6180
J. Phys. Chem. B 1997, 101, 6180-6183
Crystal-Orientation Dependence of Raman Spectra of Natural Air Hydrate Single Crystal Tomoko Ikeda,* Hiroshi Fukazawa, and Shinji Mae Department of Applied Physics, Hokkaido UniVersity, Sapporo 060, Japan
Takeo Hondoh Institute of Low-Temperature Science, Hokkaido UniVersity, Sapporo 060, Japan
Chester C. Langway, Jr. Department of Geology, State UniVersity of New York at Buffalo Amherst, New York 14226 ReceiVed: October 11, 1996; In Final Form: April 14, 1997X
The polarized Raman spectra of a natural air hydrate single crystal from a deep ice core recovered at Dye-3 Greenland have been measured in order to examine the crystal-orientation dependence of the Raman spectra. Since the crystal had facets, the orientation of the crystal was determined by using the Miller indices of facets. When the angle θ between the polarization plane of the incident laser beam and the direction of [111] of the crystal varied, it was observed that the intensities of the stretching modes of the two major guest molecules (nitrogen and oxygen) varied with θ. Since the dodecahedron cage in the air hydrate are distorted along the 〈111〉 axis, the variations of the scattering intensities of N2 and O2 have been calculated by using a simple model that assumes N2 and O2 are on the plane of {111} in the dodecahedron cage. The results obtained from experiments are consistent with the calculations made by using this simple model. We concluded that the anisotropy of the intensities of N2 and O2 was caused by the anisotropic rotation of the guest molecules in the distorted dodecahedron cage.
Introduction Many air bubbles are formed in polar ice sheets when the firn changes into ice. In response to the increasing pressure, the size of the bubbles decreases with depth. Below a certain depth, the bubbles start to shrink faster than expected and finally become invisible. Although not visible to the naked eye, the unit mass of the bubble-free ice included almost the same volume of air as the unit mass of bubbly ice.1 It was hypothesized that air exists in ice structures in the form of natural air hydrates by Miller.2 Shoji and Langway3 first found natural air hydrates contained in the Dye-3 ice cores by using an optical microscope examination in 1982. Most solid-gas hydrates form one of two distinct crystallographic structures, Stackelberg’s structure I or II,4 depending on the molecular diameters of the guest molecules enclathrated. Miller5 suggested structure I for the natural air hydrate, based on the general rule that guest molecules with maximum van der Waals diameters up to 5.8 Å form structure I. However, Davidson et al. found that the synthetic argon, krypton,6 oxygen, and nitrogen7 hydrates formed structure II by using X-ray and neutron diffraction. This finding suggests that very small molecules such as argon, krypton, nitrogen, and oxygen are preferentially enclathrated in the smaller cages (dodecahedron) of structure II. Hondoh et al.8 revealed that the natural air hydrates in the polar ice core (Dye-3 1500 m) are composed of a single crystal by using X-ray diffraction. Moreover the crystallographic structure also was determined to be the structure II clathrate hydrate because the size of the two major atmospheric gases nitrogen and oxygen are small enough. The first Raman scattering investigations on the natural air hydrates in the Dye-3 ice core (1501 m depth) was achieved X
Abstract published in AdVance ACS Abstracts, June 15, 1997.
S1089-5647(96)03164-1 CCC: $14.00
by Nakahara et al.9 From the observation of their molecular vibrations they identified the major guest molecules in the natural air hydrates as nitrogen and oxygen. Because the intensity of Raman scattering for the normal mode of molecules is proportional to the number of molecules present, the composition ratios of N2 and O2 were estimated to be 1.6-1.9 by comparing the ratios of the peak intensities of N2 and O2. The estimation was performed under the assumption that the Raman spectra of the air hydrates were isotropic because of their cubic symmetry and the diameter of N2 and O2 molecules small enough to undergo isotropic rotation in a cavity. However, we found that the Raman spectra of the natural air hydrate single crystals in the ice cores from Vostok, Antarctica, was anisotropic.10 When the angle that the polarization plane of the incident laser beam makes with the arbitrary direction varied, the peak intensities of N2 and O2 also varied. The crystal orientation of these samples (the Vostok ice cores) could not be determined, because the shape of almost all the air hydrates was spherical and the determination of the crystal orientation by using X-ray diffraction was very difficult. In the present study, the crystal orientation dependence of the Raman spectra of the natural air hydrate single crystal was measured in the Dye-3 ice core (1501 m depth). We chose to examine a single crystal that had clear facets as in Figure 1. Using X-ray diffraction, the facets of the natural air hydrates in Dye-3 ice cores were identified as the Miller indices {111} by Hayakawa et al. (1986, unpublished results). We rotated the polarization plane of the incident laser beam around a given direction of [111] of the crystal with clear facets. The peak intensities of the stretching modes of N2 and O2 and the symmetric stretching mode of water changed with the rotation. Since the dodecahedron cage in a structure II hydrate is distorted along the 〈111〉 axis,11,12 we can assume a simple model where the guest molecule (N2 or O2) undergoes two-dimensional rotation on the plane of {111} in a dodecahedron cage. The © 1997 American Chemical Society
Natural Air Hydrate Single Crystal
J. Phys. Chem. B, Vol. 101, No. 32, 1997 6181
Figure 1. Triangular platelet crystal of the natural air hydrate single crystal in the Dye-3 ice core (1501 m depth). θ is the angle which the polarization plane of the incident beam makes with the direction of θ ) 0°. [111], [1h11h], [1h1h1], and [11h1h] are rotation triad axes of symmetry.
variations of the scattering intensities were calculated under this assumption and were in agreement with the observed results. Thus, we concluded that the anisotropy of Raman spectra was caused by the distortion of the dodecahedron cage along the 〈111〉 axis. Experimental Section In the present experiments, rectangular ice specimen in blocks of 5 × 3 mm3 was cut from the Dye-3 ice core (1501 m depth) kept in a cold room at about 223 K before measurements. The single-crystal ice Ih surrounding the single-crystal air hydrate maintained a sufficiently high pressure on the specimens so as to stabilize the air hydrate. Although there are various shapes of natural air hydrate crystals,3 we selected a single crystal that had clear facets as shown in Figure 1. The size of the crystal is about 60 µm. It’s shape is a platelet with the larger planes being parallel. The angle that the larger planes make with the horizontal plane was about 10°. Its thickness is about 20-40 µm. Since the facets of the air hydrate single crystal are the lattice plane of {111}, four rotation triad axes of symmetry [111], [1h11h], [1h1h1], and [11h1h] are shown in Figure 1. The angles that [111], [1h11h], [1h1h1], and [11h1h] axes make with the direction of θ ) 0° are 12°, 117°, 97°, and 114°, respectively. A series of Raman spectra have been measured with Jobin Yvon Ramanor T64000. The excitation energy for Raman emission was produced by a NEC Ar-ion laser using monochromatic radiation of 514.5 nm with an output of 300 mW. This instrument allows simultaneous recording over the frequency range 25-4000 cm-1, which includes the expected N2 and O2 stretching modes (2323 and 1547 cm-1, respectively9,10,13-15) and H2O stretching modes and translational lattice vibration modes (3135 and 211 cm-1, respectively9,10,16,17). The incident laser beam has the direction of the negative Z axis in Figure 1. The X axis is the direction that made the minimum angle of 12° with the [111] axis. The polarization plane of the incident laser beam was rotated at intervals of 30° with respect to the direction of θ ) 0° (i.e., the direction of the X axis) by using a polarizer. The polarized laser beam was focused on the single crystal of clathrate hydrate with a diameter of 1 µm under an optical microscope. The backscattered light leaves the sample in the positive Z direction and is connected to a spectrometer through a depolarizer. During the experiments, a continuous flow of nitrogen gas maintained the samples at 248 ( 0.1 K.
Figure 2. Crystal-orientation dependence of Raman spectra of the triangular platelet crystal of the natural air hydrate single crystal in the Dye-3 ice core (1501 m depth).
Results and Discussion Figure 2 shows the spectral variation with angle θ. Two sharp peaks for N2 and O2 can clearly be seen at 2323 and 1547 cm-1, respectively, and the frequencies are independent of θ. The peak frequencies observed are identical with those of the natural air hydrates reported previously.9,10,13-15 The broad band observed at 3135 cm-1 is the O-H stretching vibration of water molecules. The frequency of the O-H stretching vibration observed is identical with that of tetrahydrofuran structure II hydrate.16,17 The frequency is about 5 cm-1 higher than that of hexagonal ice. In contrast, Nakahara et al.9 indicated that the spectrum of water molecules in the natural air hydrate is
6182 J. Phys. Chem. B, Vol. 101, No. 32, 1997
Ikeda et al.
Figure 3. (a) Crystal-orientation dependence of the scattering intensities of N2 and O2 stretching modes. The open circles and open triangles are the experimental data for the integrated intensity of N2 and O2. The broken line is the calculation for N2 and O2 by using expression 5. (b) Relationship between the three angles Φj(θ), βj(θ), and γ. E(θ) is the direction of the polarization plane of the incident laser beam.
almost the same as that of hexagonal ice. We consider that the difference in the frequencies is caused by the surrounding ice matrix. The broad band observed at 211 cm-1 is the translational lattice vibration mode. The frequency observed is identical with that of tetrahydrofuran structure II hydrate.17 The features of this band are similar to those seen in the spectrum of hexagonal ice, although the frequency is about 8 cm-1 lower than that of hexagonal ice reported.17,19-24 For hexagonal ice, the intensity of peak at 294 cm-1 depends on the crystal orientation.19,23,24 In contrast, the peak of the natural air hydrate is somewhat broad, and the intensity is independent of θ. The isotropy of the translational lattice vibration mode is thought to be due to the following: (1) the cubic structure of the hydrate cage causes the isotropy; (2) the symmetry of the lattice mode with respect to the molecular-centered coordinate system, which reflects the cubic symmetry of the clathrate cage, is non-totally symmetric. The Raman intensity of non-totally symmetric modes is insensitive to the rotation of the input polarization. Therefore, the observed spectral intensities are normalized by the peak height of the translational lattice vibration mode at 211 cm-1. N2 and O2 Stretching Modes. Figure 2 shows that the peak intensities of N2 and O2 stretching modes vary with the variation of the angle θ. The N2/O2 integrated intensity ratio also varies between 8.06 and 10.33 with the variations of the angle θ, with an average ratio of 9.16. In contrast, Nakahara et al.9 reported that the N2/O2 integrated intensity ratios were 1.4-1.7 for natural air hydrates from the Dye-3 ice core (1501 m in depth). This difference between the results of the present study and earlier results is thought to be due to the difference in the N2/O2 molecular ratio from crystal to crystal. Figure 3a shows the variation of the integrated intensities (arbitrary unit) of the N2 and O2 stretching modes. The open circles and the solid triangles are the data for the integrated intensities of N2 and O2, respectively. It can be seen that both the peaks are at their maximum at θ ) 30° and at their minimum at θ ) 120°, and the period of the variations is 180°. The observed period is identical with that of the Vostok ice cores.10 For the dodecahedron cage in the structure-II clathrate hydrate, the center-to-vertexes distance along the 〈111〉 axis is about 0.2 Å smaller than that equatorial to the 〈111〉 axis.11,12 Consequently, the structure of the dodecahedron cage is distorted along the 〈111〉 axis. On the other hand, the hexakaidecahedron cage is almost spherical in shape.11,12 It can be considered that N2 and O2 molecules are the most stable on the plane of {111} in the dodecahedron cage, because the repulsive interaction between a guest molecule and the adjacent water molecules
along the 〈111〉 axis is stronger than that perpendicular to the 〈111〉 axis. Hence, the guest molecules (N2 or O2) do not rotate completely isotropically in a dodecahedron cage but rotate preferentially on the plane of {111}. The crystal-orientation dependence of the scattering intensity can be calculated by using a simple model, as follows. The intensity of Raman scattering is given by
I(Φ) ∝ |r′E(Φ)|2
(1)
where r′ ) ∂r/∂Q is the polarizability tensor with respect to the normal coordinate Q in any coordinate system.25 E(Φ) ) [E0 cos(Φ), E0 sin(Φ), 0] is the electric field vector of the incident laser beam when the polarization plane is oriented at an angle of Φ with respect to the direction of the axis of the guest molecule, and E0 is the magnitude of the electric field of the incident laser beam. If the axis of the uniaxial molecules such as N2 and O2 is oriented in the x-axis direction, the components of the polarizability derivative are given by
[
R′| 0 0 r′ ) 0 R′⊥ 0 0 0 R′⊥
]
(2)
Here, R′| and R′⊥ are the molecular polarizability derivatives parallel and perpendicular to the axis, respectively.26 Then I(Φ) is given by
I(Φ) ∝ [(R′| cos(Φ))2 + (R′⊥ sin(Φ))2]E02
(3)
To simplify the model, it is assumed that the guest molecule (N2 or O2) in a dodecahedron cage vibrates with rotation twodimensionally on the plane of {111} and that in a hexakaidecahedron cage vibrates with isotropic rotation three-dimensionally. When j is the jth axis in the four rotation triad axes of symmetry 〈111〉, βj(θ) is the angle that the polarization plane makes with the axis of 〈111〉j, and γ is the angle which the axis of the guest molecule makes with the arbitrary direction γ ) 0 on the plane of {111}j. It is assumed that the probability that a guest molecule orientates a direction of γ is constant with respect to all directions on the plane of {111} for the dodecahedron cage. As the relationship between the three angles, Φj(θ), βj(θ), and γ is as Figure 3b, Φj(θ) is related by the equation
cos Φj(θ) ) sinβj(θ)‚sinγ The total scattering intensity of the angle θ is given by
(4)
Natural Air Hydrate Single Crystal
[(
I(θ) ∝ NL
)
R′| + 2R′⊥ 3
2
J. Phys. Chem. B, Vol. 101, No. 32, 1997 6183 4
+ NS
∫0 ∑ j)1
π
]
Ij(θ) dγ E02
(5)
where NL and NS are the numbers of guest molecules in the large and the small cages, respectively. From the expressions 1-3, expression 4 becomes
[(
I(θ) ∝ NL
)
R′| + 2R′⊥
{
3
2
+
}]
4 π NS R′⊥2 + (R′|2 - R′⊥2) (sin βj(θ))2 E02 (6) 2 j)1
∑
When it is assumed that the NL/NS molecular ratios for both N2 and O2 are equal to 0.5, the variation of the integrated intensities I(θ) of N2 and O2 shown as a broken line in Figure 3a was determined by using expression 5. For both N2 and O2, the calculated intensities I(θ) are at their maximum at θ ) 39° and at their minimum at θ ) 129°, and the period is 180°. From Figure 3, it can be seen that the calculations are consistent with the experimental results. Therefore, it can be concluded that the variations of the peak intensities of N2 and O2 stretching modes are caused by the distortion of the dodecahedron cage along the direction of the 〈111〉 axis. To simplify the model, it was assumed that the guest molecule rotates anisotropically in a hexakaidecahedron cage, because the hexakaidecahedron cage is almost spherical in shape.11,12 However, there are small attractive interactions between a guest molecule in a hexakaidecahedron cage and the adjacent guest molecules in the dodecahedron cages. Therefore, there is a possibility that the guest molecules in the hexakaidecahedron cage influence the variation of the peak intensities of N2 and O2 stretching modes. In the case of the spherical type hydrate, the period of variation of peak intensities of N2 and O2 could be divided into 180° and 90° depending on the crystal.10 From the present results, we conclude that the period of variation is due to the Miller indices of the lattice plane perpendicular to the incident laser beam. O-H Stretching Vibration Mode. The intensity of the peak at 3135 cm-1 in the O-H stretching vibration mode also varies with θ. The variation of the O-H stretching vibration mode corresponds to the variations of the peak intensities of N2 and O2 stretching modes. Namely, the peak height of the symmetric stretching mode of water molecules also depends on the direction of the 〈111〉 axis. It can be considered that the variation of the intensity of the peak at 3135 cm-1 is caused by the following mechanism. The anisotropic nature of the Raman spectra of hexagonal ice was reported by Schere and Snyder.19 For hexagonal ice, the intensity of the peak at 3130 cm-1 (it has been assigned to the symmetric stretching mode18,19) for the polarization plane perpendicular to the c-axis is higher than that for the parallel. They indicated that the anisotropy suggests that those hydrogen bonds that statistically parallel to the c-axis are slightly more linear than those that are equatorial to the c-axis.
The structure of the dodecahedron cage in the structure II clathrate hydrate is distorted in the direction of the 〈111〉 axis. For the dodecahedron cage, the average strength of the hydrogen bond parallel to the 〈111〉 axis is stronger than that perpendicular to the 〈111〉 axis, since the average O-O distance parallel to the 〈111〉 axis is shorter than that perpendicular to the 〈111〉 axis. Therefore, the hydrogen bonds along the 〈111〉 axis are slightly more linear than those equatorial to the 〈111〉 axis. The symmetric stretching mode of water molecules is symmetric mode A1 for C2V symmetry.27 However, when a free water molecule becomes H-bonded, the symmetry is partially broken. Because there is a difference in the strength of the hydrogen bond between that parallel to the 〈111〉 axis and that equatorial to the 〈111〉 axis, the symmetry of the symmetric stretching vibration is broken in the direction parallel to the 〈111〉 axis, but the symmetry on the direction perpendicular to the 〈111〉 axis is maintained. Therefore, the peak height of the symmetric stretching mode for the polarization plane perpendicular to the 〈111〉 axis is higher than for the parallel plane. It has been concluded that the anisotropy of the Raman spectra of the natural air hydrate is caused by the distortion of the dodecahedron cage. Therefore, we consider that the crystal orientation is an important factor for the Raman spectroscopic study of the structure II clathrate hydrate. References and Notes (1) Gow, A. J. J. Geophys. Res. 1971, 76, 2533. (2) Miller, S. L. Science 1969, 165, 489. (3) Shoji, H.; Langway, Jr., C. C. Nature 1982, 298, 548. (4) Stackelberg, M. von; Muller, H. R. Z. Elektrochem. 1954, 58, 25. (5) Miller, S. L. Physics and Chemistry of Ice; Whalley, E., Jones, S. J., Gold, L. W., Eds.; University of Toronto Press: Toronto, 1973; p 42. (6) Davidson, D. W.; Handa, Y. P.; Ratcliffe, C. I.; Tse, J. S. Nature 1984, 311, 142. (7) Davidson, D. W.; Gough, S. R.; Handa, Y. P.; Ratcliffe, C. I.; Ripmeester, J. A.; Tse, J. S. J. Phys. 1987, 48, CI-537. (8) Hondoh, T.; Anzai, H.; Goto, A.; Mae, S.; Higashi, A.; Langeay, Jr., C. C. J. Inclus. Phenom. Recogn. Chem. 1990, 8, 17. (9) Nakahara, J.; Sigesato, Y.; Higashi, A.; Hondoh, T.; Langeay, Jr., C. C. Philos. Mag. B 1988, 57, 421. (10) Ikeda, T.; Fukazawa, H.; Hondoh, T.; Lipenkov, V. Y; Duval, P.; Mae, S. Int. Proc. 2nd Int. Conf. Natural Gas Hydrate 1996, 117. (11) Davidson, D. W. In WatersA ComprehensiVe Treates; Franks, F., Eds.; Plenum Press: New York, 1973; p 142. (12) Mak, T. C. W.; McMullan, R. K. J. Chem. Phys. 1965, 42, 2732. (13) Fukazawa, H.; Ikeda, T.; Hondoh, T.; Lipenkov, V. Y.; Duval, P.; Mae, S. Int. Proc. 2nd Int. Conf. Natural Gas Hydrate 1996, 237. (14) Pauer, F.; Kipfstuhl, J.; Kuhs, W. F. Geophys. Res. Lett. 1995, 22, 969. (15) Pauer, F.; Kipfstuhl, J.; Kuhs, W. F. Geophys. Res. Lett. 1996, 23, 177. (16) Johari, G. P.; Chew, H. A. M. Nature 1983, 303, 142. (17) Johari, G. P.; Chew, H. A. M. Philos. Mag. B 1984, 49, 281. (18) Whalley, E. Can. J. Chem. 1977, 55, 3429. (19) Scherer, J. R.; Snyder, R. G. J. Chem. Phys. 1977, 67, 4794. (20) Wong, P. T. T.; Whalley, E. J. Chem. Phys. 1976, 64, 2359. (21) Johari, G. P.; Chew, H. A. M.; Sivakumar, T. C. J. Chem. Phys. 1984, 80, 5163. (22) Johari, G. P.; Sivakumar, T. C. J. Chem. Phys. 1978, 69, 5557. (23) Faure, P.; Chosson, A. J. Glaciol. 1978, 21, 65. (24) Fukazawa, H.; Ikeda, T.; Hondoh, T.; Lipenkov, V. Y.; Mae, S. Physica B 1996, 219, 220, 466. (25) Sherwood, P. M. A. Vibrational spectroscopy of solids; Cambridge at the University Press: Cambridge, 1972. (26) Brith, M.; Ron, A.; Schenepp, O. J. Chem. Phys. 1969, 51, 1318. (27) Walrafen, G. E. J. Chem. Phys. 1964, 40, 3249.
