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The Effect of Environment on the Reaction of Water on the Ceria(111) Surface: A DFT+U Study Zongxian Yang,*,†,‡ Qinggao Wang,† Shuyi Wei,† Dongwei Ma,† and Qiang Sun§ College of Physics and Information Engineering, Henan Normal UniVersity, Xinxiang, Henan, 453007, People’s Republic of China, Henan Key Laboratory of PhotoVoltaic Materials, Xinxiang 453007, People’s Republic of China, and School of Physics and Engineering, Zhengzhou UniVersity, Zhengzhou 450052, People’s Republic of China ReceiVed: February 3, 2010; ReVised Manuscript ReceiVed: July 28, 2010
The interaction of a water molecule with the (111) surfaces of stoichiometric and reduced ceria is investigated using first principle density functional theory with the inclusion of the on-site Coulomb interaction (DFT+U). It is found that on the stoichiometric ceria(111) surface, the water molecule is adsorbed spontaneously through single hydrogen bond configuration. In contrast, on the lightly reduced ceria(111), there exist both molecular adsorption (no-H-bond configuration) and dissociative adsorption (surface hydroxyl) modes. It is obvious that oxygen vacancies can enhance the interaction of water with the substrate. Phase diagrams for stoichiometric and reduced ceria(111) surfaces in equilibrium with water vapor in the complete range of experimentally accessible gas phase condition are calculated and discussed combining the DFT results and thermodynamics data using the ab initio atomistic thermodynamic method. We present a detailed analysis of the stability of the water-ceria system as a function of the ambient conditions, and focus on two important surface processes for water adsorption on the stoichiometric and on the lightly reduced surfaces, respectively. 1. Introduction The uses of ceria (CeO2) as an important component in catalysts and as an electrolyte for solid oxide fuel cells rely on its notorious capability of storing and releasing oxygen.1 In these applications, water acts either as a reactant (e.g., the water-gas shift reaction2) or as a product/spectator (e.g., selective oxidation reactions3). The CeO2(111) surface is known as the most stable surface among the low index surfaces of ceria. Therefore, it is essential to investigate the interaction of water with CeO2(111). Kundakovic et al.4 investigated the interaction of water with the Rh-vapor deposited CeO2(111) using soft X-ray photoemission spectroscopy and thermal desorption spectroscopy. Only molecularly adsorbed water was detected on Rh/stoichiometric ceria surfaces, while Rh/reduced ceria surface is more reactive and promotes dissociation of H2O, where both chemisorbed water and hydroxyls were identified. In the absence of Rh, chemisorbed water desorbs below 300 K and hydroxyls decompose above 500 K to give H2 as a desorption product. Earlier experiment5 has also shown the formation of hydrogen from water adsorption accompanying the reoxidation of reduced oxide at 573 K. However, further surface reduction was found by Henderson et al. and others when the reduced ceria(111) was exposed to water.3,6 More recently, strong adhesion of water to CeO2(111) was observed by using dynamic scanning force microscopy.7 It was found that water readily adsorbs on the CeO2(111) surface and forms hydroxide if oxygen vacancies are present.8 All these conflicting results on whether or not water decomposes on the reduced surface suggest that the adsorption behaviors of H2O on the ceria surfaces are strongly related to the nature of the surfaces used in the experiments. * To whom correspondence should be addressed. E-mail: yzx@ henannu.edu.cn. † Henan Normal University. ‡ Henan Key Laboratory of Photovoltaic Materials. § Zhengzhou University.
Besides the experimental works mentioned above, theoretically, Kumar and Schelling9 found that a water molecule is attached more strongly to the surface when oxygen vacancies are introduced in surface layers using standard density functional theory (DFT), while water decomposition was found using the DFT+U method and a larger supercell.10 Recently, Fronzi et al.11 investigated water molecule adsorption on the stoichiometric and reduced ceria(111) surface with the standard DFT method, which shed a light on the discrepancy of whether or not water spontaneously decomposes on lightly reduced ceria. Although it has been reported that the subsurface O vacancy is almost as stable as the surface vacancy with small energy difference depending on the calculation methods12-14 and the subsurface O can serve as the nucleation center for the surface O vacancy cluster,14 it is more relevant that the surface oxygen ions and oxygen vacancies are involved in the initial reaction. We consider only the surface oxygen vacancies as others did.10,15 A microscopic understanding of the different functions of the ceria surfaces with and without vacancies requires the knowledge of their complex surface atomic structures, which may be influenced by temperature and partial pressure in the surrounding environment.16 Although it is quite obvious that such variations as in the CeO2(111) surface structure and composition may affect the function in applications, systematic studies on this topic are rare. To this end, we constructed a phase diagram using the ab initio atomistic thermodynamic method, which provides a link between the DFT results and environmental effects.17,18 The organization of this work is as follows. The description of the model and the theoretical method employed is given in section 2. Results and discussion are given in section 3, and the conclusion is summarized in section 4. 2. Model and Calculation Methods 2.1. Description of the Model Systems. The free H2O and H2 molecules were simulated by using a large unit cell with
10.1021/jp101057a 2010 American Chemical Society Published on Web 08/18/2010
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dimensions of 8 × 8 × 10 Å3. The calculated equilibrium bond lengths of H2O and H2 are 0.986 and 0.751 Å, respectively; the values reported in previous literature15 are 0.957 and 0.740 Å; the calculated band angle of H2O (104.8°) agrees well with the earlier literature value (104.7°).15 Calculations for bulk CeO2 were performed for a 12-atom unit cell. Our optimized lattice constant for stoichiometric CeO2 is 5.48 Å; the experimental value is 5.41 Å.1 The (111) surfaces were created by cleaving the optimized bulk cells and were modeled as slabs, periodically repeated (in z), consisting of nine atomic layers. The choice of the slab thickness was based on our testing as reported in our previous paper.19 A vacuum layer of 15 Å was introduced on top of the free surface to separate the films. The x and y dimensions of the unit cells were fixed at the calculated equilibrium lattice parameter for bulk ceria. The bottom three atomic layers were fixed at their bulk positions to mimic the bulk. The positions of the ions in the remaining layers were fully optimized in x, y, and z (under the restriction of fixed cell parameters). The lightly reduced systems were created by removing one oxygen atom from the top layer of the CeO2(111) and the six upper layers were reoptimized. The highly reduced systems were created by removing the whole sublayer of oxygen (Osub) and the remaining five upper layers were reoptimized. For the adsorption of water, a H2O molecule was placed on one side of the relaxed slabs. Three layers at the bottom were fixed and the remaining layers, as well as the adsorbate, are allowed to fully relax. The leading errors induced by the existence of dipole moment in the supercells were corrected by using the methods as implemented in the VASP code.20-22 2.2. Calculations. It is known that the standard DFT formulation with LDA or GGA functionals usually fails to describe strongly correlated electrons because of a deficient treatment of electron correlation, combined with an incomplete cancellation of the self-interaction in the Coulomb and exchange integrals.23 In the current paper, we have used the DFT+U method,24 where a Hubbard parameter U was introduced for the Ce 4f electrons, to describe the on-site Coulomb interaction; this helps to remove the self-interaction error and improves the description of correlation effects. It is true, as mentioned by Fronzi et al., that the DFT+U method has some deficiency, e.g. there is no unique U that at the same time gives a reasonable description of structural parameters, relative energies of different oxides, and spectroscopic properties; the dependence of the energetics on the choice of U and projector functions; etc.11 However, to our knowledge, many authors suggested that it is crucial to consider the correlation U term in studies of redox properties.25-27 The DFT+U method can correctly describe the electronic structure of reduced ceria and the tendency of the energy variation, although sometimes it overestimates the adsorption energy. It has been shown that by choosing an appropriate U parameter to account for the strong on-site Coulomb repulsion among the localized Ce 4f electrons, it is possible to consistently describe the structural, thermodynamic, and electronic properties of CeO2, Ce2O3, and CeO2-x, which enables modeling of redox processes involving ceria-based materials.25-27 In contrast, it has been proven that plain DFT wrongly describes the electronic structure of the reduced ceria. We have chosen a U value of 5.0 eV based on the results of our test calculations and previous work25-27 which indicated that only with U g 5 eV can the localization of the Ce 4f electrons in the partially reduced ceria be properly described. Spin-polarized DFT+U calculations were performed with use of the Vienna ab initio simulation package (VASP).21 The
Yang et al. electron exchange and correlation interactions were treated within the GGA by using the Perdew-Burke-Ernzerhof (PBE) functional.28 The projector-augmented wave method (PAW)29 with gradient-corrected functions was applied to treat the core electrons. The cerium 5s, 5p, 5d, 4f, 6s electrons, oxygen 2s, 2p electrons, and hydrogen 1s electrons were treated as valence electrons. The Kohn-Sham orbitals were expanded in plane waves with a kinetic energy cutoff of 30 Ry. The Brillouinzone integrations were performed with Monkhorst-Pack (MP) grids30 and a Gaussian smearing30 of SIGMA ) 0.2 eV. The final results were extrapolated to those of SIGMA ) 0 eV. MP grids of 8 × 8 × 8 k-points were used for the bulk unit cell (i.e., the stoichiometric bulk) and MP grids of 4 × 4 × 1 k-points for the surfaces [i.e., the (111) surfaces of CeO2 and CeO2-x], based on convergence studies (e.g., the total energies of the ceria(111) with and without water adsorbate are converged within 0.02 eV for the MP grids changing from 2 × 2 × 1 to 4 × 4 × 1, and the structures are converged with the same criterion). To take into account the environmental effects, the Gibbs free energy G(T,P) of the whole system was calculated as a function of temperature (T) and pressure (P) from the DFT+U results, as done elsewhere.16-18,31 The DFT+U calculated energy EDFT+U represents Gibbs free energy at zero temperature in vacuum or Helmholtz free energy at zero temperature. For a gas-surface interfacial reaction
surface 1 + gas 1 f surface 2
(1)
where surface 1 represents a reactant in the solid phase, gas 1 represents a reactant in th gas phase, and surface 2 represents a product in the solid phase with adsorbate. The change of Gibbs free energy for reaction 1 can be written as:32
∆G ) Gsurface2 - Gsurface1 - Ggas1
(2)
where the Gibbs free energies (Gsurface1, Gsurface2) of solid phase reagents have relatively small variation and can be approximated by the energy computed by DFT+U.33 On the contrary, the Gibbs free energy of the gas phase will be strongly affected by temperature and pressure (Pgas) and can be written as:32-34
Ggas(T, P) ) EDFT+U + ∆Hgas(T, P0) - T∆Sgas + gas KBT ln(P/P0)
(3)
The first term is the DFT+U result; the second and third terms are the contribution of gas enthalpy and entropy under atmospheric pressure (P0 ) 1 atm), respectively, which could be looked up in a thermodynamic database;33,35 the fourth term is a pressure-dependent contribution32-34 (where KB is Boltzmann constant and P0 is the atmospheric pressure). Accordingly, we can construct the phase diagram to identify the surface atomic structure at a certain temperature and pressure. It should be kept in mind that this method only gives us a rough statistical result to link the DFT result with the real environment. As to how the phase changes take place, it is a matter of molecule dynamics; the phase diagram could not give more details on this topic. 3. Results and Discussion 3.1. The Reduced Ceria(111) Surface. The reduced ceria(111) surface (Figure 1a,b) is created by removing one of
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Figure 1. (a) Side view of reduced ceria(111) with excess electrons localized on next-nearest cerium ions, the numbers represent the distances between the Ce3+ cations and oxygen vacancy; (b) top view of reduced ceria(111); and (c) TDOS of reduced ceria(111). The isosurface values for the gap states image shown in panel a and in the following figures are 0.02 e/Å3.
the surface oxygen atoms from the relaxed stoichiometric ceria(111). The oxygen vacancy formation energy Ev is defined as:
Ev ) ECeO2v + 1/2EO2 - ECeO2
(4)
where ECeO2v and ECeO2 are the total energies of reduced and stoichiometric ceria(111) surfaces, respectively; EO2 is the ground state energy of the oxygen molecule in the gas phase. The value of oxygen vacancy formation energy calculated in this paper is 2.65 eV, which is smaller as compared with the value reported recently (2.87 eV).36 A small gap state peak appeared in the total density of states (TDOS) plots near the Fermi level (Figure 1c), which represents two excess electrons localized on a next-nearest neighboring (NNN) surface cerium and a NNN subsurface cerium after the formation of an oxygen vacancy based on our partial charge analyses (Figure 1a). This structure is denoted as “NNN-NNN structure”, which agrees well with the recent paper37,38 which reported that excess electrons prefer to localize on the Ce ions which are next-nearest neighbor to the vacancy (in other words, the vacancy is surrounded by Ce4+ cations instead of Ce3+ cations), but at variant with the previous papers26,36 which found that the two electrons localized on two surface cerium ions nearest neighbor to the vacancy (which has been proved to be a metastable structure). Since the studied system has multiple local minima, the formation energy of an oxygen vacancy is sensitive to the excess-electron localization sites.37 A more stable structure (i.e., the one with lower oxygen vacancy formation energy and both excess electrons localized on two Ce ions next-nearest neighbor to the vacancy) with respect to the excess electron localization is found in the current study.
3.2. The Adsorption of Water. On the stoichiometric ceria(111) surface, three adsorbed structures have been suggested by Henderson et al.:3 no-H-bonds configuration, one-H-bond configuration, and two-H-bonds configuration. The symmetry of the stoichiometric ceria surface itself corresponds to C3V pointgroup symmetry. As a result, a water molecule adsorbed in the so-called C3V geometry (no-H-bonds configuration) will experience a different environment for both of the hydrogen ions. It therefore seems that the symmetry axis of the H2O molecule will tilt somewhat away from the [111] surface normal. If the tilting is significant, the possibility exists that the water molecule will form one or two H-bonds with surface oxygen ions.9 Similarly, a starting structure with two-H-bonds spontaneously breaks one of the hydrogen bonds and forms a one-H-bond structure, which has an even lower energy as compared with the two-H-bonds structure.9 The strength of the adsorption can be measured by the adsorption energy, Ead, which is defined as:
Ead ) EH2O + ECeO2 - EH2O/CeO2
(5)
On the basis of the calculated results of Chen et al.15 and Kumar et al.,9 three configurations (with no-, one-, and twoH-bonds, respectively) for water molecule adsorption are considered with the O of water (denoted as O*) nearly at the top of a cerium atom. A final stable configuration for the adsorbed H2O molecule is reached, which has the one-H-bond structure. The calculated adsorption energy for this configuration is 0.57 eV (Figure 2a), which agrees with the previous calculated values (0.58 and 0.56 eV)9 and is in agreement with the experiment results (0.56-0.61 eV) reported by Prin et al.,39 while a smaller adsorption energy (0.30 eV) was reported by
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Figure 2. The optimized configurations of water molecule on stoichiometric ceria(111): side view (up) and top view (down) of (a) one-H-bond configuration and (b) nearly decomposed configuration. The numbers represent the corresponding structure parameters.
Watkins et al.10 In Figure 2a, a hydrogen atom (Hb) of water binds to a lattice oxygen (Osurf) ion with a hydrogen bond of 1.62 Å, which stretches the O*-H bond by 0.045 Å and increases the bond angle by 4.3° as compared with the corresponding values of a free water molecule. The lattice O (Osurf) binding to Hb was drawn out by 0.2 Å above the surface. If the Hb atom that binds to the surface oxygen (Osurf) is stretched even further toward Osurf, we get a structure as shown in Figure 2b, which corresponds to a nearly decomposed configuration on stoichiometric ceria(111) with a very short hydrogen bond (1.04 Å). In this configuration, the O*-H bond of water was elongated to 1.52 Å and the shortest O*-Ce distance between water and the surface Ce is 2.25 Å, and the adsorption energy (0.55 eV) is very close to that for the configurations in Figure 2a and the value (0.65 eV) reported in previous literature.10 Two kinds of reduced state are considered for the reaction of the water molecule on the ceria(111) surface: a lightly reduced surface (only a surface O atom is removed) and a highly reduced ceria surface (a whole subsurface oxygen layer is removed), which is favorable under extremely oxygen-poor conditions.40 On the lightly reduced ceria(111), we have put the water molecule initially on different sites, e.g. the top sites of oxygen vacancy, Ce, Ce-h (i.e., the triangle center of the three surface cerium cations), and so on, with different configurations (e.g., no-, one-, and two-H-bonds). It is found that the water molecule can be adsorbed through the no-H-bonds configuration (Figure 3a) with an adsorption energy of 0.54 eV, which is smaller than the reported value (0.80 eV) of Watkins et al.10 The difference mainly arises from the different reference systems used for the reduced ceria(111), as discussed in section 3.1; the reference system used in this paper corresponds to an energy minimum structure with the most preferable electron localization configuration (i.e., the NNN-NNN structure), while in Watkins et al.’s
paper,10 a NN-NN structure was used as the reference. The bond angle and the O*-H bond lengths in the adsorbed water molecule increase by 1.3° and 0.003 Å, respectively, as compared with the values of a free water molecule. It is also found that the water molecule prefers to decompose near the oxygen vacancy site once its hydrogen atom(s) lean toward the lattice oxygen ions (one-H-bond configuration or two-H-bonds configuration) and form a hydroxyl surface (as shown in Figure 3b) with the surface hydroxyl (O-H) bond lengths of 0.986 Å and an energy release of about 2.11 eV, which are close to the corresponding values (0.972 Å and 2.18 eV, respectively) reported by Chen et al.15 Therefore, the decomposed adsorption with the formation of the hydroxyl surface would be the most preferable structure on the reduced ceria(111) surface. On the hydroxyl surface, we found that covalent bonds formed between H atoms and surface oxygen atoms based on charge distribution analyses. The total density of states (TDOS) for the hydroxyl surface is shown in Figure 4a. There are two gap state peaks located below and above the O 2p derived band, and denoted as “b” and “c”, respectively. The former corresponds to the covalent bonds of the two hydroxyls (Figure 4b) and the latter to the two Ce3+ cations (Figure 4c). Although the oxygen atom (O*) of water is localized at the oxygen vacancy site when the water molecule decomposes on the lightly reduced ceria(111) surface, the surface has not been oxidized. Only when the hydroxyls dissociate and a hydrogen molecule forms can the surface be oxidized. However, the energy needed in this process is 2.05 eV, which is quite high, suggesting that the hydroxyls are quite stable and unlikely to dissociate in this way. It should be noted that only the molecular adsorption structure was found for water on the lightly reduced ceria surface by using plain DFT,9,11 while both the molecular adsorption structure and the hydroxyls adsorption structure were found on the lightly reduced ceria surface in this work by using DFT+U. In experiment, both water molecules and hydroxyls were found
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Figure 3. The optimized configurations of a water molecule on the reduced ceria(111): side view (up) and top view (down) of (a) no-H-bond configuration and (b) hydroxyl surface. The numbers represent the corresponding structure parameters.
Figure 4. (a) The TDOS of the hydroxyl surface with the gap state peak “b” corresponding to the covalent bonds of the surface hydroxyl and gap state peak “c” to the excess electrons localized on two Ce3+ ions; (b) the single state image corresponding to the gap state peak “b”; and (c) the single state image corresponding to the gap state peak “c”.
on reduced ceria at low temperature,4 which agree well with our calculated result, while in the recent similar work using the plain DFT method,11 the calculated energy barrier for water dissociation is as high as 2.35 eV, which deviates from the experimental result (i.e., water readily adsorbs on the surface and forms hydroxide if oxygen vacancies are present).8 In a word, the plain DFT method could not correctly describe the behavior of the water molecule on reduced ceria. The upper layers of the highly reduced surface resemble the Ce2O3(0001) surface, which have been reported recently.40 It is well-known that the O ion of water prefers to bond to Ce ions of the surface, so two sites (Ce-top site and O-hollow site) of
the highly reduced surface are considered for water adsorption with different initial configurations (i.e., no-H-bonds configuration, one-H-bond configuration, and two-H-bonds configuration). The one-H-bond configuration is found exclusively on the highly reduced surface, which is shown in Figure 5. Two kinds of one-H-bond-configuration (due to the different initial adsorption sites) are found, and the corresponding structures are shown in Figure 5, panels a and b, respectively. The structures of the adsorbed water molecules only vary a little as compared with that of the free water molecule. The corresponding adsorption energy is 0.43 and 0.37 eV, which are much smaller compared with the adsorption energy on the stoichio-
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Figure 5. The structure of water molecule adsorbed on highly reduced ceria surface: (a) the side view of Ce-top, (a′) the top view of Ce-top site, (b) the side view of hollow site, and (b′) the top view of hollow site.
metric or lightly reduced ceria surface. It is evident that the interaction of water with the highly reduced surface is weaker as compared to that with the lightly reduced ceria. In a word, the interaction of water and ceria surface is strongly related to the degree of surface reduction (oxygen vacancy density). 3.3. Phase Diagram. To take into consideration the environmental effects, the Gibbs free energy G(T,P) of the whole system is calculated as a function of temperature (T) and pressure (P) from the DFT+U results using the ab initio atomistic thermodynamic method as described in section 2, which allows a link between the DFT+U results and environmental effects.17,18 Phase diagrams for stoichiometric and reduced ceria(111) surfaces in equilibrium with water vapor in the complete range of experimentally accessible gas phase condition are calculated and discussed combining the DFT+U results and thermodynamics data. For the surface that contains adsorbate (e.g., larger molecules or in hydrogen containing environment), vibrational effects on the surface free energy or Gibbs free energy of adsorption would be important.34 In such cases, it may be sufficient to only consider some prominent vibrational modes.11,16,34 The vibrational free energy within the harmonic approximation for n fundamental modes (with frequencies of ωi) of the system can be expressed as:34 n
[
Fvib(T) ) Σ Fvib(T, ωi) )
(
i)1
( ))]
-pωi 1 Σ pωi + KBT ln 1 - exp i)1 2 KBT n
;
(6)
vib vib (T) - Ffree (T) Fvib,ad(T) ) Fadsorbate vib vib,ad where Fvib (T) are vibrational energies adsorbate(T), Ffree(T), and F of the adsorbed molecule (adsorbate), the free gas molecule,
and their change arising from the adsorbate-surface interaction, respectively. The Fvib,ad(T) would be calculated based on eq 634 and obtained from detailed vibrational analysis of the various surface species, diagonalizing the complete dynamic matrix while leaving the substrate fixed. For water on the stoichiometric ceria(111), the prominent reactions are the one-H-bond configuration (as shown in Figure 2a) and the nearly decomposed configuration, HO-H/ CeO2(111), as shown in Figure 2b, which can be described as:
H2O + CeO2 f H2O/CeO2 H2O + CeO2 f HO - H/CeO2
(7)
During these processes, the variation of Gibbs free energy can be expressed as:32 DFT+U DFT+U ∆G(T, P) ) Etotal + Fvib,ad(T) - EHDFT - ECeO 2O 2
∆HH2O(T, P0) + T∆SH2O - KBT ln(PH2O /P0) (8) DFT+U DFT+U where Etotal and ECeO are the calculated total energies (at 2 the DFT+U level) for the surface systems with and without is that for the free H2O molecule in the ground adsorbate, EHDFT 2O state, Fvib,ad(T) is the contribution of vibrational free energy arising from the effect of the surface and calculated by eq 6, and the last three terms are the water chemical potential relevant to temperature and vapor partial pressure. The calculated Fvib,ad(T), as a function of temperature (T), for different adsorption geometries are shown in Figure 6. If the water partial pressure is fixed at 1 atm, the chemical potential of water would be only related to temperature. Then, for water
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J. Phys. Chem. C, Vol. 114, No. 35, 2010 14897 DFT+U DFT+U ∆G(T, P) ) Etotal + Fvib,ad(T) - EHDFT - ECeO 2O 2-x
∆HH2O(T, P0) + T∆SH2O - KBT ln(PH2O/P0) (12) The meaning for each term is the same as that in eq 8 but for a lightly reduced surface, CeO2-x(111), as the substrate. Finally, the process for the decomposition of the water molecule on the lightly reduced ceria surface with formation of a hydrogen molecule and stoichiometric ceria surface can be described as:
H2O + CeO2-x f H2 + CeO2
(13)
This process would be affected by water and hydrogen pressure and the variation of Gibbs free energy can be expressed as: Figure 6. The change of vibrational free energies due to adsorbate-surface interaction, Fvib,ad(T), as a function of temperature for different adsorption geometries: (a) one-H-bond configuration of H2O/CeO2(111); (b) nearly decomposed configuration, HO-H/CeO2(111); (c) no-Hbonds configuration of H2O/CeO2-x(111); and (d) hydroxyl surface, 2OH/CeO2-x(111).
adsorbed on stoichiometric ceria(111), the variation of Gibbs free energy can be expressed as: DFT+U DFT+U ∆G(T, P) ) Etotal + Fvib,ad(T) - EHDFT - ECeO 2O 2
∆HH2O(T, P0) + T∆SH2O (9) Analyses of the Gibbs free energy of water show that the contribution of water enthalpy and entropy is less than 0.1 eV at temperatures as high as 700 K. Therefore, we can roughly estimate whether or not a water molecule can be adsorbed on a stoichiometric ceria(111) by neglecting the contribution from enthalpy and entropy. Combining eq 5, the variation of Gibbs free energy can be written as:
∆G(T, P) ) Fvib,ad(T) - EDFT+U ad
(10)
DFT+U , according to With our calculated value (0.55 eV) of Ead vib,ad (T) shown in Figure 6 (line A) and eq 10, the calculated F the condition for stable adsorption (∆G(T,P) < 0) requires Fvib,ad < 0.55 eV, which corresponds to a temperature range of T < 820 K. Therefore we can conclude that, for temperature T < 820 K, the adsorption of the water on the stoichiometric CeO2(111) surface is stable, while at higher temperatures water desorbs into the gas phase. This tendency agrees well with the recent DFT results.11 For water on the lightly reduced ceria(111), the typical resulting geometries are the “no-H-bond configuration, H2O/ CeO2-x(111)” (as shown in Figure 3a) and the “hydroxyl surface, 2OH/CeO2-x(111)” (as shown in Figure 3b), which can be described as:
H2O + CeO2-x f H2O/CeO2-x H2O + CeO2-x f 2OH/CeO2-x
(11)
The variation of Gibbs free energy for these processes can be expressed as:
DFT+U DFT+U ∆G(T, P) ) ECeO + EHDFT - ECeO - EHDFT + 2 2 2-x 2O
∆HH2(T, P0) - ∆HH2O(T, P0) - T(∆SH2 - ∆SH2O) + KBT ln(PH2 /PH2O) (14) For the reaction of water with the stoichiometric ceria(111) and the lightly reduced ceria(111), the phase diagram boundaries determined by eqs 8 and 12 are shown in Figures 7 and 8, respectively. The reaction would take place when the Gibbs free energy decreases (∆G(T,P) < 0). For the stoichiometric ceria(111) (Figure 7), the phase boundaries for the nearly decomposed water configuration and the one-H-bond configuration are almost the same. Therefore, only the phase boundary for the one-H-bond adsorption is presented in Figure 7 for clarity. It is evident that at certain temperatures (e.g., line I), when vapor partial pressure is too low, there would be no interaction between water molecules and the surface. Water molecules begin to be adsorbed on the surface with the “nearly decomposed configuration” or the “one-H-bond configuration” when the water partial pressure increases to a certain value. On the other hand, at certain partial pressures (e.g., line II), water molecules would be adsorbed on the surface at lower temperature, while desorbed from the surface at higher temperature. In experiment, it is also discerned that water molecules desorb from the oxidized surface below 300 K at ultrahigh vacuum (UHV) systems,3,4 which agrees well with our calculated result. At the water partial pressure of 1 atm, the water desorbs from the surface at nearly 700 K, which agrees well with the recently calculated result.11 Comparing the transition temperature (700 K) with the one obtained by neglecting the enthalpy and entropy contributions (820 K), it is obvious that the latter has the effect of stabilizing water adsorption on the surface. The overall effect is to increase the transition temperature by 120 K, therefore, it might not be sufficient to fully describe the phase transition by neglecting the enthalpy and entropy contributions to the free energy at high temperature. On the lightly reduced ceria(111) (Figure 8a), the adsorbate behaves differently at different water partial pressure ranges. For example, at certain water partial pressures (e.g., line I), the adsorbed water molecules would dissociate and form hydroxyls with increasing temperature. At lower water partial pressure (e.g., line II), water molecules are adsorbed on the substrate initially at lower temperature (1020 K). At even lower vapor partial pressure (e.g., line III), surface hydroxyls form
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Figure 7. The phase diagram of water molecule on stoichiometric ceria(111).
initially at lower temperature ( 700 K. Compared with the stoichiometric ceria(111) surface, the reaction of water and ceria is enhanced by the oxygen vacancy; in other words, water prefers to dissociate on lightly reduced surface at low temperature, even at ultrahigh vacuum, which agrees well with experimental results.8 Finally, the process that water molecules dissociate and reoxidize the lightly reduced ceria(111) is considered. The phase diagram for the reaction of “H2O + CeO2-x f H2 + CeO2” is
Yang et al. determined by eq 14 and shown in Figure 8b. As mentioned above, this reaction would be affected by the partial pressure of water and hydrogen. For example, water molecules can be used to oxidize the lightly reduced CeO2(111) if the gas partial pressure ratio of ln(PH2/PH2O) is lower than 1.65 at 400 K, while the reaction would take place at a much lower gas partial pressure ratio of ln(PH2/PH2O) < 0.85 if the temperature is 800 K. In other words, the reaction that water molecules reoxidize the lightly reduced CeO2(111) to generate hydrogen molecules prefers to take place at low and intermediate temperatures, which is mainly due to the variation of entropy and enthalpy with temperature. As catalysts, ceria based materials are usually used for WGS or CO preferential oxidation reactions to attain high purity hydrogen.41-44 It is noteworthy that all those reaction processes proceed at low temperature (T < 570 K).41-44 Our calculated results show that hydrogen may react with the stoichiometric CeO2(111) surface and be oxidized to form water at higher temperature, which is not desired to attain high purity hydrogen. Henderson et al. observed additional reduction of a reduced ceria(111) surface by using X-ray photoelectron spectroscopy (XPS) and temperature programmed desorption (TPD).3 We notice that in their experiment, the reduction of the surface is severe (on the order of 30% oxygen vacancy sites). In this case the structure of the surface may become a Ce2O3-like structure instead of maintaining the cubic structure. Kumar et al.9 used a small supercell to model the reduced system (containing an oxygen vacancy at 50% of the surface oxygen sites), which may transform into a Ce2O3-like structure; therefore, they did not find water decomposition on the reduced ceria surface. Perrichon et al.45 found that when the hexagonal Ce2O3 phase formed, the reoxidation cannot be completed at 294 K by an oxygen molecule. Esch et al.14 reported that an oxygen vacancy cluster is more stable than a single oxygen vacancy; this may be understandable because when an oxygen vacancy cluster is formed, the local phase of the system may relax to a Ce2O3like structure. Therefore we can conclude that, whether water reoxidizes the surface or not, it is not only related to temperature and water partial pressure, but also a matter of the degree of surface reduction (and hence the oxygen vacancy density). Once the Ce2O3 phase is formed (a fully reduced ceria), it corresponds to a stoichiometric hexagonal structure with Ce(III); therefore, no oxygen vacancy is available, which is not favorable for water dissociation. This agrees well with our DFT+U calculated result
Figure 8. (a) The phase diagram of water molecule on the lightly reduced ceria(111) and (b) the phase diagram for the reoxidization of the reduced ceria(111) by water.
Analysis of the Stability of the Water-Ceria System that water adsorbed molecularly on the highly reduced CeO2(111) surface. 4. Conclusions The reactions of water with stoichiometric and reduced ceria(111) are investigated by with use of DFT+U method. It is found that on the stoichiometric ceria(111) surface, the water molecule is adsorbed spontaneously through the single hydrogen bond configuration. In contrast, on the lightly reduced ceria(111), there exist both molecular adsorption (no-H-bonds configuration) and dissociative adsorption (surface hydroxyl) modes. It is obvious that oxygen vacancies can enhance the interaction of water with the substrate. However, the interaction of water with the ceria surface is strongly related to the degree of surface reduction. The interaction of water with the highly reduced surface is weaker as compared to that with the lightly reduced ceria surface. Using the ab initio atomistic thermodynamic method which combines the DFT+U result and thermodynamics data, phase diagrams for stoichiometric and reduced ceria(111) surfaces in equilibrium with water vapor in the complete range of experimentally accessible gas phase conditions are calculated. Our phase diagrams agree well with the results of previous experiments and recent theoretical work. Especially, it is shown that the reaction of reoxidizing the reduced ceria(111) with water is preferable at lower temperature due to the variation of entropy and enthalpy with temperature and gas partial pressure. Acknowledgment. This work was supported by the National Natural Science Foundation of China (Grant No. 10674042) and Innovation Scientists and Technicians Troop Construction Projects of Henan Province, China (Grant No. 104200510014). We thank Prof. Tom Woo and Mr. Arif Ismail (University of Ottawa) for help in polishing the English of the manuscript. References and Notes (1) Kaspar, J.; Fornasiero, P.; Graziani, M. Catal. Today 1999, 50, 285. (2) Gorte, R. J.; Zhao, S. Catal. Today 2005, 104, 18. (3) Henderson, M. A.; Perkins, C. L.; Engelhard, M. H.; Thevuthasan, S.; Peden, C. H. F. Surf. Sci. 2003, 526, 1. (4) Kundakovic, L.; Mullins, D. R.; Overbury, S. H. Surf. Sci. 2000, 457, 51. (5) Otsuka, K.; Hatano, M.; Morikawa, A. J. Catal. 1983, 79, 493. (6) Berner, U.; Schierbaum, K.; Jones, G.; Wincott, P.; Haq, S.; Thornton, G. Surf. Sci. 2000, 467, 201. (7) Gritschneder, S.; Iwasawa, Y.; Reichling, M. Nanotechnology 2007, 18, 044025. (8) Gritschneder, S.; Reichling, M. Nanotechnology 2007, 18, 044024. (9) Kumar, S.; Schelling, P. K. J. Chem. Phys. 2006, 125, 204704.
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