Nonstoichiometry in Bixbyite-Type Vanadium Sesquioxide - American

Article pubs.acs.org/JPCC

Nonstoichiometry in Bixbyite-Type Vanadium Sesquioxide C. Reimann,† D. Weber,‡ M. Lerch,‡ and T. Bredow*,† †

Mulliken Center for Theoretical Chemistry, Universität Bonn, Beringstr. 4, D-53115 Bonn, Germany Institut für Chemie, TU Berlin, Straße des 17. Juni 135, D-10623 Berlin, Germany

‡

S Supporting Information *

ABSTRACT: Recently, a metastable bixbyite-type polymorph of vanadium sesquioxide V2O3 has been synthesized from vanadium trifluoride. During the preparation, a very low oxygen partial pressure was necessary to prevent oxidation to higher valent vanadium oxides. In order to provide a quantitative description of the oxidation process, periodic quantum-chemical calculations at density-functional theory level were performed to study the thermodynamics of oxygen incorporation into bixbyite-type V2O3. Different defect structures for nonstoichiometric phases with the general composition V2O3+x are discussed, obtained either by removing single atoms from their respective lattice positions or by introducing additional atoms into empty lattice sites. We show that the stoichiometric phase is likely to incorporate excess oxygen into the empty 16c Wyckoff position under ambient pressure. Taking into account the equilibrium of nonstoichiometric phases with the gas phase, we arrive at an estimate of 10−17 bar for the oxygen partial pressure as the upper limit for stabilizing the stoichiometric phase under reaction conditions.

■

INTRODUCTION A large number of experimental and theoretical studies have been conducted on vanadium sesquioxide as it shows a metal− insulator transition (MIT), which is characteristic for Mott− Hubbard systems.1−7 At low temperatures, it is an antiferromagnetic insulator with a monoclinic crystal structure (M1), while above ≈170 K it turns into a paramagnetic conductor with a rhombohedral corundum-type structure.2−6 The MIT is a consequence of the strong coupling between electrons in localized d-orbitals.8 Recently, we reported the synthesis and characterization of a new bixbyite-type polymorph of vanadium sesquioxide.9 The new phase was obtained by heating vanadium triflouride for 2.5 h to 873 K in reaction gas atmosphere (10 vol % H2 in Ar, water-saturated). Our quantum-chemical calculations at density-functional theory (DFT) level confirmed the metastability of the new phase and predicted that the bixbyite-type structure is approximately 9−11 kJ mol−1 less stable than the well-known corundum-type phase.9,10 The bixbyite structure is often described by its relationship to the fluorite structure, where the anions form a simple cubic array with a cation in the center of alternate cubes. An idealized description of bixbyite is obtained by removal of one-quarter of the anions so that the empty sites lie on nonintersecting 3-fold axes.11 It has been noted before by Hyde and Eyring that these axes are oriented along ⟨111⟩.12 An alternative description involving body-centered cubic packing of rods consisting of anion vacancies has been given by O’Keeffe and Andersson.13 Real bixbyite (SG Ia3̅) is distorted from the ideal structure due to anion−anion repulsion12 as shown for V2O3 in Figure 1. Here the cations are distributed over two crystallographically distinct Wyckoff positions (8a and 24d) while the anions occupy the 48e general position. © 2013 American Chemical Society

Figure 1. Conventional unit cell of bixbyite-type V2O3 (larger blue spheres: V; smaller red spheres: O). The green octahedra designate the 8b position (left), while the yellow tetrahedra mark the 16c Wyckoff position (right) which corresponds to oxygen anion defects introduced into the fluorite structure.

Experimental findings suggest that V2O3 with bixbyite structure readily incorporates small amounts of excess oxygen so that the synthesis of the stoichiometric sesquioxide requires careful adjustment of experimental parameters.9 In order to quantify this effect and to provide a prediction of the oxygen partial pressure necessary for stabilization of vanadium sesquioxide, we modeled the thermodynamics of oxygen incorporation into bixbyite-type V2O3 using periodic quantum-chemical calculations at DFT level. Received: July 4, 2013 Revised: August 30, 2013 Published: September 9, 2013 20164

dx.doi.org/10.1021/jp406622u | J. Phys. Chem. C 2013, 117, 20164−20170

The Journal of Physical Chemistry C

■

Article

COMPUTATIONAL DETAILS

Periodic spin-polarized DFT calculations with localized Gaussian basis sets were conducted with the CRYSTAL09 program package.14,15 As V2O3 is a member of the family of strongly correlated materials, it is necessary to employ the DFT/Hartree−Fock hybrid approach or the DFT+U method in order to arrive at an at least qualitatively correct description of the electronic structure.16−20 However, we demonstrated before that the Perdew−Wang exchange-correlation functional (PWGGA)21 reproduces structural parameters and energetics of the known V2O3 phases almost as well as the PWXPW hybrid functional or the PBE+U method.9,10 We will demonstrate in the next section that these findings also apply for the mixed-valence vanadium oxides belonging to the Magnéli phases. In the present study the use of the pure GGA functional is very appealing because of the higher computational effort connected with the hybrid method due to the calculation of exact exchange and the large number of atoms present in the bixbyite primitive unit cell (V16O24). Therefore, we employed the PWGGA functional in most structure relaxations and frequency calculations and used the PWXPW hybrid functional (constructed from PWGGA exchange and correlation functionals, combined with 12% of exact exchange), which we found earlier to perform best for the vanadium sesquioxide system,10 only in our final thermodynamical assessment. In all calculations we used effective core potentials (ECP) developed by the Cologne group22,23 for vanadium, oxygen, and nitrogen, employing the valence basis sets (double-ζ quality) listed in the Supporting Information. Only ferromagnetic spin arrangements of the V3+/V4+ ions with formal configurations s 0d2/s0d1 were considered which correspond to the energetically preferred spin ordering with PWGGA. We have shown before that hybrid methods favor antiferromagnetic coupling in bixbyite-type V2O3, the ferromagnetic phase is, however, only about 0.6 kJ mol−1 less stable at the PWXPW level.10 Thus, we did not consider the computationally more demanding antiferromagnetic spin structures in this study. Structure relaxations were performed either with constraints to enforce a cubic Bravais lattice or without any symmetry constraints (corresponding to space group P1) as has been noted in the text. Zero-point and thermal contributions to the enthalpy were calculated within the quasi-harmonic approximation by performing frequency calculations at the Γ point.24−26

Figure 2. Mean absolute percentage deviation (MAPD) of the calculated lattice parameters with respect to the experimental reference values (corresponding vanadium oxide phases V2O3+x from left to right: M1-V2O3, V3O5, V4O7, V5O9, V6O11, V7O13, M1-VO2).

shows somewhat larger errors for the remaining phases, while PWGGA gives slightly better results for x > 0.5. Furthermore, we computed atomization enthalpies ΔaH with both functionals, neglecting zero-point vibration and entropy contributions. In Table 1 our results for ΔaH are compared to Table 1. Comparison of Calculated Atomization Enthalpies ΔaH (kJ mol−1) for Several Vanadium Oxide Magnéli Phases VO(3+x)/2 with Experimental Reference Values34

a

x

phase

expt

PWGGA

PWXPW

0.000 0.333 0.500 0.600 0.667 0.714 1.000

VO3/2 VO5/3 VO7/4 VO9/5 VO11/6 VO13/7 VO2/1

1499 1591 1625 1643 1655 1663a 1723

1476 1571 1611 1645 1662 1674 1742

1419 1502 1534 1561 1568 1586 1649

Calculated from the Giauque function.34

reference values for the investigated vanadium oxides that we determined using tabulated values for the enthalpies of formation.34 The atomization enthalpies, calculated with respect to the elemental formula VO(3+x)/2, increase almost linearly with x. The results obtained with PWGGA are quite close to the reference values with an error of approximately ±20 kJ mol−1. However, PWGGA underestimates ΔaH slightly for x < 0.5, but overestimates it for x > 0.6, and thus increases the stability of vanadium oxides with higher oxidation state. PWXPW, on the other hand, consistently underestimates all the reference atomization enthalpies by approximately 70−90 kJ mol−1. If energy differences are considered that relate two different Magnéli phases with each other, one obtains slightly more accurate results with the hybrid functional due to error compensation (e.g., ΔaH(x = 1) − ΔaH(x = 0) = 224 (expt), 266 (PWGGA), and 230 kJ·mol−1 (PWXPW)). It is noteworthy that the PWXPW result can be further improved by including the zero-point energy in the calculations (e.g., E0(x = 0) = 18 kJ mol−1, E0(x = 0.125) = 19 kJ mol−1). In summary, both structural and energetical properties of the vanadium oxide phases are reproduced quite accurately using either a pure density functional or a hybrid method. Of course,

■

RESULTS The performance of the employed computational methods when applied to the strongly correlated systems V2O3 and V3O5 was demonstrated before.9,10,27 Here we further assess the quality of our theoretical approach by performing structure relaxations for a series of nonstoichiometric vanadium oxides that belong to the well-known Magnéli phases with the composition V2O3+x, limiting x to the interval [0,1]. For computational reasons we restricted these tests to the phases M1-V2O3, V3O5, V4O7, V5O9, V6O11, V7O13, and M1-VO2. Comparing our computed values for the lattice constants (a, b, c, α, β, γ) with those obtained from experiment,28−33 we find that the mean absolute percentage deviation (MAPD) is lower than 1% in all cases (Figure 2). Thus, the pure GGA functional as well as the hybrid method reproduces the structural data for all of these strongly correlated vanadium oxides well. Notably the PWXPW hybrid functional performs best for x ≤ 0.5 and 20165



Article

observed that oxygen-deficient phases (x < 0) are energetically unstable with respect to V2O3 and thus are unlikely to occur. More importantly, however, the stoichiometric V2O3 is less stable than bixbyite-type vanadium oxides with x > 0, indicating that V3+ will be readily oxidized. The reaction energies for x > 0 do not allow an immediate conclusion whether the addition of oxygen or the removal of vanadium is preferred due to the different amount of excess oxygen x. Unfortunately, we cannot simply use the appropriate supercells in order to get identical V:O ratios for the different defect types VV and Oi, as increasing the cell size would lead to an unacceptable increase in computation time. We can, however, rely on additional information, e.g., the density that is directly available from the structure relaxations and from experiment. After geometry optimization at the PWGGA level, we obtained a lattice constant a = 9.35 Å for the stoichiometric bixbyite-type polymorph, which is in good agreement with the experimental value a = 9.3947(1) Å.9 Using the theoretical lattice constant, the density has been calculated as ρ = 4.87 g cm−3. Comparing this value to those for the nonstiochiometric phases listed in Table 2, the density decreases for the Vdeficient systems with x = 0.200 (ρ ≈ 4.7 g cm−3) while it increases in the case of oxygen excess (x = 0.125 and x = 0.250: ρ ≈ 4.9 g cm−3). From experiment, only the value for the nearly stoichiometric phase V2O3.01 (ρ = 4.79 g cm−3) is known9 so that apparently the accuracy of our calculations is not good enough to allow an immediate comparison with the calculated densities. Therefore, we will make use of earlier results for another bixbyite-type compound in order to determine the trend in the densities which is to be expected. A few years ago bixbyite-type vanadium oxide nitride with anion excess (V2O3.07N0.13) has been investigated.37 In order to elucidate whether vanadium vacancies or excess anions predominate in this system, we performed structure relaxations for the model systems V16O24N (V2O3N0.125), V16O25N (V2O3.125N0.125), and V15O23N (V2O3.067N0.133). In all cases studied, N was found to prefer the 48e over the 16c Wyckoff position, with different N/O distributions causing only small energy variations in the order of a few kJ mol−1. When comparing the theoretical densities and lattice constants with the experimental values, we find a similar trend as for the V2O3+x phases in the last paragraph: For the vanadium-deficient phases V15O23N, the calculated lattice constants (a = 9.31−9.32 Å) as well as densities (ρ = 4.70−4.72 g cm−3) are much lower than the reference values from experiment (a = 9.3966 Å; ρ = 4.89 g cm−3), while the values for V16O24N (a = 9.37−9.38 Å; ρ = 4.88−4.90 g cm−3) and V16O25N (a = 9.38−9.40 Å; ρ = 4.92−4.94 g cm−3) fit well despite the small differences in composition. The results also confirm that a higher number of excess anions leads to an increase of the lattice constant as well as the density. Transferring these findings to the V2O3+x phases with x > 0, we expect an increase in density with respect to stoichiometric V2O3, despite the differences in the ionic radii and masses of nitrogen and oxygen that hamper a direct comparison. Therefore, those structures where vanadium was removed are excluded from the following discussions. Incorporation of Excess Oxygen. Concentrating on the effects of oxygen excess on the structural and thermodynamic properties of bixbyite-type V2O3+x, we continued the process described above by filling the remaining 16c vacancies gradually according to the reaction in eq 1 with x in the interval [0,1]. While the first nonstoichiometric oxide V16O25 (x = 0.125) is

only the hybrid method is expected to give meaningful results with respect to electronic properties like the orbital ordering or the underlying magnetism.35,36 Stability of Bixbyite-Type Vanadium Oxides. All thermodynamic properties considered in this article are related to the formal reaction equation x V2O3 + O2 (g ) ⇌ V2O3 + x (1) 2 We started by performing structure relaxations of several different nonstoichiometric bixbyite-type vanadium oxides, keeping as many symmetry operations as possible and enforcing a cubic lattice in order to reduce computation times. The resulting total energies can be considered functions of x according to eq 1 and will be used to determine the interval for x that is relevant under experimental conditions. Since we are interested only in the thermodynamic properties under equilibrium conditions, we did not study the actual mechanism of oxygen incorporation. This would involve O2 adsorption, dissociation, and migration into the lattice, where each step is connected with a specific activation barrier. Thus, the overall kinetics governing the process of oxygen insertion into bixbyitetype V2O3 are too complex to be studied at quantum-chemical level with the available computational resources. The simplest nonstoichiometric structures V2O3+x are those where either an atom is removed from its crystallographic position or an excess atom is incorporated at an empty lattice site. Following this procedure we first investigated a number of oxygen-deficient phases, generated either by removing O atoms from the 48e general Wyckoff position of space group Ia3̅ or by introducing additional V atoms into the 8b and 16c positions. Phases with oxygen excess were constructed by placing O atoms at the unoccupied special Wyckoff positions (8b and 16c) or by creating vanadium vacancies (removing vanadium atoms from the 8a or 24d position). In order to obtain small values for x as they appear under experimental conditions, we inserted/removed one atom at a time into/from the primitive bixbyite unit cell (V16O24), thereby reducing the symmetry of the system. This way we obtained defect structures with the compositions V17O24 (x = −0.176), V16O23 (x = −0.125), V16O25 (x = 0.125), V15O24 (x = 0.200), and V16O26 (x = 0.250). The reaction energies with respect to the perfect stoichiometric bixbyite phase are given in Table 2. It is Table 2. Calculated Reaction Energies (T = 0 K, Zero-Point and Thermal Contributions Not Included) ΔRE (kJ mol−1) and Densities ρ (g cm−3) for Nonstoichiometric Vanadium Sesquioxides V2O3+x According to Eq 1a +V(8b) +V(16c) −O(48e) +O(8b) +O(16c) −V(8a) −V(24d) +2O(16c)

x

ΔRE

ρ

−0.176 −0.176 −0.125 +0.125 +0.125 +0.200 +0.200 +0.250

94.2 90.9 89.4 −10.5 −32.2 −63.4 −63.2 −68.2

4.97 4.98 4.75 4.91 4.90 4.70 4.71 4.93

a

The relationship to the underlying bixbyite-type structure is noted by the addition (+) or removal (−) of atoms to/from Wyckoff positions (SG Ia3̅) in the unit cell. All numbers correspond to fully relaxed structures keeping as many symmetry operations as possible. 20166



Article

vibrational and entropic contributions to the Gibbs energy G per formula unit at standard temperature (T = 298 K).24,25 x ΔR G(x) = G V2O3+x − G V2O3 − GO2 (2) 2 Contributions from the configurational entropy were not taken into account since they are much smaller (1−2 kJ mol−1) than the variations of ΔRG with x. Our results are presented in Figure 4, giving the reaction energy ΔRE (at T = 0 K) and

obtained by simply occupying an abritrary 16c Wyckoff position, there are more possibilities for placing the excess oxygen atoms when constructing the next composition, V16O26 (x = 0.250). In this and the following cases, we always started from the vanadium oxide with a lower oxygen excess, optimized all possible configurations obtained by introducing the next O atom, and finally chose the structure that gave the lowest energy. We assumed that each additional O atom will form an O2− ion so that the number of unpaired electrons is reduced as V3+ ions are effectively oxidized to V4+ with increasing x. For x = 1 vanadium dioxide is obtained on the product side with a distorted fluorite-type structure. As VO2 with fluorite structure would be an unrealistic high-energy polymorph, it is expected that it will undergo large atomic displacements during geometry optimization. For each model system we performed two structure relaxations using the PWGGA functional in which we optimized the atomic positions without any symmetry constraints and either enforced cubic unit cell deformations or allowed the cell parameters (a, b, c, α, β, γ) to vary freely. The dependence of the cubic lattice parameter acubic, obtained from the constrained structure relaxations, on the oxygen excess parameter x is shown in Figure 3 (left axis).

Figure 4. Dependence of the calculated reaction energies ΔRE (white symbols) and free enthalpies ΔRG (gray symbols) on the amount of excess oxygen x. The values for the electronic and Gibbs energies were calculated for structures obtained by allowing only cubic cell deformations (circles) or by unconstrained geometry optimization (triangles).

Gibbs energy ΔRG (at T = 298 K) as a function of the oxygen excess x. Compared with the electronic reaction energies, the inclusion of zero-point energy, vibrational enthalpy, and entropy reduces the stabilization of phases with x > 0 only slightly. This effect is more pronounced for larger values of x. There is a substantial deviation between the free reaction enthalpies for the constrained and unconstrained calculations for x > 0.8, which corresponds to the larger structural relaxations in this region. Notably in the interval [0.0, 0.5] the increase of x lowers the Gibbs energy of the system by a constant amount of ≈30 kJ mol−1 for each oxygen atom added to the primitive unit cell (Δx = 0.125). The small changes of the energetics due to the inclusion of finite temperature contributions to the total energy are not sufficient to stabilize bixbyite-type V2O3 with respect to the corresponding nonstoichiometric oxygen-rich vanadium oxides at ambient conditions. Influence of the Oxygen Partial Pressure. So far the determined values for the free reaction enthalpies imply equilibrium of V2O3+x with an oxygen atmosphere that has an unrealistically high partial pressure of 1 bar. In order to arrive at an expression including the oxygen partial pressure on the basis of our DFT results, it is necessary to include the oxygen chemical potential in the calculation of the Gibbs energy explicitly.38−40 Taking into account that bixbyite-type V2O3 is potentially a strongly correlated material, it is likely that a more accurate description of the electronic structure can be obtained using hybrid methods.41,42 Therefore, we employed the more accurate PWXPW hybrid functional10 instead of the PWGGA functional in frequency calculations with oxygen excess x = 0 and x = 0.125. It turned out, however, that the trend for G(x) at low temperatures is similar for PWGGA and PWXPW . Because of the quasilinear behavior of G(x) (Figure 4) for small

Figure 3. Dependence of the calculated lattice parameters on the oxygen excess parameter x. The lattice parameter acubic (left axis, circles) has been obtained from structure relaxations where only cubic cell deformations were allowed. The mean absolute percentage deviation (MAPD) of the lattice parameters a, b, c (obtained from unconstrained geometry optimizations) from acubic (right axis, gray bars) increases as x → 1, indicating that phases undergo stronger cell deformations as their composition approaches VO2.

For small values of x the cubic lattice parameter a increases almost linearly, accompanied by relatively small differences between constrained and unconstrained structure relaxation (Figure 3, bar plots). Relaxations that involve more significant deviations from the cubic starting point appear only for x > 0.7. The flattening of the curve around x = 0.5 is connected to the appearance of a bixbyite-derived vanadium oxide with the elemental formula V4O7. This particular vanadium oxide, however, is different from the well-known Magnéli phase with the same composition,30 which turns out to be about 124 kJ mol−1 more stable after structure relaxation at the PWGGA level. We therefore assume the existence of an activation barrier that prevents the transformation of the bixbyite-derived V4O7 to the Magnéli phase. Using the fully relaxed structures, we performed frequency calculations employing the PWGGA functional in all cases (constrained and unconstrained optimizations) to obtain 20167



Article

values of x, we did not study larger supercells to determine the x → 0 limit. Assuming that O2 complies to the ideal gas law the expression for the dependence on temperature and pressure reads ⎛ p⎞ GO2(T , p) = GO2(T , p0 ) + RT ln⎜ 0 ⎟ ⎝p ⎠

In order to carry out the synthesis, a mixture of H2/Ar was led through a water-filled washing flask. Apparently, this procedure leads to an unmanageable number of influencing parameters (e.g., gas flow rate, flow profile, etc.) that must be taken into account. Hence, we are not able to determine the exact partial pressures of H2/H2O in the reaction gas. Instead, in order to get a rough estimation of the oxygen partial pressure pO2 directly, we carried out similar experiments in the systems cobalt−oxygen, iron−oxygen, and nickel−oxygen. In all cases we found the particular oxide (Co3O4, Fe2O3, NiO) to be reduced to the metal. Comprising the information found in the literature,47−49 these findings point to the fact that under the synthesis conditions described above the oxygen partial pressure is in the order of at most 10−19 bar. These results support our previous statement on the synthesized bixbyitetype V2O3 to have the ideal A2X3 stoichiometry.

(3)

We calculated the numerical values for GO2(T,p0) at a given temperature directly by performing a frequency calculation for the O 2 molecule. They can also be obtained from thermochemistry databases43,44 as has been done by Reuter and Scheffler.45 The effect of varying oxygen partial pressure onto the Gibbs energy is shown in Figure 5 where ΔRG is plotted as a function

■

CONCLUSIONS First-principles calculations were employed to assess the thermodynamic stability of bixbyite-type V2O3 in oxygen atmosphere. We demonstrated that this metastable phase of vanadium sesquioxide is likely to form nonstoichiometric compounds with the general composition V2O3+x by incorporating excess oxygen atoms into the 16c Wyckoff position. Inclusion of up to 0.7 equiv of oxygen is possible without significant structural transformations. However, for x ≈ 0.5, high-energy polymorphs are obtained that are unlikely to persist under reaction conditions. In general, incorporation of additional oxygen atoms is found to be preferred thermodynamically so that special attention has to be paid to control the oxygen partial pressure pO2 during the synthesis. The calculated value for pO2 < 10−17 bar necessary for stabilization of the stoichiometric phase at T = 873 K is in semiquantitative agreement with the experimental observation.

■

Figure 5. Dependence of the free Gibbs energy ΔRG on the logarithm of the oxygen partial pressure ln(p/p0) for x = 0.125 in the temperature range 773−973 K.

* Supporting Information

Valence basis sets for periodic calculations with CRYSTAL09 for N, O, and V based on the Cologne ab initio effective core potentials. This material is available free of charge via the Internet at http://pubs.acs.org.

■

of ln(p/p0) for x = 0.125. The stoichiometric V2O3 phase is stabilized if ΔRG > 0 kJ mol−1, which is only possible at high temperatures and low oxygen partial pressures. Under synthesis conditions (T = 873 K),9 bixbyite-type V2O3 is thus stabilized at oxygen partial pressures below pO2 ≈ 10−17 bar according to our results. At even higher temperatures it is expected that the pressure limit is shifted to larger values (e.g., pO2 < 10−14 bar is sufficient for T = 973 K). Experimentally, these conditions were introduced by the H2/ H2O equilibrium using titanium as reductand. During the synthesis, oxygen is generated in situ due to water dissociation 2H 2O ⇌ 2H 2 + O2

*E-mail [email protected]; Ph +49 (0)228 73 3839; Fax +49 (0)228 73 9064 (T.B.). Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS Financial support from the DFG priority program 1415 is gratefully acknowledged. We especially thank the Regionales Rechenzentrum (Universität zu Köln) for providing considerable amounts of computation time on their HPC resources.

(4)

■

K p = pH O (pH pO ) 2

2

2

REFERENCES

(1) Mott, N. Metal-Insulator Transition. Rev. Mod. Phys. 1968, 40, 677−683. (2) Morin, F. Oxides Which Show a Metal-to-Insulator Transition at the Neel Temperature. Phys. Rev. Lett. 1959, 3, 34−36. (3) Moon, R. Antiferromagnetism in V2O3. Phys. Rev. Lett. 1970, 25, 527.

−1

2

AUTHOR INFORMATION

Corresponding Author

so that under synthesis conditions the oxygen pressure pO2 is in equilibrium with the partial pressures of water and hydrogen.46 2

ASSOCIATED CONTENT

S

(5)

Numerical values for the equilibrium constant Kp are available from ref 43 so that, in principle, pO2 can be determined as a function of pH2OpH2−1. 20168



Article

(4) Dernier, P.; Marezio, M. Crystal Structure of the LowTemperature Antiferromagnetic Phase of V2O3. Phys. Rev. B 1970, 2, 3771−3776. (5) Warekois, E. Low-Temperature X-Ray Diffraction Studies on Vanadium Sesquioxide. J. Appl. Phys. 1960, 31, 346S−347S. (6) Rozier, P.; Ratuszna, A.; Galy, J. Comparative Structural and Electrical Studies of V2O3 and V2−xNixO3 (0 < x < 0.75) Solid Solution. Z. Anorg. Allg. Chem. 2002, 628, 1236−1242. (7) Edwards, P. P.; Ramakrishnan, T. V.; Rao, C. N. R. The MetalNonmetal Transition: A Global Perspective. J. Phys. Chem. 1995, 99, 5228−5239. (8) Anisimov, V.; Izyumov, Y. In Electronic Structure of Strongly Correlated Materials; Cardona, M., Fulde, P., von Klitzing, K., Merlin, R., Queisser, H.-J., Störmer, H., Eds.; Springer Series in Solid-State Sciences: Springer: Berlin, 2010; Vol. 163 (9) Weber, D.; Stork, A.; Nakhal, S.; Wessel, C.; Reimann, C.; Hermes, W.; Müller, A.; Ressler, T.; Pöttgen, R.; Bredow, T.; et al. Bixbyite-Type V2O3 − A Metastable Polymorph of Vanadium Sesquioxide. Inorg. Chem. 2011, 50, 6762−6766. (10) Wessel, C.; Reimann, C.; Müller, A.; Weber, D.; Lerch, M.; Ressler, T.; Bredow, T.; Dronskowski, R. Electronic Structure and Thermodynamics of V2O3 Polymorphs. J. Comput. Chem. 2012, 33, 2102−2107. (11) O’Keeffe, M.; Hyde, B. An Alternative Approach to NonMolecular Crystal Structures With Emphasis on the Arrangements of Cations. In Cation Ordering and Electron Transfer; Gleitzer, C., Goodenough, J., Hyde, B., O’Keeffe, M., Weser, U., Eds.; Springer: Berlin, 1985; Vol. 61, pp 77−144. (12) Hyde, B. G.; Eyring, L. In Rare Earth Research III; Eyring, L., Ed.; Gordon and Breach: New York, 1965. (13) O’Keeffe, M.; Andersson, S. Rod Packings and Crystal Chemistry. Acta Crystallogr., Sect. A 1977, 33, 914−923. (14) Dovesi, R.; Orlando, R.; Civalleri, B.; Roetti, C.; Saunders, V.; Zicovich-Wilson, C. CRYSTAL: a Computational Tool for the Ab Initio Study of the Electronic Properties of Crystals. Z. Kristallogr. 2005, 220, 571−573. (15) Dovesi, R.; Saunders, V.; Roetti, C.; Orlando, R.; ZicovichWilson, C. M.; Pascale, F.; Civalleri, B.; Doll, K.; Harrison, N.; Bush, I. et al. CRYSTAL09 User’s Manual. University of Torino: Torino, 2009. (16) Di Valentin, C.; Pacchioni, G.; Selloni, A. Reduced and n-Type Doped TiO2: Nature of Ti3+ Species. J. Phys. Chem. C 2009, 113, 20543−20552. (17) Dalverny, A.-L.; Filhol, J.-S.; Lemoigno, F.; Doublet, M.-L. Interplay between Magnetic and Orbital Ordering in the Strongly Correlated Cobalt Oxide: A DFT+U Study. J. Phys. Chem. C 2010, 114, 21750−21756. (18) Janotti, A.; Van de Walle, C. G. LDA+U and Hybrid Functional Calculations for Defects in ZnO, SnO2, and TiO2. Phys. Status Solidi B 2011, 248, 799−804. (19) Tunega, D. Theoretical Study of Properties of Goethite (αFeOOH) at Ambient and High-Pressure Conditions. J. Phys. Chem. C 2012, 116, 6703−6713. (20) Islam, M. M.; Wilkening, M.; Heitjans, P.; Bredow, T. Insights into Li+ Migration Pathways in α-Li3VF6: A First-Principles Investigation. J. Phys. Chem. C 2012, 3, 3120−3124. (21) Perdew, J.; Chevary, J.; Vosko, S.; Jackson, K.; Pederson, M.; Singh, D.; Fiolhais, C. Atoms, Molecules, Solids, and Surfaces: Applications of the Generalized Gradient Approximation for Exchange and Correlation. Phys. Rev. B 1992, 6671−6687. (22) Burkatzki, M.; Filippi, C.; Dolg, M. Energy-Consistent Pseudopotentials for QMC Calculations. J. Chem. Phys. 2007, 126, 234105. (23) Burkatzki, M.; Filippi, C.; Dolg, M. Energy-Consistent SmallCore Pseudopotentials for 3d-Transition Metals Adapted to Quantum Monte Carlo Calculations. J. Chem. Phys. 2008, 129, 164115. (24) Pascale, F.; Zicovich-Wilson, C.; Lopez, F.; Civalleri, B.; Orlando, R.; Dovesi, R. The Calculation of the Vibration Frequencies of Crystalline Compounds and Its Implementation in the CRYSTAL Code. J. Comput. Chem. 2004, 25, 888−897.

(25) Zicovich-Wilson, C.; Pascale, F.; Roetti, C.; Saunders, V.; Orlando, R.; Dovesi, R. The Calculation of the Vibration Frequencies of Alpha-Quartz: the Effect of Hamiltonian and Basis Set. J. Comput. Chem. 2004, 25, 1873−1881. (26) Pascale, F.; Zicovich-Wilson, C. M.; Orlando, R.; Roetti, C.; Ugliengo, P.; Dovesi, R. Vibration Frequencies of Mg3Al2Si3O12 Pyrope. An ab Initio Study with the CRYSTAL Code. J. Phys. Chem. B 2005, 109, 6146−6152. (27) Weber, D.; Wessel, C.; Reimann, C.; Schwickert, C.; Müller, A.; Ressler, T.; Pöttgen, R.; Bredow, T.; Dronskowski, R.; Lerch, M. Nosovite-Type V3O5: A New Binary Oxide of Vanadium. Inorg. Chem. 2012, 51, 8524−8529. (28) Rozier, P.; Ratuszna, A.; Galy, J. Comparative Structural and Electrical Studies of V2O3 and V2−xNixO3 (0 < x < 0.75) Solid Solution. Z. Anorg. Allg. Chem. 2002, 628, 1236−1242. (29) Åsbrink, S. The Crystal Structure of and Valency Distribution in the Low-Temperature Modification of V3O5. The Decisive Importance of a Few Very Weak Reflexions in a Crystal-Structure Determination. Acta Crystallogr., Sect. B 1980, 36, 1332−1339. (30) Hodeau, J.-L.; Marezio, M. The Crystal Structure of V4O7 at 120 K. J. Solid State Chem. 1978, 23, 253−263. (31) Page, Y. L.; Bordet, P.; Marezio, M. Valence Ordering in V5O9 below 120 K. J. Solid State Chem. 1991, 92, 380−385. (32) Horiuchi, H.; Morimoto, N.; Tokonami, M. Crystal Structures of VnO2n−1 (2 ≤ n ≤ 7). J. Solid State Chem 1976, 17, 407−424. (33) Rogers, K. D. An X-ray Diffraction Study of Semiconductor and Metallic Vanadium Dioxide. Powder Diffr. 1993, 8, 240−244. (34) Brewer, L.; Ebbinghaus, B. B. The Thermodynamics of the Solid Oxides of Vanadium. Thermochim. Acta 1988, 129, 49−55. (35) Ganduglia-Pirovano, M. V.; Da Silva, J. L. F.; Sauer, J. DensityFunctional Calculations of the Structure of Near-Surface Oxygen Vacancies and Electron Localization on CeO2(111). Phys. Rev. Lett. 2009, 102, 026101. (36) Ma, Z.; Yi, Z.; Sun, J.; Wu, K. Electronic and Photocatalytic Properties of Ag3PC4VI (CO, S, Se): A Systemic Hybrid DFT Study. J. Phys. Chem. C 2012, 116, 25074−25080. (37) Nakhal, S.; Hermes, W.; Ressler, T.; Pöttgen, R.; Lerch, M. Synthesis, Crystal Structure and Magnetic Properties of Bixbyite-Type Vanadium Oxide Nitrides. Z. Naturforsch. 2009, 64b, 281−286. (38) Henzler, M.; Göpel, W. Oberflächenphysik des Festkörpers; Teubner: Stuttgart, 1991. (39) Nerikar, P.; Watanabe, T.; Tulenko, J. S.; Phillpot, S. R.; Sinnott, S. B. Energetics of Intrinsic Point Defects in Uranium Dioxide from Electronic-Structure Calculations. J. Nucl. Mater. 2009, 384, 61−69. (40) Finazzi, E.; Di Valentin, C.; Pacchioni, G. Boron-Doped Anatase TiO2: Pure and Hybrid DFT Calculations. J. Phys. Chem. C 2009, 113, 220−228. (41) Tran, F.; Blaha, P.; Schwarz, K.; Novák, P. Hybrid ExchangeCorrelation Energy Functionals for Strongly Correlated Electrons: Applications to Transition-Metal Monoxides. Phys. Rev. B 2006, 74, 155108. (42) Prodan, I. D.; Scuseria, G. E.; Sordo, J. A.; Kudin, K. N.; Martin, R. L. Lattice Defects and Magnetic Ordering in Plutonium Oxides: A Hybrid Density-Functional-Theory Study of Strongly Correlated Materials. J. Chem. Phys. 2005, 123, 014703. (43) Barin, I.; Knacke, O. Thermochemical Properties of Inorganic Substances; Springer-Verlag: Heidelberg, 1973. (44) Stull, D.; Prophet, H. JANAF Thermochemical Tables, 2nd ed.; National Bureau of Standards (U.S.): Washington, DC, 1971. (45) Reuter, K.; Scheffler, M. Composition, Structure, and Stability of RuO2(110) as a Function of Oxygen Pressure. Phys. Rev. B 2001, 65, 035406. (46) Brückner, W.; Oppermann, H.; Reichelt, W.; Terukow, J.; Tschudnowski, F.; Wolf, E. Vanadium Oxide; Akademie-Verlag: Berlin, 1983. (47) Róg, G.; Langanke, B.; Borchardt, G.; Schmalzried, H. Determination of the Standard Gibbs Free Energies of Formation of the Silicates of Cobalt, Magnesium, and Strontium by e.m.f. Measurements. J. Chem. Thermodyn. 1974, 6, 1113−1119. 20169



Article

(48) Giddings, R. A.; Gordon, R. S. Review of Oxygen Activities and Phase Boundaries in Wustite as Determined by Electromotive-Force and Gravimetric Methods. J. Am. Ceram. Soc. 1973, 56, 111−116. (49) Kemori, N.; Katayama, I.; Kozuka, Z. Measurements of Standard Molar Free Energies of Formation of the Lower Oxides of Ni, Cu and Co by an EMF Method at High Temperatures. J. Jpn. I. Met. 1977, 41, 803−808.

20170


Nonstoichiometry in Bixbyite-Type Vanadium Sesquioxide - American

Recommend Documents