2 O 8 system. The formation of oxygen vacancies was expected to be activated by Ti substitution because the Ti-O bond is weaker than the Zr-O bond as a result of the greater electronegativity of Ti 4+ (the electronegativities estimated by the empirical model 31 were 1.73 and 1.61 for Ti 4+ and Zr 4+ , respectively). Therefore, 8 O b sites were chosen as vacancy formation sites. The remaining task was to determine the Ti substitution sites.
Several combinations of Zr sites can be replaced by Ti atoms. We examined the calculated total energies of all the symmetrically independent combinations of Ti substitution sites to determine the most stable combination (see ESI † for the calculation result). This examination indicated that in the most stable state, with two Ti substitutions, the two substituted Ti atoms were adjacent to each other (see Fig. 2). Because the ionic radius of Ti 4+ is smaller than that of Zr 4+ (Zr 4+ : 0.84Å, Ti 4+ : 0.74 A), 32 the substitution caused a structure distortion around the substituted sites. This distortion could be localized using the conguration shown in Fig. 2 because the induced strain could be cancelled by adjacent substituted Ti atoms. This was considered to be the reason that two substituted Ti atoms energetically preferred the adjacent substitution sites. The oxygen vacancy formation energies of Ce 16 Ti 2 Zr 14 O 64 were computed using this atomic conguration.

Oxygen vacancy formation energy
The oxygen vacancy formation energy, E f v , relative to the gasphase O 2 molecule was computed using the following equation:  Fig. 1). Although all the O b atoms were symmetrically equivalent for N ¼ 1, some of the remaining O b atoms became inequivalent aer the vacancy formation. In this study, the oxygen vacancy formation energies were examined for all symmetrically inequivalent combinations of O b sites, and the most stable combinations were selected for E f v (N). In the case of Ce 16 Ti 2 Zr 14 O 64 , the O b atoms, some of which were coordinated to both Zr and Ti atoms, were not symmetrically equivalent even for N ¼ 1. The oxygen vacancy formation energies were computed for all the combination patterns of the O b sites, and the most stable combinations were selected for E f v (N).

Symmetry analysis and XRD pattern simulation
The XRD patterns were simulated using the VESTA program 33 to assign the theoretically obtained structure to the experimentally observed intermediate phase. The FINDSYM program 34 was used to examine the symmetry of the theoretically obtained crystals and compare them with the space group of the intermediate phase. The tolerance parameters of the program were set as follows: lattice: 0.01, position: 0.1, and rotational moment: 0.1. dependence of the formation energy on N appeared to be a sigmoid function, indicating that the E f v (N) values could be categorized into two groups: low-energy (rst four) and highenergy (last three) groups. The vacancy formation energies of the high-energy group were less than 0.5 eV. These were signicantly smaller than those of other materials (e.g., 2.09 eV for tetragonal Ce 2 Zr 2 O 8 (ref. 14)). This indicated that k-Ce 2 Zr 2 O 8 can release oxygen at relatively low temperatures, making it an excellent OSC material. The oxygen vacancy formation energies at N ¼ 5 were between those of the two groups. The locations of the low-energy and h vacancy sites are shown in Fig. 4. A close examination of the structure indicated that the four vacancy sites in the low-energy group were at locations that maximized their distances. As reported in the literature, 14 the sacricial reduction of the surrounding Ce atoms can produce oxygen vacancies with little charge uctuation of the Zr atoms in the k-Ce 2 Zr 2 O 8 system. The maximized distances allow Ce atoms to efficiently inuence the vacancy sites via the sacricial reduction mechanism. It should also be noted that the lattice distortions caused by vacancy formation can be minimized by maximizing the distance. Fig. 4 shows that the h oxygen vacancy site was located at the center of the four low-energy group sites. This special location was considered to suppress the lattice distortion and make the vacancy formation energy relatively small. However, when additional oxygen vacancies were generated at the high-energy group sites, the symmetry was broken, and the additional vacancy sites had to be adjacent to the existing vacancy sites. In these cases, the distance between vacancy sites became signicantly shorter. Therefore, the additional vacancy formations could not benet from the sacricial reduction of Ce atoms, and the lattice distortions became signicantly large. Accordingly, the two distinct energy groups were attributed to the symmetry of the vacancy formation sites.

Results and discussion
In the experiment, 13    43m. Hence, the experimentally observed intermediate phase was assigned to the state aer all the oxygen vacancies were formed at the low-energy group sites. The theoretically obtained formation energy gap between the low-and high-energy groups, as shown in Fig. 3, explains the stability of this intermediate phase.
As shown in Fig. 3, the oxygen vacancy formation energies in the low-energy group were reduced by Ti substitution, whereas no signicant change was observed in the high-energy group. This indicated that the release temperatures of the oxygen atoms at the low-energy group sites decreased. In other words, the amount of oxygen released at low temperatures increased. This feature was consistent with experimental results. 17 Unlike k-Ce 16 Zr 16 O 64 , the eight oxygen sites, O b , in the Ce 16 Ti 2 Zr 14 O 64 system are not equivalent because of the Ti substitution. Based on the electronegativities of Ti (1.54) and Zr (1.33), we expected that oxygen atoms directly coordinated to Ti would be more easily released than oxygen atoms coordinated only to Zr because oxygen cannot take as many electrons from Ti as Zr. This expectation could be true if vacancies were formed without any structural relaxation, as veried by our preliminary DFT+U calculations on frozen structures. However, when the lattice relaxation was switched on, the vacancy formation energy for the oxygen atoms coordinated only to Zr was smaller than that of Ti. This stemmed from the large strain caused by the removal of oxygen coordinated directly by Ti, which has a smaller ionic radius than Zr.
Although oxygen vacancies were formed at the Zr sites regardless of the Ti substitution, the oxygen vacancy formation energies were signicantly reduced by the Ti substitution. To investigate the mechanism of this reduction, Bader charge analyses were conducted for Ce 16 Ti 2 Zr 14 O 64 and k-Ce 16 Zr 16 O 64 . The electron numbers obtained by these Bader charge analyses for all the atoms before and aer the rst oxygen vacancy formation are compared in Fig. 6. The sacricial reduction of Ce atoms was observed in the k-Ce 16 Zr 16 O 64 system, where the electron numbers of three specic Ce atoms increased when an oxygen vacancy was formed. The reduced Ce sites formed a triangle around the vacancy sites (inset in Fig. 6). However, the electron numbers of Zr atoms, which involved Zr atoms directly coordinating the oxygen vacancy sites, did not change signicantly. This result was consistent with that of a previous study, 14 although two Ce atoms instead of three were reduced during the oxygen vacancy formation in past calculations, where the supercell was xed during the calculations. This number difference was attributed to the relaxation of the supercell: two Ce atoms were reduced when the supercell was xed in our preliminary calculations. In contrast, in Ce 16 Ti 2 -Zr 14 O 64 systems, the electron amounts for the Ce atoms were already increased with the Ti substitution before the vacancy formation, as shown in Fig. 6. These electrons were conrmed to originate from the oxygen atoms (the Bader charge for the oxygen atoms was decreased by the Ti substitution). However, the number of electrons in the Zr atoms was not affected. The decrease in the number of oxygen electrons resulted in a decrease in the strength of the ionic bonds. This was considered to be the cause of the decrease in the oxygen vacancy formation energies.

Conclusion
In this study, we systematically investigated the formation of oxygen vacancies from the fully oxidized state (k-Ce 2 Zr 2 O 8 ) to the fully reduced state (Ce 2 Zr 2 O 7 pyrochlore) using rst-principles computations based on the DFT+U method. Systematic computations of the oxygen vacancy formation energies of cationordered Ce 2 Zr 2 O 8 revealed that the arrangement of vacancy sites was determined so that the distance between vacancy sites was as large as possible, and the symmetry was as high as possible. This ordered arrangement minimized the lattice distortion and maximized the benet of Ce reduction during the vacancy formation. This feature resulted in the appearance of two oxygen vacancy formation energy groups: low-and high-energy groups. The intermediate phase obtained experimentally was assigned to the state aer all the oxygen vacancies in the lowenergy group were formed on the basis of the simulated XRD spectra. The theoretically obtained oxygen vacancy energies explained the two-step oxygen absorption/release behavior observed experimentally during heating under oxidized and reduced atmospheres. In addition, this ordered vacancy formation was considered to be one of the reasons for the possibility of topotactic transformation between k-Ce 2 Zr 2 O 8 and Ce 2 Zr 2 O 7 pyrochlore. The OSC enhancement by Ti substitution at lower temperatures was also reproduced by the theoretical oxygen vacancy formation energies. The charge transfer from oxygen atoms to Ce atoms caused by the Ti substitution was considered to be the main factor for the improved OSC.

Conflicts of interest
The authors declare that they have no conicts of interest.