- Email: [email protected]
Oxidation of the Nb(1 1 0) surface by ab initio calculations
Materials Science and Engineering B 144 (2007) 27–31
Oxidation of the Nb(1 1 0) surface by ab initio calculations D.A. Kilimis, Ch.E. Lekka ∗ Department of Materials Science and Engineering, University of Ioannina, Ioannina 45110, Greece
Abstract We report ab initio (FPLAPW) results referring to the early stages of oxygen deposition on the Nb(1 1 0) surface. We considered the cases of half and full monolayer depostion and we evaluated the structural and electronic properties of the resulting overlayers. From the calculated electronic strctures, it came out that the oxygen atoms form stronger bonds with the Nb surface atoms in the [0 0 1] than in the [1 1¯ 0] direction, a fact that implies also shorter bond lengths in the former direction and different structural relaxations in the neighbouring Nb atoms. In addition, we found that the Nb–O bonding, which is attributed to d–p hybridization of double bond-like character, results in the introduction of new electronic states that lay well below the lowest states of the clean Nb face, while it also contributes into the increase of states around the Fermi level. Interestingly, the Nb–O bonding type along the preponderated direction yields free oxygen pz orbitals that can be regarded as dangling-like bonds. These results elucidate the early stages of Nb oxidation and can be used to enlighten the mechanisms of surface reactions, catalytic activity and oxides growth mechanisms. © 2007 Elsevier B.V. All rights reserved. Keywords: Niobium oxide; Electron density of states calculations; Surface energy; Surface and interface states
1. Introduction Niobium oxide surfaces have been found to exhibit extraordinary enhanced catalytic activity, selectivity and ability to prolong catalyst life when the oxide is added to known catalysts. These properties explain the technological interest for applications as gas sensors, solar cells, solid acid catalysis and selective oxidation of hydrocarbons, as catalyst for the pollution abatement and in the petrochemical industries [1–6]. Raman spectroscopy and EXAFS techniques show that the catalytic activity of the niobium oxide surface depends on the preparation process [2,4,7,8] and is related to the Nb O bond [2,4], while the coordination number of niobium atoms influences the acid sites and acidity [3]. High-resolution electron energy loss spectroscopy (HREELS), low energy electron diffraction (LEED) and Auger electron spectroscopy (AES) and X-ray photoemission spectroscopy (XPS) measurements agree that upon oxygen adsorption on the Nb(1 1 0) surface thin Nb-oxide (NbO and NbO2 ) layers are formed as a protective layer, while upon saturation one obtains signature of ionic Nb2 O5 consisted of NbO6 octahedra [7–9]. With the emergence of the nano-science and the associated nano-technology such type of oxide clusters are considered as
an ideal-initial model system to study niobium oxide surfaces and niobium oxide nanowires [10]. Indeed, a lot of experimental (triple-quadruple mass spectrometer [11], time of flight spectra [12,13]) and theoretical studies (ab initio Hartree-Fock theory [11] and density functional theory [14]) have focused on the structural and electronic properties of niobium oxide clusters. From these investigations, it came out [12–14] that: (a) neutral clusters with stoichiometry in favour of oxygen atoms have higher ionization potential and (b) the outermost Nb–O distances have double bond character while the bridged Nb–O distances exhibit single bonds [14]. Nevertheless, although some knowledge has been achieved in the nano-clusters of the Nb oxides, a detailed study of the niobium oxide surfaces including the initial oxidation mechanisms, the Nb–O bonding character and the possible electronic redistribution is still lacking. It is the aim of the present work to study the early stages of oxidation of the Nb(1 1 0) surface focusing on the structural and electronic properties of the resulting systems. In particular, we considered the cases of half and full monolayer oxygen adsorption and for the topmost layers we calculated the surface electronic density of states aiming in the characterization of the Nb–O bonding nature. 2. Computational details
∗
Corresponding author. E-mail address: [email protected] (Ch.E. Lekka).
0921-5107/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.mseb.2007.07.079
The calculations on the structural and electronic properties of oxygen on Nb(1 1 0) surface were performed using the linear
28
D.A. Kilimis, Ch.E. Lekka / Materials Science and Engineering B 144 (2007) 27–31
augmented plane wave method (LAPW) within the density functional theory (DFT) by means of the Wien2k software [15]. The LAPW method expands the Kohn-Sham in atomic like orbitals inside the atomic (Muffin Tin, MT) spheres and plane waves in the interstitial region. The corresponding values of MT for MT Nb and O atoms are RMT Nb = 2.0 Bohr and RO = 1.5 Bohr, respectively, while we treated the exchange-correlation functional using the generalized gradient approximation (GGA) in the form given by Perdew et al. [16]. We started with the total energy calculation of the Nb BCC system and we found very good agreement for the equilibrium lattice constant 0.331 nm and the bulk modulus of 1.6 Mbar compared to the experimental values 0.330 nm and 1.7 Mbar, respectively. From the three low index surfaces, we chose the Nb(1 1 0) surface since this is the energetically favoured [17]. The supercell configuration consisted of a single surface unit cell in-plane and a number of atomic layers normal to the (1 1 0) surface with vacuum equal to four equilibrium layer spacings. We performed a set of energies and geometries minimizations in order to determine the minimal number of layers and k-points for satisfactory converged calculations. We found that the total energy, surface energy and surface layer contraction converge for a slab sampled with 42 (12 × 12 × 1) in-plane k-points and at the same time the corresponding differences values between a 7th and a 9th layer slab become unimportant. It should be noted at this point that although a slab made up from 20 atomic layers with a 200 k-point mesh would be preferable [17], such a calculation employing the computationally costly LAPW method would prohibited. Given the high level of its accuracy, we decided to use smaller system and take advantage of this method since it provides the best way for the description for the interactions of the oxygen with the metallic niobium. In order to study the evolution of early stages of oxygen adsorption on the surface we considered the following cases: (a) clean Nb(1 1 0) surface, (b) soft deposition of oxygen atoms on Nb(1 1 0) that alternatively occupy the four-fold adatom position, called “half monolayer” hereafter (HML) and (c) full oxygen monolayer deposition (FML). For the HML slab we
used 48 (15 × 11 × 1) k-points, while for the FML case 36 (11 × 11 × 1) k-points. 3. Results and discussion 3.1. Relaxation results For the clean Nb(1 1 0) surface case, the calculated surface energy (1.60 J/m2 ) is in agreement with semi-empirical calculations (1.67 J/m2 ) [18], embedded atom method (EAM) (1.82 J/m2 ) [19] and modified EAM (MEAM) (1.87 J/m2 ) [20], while it is underestimated compared to the TB (2.66 J/m2 )17 and FP-LMTO (2.36 J/m2 ) calculations [21]. In addition, the calculated value for the surface layer contraction (−5.5%) is in agreement with tight binding theory (TB) data (−5.8%) [17] using 20 atomic layers and 140 k-points, while our results differ from other TB quenched molecular dynamics (TB-QMD) (−3.6%) [22], FP-LMTO (−3.7%)[21] and with the VASPPAW method (−4.3%) [23] in which 6 or 7 layer slabs and 20 k-points were used, indicating that both quantities, i.e. the surface energy and the surface layer contraction depend on the system size and the type of calculation. For the inner layers, we found expansion (+0.6%) and contraction (−2.2%) for the second and third atomic layer, respectively, which nevertheless is less significant than that of the surface layer. These results are illustrated in Fig. 1a in the form of schematic atomic representations. With arrows we denote the atomic relaxation direction, while the deviation from the unrelaxed system of the atomic positions is given in nm. For the second case, i.e. half monolayer oxygen deposition, Fig. 1b, we found that the O atoms are very strongly contracted by as much as −46.8% compared to the NbO interlayer spacing of NaCl structure [24]. This value is comparable to the −52.2% contraction compared to the bulk Nb interlayer spacing. This important relaxation affects significantly the Nb surface atoms. In particular, the Nb atoms lying in the oxygen first neighborhood and along the [0 0 1] direction, named NbA hereafter, are expanded (+3.1%), while the NbB surface
Fig. 1. Schematic atomic representations of: (a) clean Nb(1 1 0) surface, (b) HML and (c) FML. With arrows we denote the atomic relaxation direction, while the deviations from the unrelaxed atomic positions are given in nm.
D.A. Kilimis, Ch.E. Lekka / Materials Science and Engineering B 144 (2007) 27–31
atoms lying along the [1 1¯ 0] direction are contracted by a similar amount (−2.8%), resulting eventually in a rumpled surface layer. This effect implies also that the NbA –O bond length is significantly shorter (0.20 nm) from the NbB –O (0.27 nm), suggesting that the former may possibly form covalent-like bonds [25]. In addition, the strong contraction of the oxygen atoms affects the beneath Nb atoms inducing contraction (−2.2%), while the Nb second layer atoms that stand below the vacant oxygen adatom position are expanded (+3.1%) similarly to the NbA surface atom. The third layer atomic positions are also altered exhibiting contraction (−2.4%) and expansion (+1.3%) for the atoms situated under the NbA and the NbB surface atoms, respectively, indicating the strong influence of the oxygen HML on the substrate atomic relaxations. When depositing a full oxygen monolayer on the Nb(1 1 0) face, Fig. 1c, the contraction of oxygen atoms is even more pronounced (−49.1%) compared to the NbO interlayer distance of NaCl structure and −54% compared to the Nb bulk interlayer distance. In addition, the length of the Nb–O bond along the
Fig. 2. EDOS of the half monolayer case: (a) O, NbA and NbB surface atoms (solid line, dashed line and points, respectively), (b) O px , py and pz partial EDOS (solid line, dashed line and points, respectively) and (c) NbA t2g and eg partial EDOS (solid and light dashed line) as well as NbA t2g and eg partial EDOS (solid dashed and dotted line).
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[0 0 1] direction shortens even more, 0.19 nm compared to the HML case. The Nb surface layer exhibits expansion +2.9% comparable to HML value (+3.1%) for the NbA . On the contrary, the second layer exhibits stronger contraction (−3.2%) compared to the corresponding (−2.2%) of the atom lying beneath the oxygen atom in the HML case, a result that could be interpreted as a kind of planes separation between the first and second Nb layers. This effect influences also the relaxations of the third atomic layer which, however, exhibits the smallest contraction (−1.2%). 3.2. Electronic density of states In the inset of Fig. 2a, we give the clean surface EDOS in which we see that the main peaks are located around −2.62, −1.44 and −0.35 eV, in agreement with previous TB data (−2.65, −1.63 and −0.48 eV) [17] and photoemission spectroscopy results (−2.45 and −0.39 eV) [26] below the Fermi level. In addition, we see a peak at 1.18 eV that was also observed by photoemission experiments [27] at 1.33 eV above the Fermi level. In Fig. 2a, we give the EDOS of oxygen and NbA and NbB surface for the HML case. We see that the presence of oxygen
Fig. 3. EDOS of the full monolayer case: (a) O and Nb surface atoms (solid and dashed line), (b) O px , py and pz partial EDOS (solid line, dashed line and points, respectively) and (c) Nb t2g and eg partial EDOS (solid and dashed line).
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D.A. Kilimis, Ch.E. Lekka / Materials Science and Engineering B 144 (2007) 27–31
(solid line) gives rise to three very well localized peaks at the bottom of the EDOS situated at −5.60, −5.18 and −3.94 eV below the Fermi level. With the exception of the peak around −0.66 eV, the Nb surface atoms of the HML preserve their characteristic clean Nb surface states below the Fermi level and up to −4 eV. Interestingly, for lower energies we recover practically the oxygen density of states signature at −5.60 and −5.18 eV for the NbA (dashed line) and NbB (points), respectively, indicating bonding between oxygen and Nb atoms which for the NbA atoms is by far more important suggesting larger electronic overlap between O–NbA , thus explaining the contraction and the smaller bond length (0.20 nm) compared to O–NbB , Fig. 1. In Fig. 2b, the decomposition of the oxygen p orbitals shows clearly that the px , py orbitals are mainly responsible for the two lowest energy peaks (−5.60, −5.18 eV), while the new third peak at −3.94 eV has strictly pz character. In addition, the NbA ’s t2g electrons are well localized and seem to be responsible for the two lowest energy peaks denoting doublelike bonding between the Nb t2g and O px , py orbitals, Fig. 2c, in agreement with theoretical data on NbO defective structure [25]. In addition, close to the Fermi level the new less pronounced peak at (−0.66 eV) is attributed to the interaction between O py and Nb eg electrons. The contributions of the inner Nb atoms to the EDOS do not exhibit any significant features and their character becomes bulk-like as going deeper into the bulk system. In Fig. 3, we present the EDOS for the oxygen and niobium surface atoms of the FML case. Similarly to the HML case we see that the oxygen atoms are mainly responsible for the new lower
energy peaks (−6.01, −4.96 and −3.85 eV), while a new clear peak at −0.22 eV emerges and it is mainly due to the Nb surface atoms. Compared to the HML, the energy peaks below −3.50 eV are broadened and slightly displaced towards lower energies, whereas the HML peak at −0.66 eV is shifted closer to the Fermi level (−0.22 eV), Fig. 3a. We interpret this enlargement between the low and high energy states below the Fermi level as the beginning of the characteristic energy gap present in the ionic oxides. In agreement with the HML case, the O px , py electrons are bonded with the Nb t2g electrons exhibiting localized states at −6.01 and −4.96 eV, while the new peak at –0.22 eV suggests again bonding between the Nb t2g and O py electrons, Fig. 3b and c. In addition, focusing at the new peak around −3.8 eV, we note that the Nb contributions are of minor importance and that the main contributions originate from the O pz electrons. This result suggests that there is no overlap between Nb and O electronic states and therefore the pz electrons could be regarded as dangling-like bonds. The above results were unequivocally confirmed by the charge density calculations, Fig. 4. In Fig. 4a and b, we give the electronic charge densities of the clean Nb surface in the (1 1¯ 0) and (0 0 1) planes, respectively. It is clearly seen that the Nb atoms which in the former case have more electronic charge in the interstitial spaces underlying the structural anisotropy of this surface. In Fig. 4c and d, we present the electronic charge densities in the same planes for the FML case. In both figures, it is interesting to notice the strong electronic overlap between the surface Nb and oxygen atoms indicating the strength of the Nb–O bonds. In addition, we can distinguish the t2g d-electrons
Fig. 4. Electronic charge density maps: (a) clean surface in the (1 1¯ 0) plane, (b) clean surface in the (0 0 1) plane, (c) FML in the (1 1¯ 0) plane and (d) FML in the (0 0 1) plane. The gray scale is logarithmic and the dark areas indicate low electronic density.
D.A. Kilimis, Ch.E. Lekka / Materials Science and Engineering B 144 (2007) 27–31
of the second layer Nb atoms (bottom atoms in Fig. 4d) and the eg d-electrons of the Nb surface atoms (Fig. 4c). Furthermore, we can also see the pz and py orbitals of the oxygen atoms (on the top of Fig. 4c and d, respectively). Comparing the densities of the clean and covered surfaces we can easily see that presence of oxygen alters the spherical symmetry of the charge distribution around the Nb atoms (Fig. 4a and b), that characterize the metallic bonding, imposing selective directional preference on the d orbitals of the FML system, suggesting covalent-like bonding. Moreover, the surface O px and Nb t2g are absent from Fig. 4c and d indicating their involvement in the Nb–O d–p bonding, a result which compatible with the EDOS findings, Fig. 3. Last but not least, in Fig. 4c we can see the unbound oxygen pz orbitals, clear evidence for the existence of dangling-like bonds. This finding has very important implications in the Nb surface functionalization by oxygen, since it related with the surface reactivity and catalytic behaviour. 4. Conclusions In this communication, we present results obtained by FPLAPW concerning the oxygen deposition on the Nb(1 1 0) surface. Half and full monolayer deposition were considered for which we evaluated the structural and electronic properties of the resulting overlayers. We found that the oxygen atoms form stronger bonds with the Nb surface atoms in the [1 0 0] than in the [1 0 1] direction, a fact that implies shorter bond lengths in the former direction and different structural relaxations in the neighbouring Nb atoms. In addition, we found that the Nb–O bonding, which is attributed to d–p hybridization of double bond-like character, results in the introduction of new electronic states that lay well below the lowest states of the clean Nb face. Interestingly, the Nb–O bonding type along the preponderated direction yields free oxygen pz orbitals that can be regarded as dangling-like bonds. These results elucidate the early stages of Nb oxidation and can be used to enlighten the mechanisms of surface reactions, catalytic activity and oxides growth mechanisms.
31
Acknowledgements Stimulating discussions with Dr. G.A. Evangelakis are gratefully acknowledged. This work was supported by the DIK4001-1 project. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15]
[16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27]
I.E. Wachs, Proc. Int. Conf. Niobium Tantalum (1989) 679. K. Tanabe, Catal. Today 78 (2003) 65. J.-M. Jehng, I.E. Wachs, Catal. Today 16 (1993) 417. T. Ushikubo, Catal. Today 57 (2000) 331. D. Appel, Nature 419 (2002) 553. I.G. Batirev, A. Alavi, M.W. Finnis, T. Deutsch, Phys. Rev. Lett. 82 (1999) 1510. R. Franchy, T.U. Bartken, P. Gassmann, Surf. Sci. 366 (1996) 60. M. Grundner, J. Halbritter, Surf. Sci. 136 (1984) 144. K.H. Rieder, Appl. Surf. Sci. 4 (1980) 183. M. Mozetic, U. Cvelbar, Adv. Mater. 17 (2005) 2138. H.T. Deng, K.P. Kerns, A.W. Castleman, J. Phys. Chem. 100 (1996) 13386. F. Dong, S. Heinbuch, S.G. He, Y. Xie, J.J. Rocca, E.R. Bernstein, J. Chem. Phys. 125 (2006) 164318. A. Fielicke, G. Meijer, G. von Helden, J. Am. Chem. Soc. 125 (2003) 3659. J.R. Sambrano, J. Andres, A. Beltran, F. Sensato, E. Longo, Chem. Phys. Lett. 287 (1998) 620. P. Blaha, K. Schwarz, G.K.H. Madsen, D. Kuasnicka, J. Luitz, WIEN2k, Augmented Plane Wave plus Local Orbitals Program for Calculating Crystal Properties, Vienna University of Technology, Vienna, Austria, 2001. J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865. Ch.E. Lekka, M.J. Mehl, N. Bernstein, D.A. Papaconstantopoulos, Phys. Rev. B 68 (2003) 35422. G.J. Ackland, M.W. Finnis, Philos. Mag. A 54 (1986) 301. A.M. Guellil, J.B. Adams, J. Mater. Res. 7 (1992) 639. M.I. Baskes, PRB 46 (1992) 2727. M. Methfessel, D. Hennig, M. Scheffler, Phys. Rev. B 46 (1992) 4816. J.S. Luo, B. Legrand, Phys. Rev. B 38 (1988) 1728. K.I. Shein, I.R. Shein, N.I. Medvedeva, E.V. Shalaeva, M.V. Kuznetsov, A.L. Ivanovskii, Phys. Met. Metallogr. 102 (2006) 604. E. Wimmer, K. Schwarz, R. Podlousky, P. Herzig, A. Neckel, J. Phys. Chem. Solids 43 (1982) 439. J.K. Burdett, T. Hughbanks, J. Am. Chem. Soc. 106 (1984) 3101. X. Pan, M.W. Ruckman, M. Strongin, Phys. Rev. B 35 (1987) 3734. X. Pan, P.D. Johnson, M. Weinert, R.E. Watson, J.W. Davenport, G.W. Fernando, S.L. Hulbert, Phys. Rev. B 38 (1988) 7850.
Oxidation of the Nb(1 1 0) surface by ab initio calculations D.A. Kilimis, Ch.E. Lekka ∗ Department of Materials Science and Engineering, University of Ioannina, Ioannina 45110, Greece
Abstract We report ab initio (FPLAPW) results referring to the early stages of oxygen deposition on the Nb(1 1 0) surface. We considered the cases of half and full monolayer depostion and we evaluated the structural and electronic properties of the resulting overlayers. From the calculated electronic strctures, it came out that the oxygen atoms form stronger bonds with the Nb surface atoms in the [0 0 1] than in the [1 1¯ 0] direction, a fact that implies also shorter bond lengths in the former direction and different structural relaxations in the neighbouring Nb atoms. In addition, we found that the Nb–O bonding, which is attributed to d–p hybridization of double bond-like character, results in the introduction of new electronic states that lay well below the lowest states of the clean Nb face, while it also contributes into the increase of states around the Fermi level. Interestingly, the Nb–O bonding type along the preponderated direction yields free oxygen pz orbitals that can be regarded as dangling-like bonds. These results elucidate the early stages of Nb oxidation and can be used to enlighten the mechanisms of surface reactions, catalytic activity and oxides growth mechanisms. © 2007 Elsevier B.V. All rights reserved. Keywords: Niobium oxide; Electron density of states calculations; Surface energy; Surface and interface states
1. Introduction Niobium oxide surfaces have been found to exhibit extraordinary enhanced catalytic activity, selectivity and ability to prolong catalyst life when the oxide is added to known catalysts. These properties explain the technological interest for applications as gas sensors, solar cells, solid acid catalysis and selective oxidation of hydrocarbons, as catalyst for the pollution abatement and in the petrochemical industries [1–6]. Raman spectroscopy and EXAFS techniques show that the catalytic activity of the niobium oxide surface depends on the preparation process [2,4,7,8] and is related to the Nb O bond [2,4], while the coordination number of niobium atoms influences the acid sites and acidity [3]. High-resolution electron energy loss spectroscopy (HREELS), low energy electron diffraction (LEED) and Auger electron spectroscopy (AES) and X-ray photoemission spectroscopy (XPS) measurements agree that upon oxygen adsorption on the Nb(1 1 0) surface thin Nb-oxide (NbO and NbO2 ) layers are formed as a protective layer, while upon saturation one obtains signature of ionic Nb2 O5 consisted of NbO6 octahedra [7–9]. With the emergence of the nano-science and the associated nano-technology such type of oxide clusters are considered as
an ideal-initial model system to study niobium oxide surfaces and niobium oxide nanowires [10]. Indeed, a lot of experimental (triple-quadruple mass spectrometer [11], time of flight spectra [12,13]) and theoretical studies (ab initio Hartree-Fock theory [11] and density functional theory [14]) have focused on the structural and electronic properties of niobium oxide clusters. From these investigations, it came out [12–14] that: (a) neutral clusters with stoichiometry in favour of oxygen atoms have higher ionization potential and (b) the outermost Nb–O distances have double bond character while the bridged Nb–O distances exhibit single bonds [14]. Nevertheless, although some knowledge has been achieved in the nano-clusters of the Nb oxides, a detailed study of the niobium oxide surfaces including the initial oxidation mechanisms, the Nb–O bonding character and the possible electronic redistribution is still lacking. It is the aim of the present work to study the early stages of oxidation of the Nb(1 1 0) surface focusing on the structural and electronic properties of the resulting systems. In particular, we considered the cases of half and full monolayer oxygen adsorption and for the topmost layers we calculated the surface electronic density of states aiming in the characterization of the Nb–O bonding nature. 2. Computational details
∗
Corresponding author. E-mail address: [email protected] (Ch.E. Lekka).
0921-5107/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.mseb.2007.07.079
The calculations on the structural and electronic properties of oxygen on Nb(1 1 0) surface were performed using the linear
28
D.A. Kilimis, Ch.E. Lekka / Materials Science and Engineering B 144 (2007) 27–31
augmented plane wave method (LAPW) within the density functional theory (DFT) by means of the Wien2k software [15]. The LAPW method expands the Kohn-Sham in atomic like orbitals inside the atomic (Muffin Tin, MT) spheres and plane waves in the interstitial region. The corresponding values of MT for MT Nb and O atoms are RMT Nb = 2.0 Bohr and RO = 1.5 Bohr, respectively, while we treated the exchange-correlation functional using the generalized gradient approximation (GGA) in the form given by Perdew et al. [16]. We started with the total energy calculation of the Nb BCC system and we found very good agreement for the equilibrium lattice constant 0.331 nm and the bulk modulus of 1.6 Mbar compared to the experimental values 0.330 nm and 1.7 Mbar, respectively. From the three low index surfaces, we chose the Nb(1 1 0) surface since this is the energetically favoured [17]. The supercell configuration consisted of a single surface unit cell in-plane and a number of atomic layers normal to the (1 1 0) surface with vacuum equal to four equilibrium layer spacings. We performed a set of energies and geometries minimizations in order to determine the minimal number of layers and k-points for satisfactory converged calculations. We found that the total energy, surface energy and surface layer contraction converge for a slab sampled with 42 (12 × 12 × 1) in-plane k-points and at the same time the corresponding differences values between a 7th and a 9th layer slab become unimportant. It should be noted at this point that although a slab made up from 20 atomic layers with a 200 k-point mesh would be preferable [17], such a calculation employing the computationally costly LAPW method would prohibited. Given the high level of its accuracy, we decided to use smaller system and take advantage of this method since it provides the best way for the description for the interactions of the oxygen with the metallic niobium. In order to study the evolution of early stages of oxygen adsorption on the surface we considered the following cases: (a) clean Nb(1 1 0) surface, (b) soft deposition of oxygen atoms on Nb(1 1 0) that alternatively occupy the four-fold adatom position, called “half monolayer” hereafter (HML) and (c) full oxygen monolayer deposition (FML). For the HML slab we
used 48 (15 × 11 × 1) k-points, while for the FML case 36 (11 × 11 × 1) k-points. 3. Results and discussion 3.1. Relaxation results For the clean Nb(1 1 0) surface case, the calculated surface energy (1.60 J/m2 ) is in agreement with semi-empirical calculations (1.67 J/m2 ) [18], embedded atom method (EAM) (1.82 J/m2 ) [19] and modified EAM (MEAM) (1.87 J/m2 ) [20], while it is underestimated compared to the TB (2.66 J/m2 )17 and FP-LMTO (2.36 J/m2 ) calculations [21]. In addition, the calculated value for the surface layer contraction (−5.5%) is in agreement with tight binding theory (TB) data (−5.8%) [17] using 20 atomic layers and 140 k-points, while our results differ from other TB quenched molecular dynamics (TB-QMD) (−3.6%) [22], FP-LMTO (−3.7%)[21] and with the VASPPAW method (−4.3%) [23] in which 6 or 7 layer slabs and 20 k-points were used, indicating that both quantities, i.e. the surface energy and the surface layer contraction depend on the system size and the type of calculation. For the inner layers, we found expansion (+0.6%) and contraction (−2.2%) for the second and third atomic layer, respectively, which nevertheless is less significant than that of the surface layer. These results are illustrated in Fig. 1a in the form of schematic atomic representations. With arrows we denote the atomic relaxation direction, while the deviation from the unrelaxed system of the atomic positions is given in nm. For the second case, i.e. half monolayer oxygen deposition, Fig. 1b, we found that the O atoms are very strongly contracted by as much as −46.8% compared to the NbO interlayer spacing of NaCl structure [24]. This value is comparable to the −52.2% contraction compared to the bulk Nb interlayer spacing. This important relaxation affects significantly the Nb surface atoms. In particular, the Nb atoms lying in the oxygen first neighborhood and along the [0 0 1] direction, named NbA hereafter, are expanded (+3.1%), while the NbB surface
Fig. 1. Schematic atomic representations of: (a) clean Nb(1 1 0) surface, (b) HML and (c) FML. With arrows we denote the atomic relaxation direction, while the deviations from the unrelaxed atomic positions are given in nm.
D.A. Kilimis, Ch.E. Lekka / Materials Science and Engineering B 144 (2007) 27–31
atoms lying along the [1 1¯ 0] direction are contracted by a similar amount (−2.8%), resulting eventually in a rumpled surface layer. This effect implies also that the NbA –O bond length is significantly shorter (0.20 nm) from the NbB –O (0.27 nm), suggesting that the former may possibly form covalent-like bonds [25]. In addition, the strong contraction of the oxygen atoms affects the beneath Nb atoms inducing contraction (−2.2%), while the Nb second layer atoms that stand below the vacant oxygen adatom position are expanded (+3.1%) similarly to the NbA surface atom. The third layer atomic positions are also altered exhibiting contraction (−2.4%) and expansion (+1.3%) for the atoms situated under the NbA and the NbB surface atoms, respectively, indicating the strong influence of the oxygen HML on the substrate atomic relaxations. When depositing a full oxygen monolayer on the Nb(1 1 0) face, Fig. 1c, the contraction of oxygen atoms is even more pronounced (−49.1%) compared to the NbO interlayer distance of NaCl structure and −54% compared to the Nb bulk interlayer distance. In addition, the length of the Nb–O bond along the
Fig. 2. EDOS of the half monolayer case: (a) O, NbA and NbB surface atoms (solid line, dashed line and points, respectively), (b) O px , py and pz partial EDOS (solid line, dashed line and points, respectively) and (c) NbA t2g and eg partial EDOS (solid and light dashed line) as well as NbA t2g and eg partial EDOS (solid dashed and dotted line).
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[0 0 1] direction shortens even more, 0.19 nm compared to the HML case. The Nb surface layer exhibits expansion +2.9% comparable to HML value (+3.1%) for the NbA . On the contrary, the second layer exhibits stronger contraction (−3.2%) compared to the corresponding (−2.2%) of the atom lying beneath the oxygen atom in the HML case, a result that could be interpreted as a kind of planes separation between the first and second Nb layers. This effect influences also the relaxations of the third atomic layer which, however, exhibits the smallest contraction (−1.2%). 3.2. Electronic density of states In the inset of Fig. 2a, we give the clean surface EDOS in which we see that the main peaks are located around −2.62, −1.44 and −0.35 eV, in agreement with previous TB data (−2.65, −1.63 and −0.48 eV) [17] and photoemission spectroscopy results (−2.45 and −0.39 eV) [26] below the Fermi level. In addition, we see a peak at 1.18 eV that was also observed by photoemission experiments [27] at 1.33 eV above the Fermi level. In Fig. 2a, we give the EDOS of oxygen and NbA and NbB surface for the HML case. We see that the presence of oxygen
Fig. 3. EDOS of the full monolayer case: (a) O and Nb surface atoms (solid and dashed line), (b) O px , py and pz partial EDOS (solid line, dashed line and points, respectively) and (c) Nb t2g and eg partial EDOS (solid and dashed line).
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(solid line) gives rise to three very well localized peaks at the bottom of the EDOS situated at −5.60, −5.18 and −3.94 eV below the Fermi level. With the exception of the peak around −0.66 eV, the Nb surface atoms of the HML preserve their characteristic clean Nb surface states below the Fermi level and up to −4 eV. Interestingly, for lower energies we recover practically the oxygen density of states signature at −5.60 and −5.18 eV for the NbA (dashed line) and NbB (points), respectively, indicating bonding between oxygen and Nb atoms which for the NbA atoms is by far more important suggesting larger electronic overlap between O–NbA , thus explaining the contraction and the smaller bond length (0.20 nm) compared to O–NbB , Fig. 1. In Fig. 2b, the decomposition of the oxygen p orbitals shows clearly that the px , py orbitals are mainly responsible for the two lowest energy peaks (−5.60, −5.18 eV), while the new third peak at −3.94 eV has strictly pz character. In addition, the NbA ’s t2g electrons are well localized and seem to be responsible for the two lowest energy peaks denoting doublelike bonding between the Nb t2g and O px , py orbitals, Fig. 2c, in agreement with theoretical data on NbO defective structure [25]. In addition, close to the Fermi level the new less pronounced peak at (−0.66 eV) is attributed to the interaction between O py and Nb eg electrons. The contributions of the inner Nb atoms to the EDOS do not exhibit any significant features and their character becomes bulk-like as going deeper into the bulk system. In Fig. 3, we present the EDOS for the oxygen and niobium surface atoms of the FML case. Similarly to the HML case we see that the oxygen atoms are mainly responsible for the new lower
energy peaks (−6.01, −4.96 and −3.85 eV), while a new clear peak at −0.22 eV emerges and it is mainly due to the Nb surface atoms. Compared to the HML, the energy peaks below −3.50 eV are broadened and slightly displaced towards lower energies, whereas the HML peak at −0.66 eV is shifted closer to the Fermi level (−0.22 eV), Fig. 3a. We interpret this enlargement between the low and high energy states below the Fermi level as the beginning of the characteristic energy gap present in the ionic oxides. In agreement with the HML case, the O px , py electrons are bonded with the Nb t2g electrons exhibiting localized states at −6.01 and −4.96 eV, while the new peak at –0.22 eV suggests again bonding between the Nb t2g and O py electrons, Fig. 3b and c. In addition, focusing at the new peak around −3.8 eV, we note that the Nb contributions are of minor importance and that the main contributions originate from the O pz electrons. This result suggests that there is no overlap between Nb and O electronic states and therefore the pz electrons could be regarded as dangling-like bonds. The above results were unequivocally confirmed by the charge density calculations, Fig. 4. In Fig. 4a and b, we give the electronic charge densities of the clean Nb surface in the (1 1¯ 0) and (0 0 1) planes, respectively. It is clearly seen that the Nb atoms which in the former case have more electronic charge in the interstitial spaces underlying the structural anisotropy of this surface. In Fig. 4c and d, we present the electronic charge densities in the same planes for the FML case. In both figures, it is interesting to notice the strong electronic overlap between the surface Nb and oxygen atoms indicating the strength of the Nb–O bonds. In addition, we can distinguish the t2g d-electrons
Fig. 4. Electronic charge density maps: (a) clean surface in the (1 1¯ 0) plane, (b) clean surface in the (0 0 1) plane, (c) FML in the (1 1¯ 0) plane and (d) FML in the (0 0 1) plane. The gray scale is logarithmic and the dark areas indicate low electronic density.
D.A. Kilimis, Ch.E. Lekka / Materials Science and Engineering B 144 (2007) 27–31
of the second layer Nb atoms (bottom atoms in Fig. 4d) and the eg d-electrons of the Nb surface atoms (Fig. 4c). Furthermore, we can also see the pz and py orbitals of the oxygen atoms (on the top of Fig. 4c and d, respectively). Comparing the densities of the clean and covered surfaces we can easily see that presence of oxygen alters the spherical symmetry of the charge distribution around the Nb atoms (Fig. 4a and b), that characterize the metallic bonding, imposing selective directional preference on the d orbitals of the FML system, suggesting covalent-like bonding. Moreover, the surface O px and Nb t2g are absent from Fig. 4c and d indicating their involvement in the Nb–O d–p bonding, a result which compatible with the EDOS findings, Fig. 3. Last but not least, in Fig. 4c we can see the unbound oxygen pz orbitals, clear evidence for the existence of dangling-like bonds. This finding has very important implications in the Nb surface functionalization by oxygen, since it related with the surface reactivity and catalytic behaviour. 4. Conclusions In this communication, we present results obtained by FPLAPW concerning the oxygen deposition on the Nb(1 1 0) surface. Half and full monolayer deposition were considered for which we evaluated the structural and electronic properties of the resulting overlayers. We found that the oxygen atoms form stronger bonds with the Nb surface atoms in the [1 0 0] than in the [1 0 1] direction, a fact that implies shorter bond lengths in the former direction and different structural relaxations in the neighbouring Nb atoms. In addition, we found that the Nb–O bonding, which is attributed to d–p hybridization of double bond-like character, results in the introduction of new electronic states that lay well below the lowest states of the clean Nb face. Interestingly, the Nb–O bonding type along the preponderated direction yields free oxygen pz orbitals that can be regarded as dangling-like bonds. These results elucidate the early stages of Nb oxidation and can be used to enlighten the mechanisms of surface reactions, catalytic activity and oxides growth mechanisms.
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Acknowledgements Stimulating discussions with Dr. G.A. Evangelakis are gratefully acknowledged. This work was supported by the DIK4001-1 project. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15]
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