Structural, Electronic, and Thermodynamic Properties

Article pubs.acs.org/JPCA

Structural, Electronic, and Thermodynamic Properties of the T and B Phases of Niobia: First-Principle Calculations Mirele B. Pinto,† Antonio Lenito Soares, Jr.,† Andy Mella Orellana,‡ Hélio A. Duarte,† and Heitor A. De Abreu*,† †

GPQIT, Departamento de Química, ICEx, Universidade Federal de Minas Gerais, Belo Horizonte 31270-901, MG, Brazil Departamento de Física, Facultad de Ciencias, Universidad de Chile, Santiago, Chile

‡

S Supporting Information *

ABSTRACT: Different polymorphs of Nb2O5 can be obtained depending on the pressure and temperature of calcination leading to different catalytic properties. Two polymorphs of niobia, T-Nb2O5 and B-Nb2O5, have been investigated by means of density functional/plane waves method. The equation of state predicted that B-Nb2O5 phase is more stable than the T-Nb2O5 at low temperature; however at high pressure both phases are stable. These results are in good agreement with the available experimental data. The calculated cohesive energies of 6.63 and 6.59 eV·atom−1 for the B-Nb2O5 and T-Nb2O5, respectively, also corroborate this conclusion, and it can be compared to the experimental value of 9.56 eV atom−1 estimated for the most thermodynamically stable phase. The topological analyses based on quantum theory of atoms in molecules (QTAIM) and electron localization function (ELF) were applied and reveal bonds with large ionic character for both phases. The B-Nb2O5 presented larger stiffness than T-Nb2O5, and the oxygen sites in the T-Nb2O5 are more compressible. The density of states comparison for both structures indicates that B-Nb2O5 has lower concentration of acid sites compared to T-Nb2O5. This result is consistent with the experimental observations that the concentration of Lewis acid sites decreases with the temperature.

1. INTRODUCTION The metal oxides present a diversity of structures and composition leading to a wide range of technological applications such as catalysts. There has been significant interest in understanding relationships between the structure and reactivity as well as active sites for specific reactions on oxide surfaces.1,2 Among the metal oxides, titania (TiO2) is probably the most widely investigated oxide surface.3,4 It is an important component in many catalysts. It is also used as support for metal catalysts,5 as biocompatible materials,6 and in addition, it is promising in solar energy conversion applications.7 After TiO2, ceria (CeO2) is one of the next most studied of oxide surfaces. Its main applications are partially due to its importance as a component in catalyst8 and also because of its promising future applications in energy and environmental technology.9 Another metal oxide that has attracted much attention is niobia, Nb2O5, due to its many remarkable properties that make it suitable for a wide range of applications.10−15 In particular, there is a growing interest in niobium containing materials with potential applications in heterogeneous catalysis.16−18 In spite of its importance, information about its structure, stability, and electronic properties is still missing in the literature. In nature, the niobium does not occur in a free state and it is usually found associated with tantalum in a mineral form, (Fe, Mn)M2O6 (M = Nb, Ta), known as columbite or tantalite, depending on which metal predominates.16 Niobium pentoxide © XXXX American Chemical Society

(Nb2O5), also known as niobia, exists in many polymorphic forms depending on the starting materials, pressure, and temperature.16,19,20 According to Schäfer et al.21 the polymorphs are classified based on the temperature in which they are obtained starting from amorphous niobium oxide, passing through the following crystalline phases: T (D2h, orthorhombic) and TT (pseudohexagonal or monoclinic) phases which crystallize at low-temperature (∼700 to 900 K), B (C2h, monoclinic) and M (D4h, tetragonal) phases at mediumtemperature (∼900 to 1200k), and H (C2h, monoclinic) phase at high-temperature (1223 K).22 A diagram showing the phase transitions as a function of temperature of Nb2O5 is presented in Scheme 1. According to Nowak and Ziolek,16 these phase transitions occur slowly in temperatures that are not welldefined and that are irreversible. The H phase is the thermodynamically most stable, while TT is the least one. All Nb2O5 polymorphs are constructed by distorted octahedra (NbO6), wherein the degree of distortion depends on whether the octahedra are connected by edges and (or) by corners. According to Schäfer et al.,21 there are several connection possibilities between the distinct octahedra, keeping the ratio O/Nb equal to 2.5. This fact justifies the different arrangements of Nb2O5 and also the existence of various niobia Received: November 11, 2016 Revised: March 14, 2017 Published: March 14, 2017 A

DOI: 10.1021/acs.jpca.6b11383 J. Phys. Chem. A XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry A

mechanism of different catalytic processes and, hence, contributing to improve its performance.17 Recently, Foo et al.29 investigated the role of Lewis and Brönsted acidic sites in the dehydration of glycerol on niobium oxide. They showed, by using FTIR spectroscopy, that there is a direct relationship between Brönsted and Lewis acidic site concentrations and the calcination temperature in the glycerol dehydration to hydroxyacetone over niobia catalysts. These results were supported by density functional (DFT) calculations using the T-Nb2O5 phase. They observed that the concentration of acidic sites decreased with the increasing of the calcination temperature, and after calcination at 1000 K there are no Brönsted acid sites on niobium oxide. The first step to understand the catalytic properties is to investigate the chemical and electronic properties of the solid.13,18,30 This work intends to contribute fulfilling the lack of information about the stability of T-Nb2O5 and B-Nb2O5 phases and their chemical bonding nature, structural and electronic properties, using DFT calculations. The nature of the chemical bonding is described using topological analysis.

Scheme 1. Phase Transition of Nb2O5 as a Function of Temperature

polymorphs. Furthermore, the T and TT phases, besides presenting Nb atoms with 6-fold (NbO 6) and 7-fold coordination (NbO7), produce distorted octahedra and pentagonal bipyramidal sites, respectively.22,23 According to Nico et al.,19 there are many contradictions regarding the structure and stability of the formed polymorphs. The Nb2O5 shows a strong surface acidity, and it was also shown to be water tolerant for many acid-catalyzed reactions.24−26 Aranda et al.27 studied the esterification reaction of palm fatty acids supported on niobia acid catalysts and zeolite. This study showed that the best catalytic performance was achieved with the calcined Nb2O5 which has higher concentration of acidic sites when compared to zeolites. Chai et al.28 investigated gas-phase dehydration of glycerol to produce acrolein (propenal) over solid Nb2O5 acid catalyst, and they observed that the catalyst performance for the dehydration reaction is significantly affected by the catalyst calcination temperature which induces the changes in the surface acidity and crystallization of Nb2O5. Understanding the morphology, concentration, and strength of acidic sites on niobium oxide is crucial for unveiling the

2. THEORETICAL APPROACH The calculations have been performed based on the density functional theory (DFT)/plane waves method with periodic boundary conditions as implemented in the Quantum Espresso package (PWscf).31 The GGA+U method was used in the rotationally invariant form32 with the on-site Coulomb correlation (U = 3, 5, 7, and 9 eV) to calculate the structural properties, cohesive energy, and bands structures of the TNb2O5 and B-Nb2O5 phases. The generalized gradient approximation (GGA) and the parametrization due to Perdew, Burke, and Ernzerhof (PBE)33 have been used for the exchange−correlation functional. The core electrons were described by ultrasoft pseudopotentials. 34 The valence electronic configurations considered in the pseudopotentials were Nb (4s2 4p6 4d4 5s1 5p0) and O (2s2 2p4). The valence

Figure 1. Unit cell of niobia (Nb2O5): T-Nb2O5 phase (a) and B-Nb2O5 phase (b). On the right side of B-Nb2O5 phase it is shown how the polyhedra are connected in the crystal structure. B


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The Journal of Physical Chemistry A Table 1. Calculated and Experimental Crystallographic Parameters of B-Nb2O5 and T-Nb2O5 phase

ref 23

T-Nb2O5 GGA+U

B-Nb2O5 GGA+U

experimental this work (PBE) this work (U = 3) this work (U = 5) this work (U = 7) this work (U = 9) PBEsol42 experimental41 this work (PBE) this work (U = 3) this work (U = 5) this work (U = 7) this work (U = 9) PBEsol42,43 HSE0643

a, Å

b, Å

c, Å

γ, deg

volume, Å3

6.175 6.275 6.289 6.289 6.294 6.321 6.176 5.560 5.646 5.631 5.618 5.606 5.596 5.549 5.569

29.175 29.430 29.418 29.404 29.409 29.741 29.425 12.740 12.916 12.902 12.898 12.897 12.904 12.822 12.748

3.930 3.905 3.813 3.894 3.894 3.897 3.923 4.883 4.933 4.929 4.927 4.925 4.923 4.902 4.879

90 90 90 90 90 90 90 105.02 103.70 103.80 103.89 104.01 104.22 104.51 104.39

708.01 721.39 705.62 720.20 721.04 732.64 713.05 334.11 349.61 347.84 346.67 345.55 344.66 337.71 335.61

NbO6 units (distorted octahedron) and NbO7 units (pentagonal bipyramidal)23 (Figure 1a). Because of the disordered positions of Nb atoms (0.5 occupancy) on the T-Nb2O5 phase, the structure was treated as follows: a position for the Nb atom closest to the origin along b axis was chosen, and the positions of the subsequent Nb atoms were chosen alternately from the previous Nb atom. Furthermore, to maintain the stoichiometry of the T-Nb2O5, it was necessary to remove two oxygen atoms of the structure. This procedure caused the change of coordination of Nb1 atom from pentagonal bipyramid (Nbpb) to distorted octahedron (Nboct). The issue of configurational disorder of the Nb atoms located in the 4g positions was not considered due to the small occupancy values and also the huge size of configurational space which should be consequently explored. The B-Nb2O5 is indexed at the space group C2/c, monoclinic crystal structure, and it contains four unit formulas per unit cell. The structure is composed of 8 cationic ions (Nb) located at the Wyckoff position 8f and 20 anionic oxygen ions (O) placed at three Wyckoff positions: 4e (O1) and two 8f (O2 and O3). In B-Nb2O5 phase the crystal structure is built up by blocks of distorted NbO6 octahedra arranged in strings composed of pairs of edge-sharing octahedra linked in a zigzag of cornersharing octahedra,41 as it is shown in Figure 1b. 3.2. Structure, Stability, and Equation of State. Table 1 compares the lattice parameters and volume calculated for the fully relaxed B-Nb2O5 and T-Nb2O5 phases (GGA and GGA+U with U = 3, 5, 7, and 9 eV) with the respective experimental values. The best fit is found for U = 3 eV for T-Nb2O5 phase and U = 9 eV for B-Nb2O5 phase. However, it is just slightly better than the GGA estimates and the differences are not larger than 0.02 Å. The predicted values are in good agreement with the available experimental data, with mean deviations of less than 2%. The lattice parameters reported in the literature calculated with other XC functionals are also in good agreement with our results. The interatomic distances obtained after optimization of the B-Nb2O5 and T-Nb2O5 phases together with the average values of bond distances and also the experimental values are shown in Supporting Information Tables S1 and S2, respectively. The PBE predicted bond distances for T-Nb2O5 and B-Nb2O5 phases that are overestimated when compared with the experimental data. However, the average bond distances Nb1pb−O for T-Nb2O5 phase is underestimated in comparison

states were expanded in plane waves with a kinetic energy cutoff of 60 and 600 Ry for the charge density cutoff. Brillouin-zone integration has been performed on a Monkhorst−Pack scheme35 using 2 × 2 × 2 for B-Nb2O5 and 4 × 2 × 4 kpoints for T-Nb2O5 for structural optimization. For the topological analysis, high quality electron density was obtained by single point calculations using 8 × 4 × 8 for B-Nb2O5 and 8 × 8 × 8 for k-points T-Nb2O5, and a Marzari−Vanderbilt smearing width of 0.02 Ry was applied in the Brillouin zone integration. All these parameters lead to accuracy of 1 mRy atom−1 in the total energy calculation. This combination of energy cutoff and k-point mesh was used to ensure convergence of the energy within 10−4 Ry and force tolerance criterion of 10−3 Ry bohr−1. Spin-polarization was not considered in the calculations based on convergence tests. The geometrical parameters were fully relaxed for both polymorphs. The thermal effects were evaluated under the quasiharmonic approximation (QHA) which includes thermal effects using the Debye model. To calculate the thermodynamic property, the Debye−Grüneisen model36 and the static energy obtained from first principle calculations were used. For the study of the mechanical properties, numerical and analytical (Birch− Murnaghan) equations of state (EOS) were used to describe the calculated energy−volume (E,V) points of the T-Nb2O5 and B-Nb2O5 phases. After these fittings it is possible to find pressure−volume (p−V) data and EOS parameters such as bulk modulus, B0, and its pressure derivative, B′0, both evaluated at zero pressure. These calculations have been performed with the GIBBS237,38 code. In order to better understand the nature of chemical bonding, analyses of the critical points of the electron density based on quantum theory of atoms in molecules (QTAIM)39 were performed using Critic240 code.

3. RESULTS AND DISCUSSION 3.1. Model Structure. The unit cell of the T-Nb2O5 phase belongs to the orthorhombic crystal family with space group Pbam. The conventional unit cell associated with these structures is composed of 16.8 and 42 Nb and O atoms, respectively. There are 16 cationic ions (Nb) located at four Wyckoff positions 8i with half occupancy and the O atoms are located at 11 Wyckoff positions: one 2b, four 4g, and six 4h. The remaining 0.8 Nb atoms are randomly distributed in three Wyckoff positions 4g with occupancies of 0.08, 0.08, and 0.04. In the T phase Nb atoms are in two different environments: C


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hardness of a material. The bulk modulus (B) of the niobia bulk was calculated according to eq 2.48

to the experimental value. This is probably due to the oxygen atom removed in the center of the unit cell, wherein the coordination environment changed from pentagonal bipyramid Nb1pb to octahedron Nb1(oct). The same behavior is observed for T-Nb2O5 phase using GGA+U (Table S2). Cohesive energy of T-Nb2O5 and B-Nb2O5 phases was calculated using eq 1: E cohesive =

⎛ ∂P ⎞ B = −V ⎜ ⎟ ⎝ ∂V ⎠

The bulk modulus values are 218.3 GPa for T-Nb2O5 phase and 225.6 GPa for the B-Nb2O5 phase; then the B-Nb2O5 phase is the less compressible. As far as we know, there is no information about the experimental value of the niobia bulk modulus reported in the literature. The rutile, a polymorph of titania (TiO2), has similar structure to B-Nb2O5 phase, and it presents experimental bulk modulus values of 211 GPa and theoretical (DFT-PBE) of 229.2 GPa.49 The bulk modulus values found in this study are comparable to the theoretical and experimental values found for rutile. Through PBEsol/plane wave calculations, Valencia-Balviń et al.42 found 110 and 174 GPa values of the bulk modulus for the T-Nb2O5 and B-Nb2O5, respectively. Experimentally, there are controversies about the exact conditions in which these phases are stable; therefore the phase diagram of niobia was not fully determined yet.22,44,50−52 According to Schäer et al.21 the T-Nb2O5 and B-Nb2O5 phases are formed under atmospheric pressure at low and medium temperature, respectively. However, some studies44,51,53 indicate that B-Nb2O5 phase is stable at room temperature and high pressure and the T-Nb2O5 phase exhibits stability at high pressures. The most appropriate thermodynamic function to evaluate the stability of a solid under pressure at 0 K is the enthalpy (H) (eq 3). The plot in Figure 2a shows that at high pressures the B-Nb2O5 phase is more stable than T-Nb2O5; however at a pressure of approximately 13 GPa there occurs a transition phase from B-Nb2O5 to T-Nb2O5. According to the literature, the T-Nb2O5 and B-Nb2O5 phases are stable at high pressures, showing that the results are in agreement with the experimental data.50,53,54

−(E Nb2O5 − 2E Nb − 5EO) NNb + NO

(1)

where Ecohesive is the cohesive energy per atom and ENb2O5, ENb, and EO are the total energy of niobia per molecular formula (there are four molecular formula for B-Nb2O5 and eight for TNb2O5 in each unit cell) and isolated atomic energies of niobium (2S + 1 = 6) and oxygen (2S + 1 = 3), respectively. NNb and NO are the numbers of niobium and oxygen atoms in the molecular formula. The energies of Nb and O atoms were obtained considering each atom located in a cubic box with lattice parameters a = b = c = 10 Å. The cohesive energy values are presented in Table 2 indicating that B-Nb2O5 phase is more stable consistent with Table 2. Cohesive Energies (Ecohesive) Calculated through GGA Approximation for T-Nb2O5 and B-Nb2O5 Phases and the Experimental Value for H-Nb2O5 Phase (298.15 K and 1 atm) B-Nb2O5 T-Nb2O5

Ecohesive (calc), eV·atom−1

Ecohesive (H-Nb2O5), eV·atom−1

6.63 6.59

9.5646,47

(2)

the experimental data. The cohesive energy was also calculated with GGA+U approximation (Table S3). It can be seen that these values follow the same thermodynamical tendency.21,44 According to Zhou et al.,45 DFT+U method is sensitive to the specific chemical environment. In this sense, they argue that the determination of the Hubbard correction term (U) should be made very carefully, since slight changes in the U values may lead to different relative stability. The calculated cohesive energies are at least 3 eV atom−1 smaller than the experimental estimate of the most stable phase H-Nb2O5. This difference increases if the GGA+U approximation is used (see Table S3 of the Supporting Information). The elastic constants of the solid are important parameters because they can provide information about the intrinsic

H = E + pV p=

⎛ ∂E ⎞ ⎜ ⎟ ⎝ ∂V ⎠T

(3)

(4)

To estimate the stability of the phases at different temperatures, we used the quasiharmonic Debye model. The model used to find the Debye temperature θ(V) was Debye−Grüneisen model.26 The nonequilibrium Gibbs function can be written as

Figure 2. (a) Enthalpy−pressure at 0 K and (b) Gibbs free energy−temperature at 0 GPa diagrams for T-Nb2O5 and B-Nb2O5 phases. The curves were calculated using the GGA approximation. D


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The Journal of Physical Chemistry A * (x ,V ;T ) G*(x ,V ;p ,T ) = Esta(x ,V ) + pV + Fvib

(5)

c=

where Esta(x,V) is the total energy of the crystal determined by electronic structure calculations, pV corresponds to the constant hydrostatic pressure condition, and Fvib * is the vibrational Helmholtz free energy, which includes both the vibrational contribution to the internal energy and the −TS constant temperature condition term. Therefore, from the static energy obtained from the PWscf calculations it is possible to build the free energy at any temperature in this model. One can note from Figure 2b that at low temperatures the B-Nb2O5 phase is more stable than T-Nb2O5. This result agrees with some experimental works which showed that the B-Nb2O5 phase presents lower Gibbs free energy than the T-Nb2O5 phase at low temperatures.21,51 The transition temperature from B-Nb2O5 to T-Nb2O5 phases occurs within the range of expected values, about 600 K. 3.3. Chemical Bonding and Local Properties. QTAIM39 analysis was performed for the B-Nb2O5 and T-Nb2O5 phases. The QTAIM formalism extracts the bonding information from electronic density that is also used as a quantum mechanical observable for performing numerical integrations where the gradient vector is the basic condition to determine the molecular topology. In QTAIM formalism the unit cell volume is partitioned in a particular division of real space (atomic basins) which permits the study of the local properties. In order to investigate the bonding and topological properties, a single point calculation of the optimized B-Nb2O5 and T-Nb2O5 structures was carried out to generate the full electron density. In Table 3 are shown the QTAIM volumes and charges

atom

T-Nb2O5

Nboct Nbpb O1 O2 O3 total Nboct O1 O2 O3 total

B-Nb2O5

χ 1.60 3.44

1.60 3.44

V (bohr3)

Q (e)

69.041 (12) 67.890 (4) 118.643 (4) 105.454 (16) 90.737 (20) 5076.628 67.083 (8) 98.634 (4) 92.835 (8) 85.514 (8) 2357.992

2.725 2.718 −1.033 −1.052 −1.143

N

∑ Ω

Q (Ω) OS(Ω)

(6)

Values close to 1 indicate that the crystal is more ionic and close to 0 is more covalent. The value of c for T-Nb2O5 and BNb2O5 phases are 0.87 and 0.77, respectively, which indicate solids with a large ionic character. According to Mori-Sánchez56 the c parameter found for rutile was 0.77, which again shows a structural similarity of the B-Nb2O5 phase with the rutile. The nuclear critical points (NCP) are surrounded by surfaces where the gradient flux of the electron density is zero forming the atomic basins. On 2D surface the minimum charge density is perpendicular to the surface which is localized between two neighboring atomic basins, and it is classified as bond critical point (BCP). When the bond paths are connected to form a ring, one point is found inside the ring; this is classified as ring critical point (RCP). When multiple rings are connected and one interstitial space is encapsulated, one point is found inside this space and it is classified as cage critical point (CCP). The critical points (CPs) of the T-Nb2O5 and B-Nb2O5 phases are shown in Figures 3 and 4, respectively. The properties of all CPs are shown in Tables S4 and S5. Figure 5 shows the nonequivalent BCPs of the T-Nb2O5 and B-Nb2O5 phases, and their respective descriptions are listed in Table 4. One important data is the Laplacian value of the electron density. This is a measurement of the curvature of the function in three dimensions obtained from second partial derivatives. If the Laplacian of any scalar field has a negative value, it represents a locally concentrated electron density; however if the Laplacian is positive, it represents a locally depleted electron density. As one can see from Table 4, there is no Laplacian with negative value, indicating a Nb−O ionic bonding character in the T-Nb2O5 and B-Nb2O5 phases, which justifies the high degree of ionicity found in both polymorphs. Electron localization function (ELF)57−60 was generated for the Nb−O bonding for both niobia phases. Figure 6a shows the ELF map in the (001) direction in the T-Nb2O5 phase, and Figure 6b shows two different planes in B-Nb2O5 phase containing different Nb−O bonds. It is important to mention that it is not observed electron localized between Nb and O atoms in any studied phases. Furthermore, the ELF small value (range of 0.2) also suggests small charge concentration between the Nb−O bonds, evidencing the ionic character of the Nb−O bonds. Thus, the ELF analysis agrees with the positive Laplacian values at the BCPs (Table 4). The local properties can be obtained calculating the local compressibility of the Nb and O atoms. Using basin volumes, it is possible to decompose the bulk modulus to contributions of each atomic basin:

Table 3. QTAIM Topological Volumes and Charges in the T-Nb2O5 and B-Nb2O5 Phasesa phase

1 N

2.723 −1.071 −1.018 −1.169

a The values in parentheses are the number of the basins. χ is Pauling’s electronegativity value.

resulting from integration of the basins. According to the atomic basins topology, distinct volumes and charges are found for the oxygen atoms in both phases and these atoms were called O1, O2, and O3. The occupation volumes of basins show that O3 atoms occupy larger volume (35.74%) in the unit cell phase and the O2 atoms (31.49%) in B-Nb2O5 phase. The charge values related to each basin follow the trend of the electronegativity scale proposed by Linus Pauling, χ,55 with Bader charge around 2.7e and 1.1e for Nb and O atoms, respectively. The ionicity (c)56 can be used to evaluate the global charge transfer by averaging the ratios between topological charges Q(Ω) and nominal oxidation states OS(Ω) (taking as Nb5+ and O2−) and N is the number of nonequivalent atoms in the unit cell.

k=

∑ fΩ k Ω Ω

(7)

V

where fΩ = VΩ is the fraction of the cell volume occupied by Ω basin and the local compressibility of a basin, kΩ, is defined similarly to the compression of the whole crystal (eq 2): kΩ =

1 1 ⎛ ∂V ⎞ = − ⎜ Ω⎟ BΩ VΩ ⎝ ∂P ⎠

(8)

Thus the local compressibility depends only on atomic basins.36 Therefore, when the cell volume is split into different atomic E


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Figure 3. (a) Critical points of the unit cell of T-Nb2O5 phase: NCP (nuclear, core or attraction) shown by the atomic positions of Nb and O; BCP (bond critical points) in yellow, RCP (ring critical points) in brown, and CCP (cage critical points) in blue. (b) RCP in brown and the CCP in blue are highlighted. For a better view of the CCPs, the unit cell was doubled in the c axis.

Figure 4. (a) All the critical points of the unit cell of B-Nb2O5 phase are NCP (nuclear, core or attraction) shown by the atomic positions of Nb and O; BCP (bond critical points) in yellow and RCP (ring critical points) in brown. (b) RCP in brown is highlighted.

Figure 5. (a) BCPs in octahedral environments and pentagonal bipyramid in the T-Nb2O5 phase and (b) BCP in octahedral environments in the BNb2O5 phase.

showed that anionic species has a higher compressibility than the cations.48,61 However, in B-Nb2O5 phase the compressibility values are the same in all the atomic basins of the unit cell. 3.4. Electronic Properties. Figure 7 shows the band structure and the projected density of states (PDOS) of the TNb2O5 (a) and B-Nb2O5 (b) phases. The band structure diagram was calculated using the K-points path suggested by Bilbao Crystallographic Server.62 For the T-Nb2O5 phase the Kpoints path is the orthorhombic system, with space group Pbam (No. 55) and for the B-Nb2O5 phase is the monoclinic system, with space group C2/c (No. 15). The band structure shows that

contributions, it is possible to provide knowledge of the mechanical properties of solids into local contributions. Table 5 shows the QTAIM partition of the compressibility and bulk modulus considering the contribution of the basins Nb and O for of T-Nb2O5 and B-Nb2O5 phases. In both phases the oxygen atoms showed higher volume fraction than niobium atoms in the unit cell (Table 5). According to eq 8, the O3 atom dominates the atomic contribution to the macroscopic compressibility in T-Nb2O5 phase. This is the expected result given that the oxygen O3 is the most anionic species of the crystalline structure (Table 3). It agrees with other studies that F


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The Journal of Physical Chemistry A Table 4. Chemical Meaning (CM) and Bond Critical Point (BCP), Average Bond Distance (d̅) and Density (ρ), ̅ and 2 Laplacian (∇ ρ) Values of the T-Nb2O5 and B-Nb2O5 Phases phase

CM

BCP

d̅, Å

ρ̅, e ao−3

∇2ρ̅, e ao−5

T-Nb2O5

Nb1oct−O1 Nb1oct−O3 Nb2pb−O2 Nb2pb−O3 Nb3oct−O2 Nb3oct−O3 Nb4oct−O2 Nb4oct−O3 Nb1oct−O1 Nb1oct−O2 Nb1oct−O3

b1,b4 b2,b3,b5,b6 b7,b11,b13 b8,b9,b10,b12 b15,b17,b18 b14,b16,b19 b21,b22,24 b20,b23,b25 b2 b1,b4 b3,b5,b6

1.99 2.00 1.95 2.17 1.95 2.03 1.96 1.96 2.07 1.86 2.11

0.092 0.129 0.105 0.082 0.125 0.098 0.143 0.107 0.102 0.188 0.096

0.132 0.387 0.282 0.233 0.409 0.279 0.492 0.339 0.345 0.600 0.315

B-Nb2O5

Table 5. QTAIM Partition of the Compressibility and Bulk Modulus of T-Nb2O5 and B-Nb2O5 into Atomic Basin Contribution (Ω) Ω T-Nb2O5

B-Nb2O5

oct

Nb Nbpb O1 O2 O3 Nb O1 O2 O3

fΩ

kΩ, TPa−1

BΩ, GPa

0.165 0.053 0.089 0.331 0.359 0.226 0.167 0.314 0.291

4.222 4.474 4.474 4.443 4.830 4.430 4.430 4.430 4.430

236.8 223.4 223.4 225.0 207.0 225.6 225.6 225.6 225.6

orbitals. Furthermore, the density of states of d-orbitals in the T-Nb2O5 phase is higher than B-Nb2O5 phase (Figure S1a). The present results are in agreement with the study performed by Foo et al.,29 who observed that there is a relationship between the temperature of crystallization of polymorphs of niobia and the concentration of Lewis and Brönsted acidic sites. The oxygen atom is responsible for the most part of the valence band of both phases, mainly due to its p orbitals (Figure S1b). In T-Nb2O5 there are two distinct coordination sites of Nb; however there were no significant differences between the DOS of Nboct and Nbpb atoms (Figure 7a.). It is known that systems containing d and f orbitals can have a strong electron correlation. Therefore, the approach GGA+U method (or LDA+U) is more adequate providing results in a reasonable agreement with experiments. Figures 8 and 9 contain the band structure diagrams for B-Nb2O5 and T-Nb2O5 under different U values for GGA+U calculations, respectively. The band gap increases with the value of the U parameter (Table 6); this result confirms the fact that a Hubbard-like correction term (U) substantially improves the accuracy of the calculated band gap, compared to the conventional GGA. However, the description of the electronic structure of these oxides by GGA and GGA+U methods do not present significant differences. The use of U parameter is an open question in the literature, and other characteristics of the electronic structure should be examined. For example, the electronic structure could be improved by adding U to the O (2p) levels. It has been shown elsewhere that these occupied states can be considerably influenced by Coulomb on-site

both phases are semiconductors with indirect band gap, and the gap values calculated are EgT‑Nb2O5 = 2.10 eV (Z → X) and EgB‑Nb2O5 = 2.55 eV (M → Y). In the literature, independent of the polymorph, the Nb2O5 is considered a semiconductor with wide range of band gap values.19 However, the experimental gap value most commonly found is about 3.6 eV.43 The gap values are underestimated as it is expected for GGA XC functionals.63 Pérez-Walton et al.43 and Weibin et al.64 estimated a value of 2.50 and 2.55 eV using DFT/PBEsol and DFT/GGA-PW91 levels of theory, respectively, for the BNb2O5. Clima et al.54 calculated a band gap of 1.6 eV for TNb2O5 using the DFT/LDA. The hybrid functionals can be applied to many classes of solids and are known to give more accurate results. For example, using Heyd−Scuseria−Ernzerhof (HSE06) hybrid functional, Pérez-Walton et al.43 showed a reduction in the error from 29% in the band gap value, using GGA (2.55 eV), to approximately 14%, using HS06 (4.1 eV) for B-Nb2O5. It is important to mention that the value of 3.6 eV described in the literature is not attributed to any Nb2O5 specific phase, and the experimental values found in the literature are in the range of 3.4−4.2 eV.19 The T-Nb2O5 and B-Nb2O5 projected DOS are shown on the right side of each band structure in Figure 7. One can observe that both minerals show similar features between the valence and conduction bands, wherein the Nb atom has the largest contribution in the conduction band, especially in d-

Figure 6. ELF maps for (a) T-Nb2O5 phase and (b) B-Nb2O5 phase. Oxygen and niobium atoms in red and green, respectively. G


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Figure 7. Band structure and projected DOS calculated with GGA for T-Nb2O5 (a) and B-Nb2O5 (b) phases.

Figure 8. Band structures of the B-Nb2O5 phase: (a) U = 3 eV, (b) U = 5 eV, (c) U = 7 eV, (d) U = 9 eV.

interaction.65−69 However, the use of such approach is beyond the scope of the present work.

experimental estimate, which suggests that the treatment of correlation effects (U) should be used carefully, in particular, in the phase stability study. The B-Nb2O5 phase was shown to be stable at low temperatures according to Gibbs free energy analysis, which is in good agreement with the available experimental data. At 0 K the B-Nb2O5 phase was shown to be thermodynamically stable under high pressure (9 GPa); however at pressures above 13 GPa, a transition phase from BNb2O5 to T-Nb2O5 can be observed. All thermodynamic properties obtained in this work of the T-Nb2O5 and B-Nb2O5 phases agree with the niobia phase diagrams found in the literature. The AIM and ELF topological analyses indicate that there are no Nb−Nb and O−O bonds in T-Nb2O5 and B-Nb2O5 phases; in addition they confirm that the Nb−O bond presents ionic character. The global ionic character is 87% and 77% for T-Nb2O5 and B-Nb2O5 phases, respectively. Bond critical

4. FINAL REMARKS The stability and structural, topological, and electronic properties of the T and B phases of niobium pentoxide were investigated using PBE/plane waves method. For both phases, the structural parameters are in good agreement with the experimental data and also with previously reported calculated values. In addition, the U values 3 and 9 eV improve the description of the structural properties for phases T-Nb2O5 and B-Nb2O5, respectively. The B-Nb2O5 phase cohesive energy (6.63 eV·atom−1) is slightly larger than the T-Nb2O5 cohesive energy (6.59 eV·atom−1) using the GGA approximation and about 3 eV smaller than the experimental estimate of the most stable H-Nb2O5 phase. The use of GGA+U calculations led to cohesive energy values with larger difference with respect to the H


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Figure 9. Band structures of the T-Nb2O5 phase: (a) U = 3 eV, (b) U = 5 eV, (c) U = 7 eV, (d) U = 9 eV.

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Table 6. Band Gap with GGA and GGA+U Calculations for T-Nb2O5 and B-Nb2O5 Phases exptl GGA GGA+U GGA+U GGA+U GGA+U

(3 (5 (7 (9

T-Nb2O5, eV

B-Nb2O5, eV

3.60 2.10 1.97 2.20 2.26 2.45

3.60 2.55 2.73 2.85 2.84 3.04

eV) eV) eV) eV)

Corresponding Author

*E-mail: [email protected]. Phone: +55(31)3409-5748. ORCID

Heitor A. De Abreu: 0000-0001-5324-6010 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank the support of the Brazilian agencies Fundaçaõ de Amparo à Pesquisa do Estado de Minas Gerais (FAPEMIG), ́ Conselho Nacional para o Desenvolvimento Cientifico e Tecnológico (CNPq), and Coordenaçaõ de Aperfeiçoamento de Pessoal de Ensino Superior (CAPES) which are also gratefully acknowledged. The National Institute of Science and Technology for Mineral Resources, Water and Biodiversity INCT-ACQUA (http://www.acqua-inct.org) and PRONEX/ CNPq/FAPEMIG (CEXAPQ-03155-15 and CEXAPQ01626-14) have also supported this work. This work was partially supported by the supercomputing infrastructure of the NLHPC (ECM-02) (Powered@NLHPC) and the Project RC130006 CILIS, granted by Fondo de Innovación para la Competitividad del Ministerio de Economia, Fomento y Turismo, Chile.

points (BCPs) were determined based on the QTAIM analysis of their electronic densities and can assist in the determination of cleavage planes in the crystalline structure. The calculated volumes of each basin show that the bulk compressibility of BNb2O5 is the same as the local compressibility, but in T-Nb2O5 phase the higher compressibility occurs in the O3 atom (more anionic species, Table 3). Finally, according to the projected DOS/atom, the contribution from Nb d orbitals to the conduction band is larger for the T-Nb2O5 phase (low-temperature) than for the BNb2O5 phase (medium temperature). This result suggests that the concentration of Lewis acid sites decreases with increasing calcination temperature.

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AUTHOR INFORMATION

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ASSOCIATED CONTENT

S Supporting Information *

REFERENCES

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The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.6b11383. Projected DOS calculated of T-Nb2O5 and B-Nb2O5 phases/atom, showing the contributions of each atomic orbital to the DOS (PDF) I


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K
