J. Phys. Chem. C 2010, 114, 15403–15409
15403
Electronic Structure and Redox Properties of the Ti-Doped Zirconia (111) Surface Hasani R. Chauke,† Phathutshedzo Murovhi,† Phuti E. Ngoepe,† Nora H. de Leeuw,‡ and Ricardo Grau-Crespo*,‡ Materials Modelling Centre, UniVersity of Limpopo, PriVate Bag X1106, SoVenga, 0727, South Africa, and Department of Chemistry, UniVersity College London, 20 Gordon Street, London WC1H 0AJ, U.K. ReceiVed: April 8, 2010; ReVised Manuscript ReceiVed: July 28, 2010
We have applied density functional theory calculations with Hubbard corrections (DFT+U) to investigate the structural, electronic, and redox properties of Ti-substituted zirconia (111) surfaces. The calculations show that titanium dopants are likely to accumulate at the oxide surface, where an isolated dopant is 0.25 eV more stable than in the bulk. We have investigated in detail the relative distribution of dopants and oxygen vacancies at the surface and report the most stable configurations for each composition. It is found that the formation energy of oxygen vacancies decreases substantially in titanium-substituted surfaces with respect to undoped surfaces. The analysis of the electronic structure of the doped and reduced surfaces reveals that, when an O vacancy is created around an isolated Ti dopant, a Ti4+ f Ti2+ reduction takes place, with the reduced cation in a high-spin configuration. However, if the vacancy is created in the vicinity of a pair of dopants, each Ti atom adopts a +3 oxidation state with an additional decrease in the vacancy formation energy. I. Introduction Zirconia (ZrO2) is one of the most important ceramic materials in modern technology. Its versatility arises from a combination of convenient mechanical properties (high flexural strength and good fracture toughness), high-temperature stability, and other, more specific functional properties.1 For example, its high ionic conductivity, in particular when doped with lower-valence cations, leads to applications in gas sensors2 and solid oxide fuel cells,3 while its high permittivity of around 20 makes it a promising material for gate dielectrics.4,5 Zirconia is also widely used as a support material in catalysis6-8 and as an inert crucible in metal casting,9 and the negligible radioactivity of the component ions means that it can also be employed safely as implant material in biomedical applications.10 The interface of zirconia with metals plays a significant role in many of these applications.11 In particular, the interaction of zirconia ceramics with titanium, which is the focus of the present work, significantly affects the surface properties of titanium alloys obtained by precision casting. It is well-known that Ti melts can react strongly with zirconia surfaces to form a chemically differentiated interface.12 Some authors have pointed out that Ti can react with oxygen from the zirconia surface to form titanium oxide,13 and also that zirconium can enter the titanium lattice at ZrO2/Ti interfaces.14 On the ceramic side, experimental studies have shown that contact with titanium melts during the casting process produces a complex interface including an oxygen-deficient zirconia surface ZrO2-x.9 Zirconia/titanium interfaces are also of interest in some biomedical applications. For example, both titanium alloys and zirconia ceramics can be used as dental implant materials, and therefore coupling both materials to give a convenient combination of properties could be a promising approach.15 To this end, Correia et al. have used electron microscopy and different * To whom correspondence should be addressed. E-mail: r.grau-crespo@ ucl.ac.uk. † University of Limpopo. ‡ University College London.
spectroscopic techniques to investigate the composition of ZrO2/Ti joints formed at high temperatures (1600-1770 K) and have identified several phases at the interface, including reduced zirconia and Ti-doped reduced zirconia with tetragonal structure, as well as other mixed Ti-Zr oxides.16 Besides the unintentional mixing at the Ti/ZrO2 interfaces described above, there are also a number of applications where Ti is purposely doped into the ceramic material to achieve certain target properties. For example, Ti-doped zirconia, with the cubic fluorite structure stabilized by Y3+ atoms, has been investigated as an anode material for solid oxide fuel cells.17 The solubility of Ti in stabilized cubic zirconia has been tested by Feighery et al.,18 who found that up to 18 atom % Ti4+ can be incorporated into ZrO2 at 1773 K. It has been suggested that Ti doping can improve the dielectric properties of zirconium and hafnium oxides for applications in gate capacitors.19,20 TiO2-ZrO2 mixed oxides also find a number of important applications in heterogeneous catalysis.21 It is therefore clear that a fundamental understanding of the effect of titanium doping on the properties of zirconia surfaces will be useful for the development of these applications. We report here the results of a theoretical investigation into the properties of a Ti-doped zirconia surface. We focus on the electronic and redox properties of the surface as a function of Ti content and attempt to correlate our results with experimental observations. We will show that the presence of Ti at the surface drastically changes the chemical behavior of the surface, which becomes easily reducible due to the flexible oxidation states of the Ti centers. II. Methodology We have used quantum-mechanical calculations based on the density functional theory (DFT) with periodic boundary conditions to investigate the doped and undoped zirconia surfaces. Our structural model is based on the geometry of cubic zirconia, which is the stable polymorph of pure ZrO2 only at high temperatures (above ∼2600 K).22 However, the cubic phase can be stabilized at much lower temperatures by doping with lower-
10.1021/jp103181q 2010 American Chemical Society Published on Web 08/24/2010
15404
J. Phys. Chem. C, Vol. 114, No. 36, 2010
Figure 1. Slab model used to represent the O-terminated ZrO2(111) surface. Red (dark) and blue (light) spheres correspond to oxygen and zirconium atoms, respectively.
valence cations, e.g., Y3+ or Ca2+, and this is the phase present in many ceramic applications (e.g., refs 23-26). We note that doping only with Ti does not seem to stabilize the cubic phase of zirconia,27 although for the sake of simplicity in this study we will ignore the presence of other dopants apart from Ti in the bulk or the surface of the material. Cubic zirconia adopts the fluorite (CaF2) structure, which has a face-centered cubic unit cell with space group Fm3m. In this structure, each cation is coordinated to eight equivalent nearest-neighbor anions at the corners of a cube, while each anion is tetrahedrally coordinated to four cations. The (111) surface has been found to be the most stable surface of zirconia in a number of theoretical studies, using both interatomic potentials and quantum-mechanical methods,28-30 and has been observed in the experimental characterization of thin films of zirconia.31 Oxygen termination is required for the surface to be nonpolar,28 which in a fluorite-structured crystal is also more stable than a cation-terminated reconstructed dipolar (111) surface.32 The cubic zirconia (111) surface is represented in our calculations by oxygen-terminated slabs, which repeat periodically in the direction perpendicular to the surface, separated by a vacuum gap of ∼15 Å. Based on the results of previous work, each slab contains nine atomic layers (three O-Zr-O trilayers), which was shown to be sufficient to obtain convergence of the surface properties.33 Parallel to the surface, the supercell consists of a 2 × 2 array of hexagonal surface unit cells. Each unit cell contains one ZrO2 unit at the surface, and therefore the three-layer simulation supercell contains 36 atoms in total, with four oxygen ions at each surface (Figure 1). The same slab model has been used previously in the investigation of the c-ZrO2(111) and the isostructural CeO2(111) surfaces at the DFT level.33-36 Based on the results of convergence tests in previous work,33 the positions of the four atomic layers at the bottom of the slab were kept fixed at the bulk positions, while the first five layers of the top face, where we dope the metallic atoms, were fully relaxed. All calculations were carried out using the VASP code,37-40 which uses a basis set of plane waves to solve the KohnSham equations with periodic boundary conditions. We have used the generalized gradient approximation (GGA), with a density functional built from the Perdew and Zunger41 local functional, and the gradient corrections by Perdew et al.42 In order to improve the description of the Ti d electrons, we use a Hubbard-type correction for these orbitals following the so-called DFT+U (or GGA+U) approach, which acts by altering the one-electron potential locally for the specified orbitals of the metal atoms (e.g., Ti d orbitals), reducing the hybridization with the ligands (e.g., O atoms).43-45 Previous
Chauke et al. work has shown that the introduction of this correction (or alternatively, a fraction of exact exchange as calculated from Hartree-Fock theory) is essential for the description of the electronic, magnetic, and surface properties of many transition metal and rare earth compounds.46-51 We have employed an effective Hubbard parameter Ueff ) 3 eV for the Ti d orbitals, which has been found by Nolan et al. to be the optimal value to reproduce the experimental electronic structure of Ti-doped TiO2 surfaces, using the same functional and general settings as in this work.52 Moreover, we will show below that the choice of Ueff values within certain limits does not change significantly the conclusions. The interaction between the valence electrons and the core was described with the projected augmented wave (PAW) method53 in the implementation of Kresse and Joubert.54 The core electrons, up to 3s in Ti, 4p in Zr, and 1s in O, were kept frozen in their atomic reference states. The number of plane waves in VASP is controlled by a cutoff energy, which in our surface calculations was set to Ecut ) 415 eV. The cell parameter was obtained for the cubic zirconia bulk crystal using an increased cutoff (500 eV) to minimize Pulay errors, and a 4 × 4 × 4 k-point mesh to sample the reciprocal space. The resulting cell parameter was a ) 5.130 Å, which is less than 1% above the experimental value of 5.090 Å (this value is an extrapolation to 0 K using the thermal expansion data in ref 55 as given in ref 56). Structural optimizations of the surface model were then performed with fixed cell parameters using a conjugate gradients technique with an iterative relaxation of the atomic positions until the forces on the atoms were all less than 0.01 eV/Å. For all geometry optimizations at the surface, a 3 × 3 × 1 k-point mesh was used, while at the final single-point runs for the calculation of the electronic density of states, a denser mesh of 5 × 5 × 1 k-points was employed. In order to calculate reaction energies, the energies of the O2 molecule, Ti metal, and bulk ZrO2 were obtained with VASP, using the same oxygen PAW potential, cutoff energy, and other precision parameters as in the surface calculations. The O2 molecule was calculated as a spin triplet, and we obtained an equilibrium bond distance d[O-O] ) 1.235 Å, similar to previous reports.57,58 It should be noted that GGA calculations tend to overbind the O2 molecule and therefore vacancy formation energies predicted within this approximation are typically too low.59 The cell parameter of bulk cubic zirconia was optimized to a ) 5.130 Å, which is less than 1% above the experimental value of 5.090 Å (this value is an extrapolation to 0 K using the thermal expansion data in ref 55 as given in ref 56). The charge states of the ions at the surface were discussed on the basis of a Bader analysis, which consists of integrating the electron density in a region defined for each atom in such a way that the density gradient flux through the dividing surfaces is zero.60 An algorithm and a program developed for this purpose by Henkelman et al. have been employed.61,62 Differences in Bader charges and the analysis of the electronic density of states (DOS) allow us to assign approximate oxidation states to the dopant ions, so we can identify them as Ti4+, Ti3+, or Ti2+ even if their Bader charges are different from the formal values. We have also used an electron localization function (ELF), as defined by Becke and Edgecombe63 and Silvi and Savin,64 to illustrate the localization of excess electrons upon the creation of oxygen vacancies at the surface. The ELF measures electron localization within a scale from 0 (low) to 1 (high), and it is a convenient way to examine the electron redistribution upon anion vacancy formation in solids.35,65
Ti-Doped Zirconia (111) Surface
J. Phys. Chem. C, Vol. 114, No. 36, 2010 15405
III. Results and Discussion Ti Doping of Fully Oxidized Zirconia and Dopant Segregation at the (111) Surface. First, we consider the Zr substitution by Ti in the fully oxidized bulk and (111) surface of zirconia. In this case, Ti enters the lattice with the same formal oxidation state as the original Zr ions, and therefore no charge compensation is required upon substitution. For both the bulk and the surface model the overall composition is then Zr11TiO24, which corresponds to 8.33% Ti doping. In order to make a precise comparison, the bulk simulation cell has the same orientation of its axes as the surface model, except that the vacuum gap was left at zero. Our calculations show that in a direct comparison Ti doping of the (111) surface is 0.25 eV more stable than in the bulk. This energy corresponds to the absolute value of the segregation enthalpy of isolated Ti dopants to that surface, if we neglect any effects from the interaction of the dopant with its images in neighboring cells. These effects should be small considering that (i) the same lateral interaction is present in both the bulk and the surface model and therefore cancels out when obtaining the energy difference, (ii) the images are separated by more than 7 Å, and (iii) the dopant has the same charge state as the original cation and therefore no long-range effects should be expected. The value of the segregation enthalpy ∆Hseg ) -0.25 eV (negative sign indicating higher stability of substitution at the surface) allows us to estimate the relative Ti occupancy of surface and bulk sites at thermodynamic equilibrium, assuming a low dopant concentration, using the expression:
[ ]
Tisurf ) e-∆Hseg/kBT Tibulk
(1)
where kB ) 8.6173 × 10-5 eV/K is Boltzmann’s constant. For example, at T ) 1000 K the equilibrium Ti occupancy of the (111) surface cation sites of zirconia is expected to be ∼18 times higher than the Ti occupancy of bulk cation sites. Therefore, we can expect that whenever a Ti-doped zirconia ceramic is subjected to temperatures high enough to allow dopant diffusion, the Ti dopants will accumulate at the surface. The oxidation state of Ti4+ at the surface is confirmed by the analysis of the projection of the electronic density of states (DOS) on the Ti 3d orbitals (Figure 2a), where it is clear that the d levels of the dopant lie above the Fermi energy. The projected DOS for the doped bulk is not shown in the figure, but it looks very similar. In order to gain insight into the energetics of the doping process of the zirconia surface with Ti (which we will consider comes from titanium metal, because of the practical importance of Ti/ZrO2 interfaces), we have calculated the energy of the formal reaction:
Zr12O24(slab) + Ti(bulk) + O2(gas) f Zr11TiO24(slab) + ZrO2(bulk)
Figure 2. Projection of the electronic partial density of states (PDOS) on the Ti 3d orbital (a) for the fully oxidized surface with one Ti dopant per cell (Zr11TiO24), (b) for the surface with one Ti dopant and one oxygen vacancy per cell (Zr11TiO230), and (c) for the surface with two Ti dopants and one oxygen vacancy per cell (Zr10Ti2O230).
(2)
where the substituted Zr cation is displaced to a bulk position in the zirconia phase. This reaction is very exothermic (-8.59 eV) even before applying a correction for the overbinding of the O2 molecule in the GGA approximation, which would make the reaction energy more negative. If we wanted to estimate the reaction free energy, the most important correction would come from substituting the energy of the oxygen molecule for
its chemical potential at the pressure and temperature of interest. This would make the reaction free energy less negative but not by much; for example, at 900 K and 1 bar of oxygen partial pressure the correction is of around 2 eV, according to values taken from thermodynamic tables.66 This simple analysis suggests that the incorporation of Ti from the metallic phase into the zirconia (111) surface is thermodynamically a highly favorable process. Effect of Ti Doping on the Formation of Oxygen Vacancies at the Surface. We now discuss the effect of Ti dopants on the redox properties of the surface. First, we review the formation of neutral oxygen vacancies at the perfect, undoped zirconia surface, as discussed previously in ref 35. Two positions of the oxygen vacancies were investigated, one in the outmost oxygen layer Ou (up) and the other in the subsurface oxygen layer Od (down) in the top ZrO2 trilayer (Figure 1). The vacancy formation energies (VFE), corresponding to the energy change in the reaction
Zr12O24(slab) f Zr12O230(slab) + 1/2O2(gas)
(3)
where 0 denotes an oxygen vacancy, were calculated to be 5.85 eV for the Ou vacancy and 5.38 eV for the Od vacancy, in agreement with the values obtained in ref 35 (small differences of less than 0.7% are due to slightly different calculation settings). The high values of the VFEs are expected from the well-known low reducibility of zirconia. Zr3+ cations have been detected by some authors in zirconia-related materials (e.g., ref 67), but this is not a very stable species. Upon creation of the vacancy the electrons prefer to remain localized at the vacancy site, forming an F center, and the vacancy defect is said to be
15406
J. Phys. Chem. C, Vol. 114, No. 36, 2010
Chauke et al.
Figure 3. Electron localization function (ELF) plot for the (111) surface of zirconia with one oxygen (Od type) vacancy (a) in the absence of dopants and (b) when a Ti dopant is present at the surface.
neutral as it has the same charge state as the original O2- ion at that site. An illustration of this electron distribution in a vacancy on an undoped zirconia surface is given in Figure 3a, where the electron localization function (ELF) is plotted in a plane that contains some oxygen anions and the vacancy site. The ELF is high in the region of the oxygen vacancy, showing that the electrons remain trapped in the defect site, and the Zr atoms are thus not changing their oxidation states. The presence of a Ti atom at the surface drastically changes the picture given above. We have investigated the formation of oxygen vacancies at the Ti-doped surface following the reaction
Zr11TiO24(slab) f Zr11TiO230(slab) + 1/2O2(gas)
(4)
and considering four different relative positions of the vacancy with respect to the dopant: (i) Ou vacancy nearest-neighbor (NN) to Ti (there are three symmetrically equivalent configurations of this type), (ii) Od vacancy nearest-neighbor (NN) to Ti (there are also three symmetrically equivalent configurations of this type), (iii) Ou vacancy next nearest-neighbor (NNN) to Ti, and (iv) Od vacancy next nearest-neighbor (NNN) to Ti. Our results indicate that, for all configurations, a reduction of the Ti species takes place, which is illustrated for case (iv) in the projected DOS in Figure 2b, where a clear peak of Ti d character appears below the Fermi level. The ELF plot of Figure 3b shows the localization of the excess electrons at the dopant site. In contrast with the undoped surface, no electrons are left at the vacancy position, making the oxygen vacancy defect positively charged with respect to the original anion site. Since no modification of the electronic states of the Zr ions appears to occur either, it is safe to conclude that the two excess electrons are located at the dopant, which adopts a formal Ti2+ charge state. The reduction of the Ti center is confirmed by the Bader analysis, showing Ti charges between 1.6 and 1.8 au, depending on the position of the vacancy, well below the values in the fully oxidized surface (2.33 au) and bulk (2.40 au). The DOS and ELF plots of Figures 2b and 3b correspond to the most stable configuration, which is the one with a subsurface (Od) vacancy in NNN position with respect to the dopant. In this configuration, the Ti dopant is connected to 3 Od ions at 2.27 Å, and to one other O atom in the layer below, but the neighboring Ou atoms shift away from the dopant to distances of 2.57 Å (Figure 4). The local geometry around the dopant and the vacancy is different for other configurations, but in all cases the electronic picture is similar. For all geometric configurations, we identified two types of spin solutions, one with two unpaired electrons per cell and
Figure 4. The most stable configuration of the zirconia (111) surface with one Ti dopant and one oxygen vacancy (Zr11TiO230). For clarity, only the atoms in the top trilayer are represented. Ti-O distances are given in angstroms.
one without unpaired electrons, which correspond to the highspin (HS) and low-spin (LS) states, respectively, of the Ti2+ ion with 3d2 electronic configuration. All the vacancy formation energies are listed in Table 1. Regardless of the vacancy position, we find that the magnetic (HS) state of the dopant is always more stable, by up to ∼0.5 eV, than the nonmagnetic LS configuration. The magnetic ground state of Ti2+ is consistent with the state of this dopant cation in other fluorite-type crystals.68,69 An interesting aspect of the reduction of the surface in the presence of Ti dopants is the decrease in the magnitude of the oxygen vacancy formation energy. For the most stable position of the vacancy with respect to the dopant, this energy is 3.66 eV, down from 5.38 eV at the undoped surface. Clearly, the ability of Ti centers to accommodate the excess electrons makes it less energetically expensive to remove a neutral oxygen, similarly to what has been observed for gold-doped zirconia surfaces, although the reducibility of the surface does not increase as drastically upon Ti doping as in the case of Au doping.35 Other recent computational studies have described the increase in reducibility of oxide surfaces when doped with ions that have a flexible oxidation state.70-72 It is therefore not surprising that a Ti-doped reduced zirconia region has been observed experimentally at the interface between ceramic zirconia and metallic titanium. It is also interesting that for the most stable configuration the vacancy is not in an NN position with respect to the dopant, where the dopant-defect electrostatic interaction would be most favorable. However, the positioning of the vacancy in an NNN site is not that surprising considering previous results in zirconia and similar materials. For example, it has been calculated that in Ca-stabilized zirconia oxygen vacancies prefer NNN instead of NN sites.73 It has also been reported recently that at the ceria (111) surface, which is isostructural with the surface investigated in this work, the most favorable relative position of an oxygen vacancy is in a NNN position with respect to the reduced Ce cation.74 In all these cases, lattice relaxation effects dominate over electrostatics to determine the position of the anion vacancy. Redox Properties of the Surface at Higher Ti Concentrations. Considering that high levels of Ti doping of ZrO2 have been reported in some experimental studies (e.g., 27 mol % in ref 27), and that, according to our results, strong Ti segregation to the surface is expected, we investigate now the incorporation of a second Ti ion and its effect on the redox behavior of the
Ti-Doped Zirconia (111) Surface
J. Phys. Chem. C, Vol. 114, No. 36, 2010 15407
TABLE 1: Vacancy Formation Energies (VFE) at the Pure and Ti-Substituted (111) Surface of Cubic Zirconiaa reduction process
description of resulting surface
Zr12O24(slab) f Zr12O230(slab) + /2O2(gas) 1
Ou vacancy Od vacancy Ou vacancy NN to HS (LS) Ti Od vacancy NN to HS (LS) Ti Ou vacancy NNN to HS (LS) Ti Od vacancy NNN to HS (LS) Ti Ou vacancy NN to both Ti Od vacancy NN to both Ti Ou vacancy NN to TiA and NNN to TiB Od vacancy NN to TiA and NNN to TiB
Zr11TiO24(slab) f Zr11TiO230(slab) + 1/2O2(gas)
Zr10Ti2O24(slab) f Zr10Ti2O230(slab) + 1/2O2(gas)
a
VFE (eV) 5.85 5.38 4.41 4.40 4.60 3.66 3.28 3.48 3.68 3.13
(4.93) (4.31) (5.05) (4.11)
The most stable configuration for each composition is marked in bold.
(111) surface. Analogously to eq 2, we can calculate the energy required for incorporating this second dopant as
Zr11TiO24(slab) + Ti(bulk) + O2(gas) f Zr10Ti2O24(slab) + ZrO2(bulk)
(5)
Because of the 2 × 2 periodicity of our slab, in the absence of other defects there is only one possible configuration for the double Ti/Zr substitution at the surface layer, which results in alternating chains of only Ti and only Zr atoms across the surface. This second substitution is slightly more exothermic than the first one (-8.77 eV for eq 5 compared to -8.59 for eq 2). We have also tried the incorporation of the second Ti dopant in the subsurface cation layer, but this is less stable than the surface substitution by 0.12 eV. Before creating any oxygen vacancy, the two Ti atoms in the surface are in a formal +4 oxidation state, as was the case for one dopant per cell, and with a very similar Bader charge of ∼2.3 au. The creation of a vacancy at this heavily doped surface is represented by the equation
Zr10Ti2O24(slab) f Zr10Ti2O230(slab) + 1/2O2(gas)
(6)
(if we include all the atoms in the slab model). Again, we need to consider four different positions of the vacancy with respect to the Ti atoms: (i) Ou vacancy NN to both Ti atoms, (ii) Od vacancy NN to both Ti atoms, (iii) Ou vacancy NN to one Ti atom (which we call TiA) and NNN to the other (TiB), and (iv) Od vacancy NN to TiA and NNN to TiB. The vacancy formation energies depend significantly on the position of the vacancy, as can be seen in Table 1. The lowest energy configuration is again the one with a subsurface (Od) vacancy NN to one Ti (case iv, see Figure 5). In this case, the vacancy formation energy is 3.13 eV, which is more than half an electronvolt lower than for an isolated dopant (3.66 eV). In order to understand this effect from dopant accumulation, we consider the electronic structure of the atoms at the surface. Despite the asymmetry of the vacancy position with respect to the dopants, both Ti ions seem to adopt the same formal oxidation state Ti3+, instead of forming a (Ti4+, Ti2+) pair, as confirmed by the projected DOS in Figure 2c. Each Ti atom contributes a 3d peak below the Fermi level, showing that both Ti atoms are reduced. These peaks are smaller than the one observed for the Ti2+ ion in the surface with one isolated dopant (Figure 2b), as expected from a change from 3d2 to 3d1 occupancies. This interpretation is also supported by the Bader analysis, which yields effective charges of 2.06 and 2.09, which are intermediate between those calculated for Ti4+ (2.3-2.4)
Figure 5. The most stable configuration of the zirconia (111) surface with 2 Ti/Zr substitutions and one oxygen vacancy (Zr10Ti2O230). For clarity, only the atoms in the top trilayer are represented. Ti-O distances are given in angstroms.
and for Ti2+ (1.6-1.7). In order to check whether the electronic picture described here is affected by the size of the simulation cell, we performed a test calculation using a 3 × 3 extension of the surface (slab composition Zr25Ti2O530), using the most stable relative configuration of the vacancy with respect to the dopants as obtained from the 2 × 2 calculations, but we obtained the same electronic redistribution, with very similar Bader charges on the Ti centers. Our results therefore strongly indicate that when more than one Ti dopant is available near the oxygen vacancy site, the excess electrons distribute themselves over separate Ti centers, forming Ti3+ species, instead of moving to the same Ti center to form a Ti2+ cation. We also found that all the other configurations, with different relative positions of the vacancy with respect to the dopants, led to the same qualitative picture (Ti4+ reduced to Ti3+) as the lowest-energy solution. Since Ti3+ has a magnetic moment associated with its 3d1 electron, we have attempted to obtain the magnetic coupling between the two dopants by calculating the energies associated with both ferromagnetic (FM) and antiferromagnetic (AFM) orientation of the spin moments. For the configurations with vacancies in Ou positions, we managed to obtain both FM and AFM solutions, but the differences in energies between them were too small (1-2 meV), compared with the general precision of the DFT calculations, to allow any quantitative description of the coupling (other than the magnetic coupling being very weak). In the case of vacancies in Od position, we did not manage to obtain AFM solutions at all. This is not indicative of any strong magnetic coupling but results from the coexistence of other electronic solutions with the same equipartition of up and down electrons. For example, for the configuration with an Od vacancy NN to one Ti atom, the lowest-energy solution described above was obtained with
15408
J. Phys. Chem. C, Vol. 114, No. 36, 2010
FM alignment between the Ti spins (as reflected in the absence of spin-down d contributions in Figure 2c). Trying to force an AFM by fixing to zero the difference between up and down electrons instead led to a nonmagnetic solution with one Ti4+ ion and one low-spin Ti2+ ion, which was ∼0.7 eV higher in energy than the ground state. The possibility of such an excited state is clear from the projected DOS diagram of Figure 2c: the occupied d orbital closer to the Fermi level corresponds to a Ti atom (B) which is different from the Ti atom (A) that contributes to the bottom of the conduction band, and therefore the lowest energy d-d excitation corresponds to the TiA3+ + TiB3+ f TiA2+ + TiB4+ electron transfer. Effects of the Choice of Hubbard Parameter. In all our calculations, we have used a sensible value of the Ueff parameter (3 eV) which has been shown to optimize the GGA+U description of Ti 3d orbitals in comparison with experimental information, i.e., the electronic properties of Ti adsorption at TiO2 surfaces (see ref 52 for details). However, different values have been suggested by other authors, depending on the specific material and properties under investigation and the density functional employed. For example, Calzado et al.50 have found that the best description of the electronic structure of reduced rutile (TiO2) is achieved for Ueff ) 5.5 eV, although this result was obtained using a functional based on the local density approximation (LDA) which typically requires larger Hubbard U corrections than GGA functionals.46,75 Finazzi et al.76 have shown that pure GGA does not reproduce the correct electronic structure of oxygen vacancies in anatase and that the qualitative picture obtained with GGA+U depends strongly on the particular Ueff value. According to these authors, the best agreement with the results from the hybrid functional B3LYP, which typically provides a good description of the electronic properties of transition metal oxides, is achieved for Ueff ) 3 eV. Other authors have suggested lower (e.g., 1.8 eV in ref 77) or higher (e.g., 4.2 eV in ref 78) values for the Ti 3d Ueff parameter in GGA+U calculations. Therefore, it is pertinent to discuss here the effect of the choice of Ueff parameter on our conclusions. We have recalculated the electronic structure and energy of the doped surface with and without vacancies using the most stable configuration for each composition for Ueff values between 0 (pure GGA) and 5 eV. In each calculation the geometry was fully relaxed. The Bader charge associated with the Ti atoms in each structure is shown in Figure 6a as a function of Ueff. It is clear from this plot that the nature of the solutions does not change for Ueff values between 1 and 5 eV: in all these cases, there are three well-defined charge states that can be identified formally as Ti4+ (the isolated dopant at the oxidized surface), Ti3+ (each of the two dopants associated with a single oxygen vacancy) and Ti2+ (isolated dopant associated with an oxygen vacancy). Only in the GGA limit (Ueff ) 0) does the nature of the solution in one of the structures (Zr10Ti2O23) change appreciably, giving a (Ti2+, Ti4+) pair instead of two Ti3+ ions. Since GGA+U has been found in several studies to improve the results of pure GGA, it is reasonable to expect that in this case too the GGA+U picture is the correct one. This qualitative picture does not change with the particular choice of Ueff value in the range normally used by other authors. In more quantitative terms, the choice of Ueff does have a significant effect on the calculated values of the vacancy formation energies, which range from 4.6 eV (4.3 eV) in the GGA limit to 2.8 eV (2.1 eV) for Ueff ) 5 eV in the presence of one isolated Ti dopant (two neighboring Ti dopants), as can be seen in Figure 6b. However, our conclusion about the higher formation energy of vacancies around isolated Ti atoms is not
Chauke et al.
Figure 6. (a) Bader charge on Ti atoms and (b) vacancy formation energy (VFE) corresponding to the most stable structure for each composition, as functions of the Hubbard parameter (Ueff) for Ti 3d states.
changed: regardless of the value of Ueff, it is easier to create an oxygen vacancy in the presence of more than one Ti dopant, when two Ti3+ species can be formed, rather than one Ti2+. IV. Summary We have presented a theoretical investigation of the state of Ti dopants at the unreduced and reduced (111) surfaces of cubic zirconia. Our results indicate that the incorporation of Ti in lattice positions at a zirconia surface from Ti metal is a thermodynamically favorable process, and that this dopant will prefer to remain at the ceramic surface rather than migrate to the bulk. We have shown that the presence of Ti dopants significantly modifies the properties of the zirconia surface, which becomes more reducible because of the flexible oxidation state of the Ti centers. If a vacancy is created near an isolated Ti dopant, a Ti2+ species is formed, but if two Ti atoms are available near the vacancy site, two Ti3+ centers are formed, which is energetically more favorable. Our results do not depend critically on the choice of Hubbard parameter in the GGA+U approach, although the absolute value of the vacancy formation energies does change significantly with this parameter, and future experimental verification would therefore be of real value. Acknowledgment. The work is supported by AMTS at the CSIR and the Royal Society-National Research Foundation collaboration between the University of Limpopo in South Africa and a number of universities in the UK, and the South African Research Chair Initiative of the Department of Science and Technology. Financial support from EPSRC grant EP/ C51744X is acknowledged. Computer resources on HECToR were provided via our membership of the Materials Chemistry HPC Consortium, which is funded by EPSRC (EP/F067496). References and Notes (1) Heuer, A.; Hobbs, L. W. Science and Technology of Zirconia; American Ceramic Society: Westerville, OH, 1981; Vol. 3. (2) Fergus, J. W. J. Mater. Sci. 2003, 38, 4259. (3) Fergus, J. W. J. Power Sources 2006, 162, 30.
Ti-Doped Zirconia (111) Surface (4) Thompson, D. P.; Dickins, A. M.; Thorp, J. S. J. Mater. Sci. 1992, 27, 2267. (5) Zhao, X. Y.; Vanderbilt, D. Phys. ReV. B 2002, 65, 064512. (6) Antolini, E.; Gonzalez, E. R. Solid State Ionics 2009, 180, 746. (7) Reddy, B. M.; Patil, M. K. Curr. Org. Chem. 2008, 12, 118. (8) Gelin, P.; Primet, M. Appl. Catal., B 2002, 39, 1. (9) Lin, K. F.; Lin, C. C. J. Mater. Sci. 1999, 34, 5899. (10) Manicone, P. F.; Iommetti, P. R.; Raffaelli, L. J. Dent. 2007, 35, 819. (11) Munoz, M. C.; Gallego, S.; Beltran, J. I.; Cerda, J. Surf. Sci. Rep. 2006, 61, 303. (12) Economos, G.; Kingery, W. D. J. Am. Ceram. Soc. 1953, 36, 403. (13) Wang, L. D.; Oki, T. J. Ceram. Soc. Jpn. 1995, 103, 680. (14) Ruh, R. J. Ceram. Soc. Jpn. 1963, 46, 301. (15) Gahlert, M.; Rohling, S.; Wieland, M.; Sprecher, C. M.; Kniha, H.; Milz, S. Clin. Oral Implant. Res. 2009, 20, 1247. (16) Correia, R. N.; Emiliano, J. V.; Moretto, P. J. Mater. Sci. 1998, 33, 215. (17) Fergus, J. W. Solid State Ionics 2006, 177, 1529. (18) Feighery, A. J.; Irvine, J. T. S.; Fagg, D. P.; Kaiser, A. J. Solid State Chem. 1999, 143, 273. (19) Dutta, G.; Hembrarn, K.; Rao, G. M.; Waghmare, U. V. J. Appl. Phys. 2008, 103, 016102. (20) Triyoso, D. H.; Hegde, R. I.; Zollner, S.; Ramon, M. E.; Kalpat, S.; Gregory, R.; Wang, X. D.; Jiang, J.; Raymond, M.; Rai, R.; Werho, D.; Roan, D.; White, B. E.; Tobin, P. J. J. Appl. Phys. 2005, 98, 054104. (21) Reddy, B. M.; Khan, A. Catal. ReV.sSci. Eng. 2005, 47, 257. (22) Masahiro, Y. Am. Ceram. Soc. Bull. 1988, 67, 1950. (23) Lemonnier, S.; Grandjean, S.; Robisson, A. C.; Jolivet, J. P. Dalton Trans. 2010, 39, 2254. (24) Darby, R. J.; Farnan, I.; Kumar, R. V. AdV. Appl. Ceram. 2009, 108, 506. (25) Kilo, M. Cation transport in stabilised zirconias. In Defects and Diffusion in Ceramics: An Annual RetrospectiVe VII; Trans Tech Publications Inc.: Zurich, Switzerland, 2005; Vol. 242-244; p 185. (26) Suarez, G.; Garrido, L. B.; Aglietti, E. F. Mater. Chem. Phys. 2008, 110, 370. (27) Troitzsch, U. J. Am. Ceram. Soc. 2006, 89, 3201. (28) Christensen, A.; Carter, E. A. Phys. ReV. B 1998, 58, 8050. (29) Gennard, S.; Cora, F.; Catlow, C. R. A. J. Phys. Chem. B 1999, 103, 10158. (30) Balducci, G.; Kaspar, J.; Fornasiero, P.; Graziani, M.; Islam, M. S. J. Phys. Chem. B 1998, 102, 557. (31) Paulidou, A.; Nix, R. M. Phys. Chem. Chem. Phys. 2005, 7, 1482. (32) de Leeuw, N. H.; Cooper, T. G. J. Mater. Chem. 2003, 13, 93. (33) Grau-Crespo, R.; Hernandez, N. C.; Sanz, J. F.; De Leeuw, N. H. J. Phys. Chem. C 2007, 111, 10448. (34) Branda, M. M.; Castellani, N. J.; Grau-Crespo, R.; de Leeuw, N. H.; Hernandez, N. C.; Sanz, J. F.; Neyman, K. M.; Illas, F. J. Chem. Phys. 2009, 131, 094702. (35) Grau-Crespo, R.; Hernandez, N. C.; Sanz, J. F.; de Leeuw, N. H. J. Mater. Chem. 2009, 19, 710. (36) Hernandez, N. C.; Grau-Crespo, R.; de Leeuw, N. H.; Sanz, J. F. Phys. Chem. Chem. Phys. 2009, 11, 5246. (37) Kresse, G.; Furthmuller, J. Comput. Mater. Sci. 1996, 6, 15. (38) Kresse, G.; Furthmuller, J. Phys. ReV. B 1996, 54, 11169. (39) Kresse, G.; Hafner, J. Phys. ReV. B 1993, 48, 13115. (40) Kresse, G.; Hafner, J. J. Phys.sCondens. Matter 1994, 6, 8245. (41) Perdew, J. P.; Zunger, A. Phys. ReV. B 1981, 23, 5048. (42) Perdew, J. P.; Chevary, J. A.; Vosko, S. H.; Jackson, K. A.; Pederson, M. R.; Singh, D. J.; Fiolhais, C. Phys. ReV. B 1992, 46, 6671.
J. Phys. Chem. C, Vol. 114, No. 36, 2010 15409 (43) Anisimov, V. I.; Zaanen, J.; Andersen, O. K. Phys. ReV. B 1991, 44, 943. (44) Liechtenstein, A. I. Phys. ReV. B 1995, 52, R5467. (45) Dudarev, S. L.; Botton, G. A.; Savrasov, S. Y.; Humphreys, C. J.; Sutton, A. P. Phys. ReV. B 1998, 57, 1505. (46) Rohrbach, A.; Hafner, J.; Kresse, G. J. Phys.sCondens. Mat. 2003, 15, 979. (47) Grau-Crespo, R.; Cora, F.; Sokol, A. A.; de Leeuw, N. H.; Catlow, C. R. A. Phys. ReV. B 2006, 73, 035116. (48) Nolan, M.; Parker, S. C.; Watson, G. W. Surf. Sci. 2005, 595, 223. (49) Wilson, E. L.; Grau-Crespo, R.; Pang, C. L.; Cabailh, G.; Chen, Q.; Catlow, C. R. A.; Brown, W. A.; de Leeuw, N. H.; Thornton, G. J. Phys. Chem. C 2008, 112, 10918. (50) Calzado, C. J.; Hernandez, N. C.; Sanz, J. F. Phys. ReV. B 2008, 77, 045118. (51) Graciani, J.; Plata, J. J.; Sanz, J. F.; Liu, P.; Rodriguez, J. A. J. Chem. Phys. 2010, 132, 104703. (52) Nolan, M.; Elliott, S. D.; Mulley, J. S.; Bennett, R. A.; Basham, M.; Mulheran, P. Phys. ReV. B 2008, 77, 235424. (53) Blochl, P. E. Phys. ReV. B 1994, 50, 17953. (54) Kresse, G.; Joubert, D. Phys. ReV. B 1999, 59, 1758. (55) Aldebert, P.; Traverse, J. P. J. Am. Ceram. Soc. 1985, 68, 34. (56) Stefanovich, E. V.; Shluger, A. L.; Catlow, C. R. A. Phys. ReV. B 1994, 49, 11560. (57) Grau-Crespo, R.; Moreira, I. D. R.; Illas, F.; de Leeuw, N. H.; Catlow, C. R. A. J. Mater. Chem. 2006, 16, 1943. (58) Sun, G. Y.; Kurti, J.; Rajczy, P.; Kertesz, M.; Hafner, J.; Kresse, G. J. Mol. Struct.sTheochem 2003, 624, 37. (59) Wang, L.; Maxisch, T.; Ceder, G. Phys. ReV. B 2006, 73, 195107. (60) Bader, R. F. W. Atoms in Molecules: A Quantum Theory; Oxford University Press: London, 1994. (61) Sanville, E.; Kenny, S. D.; Smith, R.; Henkelman, G. J. Comput. Chem. 2007, 28, 899. (62) Henkelman, G.; Arnaldsson, A.; Jonsson, H. Comput. Mater. Sci. 2006, 36, 354. (63) Becke, A. D.; Edgecombe, K. E. J. Chem. Phys. 1990, 92, 5397. (64) Silvi, B.; Savin, A. Nature 1994, 371, 683. (65) Mori-Sanchez, P.; Recio, J. M.; Silvi, B.; Sousa, C.; Pendas, A. M.; Luana, V.; Illas, F. Phys. ReV. B 2002, 66, 075103. (66) Chase, M. W. J. NIST-JANAF Thermochemical Tables, 4th ed.; American Institute of Physics: New York, 1998. (67) Punnoose, A.; Seehra, M. S. Catal. Lett. 2002, 78, 157. (68) Yunusov, N. B.; Zentsov, V. P. Phys. Status Solidi BsBasic Res. 1978, 88, 87. (69) Hoffmann, S. K.; Lijewski, S.; Goslar, J.; Ulanov, V. A. J. Magn. Reson. 2010, 202, 14. (70) Shapovalov, V.; Metiu, H. J. Catal. 2007, 245, 205. (71) Chretien, S.; Metiu, H. Catal. Lett. 2006, 107, 143. (72) Roldan, A.; Boronat, M.; Corma, A.; Illas, F. J. Phys. Chem. C 2010, 114, 6511. (73) Dwivedi, A.; Cormack, A. N. Philos. Mag. A 1990, 61, 1. (74) Ganduglia-Pirovano, M. V.; Da Silva, J. L. F.; Sauer, J. Phys. ReV. Lett. 2009, 102, 026101. (75) Loschen, C.; Carrasco, J.; Neyman, K. M.; Illas, F. Phys. ReV. B 2007, 75, 035115. (76) Finazzi, E.; Di Valentin, C.; Pacchioni, G.; Selloni, A. J. Chem. Phys. 2008, 129, 154113. (77) Palacios, P.; Sanchez, K.; Conesa, J. C.; Wahnon, P. Phys. Status Solidi AsAppl. Mater. Sci. 2006, 203, 1395. (78) Morgan, B. J.; Watson, G. W. Surf. Sci. 2007, 601, 5034.
JP103181Q
