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J. Phys. Chem. C 2007, 111, 8314-8320
Structural Transformation of (110) Ultrathin Films of Tetragonal Zirconia Induced by Polarity Rafael An˜ ez,*,† Anı´bal Sierraalta,† and Philippe Sautet*,‡ Laboratorio de Quı´mica Computacional, Centro de Quı´mica, Instituto Venezolano de InVestigaciones Cientı´ficas, Apartado 21827, Caracas, Venezuela, and Laboratoire de Chimie, Institut de Chimie de Lyon, UniVersite´ de Lyon, Ecole Normale Supe´ rieure de Lyon, CNRS, 46, alle´ e d’Italie, 69364 Lyon cedex 07, France ReceiVed: March 10, 2007; In Final Form: April 10, 2007
The (110) surface of tetragonal zirconia is polar and hence intrinsically unstable. It is however proposed to be present in samples of sulfated zirconia catalysts. The processes enabling the stabilization of this termination of tetragonal zirconia, by relaxation or reconstruction, have been studied with periodic density functional theory. The bulk terminated surface shows huge relaxation by dimerization of layers, however keeping a high unstable surface energy. The most stable surface is oxygen terminated but with an oxygen content reduced by a factor of 2 compared to the bulk terminated case. For ultrathin films, this surface reconstruction is accompanied by a structural transformation of the bulk, which completely cancels the polarity and creates a distorted (001) surface. Other surface contents have been studied with non stoichiometric slabs, without showing more stable solutions.
Introduction In 1979, Arata et al.1 reported that sulfated zirconia (SZ) exhibits a high activity in the catalytic isomerization of hydrocarbons. This compound was considered as a superacid solid or at least as a very strong solid acid. While earlier studies supported superacidity as the primary source of the catalytic activity,2,3 there is increasing evidence that this might not be the case.4 There is hence a high interest to determine which property induces the activity of SZ for the isomerization process. On the other hand, the conventional catalysts for the isomerization process (HF and H2SO4) have several drawbacks, since they are liquid, corrosive, and toxic. For these reasons, a solid superacid could be a good substitute. Zirconia ZrO2 has three phases in the bulk: monoclinic, tetragonal, and cubic. The tetragonal phase was shown to be present after standard catalyst preparation and was shown to give highly active SZ,5 although active solids from monoclinic zirconia were also recently created.6 Santiestaban et al.7 studied the surface structure of SZ by high-resolution transmission electron microscopy (HRTEM) and found that the presence of SO4-2 groups stabilizes small tetragonal ZrO2 crystallites. Moreover, they reported that the (110) surface of tetragonal SZ is the most abundant crystallographic plane when zirconia is sulfated. This result is surprising since this termination is polar and hence a priori unstable. Using periodic first principle calculation, Haase et al.8 showed that the crystal faces that are favorably exposed by the tetragonal phase of zirconia are (101) and (001) in this order but did not consider the (110) termination. These nonpolar (101) and (001) surfaces have also been the subject of other theoretical studies.28,29 Galva´n et al.9 using similar methodology considered the polar (110) tetragonal zirconia surface and the adsorption of sulfate groups. However, * Corresponding authors. E-mail addresses:
[email protected] (P.S.) and
[email protected] (R.A.). † Instituto Venezolano de Investigaciones Cientifı´cas. ‡ Institut de Chimie de Lyon.
a detailed understanding of the stability, structure, and possible reconstruction of the (110) polar surface of ZrO2 is still lacking. This has important implications for the structure of the sulfated zirconia catalyst. In addition, polar surfaces show specific behaviors, and the understanding of the mechanisms allowing to stabilize them is a subject of recent interest. According to classical electrostatic criteria, the stability of a surface depends on the characteristics of the charge distribution in the structural unit which repeats itself in the direction perpendicular to the surface.10 According to Tasker,11 insulating surfaces can be classified in three types (see Scheme 1): surfaces of type 1 and 2 show a zero dipole moment in the repeat unit but differ in the charge Q borne by their layers; the polar type 3 surface presents a nonzero dipole moment not only on the outer layers but also on all of the repeat units throughout the materials, which results in a diverging electrostatic contribution to the surface energy.12 The (110) tetragonal zirconia surface is of type 3 according to the Tasker classification which explains its intrinsic instability. Several scenarios can be proposed in order to cancel this macroscopic component of the dipole moment, by a modification of the charge density of the outer layer: electronic redistribution at the surface, nonstoichiometric composition of the surface layer, or chemical modification at the surface. Reconstruction is hence a common process that occurs on the polar surfaces to decrease the surface energy. Several works have been reported about surface reconstructions of metal oxides.13,14 Another mechanism involving a structural transformation of the bulk has been recently proposed. Goniakowski et al.15 reported that ultrathin film of MgO in the polar (111) direction is stabilized by a modification of the bulk structural phase. A similar process was also demonstrated in a range of wurtzite films (such as ZnO).27 This opens the way for a growth of oxide films along polar orientation and for the synthesis of artificial materials with an unusual crystallographic structure and properties. In the present paper, the structure and stability of the (110) surface of ZrO2 are studied using periodic density functional
10.1021/jp071950a CCC: $37.00 © 2007 American Chemical Society Published on Web 05/23/2007
Ultrathin Films of Tetragonal Zirconia SCHEME 1: Classification of Insulating Surfaces According to Taskera
a Q and µ are the layer charge density and the dipole moment in the repeat unit perpendicular to the surface.
calculations and are compared with the nonpolar (101) surface. The surface is modeled by a periodic slab of increasing thickness, up to 10 ZrO2 layers. Several mechanisms such as relaxation, reconstruction, and nonstoichiometric terminations are explored in order to stabilize the surface. We show that for ultrathin films, structural transformations in the bulk are a powerful means to circumvent the surface polarity problem. Computational Aspects. Geometry optimizations were performed using the Vienna ab initio simulation program (VASP).16,17 Kohn-Sham equations were solved with the generalized gradient approximation (GGA) proposed by Perdew and Wang.18 The projector-augmented-wave (PAW) method of Blo¨chl19 in the formulation of Kresse and Joubert20 was applied to describe electron-ion interactions. Standard PAW potentials were used for O and Zr. Brillouin-zone sampling was performed on Monkhorst-Pack special points21 using a Methfessel-Paxton integration scheme. The plane-wave cutoff was set to 400 eV throughout all calculations except for the optimization of bulk unit cell parameters where an 800 eV plane-wave cutoff was used. Sufficient convergence with respect to energy cutoff was confirmed. For the structural relaxations, the in-plane lattice parameters of the slabs were in most cases frozen to that of the bulk, which is an adequate model for zirconia thin films deposited on a support (metal, oxide). In addition however, a complete series of calculations were repeated with relaxed in-plane lattice parameters in order to check the influence of this cell deformation on the surface reconstruction and relaxation process. Bulk Tetragonal Zirconia. Tetragonal zirconia bulk was optimized starting with the experimental structure.22 The convergence with k-point sampling was tested, and a 4 × 4 × 4 Monkhorst-Pack k-points mesh already gives a converged total energy. The geometric parameters obtained, a ) 3.64 Å and c ) 5.30 Å, are in good agreement with the experimental values, a ) 3.64 Å and c ) 5.27 Å, the deviation with respect to the experimental data being less than 1%. The result is consistent with that reported by Hofmann et al.23 (a ) 3.64 Å, c ) 5.29 Å) with a similar approach. The cubic structure shows a calculated lattice vector of a ) 5.15 Å with a unit cell containing 4 (instead of 2) ZrO2 formula units. With the same choice of unit cell, the parameters of the tetragonal structure are a ) 5.15 Å and c ) 5.30 Å. The transformation from cubic to tetragonal is associated with a lengthening of the cell along the c direction and is associated with the displacement of the oxygen atom in the c direction by 0.33 Å, half of them upward and the other half downward. The O layer is hence split into two sub-layers separated by 0.66 Å in the c direction. Thermodynamics. The appropriate quantity to describe the stability of this system is the surface Gibbs free energy which also depends on the number of zirconium atoms, NZr, and oxygen atoms, NO. The surface Gibbs free energy is defined as
J. Phys. Chem. C, Vol. 111, No. 23, 2007 8315
γ(T,p) )
1 [G(T,p,NZr,NO) 2A bulk (T,p) - (2NZr - NO)µO(T,p)] (1) NZrgZrO 2
with A, the area of the surface unit cell, and NZr and NO, the numbers of zirconium and oxygen atoms in the threedimensional super cell, respectively. µZr and µO are the chemical bulk potential of zirconium and oxygen atoms respectively, gZrO (T,p) 2 is the Gibbs free energy of the bulk per formula unit and G(T,p,NZr,NO) is the total Gibbs free energy of the super cell. In our case, we normalize the Gibbs free energy to 2A because we are using a slab with two equivalent surfaces. The range of the oxygen chemical potentials between oxygen poor and oxygen rich environments is26 bulk Total (0,0) - gbulk 1/2[gZrO Zr (0,0)] < µO(T,p) < 1/2EO2 2
(2)
To set the oxygen rich chemical potential to zero, we introduce ∆µO ) µO(T,p) - 1/2EOTotal , and the surface energy is 2 plotted versus ∆µO in the range
1/2∆Gf(0,0) < ∆µO < 0
(3)
where ∆Gf(T,p) is the formation Gibbs free energy of the oxide. We compute ∆Gf(0,0) ) -10.35 eV for tetragonal zirconia, and it is in good agreement with the reported experimental value24 (-11.40 eV when T f 0). The possible interval for ∆µO is hence [-5.17 eV, 0 eV]. The relevant set of conditions for this study of surface energies is the temperature range for which the oxide is synthesized (i.e., temperature lower than 1100 K). For the relation between µO(T,p), T and p are described by the equation
()
1 p µO(T,p) ) µO(T,pο) + kTLn o 2 p
(4)
where µO(T,po) can be obtained using the experimental values for enthalpy and entropy at different temperatures25 and using eq 5.
µO(T,po) ) µO-rich (0 K,po) + 1/2∆G(∆T,po,O2) ) O 1/2[H(T,po,O2) - H(0 K,po,O2)] 1/2T[S(T,po,O2) - S(0 K,po,O2)] (5) If we restrict ourselves to temperatures lower than 1100 K, for a normal pressure of oxygen, this limits the interval for the oxygen chemical potential to [-1.1 eV, 0 eV]. Results The (110) and (101) tetragonal zirconia surfaces were calculated with slabs containing from 2 to 10 ZrO2 layers. In the first part of the paper, all atoms of the model slab were allowed to relax, keeping the box parameters constant. The lateral view of the bulk terminated (110) surface is shown in Figure 1A, and it yields alternating Zr and O layers. The 1 × 1 surface cell contains 2 Zr and 4 O atoms per layer. In the bulk of tetragonal zirconia, these layers are equally spaced by 1.288 Å in the (110) direction, hence giving a characteristic polar termination. The c axis of the tetragonal ZrO2 distortion is in the surface plane (x direction of Figure 1A), and hence, the O atoms are displaced along this direction one with respect to the other by 0.6 Å in the bulk. The stoichiometric bulk terminated slab of Figure 1A shows 1 Zr and 1 O termination.
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Figure 1. Lateral views of the bulk termination for the (A) (110) surface and (B) (101) surface of tetragonal zirconia. Zirconium atoms in dark spheres and oxygen atoms in light spheres.
Figure 2. Surface energy versus number of layers for the bulk terminated (110) and (101) surfaces of tetragonal zirconia.
TABLE 1: Surface Energy (J/m2) versus Slab Number of Layers for the (110) and (101) Surfaces of Tetragonal Zirconia number of layers
(110)
(101)
(110)hO
(110)hZr
2 3 4 5 6 10
3.460 3.993 4.310 4.530 4.682 5.040
1.007 1.048 1.055 1.063 1.066 1.069
1.050 1.124 1.167 1.199 1.222 1.317
2.449 2.452 2.473 2.473 2.475 2.485
Surface energies for an increasing slab thickness are given in Table 1 and Figure 2. As expected for the (110) polar case, the surface energy is very high and convergence is not reached for 10 Zr and O layers (this surface energy is the average between the O and the Zr termination). It was shown that the surface energy of bulk terminated polar surfaces in fact converges, but very slowly, as the inverse of the number of layers.30 In addition, the associated electronic redistribution between both terminations (metallization) is energetically unfavorable. The interlayer spacing for the 10 layer thick slab is sketched in Figure 3. A strong dimerization occurs perpendicular to the surface, one Zr-O separation being decreased (by up to 0.6 Å, i.e. 45%) while the next one is increased, with respect to the bulk case. The dimerization extends through the bulk part of the slab. This clearly reduces the charge separation (and hence the dipole moment) in the repeated ZrO2 unit cell and is a first (not very successful) way to attenuate the polarity. In contrast, the (101) surface can be seen as the repetition of O-Zr-O units with a zero dipole moment. It is hence a nonpolar surface and, as a result, its behavior is much simpler. The model slab of Figure 1B shows two similar O terminations. The surface energy is already converged for a thickness of 5 ZrO2 layers (see Table 1), and the low surface energy (1.07 J/m2) is typical for a stable surface. Figure 4 shows the change
of interlayer distances for the 10 layer (101) surface, compared to the bulk termination geometry. The surface relaxation is much more moderate with a maximum interlayer spacing variation of 5% and is quickly damped after two ZrO2 layers. These values are in good agreement with the data reported by Hasse et al.8 in a previous study (1.05 J/m2 for a 5 layer thick model) and with the result of Eichler et al.28 (1.07 J/m2 for a 10 layer thick model). If we return to the (110) surface, a way to cure the polarity is to reduce the charge density of the outer layer. For a symmetric alternation of positively and negatively charged layers, the macroscopic dipole is canceled if the charge density is divided by 2 in the outer layer. This is the case for ZrO2 if two of the four O atoms in the O termination of Figure 1A are removed. These two O atoms can be placed on the Zr termination, hence making the slab symmetric and keeping the overall stoichiometry. This reconstructed termination with half oxygen content will be called (110)hO. The four oxygen atoms are initially arranged as a square, and the most stable situation corresponds to keeping (and forming on the other side of the slab) a diagonal of this square. The relative position of these oxygen atoms on the two surfaces, yielding a C2h or D2 symmetry of the slab, has also been optimized. Slabs with an even number of layers yield a more stable C2h arrangement, while those with an odd number of layers are preferentially of D2 symmetry. Similarly, a half Zr terminated surface can be generated by removing one of the two Zr atoms of the Zr termination and moving it on the O termination at the other side of the slab. This reconstructed termination with half zirconium content will be called (110)hZr. The surface energy for the (110)hO surface (Table 1) is very moderate, and its convergence with slab thickness is greatly improved, compared with the bulk termination case. The difference between 5 and 6 layers is 23 mJ/m2 (versus 152 mJ/m2 for the nonreconstructed (110) surface). However, the surface energy does not converge completely. The relaxed interlayer spacing for the 10 layer (100)hO slab are shown in Figure 5. The oxygen in the layer does not have the same z any more, and the average value is considered for the plot. Clearly, the relaxation is much more moderate than for the bulk terminated surface, and it is mostly localized at the surface. The most important geometric change lies in the position of oxygen atoms within the O layer. As explained before, in the bulk, and in the bulk terminated surface, the O atoms are displaced from the high-symmetry position in the x direction, parallel to the surface. This results from the bulk tetragonal distortion. In contrast, for the (110)hO termination, this displacement of the O atoms is rotated and is now appearing along the z direction (see Figure 6). This is the case not only for the surface layers but also for all of the layers of the slab. Hence, the bulk structure of the slab is transformed, and the slab now appears like a distorted (001) surface of ZrO2. This (001) termination has been experimentally reported as one of the preferential surfaces on the tetragonal zirconia.7 For such a surface, the O displacement is along the z direction, but the bulk lattice vectors would be 5.15 Å along x and y and 5.3 Å along z. Here, lattice vectors along x and y are constrained to 5.3 and 5.15 Å, respectively, while the separation between pseudo-unit cells in the z direction can relax itself, as seen by the overall increase of interlayer spacing by ∼2% in the central part of the slab (Figure 5). This is hence equivalent to a (001) slab in which the cell parameter is submitted to a tensile strain of 0.15 Å in the b direction. On one hand, this has a big advantage for the surface stability, since the (001) termination
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J. Phys. Chem. C, Vol. 111, No. 23, 2007 8317
Figure 3. Change of interlayer distances for the 10 layer bulk terminated (110) surface of tetragonal zirconia.
Figure 4. Change of interlayer distances for the 10 layer bulk terminated (101) surface of tetragonal zirconia.
of the new bulk description is nonpolar. In other words, the change in surface O content and the buckling of the O layer now allows for the description of the surface as a repetition of nonpolar (OZrO) layers. On the other hand, this distortion of the cell along b has a cost, which can be estimated to be 0.065 eV per ZrO2 unit, that is, 0.13 eV per each added ZrO2 layer (each layer consists of 2 ZrO2 units). This can be translated to a bulk contribution to the surface energy of 0.02 J/m2 per layer. This cost for the distortion of the bulk is directly proportional to the slab thickness, and it explains why the surface energy does not completely converge with an increasing number of layers (since it has a bulk contribution).
The specific energy variation as a function of the number of layers is given in Figure 7. This clearly shows that after five layers, the energy varies linearly with the number of ZrO2 layers, with a slope of 0.02 eV per added layer. This is fully consistent with the previous analysis in terms of the distortion of the bulk unit cell. This energy drift is completely related to the increased number of distorted bulk-like layers in the model. For thin slabs, the energy gain from a nonpolar surface is larger than the cost to distort the bulk part of the slab. For thick systems, the related destabilization in the bulk will not be bearable any more. A second model approach is to freeze the central part of the layer to the bulk structure of tetragonal zirconia. For slabs
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Figure 5. Change of interlayer distances for the 10 layer reconstructed (110)hO surface of tetragonal zirconia.
Figure 6. Lateral views of the (110)hO surface (A) before the optimization and (B) after the optimization. A 2 × 2 unit cell has been used to improve the visualization. Zirconium atoms in dark spheres and oxygen atoms in light spheres.
containing n ZrO2 layers, we have relaxed four layers (two at each surface), and the n - 4 inner layers are frozen (see Table 2). The surface energy converges well in this case with an increased number of layers, and the value for 10 layers is shown as a dashed line in Figure 7. Such a solution is clearly less stable than the previously described bulk distortion for thin slabs but becomes favorable for thick slabs, with an estimated crossing for a thickness of 23 layers. Figure 8 shows the surface relaxation for the frozen bulk model, with a Zr-O dimerization clearly localized at the upper surface layer. Additionally, the modified Zr termination (110)hZr with a half Zr content at the surface shows a very good convergence of the surface energy with slab thickness but is less stable with a surface energy of 2.48 J/m2 (Table 1). In the calculated models up to this point, the in-plane parameters of the slabs have been kept frozen to that of the related bulk structure, which is relevant either for thick slabs or for thin ones supported on a metal or oxide surface (although the constraint could be modulated by the support in this case). The unit cell parameters can be further relaxed in order to check the influence of these in-plane cell parameters on the previously described relaxation mechanism for the (110)hO termination of the polar surface. This was done for slabs of thickness from 2 to 10 layers and for each slab symmetry (C2h or D2) depending
Figure 7. Surface energy versus number of layers for the reconstructed (110)hO surfaces for constrained in-plane lattice parameters (solid line) or relaxed lattice parameters (dotted line). The linear interpolation for the constrained cell results was calculated with the last five points. The surface energy for the 10 layer (110)hO surface freezing 6 ZrO2 layers in the bulk is shown as a horizontal dashed line.
TABLE 2: Surface Energy (J/m2) versus Slab Number of Layers for the (110)hO Surface with Frozen Layers in the Central Part of the Slab number of layers
number of frozen layers
surface energy
6 7 8 9 10
2 3 4 5 6
1.839 1.466 1.630 1.631 1.636
on the relative position of the upper and lower half-oxygenated terminations. The results are given in Table 3 and in Figure 7 (triangles and dotted line). As in the case of the calculations with the frozen unit cell, slabs with an even number of layers are more stable with a C2h symmetry, while those with an odd
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J. Phys. Chem. C, Vol. 111, No. 23, 2007 8319
Figure 8. Change of interlayer distances for the 10 layer (110)hO surface freezing 6 ZrO2 layers in the bulk.
TABLE 3: Optimum Slab Symmetry (C2h or D2), Surface Energy (J/m2), and In-Plane Lattice Parameters versus Slab Number of Layers for the (110)hO Slabs, Allowing In-Plane Relaxation of the Lattice Parameters number of layers
slab symmetry
surface energy (J/m2)
a (Å)
b (Å)
R (deg)
2 3 4 5 6 7 8 9 10
C2h D2 C2h C2h C2h D2 C2h D2 C2h
0.54 1.14 0.84 1.16 1.01 1.28 1.12 1.33 1.21
5.19 5.10 5.17 5.28 5.15 5.13 5.15 5.14 5.15
5.19 5.10 5.16 5.18 5.15 5.13 5.15 5.14 5.15
100 90 97 99 95 90 94 90 87
number generally prefer the D2 termination. However, the even and odd number of layer slabs behave differently upon unit cell relaxation: only the energy of the even number of layer slabs is significantly stabilized. This is especially the case for the very thin slabs (n ) 2 or 4) while for the 10 layer slabs the stabilization is only 0.1 J/m2 for the surface energy. The slabs with an odd number of layers, with D2 symmetry, show only a marginal decrease of the unit cell energy upon lattice relaxation (∼0.1 eV) and at the same time a reduction of the unit cell area (from -5% for n ) 3 to -3% for n ) 9). As a result, this leads to an unusually slight increase of the surface energy upon relaxation. A singularity happens for n ) 5, where the significantly stabilized C2h termination becomes more stable than the initial D2 one. The in-plane lattice parameter relaxation generally leads to an equalization of the a and b parameters which is consistent with the transformation toward a (001) structure of the layer, as proposed above. This lattice relaxation will clearly increase the stability domain of this (001) type structure as a function of slab thickness, with respect to the surfaces where the inner bulk layers are constrained to the (110) structure. Up to now, only stoichiometric slabs have been considered, with an overall ZrO2 formula. The surface can however show an excess or a depletion of oxygen. In order to compare the stability of these nonstoichiometric terminations, it is necessary, as explained in Thermodynamics, to estimate the surface free
Figure 9. Surface free energy as a function of oxygen excess chemical potential for various stoichiometric and nonstoichiometric terminations of (110) tetragonal zirconia surfaces (see text for description).
energy as a function of the chemical potential of the Zr and O atoms. If we consider that the surface is in equilibrium with a bulk of ZrO2, then the Zr and the O chemical potentials are related, and we will consider here the chemical potential of O as variable, in the interval [-1.1 eV, 0 eV]. The surface energy as a function of excess chemical potential of oxygen is shown in Figure 9. Three nonstoichiometric surfaces have been considered: (a) (NS4O) surface with four oxygen atoms at each surface layer of the slab (four oxygen atoms added with respect to (110) or (110)hO), (b) (NS3O) surface with three oxygen atoms at each surface (two oxygen atoms added with respect to (110) or (110)hO), and (c) (NS1O) surface with one oxygen atom at each surface (two oxygen atoms removed with respect to (110) or (110)hO). Each structure is built from a five layer slab base. The previously calculated stoichiometric slabs are also indicated as horizontal lines (independent of the oxygen chemical potential). The energy for the (110)hO termination, using the 10 layer slab with a inner part constrained to the bulk structure, is also given (const. (110)).
8320 J. Phys. Chem. C, Vol. 111, No. 23, 2007 The most stable structure corresponds to the lowest curve on the graph. The half oxygenated termination (110)hO is hence the most stable in the range of the O chemical potential. The nonstoichiometric structures are positioned in between this case and the bulk terminated (110) situation. At the normal pressure of oxygen, and for a temperature lower than 700 K, the second most stable structure is NS3O, with a slight excess of oxygen. These results demonstrate that nonstoichiometric terminations do not provide more stable structures in the case of ZrO2(110) and that the surface reconstruction of this polar surface is an excellent way to reduce the polarity and the surface instability. Conclusion The (110) surface of tetragonal zirconia is a polar and hence intrinsically unstable surface. Relaxation and reconstruction processes have been considered in order to stabilize this surface. The bulk terminated stoichiometric slab shows a huge relaxation by Zr-O layer dimerization, with up to 45% change in interlayer spacing. The polarity problem is not solved with a high surface energy and a slow convergence upon the number of layers. In contrast, a reconstruction dividing the charge density by two at the surface is, as expected, a very efficient way to stabilize the surface, especially for the O termination. For thin slabs, the most stable situation surprisingly shows a change in the bulk structure with a rotation from in-plane to normal tetragonal oxygen displacement. The slab can then be seen as a distorted (001) surface of ZrO2. This surface is not polar anymore, which results in a strong reduction of the surface energy. However, this is produced at the cost to distort the bulk, which is only acceptable for thin layers. The surface energy is further reduced by a relaxation of the in-plane lattice parameters but only for slabs containing an even number of layers. Thick layers can be modeled by applying a constraint on the position of the inner layers of the slab, freezing them to the bulk structure. This shows that the surface reconstruction efficiently stabilizes the surface, even in the absence of a bulk distortion. The exploration of other oxygen or zirconium concentrations at the surface was possible from the evaluation of the surface free energy for nonstoichiometric slabs, but this did not yield a more stable solution. The possibility to stabilize polar terminations of oxide surfaces is an important tool for the engineering of new oxide
An˜ez et al. structures in thin nanostructures or thicker systems. For tetragonal ZrO2, the (110) termination can be brought by reconstruction to a surface energy close to that of the most stable (101) surface, rending possible its stability in the sulfated zirconia samples. References and Notes (1) Hino, M.; Kobayashi, S.; Arata, K. J. Am. Chem. Soc. 1979, 101, 6439. (2) Jin, T.; Yamaguchi, T.; Tanabe, K. J. Phys. Chem. 1986, 90, 4794. (3) Moterra, C.; Cerrato, G.; Pinna, F.; Signoretto, M. J. Catal. 1995, 157, 109. (4) Drago, R.; Kob, N. J. Phys. Chem. B 1997, 101, 3360. (5) Tabora, J.; Davis, R. J. Am. Chem. Soc. 1996, 118, 12240. (6) Stichert, W.; Schu¨th, F.; Kuba, S.; Kno¨zinger, H. J. Catal. 2001, 198, 277. (7) Benaı¨ssa, M.; Santiesteban, J. G; Dı´az, G; Chang, C. D; Jose´Yacama´n, M. J. Catal. 1996, 161, 694. (8) Hasse, F.; Sauer, J. J. Am. Chem. Soc. 1998, 120, 13503. (9) Ireta, J.; Aparicio, F.; Viniegra, M.; Galva´n, M. J. Phys. Chem. B 2003, 107, 811. (10) Noguera, C. J. Phys.: Condens. Matter. 2000, 12, R367. (11) Tasker, P. W. J. Phys. C: Solid State Phys. 1979, 12, 4977. (12) Nosker, R. W.; Mark, P.; Levine, J. D. Surf. Sci. 1970, 19, 291. (13) Haugk, M.; Elsner, J.; Frauenheim, Th. J. Phys.: Condens. Matter 1997, 9, 7305. (14) Warschkow, O.; Asta, M.; Erdman, N.; Poeppelmeier, K. R.; Ellis, D. E.; Marks, L. D. Surf. Sci. 2004, 573, 446. (15) Goniakowski, J.; Noguera, C. Phys. ReV. Lett. 2004, 21, 215702. (16) Kresse, G.; Hafner, J. Phys. ReV. B 1993, 47, 558. (17) Kresse, G.; Furthmu¨ller, J. Phys. ReV. B 1996, 54, 11169. (18) Perdew, J.; Wang, Y. Phys. ReV. B 1992, 45, 13244. (19) Blo¨chl, P. Phys. ReV. B 1994, 50, 17953. (20) Kresse, G.; Joubert, D. Phys. ReV. B 1999, 59, 1758. (21) Monkhorst, H.; Pack, J. Phys. ReV. B 1976, 13, 5188. (22) Teufer, G. Acta Cristallogr. 1962, 15, 1187. (23) Hofmann, A.; Sauer, J. J. Phys. Chem. B 2004, 108, 14652. (24) CRC Handbook of Chemistry and Physics, 84th ed.; CRC Press, 2004. (25) Stull, D. R; Prophet, H. JANAF Thermochemical Tables, 2nd ed.; U.S. National Bureau of Standards: Washington, DC, 1971. (26) Reuter, K.; Scheffler, M. Phys. ReV. B 2001, 65, 035406. (27) Freeman, C. L.; Claeyssens, F.; Allan, N. L.; Harding, J. H. Phys. ReV. Lett. 2006, 96, 066102. (28) Eichler, A.; Kresse, G. Phys. ReV. B 2004, 69, 045402. (29) Orlando, R.; Pisani, C.; Ruiz, E.; Sautet, P. Surf. Sci. 1992, 275, 482. (30) Kresse, G.; Dulub, O.; Diebold, U. Phys. ReV. B 2003, 68, 245409.
