- Email: [email protected]
Neutron powder diffraction study of methane hydrate by the Rietveld refinement and maximum entropy method
ARTICLE IN PRESS
Physica B 385–386 (2006) 567–570 www.elsevier.com/locate/physb
Neutron powder diffraction study of methane hydrate by the Rietveld refinement and maximum entropy method Akinori Hoshikawa, Naoki Igawa, Hiroki Yamauchi, Yoshinobu Ishii Quantum Beam Science Directorate, Japan Atomic Energy Agency, Tokai-mura, Ibaraki 319-1195, Japan
Abstract A neutron powder diffraction study was carried out to clarify the crystal structure of deuterated methane hydrate (CD4 nD2 O, n 5:75). The diffraction data were analyzed by both the Rietveld method and the maximum entropy method (MEM). The structure analysis showed that only small cage had some vacancies of CD4 . This result was in agreement with a Langmuir isotherm. In addition, the density distribution by MEM indicated that the D atoms of CD4 were localized in the large cage and that the C atom was located at off-center of the large cage. r 2006 Elsevier B.V. All rights reserved. PACS: 61.12.Ld; 61.46.+w Keywords: Methane hydrate; Neutron powder diffraction
Methane hydrate (MH) is of great interest as an energy resource in the next generation because a large amount of methane is deposited on the seafloor as MH. It is known that MH forms structure I (sI) at the water depth of about 3000 m. For sI clathrate hydrate, McMullen et al. determined the crystallographic structure of the host lattice in a single crystal X-ray diffraction study of ethylene oxide (EO, C2 H4 O) hydrate [1]. Hollander et al. determined the atomic coordinates of the D atoms of the host lattice in a single crystal neutron diffraction study of deuterated EO hydrate [2]. Their results [1,2] indicated that the host lattice consists of two types of cages (small and large cages). These cage structures (host lattice) can accommodate guest molecules such as methane molecule (CH4 , CD4 ). Recently, Gutt et al. [3] and Baumert et al. [4] reported the crystal structure of fully deuterated MH (CD4 nD2 O, nX5:75 in neutron powder diffraction studies. For the CD4 molecules, they observed a spherically symmetric scattering density around the center of both types of cages. However, the cage occupancy of CD4 was not measured because the
Corresponding author. Tel.: +81 29 284 3910; fax: +81 29 284 3889.
E-mail address: [email protected] (A. Hoshikawa). 0921-4526/$ - see front matter r 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2006.05.361
structure model for the CD4 molecule in the cages was not clear. The present study was performed to clarify the cage occupancy of CD4 by neutron powder diffraction. In addition, we determined the structure model of CD4 in the cages. Powder specimens of deuterated MH were produced from granular D2 O ice (grain sizeo106 mm) and pressurized CD4 gas (99.9% purity, about 7 MPa) for 263–278 K. Further, the specimens were packed into a cylindrical vanadium cell (internal diameter: 9.4 mm, thickness: 0.3 mm, depth: 38 mm) with an aluminum flange and an indium seal at 77 K when the pressure was dropped to 0.2 MPa at the boiling point of CD4 . The neutron diffraction measurements were carried out on the high resolution powder diffractometer (HRPD) installed at Japan Research Reactor 3, Japan Atomic Energy Research Institute (JAERI). The detector bank of the HRPD is comprised of 64 3 He-detectors. The experimental set-up included a 120 collimator positioned in front of the Ge(331) vertically focusing monochromator with a take-off angle of 89 . In this configuration, the HRPD produced a monochromatic beam of neutrons with a 1:8233 A˚ wave length calibrated using silicon powder
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568
(NIST Si 640c). Data were collected with constant monitor counts and a step angle of 0:05 over the 2y range of 2:5 2160 . A closed-cycle 4He refrigerator equipped with an Si-diode temperature sensor was used to control the temperature. Neutron powder diffraction data at 7.7 K were analyzed by the Rietveld method using RIETAN2000 [5]. After Rietveld analysis, the maximum entropy method (MEM) analysis was carried out with PRIMA [6], using 128 128 128 pixels for a unit cell. The 3D graphic image of the density distribution was drawn with VENUS developed by Dilanian and Izumi. The coherent neutron scattering lengths used for the refinements were 5.803 fm for O, 6.671 fm for D and 6.646 fm for C [7]. Fig. 1 shows a Rietveld refinement pattern of fully deuterated MH at 7.7 K. The plus symbols denote the observed intensities, and the solid line shows the calculated curve for the best-fit model. The calculated peak positions for sI deuterated MH are indicated in Fig. 1 by tick marks below the diffraction pattern. No reflections of impurities were observed. Table 1 displays structure parameters of deuterated MH at 7.7 K in the Rietveld analysis. The C(1), D(11), D(12), and D(13) atoms represent the C and D atoms in the small cage. The C(2), D(21), D(22), and D(23) atoms are located in the large cage. All adjustable parameters were refined by applying nonlinear constraints for both bond length ðC2D ¼ ˚ and bond angle ðD2C2D ¼ 109:47 Þ because of 1:1 AÞ the rigid body of CD4 . In addition, we applied linear constraints: BðDð11ÞÞ ¼ BðDð12ÞÞ ¼ BðDð13ÞÞ, BðDð21ÞÞ ¼ BðDð22ÞÞ ¼ BðDð23ÞÞ, gðDð11ÞÞ ¼ gðDð12ÞÞ ¼ gðDð13ÞÞ ¼ 1 1 12gðCð1ÞÞ, gðDð21ÞÞ ¼ gðDð22ÞÞ ¼ gðDð23ÞÞ ¼ 4gðCð2ÞÞ, where B and g are the Debye–Waller factor and site occupancy, respectively. The g values of C(1) and C(2) were 0.901(9) and 1.026(6). Accordingly, the cage occupancies of CD4 in the small and large cages were 90.1% and 102.6%, respectively. Then, the total cage occupancy in a unit cell was 99.4% and the composition of deuterated MH was CD4 5:78D2 O. On the other hand, the cage occupancy can be calculated from the ideal solution model and the Langmuir constants
20000 7.7K
10000 5000 0
Δ
Intensity
15000
1000 500 -500
20
40
60
80 2θ /°
100
120
Fig. 1. Rietveld refinement pattern of deuterated MH.
140
Table 1 Structure parameters of deuterated MH at 7.7 K Atom
Site
g
x
y
z
B ðA˚ 2 Þ
Oi Ok Oc Dii Dck Dkc Dkk Dki Dik C(1) D(11) D(12) D(13) C(2) D(21) D(22) D(23)
16i 24k 6c 16i 24k 24k 24k 48l 48l 2a 24k 24k 48l 6d 24k 24k 48l
1 1 1
0.1839(2) 0 0 0.2308(3) 0 0 0 0.0661(3) 0.1175(3) 0 0 0 0.074(1)
0.1839(2) 0.3101(3)
0.1839(2) 0.1171(3)
0.28(5) 0.86(6) 0.2(1) 1.3(2) 1.1(1) 1.9(1) 1.3(1) 0.81(8) 1.05(5) 0.3(2) 0.6(3) 0.6(3) 0.6(3) 4.0(2) 4.7(2) 4.7(2) 4.7(2)
1 2 1 2 1 2 1 2 1 2 1 2
0.901(9) 0.0751(8) 0.0751(8) 0.0751(8) 1.026(6) 0.256(2) 0.256(2) 0.256(2)
1 2
1 4
0.2308(3) 0.4327(4) 0.3784(5) 0.3148(4) 0.2652(3) 0.2272(3) 0 0.094(2) 0.051(2) 0.0182(8)
0.2308(3) 0.2026(4) 0.1613(5) 0.0357(4) 0.1389(3) 0.1585(3) 0 0.025(1) 0.075(2) 0.0491(7) 0 0.402(1) 0.520(1) 0.5347(6)
1 4
1 2
0 0 0.0752(5)
0.240(1) 0.3338(9) 0.2096(4)
˚ ¯ Space group: Pm3n, a ¼ 11:8263ð1Þ A, Rwp ¼ 3:86%, Re ¼ 3:08%, RB ¼ 3:06%, S ¼ 1:2528.
for CH4 [8]. (Here, there was no information of the Langmuir constants for CD4 .) From the synthetic conditions (278 K, 7 MPa), the calculated cage occupancies were 94.5% and 98.8% in the small and large cages, respectively. As a result, the cage occupancy of CD4 was consistent with the Langmuir isotherm because the cage occupancy of the small cage was less than that of the large cage. Fig. 2a shows the scattering length density of deuterated MH in a unit cell. We isolated the small and large cages as shown in Figs. 2b and c, respectively. All figures were drawn with the same isosurface level ð5:0 fm=A˚ 3 Þ. The density distribution around the center of the cages clearly differed between the small and large cages. In the small cage, there was only spherical density distribution. On the other hand, there were oval and tetrahedral density distributions in the large cage. These density distributions in the cages corresponded to the CD4 molecule. Moreover, the oval and tetrahedral density distributions in the large cage corresponded to the D and C atoms of CD4 , respectively, because of the geometry of the CD4 . As a result, the D atoms of CD4 were localized in only the large cage. Although the C atom was located at the center of the large cage with the isotropic Debye–Waller factor in the Rietveld analysis, the density distribution for the C atom became tetrahedral in the MEM analysis. Since the MEM provides the least-biased estimate on the basis of the given information, the tetrahedral density distribution at the center of the large cage indicated that the C atom was located at off-center of the large cage. From the tetrahedral density distribution in the large cage, we could roughly estimate the atomic coordinates of the C atom in the large cage. In our estimation, the C atom
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Fig. 2. Scattering length density distribution of deuterated MH in: (a) a unit cell; (b) the small cage; and (c) the large cage.
shifted about 0:2 A˚ from the 6d site to a 24k site. Since the atomic radius of the C atom is 0:7 A˚ [9], four C atoms overlap at the center of the large cage. As a result, it had ever been difficult to find the atomic coordinates of the C atom by the Rietveld analysis. We performed a high resolution powder diffraction experiment on high-purity deuterated MH. The atomic arrangement of the D atoms in the cages was determined by the rigid body model of CD4 in the Rietveld analysis. We successfully estimated the cage occupancy by neutron powder diffraction. There were some vacancies of CD4 in the small cage as the calculated results by the Langmuir isotherm. The scattering length density distribution of the deuterated MH was obtained by the MEM. The density distribution of CD4 in the large cage indicated that the D atoms of CD4 were localized and that the C atom was located at off-center of the large cage.
The authors would like to thank Dr. H. Fukazawa of JAERI for valuable discussions regarding this work. Thanks are also due to Dr. S.H. Kirby and Dr. L.A. Stern of the U.S. Geological Survey and Prof. Y. Kiyanagi, Assoc. Prof. T. Kamiyama, and Mr. S. Ohnuma of Hokkaido University for helpful discussions on sample preparation. The authors are indebted to Mr. Y. Shimojo of JAERI for his technical support for the neutron powder diffraction experiments.
References [1] R.K. McMullan, G.A. Jeffrey, J. Chem. Phys. 42 (1965) 2725. [2] F. Hollander, G.A. Jeffrey, J. Chem. Phys. 66 (1977) 4699. [3] C. Gutt, B. Asmussen, M.R. Johnson, Y.P. Harada, J.S. Tse, J. Chem. Phys. 113 (2000) 4713.
ARTICLE IN PRESS 570
A. Hoshikawa et al. / Physica B 385–386 (2006) 567–570
[4] J. Baumert, C. Gutt, M.R. Johnson, J.S. Tse, D.D. Klug, W. Press, J. Chem. Phys. 120 (2004) 10163. [5] F. Izumi, T. Ikeda, Mater. Sci. Forum 198 (2000) 321. [6] F. Izumi, R.A. Dilanian, Recent Research Developments in Physics, vol. 3, Part II, Transworld Research Network, Trivandrum, 2002, pp. 699–726.
[7] V.F. Sears, in: E. Prince (Ed.), International Tables for Crystallography, vol. C, Kluwer Academic Publishers, Dordrecht, 2004, pp. 445–452. [8] J. Munck, S. Skjold-Jorgensen, P. Rasmussen, Chem. Eng. Sci. 43 (1988) 2661. [9] J.C. Slater, J. Chem. Phys. 41 (1964) 3199.
Physica B 385–386 (2006) 567–570 www.elsevier.com/locate/physb
Neutron powder diffraction study of methane hydrate by the Rietveld refinement and maximum entropy method Akinori Hoshikawa, Naoki Igawa, Hiroki Yamauchi, Yoshinobu Ishii Quantum Beam Science Directorate, Japan Atomic Energy Agency, Tokai-mura, Ibaraki 319-1195, Japan
Abstract A neutron powder diffraction study was carried out to clarify the crystal structure of deuterated methane hydrate (CD4 nD2 O, n 5:75). The diffraction data were analyzed by both the Rietveld method and the maximum entropy method (MEM). The structure analysis showed that only small cage had some vacancies of CD4 . This result was in agreement with a Langmuir isotherm. In addition, the density distribution by MEM indicated that the D atoms of CD4 were localized in the large cage and that the C atom was located at off-center of the large cage. r 2006 Elsevier B.V. All rights reserved. PACS: 61.12.Ld; 61.46.+w Keywords: Methane hydrate; Neutron powder diffraction
Methane hydrate (MH) is of great interest as an energy resource in the next generation because a large amount of methane is deposited on the seafloor as MH. It is known that MH forms structure I (sI) at the water depth of about 3000 m. For sI clathrate hydrate, McMullen et al. determined the crystallographic structure of the host lattice in a single crystal X-ray diffraction study of ethylene oxide (EO, C2 H4 O) hydrate [1]. Hollander et al. determined the atomic coordinates of the D atoms of the host lattice in a single crystal neutron diffraction study of deuterated EO hydrate [2]. Their results [1,2] indicated that the host lattice consists of two types of cages (small and large cages). These cage structures (host lattice) can accommodate guest molecules such as methane molecule (CH4 , CD4 ). Recently, Gutt et al. [3] and Baumert et al. [4] reported the crystal structure of fully deuterated MH (CD4 nD2 O, nX5:75 in neutron powder diffraction studies. For the CD4 molecules, they observed a spherically symmetric scattering density around the center of both types of cages. However, the cage occupancy of CD4 was not measured because the
Corresponding author. Tel.: +81 29 284 3910; fax: +81 29 284 3889.
E-mail address: [email protected] (A. Hoshikawa). 0921-4526/$ - see front matter r 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2006.05.361
structure model for the CD4 molecule in the cages was not clear. The present study was performed to clarify the cage occupancy of CD4 by neutron powder diffraction. In addition, we determined the structure model of CD4 in the cages. Powder specimens of deuterated MH were produced from granular D2 O ice (grain sizeo106 mm) and pressurized CD4 gas (99.9% purity, about 7 MPa) for 263–278 K. Further, the specimens were packed into a cylindrical vanadium cell (internal diameter: 9.4 mm, thickness: 0.3 mm, depth: 38 mm) with an aluminum flange and an indium seal at 77 K when the pressure was dropped to 0.2 MPa at the boiling point of CD4 . The neutron diffraction measurements were carried out on the high resolution powder diffractometer (HRPD) installed at Japan Research Reactor 3, Japan Atomic Energy Research Institute (JAERI). The detector bank of the HRPD is comprised of 64 3 He-detectors. The experimental set-up included a 120 collimator positioned in front of the Ge(331) vertically focusing monochromator with a take-off angle of 89 . In this configuration, the HRPD produced a monochromatic beam of neutrons with a 1:8233 A˚ wave length calibrated using silicon powder
ARTICLE IN PRESS A. Hoshikawa et al. / Physica B 385–386 (2006) 567–570
568
(NIST Si 640c). Data were collected with constant monitor counts and a step angle of 0:05 over the 2y range of 2:5 2160 . A closed-cycle 4He refrigerator equipped with an Si-diode temperature sensor was used to control the temperature. Neutron powder diffraction data at 7.7 K were analyzed by the Rietveld method using RIETAN2000 [5]. After Rietveld analysis, the maximum entropy method (MEM) analysis was carried out with PRIMA [6], using 128 128 128 pixels for a unit cell. The 3D graphic image of the density distribution was drawn with VENUS developed by Dilanian and Izumi. The coherent neutron scattering lengths used for the refinements were 5.803 fm for O, 6.671 fm for D and 6.646 fm for C [7]. Fig. 1 shows a Rietveld refinement pattern of fully deuterated MH at 7.7 K. The plus symbols denote the observed intensities, and the solid line shows the calculated curve for the best-fit model. The calculated peak positions for sI deuterated MH are indicated in Fig. 1 by tick marks below the diffraction pattern. No reflections of impurities were observed. Table 1 displays structure parameters of deuterated MH at 7.7 K in the Rietveld analysis. The C(1), D(11), D(12), and D(13) atoms represent the C and D atoms in the small cage. The C(2), D(21), D(22), and D(23) atoms are located in the large cage. All adjustable parameters were refined by applying nonlinear constraints for both bond length ðC2D ¼ ˚ and bond angle ðD2C2D ¼ 109:47 Þ because of 1:1 AÞ the rigid body of CD4 . In addition, we applied linear constraints: BðDð11ÞÞ ¼ BðDð12ÞÞ ¼ BðDð13ÞÞ, BðDð21ÞÞ ¼ BðDð22ÞÞ ¼ BðDð23ÞÞ, gðDð11ÞÞ ¼ gðDð12ÞÞ ¼ gðDð13ÞÞ ¼ 1 1 12gðCð1ÞÞ, gðDð21ÞÞ ¼ gðDð22ÞÞ ¼ gðDð23ÞÞ ¼ 4gðCð2ÞÞ, where B and g are the Debye–Waller factor and site occupancy, respectively. The g values of C(1) and C(2) were 0.901(9) and 1.026(6). Accordingly, the cage occupancies of CD4 in the small and large cages were 90.1% and 102.6%, respectively. Then, the total cage occupancy in a unit cell was 99.4% and the composition of deuterated MH was CD4 5:78D2 O. On the other hand, the cage occupancy can be calculated from the ideal solution model and the Langmuir constants
20000 7.7K
10000 5000 0
Δ
Intensity
15000
1000 500 -500
20
40
60
80 2θ /°
100
120
Fig. 1. Rietveld refinement pattern of deuterated MH.
140
Table 1 Structure parameters of deuterated MH at 7.7 K Atom
Site
g
x
y
z
B ðA˚ 2 Þ
Oi Ok Oc Dii Dck Dkc Dkk Dki Dik C(1) D(11) D(12) D(13) C(2) D(21) D(22) D(23)
16i 24k 6c 16i 24k 24k 24k 48l 48l 2a 24k 24k 48l 6d 24k 24k 48l
1 1 1
0.1839(2) 0 0 0.2308(3) 0 0 0 0.0661(3) 0.1175(3) 0 0 0 0.074(1)
0.1839(2) 0.3101(3)
0.1839(2) 0.1171(3)
0.28(5) 0.86(6) 0.2(1) 1.3(2) 1.1(1) 1.9(1) 1.3(1) 0.81(8) 1.05(5) 0.3(2) 0.6(3) 0.6(3) 0.6(3) 4.0(2) 4.7(2) 4.7(2) 4.7(2)
1 2 1 2 1 2 1 2 1 2 1 2
0.901(9) 0.0751(8) 0.0751(8) 0.0751(8) 1.026(6) 0.256(2) 0.256(2) 0.256(2)
1 2
1 4
0.2308(3) 0.4327(4) 0.3784(5) 0.3148(4) 0.2652(3) 0.2272(3) 0 0.094(2) 0.051(2) 0.0182(8)
0.2308(3) 0.2026(4) 0.1613(5) 0.0357(4) 0.1389(3) 0.1585(3) 0 0.025(1) 0.075(2) 0.0491(7) 0 0.402(1) 0.520(1) 0.5347(6)
1 4
1 2
0 0 0.0752(5)
0.240(1) 0.3338(9) 0.2096(4)
˚ ¯ Space group: Pm3n, a ¼ 11:8263ð1Þ A, Rwp ¼ 3:86%, Re ¼ 3:08%, RB ¼ 3:06%, S ¼ 1:2528.
for CH4 [8]. (Here, there was no information of the Langmuir constants for CD4 .) From the synthetic conditions (278 K, 7 MPa), the calculated cage occupancies were 94.5% and 98.8% in the small and large cages, respectively. As a result, the cage occupancy of CD4 was consistent with the Langmuir isotherm because the cage occupancy of the small cage was less than that of the large cage. Fig. 2a shows the scattering length density of deuterated MH in a unit cell. We isolated the small and large cages as shown in Figs. 2b and c, respectively. All figures were drawn with the same isosurface level ð5:0 fm=A˚ 3 Þ. The density distribution around the center of the cages clearly differed between the small and large cages. In the small cage, there was only spherical density distribution. On the other hand, there were oval and tetrahedral density distributions in the large cage. These density distributions in the cages corresponded to the CD4 molecule. Moreover, the oval and tetrahedral density distributions in the large cage corresponded to the D and C atoms of CD4 , respectively, because of the geometry of the CD4 . As a result, the D atoms of CD4 were localized in only the large cage. Although the C atom was located at the center of the large cage with the isotropic Debye–Waller factor in the Rietveld analysis, the density distribution for the C atom became tetrahedral in the MEM analysis. Since the MEM provides the least-biased estimate on the basis of the given information, the tetrahedral density distribution at the center of the large cage indicated that the C atom was located at off-center of the large cage. From the tetrahedral density distribution in the large cage, we could roughly estimate the atomic coordinates of the C atom in the large cage. In our estimation, the C atom
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569
Fig. 2. Scattering length density distribution of deuterated MH in: (a) a unit cell; (b) the small cage; and (c) the large cage.
shifted about 0:2 A˚ from the 6d site to a 24k site. Since the atomic radius of the C atom is 0:7 A˚ [9], four C atoms overlap at the center of the large cage. As a result, it had ever been difficult to find the atomic coordinates of the C atom by the Rietveld analysis. We performed a high resolution powder diffraction experiment on high-purity deuterated MH. The atomic arrangement of the D atoms in the cages was determined by the rigid body model of CD4 in the Rietveld analysis. We successfully estimated the cage occupancy by neutron powder diffraction. There were some vacancies of CD4 in the small cage as the calculated results by the Langmuir isotherm. The scattering length density distribution of the deuterated MH was obtained by the MEM. The density distribution of CD4 in the large cage indicated that the D atoms of CD4 were localized and that the C atom was located at off-center of the large cage.
The authors would like to thank Dr. H. Fukazawa of JAERI for valuable discussions regarding this work. Thanks are also due to Dr. S.H. Kirby and Dr. L.A. Stern of the U.S. Geological Survey and Prof. Y. Kiyanagi, Assoc. Prof. T. Kamiyama, and Mr. S. Ohnuma of Hokkaido University for helpful discussions on sample preparation. The authors are indebted to Mr. Y. Shimojo of JAERI for his technical support for the neutron powder diffraction experiments.
References [1] R.K. McMullan, G.A. Jeffrey, J. Chem. Phys. 42 (1965) 2725. [2] F. Hollander, G.A. Jeffrey, J. Chem. Phys. 66 (1977) 4699. [3] C. Gutt, B. Asmussen, M.R. Johnson, Y.P. Harada, J.S. Tse, J. Chem. Phys. 113 (2000) 4713.
ARTICLE IN PRESS 570
A. Hoshikawa et al. / Physica B 385–386 (2006) 567–570
[4] J. Baumert, C. Gutt, M.R. Johnson, J.S. Tse, D.D. Klug, W. Press, J. Chem. Phys. 120 (2004) 10163. [5] F. Izumi, T. Ikeda, Mater. Sci. Forum 198 (2000) 321. [6] F. Izumi, R.A. Dilanian, Recent Research Developments in Physics, vol. 3, Part II, Transworld Research Network, Trivandrum, 2002, pp. 699–726.
[7] V.F. Sears, in: E. Prince (Ed.), International Tables for Crystallography, vol. C, Kluwer Academic Publishers, Dordrecht, 2004, pp. 445–452. [8] J. Munck, S. Skjold-Jorgensen, P. Rasmussen, Chem. Eng. Sci. 43 (1988) 2661. [9] J.C. Slater, J. Chem. Phys. 41 (1964) 3199.