Journal of Molecular Structure 1033 (2013) 154–161
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Vibrational and structural properties in the dihydrate sodium tungstate and in the dihydrate sodium molybdate crystals G.D. Saraiva a,⇑, C. Luz-Lima b, P.T.C. Freire c, A.J. Ramiro de Castro c, G.P. de Sousa c, F.E.A. Melo c, J.H. Silva d, J. Mendes Filho c a
Faculdade de Educação, Ciências e Letras do Sertão Central, Universidade Estadual do Ceará, CEP 60740-000 Quixadá, Ceará, Brazil Departamento de Física, Universidade Federal do Piauí, CEP 64049-550 Teresina, Piauí, Brazil Departamento de Física, Universidade Federal do Ceará, Caixa Postal 6030, CEP 60455-760 Fortaleza, Ceará, Brazil d Universidade Federal do Ceará, Campus Cariri, CEP 63.000-000 Juazeiro do Norte, Ceará, Brazil b c
h i g h l i g h t s " Temperature-dependent Raman and IR. studies have been performed on polycrystalline crystals. " Temperature-dependent X-ray diffraction studies, have been performed on polycrystalline crystals. " Raman spectroscopic measurements of Na2WO42H2O, under hydrostatic pressure was performed. " The crystals have undergone conformational changes at around 100–120 K. " Raman measurements of Na2WO42H2O, under hydrostatic pressure undergoes a phase transition.
a r t i c l e
i n f o
Article history: Received 4 April 2012 Received in revised form 22 July 2012 Accepted 14 August 2012 Available online 23 August 2012 Keywords: Raman Infrared X-ray Molybdate Tungstates Phase transition
a b s t r a c t Temperature-dependent vibrational (Raman and infrared) spectroscopy and X-ray diffraction studies have been performed on polycrystalline Na2WO42H2O and Na2MoO42H2O crystals. Raman data at low temperature 13–300 K for sodium tungstate Na2WO42H2O was compared with the sodium molybdate Na2MoO42H2O. The infrared and the X-ray diffraction obtained in the 80–300 K suggest that both crystals have undergone conformational changes connected with an increase in the Raman intensity of NaO6 modes and the libration modes of water molecules at about 100–120 K. Additionally, Raman spectroscopy measurements of Na2WO42H2O under hydrostatic pressure (from 0 to 5 GPa) were performed. The pressure-dependent studies indicate the starting orthorhombic structure is stable in the 0.0–3.2 GPa pressure range, and undergoes a phase transition at about 3.9 GPa, associated with rotation of WO2 4 units. Ó 2012 Elsevier B.V. All rights reserved.
1. Introduction Molybdates and tungstates materials have attracted considerable scientific interest since they exhibit interesting physical properties, which are exploited for technological applications in the field of catalysis and quantum electronics [1]. Furthermore, molybdates and tungstates exhibit rich phase transition sequences, making them good prototypes materials to establish new concepts about the physics underlying the phase transitions [1,2]. In particular, the hydrated compounds of Na2WO42H2O (NWHO) and Na2MoO42H2O (NMHO) are isostructural at ambient conditions with slight difference in the unit cell dimensions [3]. ⇑ Corresponding author. E-mail address: gilberto@fisica.ufc.br (G.D. Saraiva). 0022-2860/$ - see front matter Ó 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.molstruc.2012.08.024
The sodium tungstate Na2WO42H2O (NWHO) shows0 the following0 0 dimensions in the unit cell: a = 8.454 Å A, b = 10.598 Å A, c = 13.895 Å A [4]. Nevertheless, previous structural determinations of the NWHO compound have been reported in the literature by Okada et al. [5]. Recently, Farrugia did a revisit structure termination of the sodium tungstate and thus suggesting changes in both entries for sodium tungstate in the Inorganic Crystal Structure Database [6,7]. According to [6], data were based on photographic record using Cu radiation, while Okada et al., was based on diffractometer data using Mo radiation. The reported coordinates of Mitra and Verma [4] are not correct, while those of Okada et al., have a single typographical error in the z-coordinate of O4 (which should read 0.5980). 0 The dimensions of the unit cell for NMHO are: a0 = 8.463(3) Å A, 0 0 b = 10.552(3) Å A, and c = 13.827(6) Å A; U = 1234.8 Å A3 [8]. The ðWO4 Þ2 Þ=ðMoO4 Þ2 tetrahedra are slightly elongated in the direction
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of the hydrogen bonds [8]. The atomic arrangement in these compounds are composed of alternate layers of ðWO4 Þ2 Þ= ðMoO4 Þ2 tetrahedra and water molecules in the cells. The inset to Fig. 1 shows a schematic unit cell of the hydrated sodium tungstate Na2WO42H2O. The layers are interconnected by sodium cations and hydrogen bonds. The Na (1) ion is surrounded by two oxygen atoms from water and four oxygen atoms from four different ðWO4 Þ2 groups, therefore, forming a distorted octahedron. However, the Na (2) ion is surrounded by two oxygen atoms from water and three oxygen atoms of ðWO4 Þ2 units, forming a distorted trigonal bipyramid [6]. The vibrational properties of the above stated materials have been investigated by different authors through the observation of Raman and infrared (IR) active modes, which have been previously reported [9–11]. Recently, we have also reported results of pressure-dependence Raman spectra in the Na2MoO42H2O. The vibrational study of polycrystalline orthorhombic molybdate allowed us to propose the assignment of vibrational modes [11]. The research work herein: (i) reports a conformational change in the Na2MoO42H2O and in the Na2WO42H2O compounds using Raman spectroscopy techniques to access the associated vibrational changes of both materials at low temperatures and (ii) shows that the Na2WO42H2O undergoes a phase transition in high pressure conditions.
2. Experimental The pressure and temperature-dependent Raman spectra were recorded using a triple-grating spectrometer in the subtractive mode (Jobin Yvon, T64000), equipped with a N2-cooled Charge Coupled Device (CCD) detection system. The line 514.5 nm of an Argon ion laser was used as an excitation. An Olympus microscope lens with a focal distance of f = 20.5 mm and a numeric aperture of NA = 0.35 was used to focus the laser on the sample surface. In the
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temperature-dependent studies, the slits were set for a resolution of 2 cm1. The low temperature Raman studies were performed using a closed helium flux cryostat system (Model DE202S – APD Cryogenics) with a temperature control about ±0.1 K. The Raman spectra were obtained when the temperature was lowered from 300 K to 13 K. The temperature-dependent Fourier transform infrared (FTIR) spectra were performed using a liquid nitrogen cryostat with optical access (Model VPF-100 – Janis Research Company Inc.) with a temperature control about ±0.1 K. The spectra were obtained lowering the temperature from 300 K down to 80 K, in the absorbance mode using a VERTEX 70 instrument (Bruker) with 256 scans at a spectral resolution of 2 cm1. The samples were grounded with KBr and pressed into pellets for the FTIR measurements. In situ X-ray diffraction (XRD) measurements were carried out through a Bruker AXS D8 Advance diffractometer using Bragg–Brentano geometry attached to an Anton-Par TTK450 lowtemperature chamber, in the temperature range of 80–300 K. A Cu Ka radiation (k = 1.54056 Å) was used with the diffractometer operating at 40 kV/30 mA. The measurements were performed between a range of 3–45° (2h) using a count time of 1s/step and a step size of 0.05°. A Rietveld refinement was also performed for all the diffractograms using the GSAS program. A Diamond Anvil Cell (DAC) set for operating from 0 to 10 GPa was used in this particular high-pressure study. Mineral oil (Nujol fluid) was used as the pressure transmitting medium. The standard methanol–ethanol mixture was observed to damage the NWHO sample surface in the Diamond Anvil Cell. Furthermore, the interaction between 4:1 methanol:ethanol with the NWHO partially dehydrated the crystal sample. A tiny ruby chip was used as pressure gauge for the monitoring of the energy shift in the ruby luminescent lines. The error of pressure measurement is ±0.1 GPa.
3. Results and discussion 3.1. Temperature dependence of vibrational modes for the NMHO and NWHO
Fig. 1. Raman spectra of the NHMO and the NHWO compounds in the spectral region between 20 and 1000 cm1 obtained at room temperature. Inset: unit cell of the Na2WO42H2O.
The NWHO and NMHO materials crystallize at ambient conditions, within an orthorhombic structure (D15 2h space group) with Z = 8 and 104 atoms per unit cell [8], where every ion occupies sites of the C1 symmetry including the XO4 units (see inset in Fig. 1). The orthorhombic D15 2h phase of these two compounds was confirmed through X-ray diffraction measurements. The factor group analysis leads to 309° of freedom (optical modes k = 0), excluding acoustic modes. They are distributed among the irreducible representations of the factor group D2h as 39Ag + 39B1g + 39B2g + 39B3g + 39Au + 38B1u + 38B2u + 38B3u. According to the selection rules, only Ag, B1g, B2g and B3g modes are Raman-active [9,10]. Fig. 1 shows a comparison between the Raman spectra of the NMHO and NWHO crystals at ambient conditions in the spectral range from 30 to 975 cm1. All Raman modes observed for both the NWHO and NMHO are listed in Table 1. These particular modes are in agreement with the Raman data previously reported by Mahadevan Pillai et al. [10]. The mode assignment for NMHO was made based on lattice dynamic calculations for the cubic Na2MO4 system [12,13], and the mode assignment for the NWHO was achieved by performing a comparison with other tungstates [10]. It is important to establish that as occurs with other similar crystals, such as SrWO4, SrMoO4, CaWO4 and CaMoO4, the coupling 2 between the WO2 4 and MoO4 ions and the rest of the lattice is weak, allowing us to assign vibrations as internal or external vibrations [14–16]. As a consequence, the bands appearing in the region 250–400 cm1 are associated to the m2 and m4 vibrations; the bands between 800 and 950 cm1 are associated to the m3 and m1 vibrations
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Table 1 List of observed Raman wavenumbers for the Na2MoO42H2O and the Na2WO42H2O system and the assignment according to Refs. [10–12]. xobs (cm1) stands for observed modes; a (cm1) and b (cm1) stand for the parameters of Eq. (1). The parameter b was not include on the table because the values are zero due to the weak anharmonicity. Na2MoO42H2O
Na2WO42H2O
Refs. [10–12] W0 (300 K)
13 6 T 6 300 (K) Wexp (300 K)
65 (Lattice mode) 75 (Lattice mode) 91 (Lattice mode) 120 (Lattice mode) 130 (Lattice mode) 145 (Lattice mode)
64 72 86 119 130 145.5
0.008 0.008 0.007 0.017 0.025 0.02
155 175 181 195 215 242 265 290
159 176.5
0.028 0.025
(Lattice mode) (Lattice mode) (Lattice mode) (Lattice mode) (Lattice mode) (Lattice mode) (Lattice mode) (m2 MoO4)
13 6 T 6 120 (120) Wexp (120 K)
201 206 249 258 292 309
327 (m2 MoO4)
321 331
a
0.03 0.005 0.045 0.02 0.025 0.004 0.005 0.008
W0 (300 K) 67 (Lattice mode)
120 (Lattice mode)
(m 2 MoO4) (m4 MoO4) (m4 MoO4) (m4 MoO4) (m4 MoO4)
343 357 369.5
810 833 840 849 902 912
(m3 (m3 (m3 (m1 (m1
MoO4) MoO4) MoO4) MoO4) MoO4)
170
222 276 (m2 MoO4)
251 258 292 320
0.017 0.028 0.04
330 337 345 355
701 745.5 772.5 798.5 809.5 836
0.04 0.05 0.05 0.02 0.038 0.066 0.024 0.034 0.01 0.015 0.007
846 899 908
0.009 0.002 0.01
575 606 647 663
572 608 647 663
808 838 (m3 MoO4)
3253 3271 3287 3302
0.005 0.001 0.004 0.004
of the tetrahedral MoO4 (or WO4). The vibrational properties of these compounds depend significantly on the mass of the Mo and the W metals in tetrahedron units. Only a few low-wavenumber modes showed significant dependence in the mass of the W or the Mo. Such a result indicates a strong coupling among vibrational modes. Fig. 2 shows the temperature dependence on the Raman spectrum in the NMHO and the NWHO, ranging from 8 to 300 K in the 30–450 and 825–975 cm1 of the spectral regions. In general terms, the NMHO and the NWHO Raman spectra, present the same behavior under cooling. When the temperature decreases the bandwidth of Raman bands decreases and most of the observed vibrational modes presented blue shifts in the wavenumber. Similar shift and bandwidth behaviors were also observed in the related systems [12,13]. It is also evident that the Raman spectrum at 13 K have different significant intensity relative to the room temperature spectrum. However, the number of bands does not change, therefore, the temperature dependent studies indicate that the orthorhombic
700 747 772 802.5 811 840 846 889
893 (m1 MoO4) 931 (m1 MoO4)
3170 3260 3290 (m2 H2O) 3350 3450
53.5 61.6 73 93 119 130 146.5 157.5
371 558
590 (m4 MoO4) 610 680 690
13 6 T 6 140 (K) Wexp (140 K)
177.5 188.5 200 222
335 (m2 MoO4) 337 345 365 385 410
13 6 T 6 300 (K) Wexp (300 K)
3300 (m2 H2O)
897.5 918 933 947 3264 3286 3292 3307 3325 3352
a 0.006 0.006 0.006 0.011 0.016 0.020 0.020 0.027 0.006 0.022 0.028 0.041 0.048 0.015 0.041 0.014 0.027 0.027 0.00 0.00 0.004 0.004 0.025
0.03 0.03 0.006 0.009 0.047 0.022 0.003 0.006 0.001 0.006 0.008 0.001 0.012 0.00 0.01 0.006 0.013 0.005 0.044 0.00 0.011 0.064
framework is stable in the range of 300–13 K. The observed changes in the Raman spectra can be attributed to a weak anharmonic interaction and some weak changes in interatomic interactions. The modes that are peaked below 170 cm1 can be totally deconvolutioned at 13 K. It is worthwhile to observe that in both crystals cooling leads to a decrease in the intensity for the modes below 100 cm1 and an increase in the intensity for the mode peaked at about 283 cm1. Fig. 2b and d, shows that the stretching modes of the MoO4 and WO4 are not affected by temperature. Fig. 3 shows a comparison in the temperature Raman spectra for the NMHO and the NMWO, in the spectral regions between 500–825 and 3170–3450 cm1. A remarkable change can be observed in this figure where a number of modes appear or increase intensity in the Raman spectra. The appearance of the modes in the region between 500 and 825 cm1 (Fig. 3a and c) are connected with the splitting of the water mode in the region between 3175 and 3450 cm1 (Fig. 3b and d). These results suggest that water
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157
Fig. 2. Raman spectra of the NHMO and the NHWO compounds in the region (30–430) cm1 (a) and (c), (825–950) cm1 (b) and (825–975) cm1 (d) obtained during decrease of the temperature.
molecule interaction do not affect the W–O and the Mo–O bond when temperature decreases. However, the result points out that the Na ion and the water molecules interacted more strongly. This particular interaction increase the Raman intensity of the NaO6 modes and the libration modes in the water molecules at about 100–120 K [10]. Hence, the results indicate that the structure with conformational changes, differ very slightly from the orthorhombic structure. The manner how the arrangement of the water molecules are in unit cells of the sodium molybdate and the sodium tungstate gives a fundamental insight about the mechanism driving the conformational modifications in the above compounds. The aforementioned arrangement is responsible for the stability of the sodium molybdate and the sodium tungstate, whereby when the temperature increases after the cooling, we observed that the original spectrum duly obtained is pointing to a reversible process. Fig. 4 shows that the temperature dependence in the Raman modes can be better followed through the wavenumbers vs. temperature plots. In a low temperature range (13–300 K), the wavenumbers vs. temperature fittings, were better reached by using the expected dependence due to anharmonic phonon decay as follows [17–20]:
x ¼ x0 þ a 1 þ
" # 2 3 3 þ b 1 þ þ ex 1 ey 1 ðey 1Þ2
ð1Þ
hx0 hx0 where x ¼ 2K ; y ¼ 3K ,h is the Planck’s constant divided by 2p, T is BT BT the absolute temperature, kB is the Boltzmann constant. Both wavenumber intercept x0 and a and b are constants to be obtained by fitting the experimental data. In Table 1, we listed both x0 and a and b for all the duly observed modes. The results indicate a very weak anharmonicity since a values are very small. However, one can notice that in Fig. 4, all modes located in the orthorhombic phase, exhibited a decrease in the wavenumbers with decreasing temperatures (the temperature derivative dx/dT < 0). Fig. 5 shows the temperature dependence of the FT-IR modes for the NMHO and the NMWO in spectral regions, between 400– 1000 and 1570–1900 cm1 of these materials. It is amazing that a remarkable change in the spectra of the FT-IR occurs when temperature decreases in the same region where changes were observed for the Raman modes, at about 500 and 850 cm1. Furthermore, the FT-IR modes do not show changes for the bending modes of the water molecule in the region 1570–1900 cm1 (Fig. 5). This result implies that the coupling between the water
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Fig. 3. Raman spectra of the NHMO and the NHWO compounds in the region (500–830) cm1 (a) and (c), and (3170–3449) cm1 (b) and (d), obtained during a decrease of the temperature.
molecule and the sodium ion, a lead number of modes appear in the Raman spectra region between 500 and 825 cm1 (Fig. 3a and c), which are connected with the splitting of the water modes in the region between 3175 and 3450 cm1 (Fig. 3b and d).
parameters, as well as the unit cell volume, do not change with a decrease in the temperature. Therefore, there is no discontinuity in the lattice parameters a, b and c. The XRPD results agree with the Raman results.
3.2. Low temperature X-ray powder diffraction
3.3. Conformational changes
In addition to the Raman and the infrared spectroscopy experiments, the X-ray powder diffraction measurements were carried out at several temperatures and the patterns of the Na2MoO42H2O crystal are shown in Fig. 6. The diffraction patterns of the polycrystalline Na2MoO42H2O and Na2WO42H2O crystals (not shown here) were measured from 300 K through 80 K. The Rietveld refinement was not able to show significant changes, which evidenced that the Na2WO42H2O and the Na2MoO42H2O are stable from 300 K to 80 K. The analysis of all the diffractograms using the Rietveld refinement has provided lattice parameters as a function of the temperature that does not show any significant changes according to Fig. 6. We observed that the a, b and c lattice
The present study furnishes evidence that the sodium molybdate Na2MoO42H2O and the sodium tungstate Na2WO42H2O undergo the same conformational changes under low temperature conditions. At ambient conditions NMHO and NWHO compounds crystallize with the space group D15 2h and the elements of symmetry for this group are E, 3C2, i, and 3r. The decrease in temperature shows that some modes appear or increase intensity in the Raman spectra (see Fig. 3), as those in the high wavenumber region, although this should be associated to temperature effect. However, we observe some changes of intensity of bands associated to the m2 and m4 vibrations, indicating that at about 120 K, conformational changes occur without changing in the space group of the crystals.
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159
Fig. 4. Wavenumber vs. temperature plot for the and lattice modes of the Na2XO42H2O crystals. The solid lines adjusted on solid circles, were fits of the h stretching, bending i 3 experimental data to x ¼ x0 þ a 1 þ ex21 þ b 1 þ ey31 þ ðey 1Þ for orthorhombic phase. 2
In fact, no peak appears in the low wavenumber region during the cooling process, thus confirming that no structural change takes place. Figs. 3 and 4 show that the value of temperatures lower than 120 K modes associated to NaO6 and to libration of H2O increase intensity in the spectra for both NMHO and NWHO. In summary, this result suggests that changes occurring at low temperature in the compounds of the NMHO and the NWHO, are not associated to structural phase transition, only to conformational changes. 3.4. Pressure dependence of vibrational modes with the NWHO Fig. 7 shows the pressure dependence Raman spectra of the modes located at 52, 60, 71, 77, 125, 328, 335, 841, 892 and
930 cm1 for the NWHO. Due to the small size of crystals used in this pressure-dependent experiment (an approximate volume of 103 mm3) we observed that the intensity in the Raman spectra, is lower than the intensity of the Raman temperature measurements. It is difficult to make a comparison of the pressure and the temperature-dependent spectra; however, intensity ratio of the bands, attributed to the lattice and stretchings of the terminal W– O and Mo–O bonds are larger for the particular crystal used in this pressure-dependent study (see Fig. 7). On applying pressure, Fig. 7a shows that the 52 cm1 band presents a wavenumber decrease with compression (the derivative dx/dP < 0), whereas all the other modes show a wavenumber increase with increasing pressure (the derivative dx/dP > 0). From 0.0 through 3.2 GPa, the behavior of the
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Fig. 5. FT-IR spectra recorded at different temperatures values: (a) NHMO in the spectral ranges (400–1000) cm1 (b) NHWO in the spectral ranges (400–1000) cm1.
seen as another indication of the pressure-induced structural change. Additionally, we observed that the modes located at 293 and 830 cm1 disappear in the 3.2–3.9 GPa pressure range, and the dx/dP changes for a number of modes corroborating with the evidences of a phase transition undergone by the NWHO. As final point, the 5.1 GPa and the changes related to the profiles of the Raman spectra, were analyzed. In relation to this pressure, we observed that the bands centered at about 350 cm1 and in the 900–950 cm1 spectral ranges, have great linewidths. Particularly the large linewidths of these bands (in the region where it is expected to be observed), associated with the stretching vibrations of WO4 tetrahedra, indicate disorder of the aforementioned units after the NWHO undergoes the phase transition. As a matter of fact, we also observed disorder with other members of the tungstates and the molybdates crystals, when submitted to high pressure condition [1,11,21]. Fig. 6. X-ray diffractogram of the NHMO recorded at different temperatures values.
4. Conclusions
Raman modes indicate that the orthorhombic structure is stable. Furthermore, the weak Raman modes located at 295 and 350 cm1 showed discontinuities on their frequency dependence and the intensity ratio for lines of 890 and 930 cm1 changes strongly. All these Raman modes are related with the Raman modes of the tetrahedra, and theses changes could be associated with a gradual and slight rotation of WO2 4 , which lead conformational changes at about 0.7–1.0 GPa pressure. At a pressure of about 3.9 GPa the crystal undergoes a phase transition. The abrupt changes in the Raman spectra, indicate that the NWHO exhibited a strong first-order phase transition from the orthorhombic structure to an unknown structure. The spectrum changes drastically, i.e., the Raman bands split and a new band appears below 52 cm1 for this value of pressure. As a result the numbers of the observed Raman bands remain the same, however, it decreases from 8 modes at 0.0 GPa to 7 modes at 3.9 GPa, in the low frequency region (see Fig. 7a and 7c). On the flip side, it increases from 5 modes at 0.0 GPa to 6 modes at 3.9 GPa in the high frequency region where arrows indicate the appearance of two modes (see Fig. 7b and 7d). The modes located at 71 and 77 cm1 evolved to be now very broad like a convolution of the bands. This result would be
In summary, Raman and infrared spectroscopy, as well as X-ray diffraction measurements of the polycrystalline Na2MoO42H2O and the Na2WO42H2O were performed at low temperatures. The Raman and infrared studies allowed us to monitor the stretching and bending vibrations of the MoO4 ions, as well as the translational modes as a function of the temperature. The temperature dependence of the wavenumber modes, indicates that the Na2MoO42H2O and the Na2WO42H2O underwent a conformational modification at about 120 K and 100 K, respectively. By the comparison of the Na2MoO42H2O and the Na2WO42H2O temperature dependent Raman spectra data, we observed that the Na2MoO42H2O revealed a significant conformational modification and a similar behavior also occurred when compared with the Na2WO42H2O. These results suggested that both crystals presented some conformational changes. The present study provided a significant insight into the vibrational properties of the Na2WO42H2O under hydrostatic pressure (from 0 to 5 GPa) conditions. We have duly observed that the sodium tungstate Na2WO42H2O remained in the orthorhombic structure with the 0.0–3.5 GPa ranges and it underwent a phase transition at around 3.8 GPa. This particular phase transition is connected with rotation of the WO2 4 units.
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Fig. 7. Raman spectra of the NHWO recorded at different pressure values: (a) in the spectral ranges (25–500) cm1; (b) in the spectral ranges (800–1000) cm1; (c) wavenumber vs. pressure plot for the same spectral region showed in panel (a) and (d); wavenumber vs. pressure plot for the same spectral region showed in panel (b).
Acknowledgments G.D. Saraiva acknowledges the support from MCT/CNPq official notice 14/2008 (determination # 480364/2008-7), MCT/CNPq official notice 14/2010 (determination # 476569/2010-9), FUNCAP/official notice 02/2010 (determination # BP1-0031.00135.01.00/10) and FUNCAP/official notice 05/2009 (determination # 186.01.00/09). The authors are also grateful to the following Brazilian institutions, CAPES and FUNCAP. We further acknowledge the professor A.G. Souza Filho for the critical reading of this work. References [1] G.D. Saraiva, M. Maczka, P.T.C. Freire, J. Mendes, F.E.A. Melo, J. Hanuza, Y. Morioka, A.G. Souza, Phys. Rev. B 67 (2003) 224108. [2] M. Maczka, A.G. Souza Filho, W. Paraguassu, P.T.C. Freire, J. Mendes Filho, J. Hanuza, Progr. Mater. Sci. 57 (2012) 1335. [3] C.W.F.T. Pistoriu, J. Chem. Phys. 44 (1966) 4532. [4] R.P. Mitra, H.K.L. Verma, Indian J. Chem. 7 (1969) 598. [5] K. Okada, H. Morikawa, F. Marumo, S.I. Iwai, Bull. Tokyo Inst. Technol. 120 (1974) 7.
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