Novel Delta-Ta2O5 Structure Obtained from DFT Calculations

Article pubs.acs.org/JPCC

Novel Delta-Ta2O5 Structure Obtained from DFT Calculations Z. Helali,†,‡ M. Calatayud,*,†,‡,§ and C. Minot*,†,‡,∥ †

UPMC Univ. Paris 06, UMR 7616, Laboratoire de Chimie Théorique, Sorbonne Universités, F-75005 Paris, France CNRS, UMR 7616, Laboratoire de Chimie Théorique, Université P. M. Curie, F-75005 Paris, France § Institut Universitaire de France, F-75005 Paris, France ∥ Institute of Computational and Theoretical Studies and Department of Physics, Hong Kong Baptist University, 224 Waterloo Road, Kowloon, Hong Kong ‡

S Supporting Information *

ABSTRACT: We present a novel structure (called δ′-Ta2O5) of hexagonal δ-Ta2O5 (tantala) based on first-principles calculations. Previous calculations have predicted a hexagonal structure and determined lattice constants in agreement with X-ray diffraction. Starting from this structure and determining an O-defective crystal, we have observed a strong reconstruction of the crystal structure incompatible with the pristine one. We show that this reconstruction must already be present in stoichiometric tantalum oxide, and we provide its geometrical and electronic structure. The energy stabilization is explained by a decreased O−O repulsion, by a more reasonable coordination of the tantalum atoms, and by an increase in the electronic gap.

1. INTRODUCTION Tantalum oxide (Ta2O5) is a semiconducting material with many potential applications both because of its catalytic properties1−3 and because of its high dielectric constant and its excellent step coverage characteristics.4−6 Compared with other metal oxides of group V, the much higher density of active sites (7 times the number of V2O5) is a consequence of the different morphology of the crystal.2 Tantala is interesting as bulk, as supported metal oxide or thin films, or inserted in a zeolite framework.7,8 In this work we will focus on the structural determination of the bulk material. Since the first determination of bulk tantala,9 the structural information is partial or even contradictory. The characterization of its electronic structure has prompted a number of computational studies aiming at building structural models compatible with experimental data, especially regarding the band gap.10 Two phases exist at low or room temperature: hexagonal δ and orthorhombic β.11 X-ray diffraction provides lattice constants for the unit cell12 of the δ phase. From there, Fukumoto et al.4 have calculated a larger unit cell by doubling the cell vectors to fit with the experimental measure of the density and proposed a hypothetical structure by minimizing the energy using local-density approximation (LDA) calculations. This structure has been used to calculate electronic structures and transport properties.11,13−15 From density functional theory based LDA and generalized gradient approximation (GGA) calculations,16 the hexagonal δ phase is supposed to be that of the lowest energy. Recently, a new crystal structure has been proposed as a simplified model for the Ta2O5 bulk structure.10 Besides the uncertain character© 2014 American Chemical Society

ization of the crystallographic unit cell of Ta2O5, the computational determination of the band gap is an issue due to the technological applications. The experimental value is measured to be of 3.9−4.0 eV,17,18 while standard generalized gradient approximation calculations report the hexagonal δ phase to present a larger band gap than the β phase (1.06 vs 0.2 eV from GGA calculations11). Recently the use of hybrid functionals results in a calculated value of 3.7 eV.10 Additionally, some difficulties in the characterization arise mainly due to the presence of dopants and defects such as oxygen deficiency (see refs 19 and 20 and references therein). To sum up, the structural information on Ta2O5 is unclear, and the present paper provides a new structure thermodynamically more stable than the previous ones reported. It was obtained from the optimization of an oxygen-vacant structure and points out the important role of the structural defects in the stabilization of bulk structures.

2. COMPUTATIONAL DETAILS The calculations have been performed with the VASP.4.6 code,21−23 using the PBE functional.24 The core electrons were frozen within the Projector Augmented Wave (PAW) method, whereas valence electrons (Ta: 5p65d36s2; O: 2s22p4) are treated explicitly by a plane wave basis set (500 eV). The precision option has been set to high. This procedure Received: March 28, 2014 Revised: May 21, 2014 Published: May 30, 2014 13652

dx.doi.org/10.1021/jp503088h | J. Phys. Chem. C 2014, 118, 13652−13658

The Journal of Physical Chemistry C

Article

Figure 1. Selected views of the hexagonal δ-Ta2O5 (large circles are Ta atoms, small are O atoms). The unit cell shown corresponds to a 2 × 2 cell. Two different Ta sites are present: 8-fold coordinated (Ta1, Ta3, Ta9, and Ta11) and 6-fold coordinated (Ta2, Ta4, and Ta5, etc.). Two inequivalent oxygen sites are present: 2-fold coordinated at the vertical between two Ta-containing layers (O2v) and 3-fold coordinated connecting Ta sites horizontally in the same layer (O3h).

1). Andreoni and Pignedoli26 have suggested that optimization under no symmetry constraint should improve the structure since vibrational analysis revealed imaginary frequencies. They obtained very small distortions associated with an energy gain of a few millielectronvolts. To avoid symmetry constraints we have considered a 2 × 2 unit cell as displayed in Figure 1. The procedure followed to obtain the new structure is schematized in the Supporting Information. Starting from the ideal hexagonal structure, we have created an oxygen vacancy by removing a 2-fold oxygen atom, i.e., an oxygen atom vertically bridging two 6-fold coordinated Ta atoms, thus breaking the 6-fold symmetry. The ionic relaxation and the lattice parameters have been calculated, however, maintaining the P6/mmm symmetry. This led to a strong exothermic restructuration. Then, we added an oxygen atom in the initial position to recover the stoichiometric composition and reoptimized within the P6/mmm spatial group. This led to the hexagonal structure shown in Figure 2 with an energy gain of 1.57 eV per Ta2O5 unit relative to the P6/mmm structure. We have tried to improve the energetics of the reconstructed structure in several ways. First, the optimization of the 2 × 2 structure without symmetry led to the break of the hexagonal spatial group as can be seen in Table 1. In this new structure a and b parameters are different, and the γ angle is of 122°. The energy gain per Ta2O5 unit reaches 1.66 eV. As can be seen in Table 1, the distortions from the hexagonal symmetry are small, but they do not correspond to an artifact in the optimization procedure: imposing a = b and γ = 120° and optimizing the c

guarantees that the absolute energies are converged to a few millielectronvolts, and it ensures that the stress tensor is converged within a few kilobar (indeed in all the systems calculated the Pulay stress is found to be 0.00 kbar). The lattice parameters and atomic positions were totally relaxed using ISIF = 3. This allows calculating the forces, the stress tensor, the relaxed atomic positions, and also the relaxed cell shape and its volume. The Brillouin zone was sampled following a 2 × 4 × 2 Monkhorst−Pack grid centered in the gamma point (distance between points in the reciprocal space of 0.05 Å−1). The atomprojected density of states (DOS) is done on spheres using ionic radii: Ta5+ (78 pm) and O2− (140 pm). The structure visualization was made with the VESTA graphical package.25

3. Ta2O5 STRUCTURAL MODEL δ-Ta2O5 has a hexagonal structure (space group P6/mmm) made of layers connected by oxygen bridges above and below the tantalum atoms. There are four Ta atoms per 1 × 1 unit cell. One Ta atom has six neighbors in the plane leading to a total coordination of eight including the vertical neighbors (hexagonal bipyramid). The three other Ta atoms (octahedral) have four neighbors in the plane (coordination six including the vertical neighbors). The coordination eight seems excessive, and the O−O distance (2.346 Å) in the set of six neighbors in the plane seems too short to avoid a local repulsion. Oxygen sites are either 2-fold (in the vertical between two Tacontaining layers, labeled O2v in Figure 1) or 3-fold (located horizontally in the Ta-containing layer, labeled O3h in Figure 13653



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Figure 2. Selected views of the reconstructed 2 × 2 hexagonal structure. Tantalum sites are 7-fold coordinated (Ta1, Ta3, Ta11, Ta13, and Ta15) or 6-fold. Three inequivalent oxygen sites are present: two-fold coordinated (O2h inside the Ta-containing layer and O2v connecting two layers) and three-fold ones (O3h in the Ta-containing layer).

Table 1. Cell Vectors of the Ta2O5 Structure Obtained after Optimization and the Corresponding Total Energy (Distances in Å, Angles in degrees, Energy in eV)a Ta2O5

a

b

c

γ

TOTEN

ref

δ-reconstructed full relaxed δ-reconstructed hexagonal P6/mmm full relaxed (exptl lattice parameters12) 2 × 2 structure hexagonal full relaxed, symmetry

14.802 14.837 14.496 14.676

14.896 14.837 14.496 14.676

7.737 7.735 7.76 7.76

122 120 120 120

−1090.37 −1088.85 −1063.74

this work this work this work 11 calcd

The loss of symmetry leads to small deviations from the hexagonal structure that are not significant (a slightly differs from b, and γ = 122° is slightly different from 120°). Calcd: calculated. Exptl: experimental. a

parameter led to a less stable structure. This confirms the small deviations from pure hexagonal symmetry. Note that the smallness of the variations may be not perceptible to experiment. Also, we have tried to move the O2v atoms in the vertical direction to check the stability of a short TaO bond. Short VO bonds are stable in the V2O5 layered structure. After optimization, the initial structure, i.e., the 2-fold oxygen sites equidistant to two Ta sites, is recovered, which means that TaO bonds would not be stable in the structure. 3.1. Reconstructed δ′-Ta2O5 Structure. To gain a better understanding of the reconstruction process we have calculated the difference between the positions of the structures before and after reconstruction. For the sake of simplicity, only the hexagonal structures have been considered with a = b = 14.496 Å and c = 7.76 Å. Table 2 summarizes the most important displacements found, and the complete list and the hexagonal structures before and after reconstruction are available as Supporting Information. Figure 3 displays the most relevant displacements observed. All the displacements are found to

Table 2. Displacements in Å for Selected Atoms in the Hexagonal Found after Reconstructiona

a

atoms

Ta label

Δx

Δy

Δz

Ta O2v O2v O3h O3h O3h

1 1−1′ 5−5′ 3−7−8 1−4−16 8−9−12

0.38 0.40 0.19 0.09 −1.26 1.35

0.05 0.21 0.30 1.82 −0.70 −0.32

0.00 0.00 0.00 0.01 −0.01 0.00

Labeling of Ta atoms in Figure 2.

occur in the xy-plane, and the movements in the z direction are negligible. This result supports the structures found by different optimization protocols used, in particular the fact that moving the O2v in the c direction becomes during the optimization equidistant to the two Ta-containing layers. The tantalum displacements are moderate, at most 0.38 Å. The Ta atoms initially equivalent by translation symmetry in 13654



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at the edges of valence and conduction bands. The decrease in coordination shrinks the bands and increases the gap. This is reflected in the calculated DOS. Such an increase is an index of stability. To gain further understanding on the electronic structure, we have performed a Bader analysis.27 The Bader charges calculated for selected atoms in both the perfect and the reconstructed structures are given in Table 3. The charge on the Ta sites depends on the coordination. In the hexagonal structure there are two inequivalent Ta sites, Ta8f charged +2.99 |e| and Ta6f charged +3.12 |e|. This is unexpected since the lower coordination should carry a lower charge due to the presence of less neighboring oxygen atoms. On the contrary, the reconstructed structure shows a broader distribution of geometrical environment around Ta: Ta7f charged +2.99 |e|, Ta6f with a neighboring oxygen (sites 3, 5, 7, 9) charged +2.95 | e|, and distorted octahedral Ta6f charged between +2.90 |e| and +3.03 |e|. The charge on Ta atoms in the reconstructed structure is overall smaller than in the hexagonal case and seems to be connected with the higher stability of the former. As regards the oxygen sites, they appear more negatively charged in the hexagonal structure: the O2v sites between −1.18 |e| and −1.25 |e| and the O3h sites between −1.20 |e| and −1.29 |e|. Here, the higher coordination of oxygen leads to a more negative charge as expected, and the O2v sites are less charged than the oxygen sites O3f in the plane. The reconstructed structure shows oxygen less negatively charged: O2v around −1.14 |e|, O2h charged −1.23 |e|, and O3h −1.18 |e| to −1.20 |e|. Relaxation induces an important change in the coordination of oxygen, creating O2h from hexagonal O3h sites. The hexagonal O3h that evolves to O2h possesses a higher negative charge; for instance, the O3h(2−3−7) site has −1.29 |e| before relaxation, and it becomes O2h (2−7) with −1.23 |e| (see Table 3). We can therefore give some general trends about the relaxation driving force which is related to obtaining a more balanced charge distribution with overall smaller charge on the atoms.

Figure 3. Selected atoms displacements indicated by arrows, top and side views.

the P6/mmm 2 × 2 structures become inequivalent. The new structure does not maintain a 6-fold coordination in the plane for the most coordinated Ta atoms. For two of them (at the vertex and the center of the unit cell shown in Figure 2, Ta1 and Ta11) the coordination in the plane is reduced to 5 (a total of 7 including the vertical neighbors; they form a pentagonal bipyramid). For the two others (Ta3 and Ta9) the coordination in the plane is 4; however, these four ligands leave an open space toward a fifth oxygen located at 3.20 Å adding a fifth weak interaction in the plane. The oxygen sites are more mobile and show major displacements in the Ta-containing plane, up to 1.82 Å for O3h Ta(1−4−16) and Ta(8−9−12). As a consequence, some of them become 2-fold coordinated in the plane: O2h between Ta(2−7), Ta(3−8), Ta(8−9),and Ta(5−10). The oxygen sites out of the Ta-containing plane show moderate displacements in the xy directions, at most 0.40 Å. In summary the reconstruction mainly involves the displacement of oxygen sites in the Ta-containing plane leading to a decrease in the tantalum coordination. Such rearrangement effectively increases the O−O distances found in the unreconstructed hexagonal structure, thus decreasing repulsion and stabilizing the final reconstructed structure. 3.2. Electronic Structure. The higher stability of the new phase is confirmed by the electronic structure analysis. The density of states (DOS) is shown in Figure 4 and Figure S1 (Supporting Information). It can be observed that the energy gap of the δ′-phase is increased with respect to the initial δphase geometry, even though it remains lower than the experimental measurement as expected from DFT insufficiencies: it passes from 0.93 eV in the hexagonal unreconstructed structure to 1.96 eV for the reconstructed one. The relative smallness of the gap before reconstruction is explained by the large coordination of the atoms whose projection was principal

4. REDUCIBILITY OF δ′-TA2O5 The reconstruction observed after the formation of an oxygen vacancy is a clear example of the importance of the presence of defects in solid structures. In particular, oxygen vacancies are common defects in metal oxides with an impact on their geometry and electronic structure.28−30 To gain more understanding on reduced tantala, we have carried out a systematic study on the formation of oxygen vacancies in the reconstructed δ′-Ta2O5 bulk. We removed one oxygen atom out of the 80 in the unit cell, sampling all the possible representative sites. The energy needed to remove an oxygen site is calculated as MOx = MOx − 1 + 1/2O2 E vac = E(MOx − 1) + 1/2E(O2 ) − E(MOx )

where Ei are the total energies of the stoichiometric, defective slabs, and the O2 molecule in the gas phase. The more positive the value of Evac, the more energy is needed to remove the oxygen. Since the removal of an oxygen leaves two electrons in the surface, we have switched to spin-polarized calculations and considered the singlet (Nα−Nβ = 0) and triplet (Nα−Nβ = 2) solutions. Table 4 summarizes the results obtained for the most relevant cases, and more detail can be found in Table S3 (Supporting Information). 13655



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Figure 4. Total and atom-projected density of states for the unreconstructed and reconstructed δ′-Ta2O5 structures. Labeling as in Figure 2. Y-axis in arbitrary units, x-axis in eV. 13656



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Table 3. Bader Charges in |e| for Selected Atoms in the Hexagonal and Reconstructed Structuresa atoms

Ta label

hexagonal

reconstructed

Ta8f Ta7f Ta6f

1,3,9,11 1,11,13,15 3,5,7,9 2,6,8,10,16 4,12,14 1−1′ 5−5′ 5−10/2−7 1−2−6 6−7−11 2−3−7

2.99 3.12 3.12 3.12 −1.18 −1.25 −1.23 −1.20 −1.29

2.99 2.95 3.03 2.90 −1.15 −1.14 −1.23 −1.20 −1.18 to O2h 2−7

O2v O2h O3h O3h O3h a

in the present work may exist. Further experiments on tantala polymorphs are needed to fully characterize the structure and reactivity of such promising materials. In particular, molecular spectroscopies like infrared or Raman may provide accurate information on local geometries and thus help understand the mechanisms of structural stabilization in tantala materials.

5. CONCLUSION In conclusion, we present a novel structure of hexagonal δTa2O5 tantala that we call δ′-Ta2O5 tantala, based on firstprinciples calculations. Previous calculations have predicted a hexagonal structure and determined lattice constants in agreement with X-ray diffraction. Starting from this structure and determining an O-defective crystal we have observed a strong reconstruction of the crystal structure. The energy stabilization is explained by a decrease of the O−O repulsion, by a more reasonable coordination of the tantalum atoms, and by an increase of the electronic gap. This reconstruction is consistent with X-ray data and should be already present in the stoichiometric tantalum oxide. Removal of oxygen sites leads to important local reorganizations in the layer showing large structural flexibility. Further experiments are needed to confirm the stability of reconstructed tantala structures and their reactivity, allowing a deeper understanding of such promising materials. We provide the structural data for the novel structure and hope they will be useful for both experimentalists and theoreticians willing to explore it.

Labelling of Ta atoms in Figures 1 and 2.

Table 4. Oxygen Vacancy Formation Energies Evac in eV (Labeling in Figure 3)a oxygen removed

singlet

triplet

O2v O2h O3h

5.70−6.08 5.10−5.35 4.50−5.97

5.79−5.98 5.55−5.83 5.23−6.27

a

Since there are several inequivalent atoms of each type, we give the range of Evac (see details in Table S4 (Supporting Information)).

■

It might be expected that the lowest coordinated oxygen atoms exhibit lower Evac values than 3-fold sites. According to this general rule, removing a 2-fold oxygen atom would involve breaking two Ta−O bonds, while a 3-fold would involve breaking three Ta−O bonds and should be energetically less favorable. However, Table 4 indicates that the energetic cost for removing 3-fold oxygen (O3h 4.50 eV) is smaller than for 2-fold ones (O2h 5.10 eV, O2v 5.70 eV). The relaxation of the reduced structure can explain that unexpected result: after removal of the 3-fold O (Ta 6−10−11), three Ta−O bonds are broken, but relaxation induces the formation of an additional Ta−O bond between O2h(5−10) and Ta 10. This behavior is observed for almost all the structures studied when an O3h is removed. For the 2-fold sites, those sites located in the Ta-containing layer O2h lead to smaller Evac values than the O2v bonding two Ta-containing layers. We conclude that the O sites binding two Ta-containing layers are stable and difficult to remove. On the contrary, oxygen atoms in the Ta-containing layer can be more easily removed due to an efficient reorganization of the atoms in the layer. Interestingly, the presence of O2h in the Tacontaining layer seems to be necessary: we have built systems without any O2h in the layer, and they result to be energetically not favorable, evolving to the break of some bonds and forming O2h sites. The presence of O2h may help decrease the structural stress by providing more flexibility in the structure. With regard to the electronic state, singlet states are preferred to triplet states, which is an indication of some irreducible character. This is consistent with the poor reducibility of Ta2O5 compared with V2O5.2 We conclude that the relaxation effects after formation of an oxygen vacancy are important and help stabilize reduced structures by an efficient reorganization of the Ta-containing layers. The layered structure would be preserved upon reduction, and in-plane rearrangements, involving exchange between 2-fold and 3-fold O atoms, are easy. This might indicate that other structures more stable than those reported

ASSOCIATED CONTENT

* Supporting Information S

Scheme 1: Optimization procedure. Table S1: Optimized parameters obtained from constrained optimizations. Table S2: Atomic displacements before and after reconstruction of the hexagonal structures. Table S3: calculated oxygen vacancy formation energies, in eV. See labeling in Figure 2. Figure S1: atom-projected density of states. File S1: Hexagonal structure before reconstruction (CONTCAR format file). File S2: Hexagonal structure after reconstruction (CONTCAR format file). This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected] (Prof. C. Minot). *E-mail: [email protected] (Dr. M. Calatayud). Phone: +33 1 44 27 25 05. Fax: +33 1 44 27 41 17. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was performed using HPC resources from GENCICINES/IDRIS (Grant 2012-x2012082131, 2013-x2013082131) and the CCRE-DSI of P. M. Curie University. Authors acknowledge Koichi Momma and Fujio Izumi for providing the VESTA programme.

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REFERENCES

(1) Chen, Y.; Fierro, J. L. G.; Tanaka, T.; Wachs, I. E. Supported Tantalum Oxide Catalysts: Synthesis, Physical Characterization, and Methanol Oxidation Chemical Probe Reaction. J. Phys. Chem. B 2003, 107, 5243−5250.

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(2) Wachs, I. E.; Chen, Y.; Jehng, J.-M.; Briand, L. E.; Tanaka, T. Molecular Structure and Reactivity of the Group V Metal Oxides. Catal. Today 2003, 78, 13−24. (3) Zhu, Y.; Yu, F.; Man, Y.; Tian, Q.; He, Y.; Wu, N. Preparation and Performances of Nanosized Ta2O5 Powder Photocatalyst. J. Solid State Chem. 2005, 178, 224−229. (4) Fukumoto, A.; Miwa, K. Prediction of Hexagonal Ta2O5 Structure by First-Principles Calculations. Phys. Rev. B 1997, 55, 11155−11160. (5) Shinriki, H.; Nakata, M. UV-O3 and Dry-O2: Two-Step-Annealed Chemical Vapor-Deposited Ta2O5 Films for Storage Dielectrics of 64Mb Drams. IEEE Trans. Electron Devices 1991, 38, 455−462. (6) Zaima, S.; Furuta, T.; Yasuda, Y.; Iida, M. Preparation and Properties of Ta2O5 Films by Lpcvd for Ulsi Application. J. Electrochem. Soc. 1990, 137, 1297−1300. (7) Tielens, F.; Shishido, T.; Dzwigaj, S. What Do the Tantalum Framework Sites Look Like in Redox Zeolites? A Combined Theoretical and Experimental Investigation. J. Phys. Chem. C 2010, 114, 9923. (8) Wojtaszek, A.; Ziolek, M.; Dzwigaj, S.; Tielens, F. Competition between TO and T-OH Groups in Vanadium, Niobium and Tantalum Bea Zeolite. Chem. Phys. Lett. 2011, 70, 70. (9) Spyridelis, J.; Delavignette, P.; Amelinckx, S. On the Superstructures of Ta2O5 and Nb2O5. Phys. Status Solidi B 1967, 19, 683− 704. (10) Nashed, R.; Hassan, W. M. I.; Ismail, Y.; Allam, N. K. Unravelling the Interplay of Crystal Structure and Electronic Band Structure of Tantalum Oxide (Ta2O5). Phys. Chem. Chem. Phys. 2013, 15, 1352−1357. (11) Gu, T.; Wang, Z.; Tada, T.; Watanabe, S. First-Principles Simulations on Bulk Ta2o5 and Cu/Ta2O5/Pt Heterojunction: Electronic Structures and Transport Properties. J. Appl. Phys. 2009, 106, 03713. (12) Terao, N. Structure des Oxides de Tantale. Jpn. J. Appl. Phys. 1967, 6, 21−34. (13) Ivanov, M.; Perevalov, T.; Aliev, V.; Gritsenko, V.; Kaichev, V. Ab Initio Simulation of the Electronic Structure of d-Ta2O5 with Oxygen Vacancy and Comparison with Experiment. J. Exp. Theor. Phys. 2011, 112, 1035−1041. (14) Ivanov, M. V.; Rzhanov, A. V.; Perevalov, T. V.; Aliev, V. S.; Gritsenko, V. A.; Kaichev, V. V. Electronic Structure of d -Ta2O5 with Oxygen Vacancy: Ab Initio Calculations and Comparison with Experiment. J. Appl. Phys. 2011, 110, 024115. (15) Wu, Y.-N.; Li, L.; Cheng, H.-P. First-Principles Studies of Ta2O5 Polymorphs. Phys. Rev. B 2011, 83, 144105. (16) Sahu, B. R.; Kleinman, L. Theoretical Study of Structural and Electronic Properties of Ta2O5. Phys. Rev. B 2004, 69, 165202. (17) Chun, W.-J.; Ishikawa, A.; Fujisawa, H.; Takata, T.; Kondo, J. N.; Hara, M.; Kawai, M.; Matsumoto, Y.; Domen, K. Conduction and Valence Band Positions of Ta2O5, TaON, and Ta3N5 by UPS and Electrochemical Methods. J. Phys. Chem. B 2003, 107, 1798−1803. (18) Parida, K. M.; Mahanta, S. K.; Martha, S.; Nashim, A. Fabrication of NiO/Ta2O5 Composite Photocatalyst for Hydrogen Production under Visible Light. Int. J. Energy Res. 2013, 37, 161−170. (19) Kimura, H.; Mizuki, J.; Kamiyama, S.; Suzuki, H. Extended XRay Absorption Fine Structure Analysis of the Difference in Local Structure of Tantalum Oxide Capacitor Films Produced by Various Annealing Methods. Appl. Phys. Lett. 1995, 66, 2209−2211. (20) Shinriki, H.; Hiratani, N.; Nakao, A.; Tachi, S. Extended Abstracts 1991 Int. Conf. on Solid State Devices and Materials, Yokohama; Business Center for Academic Societies Japan: Tokyo 1991; p 198. (21) Kresse, G.; Furthmüller, J. Efficient Iterative Schemes for Ab Initio Total-Energy Calculations Using a Plane-Wave Basis Set. Phys. Rev. B 1996, 54, 11169−11186. (22) Kresse, G.; Furthmüller, J. Efficiency of Ab-Initio Total Energy Calculations for Metals and Semiconductors Using a Plane-Wave Basis Set. Comput. Mater. Sci. 1996, 6, 15−50. (23) Kresse, G.; Hafner, J. Ab Initio Molecular Dynamics for OpenShell Transition Metals. Phys. Rev. B 1993, 48, 13115−13118.

(24) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1996, 77, 3865−3868. (25) Momma, K.; Izumi, F. Vesta: A Three-Dimensional Visualization System for Electronic and Structural Analysis. J. Appl. Crystallogr. 2008, 41, 653−658. (26) Andreoni, W.; Pignedoli, C. A. Ta2O5 Polymorphs: Structural Motifs and Dielectric Constant from First Principles. Appl. Phys. Lett. 2010, 96, 062901. (27) Henkelman, G.; Arnaldsson, A.; Jonsson, H. A Fast and Robust Algorithm for Bader Decomposition of Charge Density. Comput. Mater. Sci. 2006, 36, 354−360. (28) Calatayud, M.; Markovits, A.; Menetrey, M.; Mguig, B.; Minot, C. Adsorption on Perfect and Reduced Surfaces of Metal Oxides. Catal. Today 2003, 85, 125−143. (29) Bouzoubaa, A.; Markovits, A.; Calatayud, M.; Minot, C. Comparison of the Reduction of Metal Oxide Surfaces: TiO2-Anatase, TiO2-Rutile and SnO2-Rutile. Surf. Sci. 2005, 583, 107−117. (30) Vecchietti, J.; Collins, S.; Xu, W. Q.; Barrio, L.; Stacchiola, D.; Calatayud, M.; Tielens, F.; Delgado, J. J.; Bonivardi, A. Surface Reduction Mechanism of Cerium-Gallium Mixed Oxides with Enhanced Redox Properties. J. Phys. Chem. C 2013, 117, 8822−8831.

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Novel Delta-Ta2O5 Structure Obtained from DFT Calculations

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