- Email: [email protected]
Theoretical studies on electronic structure and optical properties of Bi2WO6
Optik 158 (2018) 962–969
Contents lists available at ScienceDirect
Optik journal homepage: www.elsevier.de/ijleo
Original research article
Theoretical studies on electronic structure and optical properties of Bi2 WO6 Xing Liu, Hui-Qing Fan ∗ State Key Laboratory of Solidification Processing, School of Materials Science and Engineering, Northwestern Polytechnical University, Xi’an 710072, PR China
a r t i c l e
i n f o
Article history: Received 23 November 2017 Accepted 23 December 2017 Keywords: First-principles Bi2 WO6 Electronic structure Optical properties
a b s t r a c t Electronic structure, density of states and optical properties of Bi2 WO6 are investigated using the plane waves ultrasoft pseudopotential method based on the density functional theory (DFT). The Bi2 WO6 was indirect band-gap semiconductors materials, because the top of the valence band and the bottom of the conduction band are not at the same point, which of band gap was found to be 2.595 eV by the electronic structure calculation. Analysis of the density of states indicated that the valence band was consisted with Bi-6s and O2p states, and the conduction band was composed of W-5d and Bi-6p states. In order to understand optical properties of Bi2 WO6 , the dielectric function, conductivity, refractive index, absorption coefficients, reflectivity and loss function are studied and analyzed, which shown that the static dielectric constant is 2.83, the refractivity index is 1.68. The results can offer a theoretical basis for the research and application in future. © 2017 Elsevier GmbH. All rights reserved.
1. Introduction Bi2 WO6 , because of the excellent physical and chemical properties, such as ferroelectricity, piezoelectricity, catalytic behavior, nonlinear dielectric susceptibility [1–4], has been widely applied in the related fields [5–8]. Recently, many experimental and theoretical methods study the performance of Bi2 WO6 . Zhai et al. [9] prepared flower-like Bi2 WO6 via a simple hydrothermal route using the non-ionic surfactant F127 (EO–PO–EO) as the morphology director and found that Bi2 WO6 exhibited improved photo-catalytic performances. Phu et al. [10] synthesized Bi2 WO6 nanoparticles by fast microwave-assisted method and achieved high photo-catalytic activity under visible-light-irradiation. Ma¸czka et al. [11] used hydrothermal crystallization method for preparing of nanosized Bi2 WO6 , Raman spectroscopy studies have also revealed that the modes are mainly the incident light and the scattered light polarization perpendicular to the layer intensity is reduced. But, up to date, the report about the band structure, electronic and optical properties of Bi2 WO6 by first-principles is still lacking. It is worth pointing out that although there are a lot of experimental methods can be used to study the electronic and optical properties of a material, but the experimental results still exist a lot of uncertainty. Theoretical calculation results can be as a basis for experiments and verification, from the microscopic interpretation of the principle of macroscopic phenomena. The research and application of Bi2 WO6 have very important significance. In this paper, using the first principle to carry out theoretical calculation of Bi2 WO6 , optimization of geometric structure, and the electronic structure and optical
∗ Corresponding author. E-mail addresses: xingliu [email protected] (X. Liu), [email protected] (H.-Q. Fan). https://doi.org/10.1016/j.ijleo.2017.12.124 0030-4026/© 2017 Elsevier GmbH. All rights reserved.
X. Liu, H.-Q. Fan / Optik 158 (2018) 962–969
963
properties are calculated according to the optimized structure. The relation between the microscopic electron migration and the macroscopic optical properties of the crystal are analyzed. 2. Computational details In this work, we used the generalized gradient approximation (GGA) [12] in the Perdew–Burke–Eruzerh [13] to calculate the band structure and optical properties of Bi2 WO6 , and the theoretical mechanism are discussed. The calculations have been performed by using Cambridge Sequential Total Energy Package (CASTEP) code [14,15]. Using the plane wave pseuodopotential method, the ion potential is replaced and electron wave function is carried out with the plane wave basis set. We use the GGA to correct exchange interaction between the electrons and the correlation potential. In the DFT, the Schrodinger equation of the single electron motion can be expressed as an atomic unit:
2 Zq + − − r − Rq 2 q
(r) =
2 ni i (r)
(r) dr + V (r) i (r) = εi i (r) |r − r |
(1)
(2)
i
where Zq is the nuclear charge, r is the position vector of the nuclear motion, Rq is the distance between two cores, (r) indicates the electron density, V(r) indicates the external potential field, i (r) is single electron wave function, εi is the energy of a single electron, ni indicates the number of electrons occupied by the intrinsic state. The first term is effective electron kinetic energy in the system of Eq. (1). The second represents the attractive Coulomb potential of the atoms in the system, which is expressed by the norm—conserving pseudopotential. The term is electron Coulomb potential. The fourth represents the exchange correlation energy, the concrete form is expressed by the LDA or the GGA. The electron wave function is expanded in the form of plane wave, the cut-off energy is 380 eV, and the integral point in the inverted space is divided by Monkhorst–Pack k-points 5 × 7× 4 [16]. The ions–electrons interaction was modeled by Vanderbilt-type ultrasoft pseuodopotential [17]. The valence electrons configuration for the O, Bi, and W is 2s2 2p4 , 6s2 6p3 , and 5d4 6s2 , respectively. In order to make stable configurations of the models, all the structures were geometrically optimized using BFGS [18]. The models were converged by setting the value of displacement equal to 5 × 10−5 nm and the total energy difference become equal to 5 × 10−6 eV/atom. To describe the electronic structures accurately, we used the DFT + Ud + Up method. Ma et al. [19] suggested that the Up , O value of 7 eV is suitable for oxide materials in first principles calculations. 3. Results and discussion 3.1. Structural properties In order to ensure the accuracy of the parameters used in the calculation, the structure of Bi2 WO6 is optimized to obtain the lattice constant of the ground state, the lattice parameters as follows: a = b = 8.530 Å, c = 8.475 Å. It shows that our calculation model and parameters are reasonable, which have only a 1% underestimation of the equilibrium volume compared with the experimental value [20]. But the length is a little longer, and the angle of the lattice vector is smaller than the experimental values, respectively. It means that there is a more serious inner structural distortion in geometry optimization of our computation. Based on the optimized Bi2 WO6 containing 36 atoms is constructed for further calculations. The Bi2 WO6 is composed of layers structure of alternating (Bi2 O2 )2+ and WO4 2− layers, which of O and W form octahedron [WO6 ] of the common edge from Fig.1 3.2. Electronic properties The computed band structure of Bi2 WO6 (seen Fig. 2) is consistent with the experimental results [21,22]. It can be seen from the comparison that the theoretical calculation and the experimental value can match well, indicating that the character of band structure and the trend of energy gap are reasonable and reliable. The valence band top and conduction band bottom are Y and B, respectively, so it can be inferred that Bi2 WO6 is indirect band-gap semiconductors. In order to further explore the modifications in the band structure and the optical properties, the total and partial densities of states (TDOS and PDOS) of Bi2 WO6 are calculated. For Bi2 WO6 , total density of states is mainly composed of four parts (W-5d, W-6s, O-2s and O-2p), combining with the total (a) and partial densities of states (seen Fig. 3), the top of valence band is mainly composed of O-2p and a small amount of Bi-s electronic component, the bottom of the conduction band is mainly composed of Bi-s and a small amount of O-2p orbital electron, O-2s is an inner electron, which has a strong locality, and it has no obvious interaction with other internal energy levels. Shown in Fig. 3(a–d), the valence band of Bi2 WO6 is composed of O-2p, Bi-6s, Bi-6p, and W-5d, whose conduction band is composed of W-5d, Bi-6p and a small amount of O-2p. This reveals that the hybridized energy level of O-2p and Bi-6s in the valence band is likely to result in the response of Bi2 WO6 to visible light in the W-5d energy level of the conduction band. In addition, O-2p and Bi-6s hybrid also make valence band
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Fig. 1. Crystal structure of Bi2 WO6 .
Fig. 2. The calculated energy band structure of Bi2 WO6 . The Fermi energy is set to zero and indicated by horizontal red dashed line.
more discrete, which will be beneficial to the migration of the photomous hole in the valence band, so that it has a good photocatalytic efficiency, which is consistent with the research results of Fu et al. [23]. 3.3. Optical properties The dielectric function dominates the propagation of electromagnetic waves in the medium and the interaction between electromagnetic waves and electrons. It connects the electronic structure of the solid to the physical process of the transition, and other optical spectrum such as absorption spectrum, refractive index, reflectance spectrum and conductivity can be obtained through it. Dielectric function imaginary part ε2 () mainly shows that electrons transition from occupied state to unoccupied state, calculated the energy state structure of Bi2 WO6 , according to the definition of transition probability can be directly deduced dielectric function imaginary part ε2 (). In linear response range, solid macro optical response function can usually be made light of the complex dielectric constant ε() = ε1 () + ε2 () or complex refractive index N() = n() + ik() to describe:ε1 = n2 − k2 and ε2 = 2nk, where n is the refractive index, k is extinction coefficient. According to the Kramers-Kronig dispersion relation [24] and direct transition probability, the imaginary part and the real part, absorption coefficient and reflection coefficient of the crystal dielectric function can be deduced, and the results are as follows: 82 e2 ε1 = 1 + m2 v,c
ε2 =
42 m2 ω2 v,c
2
2 e · Mcv (K) 3 d k 2 [Ec (K) − Ev (K)] [Ec (K) − Ev (K)]2 − 2 ω2 BZ
d3 k BZ
3
2 2 e · Mcv (K) ı [Ec (K) − Ev (K) − ω] 2
= ε0 ωε2 − iε0 ω(ε1 − 1) = 1 − i2
(3)
(4) (5)
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Fig. 3. The calculated total (a) and partial densities of states (b, c and d) for Bi2 WO6 .
ε2 (ω)
L(ω) =
I(ω) =
(6)
ε21 (ω) + ε22 (ω) √
ε21 (ω) + ε22 (ω) − ε1 (ω)]
2[
ε (ω) + jε (ω) − 1 2 1 2 R(ω) = ε1 (ω) + jε2 (ω) + 1
(7)
(8)
ε21 (ω) + ε22 (ω) + ε1 (ω)
n(ω) =
2
k(ω) =
1 2
(9)
ε21 (ω) + ε22 (ω) − ε1 (ω) 2
Where c, v represents the CB and VB respectively, BZ is the first Brillouin zone, K is the reciprocal lattice vector, for the Planck
2
constant. e · Mcv (K) for the momentum transition matrix element, ω as the angular frequency, the Ec (K) and Ev (K) are the intrinsic level of the conduction band and valence band, respectively. These relations reveal the luminescence mechanism of electronic transitions, which is the theoretical basis of the analysis of electronic structure and optical properties. In addition, other optical properties can be derived from the real ε1 (ω) and imaginary ε2 (ω). Such as energy-loss spectrum L(ω), absorption coefficient I(ω), optical reflectivity R(ω) and refractive index n(ω) can be shown in Eqs. (4)–(9). Fig. 4 shows the real and imaginary parts of the dielectric function, which can be obtained by Eqs. (3) and (4). It can be seen, when the photon energy is 0, the static dielectric constant of Bi2 WO6 is 2.83. As the energy of the photon increases, the real part of the dielectric function rises rapidly, reaching the maximum (5.14) at about 3.80 eV. Comparison of the band structure and density of states for Bi2 WO6 , there are three main band regions, the largest band appears near the Fermi surface, the band width is narrow, mainly composed of O-2p and Bi-6s orbitals, and the density is high, and the density is high, the transition between them will form the strongest absorption peak of ε2 curve. The second band appears which are composed of O-2s and W-5d orbitals, formed ε2 absorption two weak peaks at the 13.39 and 42.92 eV. The optical properties of the materials commonly used to describe the photoconductivity, photoconductivity and dielectric function, the Eqs. (3)–(5) can be seen, there is a consistent one-to-one match between the real part of photoconductivity and the imaginary part of the dielectric function. It is directly related to the electronic structure, characterization of the electrons transitions between the occupied and unoccupied state. Fig. 5 is the result of Bi2 WO6 photoconductive, the calculated 1 have 4 peaks, with the photon energy, increased from 0 eV, 1 began to increase and the formation of two strong
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Fig. 4. Calculated the dielectric function ε() of Bi2 WO6 .
Fig. 5. Calculated the conductivity of Bi2 WO6 .
Fig. 6. The optical properties for energy-loss function L(ω) of Bi2 WO6 .
peaks at 4.86 eV and 42.80 eV, then 1 rapidly decreased to a minimum in the 11.81 eV. Then with the increase of photon energy, 1 began to increase and the formation of two weak peak in 13.51 and 20.08 eV. In region of 14.94–17.37 eV, 22.31 and 38.43 eV, and more than 48.62 eV, the real part of the photoconductivity is almost zero, that almost no Bi2 WO6 on high frequency electromagnetic wave absorption (Fig. 5). Electronic energy loss is made after the outer electronic material absorption transition to higher orbit absorption, so in addition to variety identification materials, but also can analyze the material gap, bond strength and type, can be said to be a good analytical method, namely electron spectroscopy loss. It can be seen from Fig. 6 that there are four obvious peaks. The peaks are at 9.56, 13.60, 20.18 and 43.23 eV. The energy loss is near 11.2 eV, and the high energy region has a minimal loss. The peak of energy loss near 10 eV, which indicates that the loss energy range is very narrow, and it is very beneficial for the crystal to reduce energy loss and improve the crystal optical storage efficiency.
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Fig. 7. The optical properties for reflectivity R() of Bi2 WO6 .
Fig. 8. The optical properties for absorption coefficient I() of Bi2 WO6 .
Reflection spectrum is the reflection of electromagnetic radiation ability, varies with the reflection of electromagnetic wave wavelength characteristics, depending on the nature of the material, or the same properties of materials in the composition, surface structure, and the reflection spectral characteristics are also different, constitutes the difference of reflectance spectral curve. Bi2 WO6 reflection spectrum of the calculation results as shown in Fig. 7, starting from 0 eV, reflection coefficient increased with the increase of electron energy, in 5 eV and 10 eV form two strong absorption peak, then the reflection coefficient sharply reduced to zero. It then began to increase and formed three reflecting peaks at 142,142.5 eV. To emphasize the point that, for the semiconductor materials, when the incident light to the role of material surface, will have strong absorption of incident light intensity of the phenomenon, the reflection spectrum is a very strong absorption peak, and the reflection coefficient is zero (Fig. 7). The absorption coefficient of the material indicates the percentage of light intensity attenuation of the light wave in the medium. The absorption spectra of Bi2 WO6 are shown in Fig. 8. From 0 eV, the absorption coefficient increases with the increase of electron energy, and the two strongest absorption peaks are formed at 5.48 and 7.43 eV positions, and then decreases, and almost decreases to zero when the electron energy is 11.2 eV. Subsequently, the absorption peak was formed at 13.51, 20.09 and 42.97 eV. The absorption peak of 42.97 eV is formed by the transition between W-6p and Fermi. The two absorption peaks (13.51, 20.09) in the middle are the formation of O-2s → O-2p and Bi-6s → Bi-6p transitions, respectively. The corresponding relation between absorption coefficient and optical conductivity: a = 1 /ε0 cn It can be seen that the real part of the optical conductivity is proportional to the absorption coefficient, so their characteristic peak position is almost one-to-one. As we know, the refractive index and extinction coefficient are proportional to the real part and the imaginary part of the dielectric constant, respectively. The refractive index n() and extinction coefficient k() as shown in Fig. 9. By comparison, n(ω) spectral characteristics and the real part ε1 (ω) of dielectric function (Fig. 4) are very similar, this means that the static dielectric constant ε1 (0) corresponding to the static refraction index n(0), it is found that the static refractive index, n(0) is 1.68, with the increase of the energy becomes smaller, and then began to increase in the position until the formation of a peak, and then sharply decreased, the maximum of that is about 2.33 at 4.01 eV and the minimum of that is about 0.34 at
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Fig. 9. The optical properties for refractive index n() and extinction coefficient k() of Bi2 WO6 .
that there are four obvious
9.14 eV in the 0–10 eV region. The extinction coefficient increases from 0eV to 7.5 eV, the first high peak, and then decreased with the increase of energy until 10 eV began to increase, and the three peaks are formed in 12.5 eV, 20 and 32.5 eV. 4. Conclusions In summary, using CASTEP to optimize the structure of Bi2 WO6 , the results of optimization are very close to the experimental results, thus the theoretical calculation results are accuracy, the model and calculation method are reasonable and reliable. Firstly, the electronic structure and optical properties of Bi2 WO6 are calculated and analyzed on the basis of optimized structure. Through the analysis of band structure and density of states, Bi2 WO6 is indirect band-gap materials (Eg = 2.595 eV), the valence and conduction band mainly contributed by O-2p and Bi-6s states, the formation of covalent bonds. What’s more, by calculating the dielectric function, the energy loss function, the reflection spectrum and the absorption spectrum, we obtained the static dielectric constants is 2.83, the refractivity index is 1.68, which of the peaks are obviously and related to the transition of the electron. The calculation results of optical properties show that the Bi2 WO6 has obvious anisotropy, and the visible light has good transmittance, so it can offer a theoretical basis for the research and catalytic application of Bi2 WO6 in future. Funding This work was supported by the National Natural Science Foundation (51672220), and 111 Program (B08040) of MOE, the National Defense Science Foundation (32102060303), the Xi’an Science and Technology Foundation, the Shaanxi Provincial Science Foundation and NPU Gaofeng Project (17GH020824) of China. References [1] R.L. Withers, J.G. Thompson, A.D. Rae, The crystal chemistry underlying ferroelectricity in Bi4 Ti3 O12 , Bi3 TiNbO9 , and Bi2 WO6 , J. Solid State Chem. 94 (2) (1991) 404–417. [2] S. Phapale, D. Das, R. Mishra, Standard molar enthalpy of formation of Bi2 WO6 (s) and Bi2 W2 O9 (s) compounds, J. Chem. Thermodyn. 63 (4) (2013) 74–77. [3] P. Zhang, J. Zhang, A.J. Xie, et al., Hierarchical flower-like Bi2 WO6 hollow microspheres: facile synthesis and excellent catalytic performance, RSC Adv. 5 (2015) 23080–23085. [4] H. Djani, P. Hermet, P. Ghosez, First principle characterization of the P21 ab ferroelectric phase of Aurivillius Bi2 WO6 , J. Phys. Chem. C 118 (25) (2014) 13514. [5] L. Zhang, W. Wang, M. Shang, et al., Bi2 WO6 @carbon/Fe3 O4 microspheres: preparation, growth mechanism and application in water treatment, J. Hazard. Mater. 172 (1193) (2009) 172. [6] Y.T. Bai, X.M. Gao, Hydrothermal synthesis of Bi2 WO6 and its application in the photocatalytic oxidative of phenol, J. Yanan Univ. (2014). [7] Y. Wu, X. Gao, F. Fu, Cu – Bi2 WO6 catalyst synthesized by hydrothermal method and its application in photo catalytic oxidation desulfurization, Chem. Eng. Oil Gas 41 (4) (2012) 366–378. [8] H. Takeda, T. Nishida, S. Okamura, et al., Crystal growth of bismuth tungstate Bi2 WO6 by slow cooling method using borate fluxes, J. Eur. Ceram. Soc. 25 (12) (2005) 2731–2734. [9] J. Zhai, H. Yu, H. Li, et al., Visible-light photocatalytic activity of graphene oxide-wrapped Bi2 WO6 hierarchical microspheres, Appl. Surf. Sci. 344 (2015) 101–106. [10] N.D. Phu, L.H. Hoang, X.B. Chen, et al., Study of photocatalytic activities of Bi2 WO6 nanoparticles synthesized by fast microwave-assisted method, J. Alloys Compd. 647 (2015) 123–128. [11] M. Ma¸czka, L. Macalik, K. Hermanowicz, et al., Phonon properties of nanosized bismuth layered ferroelectric material—Bi2 WO6 , J. Raman Spectrosc. 41 (9) (2009) 1059–1066. [12] Y.M. Juan, E. Kaxiras, R.G. Gordon, Use of the generalized gradient approximation in pseudopotential calculations of solids, Phys. Rev. B 51 (1995) 9521–9525. [13] M. Ernzerhof, G.E. Scuseria, Assessment of the Perdew–Burke–Ernzerhof exchange-correlation functional, J. Chem. Phys. 110 (11) (1999) 5029–5036. [14] S.J. Clark, M.D. Segall, C.J. Pickard, et al., First principles methods using CASTEP, Z. Kristallogr. Cryst. Mater. 220 (5/6/2005) (2009) 567–570. [15] Y. Imai, M. Mukaida, T. Tsunoda, Calculation of electronic energy and density of state of iron-disilicides using a total-energy pseudopotential method, CASTEP, Thin Solid Films 381 (2) (2001) 176–182.
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D.J. Chadi, Special points for Brillouin-zone integrations, Phys. Rev. B Condens. Matter 13 (12) (1976) 5188–5192. D. Vanderbilt, Soft self-consistent pseudopotentials in a generalized eigenvalue formalism, Phys. Rev. B Condens. Matter 41 (11) (1990) 7892–7895. B.G. Pfrommer, M. Cote, S.G. Louie, M.L. Cohen, Relaxation of crystals with the quasi-Newton method, J. Comput. Phys. 131 (1997) 233–240. X. Ma, B. Lu, D. Li, R. Shi, C. Pan, Y. Zhu, J. Phys. Chem. C 115 (2011) 4680–4687. J. Hill, K.S. Choi, Synthesis and characterization of high surface area CuWO4 and Bi2WO6 electrodes for use as photoanodes for solar water oxidation, J. Mater. Chem. A 1 (16) (2013) 5006–5014. T. Juestel, C.R. Ronda, Tungstate-based scintillating materials for detecting radiation: US, US20110147595 A1[P]. 2014. Y. Zhou, Z. Tian, Z. Zhao, et al., High-yield synthesis of ultrathin and uniform Bi2WO6 square nanoplates benefitting from photocatalytic reduction of CO2 into renewable hydrocarbon fuel under visible light, ACS Appl. Mater. Interfaces 3 (9) (2011) 3594–3601. H. Fu, C. Pan, W. Yao, et al., Visible-light-induced degradation of rhodamine B by nanosized Bi2 WO6 , J. Phys. Chem. B 109 (47) (2005) 22432. D. Brunner, H. Angerer, E. Bustarret, et al., Optical constants of epitaxial AlGaN films and their temperature dependence, J. Appl. Phys. 82 (10) (1997) 5090–5096.
Contents lists available at ScienceDirect
Optik journal homepage: www.elsevier.de/ijleo
Original research article
Theoretical studies on electronic structure and optical properties of Bi2 WO6 Xing Liu, Hui-Qing Fan ∗ State Key Laboratory of Solidification Processing, School of Materials Science and Engineering, Northwestern Polytechnical University, Xi’an 710072, PR China
a r t i c l e
i n f o
Article history: Received 23 November 2017 Accepted 23 December 2017 Keywords: First-principles Bi2 WO6 Electronic structure Optical properties
a b s t r a c t Electronic structure, density of states and optical properties of Bi2 WO6 are investigated using the plane waves ultrasoft pseudopotential method based on the density functional theory (DFT). The Bi2 WO6 was indirect band-gap semiconductors materials, because the top of the valence band and the bottom of the conduction band are not at the same point, which of band gap was found to be 2.595 eV by the electronic structure calculation. Analysis of the density of states indicated that the valence band was consisted with Bi-6s and O2p states, and the conduction band was composed of W-5d and Bi-6p states. In order to understand optical properties of Bi2 WO6 , the dielectric function, conductivity, refractive index, absorption coefficients, reflectivity and loss function are studied and analyzed, which shown that the static dielectric constant is 2.83, the refractivity index is 1.68. The results can offer a theoretical basis for the research and application in future. © 2017 Elsevier GmbH. All rights reserved.
1. Introduction Bi2 WO6 , because of the excellent physical and chemical properties, such as ferroelectricity, piezoelectricity, catalytic behavior, nonlinear dielectric susceptibility [1–4], has been widely applied in the related fields [5–8]. Recently, many experimental and theoretical methods study the performance of Bi2 WO6 . Zhai et al. [9] prepared flower-like Bi2 WO6 via a simple hydrothermal route using the non-ionic surfactant F127 (EO–PO–EO) as the morphology director and found that Bi2 WO6 exhibited improved photo-catalytic performances. Phu et al. [10] synthesized Bi2 WO6 nanoparticles by fast microwave-assisted method and achieved high photo-catalytic activity under visible-light-irradiation. Ma¸czka et al. [11] used hydrothermal crystallization method for preparing of nanosized Bi2 WO6 , Raman spectroscopy studies have also revealed that the modes are mainly the incident light and the scattered light polarization perpendicular to the layer intensity is reduced. But, up to date, the report about the band structure, electronic and optical properties of Bi2 WO6 by first-principles is still lacking. It is worth pointing out that although there are a lot of experimental methods can be used to study the electronic and optical properties of a material, but the experimental results still exist a lot of uncertainty. Theoretical calculation results can be as a basis for experiments and verification, from the microscopic interpretation of the principle of macroscopic phenomena. The research and application of Bi2 WO6 have very important significance. In this paper, using the first principle to carry out theoretical calculation of Bi2 WO6 , optimization of geometric structure, and the electronic structure and optical
∗ Corresponding author. E-mail addresses: xingliu [email protected] (X. Liu), [email protected] (H.-Q. Fan). https://doi.org/10.1016/j.ijleo.2017.12.124 0030-4026/© 2017 Elsevier GmbH. All rights reserved.
X. Liu, H.-Q. Fan / Optik 158 (2018) 962–969
963
properties are calculated according to the optimized structure. The relation between the microscopic electron migration and the macroscopic optical properties of the crystal are analyzed. 2. Computational details In this work, we used the generalized gradient approximation (GGA) [12] in the Perdew–Burke–Eruzerh [13] to calculate the band structure and optical properties of Bi2 WO6 , and the theoretical mechanism are discussed. The calculations have been performed by using Cambridge Sequential Total Energy Package (CASTEP) code [14,15]. Using the plane wave pseuodopotential method, the ion potential is replaced and electron wave function is carried out with the plane wave basis set. We use the GGA to correct exchange interaction between the electrons and the correlation potential. In the DFT, the Schrodinger equation of the single electron motion can be expressed as an atomic unit:
2 Zq + − − r − Rq 2 q
(r) =
2 ni i (r)
(r) dr + V (r) i (r) = εi i (r) |r − r |
(1)
(2)
i
where Zq is the nuclear charge, r is the position vector of the nuclear motion, Rq is the distance between two cores, (r) indicates the electron density, V(r) indicates the external potential field, i (r) is single electron wave function, εi is the energy of a single electron, ni indicates the number of electrons occupied by the intrinsic state. The first term is effective electron kinetic energy in the system of Eq. (1). The second represents the attractive Coulomb potential of the atoms in the system, which is expressed by the norm—conserving pseudopotential. The term is electron Coulomb potential. The fourth represents the exchange correlation energy, the concrete form is expressed by the LDA or the GGA. The electron wave function is expanded in the form of plane wave, the cut-off energy is 380 eV, and the integral point in the inverted space is divided by Monkhorst–Pack k-points 5 × 7× 4 [16]. The ions–electrons interaction was modeled by Vanderbilt-type ultrasoft pseuodopotential [17]. The valence electrons configuration for the O, Bi, and W is 2s2 2p4 , 6s2 6p3 , and 5d4 6s2 , respectively. In order to make stable configurations of the models, all the structures were geometrically optimized using BFGS [18]. The models were converged by setting the value of displacement equal to 5 × 10−5 nm and the total energy difference become equal to 5 × 10−6 eV/atom. To describe the electronic structures accurately, we used the DFT + Ud + Up method. Ma et al. [19] suggested that the Up , O value of 7 eV is suitable for oxide materials in first principles calculations. 3. Results and discussion 3.1. Structural properties In order to ensure the accuracy of the parameters used in the calculation, the structure of Bi2 WO6 is optimized to obtain the lattice constant of the ground state, the lattice parameters as follows: a = b = 8.530 Å, c = 8.475 Å. It shows that our calculation model and parameters are reasonable, which have only a 1% underestimation of the equilibrium volume compared with the experimental value [20]. But the length is a little longer, and the angle of the lattice vector is smaller than the experimental values, respectively. It means that there is a more serious inner structural distortion in geometry optimization of our computation. Based on the optimized Bi2 WO6 containing 36 atoms is constructed for further calculations. The Bi2 WO6 is composed of layers structure of alternating (Bi2 O2 )2+ and WO4 2− layers, which of O and W form octahedron [WO6 ] of the common edge from Fig.1 3.2. Electronic properties The computed band structure of Bi2 WO6 (seen Fig. 2) is consistent with the experimental results [21,22]. It can be seen from the comparison that the theoretical calculation and the experimental value can match well, indicating that the character of band structure and the trend of energy gap are reasonable and reliable. The valence band top and conduction band bottom are Y and B, respectively, so it can be inferred that Bi2 WO6 is indirect band-gap semiconductors. In order to further explore the modifications in the band structure and the optical properties, the total and partial densities of states (TDOS and PDOS) of Bi2 WO6 are calculated. For Bi2 WO6 , total density of states is mainly composed of four parts (W-5d, W-6s, O-2s and O-2p), combining with the total (a) and partial densities of states (seen Fig. 3), the top of valence band is mainly composed of O-2p and a small amount of Bi-s electronic component, the bottom of the conduction band is mainly composed of Bi-s and a small amount of O-2p orbital electron, O-2s is an inner electron, which has a strong locality, and it has no obvious interaction with other internal energy levels. Shown in Fig. 3(a–d), the valence band of Bi2 WO6 is composed of O-2p, Bi-6s, Bi-6p, and W-5d, whose conduction band is composed of W-5d, Bi-6p and a small amount of O-2p. This reveals that the hybridized energy level of O-2p and Bi-6s in the valence band is likely to result in the response of Bi2 WO6 to visible light in the W-5d energy level of the conduction band. In addition, O-2p and Bi-6s hybrid also make valence band
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Fig. 1. Crystal structure of Bi2 WO6 .
Fig. 2. The calculated energy band structure of Bi2 WO6 . The Fermi energy is set to zero and indicated by horizontal red dashed line.
more discrete, which will be beneficial to the migration of the photomous hole in the valence band, so that it has a good photocatalytic efficiency, which is consistent with the research results of Fu et al. [23]. 3.3. Optical properties The dielectric function dominates the propagation of electromagnetic waves in the medium and the interaction between electromagnetic waves and electrons. It connects the electronic structure of the solid to the physical process of the transition, and other optical spectrum such as absorption spectrum, refractive index, reflectance spectrum and conductivity can be obtained through it. Dielectric function imaginary part ε2 () mainly shows that electrons transition from occupied state to unoccupied state, calculated the energy state structure of Bi2 WO6 , according to the definition of transition probability can be directly deduced dielectric function imaginary part ε2 (). In linear response range, solid macro optical response function can usually be made light of the complex dielectric constant ε() = ε1 () + ε2 () or complex refractive index N() = n() + ik() to describe:ε1 = n2 − k2 and ε2 = 2nk, where n is the refractive index, k is extinction coefficient. According to the Kramers-Kronig dispersion relation [24] and direct transition probability, the imaginary part and the real part, absorption coefficient and reflection coefficient of the crystal dielectric function can be deduced, and the results are as follows: 82 e2 ε1 = 1 + m2 v,c
ε2 =
42 m2 ω2 v,c
2
2 e · Mcv (K) 3 d k 2 [Ec (K) − Ev (K)] [Ec (K) − Ev (K)]2 − 2 ω2 BZ
d3 k BZ
3
2 2 e · Mcv (K) ı [Ec (K) − Ev (K) − ω] 2
= ε0 ωε2 − iε0 ω(ε1 − 1) = 1 − i2
(3)
(4) (5)
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Fig. 3. The calculated total (a) and partial densities of states (b, c and d) for Bi2 WO6 .
ε2 (ω)
L(ω) =
I(ω) =
(6)
ε21 (ω) + ε22 (ω) √
ε21 (ω) + ε22 (ω) − ε1 (ω)]
2[
ε (ω) + jε (ω) − 1 2 1 2 R(ω) = ε1 (ω) + jε2 (ω) + 1
(7)
(8)
ε21 (ω) + ε22 (ω) + ε1 (ω)
n(ω) =
2
k(ω) =
1 2
(9)
ε21 (ω) + ε22 (ω) − ε1 (ω) 2
Where c, v represents the CB and VB respectively, BZ is the first Brillouin zone, K is the reciprocal lattice vector, for the Planck
2
constant. e · Mcv (K) for the momentum transition matrix element, ω as the angular frequency, the Ec (K) and Ev (K) are the intrinsic level of the conduction band and valence band, respectively. These relations reveal the luminescence mechanism of electronic transitions, which is the theoretical basis of the analysis of electronic structure and optical properties. In addition, other optical properties can be derived from the real ε1 (ω) and imaginary ε2 (ω). Such as energy-loss spectrum L(ω), absorption coefficient I(ω), optical reflectivity R(ω) and refractive index n(ω) can be shown in Eqs. (4)–(9). Fig. 4 shows the real and imaginary parts of the dielectric function, which can be obtained by Eqs. (3) and (4). It can be seen, when the photon energy is 0, the static dielectric constant of Bi2 WO6 is 2.83. As the energy of the photon increases, the real part of the dielectric function rises rapidly, reaching the maximum (5.14) at about 3.80 eV. Comparison of the band structure and density of states for Bi2 WO6 , there are three main band regions, the largest band appears near the Fermi surface, the band width is narrow, mainly composed of O-2p and Bi-6s orbitals, and the density is high, and the density is high, the transition between them will form the strongest absorption peak of ε2 curve. The second band appears which are composed of O-2s and W-5d orbitals, formed ε2 absorption two weak peaks at the 13.39 and 42.92 eV. The optical properties of the materials commonly used to describe the photoconductivity, photoconductivity and dielectric function, the Eqs. (3)–(5) can be seen, there is a consistent one-to-one match between the real part of photoconductivity and the imaginary part of the dielectric function. It is directly related to the electronic structure, characterization of the electrons transitions between the occupied and unoccupied state. Fig. 5 is the result of Bi2 WO6 photoconductive, the calculated 1 have 4 peaks, with the photon energy, increased from 0 eV, 1 began to increase and the formation of two strong
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Fig. 4. Calculated the dielectric function ε() of Bi2 WO6 .
Fig. 5. Calculated the conductivity of Bi2 WO6 .
Fig. 6. The optical properties for energy-loss function L(ω) of Bi2 WO6 .
peaks at 4.86 eV and 42.80 eV, then 1 rapidly decreased to a minimum in the 11.81 eV. Then with the increase of photon energy, 1 began to increase and the formation of two weak peak in 13.51 and 20.08 eV. In region of 14.94–17.37 eV, 22.31 and 38.43 eV, and more than 48.62 eV, the real part of the photoconductivity is almost zero, that almost no Bi2 WO6 on high frequency electromagnetic wave absorption (Fig. 5). Electronic energy loss is made after the outer electronic material absorption transition to higher orbit absorption, so in addition to variety identification materials, but also can analyze the material gap, bond strength and type, can be said to be a good analytical method, namely electron spectroscopy loss. It can be seen from Fig. 6 that there are four obvious peaks. The peaks are at 9.56, 13.60, 20.18 and 43.23 eV. The energy loss is near 11.2 eV, and the high energy region has a minimal loss. The peak of energy loss near 10 eV, which indicates that the loss energy range is very narrow, and it is very beneficial for the crystal to reduce energy loss and improve the crystal optical storage efficiency.
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Fig. 7. The optical properties for reflectivity R() of Bi2 WO6 .
Fig. 8. The optical properties for absorption coefficient I() of Bi2 WO6 .
Reflection spectrum is the reflection of electromagnetic radiation ability, varies with the reflection of electromagnetic wave wavelength characteristics, depending on the nature of the material, or the same properties of materials in the composition, surface structure, and the reflection spectral characteristics are also different, constitutes the difference of reflectance spectral curve. Bi2 WO6 reflection spectrum of the calculation results as shown in Fig. 7, starting from 0 eV, reflection coefficient increased with the increase of electron energy, in 5 eV and 10 eV form two strong absorption peak, then the reflection coefficient sharply reduced to zero. It then began to increase and formed three reflecting peaks at 142,142.5 eV. To emphasize the point that, for the semiconductor materials, when the incident light to the role of material surface, will have strong absorption of incident light intensity of the phenomenon, the reflection spectrum is a very strong absorption peak, and the reflection coefficient is zero (Fig. 7). The absorption coefficient of the material indicates the percentage of light intensity attenuation of the light wave in the medium. The absorption spectra of Bi2 WO6 are shown in Fig. 8. From 0 eV, the absorption coefficient increases with the increase of electron energy, and the two strongest absorption peaks are formed at 5.48 and 7.43 eV positions, and then decreases, and almost decreases to zero when the electron energy is 11.2 eV. Subsequently, the absorption peak was formed at 13.51, 20.09 and 42.97 eV. The absorption peak of 42.97 eV is formed by the transition between W-6p and Fermi. The two absorption peaks (13.51, 20.09) in the middle are the formation of O-2s → O-2p and Bi-6s → Bi-6p transitions, respectively. The corresponding relation between absorption coefficient and optical conductivity: a = 1 /ε0 cn It can be seen that the real part of the optical conductivity is proportional to the absorption coefficient, so their characteristic peak position is almost one-to-one. As we know, the refractive index and extinction coefficient are proportional to the real part and the imaginary part of the dielectric constant, respectively. The refractive index n() and extinction coefficient k() as shown in Fig. 9. By comparison, n(ω) spectral characteristics and the real part ε1 (ω) of dielectric function (Fig. 4) are very similar, this means that the static dielectric constant ε1 (0) corresponding to the static refraction index n(0), it is found that the static refractive index, n(0) is 1.68, with the increase of the energy becomes smaller, and then began to increase in the position until the formation of a peak, and then sharply decreased, the maximum of that is about 2.33 at 4.01 eV and the minimum of that is about 0.34 at
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Fig. 9. The optical properties for refractive index n() and extinction coefficient k() of Bi2 WO6 .
that there are four obvious
9.14 eV in the 0–10 eV region. The extinction coefficient increases from 0eV to 7.5 eV, the first high peak, and then decreased with the increase of energy until 10 eV began to increase, and the three peaks are formed in 12.5 eV, 20 and 32.5 eV. 4. Conclusions In summary, using CASTEP to optimize the structure of Bi2 WO6 , the results of optimization are very close to the experimental results, thus the theoretical calculation results are accuracy, the model and calculation method are reasonable and reliable. Firstly, the electronic structure and optical properties of Bi2 WO6 are calculated and analyzed on the basis of optimized structure. Through the analysis of band structure and density of states, Bi2 WO6 is indirect band-gap materials (Eg = 2.595 eV), the valence and conduction band mainly contributed by O-2p and Bi-6s states, the formation of covalent bonds. What’s more, by calculating the dielectric function, the energy loss function, the reflection spectrum and the absorption spectrum, we obtained the static dielectric constants is 2.83, the refractivity index is 1.68, which of the peaks are obviously and related to the transition of the electron. The calculation results of optical properties show that the Bi2 WO6 has obvious anisotropy, and the visible light has good transmittance, so it can offer a theoretical basis for the research and catalytic application of Bi2 WO6 in future. Funding This work was supported by the National Natural Science Foundation (51672220), and 111 Program (B08040) of MOE, the National Defense Science Foundation (32102060303), the Xi’an Science and Technology Foundation, the Shaanxi Provincial Science Foundation and NPU Gaofeng Project (17GH020824) of China. References [1] R.L. Withers, J.G. Thompson, A.D. Rae, The crystal chemistry underlying ferroelectricity in Bi4 Ti3 O12 , Bi3 TiNbO9 , and Bi2 WO6 , J. Solid State Chem. 94 (2) (1991) 404–417. [2] S. Phapale, D. Das, R. Mishra, Standard molar enthalpy of formation of Bi2 WO6 (s) and Bi2 W2 O9 (s) compounds, J. Chem. Thermodyn. 63 (4) (2013) 74–77. [3] P. Zhang, J. Zhang, A.J. Xie, et al., Hierarchical flower-like Bi2 WO6 hollow microspheres: facile synthesis and excellent catalytic performance, RSC Adv. 5 (2015) 23080–23085. [4] H. Djani, P. Hermet, P. Ghosez, First principle characterization of the P21 ab ferroelectric phase of Aurivillius Bi2 WO6 , J. Phys. Chem. C 118 (25) (2014) 13514. [5] L. Zhang, W. Wang, M. Shang, et al., Bi2 WO6 @carbon/Fe3 O4 microspheres: preparation, growth mechanism and application in water treatment, J. Hazard. Mater. 172 (1193) (2009) 172. [6] Y.T. Bai, X.M. Gao, Hydrothermal synthesis of Bi2 WO6 and its application in the photocatalytic oxidative of phenol, J. Yanan Univ. (2014). [7] Y. Wu, X. Gao, F. Fu, Cu – Bi2 WO6 catalyst synthesized by hydrothermal method and its application in photo catalytic oxidation desulfurization, Chem. Eng. Oil Gas 41 (4) (2012) 366–378. [8] H. Takeda, T. Nishida, S. Okamura, et al., Crystal growth of bismuth tungstate Bi2 WO6 by slow cooling method using borate fluxes, J. Eur. Ceram. Soc. 25 (12) (2005) 2731–2734. [9] J. Zhai, H. Yu, H. Li, et al., Visible-light photocatalytic activity of graphene oxide-wrapped Bi2 WO6 hierarchical microspheres, Appl. Surf. Sci. 344 (2015) 101–106. [10] N.D. Phu, L.H. Hoang, X.B. Chen, et al., Study of photocatalytic activities of Bi2 WO6 nanoparticles synthesized by fast microwave-assisted method, J. Alloys Compd. 647 (2015) 123–128. [11] M. Ma¸czka, L. Macalik, K. Hermanowicz, et al., Phonon properties of nanosized bismuth layered ferroelectric material—Bi2 WO6 , J. Raman Spectrosc. 41 (9) (2009) 1059–1066. [12] Y.M. Juan, E. Kaxiras, R.G. Gordon, Use of the generalized gradient approximation in pseudopotential calculations of solids, Phys. Rev. B 51 (1995) 9521–9525. [13] M. Ernzerhof, G.E. Scuseria, Assessment of the Perdew–Burke–Ernzerhof exchange-correlation functional, J. Chem. Phys. 110 (11) (1999) 5029–5036. [14] S.J. Clark, M.D. Segall, C.J. Pickard, et al., First principles methods using CASTEP, Z. Kristallogr. Cryst. Mater. 220 (5/6/2005) (2009) 567–570. [15] Y. Imai, M. Mukaida, T. Tsunoda, Calculation of electronic energy and density of state of iron-disilicides using a total-energy pseudopotential method, CASTEP, Thin Solid Films 381 (2) (2001) 176–182.
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