Surface Science 602 (2008) 2734–2742

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Surface Science

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Vacancy formation and CO adsorption on gold-doped ceria surfaces

Michael Nolan a,*, Victor Soto Verdugo b, Horia Metiu b

a Tyndall National Institute, Lee Maltings, Prospect Row, Cork, Irelandb Department of Chemistry and Biochemistry, University of California, Santa Barbara, USA

a r t i c l e i n f o

Article history:Received 16 November 2007Accepted for publication 24 June 2008Available online 10 July 2008

Keywords:Density functional calculationsAdsorptionCatalysisSurface defectsDopingCeria

0039-6028/$ - see front matter � 2008 Elsevier B.V. Adoi:10.1016/j.susc.2008.06.028

* Corresponding author. Fax: +353 21 4270 271.E-mail addresses: michael.nolan@tyndall.ie (M. N

(H. Metiu).

a b s t r a c t

We study the effect of gold doping on oxygen vacancy formation and CO adsorption on the (110) and(100) surfaces of ceria by using density functional theory, corrected for on-site Coulomb interactions(DFT + U). The Au dopant substitutes a Ce atom in the surface layer, leading to strong structural distor-tions. The formation of one oxygen vacancy near a dopant atom is energetically ‘‘downhill” while the for-mation of a second vacancy around the same dopant requires energy. When the surface is in equilibriumwith gaseous oxygen at 1 atm and room temperature there is a 0.4 probability that no oxygen atom leftthe neighborhood of a dopant. This means that the sites where the dopant has not lost oxygen are veryactive in oxidation reactions. Above 400 K almost all dopants have an oxygen vacancy next to them andan oxidation reaction in such a system takes place by creating a second vacancy. The energy required toform a second vacancy is smaller on (110) than on (100). On the (110) surface, it is much easier to form asecond vacancy on the doped surface than the first vacancy on the undoped surface. The energy requiredto form a second oxygen vacancy on (100) is comparable to that of forming the first vacancy on theundoped surface. Thus doping makes the (110) surface a better oxidant but it has a small effect onthe oxidative power of the (100) surface. On the (110) surface CO adsorption results in formation of acarbonate-like structure, similar to the undoped surface, while on the (100) surface direct formationof CO2 is observed, in contrast to the undoped surface. The Au dopant weakens the bond of the surround-ing oxygen atoms to the oxide making it a better oxidant, facilitating CO oxidation.

� 2008 Elsevier B.V. All rights reserved.

1. Introduction

Cerium oxide is used in oxidation and dehydrogenation cataly-sis [1,2]. In most cases the molecule to be oxidized takes oxygenfrom the surface creating oxygen vacancies on it. The oxygen mol-ecule from the gas phase annihilates the vacancies closing thus thecatalytic cycle. Ceria surfaces have a relatively small oxygen va-cancy formation energy, which arises from the ability of ceria tochange oxidation state from (formally) +4 to (formally) +3.

Doping of ceria with other metallic elements, such as Zr, hasbeen shown to enhance thermal stability [3,4] and to promote cat-alytic activity [1–11]. It is believed that doping facilitates thereduction of ceria [4–12] by weakening Ce–O bonds around thedopant. A number of computational studies have demonstratedthat the oxygen vacancy formation energy is lower when the sur-face is doped with Zr [3,4,11].

Recent calculations [12] have shown that replacing a Ce atomon the CeO2(111) surface enhances CO oxidation. The Ce–O anddopant–O bonds are weakened upon formation of the doped mate-

ll rights reserved.

olan), metiu@chem.ucsb.edu

rial, reducing the oxygen vacancy formation energy and enhancingthe reactivity of the surface.

In this paper, we use density functional theory corrected for on-site Coulomb interactions (DFT + U) to study the effect of dopingthe (110) and (100) surfaces with Au on oxygen vacancy forma-tion and on CO adsorption. Comparison is made with previousstudies of CO adsorption on the undoped surfaces [13–15]. Weare interested in the (110) and (100) surfaces, because they areexposed on nanorods [16,17] and nanoparticles [15–17] and showenhanced activity compared to the (111) surface [13–17] andcomputational work from Liu et al. shows that gold on the (111)surface enhances CO oxidation [18].

2. Methods

We use a slab to describe ceria surface and a plane wave basisset to describe the wave functions of the valence electrons [19].The projector augmented wave (PAW) approach of Blöchl [20] de-scribes the interaction between the core and the valence electrons.The Ce core is [Xe], [He] on O and C and [Xe] on Au and for Ce, weuse the PAW potential with 12 valence electrons, treating the 4felectrons are valence. The plane wave cut-off energy is 396 eV;compared to a 500 eV cut-off, there is little change in properties

M. Nolan et al. / Surface Science 602 (2008) 2734–2742 2735

such as vacancy formation energies and in refs. [21,22] conver-gence tests for the technical parameters discussed below were per-formed. The Perdew–Burke–Ernzerhof (PBE) functional [23]accounts for exchange and correlation. In common with earlierstudies [13,14,21,22,24–26], we use density functional theory(DFT) corrected for on-site Coulomb interactions (DFT + U), whereU = 5 eV and is applied to the Ce 4f states. The details of this ap-proach and the choice of U are discussed extensively in [21,22].Briefly, due to the fact that the self interaction of an electron isnot correctly cancelled in DFT, there is an artificial barrier to elec-tronic localisation, since the self interaction is biased towards delo-calising electronic states. The introduction of the on-site Coulombinteraction, U, helps to remove some of the self-interaction error,reducing the artificial barrier to localisation, forming localised elec-tronic states, in agreement with experiment and contrary to theGGA result. The actual value of U is usually chosen to recover thecorrect value of an experimentally measured parameter, e.g. themagnetic moment or the band gap. For the present system, thisis difficult, since we are dealing with a defect state. In the presentwork, we choose a value of U that leads to localisation of two elec-trons in the Ce 4f states for each oxygen vacancy and an electronicstructure corresponding to that observed in experimental UPSspectra [21,22]. While we have taken an empirical route to deter-mine U, there has been recent work, attempting to compute U fromfirst principles [27,28]. While this can remove the empiricism inDFT + U computations, U is still generally fitted to reproduce theproperty of interest [21,22,27,28]. k-Point sampling is performedusing the Monkhorst–Pack scheme, with a (2 � 2 � 1) grid andFermi level smearing is performed using the Methfessel–Paxtonscheme [29].

The (110) surface is a type II surface with neutral stoichiome-tric planes so that no dipole moment is present upon cleaving.The (100) surface is a type III surface [22,30] with a non-zero di-pole moment. For the (110) and (100) surface calculations a thick-ness of 11.5 Å (seven atomic layers) and 10.94 Å (nine layers) wasrequired. Moving half of the oxygen atoms from one face of theslab to the other removes the dipole [22,31]. The vacuum layer is15 Å on both surfaces. The vacancy is formed by removing one oxy-gen atom from the surface. In common with the vast majority ofpublications on the topic of oxygen vacancies in ceria, we studyneutral oxygen vacancies. This allows for comparison with theseprevious studies. Oxygen vacancy defects can result in F-centres(trapped electrons at the site of the oxygen vacancy) or reducedmetal cations. In ceria, there is no evidence of F-centres are and in-stead, the metal cation is reduced. While there have been recentstudies which have examined different charge states of oxygenvacancies in ceria [32], in catalysis, the oxide is not in contact withan electron reservoir (which enables charge transfer to the oxide)and the question of the charge state of the vacancy does not arise.

On both surfaces, we use a surface supercell with eight surfaceoxygen atoms so that formation of one oxygen vacancy gives a va-cancy concentration of 12.5% at the surface and an overall vacancyconcentration of between 1.6% and 3.3%, depending on surface andnumber of vacancies (see Section 3). These supercells are signifi-cantly larger than in previous calculations on ceria surfaces[21,22,25] reducing defect–defect interactions and allowing bettertreatment of an adsorbed molecule. Upon introduction of the dop-ant and the vacancy, we relax all layers except the bottom two. Forthe ionic relaxation in a fixed lattice, the forces are relaxed untilthey are less than 0.02 eV/Å.

CO was adsorbed at these surfaces in a number of configura-tions to probe the dependence of adsorption energy on the adsorp-tion site. To investigate further the nature of adsorbed species, weuse a mass weighted diagonalization of the second derivative ma-trix in a fixed lattice to compute the vibrational frequencies of ad-sorbed CO, which we compare to the available experimental data.

3. Results

3.1. The structure of the stoichiometric, doped surfaces

We show the relaxed surfaces for the Au-doped (110) and(100) surfaces in Fig. 1a and b; the dopant is the grey spherein the outermost layer in each surface (we did not consider dop-ing in subsurface layers of the surfaces [12]). In the (110) surface,neutral layers of CeO2 stoichiometry are present. The Ce atoms inthe surface layer are coordinated to two pairs of surface oxygenatoms and a pair of subsurface oxygen atoms. Each subsurfaceoxygen atom is coordinated with a subsurface Ce atom. Upondoping, the Au atom moves outward from its initial lattice site(Fig. 1a), the oxygen atoms in the first subsurface layer move to-wards the bulk, away from the dopant, resulting in dopant-to-oxygen distances of 2.81 Å, compared to Ce–O distances of2.21 Å in the undoped surface. The oxygen atoms neighboringthe dopant in the surface layer move outwards, resulting in elon-gated Ce–O distances between Ce in the first subsurface layer andoxygen in the surface layer; these are 2.46 Å, compared to 2.33 Åfor the undoped surface. The oxygen atoms in the subsurfacelayer that are nearest to the dopant are pulled towards the dop-ant, resulting in Au–O distances of 2.09 Å, compared to a Ce–Odistance of 2.32 Å in the undoped surface. This displacement ofoxygen atoms elongates one pair of Ce–O distances involvingthe surface Ce atom neighboring the dopant to 2.74 Å and short-ens the other pair to 2.26 Å.

The undoped (100) surface shows a zigzag structure of –Ce–O–Ce–O–, with 2-coordinated oxygen atoms in the surface layer.These Ce–O distances are 2.19 Å and the distance to subsurfaceoxygen from Ce is 2.50 Å. Upon doping with Au, we find somedistortions to the atomic structure around the dopant site. Sim-ilar to the (110) surface, the dopant moves outwards and pullsan oxygen atom from the next sublayer with it. This dopant dis-placement is more pronounced on (110) than on (100). The dis-tance from the dopant to the surface oxygen atoms is 1.94 Å,substantially shorter than the Ce–O distance in the undoped sur-face (which is 2.19 Å). Looking down on the surface, we see thatthe subsurface oxygen atoms are repelled away from the dopant.These oxygen atoms have a shortened distance to surface Ce of2.33 Å. The oxygen atoms in the surface layer nearest the dopantare pulled towards the dopant, so that distances to the nearestCe ions are elongated to 2.24 Å. Such displacement indicates aweakening of the Ce–O bonds involving these oxygen atoms,which should increase the reactivity of the doped surface. Upondoping into both surfaces and upon vacancy formation, the Auatom is oxidised, resulting in the formation of Aud+; Au chargesare +0.45 electrons and +0.1 electrons in the doped (110) and(100) surfaces. The presence of this species is independent ofusing DFT or DFT + U.

3.2. Oxygen vacancy formation in the doped surfaces

For both surfaces doped with Au, we consider formation of oneoxygen vacancy, both ‘‘near” the dopant (a distance of 2.08 Å (110)and 1.96 Å (100) from the dopant) and ‘‘away” from the dopant (adistance of 7.10 Å (110) and 7.00 Å (100) from the dopant). Fortwo oxygen vacancies, we consider a number of vacancy patterns,(i) both vacancies near the dopant, (ii) one vacancy near the dopantand one vacancy far away from the dopant or (iii) both vacanciesfar away from the dopant. For this scenario, we discuss the moststable patterns in Section 3.3.

The formation energy of the first oxygen vacancy (giving a va-cancy concentration in the slab model of 1.8% in (110) and 1.6%in (100)) is given by

Fig. 1. Ceria surfaces doped with Au. (a) (110) and (b) (100). The dopant is the large grey sphere and the atoms of the first surface layers are indicated as large spheres,Ce = white and O = red. The figures in the left-hand side show a side view of the surface and the ones on the right-hand side present a top view of the surface. (Forinterpretation of the references in colour in this figure legend, the reader is referred to the web version of this article.)

2736 M. Nolan et al. / Surface Science 602 (2008) 2734–2742

Evac;1 1 0 ¼ ½EðCeO1:964Þ þ Eð1=2O2Þ� � EðCeO2Þ; ð1aÞEvac;1 0 0 ¼ ½EðCeO1:968Þ þ Eð1=2O2Þ� � EðCeO2Þ: ð1bÞ

For the second oxygen vacancy (giving a vacancy concentration of3.6% on (110) and 3.2% on (100)) we use

Evac;1 0 0 ¼ ½EðCeO1:928Þ þ Eð1=2O2Þ� � EðCeO1:92Þ; ð2aÞEvac;1 0 0 ¼ ½EðCeO1:936Þ þ Eð1=2O2Þ� � EðCeO1:92Þ: ð2bÞ

The subscript on the oxygen indicates the stoichiometry in the en-tire surface slab upon removal of one or two oxygen atoms. If theresulting energy is negative (exothermic) an oxygen vacancy isthermodynamically stable, whereas a positive energy signifies anenergy cost to form the vacancy.

We consider first the formation of one oxygen vacancy from thedoped surface. In the (110) surface the vacancy site near the dop-ant involves removing one of the surface oxygen atoms closest tothe dopant. In Fig. 2a and b we show the structure of the surfaceafter removing an oxygen atom next to the dopant. The structureof the surface when we make an oxygen vacancy away from thedopant is shown in Fig. 2c and d. In both cases the dopant remainsat its lattice site after the vacancy is formed. For the (100) surface,we show the structure of the surface with a vacancy in Fig. 3a–d.

The vacancy formation energy for the first oxygen vacancy onthe (110) surface is �0.08 eV, when the vacancy is near the dopantand it is +0.15 eV when the vacancy is away from the dopant. Inboth cases the formation energies are substantially smaller thanon the undoped surface (for which the energy of forming one va-cancy is 2.07 eV [22]). For the (100) surface, the vacancy formationenergies are �0.82 eV and +0.28 eV for a vacancy near the dopantand away from the dopant, respectively. Again, these energies aresubstantially smaller than in the undoped surface (which is 2.22 eV[21,22]).

The key finding is that upon doping of the (110) and (100) sur-faces with Au, the oxygen vacancy formation energy is negative,indicating that if the system is in equilibrium, oxygen vacancieswill be thermodynamically favourable. By lengthening of the Ce–O distances around the dopant site, doping makes removal of aneighboring oxygen atom rather facile. It is interesting to note thatthe vacancy formation energy in the (111) surface calculated withDFT is �0.36 eV for a vacancy neighboring the dopant and +0.56 eVfor a vacancy outside the first coordination shell of the dopant.

Thus, assuming the energetics of vacancy formation are reasonablydescribed with DFT (we have computed a lowering of the forma-tion energy by 0.41 eV with DFT + U on the undoped (100) surface,compared to DFT [21]), then gold doping of ceria surfaces willmake oxygen vacancies thermodynamically favourable. Based onthese energies alone one would be inclined to think that it is theformation of the second energy vacancy that controls the oxidationactivity of the oxide surface. However, a thermodynamic analysis(the details of which are presented in the appendix) of the equilib-rium concentration of the vacancies in the presence of oxygen inthe gas phase indicates that at room temperature and oxygen pres-sure of 1 atm there are oxygen atoms near the dopant and thesewill be very reactive. At higher temperatures all oxygen next tothe dopant is gone and the formation of the second vacancy willcontrol the oxidation activity of the doped oxide surface. This is amodel in which the dopants are isolated, and we do not considerdopant clustering. While the latter can form in doped oxides, themost active sites are at the interface between the dopant and oxy-gen of the host. This interface is satisfactorily modeled by the setupin this paper and previous studies [3,4,11,12,18]. In addition, if thevacancies do not interact there will be one vacancy per dopant.However, one expects that unless the concentration of vacanciesis very low there will be some interaction and the presence ofvacancies around some dopants will make it harder to make vacan-cies around other dopants. We have not considered this interactionhere.

We now discuss briefly the atomic structure of the defectivedoped surfaces. In the (110) surface, when a vacancy forms nearthe dopant, the other oxygen atom (of the pair of oxygen atomsnear the dopant) moves off its lattice site in order to bridge thedopant and the nearest surface Ce atom, with a Ce–O distance of2.20 Å (Fig. 2a). Au–O distances are 2.07 and 2.22 Å. When the va-cancy is further away from the dopant (see Fig. 2b), an oxygenatom is displaced out of the surface layer to bridge the two surfaceCe atoms, with Ce–O distances of 2.19 Å. At the dopant site, theAu–O distances are 2.08 and 2.12 Å, with a small change comparedto the defect free doped surface. This oxygen atom also moves outof the surface layer indicating that formation of another oxygen va-cancy, involving this atom, could be rather facile. Other distortionsof the surface caused by vacancy formation are rather small.

On the (100) surface, with a vacancy near the dopant, the dop-ant moves further into the surface, presumably to increase its coor-

Fig. 2. Structures for one oxygen vacancy on the (110) surface. (a) and (b) the vacancy is near the dopant, (c) and (d) the vacancy is away from the dopant. The color scheme isthe same as Fig. 1 and the vacancy site is indicated with a ‘‘V” in the image and the figures in the left-hand side show a side view of the surface and the ones on the right-handside present a top view of the surface.

Fig. 3. Structures for one oxygen vacancy on the (100) surface. (a) and (b) the vacancy is near the dopant, (c) and (d) the vacancy is away from dopant. The color scheme is thesame as Fig. 1 and the vacancy site is indicated with a ‘‘V” in the image and the figures in the left-hand side show a side view of the surface and the ones in the right-hand sideshows how the surface appears when one looks down it.

M. Nolan et al. / Surface Science 602 (2008) 2734–2742 2737

dination. The surface oxygen atom coordinated to the dopant alsomoves into the surface, with an Au–O distance of 2.01 Å. There areno further distortions due to vacancy formation. When the vacancyis away from the dopant, there is little change to the structurearound the dopant site. The Ce–O distances neighbouring the va-cancy site are 2.05 and 2.11 Å, compared to 2.19 Å in the surfacewith no vacancies. The Au–O distances are 2.02 and 2.03 Å, whichare a little longer than in the defect free undoped surface. There areno further notable distortions to the structure in this case.

Finally, after vacancy formation, the charge state of the golddopant is hardly affected, indicating that the dopant is not involveddirectly in the vacancy formation process. Finally, both DFT and

DFT + U give qualitatively similar descriptions of the vacancy for-mation energetics in each surface, e.g. formation of the first oxygenvacancy gives an energy change of �0.56 eV and �0.82 eV in theAu-doped (100) surface with DFT and DFT + U, respectively.

3.3. The formation of a second oxygen vacancy

Since at sufficiently high temperature and an oxygen pressureof 1 atm almost all dopants have an oxygen vacancy next to them,it is the formation of a second oxygen vacancy that determines theoxidation activity of the doped surface. We use Eq. (2) to computethe formation energy of a second oxygen vacancy, where the start-

Fig. 4. Structure of two oxygen vacancies in (a) and (b) the (110) and (c) and (d) the (100) surfaces, where the vacancies are near the dopant. The vacancy sites are indicatedwith a ‘‘V” in the image. The coloring of the ions is the same as Fig. 1.

2738 M. Nolan et al. / Surface Science 602 (2008) 2734–2742

ing point is the defective, doped surface discussed in Section 3.2.The locations of the two vacancies in the most stable vacancy dis-tribution are shown in Fig. 4. In these structures, both oxygenvacancies are near the dopant, with dopant-vacancy distances gi-ven in Section 3.2. In Fig. 4a, the two vacancies lie on the same lineso that only one ‘‘V” is visible.

Beginning with a doped surface that has one oxygen vacancypresent, the formation energy of a second vacancy on the (110)surface having already a vacancy near the dopant is +0.68 eV andthe structure is shown in Fig. 4a and b. It takes +2.65 eV to forma second vacancy away from the dopant. On (100), the correspond-ing energies are 2.57 eV for the two vacancies near the dopant (Fig.4c and d and 2.26 eV where the second vacancy is away from thedopant. Compared with the undoped surface, we see that forma-tion of the second vacancy on (110) is rather easy, but only ifthe both vacancies are near the dopant. On (100) the presence ofthe dopant has little impact on the formation of the second oxygenvacancy, irrespective of the position of the second vacancy site. Therange of oxygen vacancy formation energies on these surfaces isquite broad, going from �0.08 eV (one vacancy on Au-doped(110) surface) to 2.61 eV (two vacancies, one near, on away fromthe dopant on Au-doped (110) surface) and we see that increasingthe vacancy concentration causes an increase in the formation en-ergy of the vacancy. This suggests that for the (110) surface a va-cancy concentration of 3.6% is possible, but that a similarconcentration for the (100) surface is not favourable. Further va-cancy formation will be expected to have an even larger energycost. Taken with the results of Ref. [12], these energies suggest astrong influence of the dopant on the catalytic activity of ceria sur-faces, with a notable surface dependence present.

On (110), there are two surface oxygen atoms neighboring thedopant, and the dopant–O distances are 2.02 Å, which are short-ened over the vacancy structure detailed in Section 3.2. These sur-face atoms have moved out of the surface plane, with Ce–Odistances of 2.05 and 2.08 Å. The reduced coordination of the Ceatom results in a shortening of the Ce–O distances. This also indi-cates that formation of a third oxygen vacancy near the dopant willbe less favorable. This means that there is a temperature window

in which the doped oxide provides an oxidation reaction with onlyone oxygen atom per dopant.

On the (100) surface, the outermost oxygen atoms near thedopant are displaced towards the dopant, with an accompanyingdistortion of the outermost Ce atoms and third layer oxygen atoms.Ce–O distances involving the outermost oxygen atoms are between2.09 and 2.26 Å, with the shortest Ce–O distances for those oxygenatoms nearest the dopant.

3.4. The equilibrium concentration of various types of vacancies

The vacancy formation energies can be used in a simple statis-tical model to calculate the equilibrium concentration of varioussurface oxygen vacancies when the system is in contact with gas-eous oxygen. These concentrations depend on surface temperatureand oxygen pressure. Our model assumes that we can replace thesolid with a lattice in which each dopant is a lattice site. Near eachdopant we can have one of the following species: a vacancy next tothe dopant (denoted A), a vacancy away from the dopant (denotedB) and two vacancies near the dopant (denoted C). We further as-sume that the dopant surface concentration is low and thesevacancies do not interact with each other. Finally, we neglect thechanges in the chemical potential caused by changes in vibrationalfrequencies of the solid when one of these vacancies is present. Inthis model the equilibrium concentrations of these species are af-fected only by the energy of forming them, by the configurationalentropy and by the chemical potential of gaseous oxygen. The lat-ter is as important as the formation energies. The surface concen-trations provided by this analysis will be present in the systemonly if it is carefully equilibrated by exposing the material for aslong a time as necessary, to gas phase oxygen and fixed partialpressure and temperature. The details are elementary and are gi-ven in the Appendix.

The dependence on temperature of the equilibrium concentra-tions resulting from this calculation is given in Fig. 5, for a pressureof 1 atm. On the (110) surface at 250 K, 20% of the dopants have avacancy next to them and no other type of vacancy is present. Thismeans that at equilibrium, 80% of dopants still have all the oxygen

Fig. 5. Temperature dependence of oxygen vacancy concentration on Au-dopedCeO2(110) surface. Oxygen pressure is 1.0 atm. In the legend, the entries ‘‘1 vacancynear” and ‘‘1 vacancy far” signify a single oxygen vacancy near the dopant and awayfrom the dopant, respectively. The legend entry ‘‘2 vacancies near” refers to twooxygen vacancies near the dopant.

M. Nolan et al. / Surface Science 602 (2008) 2734–2742 2739

atoms nearby. Since removal of the atoms adjacent to the dopant isexothermic it is likely that they will easily engage in oxidationreactions with molecules adsorbed on the surface. At about 400 Kthe surface lost one oxygen atom next to each dopant and veryfew vacancies away from the dopant or double vacancies are pres-ent. Because the energy to make the second vacancy is less on thedoped surface than on the undoped one, the doped surface withone oxygen vacancy near each dopant is still a better oxidant thanthe undoped one.

3.5. CO adsorption on the (110) and (100) Surfaces

In this section, we investigate CO adsorption on the doped(110) and (100) surfaces. Unlike Ref. [12], we make no attempt

Fig. 6. Relaxed adsorption structures for CO adsorbed on (a): Au-doped (110) surface (bresulting adsorption structure. The coloring of the ions is the same as Fig. 1 and the car

to study the catalytic cycle for the formation of CO2 and the healingof the vacancy. Instead, we wish to compare CO adsorption on thedoped and the undoped surfaces. The energy change upon COadsorption is

Eads ¼ ½EðCeO2 � COÞ þ EðCeO2Þ � EðCOÞ�: ð3Þ

Eads is negative when the surface with adsorbed CO is more stablethan the surface separated from the CO.

The structure of CO on the (110) surface is shown in Fig. 6a.Similar to the undoped surface, CO adsorbs to form a carbonate-like structure in which two oxygen atoms are abstracted fromthe surface to bond to the carbon of the carbonyl group. The car-bonyl bond length is 1.26 Å and the bond between the carbonand each of the two surface oxygen atoms is 1.32 Å. For the un-doped surface these distances are 1.23 Å and 1.37 Å, respectively.The adsorption energy on the doped surface is �4.70 eV, comparedto �1.95 eV on the undoped surface; the dopant greatly stabilizesthe carbonate. The calculated stretching frequency of the carbonylon the doped (110) surface is 1647 cm�1, while on the undoped(110) surface it is 1710 cm�1 [17]. The latter value is fairly closeto the measured [33,34] frequency of 1728 cm�1 for the C@Ostretch. For reference, gas phase CO has a stretching frequency of2103 cm�1. The substantial shift of C@O stretching frequency forthe doped surface can be used to identify the presence of a dopantin the surface layer. This is important since it is in general difficultto prove experimentally that a doped surface has been prepared.The doped (110) surface is distorted by CO adsorption: the dopantand the Ce atom in the same row as the dopant move out of thesurface plane and the dopant itself moves away from the Ce atomand from the carbonate.

On the (100) surface, CO reacts with the doped surface to formCO2, as shown in Fig. 6b, with an energy gain of �3.90 eV. The CO2

molecule is 1 Å above the outermost surface layer The presence ofCO2 is indicated by C–O distances of 1.16 Å and 1.19 Å, consistentwith the C–O distance of 1.16 Å for gas phase CO2. The large ener-getic stabilization of the adsorption structures indicates that thesurface oxygen atoms are very reactive, which is consistent withthe results of Section 3.2. On the (100) surface, the dopant movesoutwards to be in line with the surface oxygen atoms.

): Au-doped (100) surface. In both parts we show a front, plan and side view of thebon of the CO molecule is the mall grey sphere.

Fig. 7. Spin polarised Ce PEDOS for CO on (a) the Au-doped (110) surface and (b)the Au-doped (100) surface. The zero of energy is the top of the valence band.

2740 M. Nolan et al. / Surface Science 602 (2008) 2734–2742

The atom and angular momentum decomposed Ce partial elec-tronic density of states (PEDOS) is displayed in Fig. 7 for both sur-faces. The valence band is peak I in Fig. 7 and the unoccupied Ce 4fstates are indicated by the narrow peak III. Peak II in the PEDOSarises from the formation of reduced (formally) Ce3+ ions, in whichthe Ce 4f states are occupied. This PEDOS feature is a signature ofreduced Ce, as has been shown in many studies [21,22,25,35–37].The presence of the reduced Ce ions upon interaction with CO isconsistent with the results for the interaction of CO with the un-doped surfaces in Refs. [16,17].

3.6. Discussion

Similar to the findings for the (111) surface in Ref. [12], thepresence of an Au dopant lowers dramatically the energy for oxy-gen vacancy formation on the (110) and (100) surfaces. In fact, theenergy of vacancy formation is negative on all three CeO2 surfaces.Thus cation doping in principle enhances the oxidative power ofceria, irrespective of the surface present. However, the negative va-cancy formation energy and our thermodynamics analysis indicatethat at temperatures applicable to catalysis, the dopant will havean oxygen vacancy next to it. Therefore oxidation reactions willbe facilitated by forming a second oxygen vacancy. The vacancyformation energies show that the dopant facilitates the formationof a second oxygen vacancy on (110) but not on (100), revealinga notable surface dependence that could be exploited in the designof nanostructured ceria catalysts.

At 0 K, in the absence of oxygen in the gas phase, each dopantwill have a vacancy next to it. The exposure of the surface to1 atm of O2 changes this situation. Below room temperature mostof the dopants will have no oxygen vacancy around them. Becauseone oxygen atom next to each dopant is very weakly bound, the

surface will be a good low temperature oxidant. This does notmean that it will be a good oxidation catalyst. The oxygen vacancycreated when the surface oxidizes a molecule must be healed byadsorption of oxygen from the gas phase. Unless this reoxidationof the surface is facile the oxidation reaction will reduce the sur-face and at some point the oxidation process stops. A good oxidantneeds to give away oxygen easily. A good oxidation catalyst muststrike a balance [12]: if it gives oxygen too easily it will not beeffective in taking oxygen from the gas phase.

Another possible advantage of a doped oxide comes from thefact that there is a temperature window in which the surface willprovide only one oxygen atom per dopant. This means that theprobability that doped oxides are selective oxidation catalysts ishigh.

It is interesting to note that DFT [12] and DFT + U (this work)provide the same general trend: vacancy formation in ceria sur-faces is enhanced by Au doping, so that the qualitative results pro-vided by DFT appear to be sound. It appears that for studies where,e.g. energetics and structure are of interest, DFT and DFT + U gen-erally provide qualitatively similar results. Other recent exampleswhere DFT was used rather than DFT + U include formaldehydeon CeO2 [38], methanol on CeO2 [39] and butanediol on CeO2

(111) [40]. In addition, some studies of doped CeO2 have been pre-sented, e.g. Ni–CeO2 [41] and rare earth doping [42]. It appears thatin describing many features of these systems, the description of theelectronic structure is not critical and DFT is adequate, although itwill be worth examining this assumption (for example CO adsorp-tion is impacted by choice of DFT or DFT + U [13,43]) and we do ex-pect DFT to be problematical where the electronic structure plays akey role. This suggests that one strategy could be to use DFT for ini-tial screening of e.g. dopants or adsorption structure and DFT + U toprovide the detailed analysis of the few potentially interesting sys-tems. However, it is important to note that previous results [21]show that the magnitude of the oxygen vacancy formation energyis affected by the choice of approach, which is a reflection of thedifferent electronic structure produced by DFT and DFT + U.

With the example of CO adsorption, an intermediate step in COoxidation, we find that doping is a favourable approach to enhanc-ing the oxidation process. Similar to the undoped surface, the prod-uct formed by adsorption depends on the crystal face. On the (110)surface CO forms a carbonate while on the (100) surface CO ad-sorbs on top of the oxygen atom near the dopant and forms a struc-ture that is very close to a CO2 molecule. We trace this to thesurface structure, where the O–O distance on the (100) surface,which is similar to (111), makes it hard for two oxygen atoms tobe pulled off their lattice sites and interact with CO to form CO3.

4. Conclusions

We have presented computations of oxygen vacancy formationin and CO adsorption on gold-doped ceria (110) and (100) sur-faces, using periodic plane wave density functional theory withan on-site Coulomb correction (DFT + U). Similar to the findingsfor the (111) surface in Ref. [12], the presence of the dopant lowersdramatically the energy for oxygen vacancy formation on thesesurfaces. In fact, the energy for vacancy formation is negative onall three surfaces. Thus cation doping in principle will enhancethe oxidative power of ceria, irrespective of the surface. However,the negative vacancy formation energy and our thermodynamicanalysis indicate that at temperatures applicable to catalysis, thedopant will have an oxygen vacancy next to it. Therefore an oxida-tion reaction will be facilitated by forming a second oxygen va-cancy. The dopant facilitates the formation of a second vacancyon (110) but not on (100), revealing a surface dependence,which could be exploited in future catalytic systems based on

M. Nolan et al. / Surface Science 602 (2008) 2734–2742 2741

nanostructured ceria, which are known to expose faces other than(111). Doping results in a temperature window in which the sur-face provides a single oxygen atom per dopant, so that there is agood probability that a doped oxide will be a good selective oxida-tion catalyst. For CO adsorption, doping enhances the interaction ofthe molecule with the surface, making carbonate formation on(110) more favourable and facilitating direct formation of CO2 atthe (100) surface.

Finally, we point out that although doping enhances surfacereduction, it will be important to analyse how healing of the oxy-gen vacancy, either by oxygen or a molecule such as NOX, is im-pacted by doping.

Acknowledgements

We acknowledge the European Commission for support (NAT-CO, FP6-511925). We acknowledge a Grant of computing resourcesat Tyndall and the Science Foundation Ireland/Higher EducationAuthority funded Irish Centre for High Performance Computing(ICHEC) for provision of computing resources.

Appendix

We use a lattice model to calculate the equilibrium concentra-tion of vacancies on the surface, as a function of the oxygen pres-sure and the surface temperature. The model considers threepossible surface species: a vacancy near the dopant (denoted A),a vacancy away from the dopant (denoted B) and two vacancies(denoted C). The model assumes that the only role of the solid isto provide lattice sites for these species and that the species donot interact. This means that the partition function of the wholesystem is the partition function of the lattice multiplied with thepartition functions of each species. In addition, it is assumed thatwe can neglect the change in the partition function of the latticedue to the presence of the vacancies even though the phonon spec-trum is affected. Due to these assumptions the chemical potentialof the lattice cancels out when the equilibrium conditions are writ-ten. The free energy of the system is therefore

F ¼ �kBT

� lnM!

NA!NB!NC !ðM � NA � NB � NCÞ!ðcAqAÞ

NA ðcBqBÞNB ðcCqCÞ

NC

� �:

ðA:1Þ

Here M is the number of dopants on the surface, NX is the number ofspecies X (i.e. NA is the number of vacancies of type A), qX is the par-tition function of an isolated vacancy of type X and cX is the numberof equivalent sites for a vacancy of type X around a dopant site.

We do not include here the partition function of the solid. Thechemical potential of species X is

lX ¼ lL þoFoNX

� �T;P;NY

¼ lL þ kBT ln½hX=ðhcXqXÞ; ðX

¼ A or B or CÞ ðA:2Þ

with h = 1 � hA � hB � hC. The subscript NY indicates that the partialderivative with NX is taken by keeping the other Ns constant. Wehave added the chemical potential of the lattice which will cancelout in the equilibrium conditions.We consider three equilibria:

S$ Aþ 1=2O2; ðA:3ÞA$ B ðA:4Þ

and

A$ C þ 1=2O2: ðA:5Þ

Here S represents the surface without vacancies. The first equilib-rium is the formation of a vacancy of type A by desorbing oxygen,the second is the equilibrium between A and B achieved by the dif-fusion of the vacancy from A to B and the third is the formation of Cby desorbing oxygen from a surface that already has a vacancy Anear the dopant. The equilibrium conditions are [44]

lLlA þ 1=2lO2; ðA:6Þ

lBlA; ðA:7ÞlA ¼ lC þ 1=2lO2

ðA:8Þ

with the chemical potential lO2for diatomic oxygen given by stan-

dard formulae [45].The partition functions for various types of vacancies are

qX ¼ exp½�eX=kBT�, with eX the energy of formation of a vacancyof type X.

The equilibrium conditions provide three equations which wesolve (with Mathematica) to obtain hA, hB and hC as functions of Tand p (the partial pressure of oxygen). The energies eX are thosecalculated in the present article, the data for O2 was taken fromRef. [45] and the symmetry constants are cA = 4, cB = 8 and cC = 2.

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