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High-pressure Raman and infrared study of ZrV 2O7
Solid State Communications 141 (2007) 680–684 www.elsevier.com/locate/ssc
High-pressure Raman and infrared study of ZrV2O7 U.L.C. Hemamala a , F. El-Ghussein a , D.V.S. Muthu a,b , A.M. Krogh Andersen c , S. Carlson d , L. Ouyang a , M.B. Kruger a,∗ a Department of Physics, University of Missouri, Kansas City, MO 64110, USA b Department of Physics, Indian Institute of Science, Bangalore – 560 012, India c Department of Structural Chemistry, Stockholm University, SE-10691 Stockholm, Sweden d Lund University, MAX Lab, SE-22100 Lund, Sweden
Received 20 November 2006; received in revised form 2 January 2007; accepted 3 January 2007 by R. Merlin Available online 9 January 2007
Abstract The room-temperature Raman and infrared spectra of zirconium vanadate (ZrV2 O7 ) were observed up to pressures of 12 GPa and 5.7 GPa, respectively. The frequencies of the optically active modes at ambient pressure were calculated using direct methods and compared with experimental values. Average mode Gr¨uneisen parameters were calculated for the Raman and infrared active modes. Changes in the spectra under pressure indicate a phase transition at ∼1.6 GPa, which is consistent with the previously observed α (cubic) to β (pseudo-tetragonal) phase transition, and changes in the spectra at ∼4 GPa are consistent with an irreversible transformation to an amorphous structure. c 2007 Elsevier Ltd. All rights reserved.
PACS: 78.30-j; 81.40.Vw; 64.70.-p Keywords: E. Strain, high pressure; E. Inelastic light scattering; E. Light absorption and reflection
1. Introduction Many studies have been done on the MX2 O8 and MX2 O7 (M = Zr, Hf and X = W, Mo, V) families of compounds [1–5] and more recently the cyanides [6], which exhibit negative thermal expansion. These interesting compounds, along with their analogs that have positive thermal expansion, are worthy of further research. Because of the robustness of the negative thermal expansion of some of these compounds, they may be used to form composites that have specifically tailored thermal expansion coefficients. Pressure may be used in the synthesis of these composites; therefore, it is desirable to know the highpressure properties of negative thermal expansion compounds. Indeed, an x-ray diffraction study has shown interesting highpressure behavior for ZrV2 O7 , including phase transitions from the α (cubic) to the β (pseudo-tetragonal) structure at 1.38–1.72 GPa and amorphization above 4 GPa [2].
∗ Corresponding author.
E-mail address: [email protected] (M.B. Kruger). c 2007 Elsevier Ltd. All rights reserved. 0038-1098/$ - see front matter doi:10.1016/j.ssc.2007.01.003
The α-phase (cubic) of ZrV2 O7 is the stable structure at ambient conditions. It consists of ZrO6 octahedra whose corners share their oxygen atoms with VO4 tetrahedra. The basic crystal structure of ZrV2 O7 has been compared to that of NaCl, with the ZrO6 octahedra centered at the ideal Na sites, and the bridging oxygen of the VO4 groups centered at the Cl sites [2]. Below 100 ◦ C, ZrV2 O7 has a positive thermal expansion coefficient; however, it has strong and isotropic negative thermal expansion in the temperature range from 100 to 800 ◦ C [7,8]. Using x-ray and Raman measurements, we have recently studied HfV2 O7 , which at room pressure has a negative thermal expansion, and we observed a phase transition at 3.7 GPa [5]. ZrV2 O7 under ambient conditions has a positive thermal expansion coefficient and is isostructural to HfV2 O7 . The results from HfV2 O7 and the similarities and differences between HfV2 O7 and ZrV2 O7 [2] suggest that the highpressure behavior of ZrV2 O7 would be worthy of additional investigation. In this work we carried out high-pressure Raman and mid-infrared measurements up to pressures of 12 and 5.7 GPa, respectively.
U.L.C. Hemamala et al. / Solid State Communications 141 (2007) 680–684
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2. Experiment Powder samples of α-ZrV2 O7 were prepared as described by Carlson et al. and loaded in a Mao-Bell-type diamond anvil cell (DAC) for the Raman and infrared measurements [2]. Diamonds had culet diameters of 350 µm and spring steel gaskets had sample chamber diameters of ∼160 µm. Pressure was determined from the fluorescence shift of a small amount of ruby that was included with the sample and measured before and after data were collected. In the Raman experiment, a mixture of 4:1 methanol:ethanol was used as the pressure transmitting medium. To determine if there was an interaction between the pressure medium and sample, the Raman experiment was repeated nonhydrostatically. The results were similar to the hydrostatic data, implying that there was no interaction between the pressure medium and the ZrV2 O7 . To prevent saturated absorption in the mid-infrared measurements, the sample was diluted with KBr powder (2:98) for ambient and (5:95) for high-pressure measurements. Raman spectra were collected in back-scattering geometry using the 514.532 nm line of an argon–ion laser as the excitation source with 12–30 mW incident on the diamond anvil. A Kaiser supernotch plus filter was used to separate the laser line from the Raman scattered light, and the scattered light was dispersed in a Spectrapro 500i spectrograph and detected with a Spec10 liquid nitrogen cooled CCD detector. Raman spectra were collected up to 12 GPa (decompression to 0.6 GPa), using a 2400 g/mm grating with a slit width of 100 µm which gives spectral resolution of ∼3 cm−1 . A purged Nicolet Nexus 670 FTIR spectrometer equipped with a liquid nitrogen-cooled MCT-A detector was used for mid-infrared spectroscopy.
Fig. 1. Representative Raman and infrared spectra of ZrV2 O7 at ambient and various high pressures. The top spectrum shows the Raman modes of the sample after being decompressed from 12 GPa. The Raman spectra in the region 140–600 cm−1 were collected for 1200 s and 600–1100 cm−1 were collected for 120 s. Peaks denoted by diamonds are not due to the sample and probably a result of a slight misalignment of the notch filter. The bottom spectrum is the ambient infrared absorption spectrum of ZrV2 O7 taken outside of the DAC.
is used for self-consistent force calculations. A small atom ˚ is used to perturb the relaxed displacement of 0.02 A structure. 4. Results and discussion
3. Theory The phonon modes at the Brillouin zone center were calculated using a direct method. In this method, a small atom displacement is used to perturb the force-free optimized structure. The resulting forces on all atoms are then used to construct the force constant matrices and the dynamical matrices; the phonon modes can be obtained from the dynamical matrices. Our calculations were carried out using D. Alf¨e’s PHON program [9] with our improvements [10] and the Vienna ab-initio Simulation Package (VASP) [11,12]. We use the unit cell of ZrV2 O7 (40 atoms in the unit cell) ˚ for the present calculations since its cell size of 8.8032 A is generally considered as sufficient for phonon calculations, and the larger 3 × 3 × 3 supercell (320 atoms) would be computationally prohibitive. We use the projected augmented wave method (PAW) [13,14] with the generalized gradient approximation (GGA) of Perdew–Burke–Ernzerhof (PBE) [15] in the VASP calculations. Partial core corrections are included for the Zr and V atoms. For accurate force calculations, we use ‘PREC=Accurate’ for all VASP calculations. The plane wave energy cutoff is 500 eV. A 4 × 4 × 4 K-point sampling mesh was generated using the Monkhorst-Pak ˚ is used method [16]. A force convergence of 0.001 eV/A for geometry relaxation. A tight convergence of 0.001 meV
Reported x-ray powder diffraction studies show that α-ZrV2 O7 (cubic) undergoes a pressure-induced phase transition between 1.38 and 1.72 GPa to the β-phase (pseudotetragonal) and becomes x-ray amorphous above 4 GPa [2]. These phase transitions should be indicated by changes in the Raman and infrared spectra, such as by the addition or loss of peaks, the change in the pressure dependence of peaks, and, in the case of amorphization, significant peak broadening. α-ZrV2 O7 belongs to the space group Pa 3¯ and has a 3 × 3 × 3 supercell of a small unit cell, which contains four molecules [2]. Thus, there should be 1074 normal modes, many only weakly separated from one another owing to Davydov splitting. The structure of the high-pressure β-phase has been studied, and found to be pseudo-tetragonal [2]. Fig. 1 displays representative Raman spectra of ZrV2 O7 at various pressures. With the sample outside of the DAC, 12 Raman-active modes centered at 144, 189, 263, 280, 367, 380, 404, 511, 774, 957, 984, and 1023 cm−1 were detected. By comparison with spectra of crystals containing the VO4 tetrahedra and ZrO6 octahedra and checking with our theoretical calculations, the modes centered at 957, 984, and 1023 cm−1 are assigned to symmetric stretching of the VO4 tetrahedra, that at 774 cm−1 to the asymmetric stretching of the VO4 tetrahedra, those at 404 and 511 cm−1 to VO4 asymmetric
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Table 1 Mode Gr¨uneisen parameters (γ ) and pressure derivatives (dω/dP) of the various Raman (Part A) and IR (Part B) modes of α- and β-ZrV2 O7 Assignment
Symmetry assignment
α Phase (ambient pressure) Mode freq. (cm−1 ) exp/theory
β Phase (1.6 GPa)
dω/dP (cm−1 /GPa)
γi
Mode freq. (cm−1 )
dω/dP (cm−1 /GPa)
γi
−3.9 ± 1.38 −1.46 ± 1.6 1.39 ± 1.1 4.17 ± 1.29
−0.07 ± 0.02 −0.03 ± 0.04 0.03 ± 0.02 0.08 ± 0.02
1014 983 949 810
−2.86 ± 0.79 −4.6 ± 0.81 1.13 ± 1 −0.32 ± 0.5
−0.09 ± 0.03 −0.17 ± 0.02 0.04 ± 0.02 −0.01 ± 0.02
7.69 ± 0.73 7.28 ± 0.38 0.84 ± 2.92
0.17 ± 0.02 0.16 ± 0.01 0.02 ± 0.07
795 781 705
−1.22 ± 0.84 0.96 ± 0.36 8.92 ± 1.25
−0.06 ± 0.03 0.04 ± 0.02 0.45 ± 0.06
17.7 ± 1.86 39.4 ± 4.02 13.2 ± 2.19
0.59 ± 0.06 1.47 ± 0.15 0.56 ± 0.09
546 534 517 441 407
7.95 ± 0.85 1.19 ± 1.15 4.27 ± 0.52 12.25 ± 0.78 9.14 ± 0.89
0.52 ± 0.04 0.08 ± 0.07 0.29 ± 0.04 0.99 ± 0.07 0.8 ± 0.09
28.5 ± 1.26 18.3 ± 1.02 21.5 ± 2.98 15.7 ± 2.84 18.7 ± 4.47 2.7 ± 0.49 14.4 ± 0.7 −0.35 ± 0.2 9.05 ± 0.99
1.3 ± 0.06 0.86 ± 0.05 1.1 ± 0.15 0.92 ± 0.17 1.15 ± 0.27 0.18 ± 0.03 1.1 ± 0.06 − 0.03 ± 0.01 1.09 ± 0.22
364 304 285 273 248 225 186
19.1 ± 2.43 39.2 ± 7.19 23.47 ± 0.69 25.89 ± 3.49 36.2 ± 1.17 14.18 ± 0.31 2.89 ± 0.38
1.87 ± 0.24 4.6 ± 0.76 2.95 ± 0.09 3.39 ± 0.45 5.2 ± 0.17 2.25 ± 0.06 0.56 ± 0.01
−2 ± 1
−0.04 ± 0.02
914
−5 ± 1
5±3 9±1 5±2
0.05 ± 0.03 0.04 ± 0.02 1.2 ± 0.1 2.0 ± 0.4
761 709 667
2±1 10 ± 1.0 1±1 7±1
Part A ν s (VO4 )
ν as (VO4 )
δ as (VO4 )/ν s (ZrO6 )
δ s (VO4 )
Lattice Mode
Tg Ag Tg Tg Eg
Tg Ag
Tg Tg Eg
Tg Ag Ag
1090b 1041/1061a 1023/1028 984/881 957 868b 791a 774 705a 516b 511/511 461a 404
396b 380/382a 367/366 338a 296a 280 263/260 226/218 189/193 144
Part B ν s (VO4 ) (IR)
ν as (VO4 ) (IR)
978 910 874 822 758 700 666
−0.20 ± 0.05
0.10 ± 0.05 0.5 ± 0.05 0.1 ± 0.1 0.4 ± 0.06
The frequencies used in the calculations were experimentally measured. The theoretically determined frequencies are also listed. The reported values of χ T = 5.8 × 10−2 GPa−1 for the α phase and 2.8 × 10−2 GPa−1 for the β phase, are used in the calculation of the mode Gr¨uneisen parameters [2]. νs and νas represent symmetrical and asymmetrical stretching modes, respectively. Symmetrical and asymmetrical bending modes are represented by δs and δas . a Since these modes were not observed at ambient conditions, y-intercepts of the best-fit lines of the peaks as shown in Fig. 2 were used in calculating Gr¨uneisen parameters. b These modes were not observed experimentally.
bending in combination with ZrO6 octahedral stretching, those at 367, 380, 280 and 263 cm−1 to the symmetric bending of the VO4 tetrahedra and the vibrations at 144 and 189 cm−1 to lattice modes [17]. The above assignments and the theoretical calculations as shown in Table 1. As pressure on the sample is increased, peaks move towards higher wavenumbers, and modes appear owing to differences in pressure dependencies of closely spaced peaks. These differences can be easily seen in Fig. 2. Under ambient conditions the strong peak at 263 cm−1 has asymmetry due to the two weak shoulder peaks. These weak peaks become four peaks centered at about 232, 264, 285, and 305 cm−1 at 0.5 GPa. These shoulder peaks disappear after 1.7 GPa. At 0.5 GPa, the peak centered at 367 cm−1 under ambient conditions, becomes a doublet with centers at 373 and 385 cm−1 . At 1.6 GPa it becomes a singlet. The two weak
shoulder peaks that appear at 0.5 GPa at 352 and 405 cm−1 , cause the asymmetry of the peak at 367 cm−1 . The peak at 352 cm−1 under ambient conditions, disappears after 3.7 GPa. A weak shoulder peak at 404 cm−1 under ambient conditions disappears at around 1.1 GPa and possibly a new mode appears around 1.6 GPa. The peak at 511 cm−1 shows characteristics of a triplet around 1.6 GPa with two weak shoulder peaks centered at 483 and 518 cm−1 which appeared at 0.5 GPa, possibly contributing to this triplet. The peak at 774 cm−1 shows two weak shoulder peaks at around 793 and 702 cm−1 at 0.5 GPa. The strong peak at 774 cm−1 becomes a triplet with centers at around 780, 794, and 810 cm−1 at 1.6 GPa. This triplet becomes a doublet at around 3.2 GPa and becomes one broad peak at 4.2 GPa. Furthermore, two weak shoulder peaks appear at 957 and 1036 cm−1 around 0.5 GPa. All peaks show a discontinuity in their slope at 1.5 GPa, indicative of a structural phase change,
U.L.C. Hemamala et al. / Solid State Communications 141 (2007) 680–684
Fig. 2. Solid circles represent the pressure dependence of the frequencies of the observed Raman modes of ZrV2 O7 (140–1020 cm−1 ). Solid triangles represent the pressure dependence of the frequencies of the observed infrared modes (600–1020 cm−1 ). The vertical dashed lines delineate phase boundaries.
such as the previously reported cubic (α) to pseudo-tetragonal (β) phase transition [2]. At 3.7 GPa, the spectrum has broad peaks centered at around 429, 528, 564, and 792 cm−1 . Between 3.7 and 4.1 GPa, changes again occur in the Raman spectra. All the peaks except two broad peaks which remain even at 4.9 GPa disappear (Fig. 1). This peak broadening and disappearance of peaks is consistent with pressure-induced amorphization and therefore is in agreement with the x-ray study that reported amorphization above 4 GPa [2]. The Raman spectrum of the decompressed sample contains broad peaks, suggesting that the amorphous structure remains upon decompression. We calculated the mode Gr¨uneisen parameters for both the cubic (α) and pseudo-tetragonal (β) phases of ZrV2 O7 . The Gr¨uneisen parameter, γi = (ωi χT )−1 (∂ωi /∂ P), where ωi is the frequency of the ith mode, P is the pressure, and χT is the isothermal volume compressibility [18]. For the calculations of the Gr¨uneisen parameters, we used peak positions at ambient pressure for the α phase and peak positions at 1.6 GPa for the β phase, as the frequency, ωi . For the modes that first appear at 0.5 GPa, the y-intercept of the best fit line through the points of the corresponding mode was taken as ωi. . In Table 1, the calculated zone center Raman active modes are listed in order of decreasing wave number. Normal mode analysis shows that out of 120 vibrational phonon modes, there are three acoustic phonon modes and the remaining 117 modes have the following symmetries: 4A g + 6Au + 4E g + 6E u + 12Tg + 17Tu . Among the 49 optical phonons, 20 phonons (4A g + 4E g + 12Tg ) are Raman active and 18 phonons (18Tu ) are IR active. The bottom spectrum in Fig. 1 provides a representative infrared spectrum of ZrV2 O7 at ambient pressure, while the
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solid triangles in Fig. 2 show the frequency shifts of the infrared modes with respect to pressure. At ambient pressure, seven peaks are detectable, the peaks at 978, 910, 874, and 822 cm−1 being attributed to symmetric stretching of VO4 tetrahedra and those at 758, 700, and 666 cm−1 to asymmetric stretching [17]. Table 1 lists the mode Gr¨uneisen parameters for both the α and β phases of the material, averaging 0.58 and 1.03, respectively [17]. Positive values for the average mode Gr¨uneisen parameter implies a positive thermal expansion coefficient at room temperature. This was known for the cubic (low-pressure) phase, but was not known for the high-pressure phase. The infrared data provides no definitive evidence of a pressure-induced α − β phase transition via new modes or mode disappearance. This may be owing to minimal changes in the spectral features greater than ∼600 cm−1 , evident from the Raman spectra (Fig. 1), which show drastic changes only in the low-frequency region. However, the phase transition can be estimated from the present infrared data by comparison of frequency shifts versus pressure for different pressure regions. Using this technique, we have estimated that the phase transition occurs at around 1.5 GPa. Though slightly lower than the 1.6–1.7 GPa phase transition pressure found based upon the Raman spectra, it is within the range of uncertainty for our measurements. In agreement with the Raman measurements, the infrared spectrum of the decompressed sample suggests that the transition to the amorphous phase is irreversible. 5. Conclusion We measured the Raman and infrared spectra of zirconium pyrovanadate (ZrV2 O7 ) up to 12 and 5.7 GPa, respectively, at room temperature. The changes under pressure of the stretching and bending modes of the VO4 tetrahedra as well as the stretching modes of the ZrO6 octahedra have been studied and Gr¨uneisen parameters for the Raman and infrared active modes yielded values of 0.58 and 1.03 for the α and β phases, respectively. In agreement with the previously reported x-ray results, the spectra indicate that there is a phase transition at ∼1.6 GPa, and an irreversible transition from the β-phase to an amorphous structure at around 4 GPa. Acknowledgment This work was supported by the National Science Foundation. References [1] B. Chen, D. Penwell, M.B. Kruger, et al., J. Appl. Phys. 89 (2001) 4794. [2] S. Carlson, A.M. Krogh-Andersen, J. Appl. Cryst. 34 (2001) 7. [3] J.S.O. Evans, J.C. Hanson, A.W. Sleight, Acta Crystallogr. — Sect. B: Struct. Sci. 54 (1998) 705. [4] T.A. Mary, J.S.O. Evans, T. Vogt, et al., Science 272 (1996) 90. [5] U.L.C. Hemamala, F. El-Ghussein, A.M. Goedken, et al., Phys. Rev. B 70 (2004) 4114. [6] A.L. Goodwin, C.J. Kepert, Phys. Rev. B 71 (2005) 140301. [7] N. Khosrovani, A.W. Sleight, T. Vogt, J. Solid State Chem. 132 (2) (1997) 355–360. Publisher: Academic Press, USA, 132, 355 (1997).
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[8] V. Korthuis, N. Khosrovani, A.W. Sleight, et al., Chem. Mater. 7 (1995) 412. [9] D. Alf¨e. Program available at: http://chianti.geol.ucl.ac.uk/˜dario, 1998. [10] L. Ouyang, W.Y. Ching, Phys. Status Solidi B 242 (2005) R64. [11] G. Kresse, J. Furthm¨uIler, Phys. Rev. B 54 (1996) 11169. [12] G. Kresse, J. Furthm¨uIler, Comput. Mater. Sci. 6 (1996) 15. [13] P.E. Bl¨ochl, Phys. Rev. B 50 (1994) 17953.
[14] [15] [16] [17]
G. Kresse, D. Joubert, Phys. Rev. B 59 (1999) 1758. J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865. H.J. Monkhorst, J.D. Pack, Phys. Rev. B 13 (1976) 5188. K. Nakamoto, Infrared and Raman Spectra of Inorganic and Coordination Compounds, John Wiley & Sons, New York, 1986. [18] B.A. Weinstein, R. Zallen, Light Scattering in Solids IV/Topics in Applied Physics, Springer-Verlag, Berlin, 1984.
High-pressure Raman and infrared study of ZrV2O7 U.L.C. Hemamala a , F. El-Ghussein a , D.V.S. Muthu a,b , A.M. Krogh Andersen c , S. Carlson d , L. Ouyang a , M.B. Kruger a,∗ a Department of Physics, University of Missouri, Kansas City, MO 64110, USA b Department of Physics, Indian Institute of Science, Bangalore – 560 012, India c Department of Structural Chemistry, Stockholm University, SE-10691 Stockholm, Sweden d Lund University, MAX Lab, SE-22100 Lund, Sweden
Received 20 November 2006; received in revised form 2 January 2007; accepted 3 January 2007 by R. Merlin Available online 9 January 2007
Abstract The room-temperature Raman and infrared spectra of zirconium vanadate (ZrV2 O7 ) were observed up to pressures of 12 GPa and 5.7 GPa, respectively. The frequencies of the optically active modes at ambient pressure were calculated using direct methods and compared with experimental values. Average mode Gr¨uneisen parameters were calculated for the Raman and infrared active modes. Changes in the spectra under pressure indicate a phase transition at ∼1.6 GPa, which is consistent with the previously observed α (cubic) to β (pseudo-tetragonal) phase transition, and changes in the spectra at ∼4 GPa are consistent with an irreversible transformation to an amorphous structure. c 2007 Elsevier Ltd. All rights reserved.
PACS: 78.30-j; 81.40.Vw; 64.70.-p Keywords: E. Strain, high pressure; E. Inelastic light scattering; E. Light absorption and reflection
1. Introduction Many studies have been done on the MX2 O8 and MX2 O7 (M = Zr, Hf and X = W, Mo, V) families of compounds [1–5] and more recently the cyanides [6], which exhibit negative thermal expansion. These interesting compounds, along with their analogs that have positive thermal expansion, are worthy of further research. Because of the robustness of the negative thermal expansion of some of these compounds, they may be used to form composites that have specifically tailored thermal expansion coefficients. Pressure may be used in the synthesis of these composites; therefore, it is desirable to know the highpressure properties of negative thermal expansion compounds. Indeed, an x-ray diffraction study has shown interesting highpressure behavior for ZrV2 O7 , including phase transitions from the α (cubic) to the β (pseudo-tetragonal) structure at 1.38–1.72 GPa and amorphization above 4 GPa [2].
∗ Corresponding author.
E-mail address: [email protected] (M.B. Kruger). c 2007 Elsevier Ltd. All rights reserved. 0038-1098/$ - see front matter doi:10.1016/j.ssc.2007.01.003
The α-phase (cubic) of ZrV2 O7 is the stable structure at ambient conditions. It consists of ZrO6 octahedra whose corners share their oxygen atoms with VO4 tetrahedra. The basic crystal structure of ZrV2 O7 has been compared to that of NaCl, with the ZrO6 octahedra centered at the ideal Na sites, and the bridging oxygen of the VO4 groups centered at the Cl sites [2]. Below 100 ◦ C, ZrV2 O7 has a positive thermal expansion coefficient; however, it has strong and isotropic negative thermal expansion in the temperature range from 100 to 800 ◦ C [7,8]. Using x-ray and Raman measurements, we have recently studied HfV2 O7 , which at room pressure has a negative thermal expansion, and we observed a phase transition at 3.7 GPa [5]. ZrV2 O7 under ambient conditions has a positive thermal expansion coefficient and is isostructural to HfV2 O7 . The results from HfV2 O7 and the similarities and differences between HfV2 O7 and ZrV2 O7 [2] suggest that the highpressure behavior of ZrV2 O7 would be worthy of additional investigation. In this work we carried out high-pressure Raman and mid-infrared measurements up to pressures of 12 and 5.7 GPa, respectively.
U.L.C. Hemamala et al. / Solid State Communications 141 (2007) 680–684
681
2. Experiment Powder samples of α-ZrV2 O7 were prepared as described by Carlson et al. and loaded in a Mao-Bell-type diamond anvil cell (DAC) for the Raman and infrared measurements [2]. Diamonds had culet diameters of 350 µm and spring steel gaskets had sample chamber diameters of ∼160 µm. Pressure was determined from the fluorescence shift of a small amount of ruby that was included with the sample and measured before and after data were collected. In the Raman experiment, a mixture of 4:1 methanol:ethanol was used as the pressure transmitting medium. To determine if there was an interaction between the pressure medium and sample, the Raman experiment was repeated nonhydrostatically. The results were similar to the hydrostatic data, implying that there was no interaction between the pressure medium and the ZrV2 O7 . To prevent saturated absorption in the mid-infrared measurements, the sample was diluted with KBr powder (2:98) for ambient and (5:95) for high-pressure measurements. Raman spectra were collected in back-scattering geometry using the 514.532 nm line of an argon–ion laser as the excitation source with 12–30 mW incident on the diamond anvil. A Kaiser supernotch plus filter was used to separate the laser line from the Raman scattered light, and the scattered light was dispersed in a Spectrapro 500i spectrograph and detected with a Spec10 liquid nitrogen cooled CCD detector. Raman spectra were collected up to 12 GPa (decompression to 0.6 GPa), using a 2400 g/mm grating with a slit width of 100 µm which gives spectral resolution of ∼3 cm−1 . A purged Nicolet Nexus 670 FTIR spectrometer equipped with a liquid nitrogen-cooled MCT-A detector was used for mid-infrared spectroscopy.
Fig. 1. Representative Raman and infrared spectra of ZrV2 O7 at ambient and various high pressures. The top spectrum shows the Raman modes of the sample after being decompressed from 12 GPa. The Raman spectra in the region 140–600 cm−1 were collected for 1200 s and 600–1100 cm−1 were collected for 120 s. Peaks denoted by diamonds are not due to the sample and probably a result of a slight misalignment of the notch filter. The bottom spectrum is the ambient infrared absorption spectrum of ZrV2 O7 taken outside of the DAC.
is used for self-consistent force calculations. A small atom ˚ is used to perturb the relaxed displacement of 0.02 A structure. 4. Results and discussion
3. Theory The phonon modes at the Brillouin zone center were calculated using a direct method. In this method, a small atom displacement is used to perturb the force-free optimized structure. The resulting forces on all atoms are then used to construct the force constant matrices and the dynamical matrices; the phonon modes can be obtained from the dynamical matrices. Our calculations were carried out using D. Alf¨e’s PHON program [9] with our improvements [10] and the Vienna ab-initio Simulation Package (VASP) [11,12]. We use the unit cell of ZrV2 O7 (40 atoms in the unit cell) ˚ for the present calculations since its cell size of 8.8032 A is generally considered as sufficient for phonon calculations, and the larger 3 × 3 × 3 supercell (320 atoms) would be computationally prohibitive. We use the projected augmented wave method (PAW) [13,14] with the generalized gradient approximation (GGA) of Perdew–Burke–Ernzerhof (PBE) [15] in the VASP calculations. Partial core corrections are included for the Zr and V atoms. For accurate force calculations, we use ‘PREC=Accurate’ for all VASP calculations. The plane wave energy cutoff is 500 eV. A 4 × 4 × 4 K-point sampling mesh was generated using the Monkhorst-Pak ˚ is used method [16]. A force convergence of 0.001 eV/A for geometry relaxation. A tight convergence of 0.001 meV
Reported x-ray powder diffraction studies show that α-ZrV2 O7 (cubic) undergoes a pressure-induced phase transition between 1.38 and 1.72 GPa to the β-phase (pseudotetragonal) and becomes x-ray amorphous above 4 GPa [2]. These phase transitions should be indicated by changes in the Raman and infrared spectra, such as by the addition or loss of peaks, the change in the pressure dependence of peaks, and, in the case of amorphization, significant peak broadening. α-ZrV2 O7 belongs to the space group Pa 3¯ and has a 3 × 3 × 3 supercell of a small unit cell, which contains four molecules [2]. Thus, there should be 1074 normal modes, many only weakly separated from one another owing to Davydov splitting. The structure of the high-pressure β-phase has been studied, and found to be pseudo-tetragonal [2]. Fig. 1 displays representative Raman spectra of ZrV2 O7 at various pressures. With the sample outside of the DAC, 12 Raman-active modes centered at 144, 189, 263, 280, 367, 380, 404, 511, 774, 957, 984, and 1023 cm−1 were detected. By comparison with spectra of crystals containing the VO4 tetrahedra and ZrO6 octahedra and checking with our theoretical calculations, the modes centered at 957, 984, and 1023 cm−1 are assigned to symmetric stretching of the VO4 tetrahedra, that at 774 cm−1 to the asymmetric stretching of the VO4 tetrahedra, those at 404 and 511 cm−1 to VO4 asymmetric
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Table 1 Mode Gr¨uneisen parameters (γ ) and pressure derivatives (dω/dP) of the various Raman (Part A) and IR (Part B) modes of α- and β-ZrV2 O7 Assignment
Symmetry assignment
α Phase (ambient pressure) Mode freq. (cm−1 ) exp/theory
β Phase (1.6 GPa)
dω/dP (cm−1 /GPa)
γi
Mode freq. (cm−1 )
dω/dP (cm−1 /GPa)
γi
−3.9 ± 1.38 −1.46 ± 1.6 1.39 ± 1.1 4.17 ± 1.29
−0.07 ± 0.02 −0.03 ± 0.04 0.03 ± 0.02 0.08 ± 0.02
1014 983 949 810
−2.86 ± 0.79 −4.6 ± 0.81 1.13 ± 1 −0.32 ± 0.5
−0.09 ± 0.03 −0.17 ± 0.02 0.04 ± 0.02 −0.01 ± 0.02
7.69 ± 0.73 7.28 ± 0.38 0.84 ± 2.92
0.17 ± 0.02 0.16 ± 0.01 0.02 ± 0.07
795 781 705
−1.22 ± 0.84 0.96 ± 0.36 8.92 ± 1.25
−0.06 ± 0.03 0.04 ± 0.02 0.45 ± 0.06
17.7 ± 1.86 39.4 ± 4.02 13.2 ± 2.19
0.59 ± 0.06 1.47 ± 0.15 0.56 ± 0.09
546 534 517 441 407
7.95 ± 0.85 1.19 ± 1.15 4.27 ± 0.52 12.25 ± 0.78 9.14 ± 0.89
0.52 ± 0.04 0.08 ± 0.07 0.29 ± 0.04 0.99 ± 0.07 0.8 ± 0.09
28.5 ± 1.26 18.3 ± 1.02 21.5 ± 2.98 15.7 ± 2.84 18.7 ± 4.47 2.7 ± 0.49 14.4 ± 0.7 −0.35 ± 0.2 9.05 ± 0.99
1.3 ± 0.06 0.86 ± 0.05 1.1 ± 0.15 0.92 ± 0.17 1.15 ± 0.27 0.18 ± 0.03 1.1 ± 0.06 − 0.03 ± 0.01 1.09 ± 0.22
364 304 285 273 248 225 186
19.1 ± 2.43 39.2 ± 7.19 23.47 ± 0.69 25.89 ± 3.49 36.2 ± 1.17 14.18 ± 0.31 2.89 ± 0.38
1.87 ± 0.24 4.6 ± 0.76 2.95 ± 0.09 3.39 ± 0.45 5.2 ± 0.17 2.25 ± 0.06 0.56 ± 0.01
−2 ± 1
−0.04 ± 0.02
914
−5 ± 1
5±3 9±1 5±2
0.05 ± 0.03 0.04 ± 0.02 1.2 ± 0.1 2.0 ± 0.4
761 709 667
2±1 10 ± 1.0 1±1 7±1
Part A ν s (VO4 )
ν as (VO4 )
δ as (VO4 )/ν s (ZrO6 )
δ s (VO4 )
Lattice Mode
Tg Ag Tg Tg Eg
Tg Ag
Tg Tg Eg
Tg Ag Ag
1090b 1041/1061a 1023/1028 984/881 957 868b 791a 774 705a 516b 511/511 461a 404
396b 380/382a 367/366 338a 296a 280 263/260 226/218 189/193 144
Part B ν s (VO4 ) (IR)
ν as (VO4 ) (IR)
978 910 874 822 758 700 666
−0.20 ± 0.05
0.10 ± 0.05 0.5 ± 0.05 0.1 ± 0.1 0.4 ± 0.06
The frequencies used in the calculations were experimentally measured. The theoretically determined frequencies are also listed. The reported values of χ T = 5.8 × 10−2 GPa−1 for the α phase and 2.8 × 10−2 GPa−1 for the β phase, are used in the calculation of the mode Gr¨uneisen parameters [2]. νs and νas represent symmetrical and asymmetrical stretching modes, respectively. Symmetrical and asymmetrical bending modes are represented by δs and δas . a Since these modes were not observed at ambient conditions, y-intercepts of the best-fit lines of the peaks as shown in Fig. 2 were used in calculating Gr¨uneisen parameters. b These modes were not observed experimentally.
bending in combination with ZrO6 octahedral stretching, those at 367, 380, 280 and 263 cm−1 to the symmetric bending of the VO4 tetrahedra and the vibrations at 144 and 189 cm−1 to lattice modes [17]. The above assignments and the theoretical calculations as shown in Table 1. As pressure on the sample is increased, peaks move towards higher wavenumbers, and modes appear owing to differences in pressure dependencies of closely spaced peaks. These differences can be easily seen in Fig. 2. Under ambient conditions the strong peak at 263 cm−1 has asymmetry due to the two weak shoulder peaks. These weak peaks become four peaks centered at about 232, 264, 285, and 305 cm−1 at 0.5 GPa. These shoulder peaks disappear after 1.7 GPa. At 0.5 GPa, the peak centered at 367 cm−1 under ambient conditions, becomes a doublet with centers at 373 and 385 cm−1 . At 1.6 GPa it becomes a singlet. The two weak
shoulder peaks that appear at 0.5 GPa at 352 and 405 cm−1 , cause the asymmetry of the peak at 367 cm−1 . The peak at 352 cm−1 under ambient conditions, disappears after 3.7 GPa. A weak shoulder peak at 404 cm−1 under ambient conditions disappears at around 1.1 GPa and possibly a new mode appears around 1.6 GPa. The peak at 511 cm−1 shows characteristics of a triplet around 1.6 GPa with two weak shoulder peaks centered at 483 and 518 cm−1 which appeared at 0.5 GPa, possibly contributing to this triplet. The peak at 774 cm−1 shows two weak shoulder peaks at around 793 and 702 cm−1 at 0.5 GPa. The strong peak at 774 cm−1 becomes a triplet with centers at around 780, 794, and 810 cm−1 at 1.6 GPa. This triplet becomes a doublet at around 3.2 GPa and becomes one broad peak at 4.2 GPa. Furthermore, two weak shoulder peaks appear at 957 and 1036 cm−1 around 0.5 GPa. All peaks show a discontinuity in their slope at 1.5 GPa, indicative of a structural phase change,
U.L.C. Hemamala et al. / Solid State Communications 141 (2007) 680–684
Fig. 2. Solid circles represent the pressure dependence of the frequencies of the observed Raman modes of ZrV2 O7 (140–1020 cm−1 ). Solid triangles represent the pressure dependence of the frequencies of the observed infrared modes (600–1020 cm−1 ). The vertical dashed lines delineate phase boundaries.
such as the previously reported cubic (α) to pseudo-tetragonal (β) phase transition [2]. At 3.7 GPa, the spectrum has broad peaks centered at around 429, 528, 564, and 792 cm−1 . Between 3.7 and 4.1 GPa, changes again occur in the Raman spectra. All the peaks except two broad peaks which remain even at 4.9 GPa disappear (Fig. 1). This peak broadening and disappearance of peaks is consistent with pressure-induced amorphization and therefore is in agreement with the x-ray study that reported amorphization above 4 GPa [2]. The Raman spectrum of the decompressed sample contains broad peaks, suggesting that the amorphous structure remains upon decompression. We calculated the mode Gr¨uneisen parameters for both the cubic (α) and pseudo-tetragonal (β) phases of ZrV2 O7 . The Gr¨uneisen parameter, γi = (ωi χT )−1 (∂ωi /∂ P), where ωi is the frequency of the ith mode, P is the pressure, and χT is the isothermal volume compressibility [18]. For the calculations of the Gr¨uneisen parameters, we used peak positions at ambient pressure for the α phase and peak positions at 1.6 GPa for the β phase, as the frequency, ωi . For the modes that first appear at 0.5 GPa, the y-intercept of the best fit line through the points of the corresponding mode was taken as ωi. . In Table 1, the calculated zone center Raman active modes are listed in order of decreasing wave number. Normal mode analysis shows that out of 120 vibrational phonon modes, there are three acoustic phonon modes and the remaining 117 modes have the following symmetries: 4A g + 6Au + 4E g + 6E u + 12Tg + 17Tu . Among the 49 optical phonons, 20 phonons (4A g + 4E g + 12Tg ) are Raman active and 18 phonons (18Tu ) are IR active. The bottom spectrum in Fig. 1 provides a representative infrared spectrum of ZrV2 O7 at ambient pressure, while the
683
solid triangles in Fig. 2 show the frequency shifts of the infrared modes with respect to pressure. At ambient pressure, seven peaks are detectable, the peaks at 978, 910, 874, and 822 cm−1 being attributed to symmetric stretching of VO4 tetrahedra and those at 758, 700, and 666 cm−1 to asymmetric stretching [17]. Table 1 lists the mode Gr¨uneisen parameters for both the α and β phases of the material, averaging 0.58 and 1.03, respectively [17]. Positive values for the average mode Gr¨uneisen parameter implies a positive thermal expansion coefficient at room temperature. This was known for the cubic (low-pressure) phase, but was not known for the high-pressure phase. The infrared data provides no definitive evidence of a pressure-induced α − β phase transition via new modes or mode disappearance. This may be owing to minimal changes in the spectral features greater than ∼600 cm−1 , evident from the Raman spectra (Fig. 1), which show drastic changes only in the low-frequency region. However, the phase transition can be estimated from the present infrared data by comparison of frequency shifts versus pressure for different pressure regions. Using this technique, we have estimated that the phase transition occurs at around 1.5 GPa. Though slightly lower than the 1.6–1.7 GPa phase transition pressure found based upon the Raman spectra, it is within the range of uncertainty for our measurements. In agreement with the Raman measurements, the infrared spectrum of the decompressed sample suggests that the transition to the amorphous phase is irreversible. 5. Conclusion We measured the Raman and infrared spectra of zirconium pyrovanadate (ZrV2 O7 ) up to 12 and 5.7 GPa, respectively, at room temperature. The changes under pressure of the stretching and bending modes of the VO4 tetrahedra as well as the stretching modes of the ZrO6 octahedra have been studied and Gr¨uneisen parameters for the Raman and infrared active modes yielded values of 0.58 and 1.03 for the α and β phases, respectively. In agreement with the previously reported x-ray results, the spectra indicate that there is a phase transition at ∼1.6 GPa, and an irreversible transition from the β-phase to an amorphous structure at around 4 GPa. Acknowledgment This work was supported by the National Science Foundation. References [1] B. Chen, D. Penwell, M.B. Kruger, et al., J. Appl. Phys. 89 (2001) 4794. [2] S. Carlson, A.M. Krogh-Andersen, J. Appl. Cryst. 34 (2001) 7. [3] J.S.O. Evans, J.C. Hanson, A.W. Sleight, Acta Crystallogr. — Sect. B: Struct. Sci. 54 (1998) 705. [4] T.A. Mary, J.S.O. Evans, T. Vogt, et al., Science 272 (1996) 90. [5] U.L.C. Hemamala, F. El-Ghussein, A.M. Goedken, et al., Phys. Rev. B 70 (2004) 4114. [6] A.L. Goodwin, C.J. Kepert, Phys. Rev. B 71 (2005) 140301. [7] N. Khosrovani, A.W. Sleight, T. Vogt, J. Solid State Chem. 132 (2) (1997) 355–360. Publisher: Academic Press, USA, 132, 355 (1997).
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