Synthesis, Characterization, and Photocatalytic Properties of ZrMo2O8

May 21, 2009 - Prangya Parimita Sahoo , S. Sumithra , Giridhar Madras , and T. N. Guru Row. Inorganic Chemistry 2011 50 (18), 8774-8781. Abstract | Fu...
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J. Phys. Chem. C 2009, 113, 10661–10666

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Synthesis, Characterization, and Photocatalytic Properties of ZrMo2O8 Prangya Parimita Sahoo, Sumithra S., Giridhar Madras, and T. N. Guru Row* Solid State and Structural Chemistry Unit, Indian Institute of Science, Bangalore 560012, India ReceiVed: March 1, 2009; ReVised Manuscript ReceiVed: April 29, 2009

ZrMo2O8 was synthesized via two routes, namely, the traditional solid-state method and the solution combustion method. The compounds were characterized by powder X-ray diffraction, UV-visible spectroscopy, scanning electron microscopy, and transmission electron microscopy. The crystals belong to a trigonal crystal system, space group P3j1c (No. 163) with a ) 10.1391(6) Å, c ) 11.7084(8) Å, and Z ) 6. The band gap of the compounds was around 2.7 eV, and DFT calculations suggest the indirect nature of the band gap. The irregular MoO4 tetrahedra create a dipole and inhibit the process of electron-hole recombination, thereby making the material photoactive. The photocatalytic activity of the compounds prepared by both routes has been investigated for the degradation of various dyes under UV irradiation, and this showed the specificity of the compounds towards the degradation of non-anthraquinonic dyes. Introduction ZrMo2O8 belongs to the family AX2O8 with A ) Zr or Hf and X ) Mo or W. These compounds have generated considerable attention in recent times owing to the display of negative thermal expansion (NTE) on heating.1-5 Further, this family of compounds exhibits polymorphism with ZrMo2O8 existing in a variety of polymorphic modifications depending on pressure, temperature, and the state of hydration. At ambient pressure, the thermodynamically stable polymorphs are the trigonal RZrMo2O8 and monoclinic β-ZrMo2O8, which are stable at high and low temperatures, respectively.6,7 The cubic γ-ZrMo2O8 form has been isolated by controlled dehydration of ZrMo2O7(OH)2 · 2H2O, and the orthorhombic low-temperature form LT-ZrMo2O8 has also been identified.8,9 High-pressure synchrotron X-ray powder-diffraction studies show the transformation of R-ZrMo2O8 to a monoclinic δ-ZrMo2O8 at around 1.11 GPa and a triclinic ε phase at 2.5 GPa.10 Measurement of ac conductance in R-ZrMo2O8 with variations in pressure has been found to be mediated by structural changes.11 ZrMo2O8 gel finds important applications as inorganic ion exchangers and as a potential alternative for the preparation of 99mTc generators using 99Mo produced by neutron activation.12,13 Recently, a study of sodium and lithium insertion into the ZrMo2O8 framework was carried out to evaluate the compound as a possible energy storage device.14 It also has been observed that binary mixedoxide catalysts based on MoO3-ZrO2 have been used to catalyze several reactions, including 2-propanol dehydration, oxidative dehydrogenation (ODH) of propane, and selective oxidation of dimethyl ether to formaldehyde.15-17 “Combustion synthesis” (CS), also known as “self-propagating high-temperature synthesis”, is based on a simple technique resulting in the formation of high-purity products with reduced particle sizes and larger surface area, while stabilizing metastable phases. This technique has been extensively utilized for the synthesis of a plethora of compounds, including structural and functional ceramics, composites, alloys, intermetallics, nanomaterials, and catalysts, as summarized in reviews.18,19 * Corresponding author. Phone: +91-80-2292796. Fax: +91-80-3601310. E-mail: [email protected].

Semiconductor photocatalysis is an established technology for environment remediation20 with several applications ranging from the destruction of bacteria, wastewater treatment, odor control, production of hydrogen to the fixation of nitrogen.21 In general, oxide semiconductors with band gap energy sufficient to overcome the energy barrier of the redox potential of the H2O/ · OH are suitable as photocatalysts. In this article, we describe the synthesis and structure of the thermodynamically stable polymorph, trigonal ZrMo2O8. The description of the band structure of ZrMo2O8 based on DFT calculations indicates it is a photocatalytic material. The photocatalytic property of the polymorph prepared via combustion synthesis is compared with that of the conventionally prepared (solid-state) polymorph and commercial titania (Degussa P-25). Experimental Section Materials. MoO3 (S. D. Fine-Chem Ltd., India, 99%), Zr(NO3)4 · 5H2O (Sigma Aldrich, 99.99%), (NH4)6Mo7O24 · 4H2O (S. D. Fine-Chem Ltd., India, 99%), and glycine (S. D. FineChem Ltd., India, 99%) were used as such. ZrO2 was synthesized by heating Zr(NO3)4 · 5H2O (BDH England, 99%) for 4 h at 550 °C. Methylene blue (MB), Orange G (OG), Rhodamine B (RB), Remazol Brilliant Blue R (RBBR), Alizarin Green (AG), Congo Red (CR), and anthraquinone-2-sulfonic acid (AQ) were obtained from S. D. Fine-Chem Ltd., India. Water was double-distilled and filtered through a Millipore membrane filter prior to use. Synthesis. For the preparation of solid-state trigonal (SST) ZrMo2O8, ZrO2 and MoO3 were taken in the ratio of 1:2. The composition was ground well with an agate mortar and pestle, and the resulting mixture was fired at 700 °C for 24 h; the rate of heating was maintained at 10 °C/min with one intermediate grinding. The color of the product was white. For the combustion synthesis of trigonal (CST) ZrMo2O8, Zr(NO3)4 · 5H2O and (NH4)6Mo7O24 · 4H2O were taken as the precursors, which were dissolved in double-distilled water to prepare a clear solution. The stoichiometric ratio of oxidizer to fuel was maintained as 1 to achieve the highest exothermicity of the reaction. They were added in a petri dish and stirred with a magnetic stirrer. The fuel used for the combustion was glycine. The fuel was

10.1021/jp901897s CCC: $40.75  2009 American Chemical Society Published on Web 05/21/2009

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Figure 1. SEM images of (a) CST and (b) SST samples.

added to the reaction mixture, and the resultant mixture was fired in a preheated furnace maintained at 500 °C for 10 min. When glycine undergoes combustion with precursors, it produces heat that is absorbed by the precursors, accelerating the chemical reaction of the precursors. The redox reactions can be described as follows

(glycine) 4NH2CH2COOH + 5O2 f 2N2 + 4CO2 + 10H2O Zr(NO3)4 · 5H2O + (2/7)(NH4)6Mo7O24 · 4H2O f ZrMo2O8(CST) Characterization. The analysis of the morphology was performed with the help of an FEI Sirion scanning electron microscope (SEM). Transmission electron microscope (TEM) images for CST were taken from a JEOL 2000 FX 11 transmission microscope. UV-vis diffuse reflectance spectra were recorded on a PerkinElmer Lambda 35 UV-vis spectrophotometer. BET analysis of CST and SST was carried out using the desorption technique (Belsorp, Japan). After the phase purity of the obtained samples was confirmed by conventional X-ray powder diffraction, Rietveld quality data were collected using the Philips X-pert diffractometer with Cu KR radiation over the angular range of 10° e 2θ e 100°, with a step width of 0.02°. Photocatalytic Experiments. Photochemical Reactor. The photochemical reactor22 used in this study consists of two parts. The inner part was a jacketed quartz tube with a 3.4 cm inner diameter, 4 cm outer diameter, and 21 cm length, whereas the outer part is a Pyrex glass reactor with a 5.7 cm inner diameter and 16 cm length. A high-pressure mercury vapor lamp (HPML) of 125 W (Philips, India) was placed after the removal of the outer shell inside the jacketed quartz tube. The fluctuations in the input supply were controlled by a ballast and capacitor, connected in series with the lamp. Water, circulating through the annulus of the quartz tube, maintains the solution at ambient temperature. The solution (120 mL) is taken into the outer reactor and continuously stirred to ensure that the suspension of the catalyst is uniform. The lamp radiated predominantly at 365 nm, corresponding to the energy of 3.4 eV, and the photon flux is 5.8 × 10-6 mol of photons/s. Further details of the experimental apparatus and procedure are provided in our earlier studies.22,26

Degradation Experiments. The initial concentrations in the dye solutions varied between 15 and 100 ppm depending on the molar absorptivity (ε) of each dye. For example, the initial concentrations for the dye solutions were 100 ppm for MB, OG, RBBR, CR, and AG, whereas 15 ppm for RB. Both SST and CST were loaded at 1 g/L, and the volume of the dye solution taken was 120 mL in all the experiments. Four milliliters of the solution was drawn five times over a span of 1 h for adsorption studies. This was followed by UV experiments by switching on the lamp. The effective volume for the UV degradation experiments was 100 mL. The samples were filtered through Millipore membrane filters and centrifuged to remove the catalyst particles prior to UV analysis. Sample Analysis. All samples were analyzed with a UV-visible spectrophotometer (Lambda 32, PerkinElmer) to quantify the degradation reactions. The calibration for MB, OG, RB, RBBR, CR, AG, and AQ was based on the Beer-Lambert law at their maximum absorption wavelengths, λmax, of 664, 489, 554, 591, 497, 640, and 256 nm, respectively. Analysis of the samples using UV-vis spectrophotometer showed a continuous decrease in the UV-vis absorption at λmax of the starting material, and no new peaks were observed. Results and Discussion Crystal Structure. Powder diffraction data show the formation of single phase compounds for both CST and SST. Rietveld refinements were carried out with the help of GSAS.23 The initial coordinates were taken from the published literature of trigonal ZrMo2O8.6 The compound crystallizes in the trigonal crystal system with a ) 10.1391(6) Å, c ) 11.7084(8) Å, and space group P3j1c (No. 163). Zirconium occupies the special positions (Wycoff 2b) and 4f sites, whereas molybdenum and oxygen atoms occupy general positions (12i). Full occupancies were assigned to all the atoms, and profile refinements were carried out using GSAS. The experimental and calculated profiles for SST and CST are presented in Figure S1 in the Supporting Information. Cell parameters and residual factors are given in Table S1 in the Supporting Information. Atomic coordinates and isotropic displacement parameters are presented in Table S2 in the Supporting Information. Selected interatomic distances and angles are presented in Table S3 in the Supporting Information. The bond valence sums were calculated according to the method given by Brown and Shannon.24,25 The zirconium octahedra are regular and have normal Zr-O bond distances, whereas the MoO4 tetrahedra are distorted with one unusual short Mo-O(4) bond. The ZrO6 octahedra share all the corners

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Figure 2. TEM image of the CST sample showing (a) particle size, (b) crystallinity, and (c) EDX analysis.

with the MoO4 tetrahedra, whereas only three oxygen atoms of MoO4 tetrahedra belong to the three adjacent octahedra and the fourth oxygen atom O(4) points toward the interlayer region (see the Supporting Information, Figure S2). Morphology and Compositional Analysis. SEM images show a particle size of 40-50 nm for combustion-synthesized samples and 8-10 µm for solid-state-synthesized ZrMo2O8 (Figure 1). Images obtained for the CST samples indicate agglomeration. As we have synthesized trigonal ZrMo2O8 for the first time by combustion synthesis, we have further characterized CST by obtaining TEM images and performing energy-dispersive X-ray (EDX) analysis, which are shown in Figure 2. EDX confirmed the presence of Zr, Mo, and O only. The formula derived from the EDX analysis is ZrMo2O8. TEM images confirm the crystallinity and nanosize of the CST samples. The UV-vis diffuse spectra of the two samples are shown in Figure 3. The band gaps obtained by UV-vis diffuse reflectance spectra for the CST and SST samples are 2.70 and 2.74 eV, respectively. The BET surface areas of SST and CST were 1.0 and 10.0 m2/g. Photocatalysis. Photocatalytic degradation of the dyes MB, OG, RB, CR, RBBR, and AG was investigated. The structures of the dyes are shown in Table S4 in the Supporting Information. The lamp position in the photochemical reactor was adjusted such that no degradation was observed in the absence of UV

Figure 3. Diffuse reflectance spectra of CST and SST samples.

light or catalyst alone. XRD patterns taken before and after reaction indicate no structural change of the catalyst ZrMO2O8 (see the Supporting Information, Figure S3). Figure 4a,b shows the profiles of dye degradation in the presence of SST and CST samples. Though the surface areas of CST and SST are 10 and

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Figure 5. Variation of the degradation rate with the initial dye concentration of methylene blue.

Figure 4. UV degradation of various dyes by (a) SST and (b) CST samples and (c) nondegrading anthraquinonic dyes.

1 m2/g, respectively, the photocatalytic activities are similar because these reactions are probably not surface-controlled. This is evident because the SST with a surface area of 1 m2/g is successfully able to degrade various dyes. Figure 4a also shows the degradation of Orange G by commercial titania (Degussa P-25). It was observed that the dyes MB, OG, RB, and CR degrade effectively, whereas RBBR and AG do not. It is noteworthy that RBBR and AG contain an anthraquinone moiety, and it appears that both the catalysts are insensitive to the anthraquinone group. To further confirm the specificity, the degradation of anthraquinone-2-sulfonic acid (AQ), which has only anthraquinone as the major functional group, was tested and Figure 4c shows that the catalyst does not degrade the anthraquinonic group. The inability of these compounds to degrade anthraquinonic dyes could be due to the formation of a stable ligand between the anthraquinonic moiety and the compound. Such behavior has been observed for the chloro and nitro specificity of some molybdovanadates.26 The effect of initial concentration on the rate of the photocatalytic degradation of methylene blue was investigated over the dye concentration range of 20, 40, 75, and 100 ppm. To

quantify the reaction rates, a simple first-order rate equation,22,26 r0 ) k0C0, was used, where r0 is the initial rate, C0 is the initial concentration of the dye, and k0 is the kinetic rate constant. The initial rates were calculated using degradation up to 10 min. The overall kinetic rate constants, k0, for the degradation of methylene blue in presence of CST and SST were determined to be 0.00382 and 0.00308 min-1, respectively (Figure 5). DFT Electronic Structure Calculations. To obtain pointers to the band structure of ZrMo2O8, theoretical calculations were carried out using the plane-wave density functional theory program CASTEP.27 The exchange and correlation interactions were modeled using the generalized gradient approximation (GGA) using RBPE (revised Perdew-Burke-Ernzerhof) functional form. Ultrasoft pseudopotentials were used to account for the electron-core interactions. The valence electron configurations for Zr, Mo, and O atoms are 4d25s2, 4d55s1, and 2s22p4, respectively. A plane-wave basis with a kinetic energy cutoff of 380 eV was used to represent wave functions, and Brillouin zone integration was performed with a 3 × 3 × 2 Monkhost-Pack k-point mesh. The structural parameters for the ZrMo2O8 unit cell given as input for the calculation were taken from the output of the Rietveld refinements. The band structure diagram of ZrMo2O8 is shown in Figure S4 in the Supporting Information. The theoretical band gap is observed to be 3.09 eV. The band gap calculated by DFT is different from the experimentally observed band gap. Though the density functional theories that use ab initio calculations of the electronic structure give good structural data, they underestimate or overestimate the band gaps of semiconductors and insulators.28 For example, the band gap of Bi12TiO20 is 3.28 eV theoretically, whereas the experimental value is between 2.4 and 2.78 eV.29 The figure shows that the valence band maxima (VBM/HOMO) occur at H and K points, whereas the conduction band minima (CBM/LUMO) occur at the G [0,0,0] point, indicating an indirect band gap semiconductor nature of ZrMo2O8, where G, H, and K can be defined as direction vectors or high-symmetry points in the Brillouin zone. The partial density of states (PDOS) of ZrMo2O8 near the band gap is shown in Figure 6a, with contributions from s, p, and d orbitals. The energy spectrum can be divided into three parts, where the region of -5 to -3 eV is indicative of bonding in the material and a strong mixing of the p and d orbitals. The region near the VBM is dominated by the p orbitals, whereas those near the CBM are dominated by the d orbitals. To further explore the contributions of the individual elements to the DOS, the PDOS of the d orbitals of Zr and Mo and p orbitals of O are calculated and are shown in Figure 6b,c, respectively.

Synthesis, Characterization, and Properties of ZrMo2O8

J. Phys. Chem. C, Vol. 113, No. 24, 2009 10665 polyhedra and, hence, results in high PDOS of O(4) near the VBM. Hence, from the preliminary DFT band structure calculations using CASTEP (molecular modeling package), we infer that, when the ZrMo2O8 is excited by UV energy, which is an indirect band gap material, the oxygen 2p states near VBM get excited and make a transition to the empty states of Zr or Mo near the CBM, depending on the energy of the excited electrons. The electrons and holes created by this phenomenon participate in the photocatalytic activity. From the crystallographic information of the MoO4 bond lengths (see the Supporting Information, Table S3); it is observed that the bond lengths are unequal, leading to a distortion in the MoO4 polyhedra.6 This crystallographic distortion might create a dipole in the crystal structure, which further inhibits the electron-hole recombination process, thereby enhancing photocatalysis. As shown in previous studies,30-32 the emission spectrum of the metal molybdates is primarily due to charge transfer within the MoO42- complex. The valence and conduction bands near the band gaps are dominated by molecular orbitals associated with MoO42- and the radiative transitions in this complex. Conclusions The synthesis of ZrMo2O8 by solution combustion method offers a larger surface area and, hence, higher potency toward surface adsorption of the dyes. The correlation of the structure with the catalytic activity has been obtained both from X-ray diffraction studies and theoretical calculations based on DFT methodology. The preliminary DFT calculations suggest an indirect band gap of ZrMo2O8. The irregular MoO4 tetrahedra create a dipole and inhibit the process of electron-hole recombination, thereby making the material photoactive. The photocatalytic activity of these catalysts was determined. From the degradation experiments, it is observed that the photocatalytic activity of ZrMo2O8 synthesized by solution combustion and solid-state synthesis is similar for the degradation of all dyes. However, these compounds do not degrade anthraquinonic dyes.

Figure 6. Density of states curves of contributions from various valence orbitals for individual atoms of ZrMo2O8: (a) partial density of states arising from s, p, and d orbitals in ZrMo2O8; (b) partial density of states of d orbitals arising from Zr(1), Zr(2), and Mo atoms; (c) p orbital contribution from different oxygen atoms.

Further, from Figure 6b, the contributions from both Zr and Mo atoms toward the CBM can be observed. The contributions near the bonding region (VBM) arise mainly from Mo atoms, indicating that the major bonding in the material arises from the molybdenum d orbital and the oxygen p orbital. Further, it can be noted from Figure 6c, that the contributions to the p levels near the VBM arise mainly from different oxygen atoms. Close examination of individual oxygen atoms indicates that the highest contribution near the VBM arises from O(4), whereas in the bonding region, it comes from the O(1) atom. This information has been extracted by calculating the area under the PDOS curves of O(1) and O(4) atoms near the bonding region (-6 to -3 eV) and VBM (-1.6 to 0 eV) region, respectively. It is noteworthy that the O(4) atom has been found to be free and points toward the interlayer separation on the basis of the crystallographic studies described earlier. Also, O(4) is not shared by any other polyhedron other than MoO4, unlike the other oxygen atoms (O(1), O(2), and O(3)) present in the MoO4

Acknowledgment. P.P.S. thanks the Indian Institute of Science for a senior research fellowship. We acknowledge funding from DRDO and DST, India. Supporting Information Available: Crystallographic parameters of CST and SST (Table S1); atomic coordinates (Å) and isotropic displacement parameters (Å2) for CST and SST (Table S2); selected bond lengths, bond angles, and bond valence sums for CST and SST (Table S3); schematic diagrams of all the compounds and dyes, where the oval denotes the anthraquinonic moiety in all the nondegrading compounds and dyes (Table S4); experimental and calculated X-ray diffraction profiles of (a) SST and (b) CST (Figure S1); three-dimensional view of trigonal ZrMo2O8 along different directions (Figure S2); powder X-ray diffraction pattern of ZrMo2O8 before and after degradation of methylene blue (Figure S3); and band structure diagram of ZrMo2O8 obtained from the DFT simulation method (CASTEP) (Figure S4). This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Sleight, A. W. Inorg. Chem. 1998, 37, 2854. (2) Mary, T. A.; Evans, J. S. O.; Vogt, T.; Sleight, A. W. Science 1996, 272, 90. (3) Lind, C.; Wilkinson, A. P.; Hu, Z.; Short, S.; Jorgensen, J. D. Chem. Mater. 1998, 10, 2335.

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(4) Evans, J. S. O.; Hanson, P. A.; Ibberson, R. M.; Duan, N.; Kameswari, U.; Sleight, A. W. J. Am. Chem. Soc. 1998, 122, 8694. (5) Mittal, R.; Chaplot, S. L.; Lalla, N. P.; Mishra, R. K. J. Appl. Crystallogr. 1999, 32, 1010. (6) Auray, M.; Quarton, M.; Tarte, P. Acta Crystallogr. 1986, C42, 257. (7) Klevtsova, R. F.; Glinskaya, L. A.; Zolotova, E. S.; Klevtsov, P. V. Dokl. Akad. Nauk SSSR 1989, 305, 91. (8) Lind, C.; Wilkinson, A. P.; Rawn, C. J.; Payzant, E. A. J. Mater. Chem. 2001, 11, 3354. (9) Allen, S.; Warmingham, N. R.; Gover, R. K. B.; Evans, J. S. O. Chem. Mater. 2003, 15, 3406. (10) Carlson, S.; Andersen, A. M. K. Phys. ReV. B 2000, 61, 11209. (11) Karandikar, A. S.; Mukherjee, G. D.; Vijayakumar, V.; Godwal, B. K.; Achary, S. N.; Tyagi, A. K. J. Appl. Phys. 2006, 100, 013517. (12) Clearfield, A.; Blessing, R. H. J. Inorg. Nucl. Chem. 1972, 34, 2643. (13) Monroy-Guzma´n, F.; Dı´az-Archundia, L. V.; Ramı´rez, A. C. Appl. Radiat. Isot. 2003, 59, 27. (14) Sudorgin, N. G.; Nalbandyan, V. B.; Shukaev, I. L. Solid State Ionics 2008, 179, 503. (15) Samaranch, B.; de la Piscina, P. R.; Clet, G.; Houlla, M.; Homs, N. Chem. Mater. 2006, 18, 1581. (16) Chen, K.; Xie, S.; Iglesia, E.; Bell, A. T. J. Catal. 2000, 189, 421. (17) Liu, H.; Cheung, P.; Iglesia, E. J. Phys. Chem. B 2003, 107, 4118. (18) Patil, K. C.; Aruna, S. T.; Ekambaram, S. Curr. Opin. Solid State Mater. Sci. 1997, 2, 158.

Sahoo et al. (19) Patil, K. C.; Aruna, S. T.; Mimani, T. Curr. Opin. Solid State Mater. Sci. 2002, 6, 507. (20) Frank, S. N.; Bard, A. J. J. Am. Chem. Soc. 1977, 99, 303. (21) Hoffmann, M. R.; Martin, S. T.; Choi, W.; Bahnemannt, D. W. Chem. ReV. 1995, 95, 69. (22) Sivalingam, G.; Nagaveni, K.; Hegde, M. S.; Madras, G. Appl. Catal., B 2003, 45, 23. (23) Larson, A. C.; Von Dreele, R. B. General Structure Analysis System (GSAS); Los Alamos National Laboratory Report LAUR 86-748; Los Alamos National Laboratory: Los Alamos, NM, 2004. (24) Brown, I. D.; Shannon, R. D. Acta Crystallogr. 1973, A29, 266. (25) Brown, I. D.; Altermatt, D. Acta Crystallogr. 1985, B41, 244. (26) Mahapatra, S.; Madras, G.; Guru Row, T. N. J. Phys. Chem. C 2007, 111, 6505. (27) Clark, S. J.; Segall, M. D.; Pickard, C. J.; Hasnip, P. J.; Probert, M. I. J.; Refson, K.; Payne, M. C. Z. Kristallogr. 2005, 220, 567. (28) Robertson, J.; Xiong, K.; Clark, S. J. Thin Solid Films 2006, 496, 1. (29) Wei, W.; Dai, Y.; Huang, B. J. Phys. Chem. C 2009, 113, 5658. (30) Yoon, J.-W.; Ryu, J. H.; Shim, K. B. Mater. Sci. Eng., B 2006, 127, 154. (31) Marques, A. P. A.; de Melo, D. M. A.; Longo, E.; Paskocimas, C. A.; Pizani, P. S.; Leite, E. R. J. Solid State Chem. 2005, 178, 2346. (32) Spassky, D. A.; Ivanov, S. N.; Kolobanov, V. N.; Mikhailin, V. V.; Zemskov, V. N.; Zadneprovski, B. I.; Potkin, L. I. Radiat. Meas. 2004, 38, 607.

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