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Doping induced structural transformation in tungsten trioxide
Accepted Manuscript Doping Induced Structural Transformation in Tungsten Trioxide Zhijie Li, Shiyun Wu, Zhiguo Wang, Y.Q. Fu PII:
S0925-8388(16)30351-6
DOI:
10.1016/j.jallcom.2016.02.082
Reference:
JALCOM 36694
To appear in:
Journal of Alloys and Compounds
Received Date: 22 September 2015 Revised Date:
7 February 2016
Accepted Date: 9 February 2016
Please cite this article as: Z. Li, S. Wu, Z. Wang, Y.Q. Fu, Doping Induced Structural Transformation in Tungsten Trioxide, Journal of Alloys and Compounds (2016), doi: 10.1016/j.jallcom.2016.02.082. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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Doping Induced Structural Transformation in Tungsten
Zhijie Li,1 Shiyun Wu,2 Zhiguo Wang,1* Y.Q. Fu1,3*
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Trioxide
Corresponding author. E-mail: [email protected] (ZW); [email protected] (YF)
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*
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1 School of Physical Electronics,, University of Electronic Science and Technology of China, Chengdu, 610054, P.R. China 2 School of Physics and Mech-tronic Engineering, Sichuan University of Arts and Science, Dazhou 635000, P.R. China 3 Department of Physics and Electrical Engineering, Faculty of Engineering and Environment, University of Northumbria, Newcastle upon Tyne, NE1 8ST, UK
ABSTRACT
Effects of dopants on structural stability of monoclinic WO3 were studied using density
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functional theory. Transformation from monoclinic to cubic crystal structures was obtained by gradually increasing doping concentrations of both rhenium (Re) and electrons inside the monoclinic WO3, whereas a large distortion of WO6 octahedra was observed by gradually
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increasing doping concentrations of both niobium (Nb) and holes inside the monoclinic WO3. It was verified that RexW1-xO3 has a cubic structure if x is larger than 0.375, and the transformation
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from monoclinic to cubic structure is mainly dependent on the occupancy of the W 5d orbital. The elastic characteristics of the RexW1-xO3 decrease with the increase of the content of Re in the range of 0.375≤x≤0.875.
Keywords: Tungsten Trioxide; Phase transformation; Doping; Density functional theory
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1. Introduction Owing to its distinctive electronic and electrochromic properties, tungsten trioxide (WO3) shows promising applications in smart windows, gas sensors, solar cells and high-density optical data
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storage [1-4]. It is a complex material regarding to its crystal structure and thermal stability. The crystal structure of the WO3 is formed by WO6 octahedrons, each of which is part of a cornersharing network extending in three dimensions. The distortion of each octahedron results in
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monoclinic, triclinic, tetragonal, orthorhomic, cubic, and hexagonal structures [4]. Tailoring functionalities of the WO3 is important for its wide applications, and can be successfully
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achieved mainly in three different ways: [5] (1) by inserting mono- or divalent cations into the interstitial sites of the WO3; (2) by introducing O-vacancies; or (3) by using doping or atomic replacements in the WO3. Therefore, two types of doping strategies become possible, in either oxygen site or W site. Doping is believed as an effective and simple way to increase free carries
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and reduce potential and conduction band levels through introducing impurity elements. For example, inserting C or N into oxygen sites in the WO3 will decrease the band gap [6-9]. A set of metal dopants (such as Ti, Hf, Ta, V, Cu, etc.) for replacing tungsten in the WO3 were also
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examined experimentally and theoretically [10-15]. An interesting phenomenon is that the change of electronic properties induced by doping is
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often accompanied with evolution of crystal structure. Doping can stabilize metastable hightemperature phases at much lower temperatures. Yan et al. [16] found Nb doping (replacing W) in the WO3 results in the increase of the band gap and shift of absorption edge, and doping with 5 at% Nb ions induced phase transformation from monoclnic γ-WO3 to monoclinic ε-WO3. Regarding to this transformation, Bathe et al. [17] found cycle stability, charge storage capacity and reversibility of the WO3 films were improved upon doping with Nb ions, but coloration
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efficiency was decreased. Yan et al. [16] explained that this is mainly because W6+ (0.62 Å) has a smaller ionic radius than Nb5+ (0.64 Å), and Nb inclusion would lead to a longer bond length and a larger tilting angle. The reduction of W6+ to different fractions of W5+ with a larger radius
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leads to an expansion of cell volume. It is critical to understand the mechanisms of the structure transformation induced by doping, which could provide the opportunities to tailor the properties as required. Because Nb has one valence electron less than W, Nb doping may affect the
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oxidation states of the W, thus changing the crystal structure of the WO3.
In this work, we, for the first time, investigated the crystal structure of Nb and Re doped
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WO3 using a density functional theory (DFT), and found that the occupancy of the W 5d orbital plays an important role on the symmetry of WO3 crystal structure. These results are important for design of WO3 crystal structures with specifically required electronic properties.
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2. Simulation details
All the calculations were performed using the SIESTA code [18], which adopted a linear combination of numerical localized atomic orbital basis sets for the description of valence
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electrons [19]. Norm-conserving pseudopotentials [19] were used to describe electron-ion interaction, while the generalized gradient approximation using the Perdew-Burke-Ernzerhof
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(PBE) functional was used to describe the electron exchange-correlation. The valence electrons were taken to be 2s22p4, 6s25d4, 6s25d5 and 5s14d4 for elements of O, W, Re and Nb, respectively. The valence electron wave functions were expanded using a double-ζ basis set plus polarization functions. The distortion of each octahedron results in a monoclinic symmetry and the monoclinic unit cell is composed of eight formula units in each unit cell (8 W atoms and 24 oxygen atoms). The unit cell containing 32 atoms was used in the calculation with a 4×4×4
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Monkhorst-Pack [20] mesh for the k-point sampling. For all the simulation, the lattice parameters and atom positions were allowed to relax by using a conjugate gradient minimization until the Hellmann-Feynman force is less than 0.02 eV/Å. The lattice parameters of monoclinic WO3 at
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room temperature were constructed from the experiment [21] and then fully optimized. As the crystal structure was slightly distorted, the O-W-O angle was not 180° but varied between 163° and 177°. Lattice parameter, β, was increased from 90° in the cubic phase to 90.2° for the
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monoclinic phase. The calculated lattice parameters are: a=7.54 Å, b=7.56 Å, and c=7.81 Å, which agree well with other calculated values of a=7.50 Å, b=7.65 Å, and c=7.79 Å [22]. The
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discrepancy with the experimental data (a=7.33 Å, b=7.56 Å, and c=7.73 Å [23]) might be due to the over-estimation of the optimized values of lattice constants with respect to their actual quantities within the feature of GGA functional in PBE form [24]. The Mulliken analysis was performed to investigate the occupancy of the d and s band states of the cations [25]. Since there
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are 8 W atoms in the unit cell, we used W1-x(Re, Nb)xO3 with x=0.125, 0.25, 0.375, 0.50, 0.625, 0.75, and 0.875 to represent that 1, 2, 3, 4, 5, 6, and 7 out of the eight W atoms were replaced by (Re, Nb) atoms in the unit cell. There are many possible atomic configurations in the unit cell
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W1-x(Re, Nb)xO3 with x=0.25, 0.375, 0.50, 0.625, and 0.75, and most of key possible configurations were tested and the lattice sites for the lowest energy one are listed in table 1.
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This can also be seen from the Fig. 1 (d) where the corresponding positions of metal atoms are numbered.
3. Results and discussion
The monoclinic structure (with a space group of P21/n) of the WO3 is stable in the temperature range between 17 and 330 oC [26, 27]. The monoclinic WO3 can be considered as a
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deformed perovskite structure such as ABO3, where the A ions are missing and B ions are replaced by W. The site of A is suitable for intercalation of ions. In a monoclinic cell containing 8 W and 24 O atoms, one W atom is found to bond octahedrally to six surrounding O atoms,
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while an O atom is connected to two W atoms as illustrated in Fig. 1(d) [21]. The WO3 structure can also be considered as a structure of W-O-W like chains, where the chains are connected across the W atoms. The calculated W-O-W angles are different along a, b, and c directions,
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which are 163.12, 163.17 and 169.90°, respectively. The obtained band structures of the monoclinic WO3 with spin up is shown in Fig. 2(a). It is noted that there are no apparent
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differences between the band structures obtained for spin up and spin down of the monoclinic WO3. The selected k-points path to calculate the band structure is shown in Fig. 2(b). From Fig. 2 (a), we can see that the valence band maximum (VBM) state locates at the Г point. The valance band and conduction band are flat at Г→Z direction. The monoclinic WO3 has a direct band gap
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of 1.08 eV at the Г point as shown in Fig. 1 (a), an indirect band gap of 1.086 eV from Г to Z point. These values are less than the experimental direct band gap of 2.58 eV [28] and indirect band gap of 2.6 eV [29]. This under-estimation of band gap is a consequence of the adopted
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standard DFT used in our calculation. Calculations based on hybrid functional or GW methods can reproduce the band-gap of monoclinic WO3 [30, 31]. Spin-orbital coupling of 5d-atoms has
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an important effect on the band structure of materials [32, 33]. As we are mainly concerned with the phase transformation upon doping in the present work, we expected that this computational under-estimation of band gap and omission of the spin-orbital coupling would not significantly affect our conclusion. Projected density of states (PDOS) for the monoclinic WO3 as shown in Fig. 1 (c) confirms that the monoclinic WO3 shows a character of semiconductors. From the
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PDOS of W and O atoms, the VBM level is composed by the O 2p states, whereas CBM level is mainly composed of W 5d states. Evolutions of the lattice constants and W-O-W angles as a function of doping concentration
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are shown in Fig. 2. The lattice constants a, b and c are different in lengths with x<0.375 in the W1-xRexO3. Values of a and b are almost equivalent and increase with increasing the Re dopants, whereas value of c is decreased. As x was increased to 0.375, values of the lattice parameters a
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and b are elongated from 7.54 to 7.68 Å, while that of c is shortened from 7.81 to 7.68 Å. The W-O-W angles along a, b, and c directions are also increased to 180° with the x is increased to
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0.50. All the three lattice constants a, b and c continue to have the same effective length and the W-O-W angles are remained to be 180° with further increasing Re dopants. This means that the monoclinic WO3 transforms into a cubic phase with increasing Re doping. The results agree with the experimental observation of RezW1-zO3 which has a cubic structure as z>0.25 [34]. For the
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Nb doping, all the lattice constants of a, b and c increase with Nb dopant, and the W-O-W angles along a and b directions show insignificant changes, whereas the W-O-W angles along the c direction decrease when x<0.50 in W1-xNbxO3, which means that a large distortion of the WO6
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octahedra is obtained with increasing Nb dopants. It can be seen form Fig. 2 (c) that the lattice constants a, b and c increase linearly with increasing the Nb concentration, which obeys the
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Vegard’s law [35].
As Nb has one valence electron less than W, whereas Re has one valence electron more than W, we investigated the changes of atomic structure with electron/hole doping number between 1 and 7 in the WO3 unit cell, which corresponds to 0.125-0.875 e(h)/WO3. The electron and hole doping was performed by adding or removing electrons from the unit cell, and a compensating background was used to achieve the charge neutrality [36]. This is identical to what was obtained
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from a similar system, and is consisted of the original charged system immersed in a jellium background which fills the unit cell and neutralizes the charge to keep the net charge to be zero [37].
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The evolutions of lattice constants and W-O-W angles as a function of ratio of electron/hole are shown in Fig. 2. As can be seen from Fig. 2 (a), the changes of the lattice constants as a function of electron doping show a similar behavior as those from the Re doping. Values of a
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and b increase whereas that of c decreases until electron doping level reaches 0.375 e/WO3. All the W-O-W angles along three directions are increased to 180° with the increase of electron
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dopants up to 0.50 e/WO3 as shown in Fig. 2(b). The transformation from the monoclinic WO3 to cubic phase occurs with electron or Re doping. With the hole doping (or removing electron), the W-O-W angles along a and b directions show insignificant changes, whereas that along c direction increases but does not reach 180°.
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The elastic constants of solids provide the information of the stability and stiffness of materials and give information of lattice deformation under the external force applied to the crystals. We calculated the elastic constants of cubic W1-xRexO3 with 0.375≤x≤0.875 using the
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DFT method based on analysis of the total energy of properly strained states of the material [38]. The calculated elastic constants are listed in table 2. The traditional mechanical stability
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conditions on the elastic constants in cubic crystals are known to be C11-C12>0, C44>0, C11+2C12>0, and our results for the elastic constants listed in the table 2 obey these stability conditions, which indicates that the cubic structure of W1-xRexO3 is mechanically stable. The elastic constants such as bulk modulus and shear modulus of polycrystalline materials with isotropic microstructure (i.e. randomly oriented monocrystals) can be estimated from the elastic constants of monocrystals using the Voigt [39] or Reuss [40] approximation.
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According to the Voigt approximation [39], the bulk modulus B and shear modulus G can be calculated by equations (1) and (2):
C11 + 2C12 3
G=
3C44 + C11 − C12 5
(1)
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B=
(2)
equations [41]:
9 BG 3B + G
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E=
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The Yong’s modulus E, and the Poisson’s ratio v can be calculated using the following
1 E v = 1 − 2 3B
(3)
(4)
The calculated bulk modulus B, shear modulus G, Yong’s modulus E, and Poisson’s ratio v for
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the cubic W1-xRexO3 with 0.375≤x≤0.875 are listed in table 2. All the elastic characteristics of W1-xRexO3 under consideration decrease with the increase of the content of Re in the W1-xRexO3. The PDOS values of the WO3 doped with Re and electron along with their atomistic
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configurations are shown in Fig. 3 (a) and (b), respectively. The valence band maximum is set to be 0. It can be seen from Fig. 3 (a), multiple peaks appear within the bandgap after Re-doping,
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and the Fermi energy level (EF) shifts to higher energy levels with increasing the Re content. The semiconducting WO3 changes into metallic materials with increasing Re content. The electron doping does not affect the structures of the PDOS of the WO3 except that the EF enters into the conduction band above the band gap with increasing the electron concentration, which is similar to the rigid-band model as observed in WO3 upon different sodium intercalation [42]. The doped electrons fill the lower unoccupied energy levels of conduction band, so the WO3 also changes
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from semiconducting to metallic materials. The atomic configurations show that the distortion of the WO6 octahedra becomes less significant with electron or Re doping. W(Re)-O-W(Re) like chains easily form thus resulting in the formation of a cubic cell.
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The PDOS values of the WO3 doped with Nb and holes along with their atomistic configurations are shown in Fig. 4 (a) and (b), respectively. It can be seen the valence band comes from O 2p states near the band gap, whereas Nb 4d and W 5d states are dominant mostly
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in the lower conduction region. Large distortion of the WO6 octahedra with increasing Nb and hole contents can be clearly seen from the evolution of atomic configurations. The DOSs of
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W0.75Re0.25O3 and W0.75Nb0.25O3 calculated with more refined 15×15×15 k-point sampling are shown in Fig. 3 (a) and Fig. 4 (a), which are overlapped with the one calculated with a 4×4×4 kpoint sampling, indicating the 4×4×4 k-point sampling can guarantee the convergence of the simulation results.
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The monoclinic WO3 is a non-magnetic semiconductor, as seen from Fig. 1 (c). The Redoped WO3 shows a metallic character as seen from Fig. 3 (a). The system is spin-polarized by Nb doping, as can be seen from Fig. 4 (a). The magnetic moments are 0.5, 2, 3, 4, 5, 6, 7 µ B/unit
xNbxO3
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cell for W1-xNbxO3 with x=0.125, 0.25, 0.375, 0.50, 0.625, 0.75, and 0.875, respectively. W1shows a magnetic half-metal (HM) characteristic, in which the peculiarities of its
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spectrum (HMs are metallic for one spin direction, while semiconducting for the other spin direction [43]) are due to spin polarization of O 2p orbitals. Mulliken analysis results of the occupancy of d and s bands of Re, Nb and W are shown in Fig. 4. The occupancies are 3.71 and 0.64 electrons for the d and s bands, respectively, in the undoped WO3. The occupancy of s band shows little dependence on the doping, whereas that of the d band increases for electron and Re doping, which increases ~0.37 electron with electron
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doping of 0.875 e/WO3, and increases ~1.0 electrons in W0.125Re0.875O3. The occupancy ratio decreases for hole or Nb doping. The off-centering of W ions from its octahedron is determined by the balance between electronic Coulomb interactions and additional bonding considerations
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which stabilize the non-center-symmetric structure [44]. The off-centering of W ions results in an additional hybridization that lowers the O 2p valence band compared with the centered structure, and raises the energy of the W 5d t2g conduction band [45]. The conduction band is
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vacant and the stabilization of the valence band favors the off-centering structure for the WO3 [45]. As the WO3 is doped with Re or electrons, the electron fills the W 5d, with the occupation
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of antibonding levels in the conduction band opposing the deformations, therefore, the W moves to its center-symmetric position, and the WO3 transforms into a more symmetric structure with increased electron or Re doping. As for the Nb and hole doping, the conduction band keeps
4. Conclusion
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vacant, and the non-center-symmetric structure is favored.
In conclusion, we studied the structural stability of monoclinic WO3 doped with Re, Nb,
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electron and hole by using the first principles simulation. Nb and hole doping induced a large distortion of WO3, whereas transformation from monoclinic to cubic structure was observed with
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Re or electron doping. RexW1-xO3 was transformed into cubic structure as x>0.375. The electron doping induced the transformation at the same concentration of Re doping. Mulliken analysis of the occupancy of d and s bands showed that the extra electron occupies the d band, which is the main reason for the crystal transformation. The calculated bulk modulus B, shear modulus G, Yong’s modulus E, and Poisson’s ratio v for the cubic W1-xRexO3 decrease with the increase of Re content in the range of 0.375≤x≤0.875.
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Acknowledgement: This work was financially supported by the National Natural Science Foundation of China (11474047). Funding support from the UoA and CAPEX from Northumbria University at
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Newcastle, and Royal academy of Engineering UK-Research Exchange with China and India is acknowledged. This work was carried out at National Supercomputer Center in Tianjin, and the
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calculations were performed on TianHe-1(A).
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[42] L. Kopp, B.N. Harmon, S.H. Liu, Band structure of cubic NaxWO3, Solid State Commun., [43] R.A. de Groot, F.M. Mueller, P.G.v. Engen, K.H.J. Buschow, New Class of Materials: HalfMetallic Ferromagnets, Phys. Rev. Lett., 50 (1983) 2024-2027.
6694-6709.
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[44] N.A. Hill, Why Are There so Few Magnetic Ferroelectrics?, J. Phys. Chem. B, 104 (2000)
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[45] F. Corà, M.G. Stachiotti, C.R.A. Catlow, C.O. Rodriguez, Transition Metal Oxide Chemistry: Electronic Structure Study of WO3, ReO3, and NaWO3, J. Phys. Chem. B, 101 (1997) 3945-3952.
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Table 1 Lattice sites for the cations in the WO3 doped with Re and Nb.
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z 0.714 0.286 0.786 0.214 0.214 0.786 0.286 0.714
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x 0.496 0.504 0.996 0.004 0.496 0.504 0.996 0.004
W1-xNbxO3 W1-xRexO3 0.25 0.375 0.50 0.625 0.75 0.25 0.375 0.50 0.625 0.75 W W W Re Re Nb W Nb Nb W W W W W Re W W W W Nb W W W Re Re W W W Nb Nb W Re Re W W Nb Nb Nb Nb W W Re Re Re Re W Nb Nb W Nb W Re Re Re Re W Nb W W Nb Re W W Re Re W W W Nb Nb Re W Re W W W W Nb Nb Nb
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# 1 2 3 4 5 6 7 8
Sites y 0.750 0.250 0.754 0.246 0.750 0.250 0.746 0.254
Table 2 Theoretical values of the elastic constants (GPa), bulk modulus B (GPa), shear modulus G (GPa), Yong’s modulus E (GPa), and Poisson’s ratio v for W1-xRexO3 with 0.375≤x≤0.875
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0.375 0.500 0.625 0.750 0.875 660 650 638 632 614 60 58 57 56 53 50 51 52 53 57 260 150 377 0.258
255 149 374 0.256
251 147 370 0.254
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C11 C12 C44 B G E v
15
248 147 368 0.253
240 146 365 0.247
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Figure captions: Figure 1 (a) Band structure of monoclinic WO3 with spin up. (b) The Brillouin zone of monoclinic WO3 in the reciprocal lattice. The selected k-points path (in red) and their
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coordinates to calculate the bands structure are shown. (c) Total and projected density of states of monoclinic WO3. The top of the valence band is taken as the zero of energy. The vertical dashed line indicates the Fermi energy level (EF). (d) The monoclinic structure of WO3. W and O atoms
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are represented by the blue gray and red balls, respectively. The positions of metal atoms are
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numbered in accordance with data of table 1.
Figure 2 (a) Lattice constants and (b) the average O-W-O angle as a function of dopant concentration of electron and Re doping. (c) Lattice constants and (d) the average O-W-O angle as a function of dopant concentration of hole and Nb doping.
Figure 3 Total and projected density of states of (a) W1-xRexO3 and (b) WO3 doped with electron
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along with atomistic configuration. The DOSs of W0.75Re0.25O3 calculated with more refined 15×15×15 k-point sampling was shown, which are overlapped with the one calculated with a
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4×4×4 k-point sampling.
Figure 4 Total and projected density of states of (a) W1-xNbxO3 and (b) WO3 doped with hole
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along with atomistic configuration. The DOSs of W0.75Nb0.25O3 calculated with more refined 15×15×15 k-point sampling was shown, which are overlapped with the one calculated with a 4×4×4 k-point sampling.
Figure 5 Occupancy per W atom of 5d and 6s orbitals as a function of electron and hole doping concentrations. Mean occupancy per cation of d and s bands was presented for W1-x(Re, Nb)xO3, such as the occupancy of d band was the average value of W 5d and Re 5d in W1-xRexO3.
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Solid state transformations induced by doping in WO3 were investigated. Mechanisms of structure transformation induced by doping were clarified. RexW1-xO3 has a cubic structure as x is larger than 0.375. Electron doping induces the monoclinic to cubic transformation.
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S0925-8388(16)30351-6
DOI:
10.1016/j.jallcom.2016.02.082
Reference:
JALCOM 36694
To appear in:
Journal of Alloys and Compounds
Received Date: 22 September 2015 Revised Date:
7 February 2016
Accepted Date: 9 February 2016
Please cite this article as: Z. Li, S. Wu, Z. Wang, Y.Q. Fu, Doping Induced Structural Transformation in Tungsten Trioxide, Journal of Alloys and Compounds (2016), doi: 10.1016/j.jallcom.2016.02.082. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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Doping Induced Structural Transformation in Tungsten
Zhijie Li,1 Shiyun Wu,2 Zhiguo Wang,1* Y.Q. Fu1,3*
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Trioxide
Corresponding author. E-mail: [email protected] (ZW); [email protected] (YF)
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*
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1 School of Physical Electronics,, University of Electronic Science and Technology of China, Chengdu, 610054, P.R. China 2 School of Physics and Mech-tronic Engineering, Sichuan University of Arts and Science, Dazhou 635000, P.R. China 3 Department of Physics and Electrical Engineering, Faculty of Engineering and Environment, University of Northumbria, Newcastle upon Tyne, NE1 8ST, UK
ABSTRACT
Effects of dopants on structural stability of monoclinic WO3 were studied using density
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functional theory. Transformation from monoclinic to cubic crystal structures was obtained by gradually increasing doping concentrations of both rhenium (Re) and electrons inside the monoclinic WO3, whereas a large distortion of WO6 octahedra was observed by gradually
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increasing doping concentrations of both niobium (Nb) and holes inside the monoclinic WO3. It was verified that RexW1-xO3 has a cubic structure if x is larger than 0.375, and the transformation
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from monoclinic to cubic structure is mainly dependent on the occupancy of the W 5d orbital. The elastic characteristics of the RexW1-xO3 decrease with the increase of the content of Re in the range of 0.375≤x≤0.875.
Keywords: Tungsten Trioxide; Phase transformation; Doping; Density functional theory
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1. Introduction Owing to its distinctive electronic and electrochromic properties, tungsten trioxide (WO3) shows promising applications in smart windows, gas sensors, solar cells and high-density optical data
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storage [1-4]. It is a complex material regarding to its crystal structure and thermal stability. The crystal structure of the WO3 is formed by WO6 octahedrons, each of which is part of a cornersharing network extending in three dimensions. The distortion of each octahedron results in
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monoclinic, triclinic, tetragonal, orthorhomic, cubic, and hexagonal structures [4]. Tailoring functionalities of the WO3 is important for its wide applications, and can be successfully
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achieved mainly in three different ways: [5] (1) by inserting mono- or divalent cations into the interstitial sites of the WO3; (2) by introducing O-vacancies; or (3) by using doping or atomic replacements in the WO3. Therefore, two types of doping strategies become possible, in either oxygen site or W site. Doping is believed as an effective and simple way to increase free carries
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and reduce potential and conduction band levels through introducing impurity elements. For example, inserting C or N into oxygen sites in the WO3 will decrease the band gap [6-9]. A set of metal dopants (such as Ti, Hf, Ta, V, Cu, etc.) for replacing tungsten in the WO3 were also
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examined experimentally and theoretically [10-15]. An interesting phenomenon is that the change of electronic properties induced by doping is
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often accompanied with evolution of crystal structure. Doping can stabilize metastable hightemperature phases at much lower temperatures. Yan et al. [16] found Nb doping (replacing W) in the WO3 results in the increase of the band gap and shift of absorption edge, and doping with 5 at% Nb ions induced phase transformation from monoclnic γ-WO3 to monoclinic ε-WO3. Regarding to this transformation, Bathe et al. [17] found cycle stability, charge storage capacity and reversibility of the WO3 films were improved upon doping with Nb ions, but coloration
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efficiency was decreased. Yan et al. [16] explained that this is mainly because W6+ (0.62 Å) has a smaller ionic radius than Nb5+ (0.64 Å), and Nb inclusion would lead to a longer bond length and a larger tilting angle. The reduction of W6+ to different fractions of W5+ with a larger radius
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leads to an expansion of cell volume. It is critical to understand the mechanisms of the structure transformation induced by doping, which could provide the opportunities to tailor the properties as required. Because Nb has one valence electron less than W, Nb doping may affect the
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oxidation states of the W, thus changing the crystal structure of the WO3.
In this work, we, for the first time, investigated the crystal structure of Nb and Re doped
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WO3 using a density functional theory (DFT), and found that the occupancy of the W 5d orbital plays an important role on the symmetry of WO3 crystal structure. These results are important for design of WO3 crystal structures with specifically required electronic properties.
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2. Simulation details
All the calculations were performed using the SIESTA code [18], which adopted a linear combination of numerical localized atomic orbital basis sets for the description of valence
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electrons [19]. Norm-conserving pseudopotentials [19] were used to describe electron-ion interaction, while the generalized gradient approximation using the Perdew-Burke-Ernzerhof
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(PBE) functional was used to describe the electron exchange-correlation. The valence electrons were taken to be 2s22p4, 6s25d4, 6s25d5 and 5s14d4 for elements of O, W, Re and Nb, respectively. The valence electron wave functions were expanded using a double-ζ basis set plus polarization functions. The distortion of each octahedron results in a monoclinic symmetry and the monoclinic unit cell is composed of eight formula units in each unit cell (8 W atoms and 24 oxygen atoms). The unit cell containing 32 atoms was used in the calculation with a 4×4×4
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Monkhorst-Pack [20] mesh for the k-point sampling. For all the simulation, the lattice parameters and atom positions were allowed to relax by using a conjugate gradient minimization until the Hellmann-Feynman force is less than 0.02 eV/Å. The lattice parameters of monoclinic WO3 at
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room temperature were constructed from the experiment [21] and then fully optimized. As the crystal structure was slightly distorted, the O-W-O angle was not 180° but varied between 163° and 177°. Lattice parameter, β, was increased from 90° in the cubic phase to 90.2° for the
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monoclinic phase. The calculated lattice parameters are: a=7.54 Å, b=7.56 Å, and c=7.81 Å, which agree well with other calculated values of a=7.50 Å, b=7.65 Å, and c=7.79 Å [22]. The
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discrepancy with the experimental data (a=7.33 Å, b=7.56 Å, and c=7.73 Å [23]) might be due to the over-estimation of the optimized values of lattice constants with respect to their actual quantities within the feature of GGA functional in PBE form [24]. The Mulliken analysis was performed to investigate the occupancy of the d and s band states of the cations [25]. Since there
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are 8 W atoms in the unit cell, we used W1-x(Re, Nb)xO3 with x=0.125, 0.25, 0.375, 0.50, 0.625, 0.75, and 0.875 to represent that 1, 2, 3, 4, 5, 6, and 7 out of the eight W atoms were replaced by (Re, Nb) atoms in the unit cell. There are many possible atomic configurations in the unit cell
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W1-x(Re, Nb)xO3 with x=0.25, 0.375, 0.50, 0.625, and 0.75, and most of key possible configurations were tested and the lattice sites for the lowest energy one are listed in table 1.
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This can also be seen from the Fig. 1 (d) where the corresponding positions of metal atoms are numbered.
3. Results and discussion
The monoclinic structure (with a space group of P21/n) of the WO3 is stable in the temperature range between 17 and 330 oC [26, 27]. The monoclinic WO3 can be considered as a
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deformed perovskite structure such as ABO3, where the A ions are missing and B ions are replaced by W. The site of A is suitable for intercalation of ions. In a monoclinic cell containing 8 W and 24 O atoms, one W atom is found to bond octahedrally to six surrounding O atoms,
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while an O atom is connected to two W atoms as illustrated in Fig. 1(d) [21]. The WO3 structure can also be considered as a structure of W-O-W like chains, where the chains are connected across the W atoms. The calculated W-O-W angles are different along a, b, and c directions,
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which are 163.12, 163.17 and 169.90°, respectively. The obtained band structures of the monoclinic WO3 with spin up is shown in Fig. 2(a). It is noted that there are no apparent
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differences between the band structures obtained for spin up and spin down of the monoclinic WO3. The selected k-points path to calculate the band structure is shown in Fig. 2(b). From Fig. 2 (a), we can see that the valence band maximum (VBM) state locates at the Г point. The valance band and conduction band are flat at Г→Z direction. The monoclinic WO3 has a direct band gap
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of 1.08 eV at the Г point as shown in Fig. 1 (a), an indirect band gap of 1.086 eV from Г to Z point. These values are less than the experimental direct band gap of 2.58 eV [28] and indirect band gap of 2.6 eV [29]. This under-estimation of band gap is a consequence of the adopted
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standard DFT used in our calculation. Calculations based on hybrid functional or GW methods can reproduce the band-gap of monoclinic WO3 [30, 31]. Spin-orbital coupling of 5d-atoms has
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an important effect on the band structure of materials [32, 33]. As we are mainly concerned with the phase transformation upon doping in the present work, we expected that this computational under-estimation of band gap and omission of the spin-orbital coupling would not significantly affect our conclusion. Projected density of states (PDOS) for the monoclinic WO3 as shown in Fig. 1 (c) confirms that the monoclinic WO3 shows a character of semiconductors. From the
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PDOS of W and O atoms, the VBM level is composed by the O 2p states, whereas CBM level is mainly composed of W 5d states. Evolutions of the lattice constants and W-O-W angles as a function of doping concentration
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are shown in Fig. 2. The lattice constants a, b and c are different in lengths with x<0.375 in the W1-xRexO3. Values of a and b are almost equivalent and increase with increasing the Re dopants, whereas value of c is decreased. As x was increased to 0.375, values of the lattice parameters a
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and b are elongated from 7.54 to 7.68 Å, while that of c is shortened from 7.81 to 7.68 Å. The W-O-W angles along a, b, and c directions are also increased to 180° with the x is increased to
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0.50. All the three lattice constants a, b and c continue to have the same effective length and the W-O-W angles are remained to be 180° with further increasing Re dopants. This means that the monoclinic WO3 transforms into a cubic phase with increasing Re doping. The results agree with the experimental observation of RezW1-zO3 which has a cubic structure as z>0.25 [34]. For the
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Nb doping, all the lattice constants of a, b and c increase with Nb dopant, and the W-O-W angles along a and b directions show insignificant changes, whereas the W-O-W angles along the c direction decrease when x<0.50 in W1-xNbxO3, which means that a large distortion of the WO6
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octahedra is obtained with increasing Nb dopants. It can be seen form Fig. 2 (c) that the lattice constants a, b and c increase linearly with increasing the Nb concentration, which obeys the
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Vegard’s law [35].
As Nb has one valence electron less than W, whereas Re has one valence electron more than W, we investigated the changes of atomic structure with electron/hole doping number between 1 and 7 in the WO3 unit cell, which corresponds to 0.125-0.875 e(h)/WO3. The electron and hole doping was performed by adding or removing electrons from the unit cell, and a compensating background was used to achieve the charge neutrality [36]. This is identical to what was obtained
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from a similar system, and is consisted of the original charged system immersed in a jellium background which fills the unit cell and neutralizes the charge to keep the net charge to be zero [37].
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The evolutions of lattice constants and W-O-W angles as a function of ratio of electron/hole are shown in Fig. 2. As can be seen from Fig. 2 (a), the changes of the lattice constants as a function of electron doping show a similar behavior as those from the Re doping. Values of a
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and b increase whereas that of c decreases until electron doping level reaches 0.375 e/WO3. All the W-O-W angles along three directions are increased to 180° with the increase of electron
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dopants up to 0.50 e/WO3 as shown in Fig. 2(b). The transformation from the monoclinic WO3 to cubic phase occurs with electron or Re doping. With the hole doping (or removing electron), the W-O-W angles along a and b directions show insignificant changes, whereas that along c direction increases but does not reach 180°.
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The elastic constants of solids provide the information of the stability and stiffness of materials and give information of lattice deformation under the external force applied to the crystals. We calculated the elastic constants of cubic W1-xRexO3 with 0.375≤x≤0.875 using the
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DFT method based on analysis of the total energy of properly strained states of the material [38]. The calculated elastic constants are listed in table 2. The traditional mechanical stability
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conditions on the elastic constants in cubic crystals are known to be C11-C12>0, C44>0, C11+2C12>0, and our results for the elastic constants listed in the table 2 obey these stability conditions, which indicates that the cubic structure of W1-xRexO3 is mechanically stable. The elastic constants such as bulk modulus and shear modulus of polycrystalline materials with isotropic microstructure (i.e. randomly oriented monocrystals) can be estimated from the elastic constants of monocrystals using the Voigt [39] or Reuss [40] approximation.
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According to the Voigt approximation [39], the bulk modulus B and shear modulus G can be calculated by equations (1) and (2):
C11 + 2C12 3
G=
3C44 + C11 − C12 5
(1)
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B=
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equations [41]:
9 BG 3B + G
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E=
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The Yong’s modulus E, and the Poisson’s ratio v can be calculated using the following
1 E v = 1 − 2 3B
(3)
(4)
The calculated bulk modulus B, shear modulus G, Yong’s modulus E, and Poisson’s ratio v for
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the cubic W1-xRexO3 with 0.375≤x≤0.875 are listed in table 2. All the elastic characteristics of W1-xRexO3 under consideration decrease with the increase of the content of Re in the W1-xRexO3. The PDOS values of the WO3 doped with Re and electron along with their atomistic
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configurations are shown in Fig. 3 (a) and (b), respectively. The valence band maximum is set to be 0. It can be seen from Fig. 3 (a), multiple peaks appear within the bandgap after Re-doping,
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and the Fermi energy level (EF) shifts to higher energy levels with increasing the Re content. The semiconducting WO3 changes into metallic materials with increasing Re content. The electron doping does not affect the structures of the PDOS of the WO3 except that the EF enters into the conduction band above the band gap with increasing the electron concentration, which is similar to the rigid-band model as observed in WO3 upon different sodium intercalation [42]. The doped electrons fill the lower unoccupied energy levels of conduction band, so the WO3 also changes
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from semiconducting to metallic materials. The atomic configurations show that the distortion of the WO6 octahedra becomes less significant with electron or Re doping. W(Re)-O-W(Re) like chains easily form thus resulting in the formation of a cubic cell.
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The PDOS values of the WO3 doped with Nb and holes along with their atomistic configurations are shown in Fig. 4 (a) and (b), respectively. It can be seen the valence band comes from O 2p states near the band gap, whereas Nb 4d and W 5d states are dominant mostly
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in the lower conduction region. Large distortion of the WO6 octahedra with increasing Nb and hole contents can be clearly seen from the evolution of atomic configurations. The DOSs of
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W0.75Re0.25O3 and W0.75Nb0.25O3 calculated with more refined 15×15×15 k-point sampling are shown in Fig. 3 (a) and Fig. 4 (a), which are overlapped with the one calculated with a 4×4×4 kpoint sampling, indicating the 4×4×4 k-point sampling can guarantee the convergence of the simulation results.
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The monoclinic WO3 is a non-magnetic semiconductor, as seen from Fig. 1 (c). The Redoped WO3 shows a metallic character as seen from Fig. 3 (a). The system is spin-polarized by Nb doping, as can be seen from Fig. 4 (a). The magnetic moments are 0.5, 2, 3, 4, 5, 6, 7 µ B/unit
xNbxO3
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cell for W1-xNbxO3 with x=0.125, 0.25, 0.375, 0.50, 0.625, 0.75, and 0.875, respectively. W1shows a magnetic half-metal (HM) characteristic, in which the peculiarities of its
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spectrum (HMs are metallic for one spin direction, while semiconducting for the other spin direction [43]) are due to spin polarization of O 2p orbitals. Mulliken analysis results of the occupancy of d and s bands of Re, Nb and W are shown in Fig. 4. The occupancies are 3.71 and 0.64 electrons for the d and s bands, respectively, in the undoped WO3. The occupancy of s band shows little dependence on the doping, whereas that of the d band increases for electron and Re doping, which increases ~0.37 electron with electron
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doping of 0.875 e/WO3, and increases ~1.0 electrons in W0.125Re0.875O3. The occupancy ratio decreases for hole or Nb doping. The off-centering of W ions from its octahedron is determined by the balance between electronic Coulomb interactions and additional bonding considerations
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which stabilize the non-center-symmetric structure [44]. The off-centering of W ions results in an additional hybridization that lowers the O 2p valence band compared with the centered structure, and raises the energy of the W 5d t2g conduction band [45]. The conduction band is
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vacant and the stabilization of the valence band favors the off-centering structure for the WO3 [45]. As the WO3 is doped with Re or electrons, the electron fills the W 5d, with the occupation
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of antibonding levels in the conduction band opposing the deformations, therefore, the W moves to its center-symmetric position, and the WO3 transforms into a more symmetric structure with increased electron or Re doping. As for the Nb and hole doping, the conduction band keeps
4. Conclusion
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vacant, and the non-center-symmetric structure is favored.
In conclusion, we studied the structural stability of monoclinic WO3 doped with Re, Nb,
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electron and hole by using the first principles simulation. Nb and hole doping induced a large distortion of WO3, whereas transformation from monoclinic to cubic structure was observed with
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Re or electron doping. RexW1-xO3 was transformed into cubic structure as x>0.375. The electron doping induced the transformation at the same concentration of Re doping. Mulliken analysis of the occupancy of d and s bands showed that the extra electron occupies the d band, which is the main reason for the crystal transformation. The calculated bulk modulus B, shear modulus G, Yong’s modulus E, and Poisson’s ratio v for the cubic W1-xRexO3 decrease with the increase of Re content in the range of 0.375≤x≤0.875.
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Acknowledgement: This work was financially supported by the National Natural Science Foundation of China (11474047). Funding support from the UoA and CAPEX from Northumbria University at
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Newcastle, and Royal academy of Engineering UK-Research Exchange with China and India is acknowledged. This work was carried out at National Supercomputer Center in Tianjin, and the
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calculations were performed on TianHe-1(A).
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Table 1 Lattice sites for the cations in the WO3 doped with Re and Nb.
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z 0.714 0.286 0.786 0.214 0.214 0.786 0.286 0.714
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x 0.496 0.504 0.996 0.004 0.496 0.504 0.996 0.004
W1-xNbxO3 W1-xRexO3 0.25 0.375 0.50 0.625 0.75 0.25 0.375 0.50 0.625 0.75 W W W Re Re Nb W Nb Nb W W W W W Re W W W W Nb W W W Re Re W W W Nb Nb W Re Re W W Nb Nb Nb Nb W W Re Re Re Re W Nb Nb W Nb W Re Re Re Re W Nb W W Nb Re W W Re Re W W W Nb Nb Re W Re W W W W Nb Nb Nb
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Sites y 0.750 0.250 0.754 0.246 0.750 0.250 0.746 0.254
Table 2 Theoretical values of the elastic constants (GPa), bulk modulus B (GPa), shear modulus G (GPa), Yong’s modulus E (GPa), and Poisson’s ratio v for W1-xRexO3 with 0.375≤x≤0.875
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0.375 0.500 0.625 0.750 0.875 660 650 638 632 614 60 58 57 56 53 50 51 52 53 57 260 150 377 0.258
255 149 374 0.256
251 147 370 0.254
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C11 C12 C44 B G E v
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248 147 368 0.253
240 146 365 0.247
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Figure captions: Figure 1 (a) Band structure of monoclinic WO3 with spin up. (b) The Brillouin zone of monoclinic WO3 in the reciprocal lattice. The selected k-points path (in red) and their
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coordinates to calculate the bands structure are shown. (c) Total and projected density of states of monoclinic WO3. The top of the valence band is taken as the zero of energy. The vertical dashed line indicates the Fermi energy level (EF). (d) The monoclinic structure of WO3. W and O atoms
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are represented by the blue gray and red balls, respectively. The positions of metal atoms are
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numbered in accordance with data of table 1.
Figure 2 (a) Lattice constants and (b) the average O-W-O angle as a function of dopant concentration of electron and Re doping. (c) Lattice constants and (d) the average O-W-O angle as a function of dopant concentration of hole and Nb doping.
Figure 3 Total and projected density of states of (a) W1-xRexO3 and (b) WO3 doped with electron
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along with atomistic configuration. The DOSs of W0.75Re0.25O3 calculated with more refined 15×15×15 k-point sampling was shown, which are overlapped with the one calculated with a
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Figure 4 Total and projected density of states of (a) W1-xNbxO3 and (b) WO3 doped with hole
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along with atomistic configuration. The DOSs of W0.75Nb0.25O3 calculated with more refined 15×15×15 k-point sampling was shown, which are overlapped with the one calculated with a 4×4×4 k-point sampling.
Figure 5 Occupancy per W atom of 5d and 6s orbitals as a function of electron and hole doping concentrations. Mean occupancy per cation of d and s bands was presented for W1-x(Re, Nb)xO3, such as the occupancy of d band was the average value of W 5d and Re 5d in W1-xRexO3.
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Solid state transformations induced by doping in WO3 were investigated. Mechanisms of structure transformation induced by doping were clarified. RexW1-xO3 has a cubic structure as x is larger than 0.375. Electron doping induces the monoclinic to cubic transformation.
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