Density functional theory studies of the structure and electronic structure of pure and defective low index surfaces of ceria

Abstract

We present periodic density functional theory (DFT) calculations of bulk ceria and its low index surfaces (1 1 1), (1 1 0) and (1 0 0). We find that the surface energies increase in the order (1 1 1) > (1 1 0) > (1 0 0), while the magnitude of the surface relaxations follows the inverse order. The electronic properties of the bulk and surfaces are analysed by means of the electronic density of states and the electron density. We demonstrate that the bonding in pure ceria is partially covalent and analysis of the resulting electronic states confirms the presence of localised Ce 4f states above the Fermi level. The surface atoms show only a small change in the charge distribution in comparison to the bulk and from the DOS the main differences are due to the changes in the oxygen 2p and cerium 5 d states. Investigation of the atomic and electronic structure of an oxygen vacancy on the (1 0 0) surface shows the problems DFT can have with the description of strongly localised systems, wrongly predicting electron delocalisation over all of the cerium atoms in the simulation cell. We demonstrate an improvement in the description of the strongly correlated cerium 4f states in partially reduced ceria by applying the DFT+U methodology, which leads to the appearance of a new gap state between the valence band and the empty Ce 4f band. Analysis of the partial charge density shows that these states are localised on the Ce^III ions neighbouring the oxygen vacancy. In terms of classical defect chemistry, the vacancy is bound by two neighbouring Ce^III ions, which have been reduced from Ce^IV, i.e. ${\mathrm{V}}_{\mathrm{O}}^{··}+2{\mathrm{Ce}}_{\mathrm{Ce}}^{\prime }$. The remaining Ce ions are in the Ce^IV oxidation state. The localisation of Ce 4f electrons modifies the predicted structure of the defective surface.

Introduction

The technological importance of cerium oxide, CeO₂, particularly its important role in automobile three-way catalytic converters and in solid oxide fuel cells [1], has seen it become the focus of many experimental and computational investigations. Since the surface properties of ceria determine the catalytic activity of this material, much attention has been given to the study of the low index surfaces of ceria.

Ceria is an insulating, non-magnetic rare-earth oxide. It has a cubic fluorite structure with four cerium and eight oxygen atoms per unit cell and an experimentally determined lattice parameter of 5.411 Å [2]. Upon partial reduction of ceria, oxygen vacancies are formed [1]. In this reaction the oxidation state of Ce changes reversibly from Ce^(IV) to Ce^(III), the reaction being

$${\mathrm{O}}_{\mathrm{O}}^x+2{\mathrm{Ce}}_{\mathrm{Ce}}^x\to {\mathrm{V}}_{\mathrm{O}}^{··}+2{\mathrm{Ce}}_{\mathrm{Ce}}^{\prime }+{\displaystyle \frac{1}{2}}{\mathrm{O}}_2$$

using Kroger–Vink notation, where ${\mathrm{O}}_{\mathrm{O}}^x$ is a neutral oxygen in an oxygen lattice site, ${\mathrm{Ce}}_{\mathrm{Ce}}^x$ is a neutral cerium atom in a cerium site, ${\mathrm{V}}_{\mathrm{O}}^{··}$ is a doubly positively charged vacancy in an oxygen site and ${\mathrm{Ce}}_{\mathrm{Ce}}^{\prime }$ is a single negatively charged cerium atom (+3 oxidation state) in a cerium site. In the Ce^(III) state, a previously unoccupied 4f state is occupied, giving the electronic configuration Ce 4f¹ [3]. It is expected upon partial reduction, that the two cerium atoms neighbouring the vacancy will be reduced to Ce^(III). The reverse reaction where Ce^(III) changes to Ce^(IV) is carried out through oxidation. This redox process allows ceria to store or release oxygen, depending on the oxygen partial pressure; the oxygen storage/release capability of ceria being central to technological applications. Reduction of ceria and oxygen ion migration is energetically favourable in the low index surfaces compared to bulk [4], [5] and it is thus important to obtain an understanding of the nature of pure and reduced ceria surfaces.

In order to facilitate the study of surface structure, thin films of ceria have been grown on a number of support materials including alumina, yttrium stabilised zirconia, platinum and palladium [6], [7], [8]. Experimentally, the (1 1 1) surface is observed to be stable and undergoes little relaxation [9]. The (1 1 0) and (1 0 0) surfaces have been observed to undergo surface relaxations [9], [10]. It has been determined through STM [10], AFM [11], ion scattering spectroscopy [12] and low energy electron diffraction [13] that the (1 1 1) surface is oxygen terminated. The (1 1 0) surface has been studied by Nörenberg and Briggs using STM and electron diffraction [14], demonstrating that it is terminated with a stoichiometric layer. The least stable, and most studied, surface is (1 0 0). Cleaving this surface gives a dipole moment perpendicular to the surface and therefore requires a reconstruction since dipolar surfaces are unstable [15]. Generally removal of 50% of the terminating oxygen species is observed [4], [10], which Hermann demonstrated using angular resolved mass spectroscopy of recoiled ions [12]. Nörenberg and Harding [10] have presented an STM study of the pure and partially reduced (1 0 0) surface of ceria. These authors have found that surface relaxations take place in order to reduce the surface energy. While cation termination of the (1 0 0) surface is possible, the anion terminated (1 0 0) surface is found to have the lowest surface energy [4], [10] and is taken as the observed termination. Evidence for the appearance of naturally occurring oxygen defects was derived from the nature of the bright spots in the STM image coupled to atomistic simulations.

Despite the fundamental importance of these species to automotive catalysis, an understanding of how oxygen vacancy defects modify the properties of ceria is still lacking. It is necessary to develop our understanding of the oxygen storage mechanism in cerium dioxide, in order to develop more efficient catalysts. While the electronic structure of pure bulk ceria has been well studied, with much debate regarding the exact nature of the electronic structure, it is only in recent years that the electronic structure of reduced ceria has been studied [3], [9]. The resulting features in the UPS spectrum are dependent on the occupation of the cerium 4f states [16]. In the work of Henderson et al. [3], it was demonstrated that upon reduction of the ceria (1 1 1) surface, a new occupied Ce 4f state appears in the gap between the valence band and the previously unoccupied Ce 4f states, 1.2 eV above the valence band. Mullins et al. have observed the formation of this same peak for reduced ceria (1 1 1) thin films grown on an Ru(0 0 0 1) support [13]. This peak is due to formation of Ce³⁺ and the intensity of the XPS peak is related to the amount of Ce³⁺ present. The Ce 5d spectrum is also modified upon reduction, with a new peak appearing at a binding energy of 903.8–904.0 eV [3], [10]. These observations are characteristic of the presence of Ce³⁺ species.

The defective (1 1 1) surface has also been studied by Nörenberg and Briggs with STM [17]. No significant lateral relaxation of the surface was observed and oxygen termination of this surface was found. These authors claim that oxygen vacancy defects initially form in triangular clusters and upon further annealing form line defects, indicating that the clustering of the oxygen vacancy defects on ceria surfaces is energetically favourable. Namai et al. [11] have also observed these triangular and linear oxygen defects in the partially reduced CeO₂(1 1 1) surface. These authors have also concluded that an oxygen defect density of greater than 1 × 10¹³ cm⁻² (approximately 1% of top layer O²⁻) is necessary for vacancy clustering to occur. Oxygen vacancy clustering is also predicted from atomistic simulation to be energetically more favourable than isolated surface oxygen vacancies [4], [11]. There have been limited studies on the reduced (1 1 0) and (1 0 0) surfaces, although Mullins et al. have studied the electronic structure of reduced CeO₂(1 1 0) with UPS and have observed the appearance of the Ce 4f peak at 2.0 eV above the valence band [16].

Many studies have applied atomistic simulation methods, using interatomic potentials, abbreviated hereafter as IP, in order to gain an insight into bulk and surface properties of ceria. Interatomic potentials are parameterised analytical functions used to describe the interactions between ions in a material. The parameters in the functions are generally chosen to reproduce experimental data. A number of interatomic potentials have been developed for the calculation of the structure of bulk ceria and the surface energies and relaxed structures of ceria surfaces [4], [5], [18], [19], [20], [21], [22], [23], [24], [25], [26], [27]. In comparison, the number of studies of bulk and surfaces of ceria using ab initio methods is smaller. In CeO₂, the formal oxidation state of cerium is +4, however, two different approaches have been developed in order to treat the ground state electronic structure. In the first, cerium is seen as tetravalent with an unoccupied 4f-band (4f⁰) and a completely filled O 2p-band [28]. The second considers the ground state of ceria to be a mixture of two Ce configurations, 4f⁰ and 4f¹ with a filled O 2p valence band for the former and a partially filled O 2p-valence-band in the latter [29]. In this model, cerium is no longer strictly tetravalent.

A number of studies of ceria have been concerned with elucidating the role of the Ce 4f electrons in the electronic structure of CeO₂. In early SCF band calculations of bulk ceria Koelling et al. [30] concluded that some covalent bonding is present, so that ceria is not completely ionic. Fujimori also concluded that partial occupancy of the Ce 4f states is present [29], corresponding to the second model above. However, Wuilloud et al. [28] and Wachter et al. [31] have concluded that the cerium 4f states in CeO₂ are fully unoccupied and localised, corresponding to the first model above.

In their study of the electronic properties of bulk ceria, with Hartree–Fock theory, Hill and Catlow (who use a minimal basis set on cerium and oxygen) [32] and Gennard et al. (who use a more extended basis set) [33] have neglected completely the Ce 4f basis functions, under the assumption that doing so does not affect the bulk properties of ceria, since the Ce 4f orbitals are assumed to be unoccupied. These studies found that the bulk properties of ceria can be well described even without the Ce 4f electrons, indicating the validity of the first model. Recent density functional theory calculations of bulk CeO₂ and Ce₂O₃ were presented by Skorodumova et al., [34] in the framework of the full-potential linear muffin-tin orbital (FP-LMTO) method. The best agreement with experiment for CeO₂ was obtained by treating the cerium 4f-functions as part of the valence region. However, in studying fully reduced ceria, Ce₂O₃, the same authors found that in order for the Ce 4f electrons to be correctly localised, they had to be treated as core states. Treating the 4f electrons as valence electrons, resulted in an incorrect partially filled f-band at the Fermi level. Choosing the f electrons to be core or valence depending on the problem at hand is clearly not a satisfactory way of understanding the electronic structure of ceria.

In addition to studying the bulk properties of ceria, Gennard et al. [33] also studied the (1 1 1) and (1 1 0) surfaces using Hartree–Fock. Recently, Skorodumova et al. [35] have studied the surface energies and structures of the (1 1 1), (1 1 0) and (1 0 0) surfaces using density functional theory. Both of the ab initio studies are in agreement with atomistic simulations regarding the relative stability of the surfaces, (1 1 1) > (1 1 0) > (1 0 0), although DFT predicts smaller surface energies than atomistic simulations and Hartree–Fock [35].

In this paper we present periodic density functional theory (DFT) calculations of bulk and the three low index surfaces of pure ceria. We also consider reduction of the (1 0 0) surface through formation of oxygen vacancies on the (1 0 0) surface. We analyse the structural and electronic properties by means of the density of states, charges and the charge density. We demonstrate the presence of unoccupied Ce 4f electronic states above the Fermi level. Reduction of the (1 0 0) surface leads to occupied Ce 4f states which are found to be delocalised over all of the cerium atoms within the simulation cell using GGA-DFT. In order to correctly describe the localisation of these electrons, we use the DFT+U [36] methodology to correct this failing of DFT for the (1 0 0) surface of ceria. In addition we also examine how the DFT+U approach affects the resulting atomic structure of the defective surface.