DFT Studies of Oxygen Vacancies on Undoped and Doped La2O3

Jun 24, 2010 - more reactive, which makes the doped oxide a better oxidant. We examined doping the surface layer of. La2O3(001) and (011) with Cu, Zn,...
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J. Phys. Chem. C 2010, 114, 12234–12244

DFT Studies of Oxygen Vacancies on Undoped and Doped La2O3 Surfaces Bo Li and Horia Metiu* Department of Chemistry & Biochemistry, UniVersity of California, Santa Barbara, California 93106-9510 ReceiVed: April 21, 2010; ReVised Manuscript ReceiVed: June 8, 2010

La2O3 is one of the more efficient oxide catalysts for oxidative methane coupling. In this article, we examine the extent to which methane activation can be improved by replacing a La cation in the surface layer with other cations. The purpose of these substitutional dopants is to make the oxygen atoms in their neighborhood more reactive, which makes the doped oxide a better oxidant. We examined doping the surface layer of La2O3(001) and (011) with Cu, Zn, Mg, Fe, and Al. We have chosen dopants whose oxide formation enthalpy is less than that of La2O3. Some (Cu, Fe) are capable of having two different valence states, whereas some (Zn, Mg, Al) have only one. All of them lower substantially the energy of vacancy formation on the two faces. We use a “moderation principle” to suggest that Cu-doped La2O3 is not a good catalyst for methane activation despite lowering the energy of oxygen-vacancy formation the most. We propose that it is likely that the experimental value for the oxygen-vacancy formation energy might be affected substantially by the presence of adventitious dopants, which will then affect catalytic activity as well. We suggest that dopants affect the energy of vacancy formation in two ways: a local modification of the bond strength of the oxygen atoms to the oxide and a global effect due to a change in the Fermi level, which, in turn, can affect the charge of the oxygen vacancy and its energy of formation. 1. Introduction Recent work on oxide catalysts has shown that one can improve their performance by replacing a fraction of the cations in the oxide with another cation.1 In what follows, we call this procedure “cation doping” or simply “doping”. Density functional calculations have suggested a number of mechanisms through which doping may improve catalytic activity. (1) Some dopants weaken the bond between the oxygen atoms in the surface layer and the oxide, making it easier to make oxygen vacancies.2-5 The oxygen atoms that are easier to remove are more reactive, and the lowering of the energy of oxygen-vacancy formation is a good descriptor of the extent to which doping makes the oxide a better oxidant. For example,2,3,5 for several doped oxides, CO reacts more readily with an oxygen atom near the dopant than it would in the absence of the dopant: doping facilitates the Mars-van Krevelen mechanism6,7 for oxidation. (2) Dopants having a higher valence than the cation they replace in the oxide (e.g., Zn oxide doped with Ti) tend to adsorb O2 from the gas phase and activate it to make it a better oxidant. Calculations and experiments show that this “activated oxygen” reacts with CO and oxidizes it.8 Unlike in the Mars-van Krevelen mechanism, the oxygen atoms engaged in the oxidation reaction come from the gas phase not from the surface. (3) In some cases, doping facilitates the dissociative adsorption of molecules. This happens either because one of the fragments binds to the dopant and the other to an oxygen atom nearby or because both fragments bind to the surface oxygen atoms activated by the presence of the dopant. This behavior was exemplified by the dissociation of methanol on doped ZnO9 and by the dissociative adsorption of methane on Pt-doped CeO2.10 * To whom correspondence should be addressed. E-mail: metiu@ chem.ucsb.edu.

In this article, we study how the energy of oxygen-vacancy formation on the (001) and (011) faces of La2O3 is affected by doping the oxide with Cu, Zn, Mg, Fe, or Al. We are interested in La2O3 because it has been used as a catalyst for the oxichlorination of methane,11 for the destruction of halogenated organic compounds,12,13 and for methane oxidative coupling.14,15 Lanthanum oxide doped with Fe and Sr catalyzes methane oxidative coupling,16-18 and doping seems to improve the efficiency of the catalyst. It is natural to inquire which dopant is most effective in activating La2O3. The formation of oxygen vacancies has been studied extensively for reducible oxides, in particular, TiO2 and CeO2.19-23 The removal of an oxygen atom from these oxides causes the reduction of Ti or Ce from a formal charge of 4+ to 3+. The electrons that had been engaged in the bond between the removed oxygen and the oxide become localized on the cation after oxygen removal. Even though compounds in which La is divalent exist (e.g., LaH2, LaSe, LaS, LaTe), La has a very strong preference for being trivalent. For this reason, La2O3 is considered an irreducible oxide in the sense that chemical events at the surface of the oxide will not induce La atoms to change their valence (or formal charge). We suspect, therefore, that the electronic structure of oxygen vacancies on La2O2 will be different than that on TiO2 or CeO2. In particular, it is more likely that the electrons that were engaged in bonding the removed oxygen atom will be localized at the vacancy site. The calculations presented here confirm that this is the case. The presence of these electrons at the oxygen-vacancy site will affect the chemical properties of the defect, especially its ability to bind electrophilic reactants, such as O2. We have examined two faces of La2O3 because there is evidence that, in the case of oxides, different faces can have very different catalytic chemistry. For example, the MoS2 catalyst consists of platelets whose largest facet is unreactive; the active sites for desulfurization are at the edges of the platelets.24-27 The energies of oxygen-vacancy formation on

10.1021/jp103604b  2010 American Chemical Society Published on Web 06/24/2010

Oxygen Vacancies on Undoped and Doped La2O3 Surfaces

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Figure 1. Geometric structure of La2O3(001) surfaces. The subsurface six-coordinated oxygen is in orange in the top view. O4 is a four-coordinated oxygen and O6 is a six-coordinated oxygen.

doped CeO2 on different faces are substantially different from each other.28 The most stable Mo oxide cluster on the (101) face of anatase has the stoichiometry MoO3 and one molybdyl; on the (001) face, the stoichiometry is MoO4 (Mo takes an oxygen atom from the surface) and the cluster has two molybdyl groups.29 Substantial differences have been found between the Mo oxide clusters on two faces of γ-alumina.30 In this article, we use DFT calculations to study the energy of formation and the electronic properties of the oxygen vacancies of undoped and doped La2O3(001) and (011). The dopants are Cu, Zn, Mg, Fe, and Al. We have chosen them to cover a variety of cases. Mg is an irreducible divalent atom, whereas Cu can be mono- or divalent. Similarly, Al is irreducible trivalent, whereas Fe valence can be 2 or 3. We made these choices because we wanted to test whether the ability of the dopant to change its valence affects its ability to lower the energy of oxygen-vacancy formation. We also wanted to examine dopants whose oxides have very different energies of formation to test whether there is any correlation between this quantity and the extent to which the dopant reduces the energy of oxygen-vacancy formation.

GGA are confirmed by DFT + U. DFT + U is a semiempirical method39 in which the parameter U is chosen by fitting some experimental property. In many cases, U is chosen to bring the Kohn-Sham eigenvalues in better agreement with the observed band gap or to ensure that the energies of the Kohn-Sham states, created when an oxygen vacancy is formed, fall in the gap, etc. We do not follow this procedure for two reasons: the Kohn-Sham equations are meant to give the correct density not the single-state excitations of the system (otherwise, a manybody theory, such as GW, would not be necessary), and the chemistry is controlled by total energy differences not by the Kohn-Sham states. Therefore, we have determined the value of U for La to reproduce the heat of the reaction LaCl3(s) + H2O(g) f LaOCl(s) + 2HCl(g). We use oxidation with water to avoid reactions involving the O2 molecule because O2 is not well described by GGA-DFT. When U ) 7.5 eV, the calculated reaction energy is 1.20 eV, which is close to the experimental value40 of 1.21 eV. We find that the GGA and the GGA + U calculations are in semiquantitative agreement (see discussions following) with regard to the energy of making oxygen vacancies and the density of states. For this reason, we have used rPBE-GGA for most of the calculations reported here.

2. Computational Method

3. Results and Discussion 3.1. Vacancies on Clean La2O3 Surfaces. 3.1.1. Structures of the La2O3(001) and (011) Surfaces. The high-temperature A-form of La2O3 crystallizes in the trigonal space group P3m1, and the experimental lattice constants41 are a ) b ) 3.939 Å and c ) 6.136 Å. The calculated lattice constants are a ) b )3.933 Å and c ) 6.154 Å, in agreement with a previous calculation42 and close to the experimental values. There are two types of oxygen atoms in the bulk La2O3, one (denoted O4) is coordinated with four La atoms and the other (denoted O6) with six La atoms. In the bulk, each La atom is coordinated with seven oxygen atoms: four of them are O4, and the other three are O6. The structure of the (001) facet is shown in Figure 1. As the side view of the slab shows, the outermost atomic layer consists of O4 atoms (colored red), each connected to three La atoms. In describing the structure of the surface, we maintain the nomenclature used for the bulk (i.e., four- and sixcoordinated O atoms) even though some of the bonds were cut when the surface was created and the coordination of the atoms lowered. The layer below the O4 atoms consists of La atoms, and the O4-La distance is 2.46 Å. Below these two layers, there is a layer of O6 atoms. The distance between the O atoms and the lanthanum atoms located above them is 2.76 Å. Underneath the O6 layer, there is a layer of La atoms connected to a layer of O4 atoms below it. This strip of five atomic layers has the stoichiometry La2O3 and is repeated as one moves toward the bulk of the material.

The calculations reported here were performed by using periodic, spin-polarized, density functional theory (DFT) as implemented in the Vienna ab initio program package (VASP).31-34 The electron-ion interactions are described by the projector augmented wave (PAW) method proposed by Blo¨chl35 and implemented by Kresse.36 We used the rPBE functional37 and a plane-wave basis set with an energy cutoff of 400 eV. In some cases, GGA + U calculations were also carried out, as implemented in VASP.38 The La2O3 slab had 10 atomic layers and a 15 Å vacuum region. A 2 × 2 surface cell was employed in the calculations, and in some cases, a 3 × 3 surface cell was used to the check the influence of the cell size (i.e., the dependence of the energy of vacancy formation on vacancy concentration). During structure optimization, all ions in the unit cell were allowed to relax and no symmetry was imposed. The optimization was stopped when the force on the atoms was smaller than 0.02 eV/Å. At this time, the prevailing opinion is that GGA-DFT may have difficulties in dealing with oxides having narrow d or f bands.22 It is also believed that the GGA + U method improves the quality of the DFT calculations. These opinions are tentative: we do not know with certainty for which oxides and for which properties GGA has difficulties, nor do we know whether DFT + U or hybrid functionals cure these problems. Nevertheless, it is prudent to perform some DFT + U calculations to test whether the qualitative conclusions and the trends predicted by

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Figure 2. Geometric structure of La2O3(011) surfaces. The green circle indicates two different La atoms on the (011) surface. One has three O4 oxygen coordinations (La3), and another has four O4 oxygen coordinations (La4).

Viewed from above (see top view in Figure 1), the surface has a hexagonal structure, each hexagon containing three O4 atoms and three La atoms. The O6 atoms (colored orange) located in the third layer are seen through the centers of the hexagons. The side and the top views of the (011) face are shown in Figure 2. The top layer consists of O4 atoms. Next, there is a layer containing two kinds of La atoms, denoted La3 and La4, according to their coordination with oxygen. The (011) face is more open than the (001) face, and the O6 atoms, which, at the surface, have a 5-fold coordination, are accessible to molecules coming from the gas phase. They are located 1.03 Å below the outermost surface layer. 3.1.2. Surface Energy of the (001) and (011) Faces. The surface energy of the two faces was calculated by subtracting from the slab energy the energy of the bulk oxide having the same number of atoms as the slab and dividing the result by 2. Calculations using the rPBE functional give 0.43 J/m2 for the (001) face and 0.55 J/m2 for the (011) one. The (001) face is, therefore, more stable. As a propensity rule, we assume that, in most cases, a face having a lower surface energy is less reactive (makes weaker bonds with adsorbed molecules). A lower surface energy indicates that the surface atoms are better able to rebond and alleviate the damage done when bonds were cut to prepare the surface. We note that these are the surface energies of the ideal, flat surface used in our slab model. In reality, the surface energy depends on which molecules are adsorbed on it. In addition, the real facets are likely to have steps and defects that will also change the surface energy. Because of this, we do not expect that the crystallite shape produced by a Wulff construction based on the calculated surface energies will match closely the observed shapes. 3.1.3. Formation of Oxygen Vacancies on La2O3 Surfaces. The energy Evac(f) for forming an oxygen vacancy is defined as

TABLE 1: Oxygen-Vacancy Formation Energy (Evac(f), eV) Needed for Removing an Oxygen Atom O4 or O6 To Form an Oxygen Vacancy and 1/2 Molecule of O2 in Gasa vacancy

Evac(f)

vacancy on the (001) surface 2 × 2 unit cell, rPBE O4 O6

6.44 5.77 3 × 3 unit cell, rPBE

O4

6.33 2 × 2 unit cell, rPBE + U

O4

6.20

vacancy on the (011) surface, rPBE O4 5.98 O6 5.86 One calculation with rPBE + U is reported and one with a large supercell (lower vacancy concentration). a

vacancy decreases slightly by 0.11 eV with concentration, indicating a small repulsive interaction between vacancies. We have also calculated the energy to form an O4 vacancy, for a 2 × 2 surface supercell, with GGA + U, using the U ) 7.5 eV determined to fit the enthalpy of the reaction LaCl3(s)

Evac(f) ) Evac + E 1 O2 - Est 2

where Evac is the energy of a surface with one vacancy per supercell, E1/2O2 is half the energy of an O2 molecule in the gas phase, and Est is the energy of the same supercell with no vacancy. The energies for forming an O6 or an O4 vacancy for the (001) face are given in Table 1. The values of 6.44 and 5.77 eV, for the O4 and O6 removal, respectively, are very large (compared with ZnO, TiO2, or CeO2) in keeping with the fact that La2O3 is a very stable oxide. We report results for two vacancy concentrations, 25%, corresponding to a 2 × 2 surface unit cell, and 11%, corresponding to a 3 × 3 surface unit cell. The energy of formation of an O4

Figure 3. Top panel: the density of states (DOS) of stoichiometric La2O3(001). Second panel: the DOS of La2O3(001) missing one O4 atom per supercell, in the top layer. Third panel: the DOS for an O4 vacancy at the surface, calculated with rPBE + U. Fourth panel: the DOS for the slab with an O6 vacancy at the surface.

Oxygen Vacancies on Undoped and Doped La2O3 Surfaces

Figure 4. The top panel shows the density of states (DOS) of La2O3(011). The middle panel shows the DOS for La2O3(011) with an O4 vacancy; the bottom panel shows the DOS for an O6 vacancy on La2O3(011). The calculations were done with the rPBE functional.

+ H2O(g) f LaOCl(s) + 2HCl(g). The vacancy-formation energy obtained with GGA + U is lower than that obtained with rPBE-GGA by 0.24 eV. This is the same order of magnitude as the expected errors in DFT, and because we are interested in qualitative trends (i.e., which dopant is most effective in lowering the energy of vacancy formation), GGA is sufficient for our purpose. Moreover, the density of states of the reduced surface calculated with GGA-DFT is very similar to that calculated with GGA + U, which also reinforces the conjecture that GGA + U is not that different from GGA, for La-containing solids. 3.1.4. Electronic Structure of Oxygen Vacancies on Pure La2O3 Surfaces. The density of states (DOS) of La2O3(001) are shown in Figure 3 for (in order, from the top) a stoichiometric surface, a surface with an O4 vacancy (rPBE calculation), a surface with an O4 vacancy (rPBE + U calculation), and an O6 vacancy (rPBE calculation). Several features are noted: (1)

J. Phys. Chem. C, Vol. 114, No. 28, 2010 12237 Forming a vacancy moves the Fermi level from the top of the valence band (for the stoichiometric surface) near the bottom of the conduction band. (2) When the vacancy is formed, two filled, degenerate (one spin-up, one spin-down) Kohn-Sham states appear close to the conduction band. (3) The difference between the DOS calculated with rPBE and that calculated with rPBE + U is minor. For other oxides, the GGA DOS does not have states in the gap. This is a weakness of GGA because such states have been observed in experiments. A similar feature was also observed for the vacancies on (011) surfaces, as shown in Figure 4. Figure 5 shows constant-surface plots of the absolute value squared of the orbitals whose energy is in the gap. For both faces and for both types of vacancies (O4 or O6), the electrons in these new orbitals are localized at the vacancy site, whether we use rPBE or rPBE + U. Because of this localization, we expect that these vacancies will bind strongly and activate electrophilic reactants, such as oxygen or halogens. The behavior of the electrons in these new orbitals is different from that observed for oxygen vacancies in reducible oxides, such as TiO2 or CeO2, for which GGA predicts that the electrons are delocalized and GGA + U predicts that they are localized on the Ti or Ce atoms, converting the formal charges of the cations from 4+ to 3+. 3.2. Effect of Doping La2O3 with Cu, Zn, Mg, Fe, or Al. 3.2.1. Introduction. The large oxygen formation energy for the pure La2O3 surfaces prompted us to investigate whether doping the La2O3 surface activates the oxygen atoms in the neighborhood of the dopant. We chose Cu, Zn, and Mg because they have a lower valence than La and chose Al and Fe because they have the same valence. So far, much attention has been paid to whether the cation in the oxide is reducible or not. Here, we examine whether it makes a difference if the dopant is reducible or not. This is why we are looking at Cu, which can be mono- and divalent, and Fe, which can be di- and trivalent, and Zn, Mg, and Al, which have only one valence. Of course, the valence and/or the reducibility of the dopant is not the only factor controlling the effect of the dopant. Another factor is the energy of formation of the oxide of the dopant, which is a crude measure of the eagerness of the dopant to bind oxygen.

Figure 5. Partial charge density of the orbitals in the gap of O4 (a, c) and O6 (b, d) vacancies on La2O3(001) and (011) (top view). The isovalue is 0.02 e/Å3. For O4 vacancies, both GGA and GGA + U results are shown.

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Figure 6. Structure of La2O3(001) surfaces doped with Cu, Zn, Mg, Fe, and Al together with the undoped La2O3(001) surface (top view). The numbers from 1 to 6 indicate the six neighboring oxygens of dopants.

TABLE 2: Distance (in Å) between the Dopant in the Surface Layer of La2O3(001) and Its Six Neighboring Oxygen Atoms (As Shown in Figure 6) from rPBE Calculationsa X

X-O1

X-O2

X-O3

X-O4

X-O5

X-O6

La Cu Zn Mg Fe Al

2.36 1.82 2.01 2.05 1.89 1.78

2.36 1.82 2.01 2.05 1.89 1.78

2.36 3.88 2.01 2.05 1.89 1.78

2.76 1.86 3.36 3.31 3.37 3.37

2.76 3.79 3.36 3.31 3.37 3.37

2.76 3.79 3.36 3.31 3.37 3.37

a The first row gives the distances between La and O for the undoped oxide.

Moreover, if the oxide of the dopant has a different structure than the oxide being doped, the dopant finds that the oxygen atoms in the doped oxide are, so to speak, in the wrong place and it cannot form good bonds with them. Therefore, one expects that a dopant that has a lower valence than the cation it replaces, and whose oxide has a lower energy of formation and a different structure than the oxide being doped, will weaken the bond of the oxygen atoms nearby to the oxide more than a dopant that does not have these qualities. This will make the doped oxide a better oxidant than the undoped one. One should keep in mind that a better oxidant does not mean a better oxidation catalyst. If the oxidation mechanism is Mars-van Krevelen, the oxygen atom used to oxidize the substrate must be replaced by oxygen from the gas phase; if the oxygen is too easy to remove from the surface, it should be hard to put it back.2,3,5 As a result, the oxide is reduced and may become inactive for an oxidation reaction. 3.2.2. Structural Changes Caused by Doping. The structures of La2O3(001) surfaces with several dopants in the surface layer are shown in Figure 6. A La atom in the surface layer of the (001) face is coordinated with three O4 atoms, with a La-O distance of 2.36 Å, and to three O6 atoms, with a La-O distance of 2.76 Å (see Table 2). Doping this surface with Cu causes a large atomic rearrangement: unlike La, Cu does not bind to one of the neighboring O4 atoms (the Cu-O4 distance to one of the neighboring O4 atoms is 3.88 Å). The distance between Cu and the other two O4 oxygen atoms becomes 1.82 Å, which is much shorter (by 0.54 Å) than the corresponding La-O4 distance. The distance between Cu and the three O6 oxygens neighboring it is also very different from the La-O6 distances

in the undoped oxide: one bond is shorter by 33% (1.86 Å compared with the 2.76 Å La-O4 distance in the undoped oxide), and others are longer by 37% (3.79 Å compared with the 2.76 Å La-O6 distance in the undoped oxide). The change in the structure caused by other dopants is less dramatic. The bond lengths between the dopant and the O4 oxygens are 2.01, 2.05, 1.89, and 1.78 Å for Zn, Mg, Fe, and Al, respectively, compared with 2.36 Å for the pure oxide. The distances between the dopant and the O6 atoms are 3.36, 3.31, 3.37, and 3.37, for Zn, Mg, Fe, and Al, respectively, compared with 2.76 Å for the La-O6 distance in the pure oxide.

Figure 7. Projected density of states (PDOS) of Cu-doped La2O3(001) and O4 vacancy on Cu-doped La2O3(001) from rPBE calculations and rPBE + U calculations.

Oxygen Vacancies on Undoped and Doped La2O3 Surfaces

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Figure 8. Partial charge density of the HOMO of O4 vacancies on the Cu-doped La2O3(001) surface from rPBE and rPBE + U. The isovalue is 0.02 e/Å3. The dashed circles indicate the position of the missing oxygen.

3.2.3. Changes in the Electronic Structure Caused by Doping. In Figure 7, we show the projected density of states (PDOS) of Cu-doped La2O3(001), with and without an oxygen vacancy. We examined the Cu-doped surface because doping with Cu has the most dramatic effect on the geometry of the system. The PDOS for the Cu-doped La2O3(001) is shown in the top panel of Figure 7. This should be compared to the top panel in Figure 3, which shows the DOS for the undoped La2O3(001). Doping with Cu creates two new degenerate (spinup and spin-down), empty states just above the Fermi level, which involve the atomic orbitals of Cu and O. The PDOS, after a surface O4 atom has been removed from the surface layer, are shown in the second panel of Figure 7. Upon removal of the O4 atom (one per supercell), the degenerate states caused by doping with Cu shift below the Fermi level; the atomic orbitals of Cu and O are populated when the oxygen vacancy is created. The creation of the vacancy also causes the appearance of two degenerate states above the Fermi level. Thus, the creation of the vacancy places electrons on the Cu atoms, reducing them. Bader charge analysis shows that creating the vacancy increases the electron charge on Cu by 0.54e. It is conventional to say, in such situations, that Cu is reduced from Cu2+ to Cu+ by the formation of the vacancy, even though all computations show that the cations in oxides never have the formal charges assigned to them by inorganic chemists. Plots of the absolute value squared of the HOMO for Cudoped La2O3(001) having an O4 vacancy are shown in Figure

8. The electron in the HOMO is located on the Cu atom and the neighboring oxygens. This is different from the case of the oxygen vacancy on the undoped La2O3(001) where electrons are localized in the vacancy. Unlike Cu, which has the ability to change its valence state, such as from 2+ to 1+, by accepting an electron, Zn is only divalent. Figure 9 shows the PDOS of Zn-doped La2O3(001) without and with an O4 vacancy. The PDOS of the Zn-doped La2O3(001) surface has a small shoulder (“a” in Figure 9) above the Fermi level. This empty state corresponds to the hole created when divalent Zn replaces the trivalent La, creating an electron deficiency. The absolute value squared of this empty orbital is shown in Figure 10. The hole is located on the oxygens neighboring Zn. After a vacancy was created, there are two new localized states (“b” and “c” in Figure 9) in the gap and they are not degenerate. Figure 10 shows that they are indeed localized on the vacancy. One of them (b) is filled, and the other is unoccupied. The small shoulder observed for Zn-doped stoichiometric La2O3 disappeared. The features observed from PDOS can be understood as follows. When oxygen is removed to create a vacancy, two electrons are left behind. For undoped La2O3(001), these electrons are states in the gap, as shown in Figure 3. For Cu-doped La2O3(001), the electron is transferred to Cu and O, and the vacancy has no electron density. For Zndoped La2O3(001), the electrons fill the empty state at the top of the valence band (“a” in Figure 9) and one of the localized states of vacancy (“b”); another state is empty (“c”).

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Li and Metiu TABLE 3: Oxygen-Vacancy Formation Energy (Evac(f), eV) for Doped La2O3(001) for O4 and O6 Vacanciesa vacancy

Cu

O4 O6

0.52 0.59

O4

0.55

Zn

Mg

Evac(f), rPBE 2.01 2.59 2.52 2.57

Fe

Al

3.22 4.01

5.09 5.64

Evac(f), rPBE + U 3.70

a The first column indicates what kind of O atom is being removed. The rest of the columns give the vacancy formation energy when a dopant is present in the surface layer. The results for rPBE + U are in the last row.

Figure 9. Projected density of states (PDOS) of Zn-doped La2O3(001) and O4 vacancy on Zn-doped La2O3(001) from rPBE calculations.

3.2.4. Oxygen-Vacancy Formation on the Doped La2O3(001) Surface. The energies of vacancy formation (Evac(f)) of the doped La2O3(001) surfaces have been listed in Table 3. The Cu-doped La2O3(001) has by far the lowest vacancy formation energies: 0.52 and 0.59 eV for the O4 and O6 vacancies, respectively. The presence of Cu reduces the Evac(f) by more than 5 eV (from that of the pure La2O3 surface). For Zn, Mg, Fe, and Al, the energies of vacancy formation are 2.01, 2.59, 3.22, and 5.09 eV for O4 vacancies and 2.52, 2.57, 4.01, and 5.64 eV for O6 vacancies. It is easier to make O4 vacancies then O6 ones, when the dopant is Cu, Zn, Fe, or Al. For the Mg-doped surface, the O4 and O6 vacancies are made with equal ease. All dopants affect the Evac(f) for the O4 vacancy more than that of the O6 vacancy. One could naively think that the more stable the oxide of the dopant (MgO, Al2O3, etc.), the more strongly the dopant will

Figure 10. Partial charge density of orbitals of Zn-doped stoichiometric La2O3(001) (a) and the O4 vacancies (b, c) from rPBE calculations. The orbitals of (a-c) correspond to the labeled states in Figure 9. The isovalue is 0.02 e/Å3. The dashed circles indicate the position of missing oxygen atoms.

Oxygen Vacancies on Undoped and Doped La2O3 Surfaces

Figure 11. Relationship between the oxygen-vacancy formation energy (Evac(f)) of different doped surfaces (Cu, Zn, Mg, Fe, and Al) and the standard formation enthalpy per metal atom (∆H°) f of the metal oxide. The green line is the least-squares fitting between Evac(f) and ∆H°. f

bind with the oxygen atoms neighboring it on the surface of doped La2O3. Therefore, the larger the energy of formation of the oxide of the dopant, the larger the energy of vacancy formation in the doped oxide. In Figure 11, we have plotted the energy to form an O4 vacancy on the surface of the doped oxide versus the standard formation enthalpy of the oxide of the dopant. If a dopant forms more than one oxide, we used the formation enthalpy for all of them. For example, for Cu, we used the enthalpy of Cu2O and CuO and, for Fe, the enthalpy of FeO and Fe2O3 (the enthalpy of other iron oxides is close to that of Fe2O3). There is a fair correlation between the energy of oxygen-vacancy formation on a doped oxide and the enthalpy of the formation of the oxide of the dopant. The graph is also useful for a qualitative interpretation of the results: it suggests that the state of the Fe dopant in the lanthanum oxide is closer to that in Fe2O3 than to that in FeO because the point representing Fe2O3 is closer to the straight line in the graph. For Cu, the distinction is not as clear as for Fe because the enthalpy of formation of CuO is so close to that of Cu2O.

J. Phys. Chem. C, Vol. 114, No. 28, 2010 12241 The enthalpy of formation of the dopant’s oxide is only one of the factors influencing the energy of vacancy formation in the doped oxide. It is hard to believe that, had we studied more dopants, the results for all of them would fall on the straight line. Nevertheless, the graph has some predictive power. When we started this work, Zn was not among the dopants chosen for study. However, we decided that, for methane activation, we need a dopant with an energy of vacancy formation between that of Cu- and Mg-doped La2O3. The energy of formation of ZnO fell between that of Cu and Mg oxides. Therefore, if the line in Figure 11 had any predicting power, the energy of oxygen-vacancy formation for Zn-doped La2O3 should fall between that of Cu-doped and Mg-doped La2O3. After using the diagram to decide that a Zn dopant is a good choice, we calculated the energy of vacancy formation for Zn-doped lanthanum oxide and found that it had the value predicted by using Figure 11. The rPBE + U calculations of the energy of vacancy formation for Cu-and Fe-doped La2O3 are close to those given by rPBE, which are 0.55 and 3.70 eV, respectively. This reinforces, again, the conjecture that rPBE can be used for determining trends in the properties of doped La2O3. 3.2.5. Oxygen-Vacancy Formation on the Doped La2O3(011) Surface. The surface layer of the (011) surface has two kinds of La atoms (La3 and La4 indicated in Figure 2). We have studied in detail the energy of vacancy formation when a La4 atom is replaced with a dopant. The optimized structures of doped (011) surfaces are shown in Figure 12. La4 is surrounded by four O4 oxygens and two O6 oxygens (in Figure 12, the oxygen atoms numbered 1-4 are O4 oxygens and the atoms 5 and 6 are O6 oxygens). The distances between a La4 atom on the undoped La2O3(011) surface and the O4 oxygens in its neighborhood are 2.35 and 2.40 Å; the distance to the O6 oxygens is 2.91 Å. As can be seen in Table 4, all dopants cause similar structural changes in their neighborhood: their bonds to the four O4 atoms are shorter than the La4-O distance in the undoped oxide, and

Figure 12. Structure of La2O3(011) surfaces doped with Cu, Zn, Mg, Fe, and Al together with the undoped La2O3(011) surface (top view). La4 was replaced in the doped structures. The numbers from 1 to 6 indicate the six neighboring oxygens of dopants.

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TABLE 4: Distance (in Å) between the Dopant in the Surface Layer of La2O3(011) and Its Six Neighboring Oxygen Atoms (As Shown in Figure 12) from rPBE Calculationsa X

X-O1

X-O2

X-O3

X-O4

X-O5

X-O6

La Cu Zn Mg Fe Al

2.35 1.98 1.98 2.04 1.90 1.80

2.40 2.0 2.74 2.10 1.98 1.86

2.35 1.88 1.98 2.04 1.90 1.80

2.35 2.05 2.01 2.04 1.96 1.82

2.91 3.73 3.58 3.63 3.62 3.70

2.91 3.53 3.58 3.63 3.62 3.70

a The first row gives the La-O distance for a La atom in the first layer for the undoped oxide.

TABLE 5: Oxygen-Vacancy Formation Energy (Evac(f), eV) of the La2O3(011) Surfaces for O4 and O6 Vacanciesa vacancy O4 O6

Cu 0.58 0.51

Zn

Mg

Evac(f) 2.13 2.52 2.38 2.36

Fe

Al

3.64 4.34

5.36 5.62

a

The first column indicates what kind of O atom is being removed. The rest of the columns give the vacancy formation energy when a dopant is present in the surface layer. The values are from rPBE calculations.

Figure 13. Structure of Cu-doped La2O3(011) (top view), where La3 was replaced by Cu.

their bond to the O6 atoms is longer. These changes in the bond lengths are substantial (see Table 4). On the (001) surface, the effect of Cu on the structure was very different from that of the other dopants; on the (011) surface, all dopants cause similar changes. The vacancy formation energies on the surface of La2O3(011) doped with Cu, Zn, Mg, Fe, and Al are presented in Table 5. The results are similar to those obtained for the (001) surface. We have also performed an exploratory calculation for the case when a Cu dopant replaces a La3 atom. Evac(f) is calculated to be 1.07 and 1.12 eV for O4 and O6 vacancies, respectively. This is larger than the values obtained when La4 is replaced with Cu, by 0.49 and 0.61 eV. The optimized structure is shown in Figure 13. The Cu atom becomes 4-fold coordinated by dragging an O6 atom up to make a bond with the bond length of 1.94 Å. This is similar to the structure of the Cu-doped (001) surface where an O6 oxygen is pulled toward the surface to make a 1.86 Å long bond with Cu. 4. Conclusions We are concerned here with two catalytic mechanisms in which the oxygen atoms in the surface of the oxide catalyst play an essential role. One is the Mars-van Krevelen mechanism in which the oxygen atom responsible for the oxidation of the reactant originates from the oxide’s surface. The other

consists of the dissociative adsorption of a reactant in which the fragments bind to the oxygen atoms at the surface of the oxide. An example is alkane activation in which the breaking of the C-H bond results in binding of the H atom and the alkyl to two oxygen atoms on the surface of the oxide. Both mechanisms can be made more efficient by surface modifications that increase the chemical activity of the oxygen atoms in the surface. The energy of oxygen-vacancy formation can be used as a crude predictor of the ability of the oxygen atoms at the surface of the oxide to engage in chemical reactions. Therefore, to improve the activity of lanthanum oxide, we need surface modifications that lower the energy of oxygen-vacancy formation. This can be achieved through appropriate doping1,2,43 or by creating submonolayers of an oxide on the surface of another oxide.44,45 La2O3 is a very stable oxide. Nevertheless, it is a better catalyst for oxidative methane coupling than other oxides.46,47 The question we addressed here is whether we can improve its activity by appropriate doping. By examining the results of prior calculations,2,4,22,28,43,48 we have formulated the following propensity rules: (1) To decrease the oxygen-vacancy formation energy, the valence of the dopant should be lower than or equal to that of the cation it is replacing (La in the present case). (2) The oxide of the dopant should be less stable (as judged by the enthalpy or the Gibbs free energy of formation) than the oxide being doped. With these rules in mind, we have chosen to study doping La2O3 with Cu, Zn, Mg, Fe, and Al. From among divalent dopants, we have chosen Cu, because it is capable of two valence states, and Mg, because it is unwilling to change its valence. Zn was selected because it is an irreducible dopant (like Mg, it will not change its valence) whose enthalpy for oxide formation is lower than that of Mg. From among trivalent dopants, we picked Fe, which is multivalent, and Al, which is not. The enthalpies of formation of the oxides of these dopants are all smaller than the enthalpy of formation of lanthanum oxide. We have found that all of these dopants lower substantially the energy of oxygen-vacancy formation, as suggested by the propensity rule mentioned above. We also found that there is an approximate linear relationship between the energy of oxygen-vacancy formation and the enthalpy of formation of the oxide of the dopant. This is surprising because there are many other factors, besides the enthalpy of formation, that should come into play. The difference in valence between the dopant and La atom that it replaces should clearly play a role. If the bonds in the system are purely ionic, the dopant with a lower valence will have a lower formal charge and this will affect its ability to bind the oxygen. If the dopant-oxygen bond is purely covalent, the lower valence makes the dopant unable to bind all the oxygen atoms that La can bind, and this too will lead to a weakening of the bond of at least one oxygen atom to the surface. The distance between the dopant and the oxygen atoms in the oxide of the dopant is usually very different from the distance between the dopant and oxygen in the doped oxide. Because the bond strength depends markedly on the interatomic distance, we expect this change in distance to be a factor in determining how strongly the dopant binds oxygen. Finally, the oxide of the dopant has a different structure than the oxide being doped. As a result, the dopant finds that the oxygen atoms are in the “wrong place” and is less able to bind to them than in its own oxide. It is unlikely that the effect of all of these factors can be captured by a linear relationship between the energy of vacancy formation in the doped oxide and the enthalpy of

Oxygen Vacancies on Undoped and Doped La2O3 Surfaces formation of the oxide of the dopant. Further calculations are needed to determine how general this linear relationship is. In view of many examples that show that different faces of an oxide have rather different chemical activity, we were surprised to find that doping La2O3 did not lead to qualitative differences between the energy of oxygen-vacancy formation on the (001) and (011) faces. However, the fact that the energy of vacancy formation on the two faces is roughly the same does not necessarily mean that the two faces are equally active in breaking the C-H bond. When CH4 dissociates on the surface, CH3 and H will bind to the oxygen atoms whose bond to the oxide is weakened by the presence of the dopant. If these two oxygen atoms are very far apart, the C-H bond must be stretched very much before the fragments can start making bonds with the oxygens. This means that the activation energy for bond breaking will be high. Therefore, the distance between the activated oxygen atoms is an important factor in determining the activation energy, and this distance differs from face to face. The eagerness of the oxygen atoms to make new bonds, reflected in the magnitude of the energy of vacancy formation, does not necessarily predict the activation energy for dissociative adsorption, but it will affect the thermodynamic stability of the fragments. Doping La2O3 with Cu lowers the energy of vacancy formation the most. This means two things: This system will lose the active oxygen easily to form an oxygen vacancy, which is not eager to adsorb O2 from the gas phase. Therefore, at the high temperatures at which one expects to break the C-H bond, the surface of Cu-doped La2O3 will have an oxygen vacancy near the dopant. This reduced surface is not active toward methane dissociation into a chemisorbed CH3 and a hydroxyl. This is another example of what we call “the moderation principle”: if a surface modification makes the oxide a very strong oxidant (e.g., by making the energy of vacancy formation very small), this will not make it a good oxidation catalyst because the reaction will reduce the oxide and oxygen from the gas phase will not be efficient in reoxidizing it. A good dopant should activate the surface oxygen but not by too much.2-5 It is often suggested that, because oxygen vacancies are chemically active, they must play an important role in catalysis. This is not necessarily the case. If the oxidation reaction uses oxygen from the surface, the oxidation creates oxygen vacancies on the surface. However, because oxygen is present in the gas, the vacancies will be filled by a competing process. At steady state, the concentration of vacancies on the surface is established by the competition between reduction and oxidation. The winner of the competition is determined by the rate constants for reduction and oxidation, by the ratio between the reductant and the oxidant in the gas, and by temperature. In the case of methane oxidation, the reductant is not very active and it is likely that the concentration of vacancies on the surface is very low and irrelevant (as long as oxygen is present in the gas). However, a large vacancy concentration will be established if the temperature is high and the ratio of methane/oxygen is very high. In this case, the catalyst is the partially reduced surface and the vacancies are very likely to affect the surface chemistry. It is interesting to note that the concentration of vacancies at steady state can be manipulated by introducing in the feed controlled amounts of a strong reductant (e.g., CO), which will increase the number of vacancies on the surface. If the surface with a large vacancy concentration is a better catalyst, the addition of CO will improve performance.

J. Phys. Chem. C, Vol. 114, No. 28, 2010 12243 It is difficult to measure reliably the energy of oxygenvacancy formation in the top layer of an oxide surface. Nevertheless, it appears that most DFT calculations find that the energy for forming oxygen vacancies is surprisingly high when compared with experiments. It is conceivable that this reflects errors in DFT, but we do not believe that the errors could be so large. We proposed a possible explanation. We note that it is possible that many of the catalysts studied experimentally may be inadvertently doped. The precursors have usually a purity of 99.99%, which means that the catalyst contains 0.01% unknown impurities. By the standards of the electronic materials industry, this is a very heavy doping level. These unknown dopants can affect the energy of oxygen-vacancy formation in two ways. A “global” effect occurs because the dopants change the Fermi level. This can, in turn, change the charge of the vacancy and the energy of its formation,49-51 which will affect the catalytic properties of the oxide. In addition, if the unknown dopants have a tendency to segregate at the surface, they affect the neighboring oxygen locally, by modifying the chemical bonds of the oxygen to the oxide. In the present calculations, we see the sum of the two effects. The global effect can be identified, when it exists, by testing whether the dopant affects the oxygen-vacancy formation energy for oxygen atoms located at some distance from the dopant. There is at least one example where accidental doping affected catalysis: the activity of silica for methane partial oxidation is due to the unintended presence of Fe impurities.52 Also, Lefferts et al.53 used X-ray fluorescence and low-energy ion scattering to show that CaO, TiO2, and Na2O were present on the surface of YSZ and affected catalytic properties. Acknowledgment. We gratefully acknowledge support from the Air Force Office of Scientific Research (Grant No. FAA955006-1-0167) and the Department of Energy (Grant No. DE-FG0289ER140048). Computing resources at UCSB have been supported, in part, by the National Science Foundation under Grant No. CHE 0321368. Use of the Center for Nanoscale Materials was supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under Contract No. DE-AC02-06CH11357. We thank Matthias Scheffler for useful discussions and the Fritz Haber Institute for partial support for B.L. and hospitality for H.M. References and Notes (1) Hegde, M. S.; Madras, G.; Patil, K. C. Acc. Chem. Res. 2009, 42, 704. (2) Kim, H. Y.; Lee, H. M.; Pala, R. G. S.; Shapovalov, V.; Metiu, H. J. Phys. Chem. C 2008, 112, 12398. (3) Shapovalov, V.; Metiu, H. J. Catal. 2007, 245, 205. (4) Pala, R. G. S.; Metiu, H. J. Phys. Chem. C 2007, 111, 8617. (5) Chre´tien, S.; Metiu, H. Catal. Lett. 2006, 107, 143. (6) Mars, P.; van Krevelen, D. W. Chem. Eng. Sci. 1954, 3 (Spec. Suppl.), 41. (7) Doornkamp, C.; Ponec, V. J. Mol. Catal. A: Chem. 2000, 162, 19. (8) Pala, R. G. S.; Tang, W.; Sushchikh, M.; Park, J.; Forman, A.; Wu, G.; Kleiman-Shwarsctein, A.; Zhang, J.; McFarland, E.; Metiu, H. J. Catal. 2009, 266, 50. (9) Pala, R. G. S.; Metiu, H. J. Catal. 2008, 254, 325. (10) Tang, W.; Hu, Z.; Wang, M.; Stucky, G. D.; Metiu, H.; McFarland, E. J. Catal. 2010, in press. (11) Podkolzin, S. G.; Stangland, E. E.; Jones, M. E.; Peringer, E.; Lercher, J. A. J. Am. Chem. Soc. 2007, 129, 2569. (12) Peringer, E.; Salzinger, M.; Hutt, M.; Lemonidou, A.; Lercher, J. Top. Catal. 2009, 52, 1220. (13) Peringer, E.; Podkolzin, S.; Jones, M.; Olindo, R.; Lercher, J. Top. Catal. 2006, 38, 211. (14) Campbell, K. D.; Zhang, H.; Lunsford, J. H. J. Phys. Chem. 1988, 92, 750. (15) Squire, G. D.; Luc, H.; Puxley, D. C. Appl. Catal., A 1994, 108, 261.

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