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Compton profiles and electronic structure of monoclinic zinc and cadmium tungstates
Author’s Accepted Manuscript Compton profiles and electronic structure of monoclinic zinc and cadmium tungstates B.S. Meena, N.L. Heda, H.S. Mund, B.L. Ahuja
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S0969-806X(15)30027-X http://dx.doi.org/10.1016/j.radphyschem.2015.08.002 RPC6884
To appear in: Radiation Physics and Chemistry Received date: 22 May 2015 Revised date: 1 August 2015 Accepted date: 4 August 2015 Cite this article as: B.S. Meena, N.L. Heda, H.S. Mund and B.L. Ahuja, Compton profiles and electronic structure of monoclinic zinc and cadmium t u n g s t a t e s , Radiation Physics and Chemistry, http://dx.doi.org/10.1016/j.radphyschem.2015.08.002 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 galley proof before it is published in its final citable 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.
Compton profiles and electronic structure of monoclinic zinc and cadmium tungstates B. S. Meenaa, N. L. Hedab, H. S. Munda, and B.L. Ahujaa,* a
Department of Physics, M.L. Sukhadia University, Udaipur 313301, Rajasthan, India. Department of Pure and Applied Physics, University of Kota, Kota 324010, India.
b
Keywords: X-ray scattering: Electronic structure calculations: Electron momentum density: Density functional theory: Band structure calculations. PACS number(s): 13.60.Fz; 71.15.Ap; 71.15.Mb; 78.70.Ck * Corresponding author. Prof. B.L. Ahuja ([email protected]) Tel.: +91 941 4317048; Fax: +91 294 2411950. ABSTRACT We report the first ever Compton scattering study of ZnWO4 and CdWO4 using 20 Ci
137
Cs
Compton spectrometer at momentum resolution of 0.34 a.u. To compare the experimental Compton profiles, we have also deduced the momentum densities using density functional theory (DFT) within linear combination of atomic orbitals (LCAO) methods. It is seen that the experimental Compton profiles of both the tungstates give a better agreement with LCAO-DFT calculations within generalized gradient approximation (GGA) employing Perdew-BeckeErnzerhof (PBE) exchange and correlation energies than other approximations included in the present work. Further, energy bands, density of states (DOS) and band gaps have also been calculated using LCAO-DFT-GGA-PBE scheme and full potential linearized augmented plane wave method. Both the computational schemes show a semiconducting nature of both the tungstates, with a direct band gap at Y point of Brillouin zone. Further, a relative nature of bonding on equal-valence-electron-density scale shows more covalent character in ZnWO4 than CdWO4 which reconciles with the conclusions drawn using integrated DOS and Mulliken’s population data.
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1. Introduction The tungstate materials like ZnWO4 and CdWO4 are very useful in scintillators, optical fibers, sensors, optical recording, masers, photocatalyst devices and security systems, etc. Regarding earlier studies, Nagirnyi et al. (2002) have reported energy transfer in ZnWO4 and CdWO4 while the scintillation pulse shape discrimination is discussed by Danevich et al. (2005). Itoh et al. (2006, 2007) have reported X-ray photoelectron spectroscopy (XPS) to investigate the electronic structures, reflection, luminescence-excitation, luminescence decay kinetics, photo-stimulated luminescence and photo-induced infrared absorption in both the tungstates. Huang and Zhu (2007) have reported high photocatalytic activity of ZnWO4. Fujita et al. (2008) have performed polarized reflection and XPS measurements and also the electronic structure of CdWO4. Kalinko et al. (2009) have undertaken ab-initio calculations with density functional theory (DFT) and pseudopotential schemes along with the linear combination of atomic orbitals (LCAO) within DFT for ZnWO4. Also in case of CdWO4, DFT calculations for electronic and optical properties were performed by Abraham et al. (2000). Lacomba-Perales et al. (2008) have reported room temperature experimental band gap between 3.9-4.4 eV for ZnWO4 and 4.15 eV of CdWO4 using optical-absorption and reflectance measurements. Evarestov et al. (2009) have applied LCAO method to probe the electronic and phonon properties of ZnWO4 and compared their results with available crystallographic data. Raman and photoluminescence spectroscopic measurements of ZnWO4 have been undertaken by Kalinko and Kuzmin (2009), whereas electronic and optical properties with oxygen vacancy in CdWO4 are reported by Zhou et al. (2010). Kim et al. (2011) have combined the electronic band structure calculations and electrochemical measurements to investigate the electronic and photovoltaic properties of such materials. Brik et al. (2012) have employed DFT within CASTEP code for optical and electronic
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properties of ZnWO4 and CdWO4 and compared their results with the available XPS and reflectivity spectra. Recently, Khyzhun et al. (2013) have applied full potential linearized augmented plane wave (FP-LAPW) method to calculate the electronic properties of ZnWO4. In second attempt, Brik et al. (2013) have applied the DFT within CASTEP module to calculate the structural, electronic and elastic properties of both the tungstates at the ambient pressure and elevated pressure ranging between 5 to 10 GPa. Compton scattering is a well established technique to probe electronic properties of the materials (Cooper et al., 2004; Heda and Ahuja, 2010). In this technique, the measured quantity is known as Compton profile (CP) J(pz), which is projection of electron momentum density (EMD), r(p), along the direction of scattering vector (conventionally z-axis). Mathematically,
J ( pz ) =
òò
r(p) dpx dp y µ
d2σ . dΩ dE 2
(1)
In Eq. 1, pz is the component of linear momentum of electron along the z-axis and E2 is the energy of the scattered radiations. The r(p) can be evaluated using the momentum space wave
r function, c i ( p ) , which is derived from the Fourier transformation of real space wave function yi ( r ) .
In this paper, we report the first ever CP measurements of ZnWO4 and CdWO4 using 661.65 keV g-rays emitted by 20 Ci
137
Cs source (Ahuja et al., 2006). On the theoretical side, we have
employed the LCAO and FP-LAPW schemes (Dovesi et al., 2009; Blaha et al., 2011) to compute the theoretical CPs, energy bands, partial and total density of states (DOS), band gap and Mulliken's population (MP) data. Further, bonding aspects in these isoelectronic compounds have been analyzed using their equal-valence-electron-density (EVED) profiles.
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2. Experiment The CPs of monoclinic ZnWO4 and CdWO4 have been measured using 20 Ci
137
Cs Compton
spectrometer at resolution of 0.34 a.u. (Gaussian full width at half maximum) (Ahuja et al. 2004, 2006). In such experiments, the overall resolution factor depends upon the resolution of detector and geometrical broadening of the incident and scattered photons. In individual experiments, the incident photons of energy 661.65 keV were scattered by the polycrystalline samples at scattering angle of 160±0.6° and the data were accumulated using a high purity Ge detector (Canberra, Ge crystal size 500 mm2 and 10 mm thickness) and associated electronics. Here, the intrinsic character of the Ge crystal was maintained by cooling it at liquid nitrogen temperature (77 K). The high purity (more than 99.5 %) sample was kept in an ampoule constructed using Mylar foil on both the sides. Due to difficulties in getting the large size single crystals (say 15 mm diameter and 2 mm thickness) and to compare the relative nature of bonding in terms of EVED profiles, we have measured the isotropic profiles. The density and thickness of ZnWO4(CdWO4) were 1.33(2.60) g/cm3 and 0.55(0.42) cm, respectively. During the total exposure time of 238.15(321.84) h for ZnWO4(CdWO4), an integrated Compton intensity of 2.10 x107(5.05 x 107) photons in the momentum range -10 to +10 a.u. (Compton region) was obtained. To extract true Compton profile, the raw data were corrected for background, detector response function (limited to stripping-off the low energy tail), detector efficiency, sample absorption, Compton scattering cross-section, etc. (Timms, 1989). Further, the data were corrected for multiple scattering events (Felsteiner et al., 1974) upto triple scattering. It was found that the effect of multiple to single scattering phenomena was 10.23(10.57) % in the momentum range -10 to +10 a.u. for ZnWO4 (CdWO4). We have not corrected our data for Bremsstrahlung background contribution because its contribution in the Compton profile region
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is very small (Mathur and Ahuja, 2005). Finally, the isotropic CP was normalized to the corresponding free atom (FA) CP area 55.81 e- (61.97 e-) for ZnWO4 (CdWO4) (Biggs et al., 1975). A good agreement between the FA CPs and the experimental data in the high momentum regions validates the accuracy of data acquisition and process to extract true CPs. 3. Theory 3.1. LCAO method The directional and isotropic CPs, energy bands, partial and total DOS, MP charge transfer data and band gap have been computed using LCAO-DFT method (Dovesi et al., 2009) with local density and generalized gradient approximations (LDA and GGA, respectively). Using DFT theory, the Schrodinger equation can be written as, r r é Ñ2 ¶E xc [ρ( r )]ù r r r ρ( r ) ¢ V ( r ) d r + + + r ê ú ψ i ( r ) = ε i ψ i ( r ). ext ò r - r¢ ¶ρ( r ) úû êë 2
(2)
In Eq. 2 the first three terms in the Hamiltonian energy (left hand part) are kinetic, external potential and Coulomb exchange operators and the fourth term is the first order density derivative of Exc. The exchange-correlation density functional energy Exc for LDA/GGA is expressed as, / GGA [r(rr )] = E LDA xc
r r r r r ò r(r )e [r(r ) / r(r ), Ñ r (r ) ]dr
(3)
xc
here e xc is the exchange-correlation energy per particle in uniform electron gas and is defined differently in LDA and GGA (Dovesi et al., 2009). Further, the different kinds of exchange and correlation energies (Dovesi et al., 2009; Vosko et al., 1980; Perdew et al., 1996; Perdew et al., 2008) have been used within LDA and GGA as listed in Table 1. For the present computations, we have considered the all electron Gaussian basis sets of Zn, Cd and O taken from http://www.tcm.phy.cam.ac.uk/~mdt26/crystal.html, while due to non availability of all electron
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basis sets for W we have used its pseudopotential basis sets as reported by Wadt and Hay (1985). The basis sets were energy optimized using BILLY software (Dovesi et al., 2009). The selfconsistent field (SCF) calculations have been performed with 170 k-points in the irreducible Brillouin zone (BZ) for both ZnWO4 and CdWO4. All theoretical CPs have been normalized to corresponding FA CPs area, as mentioned in section 2. 3.2. FP-LAPW method In addition to LCAO calculations, the energy bands, partial and total DOS and band gap of both the samples have been deduced using FP-LAPW-DFT with more accurate exchange and correlation potentials of Perdew-Becke-Ernzerhof (PBE) (Blaha et al., 2011). It is worth mentioning that in FP-LAPW method, the crystal potential outside the muffin-tin (MT) atomic spheres is approximated by plane waves, while within the MT it includes spherical harmonics. The MT radii (RMT) for Zn, W and O in case of ZnWO4 were taken to be 2.02, 1.78 and 1.58 Å, while in case of CdWO4, the RMT for Cd, W and O were kept to be 2.22, 1.80 and 1.55 Å, respectively. In case of both the tungstate, the SCF cycles were achieved by using 260 k points in the irreducible BZ. The values of RMT*Kmax (Kmax being the maximum amplitude of the reciprocal lattice vector k) and lmax were set to 7 and 10 for ZnWO4 and CdWO4, respectively. In both the computational schemes (LCAO and FP-LAPW) the lattice parameters (a=4.693 Å, b=5.721 Å, c= 4.928 Å and b=90.632°) along with the atomic positions of monoclinic ZnWO4 were taken from Khyzhun et al. (2013), while these parameters for CdWO4 (a= 5.029Å, b=5.860 Å, c= 5.072 Å and b=91.519°) were taken from the work of Abraham et al. (2000). In Fig. 1, we have plotted the unit cell of AWO4 (where A = Zn or Cd) with space group P2/c (13) using the visualization code of Kokalj (2003). In both the tungstates, there are two formulae per unit in the primitive cell and two non-equivalent positions of oxygen atoms (marked as O1 and O2).
6
4. Results and Discussion 4.1. MP analysis In Table 2, we have collated the MP charge transfer data of both the tungstates using LCAODFT-VWN, LCAO-DFT-PBE and LCAO-DFT-PBEsol schemes along with the data reported by Kalinko et al. (2009), Evarestov et al. (2009) and Brik et al. (2012). All the approximations and the available data show that Zn/Cd and W play the role of donor atoms while oxygen atoms (two non-equivalent O1 and O2) behave as acceptor atoms. In the present work, the total charge transfer from donor atoms to acceptor atoms in ZnWO4(CdWO4) is 3.94(4.14) e- using LCAODFT-PBE scheme. These values from LCAO-DFT-VWN and LCAO-DFT-PBEsol are respectively 3.98(4.16) e- and 3.96(4.14) e- for ZnWO4(CdWO4). It is known that large direct charge transfer value in the MP data indicates the dominance of ionic character, whereas small value of charge transfer highlights covalent character of materials. Therefore, the MP data from present calculations and that from Brik et al. (2012) computations predict more covalent character in ZnWO4 than CdWO4. From Table 2, it is quite interesting to note that in case of both the tungstates the amount of charge donated by Zn/Cd and W is unequally distributed among oxygen atoms (O1 and O2) which indicate the non-equivalent character of the oxygen atoms. It is worth mentioning that a similar trend of unequal charge distribution was also observed in WOx (x=2 and 3) (Heda and Ahuja, 2013; Heda and Ahuja, 2015) where the charge transfer from tungsten was unequally distributed among the oxygen atoms. From Table 2, our MP charge transfer data deduced from different approximations along with the data of Brik et al. (2012) indicate that the amount of charge in W, O1 and O2 atoms are approximately same in ZnWO 4 and CdWO4, while there are significant differences in the amplitude of charge at Zn and Cd sites. Such difference may be due to the large ionic character of Cd in CdWO4 than that of Zn in
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ZnWO4. Since, the basis sets used in present computations involve sufficiently diffuse external atomic orbitals, the MP analysis is expected to be quite reliable in both the tungstates. 4.2. Energy bands and DOS In Figs. 2-5, we have plotted energy bands along with partial and total DOS of ZnWO4 and CdWO4 using FP-LAPW-DFT-PBE and LCAO-DFT-PBE schemes. Due to the similar topology of the energy bands and DOS using LCAO-DFT-VWN and LCAO-DFT-PBEsol schemes to that of reported data, we have not shown energy bands and DOS corresponding to these approximations. It is seen that except some fine structures, the energy bands and DOS are in reasonable agreement with the available data (Abraham et al., 2000; Khyzhun et al, 2013). Since the energy bands and DOS are almost similar for FP-LAPW-DFT-PBE and LCAO-DFT-PBE schemes for both the tungstates, we now discuss the energy bands and DOS derived from FPLAPW-DFT-PBE scheme as shown in Figs. 2 and 4. These energy bands and DOS of ZnWO4 and CdWO4 (Figs. 2, 4) can be divided into three major parts as discussed below: (i) The lowest energy bands in the -18.44 to -16.02 eV (-18.18 to -16.04 eV) are due to 2sp states of oxygen atoms (two non-equivalent O1 and O2) for ZnWO4 (CdWO4). (ii) The second region from -6.50 eV to Fermi energy (EF) level (-6.78 eV to EF) mainly corresponds to 3d (4d) states of Zn (Cd) and 2sp states of oxygen atoms for ZnWO4 (CdWO4). Therefore, it is evident that the 3d (4d) states of Zn (Cd) and 2sp states of oxygen atoms form valence band maxima (VBM) in ZnWO4 (CdWO4). (iii) The third region in ZnWO4 (Fig. 2) is divided in two parts, namely (a) from 3.00 to 5.07 eV which is mainly contributed by 5d states of W atoms with a small contribution of oxygen atoms (O1 and O2) and (b) 5.44 eV and above which is due to 5d states of W with a small contribution of 3d states of Zn and 2sp states of oxygen (O1 and O2). While in case of CdWO4 (Fig. 4), the
8
region starting from 3.04 eV are mainly due to 5d states of W with a small contribution of 4d states of Cd and 2sp states of oxygen (O1 and O2). It is observed that the 5d states of W atoms are mainly responsible for the conduction band minima (CBM) in both the tungstates. It is seen that the VBM and CBM occur at Y point of BZ which lead to the direct band gap in both the tungstates. The DOS curves shown in Figs. 2-5 (right hand side) also confirm the semiconducting character of both the tungstates. In Table 3, we have compiled the band gap values obtained from LCAO-DFT-VWN, LCAO-DFT-PBE, LCAO-DFT-PBEsol and FPLAPW-DFT-PBE calculations along with the available theoretical and experimental band gap data (Kalinko et al., 2009; Abraham et al., 2000; Lacomba-Perales et al., 2008; Evarestov et al., 2009; Kim et al., 2011; Brik et al., 2012; Khyzhun et al, 2013; Sun et al., 2010; Zhao et al., 2006). Our band gap using FP-LAPW-DFT-GGA scheme is less than experimental data (Nagirnyi et al., 2002; Zhao et al., 2006), although it is in good agreement with earlier theoretical data (Abraham et al., 2000; Kim et al., 2011; Brik et al., 2012; Khyzhun et al, 2013, Sun et al., 2010). It is understandable because the first principle calculations with DFT approximation underestimate the band gap of semiconductor. In case of ZnWO4, our LCAO based band gap data slightly differ from the LCAO data of Kalinko et al. (2009) which may be due to use of pseudopotential based basis sets of Zn used by these authors, while we have used the all electron Gaussian basis sets for Zn atom. To find more accurate theoretical band gap, we have also computed the band gap using FP-LAPW with the latest modified Becke-Johnson (mBJ) potential (Tran and Blaha, 2009). It is known that the mBJ potential is a simple modification of the potentials defined by Becke and Johnson (2006) and predicts more accurate value of the band gap as reported by different workers (Lacomba-Perales et al., 2008; Zhao et al., 2006). Further, we have also calculated the integrated DOS from -6.50 eV to EF (-6.78 eV to EF) for ZnWO4
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(CdWO4) as plotted in Figs. 2 and 4 to check the unequal distribution of charge transfer among two oxygen atoms in both the tungstates. It is found that in case of ZnWO4 the value of the integrated DOS for O1 atom (14.465 e-) is higher than that of O2 atom (14.344 e-), while for CdWO4 the value for O1 (14.015 e-) is less than that of O2 (14.179 e-). Therefore, the trend of integrated DOS is in tune with the MP data reported in Table 2. 4.3. Compton profiles In Figs. 6-7, we have plotted the anisotropies between the pairs of unconvoluted directional CPs of both the tungstates namely J110-J100, J001-J100 and J001-J110 using LCAO-DFT-VWN, LCAODFT-PBE and LCAO-DFT-PBEsol schemes. It is seen that general trend of oscillations in the anisotropies (J110-J100, J001-J100 and J001-J110) using all the reported approximations in both the materials is almost identical. In Figs. 6-7, after pz≥3 a.u. there is very small differences in anisotropies (J110-J100, J001-J100 and J001-J110), which is understandable because this region is dominated by core electrons whose contribution cancels out while taking the directional differences. We can correlate the various oscillations in anisotropies in momentum densities (Figs. 6-7) with degenerate states in energy bands and their cross-overs in the vicinity of EF. The positive value of anisotropies in momentum densities near pz=0.0 a.u. in ZnWO4 and CdWO4 in Figs. 6-7 (a-b) and negative value in Figs. 6-7(c) are due to the large degenerate states along G-Y [110] direction as compared to G-X [100] and G-Z [001] directions. We observe that the degenerate states along G-X [100] are higher than those of G-Z [001] direction which leads to higher momentum densities in G-X branch. Further, the negative amplitude at pz=0.7 a.u. along J110-J100 in Fig. 6(a) of ZnWO4 arises from the zone boundary of G-X (0.35 a.u.; n=2) branch. Similarly, the positive value of J001-J110 in Fig. 6(c) at pz=0.7 a.u. comes from the zone boundary of G-Z (0.33 a.u.; n=2) branch. Similarly, we can explain anisotropic effects in momentum 10
densities of ZnWO4 and CdWO4 at other pz values using energy bands and DOS. It may be mentioned that some fine structures may not be visible due to cancellation of the momentum densities while taking the differences between directional CPs. In Figs. 8 (a-b), the difference profiles between convoluted theoretical (LCAO-DFT-VWN, LCAO-DFT-PBE and LCAO-DFTPBEsol) and experimental data have been shown for ZnWO4 and CdWO4, respectively. Further, in Tables 4-5 we have included the unconvoluted CP data derived from LCAO-DFT-VWN, LCAO-DFT-PBE and LCAO-DFT-PBEsol schemes along with the experimental data with statistical error for both the tungstates. It is observed that deviations between theory and experiment using the present approximations are almost identical. In the low momentum region, LCAO-DFT-VWN, LCAO-DFT-PBE and LCAO-DFT-PBEsol schemes show different amplitudes of deviations (Tables 3 and 4, and Fig. 5) which are understandable in terms of underlying assumptions of different exchange and correlation potentials used in different approximations. We feel that differences between the theoretical and experimental Compton profiles in the region pz˂5 a.u. may be due to non-inclusion of relativistic effects and Lam– Platzman (LP) correlation correction (Cooper et al., 2004). Further, to conclude about quantitative agreement between theory (LCAO-DFT-VWN, LCAO-DFT-PBE and LCAO-DFTPBEsol based profiles) and experiment, we have undertaken χ2 fitting. It is seen that LCAODFT-PBE scheme gives the best agreement with the experimental data. A better reconciliation of LCAO-DFT–PBE based CP with experiment than to LCAO-DFT–VWN shows a superiority of GGA over the LDA in both the tungstates. 4.4. EVED profiles Now we discuss the relative nature of bonding in these tungstates by scaling the profiles on EVED scale. The EVED profiles are drawn between [J(pz)*pF] v/s pz/pF, with pF as Fermi
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momentum. The pF value of ZnWO4 (CdWO4) were taken to be 1.42 (1.34) a.u. Such method has been successfully applied to study the relative nature of bonding in different systems as reported by Reed and Eisenberger (1972), Heda et al. (2007), Arora et al. (2009), Ahuja et al. (2013, 2015), and Bhamu et al. (2013). In Fig. 9, we have plotted the EVED profiles for LCAO-DFTPBE and experiment for both the tungstates. All the EVED profiles were normalized to 21 electrons (valence) in the momentum range 0-4 a.u. It is seen from the Figs. 9(a-b) that at pz/pF =0 a.u. the theoretical (LCAO-DFT-PBE) and experimental EVED profiles of ZnWO4 are 1.97 and 8.02 % higher than those of CdWO4, respectively. Such trend suggests more localization of charge in the bond direction of ZnWO4 as compared to that in CdWO4. Since the sharpness of EVED profile represents covalent character, we conclude that ZnWO4 is more covalent than CdWO4. This trend of relative bonding of EVED is also in accordance with the MP data of Table 2 and integrated DOS. 5. Conclusions Measurements on electron momentum density of ZnWO4 and CdWO4 have been reported using 661.65 keV g-rays to test applicability of exchange and correlation potentials within local density and generalized gradient approximations. A comparison of theoretical Compton profiles (based on different exchange and correlation energies within LCAO-DFT) and corresponding experiment shows that the best agreement between experimental and theoretical profiles of both the tungstates is produced by Perdew-Burke-Ernzerhof (PBE) exchange and correlation potentials with generalized gradient approximation. Further, the energy bands, partial and total density of states (DOS), band gap and Mulliken's population (MP) data have also been reported using LCAO-DFT-PBE along with FP-LAPW within PBE scheme. Both the theories show a semiconducting nature of ZnWO4 and CdWO4. A relative nature of bonding in both the
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tungstates is reported using equal-valence-electron density profiles, MP data and integrated DOS. It is concluded that ZnWO4 has more covalent character than CdWO4. The DOS have also been discussed in terms of charge transfer in the constituents. Unconvoluted anisotropies in Compton profiles are found to be in accordance to degenerate states in energy bands. Acknowledgements Prof. R. Dovesi and Prof. P. Blaha are thanked for providing LCAO and FP-LAPW codes, respectively. The work is supported by SERB (DST), New Delhi through a major research project (Grant No. SR/S2/CMP-40/2011). One of us (BSM) is thankful to UGC, New Delhi for UGC-BSR Meritorious fellowship. HSM thanks SERB (DST), New Delhi for financial assistant under DST Fast Track Young Scientist scheme.
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References Abraham, Y., Holzwarth, N.A.W., Williams, R.T., 2000. Electronic structure and optical properties of CdMoO4 and CdWO4. Phys. Rev. B 62, 1733-1741. Ahuja, B.L., Sharma, M., Mathur, S., 2004. Electronic structure of liquid mercury using Compton scattering technique. Z. Naturforsch. 59a, 543–549. Ahuja, B.L., Sharma, M., Mathur, S., 2006. Anisotropy in the momentum density of tantalum. Nucl. Instrum. Methods Phys. Res. B 244, 419–426. Ahuja, B.L., Jain, P., Sahariya, J., Heda, N.L., Soni, P., 2013. Electronic properties of RDX and HMX: Compton scattering experiment and first-principles calculation. J. Phys. Chem. A 117, 5685–5692. Ahuja, B.L., Raykar, V., Joshi, R., Tiwari, S., Talreja, S., Choudhary, G., 2015. Electronic properties and momentum densities of tin chalcogenides: Validation of PBEsol exchange-correlation potential. Physica B 465, 21–28. Arora, G., Sharma, Y., Sharma, V., Ahmed, G., Srivastava, S.K., Ahuja, B.L., 2009. Electronic structure of layer type tungsten metal dichalcogenides WX2 (X=S, Se) using Compton spectroscopy: theory and experiment. J. Alloys Compd. 470, 452–460. Becke, A.D., Johnson, E.R., 2006. A simple effective potential for exchange. J. Chem. Phys. 124, 221101-1–221101-4. Bhamu, K.C., Sahariya, J., Ahuja, B.L., 2013. Electronic structure of ceramic CrSi2 and WSi2: Compton spectroscopy and ab-initio calculations. J. Phys. Chem. Solids 74, 765–771. Biggs, F., Mendelsohn, L.B., Mann, J.B., 1975. Hartree–Fock Compton profiles. Atomic Data Nucl. Data Tables 16, 201–308. Blaha, P., Schwartz, K., Luitz, J., 2011. An augmented plane wave plus local orbitals program for calculating crystal properties. Revised edition WIEN2K_11.1. Vienna University of Technology, Vienna, Austria, and references therein. Brik, M.G., Nagirnyi, V., Kirm, M., 2012. Ab-initio studies of the electronic and optical properties of ZnWO4 and CdWO4 single crystals. Mat. Chem. Phys. 134, 1113-1120. Brik, M.G., Nagirnyi, V., Kirm, M., 2013. First-principles calculations of the structural, electronic and elastic properties of ZnWO4 and CdWO4 single crystals at the ambient and elevated pressure. Mat. Chem. Phys. 137, 977-983.
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Cooper, M.J., Mijnarends, P.E., Shiotani, N., Sakai, N., Bansil, A., 2004. X-ray Compton Scattering, Oxford Science Publications, Oxford University Press, New York, and references therein. Danevich, F.A., Georgadze, A.Sh., Kobychev, V.V., Kropivyansky, B.N., Nagorny, S.S., Nikolaiko, A.S., Tretyak, V.I., Yurchenko, S.S., Zdesenko, S.Yu., Zdesenko, Yu.G., Bizzeti, P.G., Fazzini, T.F., Maurenzig, P.R., Solsky, I.M., Brudanin, V.B., Avignone III, F.T., 2005. Scintillation pulse shape discrimination with CaWO4, ZnWO4 and CdWO4 crystal. Fun. Mat. 12, 269-273. Dovesi, R., Saunders, V.R., Roetti, C., Orlando, R., Zicovich-Wilson, C.M., Pascale, F., Civalleri, B., Doll, K., Harrison, N.M., Bush, I.J., D’Arco, Ph., Llunell, M., 2009. CRYSTAL09 User’s Manual. University of Torino, Torino, Italy, and references therein. Evarestov, R.A., Kalinko, A., Kuzmin, A., Losev, M., Purans, J., 2009. First-principles LCAO calculations on 5d transition metal oxides: electronic and phonon properties. Integrated Ferroelectrics 108, 1-10. Felsteiner, J., Pattison, P., Cooper, M.J., 1974. Effect of multiple scattering on experimental Compton profiles: a Monte-Carlo calculation. Philos. Mag. 30, 537–548. Fujita, M., Itoh, M., Katagiri, T., Iri, D., Kitaura, M., Mikhailik, V.B., 2008. Optical anisotropy and electronic structures of CdMoO4 and CdWO4 crystals: polarized reflection measurements, x-ray photoelectron spectroscopy, and electronic structure calculations. Phys. Rev. B 77, 155118-1-155118-7. Heda, N.L., Mathur, S., Ahuja, B.L., Sharma, B.K., 2007. Compton profiles and band structure calculations of CdS and CdTe. Phys. Stat. Sol. (b) 244, 1070–1081. Heda, N.L., Ahuja, B.L., 2010. Role of in-house Compton spectrometer in probing the electronic properties. In: Ahuja, B.L. (Ed.), Recent Trends in Radiation Physics Research, Himanshu Publications, New Delhi, India, pp. 25-30. Heda, N.L., Ahuja, B.L., 2013. Electronic properties and electron momentum density of monoclinic WO3. Comput. Mater. Sci. 72, 49-53. Heda, N.L., Ahuja, U., 2015. Electronic properties and Compton scattering studies of monoclinic tungsten dioxide. Rad. Phys. Chem. 106, 33-39 Huang, G., Zhu, Y., 2007. Synthesis and photocatalytic performance of ZnWO4 catalyst. Mat. Sci. Eng. B 139, 201-208. Itoh, M., Fujita, N., Inabe, Y., 2006. X-ray photoelectron spectroscopy and electronic structures of scheelite- and wolframite-type tungstate crystals. J. Phys. Soc. Japan 75, 084705-1-084705-8. 15
Itoh, M., Katagiri, T., Aoki, T., Fujita, M., 2007. Photo-stimulated luminescence and photo-induced infrared absorption in ZnWO4. Radiat. Meas. 42, 545-548. Kalinko, A., Kuzmin, A., 2009. Raman and photoluminescence spectroscopy of zinc tungstate powders. J. Lumin. 129, 1144-1147. Kalinko, A., Kuzmin, A., Evarestov, R.A., 2009. Ab initio study of the electronic and atomic structure of the wolframite-type ZnWO4. Solid State Comm. 149, 425-428. Khyzhun, O.Y., Bekenev, V.L., Atuchin, V.V., Galashov, E.N., Shlegel, V.N., 2013. Electronic properties of ZnWO4 based on ab initio FP-LAPW band-structure calculations and X-ray spectroscopy data. Mat. Chem. Phys. 140, 588-595. Kim, D.W., Cho, I.-S., Shin, S.S., Lee, S., Noh, T.H., Kim, D.H., Jung, H.S., Hong, K.S., 2011. Electronic band structures and photovoltaic properties of MWO4 (M=Zn, Mg, Ca, Sr) compounds. J. Solid State Chem. 184, 2103-2107. Kokalj, A., 2003. Computer graphics and graphical user interfaces as tool in simulations of matter at the atomic scale. Comput. Mater. Sci. 28, 155–168. Lacomba-Perales, R., Ruiz-Fuertes, J., Errandonea, D., Martinez-Garcia, D., Segura, A., 2008. Optical absorption of divalent metal tungstates: correlation between the bandgap energy and the cation ionic radius. Euro. Phys. Lett. 83, 37002-37002-5. Mathur, S., Ahuja, B.L., 2005. Quantitative determination of Bremsstrahlung background in Compton measurements. Phys. Lett. A 335, 245–250. Nagirnyi, V., Feldbach, E., Jönsson, L., Kirm, M., Kotlov, A., Lushchik, A., Nefedov, V.A., Zadneprovski, B.I., 2002. Energy transfer in ZnWO4 and CdWO4 scintillators. Nucl. Instrum. Methods A 486, 395-398. Perdew, J.P., Burke, K., Ernzerhof, M., 1996. Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865–3868. Perdew, J.P., Ruzsinszky, A., Csonka, G.I., Vydrov, O.A., Scuseria, G.E., Constantin, L.A., Zhou, X., Burke, K., 2008. Restoring the density-gradient expansion for exchange in solids and surfaces. Phys. Rev. Lett. 100, 136406-1–136406-4. Reed, W.A., Eisenberger, P., 1972. Gamma-ray Compton profiles of diamond, silicon, and germanium. Phys. Rev. B 6, 4596–4604. Sun, H., Fan, W., Li, Y., Cheng, X., Li, P., Zhao, X., 2010. Origin of the improved photocatalytic activity of F-doped ZnWO4: a quantum mechanical study. J. Solid State Chem. 183, 3052-3057.
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Timms, D.N., 1989. Compton Scattering Studies of Spin and Momentum Densities (unpublished Ph. D. Thesis). University of Warwick, England. Tran, F., Blaha, P., 2009. Accurate band gaps of semiconductors and insulators with a semilocal exchange-correlations potential. Phys. Rev. Lett. 102, 226401-1–226401-4. Vosko, S.H., Wilk, L., Nusair, M., 1980. Accurate spin-dependent electron liquid correlation energies for local spin density calculations: a critical analysis. Can. J. Phys. 58, 1200–1211. Wadt, W.R., Hay, P.J., 1985. Ab initio effective core potentials for molecular calculations. Potentials for main group elements Na to Bi. J. Chem. Phys. 82, 284-298. Zhao, X., Yao, W., Wu, Y., Zhang, S., Yang, H., Zhu, Y., 2006. Fabrication and photoelectrochemical properties of porous ZnWO4 film. J. Solid State Chem. 179, 2562-2570. Zhou, X., Liu, T., Zhang, Q., Cheng, F., Qiao, H., 2010. Electronic structure and optical properties of CdWO4 with oxygen vacancy studied from first principles. Solid State Comm. 150, 5-8.
17
Figure captions Fig. 1. Structural sketch of AWO4 (A = Zn, Cd) plotted using software tool of Kokalj (2003). Fig. 2. FP-LAPW-DFT-PBE scheme based energy bands (left hand side) of monoclinic ZnWO4 with the Fermi energy (EF) at zero energy reference level. The positions of Γ, Z, X and Y vertices correspond to (0,0,0), (0,0,1/2), (1/2,0,0) and (0,1/2,0), respectively. Partial and total density of states for different constituents of ZnWO4 are shown in right hand side panel. Fig. 3. Same as Fig. 2 except the scheme, which is LCAO-DFT-PBE. Fig. 4. Same as Fig. 2 except the sample, which is CdWO4. Fig. 5. Same as Fig. 2 except the sample and scheme, which are CdWO4 and LCAO-DFT-PBE, respectively. Fig. 6. Anisotropies in the unconvoluted theoretical Compton profiles of monoclinic ZnWO4 along (a) J110-J100, (b) J001-J100 and (c) J001-J110 using LCAO-DFT-VWN, LCAO-DFT-PBE and LCAO-DFT-PBEsol schemes as mentioned in the text. The solid lines are drawn only to guide the eyes. Fig. 7. Same as Fig. 6 except the sample, which is monoclinic CdWO4. Fig. 8. The difference between convoluted isotropic theoretical (LCAO-DFT-VWN, LCAODFT-PBE and LCAO-DFT-PBEsol) and experimental Compton profiles for (a) ZnWO4 and (b) CdWO4 along with the experimental error (±σ) at few points. Fig. 9. Theoretical (LCAO-DFT-PBE) and experimental equal-valence-electron-density (EVED) profiles of isoelectronic ZnWO4 and CdWO4.
18
Table 1. The exchange and correlation schemes used in LDA and GGA within the framework of LCAO approximations (Dovesi et al., 2009). Scheme
Exchange
Correlations
LCAO-DFT-LDA
Dirac–Slater (Dovesi et al., 2009)
LCAO-DFT-GGA
Perdew-Becke-Ernzerhof (PBE) (Perdew et al., 1996) PBE functional revised for solids (PBEsol) (Perdew et al., 2008)
Vosko-Wilk-Nusair (VWN) (Vosko et al., 1980) PBE (Perdew et al., 1996)
LCAO-DFT-GGA
19
PBEsol (Perdew et al., 2008)
Nomenclature used in text LCAO-DFT-VWN LCAO-DFT-PBE LCAO-DFTPBEsol
Table 2. The Mulliken's population (MP) charge transfer data from donor atoms (Zn, Cd and W) to the acceptor atoms (two non-equivalent O1 and O2) in ZnWO4 and CdWO4 using the different combinations of exchange and correlation energies (DFT-VWN, DFT-PBE and DFT-PBEsol) within LCAO method as mentioned in the text.
Scheme
(a) Present calculations · LCAO-DFT-VWN · LCAO-DFT-PBE · LCAO-DFT-PBEsol (b) Kalinko et al. (2009) · LCAO-LDA · LCAO-PW91 · LCAO-PBE · LCAO-B3PW · LCAO-B3LYP · LCAO-PBE0 (c) Evarestov et al. (2009) · LCAO-B3PW (d) Brik et al. (2012) · DFT-LDA · DFT-GGA
Amount of charge transfer (e-) ZnWO4 CdWO4 Donor Acceptor Donor Acceptor atoms atoms atoms atoms Zn W O1 O2 Cd W O1 O2 1.26 1.27 1.27
2.72 2.67 2.69
1.10 1.08 1.09
0.89 0.89 0.89
1.48 1.50 1.50 1.55 1.54 1.57
3.58 3.52 3.51 3.72 3.76 3.75
1.32 1.30 1.30 1.37 1.38 1.38
1.22 1.21 1.21 1.27 1.28 1.28
1.54
2.76
1.13
1.02
1.19 1.26
1.38 2.43
0.67 0.69
0.62 0.65
20
1.43 1.44 1.46
2.73 2.70 2.68
0.93 0.92 0.93
1.15 1.15 1.14
1.25 1.30
1.38 1.43
0.69 0.71
0.63 0.65
Table 3. The band gap in ZnWO4 and CdWO4 computed using LCAO (DFT-VWN, DFT-PBE, DFT-PBEsol), FP-LAPW-PBE and the FP-LAPW-mBJ schemes along with the available data. Approach
Band gap (in eV)
(i) Theory (a) Present computations · LCAO-DFT-VWN · LCAO-DFT-PBE · LCAO-DFT-PBEsol · FP-LAPW-DFT-PBE · FP-LAPW-mBJ (b) Kalinko et al. (2009) · LCAO-LDA · LCAO-PW91 · LCAO-PBE · LCAO-B3PW · LCAO-B3LYP · LCAO-PBE0 (c) Abraham et al. (2000) · DFT-LDA (d) Evarestov et al. (2009) · LCAO-B3PW (e) Kim et al. (2011) · DFT-GGA (f) Brik et al. (2012) · DFT-LDA · DFT-GGA (g) Khyzhun et al. (2013) · FP-LAPW-GGA (h) Sun et al. (2010) · DFT-GGA (ii) Experiment · Lacomba-Perales et al. (2008) · Zhao et al. (2006)
ZnWO4
CdWO4
2.20 2.17 2.16 3.00 3.92
2.43 2.42 2.41 3.05 4.24
2.31 2.33 2.31 4.27 4.22 4.60 2.94 5.40 2.95 2.82 2.90
2.96 3.00
3.00 2.88 3.9-4.4 4.01
21
4.15
Table 4. Unconvoluted theoretical Compton profiles of monoclinic ZnWO4 computed using DFT-VWN, DFT-PBE and DFT-PBEsol schemes within LCAO approximations as mentioned in text. The experimental data have also been listed along with the statistical error (±s) at a few points. pz (a.u.) 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 1.0 1.2 1.4 1.6 1.8 2.0 3.0 4.0 5.0 6.0 7.0
LCAO-DFT-VWN 25.21 25.17 24.85 24.47 23.84 23.10 22.19 21.12 19.94 17.38 14.87 12.75 11.06 9.77 8.77 5.96 4.38 3.25 2.46 1.89
J (pz) (e/a.u.) Theory LCA-DFT-PBE LCAO-DFT-PBEsol 25.13 25.18 25.10 25.15 24.78 24.83 24.41 24.45 23.79 23.82 23.06 23.09 22.16 22.18 21.11 21.12 19.93 19.94 17.40 17.40 14.91 14.89 12.80 12.77 11.09 11.07 9.79 9.77 8.78 8.77 5.96 5.96 4.38 4.38 3.25 3.25 2.46 2.46 1.89 1.89
22
Expt. 24.81 ± 0.06 24.67 24.38 23.95 23.38 22.68 21.86 20.94 19.93 17.78 ± 0.05 15.60 13.56 11.79 10.33 9.17 ± 0.03 5.78 ± 0.02 4.14 ± 0.02 3.17 ± 0.01 2.41 ± 0.01 1.94 ± 0.01
Table 5. Unconvoluted theoretical Compton profiles of CdWO4 computed using DFT-VWN, DFT-PBE and DFT-PBEsol schemes within LCAO approximations as mentioned in text. The experimental data have also been listed along with the statistical error (±s) at a few points. pz (a.u.)
LCAO-DFT-VWN
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 1.0 1.2 1.4 1.6 1.8 2.0 3.0 4.0 5.0 6.0 7.0
27.45 27.40 27.07 26.66 25.98 25.19 24.22 23.07 21.83 19.16 16.53 14.26 12.34 10.83 9.66 6.49 4.93 3.81 2.96 2.31
J (pz) (e/a.u.) Theory LCAO-DFT-PBE LCAO-DFT-PBEsol 27.36 27.31 26.99 26.59 25.92 25.14 24.18 23.06 21.82 19.19 16.58 14.31 12.38 10.86 9.68 6.50 4.92 3.81 2.96 2.31
27.42 27.37 27.04 26.64 25.96 25.17 24.21 23.07 21.83 19.18 16.56 14.28 12.35 10.84 9.66 6.49 4.92 3.81 2.96 2.31
Expt. 26.11 ± 0.06 25.99 25.71 25.29 24.73 24.03 23.22 22.30 21.29 19.16 ± 0.04 16.98 14.88 13.05 11.45 10.19 ± 0.03 6.55 ± 0.02 4.96 ± 0.02 3.90 ± 0.01 2.95 ± 0.01 2.33 ± 0.01
Highlights · · · · ·
Presented first-ever Compton profile (CP) measurements on ZnWO4 and CdWO4. Analyzed CP data in terms of first-ever LCAO-DFT calculations. Computed energy bands and DOS using LCAO and FP-LAPW schemes. Discussed DOS in terms of Mulliken’s population. Interpreted bonding employing equal-valence-electron-density scale of CPs.
23
Figure 1
Fig. 1.
b*
Y
O
Y
O A
W
O O2
O O W
W
Z
A
Z
c*
W O1
O
G
X
X
a*
Figure 2
Fig. 2. (a)
(b) 6
Zn-s Zn-p Zn-d
4 2 0 2
W-s W-p W-d
DOS (states/eV)
Energy (eV)
1 0
O1-s O1-p
2 1 0
O2-s O2-p
1 0 18
ZnWO4 Zn W O1 O2
12 6 0 -20
-15
-10
-5
0
Energy (eV)
5
10
Figure 3
Fig. 3. (a)
(b)
W-s W-p W-d
DOS (Arb. unit)
Energy (eV)
Zn-s Zn-p Zn-d
O1-s O1-p
O2-s O2-p
ZnWO4 Zn W O1 O2
-20
-15
-10
-5
0
Energy (eV)
5
10
Figure 4
Fig. 4. (b)
(a)
Cd-s Cd-p Cd-d
W-s W-p W-d
1
DOS (states/eV)
Energy (eV)
12 8 4 0 2
0 O1-s O1-p
2 1 0
O2-s O2-p
1 0 30 24 18 12 6 0 -20
CdWO4 Cd W O1 O2
-15
-10
-5
0
Energy (eV)
5
10
Figure 5
Fig. 5. (a)
(b) Cd-s Cd-p Cd-d
DOS (Arb. unit)
Energy (eV)
W-s W-p W-d
O1-s O1-p
O2-s O2-p
CdWO4 Cd W O1 O2
-20
-15
-10
-5
0
Energy (eV)
5
10
Figure 6
Fig. 6.
0.3 0.2 0.1 0.0 -0.1 -0.2 0.2 DJ (e/a.u.)
LCAO-DFT-VWN LCAO-DFT-PBEsol LCAO-DFT-PBE
(a) J110- J100
(b) J001- J100
0.1 0.0 -0.1 0.2
(c) J001- J110
0.1 0.0 -0.1 0
1
2
3
pz (a.u.)
4
5
6
7
Figure 7
Fig. 7.
DJ(e/a.u.)
0.3 0.2 0.1 0.0 -0.1 -0.2
LCAO-DFT-VWN LCAO-DFT-PBE LCAO-DFT-PBEsol
(a) J110- J100
0.2
(b) J001- J100
0.1 0.0 -0.1 0.2
0
(c) 1J001- J110
2
3
2
3
4
5
6
7
4
5
6
7
0.1 0.0 -0.1 0
1
pz(a.u.)
Figure 8
Fig. 8. 0.4 ZnWO4
0.2
DJ (Theory-Expt.) (e/a.u.)
0.0 -0.2
LCAO-DFT-VWN LCAO-DFT-PBE LCAO-DFT-PBEsol I Error
-0.4 -0.6 1.2 CdWO4
0.8 0.4 0.0 -0.4 -0.8 0
1
2
3
pz(a.u.)
4
5
6
7
Figure 9
Fig. 9.
25
(a) LCAO-DFT-PBE
ZnWO4
20
CdWO4
15
-
J(pz)*pF (e )
10 5 0 (b) Experiment
20 15 10 5 0 0.0
0.5
1.0
1.5
2.0 pz/pF
2.5
3.0
3.5
4.0
www.elsevier.com/locate/radphyschem
PII: DOI: Reference:
S0969-806X(15)30027-X http://dx.doi.org/10.1016/j.radphyschem.2015.08.002 RPC6884
To appear in: Radiation Physics and Chemistry Received date: 22 May 2015 Revised date: 1 August 2015 Accepted date: 4 August 2015 Cite this article as: B.S. Meena, N.L. Heda, H.S. Mund and B.L. Ahuja, Compton profiles and electronic structure of monoclinic zinc and cadmium t u n g s t a t e s , Radiation Physics and Chemistry, http://dx.doi.org/10.1016/j.radphyschem.2015.08.002 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 galley proof before it is published in its final citable 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.
Compton profiles and electronic structure of monoclinic zinc and cadmium tungstates B. S. Meenaa, N. L. Hedab, H. S. Munda, and B.L. Ahujaa,* a
Department of Physics, M.L. Sukhadia University, Udaipur 313301, Rajasthan, India. Department of Pure and Applied Physics, University of Kota, Kota 324010, India.
b
Keywords: X-ray scattering: Electronic structure calculations: Electron momentum density: Density functional theory: Band structure calculations. PACS number(s): 13.60.Fz; 71.15.Ap; 71.15.Mb; 78.70.Ck * Corresponding author. Prof. B.L. Ahuja ([email protected]) Tel.: +91 941 4317048; Fax: +91 294 2411950. ABSTRACT We report the first ever Compton scattering study of ZnWO4 and CdWO4 using 20 Ci
137
Cs
Compton spectrometer at momentum resolution of 0.34 a.u. To compare the experimental Compton profiles, we have also deduced the momentum densities using density functional theory (DFT) within linear combination of atomic orbitals (LCAO) methods. It is seen that the experimental Compton profiles of both the tungstates give a better agreement with LCAO-DFT calculations within generalized gradient approximation (GGA) employing Perdew-BeckeErnzerhof (PBE) exchange and correlation energies than other approximations included in the present work. Further, energy bands, density of states (DOS) and band gaps have also been calculated using LCAO-DFT-GGA-PBE scheme and full potential linearized augmented plane wave method. Both the computational schemes show a semiconducting nature of both the tungstates, with a direct band gap at Y point of Brillouin zone. Further, a relative nature of bonding on equal-valence-electron-density scale shows more covalent character in ZnWO4 than CdWO4 which reconciles with the conclusions drawn using integrated DOS and Mulliken’s population data.
1
1. Introduction The tungstate materials like ZnWO4 and CdWO4 are very useful in scintillators, optical fibers, sensors, optical recording, masers, photocatalyst devices and security systems, etc. Regarding earlier studies, Nagirnyi et al. (2002) have reported energy transfer in ZnWO4 and CdWO4 while the scintillation pulse shape discrimination is discussed by Danevich et al. (2005). Itoh et al. (2006, 2007) have reported X-ray photoelectron spectroscopy (XPS) to investigate the electronic structures, reflection, luminescence-excitation, luminescence decay kinetics, photo-stimulated luminescence and photo-induced infrared absorption in both the tungstates. Huang and Zhu (2007) have reported high photocatalytic activity of ZnWO4. Fujita et al. (2008) have performed polarized reflection and XPS measurements and also the electronic structure of CdWO4. Kalinko et al. (2009) have undertaken ab-initio calculations with density functional theory (DFT) and pseudopotential schemes along with the linear combination of atomic orbitals (LCAO) within DFT for ZnWO4. Also in case of CdWO4, DFT calculations for electronic and optical properties were performed by Abraham et al. (2000). Lacomba-Perales et al. (2008) have reported room temperature experimental band gap between 3.9-4.4 eV for ZnWO4 and 4.15 eV of CdWO4 using optical-absorption and reflectance measurements. Evarestov et al. (2009) have applied LCAO method to probe the electronic and phonon properties of ZnWO4 and compared their results with available crystallographic data. Raman and photoluminescence spectroscopic measurements of ZnWO4 have been undertaken by Kalinko and Kuzmin (2009), whereas electronic and optical properties with oxygen vacancy in CdWO4 are reported by Zhou et al. (2010). Kim et al. (2011) have combined the electronic band structure calculations and electrochemical measurements to investigate the electronic and photovoltaic properties of such materials. Brik et al. (2012) have employed DFT within CASTEP code for optical and electronic
2
properties of ZnWO4 and CdWO4 and compared their results with the available XPS and reflectivity spectra. Recently, Khyzhun et al. (2013) have applied full potential linearized augmented plane wave (FP-LAPW) method to calculate the electronic properties of ZnWO4. In second attempt, Brik et al. (2013) have applied the DFT within CASTEP module to calculate the structural, electronic and elastic properties of both the tungstates at the ambient pressure and elevated pressure ranging between 5 to 10 GPa. Compton scattering is a well established technique to probe electronic properties of the materials (Cooper et al., 2004; Heda and Ahuja, 2010). In this technique, the measured quantity is known as Compton profile (CP) J(pz), which is projection of electron momentum density (EMD), r(p), along the direction of scattering vector (conventionally z-axis). Mathematically,
J ( pz ) =
òò
r(p) dpx dp y µ
d2σ . dΩ dE 2
(1)
In Eq. 1, pz is the component of linear momentum of electron along the z-axis and E2 is the energy of the scattered radiations. The r(p) can be evaluated using the momentum space wave
r function, c i ( p ) , which is derived from the Fourier transformation of real space wave function yi ( r ) .
In this paper, we report the first ever CP measurements of ZnWO4 and CdWO4 using 661.65 keV g-rays emitted by 20 Ci
137
Cs source (Ahuja et al., 2006). On the theoretical side, we have
employed the LCAO and FP-LAPW schemes (Dovesi et al., 2009; Blaha et al., 2011) to compute the theoretical CPs, energy bands, partial and total density of states (DOS), band gap and Mulliken's population (MP) data. Further, bonding aspects in these isoelectronic compounds have been analyzed using their equal-valence-electron-density (EVED) profiles.
3
2. Experiment The CPs of monoclinic ZnWO4 and CdWO4 have been measured using 20 Ci
137
Cs Compton
spectrometer at resolution of 0.34 a.u. (Gaussian full width at half maximum) (Ahuja et al. 2004, 2006). In such experiments, the overall resolution factor depends upon the resolution of detector and geometrical broadening of the incident and scattered photons. In individual experiments, the incident photons of energy 661.65 keV were scattered by the polycrystalline samples at scattering angle of 160±0.6° and the data were accumulated using a high purity Ge detector (Canberra, Ge crystal size 500 mm2 and 10 mm thickness) and associated electronics. Here, the intrinsic character of the Ge crystal was maintained by cooling it at liquid nitrogen temperature (77 K). The high purity (more than 99.5 %) sample was kept in an ampoule constructed using Mylar foil on both the sides. Due to difficulties in getting the large size single crystals (say 15 mm diameter and 2 mm thickness) and to compare the relative nature of bonding in terms of EVED profiles, we have measured the isotropic profiles. The density and thickness of ZnWO4(CdWO4) were 1.33(2.60) g/cm3 and 0.55(0.42) cm, respectively. During the total exposure time of 238.15(321.84) h for ZnWO4(CdWO4), an integrated Compton intensity of 2.10 x107(5.05 x 107) photons in the momentum range -10 to +10 a.u. (Compton region) was obtained. To extract true Compton profile, the raw data were corrected for background, detector response function (limited to stripping-off the low energy tail), detector efficiency, sample absorption, Compton scattering cross-section, etc. (Timms, 1989). Further, the data were corrected for multiple scattering events (Felsteiner et al., 1974) upto triple scattering. It was found that the effect of multiple to single scattering phenomena was 10.23(10.57) % in the momentum range -10 to +10 a.u. for ZnWO4 (CdWO4). We have not corrected our data for Bremsstrahlung background contribution because its contribution in the Compton profile region
4
is very small (Mathur and Ahuja, 2005). Finally, the isotropic CP was normalized to the corresponding free atom (FA) CP area 55.81 e- (61.97 e-) for ZnWO4 (CdWO4) (Biggs et al., 1975). A good agreement between the FA CPs and the experimental data in the high momentum regions validates the accuracy of data acquisition and process to extract true CPs. 3. Theory 3.1. LCAO method The directional and isotropic CPs, energy bands, partial and total DOS, MP charge transfer data and band gap have been computed using LCAO-DFT method (Dovesi et al., 2009) with local density and generalized gradient approximations (LDA and GGA, respectively). Using DFT theory, the Schrodinger equation can be written as, r r é Ñ2 ¶E xc [ρ( r )]ù r r r ρ( r ) ¢ V ( r ) d r + + + r ê ú ψ i ( r ) = ε i ψ i ( r ). ext ò r - r¢ ¶ρ( r ) úû êë 2
(2)
In Eq. 2 the first three terms in the Hamiltonian energy (left hand part) are kinetic, external potential and Coulomb exchange operators and the fourth term is the first order density derivative of Exc. The exchange-correlation density functional energy Exc for LDA/GGA is expressed as, / GGA [r(rr )] = E LDA xc
r r r r r ò r(r )e [r(r ) / r(r ), Ñ r (r ) ]dr
(3)
xc
here e xc is the exchange-correlation energy per particle in uniform electron gas and is defined differently in LDA and GGA (Dovesi et al., 2009). Further, the different kinds of exchange and correlation energies (Dovesi et al., 2009; Vosko et al., 1980; Perdew et al., 1996; Perdew et al., 2008) have been used within LDA and GGA as listed in Table 1. For the present computations, we have considered the all electron Gaussian basis sets of Zn, Cd and O taken from http://www.tcm.phy.cam.ac.uk/~mdt26/crystal.html, while due to non availability of all electron
5
basis sets for W we have used its pseudopotential basis sets as reported by Wadt and Hay (1985). The basis sets were energy optimized using BILLY software (Dovesi et al., 2009). The selfconsistent field (SCF) calculations have been performed with 170 k-points in the irreducible Brillouin zone (BZ) for both ZnWO4 and CdWO4. All theoretical CPs have been normalized to corresponding FA CPs area, as mentioned in section 2. 3.2. FP-LAPW method In addition to LCAO calculations, the energy bands, partial and total DOS and band gap of both the samples have been deduced using FP-LAPW-DFT with more accurate exchange and correlation potentials of Perdew-Becke-Ernzerhof (PBE) (Blaha et al., 2011). It is worth mentioning that in FP-LAPW method, the crystal potential outside the muffin-tin (MT) atomic spheres is approximated by plane waves, while within the MT it includes spherical harmonics. The MT radii (RMT) for Zn, W and O in case of ZnWO4 were taken to be 2.02, 1.78 and 1.58 Å, while in case of CdWO4, the RMT for Cd, W and O were kept to be 2.22, 1.80 and 1.55 Å, respectively. In case of both the tungstate, the SCF cycles were achieved by using 260 k points in the irreducible BZ. The values of RMT*Kmax (Kmax being the maximum amplitude of the reciprocal lattice vector k) and lmax were set to 7 and 10 for ZnWO4 and CdWO4, respectively. In both the computational schemes (LCAO and FP-LAPW) the lattice parameters (a=4.693 Å, b=5.721 Å, c= 4.928 Å and b=90.632°) along with the atomic positions of monoclinic ZnWO4 were taken from Khyzhun et al. (2013), while these parameters for CdWO4 (a= 5.029Å, b=5.860 Å, c= 5.072 Å and b=91.519°) were taken from the work of Abraham et al. (2000). In Fig. 1, we have plotted the unit cell of AWO4 (where A = Zn or Cd) with space group P2/c (13) using the visualization code of Kokalj (2003). In both the tungstates, there are two formulae per unit in the primitive cell and two non-equivalent positions of oxygen atoms (marked as O1 and O2).
6
4. Results and Discussion 4.1. MP analysis In Table 2, we have collated the MP charge transfer data of both the tungstates using LCAODFT-VWN, LCAO-DFT-PBE and LCAO-DFT-PBEsol schemes along with the data reported by Kalinko et al. (2009), Evarestov et al. (2009) and Brik et al. (2012). All the approximations and the available data show that Zn/Cd and W play the role of donor atoms while oxygen atoms (two non-equivalent O1 and O2) behave as acceptor atoms. In the present work, the total charge transfer from donor atoms to acceptor atoms in ZnWO4(CdWO4) is 3.94(4.14) e- using LCAODFT-PBE scheme. These values from LCAO-DFT-VWN and LCAO-DFT-PBEsol are respectively 3.98(4.16) e- and 3.96(4.14) e- for ZnWO4(CdWO4). It is known that large direct charge transfer value in the MP data indicates the dominance of ionic character, whereas small value of charge transfer highlights covalent character of materials. Therefore, the MP data from present calculations and that from Brik et al. (2012) computations predict more covalent character in ZnWO4 than CdWO4. From Table 2, it is quite interesting to note that in case of both the tungstates the amount of charge donated by Zn/Cd and W is unequally distributed among oxygen atoms (O1 and O2) which indicate the non-equivalent character of the oxygen atoms. It is worth mentioning that a similar trend of unequal charge distribution was also observed in WOx (x=2 and 3) (Heda and Ahuja, 2013; Heda and Ahuja, 2015) where the charge transfer from tungsten was unequally distributed among the oxygen atoms. From Table 2, our MP charge transfer data deduced from different approximations along with the data of Brik et al. (2012) indicate that the amount of charge in W, O1 and O2 atoms are approximately same in ZnWO 4 and CdWO4, while there are significant differences in the amplitude of charge at Zn and Cd sites. Such difference may be due to the large ionic character of Cd in CdWO4 than that of Zn in
7
ZnWO4. Since, the basis sets used in present computations involve sufficiently diffuse external atomic orbitals, the MP analysis is expected to be quite reliable in both the tungstates. 4.2. Energy bands and DOS In Figs. 2-5, we have plotted energy bands along with partial and total DOS of ZnWO4 and CdWO4 using FP-LAPW-DFT-PBE and LCAO-DFT-PBE schemes. Due to the similar topology of the energy bands and DOS using LCAO-DFT-VWN and LCAO-DFT-PBEsol schemes to that of reported data, we have not shown energy bands and DOS corresponding to these approximations. It is seen that except some fine structures, the energy bands and DOS are in reasonable agreement with the available data (Abraham et al., 2000; Khyzhun et al, 2013). Since the energy bands and DOS are almost similar for FP-LAPW-DFT-PBE and LCAO-DFT-PBE schemes for both the tungstates, we now discuss the energy bands and DOS derived from FPLAPW-DFT-PBE scheme as shown in Figs. 2 and 4. These energy bands and DOS of ZnWO4 and CdWO4 (Figs. 2, 4) can be divided into three major parts as discussed below: (i) The lowest energy bands in the -18.44 to -16.02 eV (-18.18 to -16.04 eV) are due to 2sp states of oxygen atoms (two non-equivalent O1 and O2) for ZnWO4 (CdWO4). (ii) The second region from -6.50 eV to Fermi energy (EF) level (-6.78 eV to EF) mainly corresponds to 3d (4d) states of Zn (Cd) and 2sp states of oxygen atoms for ZnWO4 (CdWO4). Therefore, it is evident that the 3d (4d) states of Zn (Cd) and 2sp states of oxygen atoms form valence band maxima (VBM) in ZnWO4 (CdWO4). (iii) The third region in ZnWO4 (Fig. 2) is divided in two parts, namely (a) from 3.00 to 5.07 eV which is mainly contributed by 5d states of W atoms with a small contribution of oxygen atoms (O1 and O2) and (b) 5.44 eV and above which is due to 5d states of W with a small contribution of 3d states of Zn and 2sp states of oxygen (O1 and O2). While in case of CdWO4 (Fig. 4), the
8
region starting from 3.04 eV are mainly due to 5d states of W with a small contribution of 4d states of Cd and 2sp states of oxygen (O1 and O2). It is observed that the 5d states of W atoms are mainly responsible for the conduction band minima (CBM) in both the tungstates. It is seen that the VBM and CBM occur at Y point of BZ which lead to the direct band gap in both the tungstates. The DOS curves shown in Figs. 2-5 (right hand side) also confirm the semiconducting character of both the tungstates. In Table 3, we have compiled the band gap values obtained from LCAO-DFT-VWN, LCAO-DFT-PBE, LCAO-DFT-PBEsol and FPLAPW-DFT-PBE calculations along with the available theoretical and experimental band gap data (Kalinko et al., 2009; Abraham et al., 2000; Lacomba-Perales et al., 2008; Evarestov et al., 2009; Kim et al., 2011; Brik et al., 2012; Khyzhun et al, 2013; Sun et al., 2010; Zhao et al., 2006). Our band gap using FP-LAPW-DFT-GGA scheme is less than experimental data (Nagirnyi et al., 2002; Zhao et al., 2006), although it is in good agreement with earlier theoretical data (Abraham et al., 2000; Kim et al., 2011; Brik et al., 2012; Khyzhun et al, 2013, Sun et al., 2010). It is understandable because the first principle calculations with DFT approximation underestimate the band gap of semiconductor. In case of ZnWO4, our LCAO based band gap data slightly differ from the LCAO data of Kalinko et al. (2009) which may be due to use of pseudopotential based basis sets of Zn used by these authors, while we have used the all electron Gaussian basis sets for Zn atom. To find more accurate theoretical band gap, we have also computed the band gap using FP-LAPW with the latest modified Becke-Johnson (mBJ) potential (Tran and Blaha, 2009). It is known that the mBJ potential is a simple modification of the potentials defined by Becke and Johnson (2006) and predicts more accurate value of the band gap as reported by different workers (Lacomba-Perales et al., 2008; Zhao et al., 2006). Further, we have also calculated the integrated DOS from -6.50 eV to EF (-6.78 eV to EF) for ZnWO4
9
(CdWO4) as plotted in Figs. 2 and 4 to check the unequal distribution of charge transfer among two oxygen atoms in both the tungstates. It is found that in case of ZnWO4 the value of the integrated DOS for O1 atom (14.465 e-) is higher than that of O2 atom (14.344 e-), while for CdWO4 the value for O1 (14.015 e-) is less than that of O2 (14.179 e-). Therefore, the trend of integrated DOS is in tune with the MP data reported in Table 2. 4.3. Compton profiles In Figs. 6-7, we have plotted the anisotropies between the pairs of unconvoluted directional CPs of both the tungstates namely J110-J100, J001-J100 and J001-J110 using LCAO-DFT-VWN, LCAODFT-PBE and LCAO-DFT-PBEsol schemes. It is seen that general trend of oscillations in the anisotropies (J110-J100, J001-J100 and J001-J110) using all the reported approximations in both the materials is almost identical. In Figs. 6-7, after pz≥3 a.u. there is very small differences in anisotropies (J110-J100, J001-J100 and J001-J110), which is understandable because this region is dominated by core electrons whose contribution cancels out while taking the directional differences. We can correlate the various oscillations in anisotropies in momentum densities (Figs. 6-7) with degenerate states in energy bands and their cross-overs in the vicinity of EF. The positive value of anisotropies in momentum densities near pz=0.0 a.u. in ZnWO4 and CdWO4 in Figs. 6-7 (a-b) and negative value in Figs. 6-7(c) are due to the large degenerate states along G-Y [110] direction as compared to G-X [100] and G-Z [001] directions. We observe that the degenerate states along G-X [100] are higher than those of G-Z [001] direction which leads to higher momentum densities in G-X branch. Further, the negative amplitude at pz=0.7 a.u. along J110-J100 in Fig. 6(a) of ZnWO4 arises from the zone boundary of G-X (0.35 a.u.; n=2) branch. Similarly, the positive value of J001-J110 in Fig. 6(c) at pz=0.7 a.u. comes from the zone boundary of G-Z (0.33 a.u.; n=2) branch. Similarly, we can explain anisotropic effects in momentum 10
densities of ZnWO4 and CdWO4 at other pz values using energy bands and DOS. It may be mentioned that some fine structures may not be visible due to cancellation of the momentum densities while taking the differences between directional CPs. In Figs. 8 (a-b), the difference profiles between convoluted theoretical (LCAO-DFT-VWN, LCAO-DFT-PBE and LCAO-DFTPBEsol) and experimental data have been shown for ZnWO4 and CdWO4, respectively. Further, in Tables 4-5 we have included the unconvoluted CP data derived from LCAO-DFT-VWN, LCAO-DFT-PBE and LCAO-DFT-PBEsol schemes along with the experimental data with statistical error for both the tungstates. It is observed that deviations between theory and experiment using the present approximations are almost identical. In the low momentum region, LCAO-DFT-VWN, LCAO-DFT-PBE and LCAO-DFT-PBEsol schemes show different amplitudes of deviations (Tables 3 and 4, and Fig. 5) which are understandable in terms of underlying assumptions of different exchange and correlation potentials used in different approximations. We feel that differences between the theoretical and experimental Compton profiles in the region pz˂5 a.u. may be due to non-inclusion of relativistic effects and Lam– Platzman (LP) correlation correction (Cooper et al., 2004). Further, to conclude about quantitative agreement between theory (LCAO-DFT-VWN, LCAO-DFT-PBE and LCAO-DFTPBEsol based profiles) and experiment, we have undertaken χ2 fitting. It is seen that LCAODFT-PBE scheme gives the best agreement with the experimental data. A better reconciliation of LCAO-DFT–PBE based CP with experiment than to LCAO-DFT–VWN shows a superiority of GGA over the LDA in both the tungstates. 4.4. EVED profiles Now we discuss the relative nature of bonding in these tungstates by scaling the profiles on EVED scale. The EVED profiles are drawn between [J(pz)*pF] v/s pz/pF, with pF as Fermi
11
momentum. The pF value of ZnWO4 (CdWO4) were taken to be 1.42 (1.34) a.u. Such method has been successfully applied to study the relative nature of bonding in different systems as reported by Reed and Eisenberger (1972), Heda et al. (2007), Arora et al. (2009), Ahuja et al. (2013, 2015), and Bhamu et al. (2013). In Fig. 9, we have plotted the EVED profiles for LCAO-DFTPBE and experiment for both the tungstates. All the EVED profiles were normalized to 21 electrons (valence) in the momentum range 0-4 a.u. It is seen from the Figs. 9(a-b) that at pz/pF =0 a.u. the theoretical (LCAO-DFT-PBE) and experimental EVED profiles of ZnWO4 are 1.97 and 8.02 % higher than those of CdWO4, respectively. Such trend suggests more localization of charge in the bond direction of ZnWO4 as compared to that in CdWO4. Since the sharpness of EVED profile represents covalent character, we conclude that ZnWO4 is more covalent than CdWO4. This trend of relative bonding of EVED is also in accordance with the MP data of Table 2 and integrated DOS. 5. Conclusions Measurements on electron momentum density of ZnWO4 and CdWO4 have been reported using 661.65 keV g-rays to test applicability of exchange and correlation potentials within local density and generalized gradient approximations. A comparison of theoretical Compton profiles (based on different exchange and correlation energies within LCAO-DFT) and corresponding experiment shows that the best agreement between experimental and theoretical profiles of both the tungstates is produced by Perdew-Burke-Ernzerhof (PBE) exchange and correlation potentials with generalized gradient approximation. Further, the energy bands, partial and total density of states (DOS), band gap and Mulliken's population (MP) data have also been reported using LCAO-DFT-PBE along with FP-LAPW within PBE scheme. Both the theories show a semiconducting nature of ZnWO4 and CdWO4. A relative nature of bonding in both the
12
tungstates is reported using equal-valence-electron density profiles, MP data and integrated DOS. It is concluded that ZnWO4 has more covalent character than CdWO4. The DOS have also been discussed in terms of charge transfer in the constituents. Unconvoluted anisotropies in Compton profiles are found to be in accordance to degenerate states in energy bands. Acknowledgements Prof. R. Dovesi and Prof. P. Blaha are thanked for providing LCAO and FP-LAPW codes, respectively. The work is supported by SERB (DST), New Delhi through a major research project (Grant No. SR/S2/CMP-40/2011). One of us (BSM) is thankful to UGC, New Delhi for UGC-BSR Meritorious fellowship. HSM thanks SERB (DST), New Delhi for financial assistant under DST Fast Track Young Scientist scheme.
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Cooper, M.J., Mijnarends, P.E., Shiotani, N., Sakai, N., Bansil, A., 2004. X-ray Compton Scattering, Oxford Science Publications, Oxford University Press, New York, and references therein. Danevich, F.A., Georgadze, A.Sh., Kobychev, V.V., Kropivyansky, B.N., Nagorny, S.S., Nikolaiko, A.S., Tretyak, V.I., Yurchenko, S.S., Zdesenko, S.Yu., Zdesenko, Yu.G., Bizzeti, P.G., Fazzini, T.F., Maurenzig, P.R., Solsky, I.M., Brudanin, V.B., Avignone III, F.T., 2005. Scintillation pulse shape discrimination with CaWO4, ZnWO4 and CdWO4 crystal. Fun. Mat. 12, 269-273. Dovesi, R., Saunders, V.R., Roetti, C., Orlando, R., Zicovich-Wilson, C.M., Pascale, F., Civalleri, B., Doll, K., Harrison, N.M., Bush, I.J., D’Arco, Ph., Llunell, M., 2009. CRYSTAL09 User’s Manual. University of Torino, Torino, Italy, and references therein. Evarestov, R.A., Kalinko, A., Kuzmin, A., Losev, M., Purans, J., 2009. First-principles LCAO calculations on 5d transition metal oxides: electronic and phonon properties. Integrated Ferroelectrics 108, 1-10. Felsteiner, J., Pattison, P., Cooper, M.J., 1974. Effect of multiple scattering on experimental Compton profiles: a Monte-Carlo calculation. Philos. Mag. 30, 537–548. Fujita, M., Itoh, M., Katagiri, T., Iri, D., Kitaura, M., Mikhailik, V.B., 2008. Optical anisotropy and electronic structures of CdMoO4 and CdWO4 crystals: polarized reflection measurements, x-ray photoelectron spectroscopy, and electronic structure calculations. Phys. Rev. B 77, 155118-1-155118-7. Heda, N.L., Mathur, S., Ahuja, B.L., Sharma, B.K., 2007. Compton profiles and band structure calculations of CdS and CdTe. Phys. Stat. Sol. (b) 244, 1070–1081. Heda, N.L., Ahuja, B.L., 2010. Role of in-house Compton spectrometer in probing the electronic properties. In: Ahuja, B.L. (Ed.), Recent Trends in Radiation Physics Research, Himanshu Publications, New Delhi, India, pp. 25-30. Heda, N.L., Ahuja, B.L., 2013. Electronic properties and electron momentum density of monoclinic WO3. Comput. Mater. Sci. 72, 49-53. Heda, N.L., Ahuja, U., 2015. Electronic properties and Compton scattering studies of monoclinic tungsten dioxide. Rad. Phys. Chem. 106, 33-39 Huang, G., Zhu, Y., 2007. Synthesis and photocatalytic performance of ZnWO4 catalyst. Mat. Sci. Eng. B 139, 201-208. Itoh, M., Fujita, N., Inabe, Y., 2006. X-ray photoelectron spectroscopy and electronic structures of scheelite- and wolframite-type tungstate crystals. J. Phys. Soc. Japan 75, 084705-1-084705-8. 15
Itoh, M., Katagiri, T., Aoki, T., Fujita, M., 2007. Photo-stimulated luminescence and photo-induced infrared absorption in ZnWO4. Radiat. Meas. 42, 545-548. Kalinko, A., Kuzmin, A., 2009. Raman and photoluminescence spectroscopy of zinc tungstate powders. J. Lumin. 129, 1144-1147. Kalinko, A., Kuzmin, A., Evarestov, R.A., 2009. Ab initio study of the electronic and atomic structure of the wolframite-type ZnWO4. Solid State Comm. 149, 425-428. Khyzhun, O.Y., Bekenev, V.L., Atuchin, V.V., Galashov, E.N., Shlegel, V.N., 2013. Electronic properties of ZnWO4 based on ab initio FP-LAPW band-structure calculations and X-ray spectroscopy data. Mat. Chem. Phys. 140, 588-595. Kim, D.W., Cho, I.-S., Shin, S.S., Lee, S., Noh, T.H., Kim, D.H., Jung, H.S., Hong, K.S., 2011. Electronic band structures and photovoltaic properties of MWO4 (M=Zn, Mg, Ca, Sr) compounds. J. Solid State Chem. 184, 2103-2107. Kokalj, A., 2003. Computer graphics and graphical user interfaces as tool in simulations of matter at the atomic scale. Comput. Mater. Sci. 28, 155–168. Lacomba-Perales, R., Ruiz-Fuertes, J., Errandonea, D., Martinez-Garcia, D., Segura, A., 2008. Optical absorption of divalent metal tungstates: correlation between the bandgap energy and the cation ionic radius. Euro. Phys. Lett. 83, 37002-37002-5. Mathur, S., Ahuja, B.L., 2005. Quantitative determination of Bremsstrahlung background in Compton measurements. Phys. Lett. A 335, 245–250. Nagirnyi, V., Feldbach, E., Jönsson, L., Kirm, M., Kotlov, A., Lushchik, A., Nefedov, V.A., Zadneprovski, B.I., 2002. Energy transfer in ZnWO4 and CdWO4 scintillators. Nucl. Instrum. Methods A 486, 395-398. Perdew, J.P., Burke, K., Ernzerhof, M., 1996. Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865–3868. Perdew, J.P., Ruzsinszky, A., Csonka, G.I., Vydrov, O.A., Scuseria, G.E., Constantin, L.A., Zhou, X., Burke, K., 2008. Restoring the density-gradient expansion for exchange in solids and surfaces. Phys. Rev. Lett. 100, 136406-1–136406-4. Reed, W.A., Eisenberger, P., 1972. Gamma-ray Compton profiles of diamond, silicon, and germanium. Phys. Rev. B 6, 4596–4604. Sun, H., Fan, W., Li, Y., Cheng, X., Li, P., Zhao, X., 2010. Origin of the improved photocatalytic activity of F-doped ZnWO4: a quantum mechanical study. J. Solid State Chem. 183, 3052-3057.
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Timms, D.N., 1989. Compton Scattering Studies of Spin and Momentum Densities (unpublished Ph. D. Thesis). University of Warwick, England. Tran, F., Blaha, P., 2009. Accurate band gaps of semiconductors and insulators with a semilocal exchange-correlations potential. Phys. Rev. Lett. 102, 226401-1–226401-4. Vosko, S.H., Wilk, L., Nusair, M., 1980. Accurate spin-dependent electron liquid correlation energies for local spin density calculations: a critical analysis. Can. J. Phys. 58, 1200–1211. Wadt, W.R., Hay, P.J., 1985. Ab initio effective core potentials for molecular calculations. Potentials for main group elements Na to Bi. J. Chem. Phys. 82, 284-298. Zhao, X., Yao, W., Wu, Y., Zhang, S., Yang, H., Zhu, Y., 2006. Fabrication and photoelectrochemical properties of porous ZnWO4 film. J. Solid State Chem. 179, 2562-2570. Zhou, X., Liu, T., Zhang, Q., Cheng, F., Qiao, H., 2010. Electronic structure and optical properties of CdWO4 with oxygen vacancy studied from first principles. Solid State Comm. 150, 5-8.
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Figure captions Fig. 1. Structural sketch of AWO4 (A = Zn, Cd) plotted using software tool of Kokalj (2003). Fig. 2. FP-LAPW-DFT-PBE scheme based energy bands (left hand side) of monoclinic ZnWO4 with the Fermi energy (EF) at zero energy reference level. The positions of Γ, Z, X and Y vertices correspond to (0,0,0), (0,0,1/2), (1/2,0,0) and (0,1/2,0), respectively. Partial and total density of states for different constituents of ZnWO4 are shown in right hand side panel. Fig. 3. Same as Fig. 2 except the scheme, which is LCAO-DFT-PBE. Fig. 4. Same as Fig. 2 except the sample, which is CdWO4. Fig. 5. Same as Fig. 2 except the sample and scheme, which are CdWO4 and LCAO-DFT-PBE, respectively. Fig. 6. Anisotropies in the unconvoluted theoretical Compton profiles of monoclinic ZnWO4 along (a) J110-J100, (b) J001-J100 and (c) J001-J110 using LCAO-DFT-VWN, LCAO-DFT-PBE and LCAO-DFT-PBEsol schemes as mentioned in the text. The solid lines are drawn only to guide the eyes. Fig. 7. Same as Fig. 6 except the sample, which is monoclinic CdWO4. Fig. 8. The difference between convoluted isotropic theoretical (LCAO-DFT-VWN, LCAODFT-PBE and LCAO-DFT-PBEsol) and experimental Compton profiles for (a) ZnWO4 and (b) CdWO4 along with the experimental error (±σ) at few points. Fig. 9. Theoretical (LCAO-DFT-PBE) and experimental equal-valence-electron-density (EVED) profiles of isoelectronic ZnWO4 and CdWO4.
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Table 1. The exchange and correlation schemes used in LDA and GGA within the framework of LCAO approximations (Dovesi et al., 2009). Scheme
Exchange
Correlations
LCAO-DFT-LDA
Dirac–Slater (Dovesi et al., 2009)
LCAO-DFT-GGA
Perdew-Becke-Ernzerhof (PBE) (Perdew et al., 1996) PBE functional revised for solids (PBEsol) (Perdew et al., 2008)
Vosko-Wilk-Nusair (VWN) (Vosko et al., 1980) PBE (Perdew et al., 1996)
LCAO-DFT-GGA
19
PBEsol (Perdew et al., 2008)
Nomenclature used in text LCAO-DFT-VWN LCAO-DFT-PBE LCAO-DFTPBEsol
Table 2. The Mulliken's population (MP) charge transfer data from donor atoms (Zn, Cd and W) to the acceptor atoms (two non-equivalent O1 and O2) in ZnWO4 and CdWO4 using the different combinations of exchange and correlation energies (DFT-VWN, DFT-PBE and DFT-PBEsol) within LCAO method as mentioned in the text.
Scheme
(a) Present calculations · LCAO-DFT-VWN · LCAO-DFT-PBE · LCAO-DFT-PBEsol (b) Kalinko et al. (2009) · LCAO-LDA · LCAO-PW91 · LCAO-PBE · LCAO-B3PW · LCAO-B3LYP · LCAO-PBE0 (c) Evarestov et al. (2009) · LCAO-B3PW (d) Brik et al. (2012) · DFT-LDA · DFT-GGA
Amount of charge transfer (e-) ZnWO4 CdWO4 Donor Acceptor Donor Acceptor atoms atoms atoms atoms Zn W O1 O2 Cd W O1 O2 1.26 1.27 1.27
2.72 2.67 2.69
1.10 1.08 1.09
0.89 0.89 0.89
1.48 1.50 1.50 1.55 1.54 1.57
3.58 3.52 3.51 3.72 3.76 3.75
1.32 1.30 1.30 1.37 1.38 1.38
1.22 1.21 1.21 1.27 1.28 1.28
1.54
2.76
1.13
1.02
1.19 1.26
1.38 2.43
0.67 0.69
0.62 0.65
20
1.43 1.44 1.46
2.73 2.70 2.68
0.93 0.92 0.93
1.15 1.15 1.14
1.25 1.30
1.38 1.43
0.69 0.71
0.63 0.65
Table 3. The band gap in ZnWO4 and CdWO4 computed using LCAO (DFT-VWN, DFT-PBE, DFT-PBEsol), FP-LAPW-PBE and the FP-LAPW-mBJ schemes along with the available data. Approach
Band gap (in eV)
(i) Theory (a) Present computations · LCAO-DFT-VWN · LCAO-DFT-PBE · LCAO-DFT-PBEsol · FP-LAPW-DFT-PBE · FP-LAPW-mBJ (b) Kalinko et al. (2009) · LCAO-LDA · LCAO-PW91 · LCAO-PBE · LCAO-B3PW · LCAO-B3LYP · LCAO-PBE0 (c) Abraham et al. (2000) · DFT-LDA (d) Evarestov et al. (2009) · LCAO-B3PW (e) Kim et al. (2011) · DFT-GGA (f) Brik et al. (2012) · DFT-LDA · DFT-GGA (g) Khyzhun et al. (2013) · FP-LAPW-GGA (h) Sun et al. (2010) · DFT-GGA (ii) Experiment · Lacomba-Perales et al. (2008) · Zhao et al. (2006)
ZnWO4
CdWO4
2.20 2.17 2.16 3.00 3.92
2.43 2.42 2.41 3.05 4.24
2.31 2.33 2.31 4.27 4.22 4.60 2.94 5.40 2.95 2.82 2.90
2.96 3.00
3.00 2.88 3.9-4.4 4.01
21
4.15
Table 4. Unconvoluted theoretical Compton profiles of monoclinic ZnWO4 computed using DFT-VWN, DFT-PBE and DFT-PBEsol schemes within LCAO approximations as mentioned in text. The experimental data have also been listed along with the statistical error (±s) at a few points. pz (a.u.) 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 1.0 1.2 1.4 1.6 1.8 2.0 3.0 4.0 5.0 6.0 7.0
LCAO-DFT-VWN 25.21 25.17 24.85 24.47 23.84 23.10 22.19 21.12 19.94 17.38 14.87 12.75 11.06 9.77 8.77 5.96 4.38 3.25 2.46 1.89
J (pz) (e/a.u.) Theory LCA-DFT-PBE LCAO-DFT-PBEsol 25.13 25.18 25.10 25.15 24.78 24.83 24.41 24.45 23.79 23.82 23.06 23.09 22.16 22.18 21.11 21.12 19.93 19.94 17.40 17.40 14.91 14.89 12.80 12.77 11.09 11.07 9.79 9.77 8.78 8.77 5.96 5.96 4.38 4.38 3.25 3.25 2.46 2.46 1.89 1.89
22
Expt. 24.81 ± 0.06 24.67 24.38 23.95 23.38 22.68 21.86 20.94 19.93 17.78 ± 0.05 15.60 13.56 11.79 10.33 9.17 ± 0.03 5.78 ± 0.02 4.14 ± 0.02 3.17 ± 0.01 2.41 ± 0.01 1.94 ± 0.01
Table 5. Unconvoluted theoretical Compton profiles of CdWO4 computed using DFT-VWN, DFT-PBE and DFT-PBEsol schemes within LCAO approximations as mentioned in text. The experimental data have also been listed along with the statistical error (±s) at a few points. pz (a.u.)
LCAO-DFT-VWN
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 1.0 1.2 1.4 1.6 1.8 2.0 3.0 4.0 5.0 6.0 7.0
27.45 27.40 27.07 26.66 25.98 25.19 24.22 23.07 21.83 19.16 16.53 14.26 12.34 10.83 9.66 6.49 4.93 3.81 2.96 2.31
J (pz) (e/a.u.) Theory LCAO-DFT-PBE LCAO-DFT-PBEsol 27.36 27.31 26.99 26.59 25.92 25.14 24.18 23.06 21.82 19.19 16.58 14.31 12.38 10.86 9.68 6.50 4.92 3.81 2.96 2.31
27.42 27.37 27.04 26.64 25.96 25.17 24.21 23.07 21.83 19.18 16.56 14.28 12.35 10.84 9.66 6.49 4.92 3.81 2.96 2.31
Expt. 26.11 ± 0.06 25.99 25.71 25.29 24.73 24.03 23.22 22.30 21.29 19.16 ± 0.04 16.98 14.88 13.05 11.45 10.19 ± 0.03 6.55 ± 0.02 4.96 ± 0.02 3.90 ± 0.01 2.95 ± 0.01 2.33 ± 0.01
Highlights · · · · ·
Presented first-ever Compton profile (CP) measurements on ZnWO4 and CdWO4. Analyzed CP data in terms of first-ever LCAO-DFT calculations. Computed energy bands and DOS using LCAO and FP-LAPW schemes. Discussed DOS in terms of Mulliken’s population. Interpreted bonding employing equal-valence-electron-density scale of CPs.
23
Figure 1
Fig. 1.
b*
Y
O
Y
O A
W
O O2
O O W
W
Z
A
Z
c*
W O1
O
G
X
X
a*
Figure 2
Fig. 2. (a)
(b) 6
Zn-s Zn-p Zn-d
4 2 0 2
W-s W-p W-d
DOS (states/eV)
Energy (eV)
1 0
O1-s O1-p
2 1 0
O2-s O2-p
1 0 18
ZnWO4 Zn W O1 O2
12 6 0 -20
-15
-10
-5
0
Energy (eV)
5
10
Figure 3
Fig. 3. (a)
(b)
W-s W-p W-d
DOS (Arb. unit)
Energy (eV)
Zn-s Zn-p Zn-d
O1-s O1-p
O2-s O2-p
ZnWO4 Zn W O1 O2
-20
-15
-10
-5
0
Energy (eV)
5
10
Figure 4
Fig. 4. (b)
(a)
Cd-s Cd-p Cd-d
W-s W-p W-d
1
DOS (states/eV)
Energy (eV)
12 8 4 0 2
0 O1-s O1-p
2 1 0
O2-s O2-p
1 0 30 24 18 12 6 0 -20
CdWO4 Cd W O1 O2
-15
-10
-5
0
Energy (eV)
5
10
Figure 5
Fig. 5. (a)
(b) Cd-s Cd-p Cd-d
DOS (Arb. unit)
Energy (eV)
W-s W-p W-d
O1-s O1-p
O2-s O2-p
CdWO4 Cd W O1 O2
-20
-15
-10
-5
0
Energy (eV)
5
10
Figure 6
Fig. 6.
0.3 0.2 0.1 0.0 -0.1 -0.2 0.2 DJ (e/a.u.)
LCAO-DFT-VWN LCAO-DFT-PBEsol LCAO-DFT-PBE
(a) J110- J100
(b) J001- J100
0.1 0.0 -0.1 0.2
(c) J001- J110
0.1 0.0 -0.1 0
1
2
3
pz (a.u.)
4
5
6
7
Figure 7
Fig. 7.
DJ(e/a.u.)
0.3 0.2 0.1 0.0 -0.1 -0.2
LCAO-DFT-VWN LCAO-DFT-PBE LCAO-DFT-PBEsol
(a) J110- J100
0.2
(b) J001- J100
0.1 0.0 -0.1 0.2
0
(c) 1J001- J110
2
3
2
3
4
5
6
7
4
5
6
7
0.1 0.0 -0.1 0
1
pz(a.u.)
Figure 8
Fig. 8. 0.4 ZnWO4
0.2
DJ (Theory-Expt.) (e/a.u.)
0.0 -0.2
LCAO-DFT-VWN LCAO-DFT-PBE LCAO-DFT-PBEsol I Error
-0.4 -0.6 1.2 CdWO4
0.8 0.4 0.0 -0.4 -0.8 0
1
2
3
pz(a.u.)
4
5
6
7
Figure 9
Fig. 9.
25
(a) LCAO-DFT-PBE
ZnWO4
20
CdWO4
15
-
J(pz)*pF (e )
10 5 0 (b) Experiment
20 15 10 5 0 0.0
0.5
1.0
1.5
2.0 pz/pF
2.5
3.0
3.5
4.0