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Application of image plate for structural studies of carbon nanotubes by high-energy X-ray diffraction
Journal of Alloys and Compounds 401 (2005) 51–54
Application of image plate for structural studies of carbon nanotubes by high-energy X-ray diffraction L. Hawelek a , J. Koloczek a , A. Burian a,∗ , J.C. Dore b , V. Honkim¨aki c , T. Kyotani d a
d
A. Chelkowski Institute of Physics, University of Silesia, ul. Uniwersytecka 4, 40-007 Katowice, Poland b School of Physical Sciences, University of Kent, Canterbury CT2 7NR, UK c European Synchrotron Radiation Facility, BP 220, F-38043 Grenoble, France Institute of Multidisciplinary Research and Advanced Materials, Tohoku University, Katahira, Sendai 980-8577, Japan Received 15 October 2004; received in revised form 4 February 2005; accepted 7 February 2005 Available online 23 May 2005
Abstract An image plate detector coupled with high-energy synchrotron radiation was used to determine the structure factor and the radial distribution function of carbon nanotubes obtained by a template CVD process. The image plate detector has proved to be a very efficient tool for structural studies of nanotubes providing diffraction data of good quality in relatively short time. The diffraction data were converted to real space yielding the radial distribution function which can be used for quantitative analysis of the atomic arrangement of the carbon nanotubes. The obtained results are compared to those of traditional experiments using a conventional point Ge detector. © 2005 Elsevier B.V. All rights reserved. Keywords: Nanostructures; X-ray diffraction; Synchrotron radiation
1. Introduction Modern functional materials often exhibit the atomic scale structures, which cannot be characterised using formalism of conventional crystallography, because their atomic arrangement does not possess the 3D periodicity. It is of the greatest importance to develop techniques that could provide information about atomic arrangement in such materials as local ordering plays an important role in determining their properties. Since the discovery of carbon nanotubes in 1991, these materials attract attention because of their extraordinary mechanical and electrical properties [1]. Although the major source of information about the structure of the carbon nanotubes comes from direct imaging techniques, such as high-resolution electron microscopy, atomic force or scanning tunnelling microscopy and local probe, such ∗
Corresponding author. E-mail address: [email protected] (A. Burian).
0925-8388/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.jallcom.2005.02.061
as electron diffraction, it is desirable to study the structure for the total sample volume. X-ray diffraction offers such a possibility. In the present work, the high-energy diffraction technique is used to obtain experimental data for the carbon nanotubes. The imaging-plate method, with the use of a third-generation synchrotron source, opens the possibility to incorporate the advantages of both. The short wavelength radiation used makes the corrections for absorption, multiple scattering and polarisation practically negligible. The 2D registration offers the possibility of simultaneous recording the diffraction pattern for a wide range of the scattering vectors K = 4π sin θ/λ, where 2θ is the scattering angle and λ is the wavelength. Such recorded 2D diffraction pattern can be readily integrated, providing 1D diffraction profiles of good quality in a relatively short interval of time, typically of about 5–10 min. Application of this experimental technique is illustrated for the investigation of carbon nanotubes produced by a CVD process [2]. The data are compared with those recorded using a traditional point-like Ge solid state detector.
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L. Hawelek et al. / Journal of Alloys and Compounds 401 (2005) 51–54
2. Experimental method and results Although the use of high-energy X-rays for diffraction studies was suggested in 1983 [3], this experimental technique has mainly developed in last decade owing to new generations of synchrotron sources and high-field wigglers which make production of hard X-rays with energy of 60–300 keV possible [4–8]. The use of high-energy X-ray photons for diffraction experiments has several advantages in comparison with conventional experiments in which a beam with energies in the range of 10–25 keV is employed. Namely, the range of the scattering vector can be extended up to a much higher value Kmax increasing significantly the real space resolution (∼2π/Kmax ). High-energy X-rays scatter mainly into forward direction in an angular range up to approximately 10◦ . Therefore, the curvature of the Ewald sphere is about 10 times smaller that that of conventional X-rays making the absorption, multiple scattering and polarisation corrections practically angle independent.
Although the recent structural studies of materials progress, conventional diffraction experiments with the most powerful sources of radiation still take many hours, especially in the case of materials with a low atomic number like carbon. In order to overcome this problem, the simplest experimental technique in which an extended area two-dimensional detector, placed behind a sample in transmission mode, has been recently used. An image plate detector has proved to be a very efficient tool for such studies [9–11]. The X-ray diffraction patterns for the carbon nanotubes, deposited into the channels of the alumina membrane by a CVD process [2], were recorded at the European Synchrotron Radiation Facility (ESRF, Grenoble) on the high-energy beamline ID15B. The samples were extracted from the alumina template, placed into the Lindemann glass capillary of 2 mm in diameter and positioned on the diffractometer axis. The monochromatic synchrotron radiation with the energy of 95.4 keV (and wave˚ was used. The sample-to-detector distance was length 0.13 A) 265 mm. A Mo foil was used as a standard to calibrate the
Fig. 1. Two-dimensional diffraction pattern of the carbon nanotubes measured on the ID15B beamline at ESRF. The energy of the experiment was 95.4 keV and the exposure time was 10 min.
L. Hawelek et al. / Journal of Alloys and Compounds 401 (2005) 51–54
Fig. 2. Raw intensity data for the carbon nanotubes and empty capillary.
image plate detector. The detecting system was a MAR online image plate scanner (2300 × 2300 pixels; the pixel size 150 m). The measurement time was 10 min. The 2D diffraction pattern is shown in Fig. 1. Such recorded 2D diffraction pattern can be readily integrated over the diffraction rings using the FIT2D software [12,13] providing 1D diffraction profile of a good statistics in a quite short time. The resulting 1D diffraction intensity is shown in Fig. 2 together with the intensity measured for the empty capillary. The intensity of the empty capillary was subtracted and then the intensity of the carbon nanotubes, after geometrical and polarisation corrections, was normalized to electron units using the tabulated values of the atomic scattering factor of carbon and the Compton intensity given in [14,15], respectively. Then, the structure factor I(K) S(K) = 2 (1) f (K)
53
is then Fourier transformed to a radial distribution function. The agreement between the two sets of diffraction data is good. Discrepancies in a low-K range can be explained by a shadowing effect caused by a beam stop used in the case of the image plate. It is noteworthy that the structure factor determined using the Ge detector is much more noisy in the high-K range, despite much longer acquisition time of a few hours. Much better counting statistics were achieved in the case of the image plate detector in only 10 min duration. Widths of the diffraction peaks are practically the same for both data sets. It is not unexpected because the sample is disordered and effect of instrumental broadening on the measured diffraction patterns is weak. Angular resolutions of both methods are 0.09◦ and 0.03◦ for the Ge and image plate detectors, respectively. ˚ −1 Both diffraction patterns exhibit peaks at K1 = 1.77 A which can be related to the (0 0 2) reflection of crystalline graphite. The presence of this peak is due to inter-layer correlations and is characteristic for the multi-wall carbon nanotubes. The inter-layer spacing, estimated from 2π/K1 , ˚ which is clearly greater than that of graphite is 3.54 A and other carbon nanotubes [16,17]. Moreover, the structure factor of the investigated nanotubes is much more attenuated when compared with that of ordered nanotubes [16,17]. In Fig. 4, the reduced radial distribution functions d(r) = 4πr[ρ(r) − ρ0 ] 2 Kmax = K[S(K) − 1]W(K) sin(Kr) dK, π 0
(2)
was computed, where I(K) is the coherent intensity and f is the atomic scattering factor of carbon. A comparison of the K[S(K) − 1] sin(πK/Kmax )/(πK/Kmax ) functions of the carbon nanotube recorded with the image plate detector and the solid state Ge detector is shown in Fig. 3 as this quantity
computed from the structure factors, shown in Fig. 3, are compared. The term W(K) = sin(πK/Kmax )/(πK/Kmax ) is the Lorch window function which reduces termination ripples [18] and ρ0 is the number density. In order to avoid problems with noise at a high-K range, the d(r) functions were ˚ −1 for both data computed taking the value of Kmax = 20 A sets. The functions agree very well; however, the slight phase ˚ and differences in peaks amplitudes shift (of about 0.005 A)
Fig. 3. K[S(K) − 1] sin(πK/Kmax )/(πK/Kmax ) functions of the carbon nanotubes determined from data measured using image plate and Ge solid state detector.
Fig. 4. Reduced radial distribution functions computed from the data shown in Fig. 3.
54
L. Hawelek et al. / Journal of Alloys and Compounds 401 (2005) 51–54
between them are observed. These discrepancies can be explained by artificial ripples going through the reduced radial distribution function, obtained from the Ge solid state detector data set, and due to a noisy part of the diffraction data. Moreover, the presence of a small amount of remaining alumina in the sample cannot be ruled out because both samples measured using the Ge and 2D detectors were taken sepa˚ rately from the purified material. The small peak seen at 2 A for the Ge detector data can be attributed to the Al–O distance. Remaining non-structural ripples leading to splitting ˚ of the radial distribution function peaks observed for r > 6 A are clearly related to noisy part of the diffraction data at the high-K range. The present image plate data are of very good quality and yield a radial distribution function that can be analysed quantitatively.
4. Conclusions In the present work, high-energy X-ray scattering experiments using synchrotron radiation have been performed on the carbon nanotubes deposited into the channels of the alumina membrane. The use of the image plate technique opens the possibility for application of this method to the study of non-crystalline materials with low atomic numbers. Analysis of the obtained radial distribution functions shows promising results. The main advantages of the present approach are the short data-acquisition time and good counting statistics. This combination opens up a broad field for future applications to materials undergoing fast chemical reactions and also to biological materials. Acknowledgment
3. Discussion Previous image plate measurements of the diffraction patterns of disordered materials have been limited to ˚ −1 for ␣-Bi4 V2 O11 and ␣-AlF3 [8], 18 A ˚ −1 Kmax = 18.5 A ˚ −1 for aqueous solutions of CaCl2 and CaBr2 [10] and 20 A for glassy GeSe2 [11]. The materials studied and described in the above-mentioned papers consisted of atoms with medium- or high-Z number. The authors have shown that the use of the image plate as the detector provides a radial distribution function of good quality confirming that this approach will be possible for studies of low-Z materials [8]. In the present work, the diffraction data for the carbon ˚ −1 , yielding the nanotubes are extended up to about 25 A radial distribution function of high quality comparable with previous achievements. This K-value is the upper limit for carbon as its atomic scattering factor approaches zero at ˚ −1 . K = 25 A The nearest neighbour distance, defined by the position ˚ and is very close to the value of the first d(r) peak, is 1.41 A ˚ found for graphite. The positions of the second and 1.42 A, ˚ and 2.84 A ˚ are practically the same as third peaks at 2.45 A those of the perfect hexagonal network structure. However, the amplitude of the third peak is clearly lower in comparison with our previous neutron diffraction studies [16,17], suggesting a highly defective structure for these nanotubes. The possible source of such kind of disorder may be the presence of the five-membered rings which causes the curvature of the nanotube walls and an observed increase in the interlayer stacking.
This work is supported by Polish Ministry of Scientific Research and Information Technology through grant 1 PO3B 01227. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18]
S. Iijima, Nature 354 (1991) 56. T. Kyotani, L. Tsai, A. Tomita, Chem. Mater. 8 (1996) 2109. P.A. Egelstaff, Adv. Chem. Phys. 53 (1983) 1. H.F. Poulsen, J. Neuefeind, H.B. Neumann, J.R. Schneider, M.D. Zeidler, J. Non-Cryst. Solids 188 (1995) 63. J. Neuefeind, M.D. Zeidler, H.F. Poulsen, Mol. Phys. 87 (1996) 189. J. Neuefeind, K.-D. Liss, Ber. Bunsenges. Phys. Chem. 100 (1996) 1341. K.-D. Liss, A. Bartels, A. Schreyer, H. Clemens, Textures Microstruct. 35 (2003) 219. P.J. Chupas, X. Qiu, J.C. Hanson, P.L. Lee, C.P. Grey, S.J.L. Billinge, J. Appl. Cryst. 36 (2003) 1342. A. Szczygielska, A. Burian, J.C. Dore, V. Honkim¨aki, S. Duber, J. Alloys Compd. 362 (2004) 307. A.M. Gaspar, M.A. Marques, M.I. Cabaco, M.I. de Barros Marques, T. Buslaps, V. Honkim¨aki, J. Mol. Liquids 110 (2004) 15. V. Petkov, D. Qadir, S.D. Shastri, Solid State Commun. 129 (2004) 239. A.P. Hammersley, S.O. Svenson, M. Hanfland, D. H¨ausermann, High Press. Res. 14 (1996) 235. A.P. Hammersley, ESRF Internal Report, ESRF98HA01T, 1998. D. Wassmaier, A. Kirfel, Acta Cryst. A 51 (1995) 416. H.H.M. Balyuzi, Acta Cryst. A 31 (1975) 600. J. Koloczek, A. Burian, J.C. Dore, A.C. Hannon, Diamond Relat. Mater. 13 (2004) 1218. A. Burian, J. Koloczek, J.C. Dore, A.C. Hannon, J.B. Nagy, A. Fonseca, Diamond Relat. Mater. 13 (2004) 1261. E.A. Lorch, J. Phys. C 2 (1969) 229.
Application of image plate for structural studies of carbon nanotubes by high-energy X-ray diffraction L. Hawelek a , J. Koloczek a , A. Burian a,∗ , J.C. Dore b , V. Honkim¨aki c , T. Kyotani d a
d
A. Chelkowski Institute of Physics, University of Silesia, ul. Uniwersytecka 4, 40-007 Katowice, Poland b School of Physical Sciences, University of Kent, Canterbury CT2 7NR, UK c European Synchrotron Radiation Facility, BP 220, F-38043 Grenoble, France Institute of Multidisciplinary Research and Advanced Materials, Tohoku University, Katahira, Sendai 980-8577, Japan Received 15 October 2004; received in revised form 4 February 2005; accepted 7 February 2005 Available online 23 May 2005
Abstract An image plate detector coupled with high-energy synchrotron radiation was used to determine the structure factor and the radial distribution function of carbon nanotubes obtained by a template CVD process. The image plate detector has proved to be a very efficient tool for structural studies of nanotubes providing diffraction data of good quality in relatively short time. The diffraction data were converted to real space yielding the radial distribution function which can be used for quantitative analysis of the atomic arrangement of the carbon nanotubes. The obtained results are compared to those of traditional experiments using a conventional point Ge detector. © 2005 Elsevier B.V. All rights reserved. Keywords: Nanostructures; X-ray diffraction; Synchrotron radiation
1. Introduction Modern functional materials often exhibit the atomic scale structures, which cannot be characterised using formalism of conventional crystallography, because their atomic arrangement does not possess the 3D periodicity. It is of the greatest importance to develop techniques that could provide information about atomic arrangement in such materials as local ordering plays an important role in determining their properties. Since the discovery of carbon nanotubes in 1991, these materials attract attention because of their extraordinary mechanical and electrical properties [1]. Although the major source of information about the structure of the carbon nanotubes comes from direct imaging techniques, such as high-resolution electron microscopy, atomic force or scanning tunnelling microscopy and local probe, such ∗
Corresponding author. E-mail address: [email protected] (A. Burian).
0925-8388/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.jallcom.2005.02.061
as electron diffraction, it is desirable to study the structure for the total sample volume. X-ray diffraction offers such a possibility. In the present work, the high-energy diffraction technique is used to obtain experimental data for the carbon nanotubes. The imaging-plate method, with the use of a third-generation synchrotron source, opens the possibility to incorporate the advantages of both. The short wavelength radiation used makes the corrections for absorption, multiple scattering and polarisation practically negligible. The 2D registration offers the possibility of simultaneous recording the diffraction pattern for a wide range of the scattering vectors K = 4π sin θ/λ, where 2θ is the scattering angle and λ is the wavelength. Such recorded 2D diffraction pattern can be readily integrated, providing 1D diffraction profiles of good quality in a relatively short interval of time, typically of about 5–10 min. Application of this experimental technique is illustrated for the investigation of carbon nanotubes produced by a CVD process [2]. The data are compared with those recorded using a traditional point-like Ge solid state detector.
52
L. Hawelek et al. / Journal of Alloys and Compounds 401 (2005) 51–54
2. Experimental method and results Although the use of high-energy X-rays for diffraction studies was suggested in 1983 [3], this experimental technique has mainly developed in last decade owing to new generations of synchrotron sources and high-field wigglers which make production of hard X-rays with energy of 60–300 keV possible [4–8]. The use of high-energy X-ray photons for diffraction experiments has several advantages in comparison with conventional experiments in which a beam with energies in the range of 10–25 keV is employed. Namely, the range of the scattering vector can be extended up to a much higher value Kmax increasing significantly the real space resolution (∼2π/Kmax ). High-energy X-rays scatter mainly into forward direction in an angular range up to approximately 10◦ . Therefore, the curvature of the Ewald sphere is about 10 times smaller that that of conventional X-rays making the absorption, multiple scattering and polarisation corrections practically angle independent.
Although the recent structural studies of materials progress, conventional diffraction experiments with the most powerful sources of radiation still take many hours, especially in the case of materials with a low atomic number like carbon. In order to overcome this problem, the simplest experimental technique in which an extended area two-dimensional detector, placed behind a sample in transmission mode, has been recently used. An image plate detector has proved to be a very efficient tool for such studies [9–11]. The X-ray diffraction patterns for the carbon nanotubes, deposited into the channels of the alumina membrane by a CVD process [2], were recorded at the European Synchrotron Radiation Facility (ESRF, Grenoble) on the high-energy beamline ID15B. The samples were extracted from the alumina template, placed into the Lindemann glass capillary of 2 mm in diameter and positioned on the diffractometer axis. The monochromatic synchrotron radiation with the energy of 95.4 keV (and wave˚ was used. The sample-to-detector distance was length 0.13 A) 265 mm. A Mo foil was used as a standard to calibrate the
Fig. 1. Two-dimensional diffraction pattern of the carbon nanotubes measured on the ID15B beamline at ESRF. The energy of the experiment was 95.4 keV and the exposure time was 10 min.
L. Hawelek et al. / Journal of Alloys and Compounds 401 (2005) 51–54
Fig. 2. Raw intensity data for the carbon nanotubes and empty capillary.
image plate detector. The detecting system was a MAR online image plate scanner (2300 × 2300 pixels; the pixel size 150 m). The measurement time was 10 min. The 2D diffraction pattern is shown in Fig. 1. Such recorded 2D diffraction pattern can be readily integrated over the diffraction rings using the FIT2D software [12,13] providing 1D diffraction profile of a good statistics in a quite short time. The resulting 1D diffraction intensity is shown in Fig. 2 together with the intensity measured for the empty capillary. The intensity of the empty capillary was subtracted and then the intensity of the carbon nanotubes, after geometrical and polarisation corrections, was normalized to electron units using the tabulated values of the atomic scattering factor of carbon and the Compton intensity given in [14,15], respectively. Then, the structure factor I(K) S(K) = 2 (1) f (K)
53
is then Fourier transformed to a radial distribution function. The agreement between the two sets of diffraction data is good. Discrepancies in a low-K range can be explained by a shadowing effect caused by a beam stop used in the case of the image plate. It is noteworthy that the structure factor determined using the Ge detector is much more noisy in the high-K range, despite much longer acquisition time of a few hours. Much better counting statistics were achieved in the case of the image plate detector in only 10 min duration. Widths of the diffraction peaks are practically the same for both data sets. It is not unexpected because the sample is disordered and effect of instrumental broadening on the measured diffraction patterns is weak. Angular resolutions of both methods are 0.09◦ and 0.03◦ for the Ge and image plate detectors, respectively. ˚ −1 Both diffraction patterns exhibit peaks at K1 = 1.77 A which can be related to the (0 0 2) reflection of crystalline graphite. The presence of this peak is due to inter-layer correlations and is characteristic for the multi-wall carbon nanotubes. The inter-layer spacing, estimated from 2π/K1 , ˚ which is clearly greater than that of graphite is 3.54 A and other carbon nanotubes [16,17]. Moreover, the structure factor of the investigated nanotubes is much more attenuated when compared with that of ordered nanotubes [16,17]. In Fig. 4, the reduced radial distribution functions d(r) = 4πr[ρ(r) − ρ0 ] 2 Kmax = K[S(K) − 1]W(K) sin(Kr) dK, π 0
(2)
was computed, where I(K) is the coherent intensity and f is the atomic scattering factor of carbon. A comparison of the K[S(K) − 1] sin(πK/Kmax )/(πK/Kmax ) functions of the carbon nanotube recorded with the image plate detector and the solid state Ge detector is shown in Fig. 3 as this quantity
computed from the structure factors, shown in Fig. 3, are compared. The term W(K) = sin(πK/Kmax )/(πK/Kmax ) is the Lorch window function which reduces termination ripples [18] and ρ0 is the number density. In order to avoid problems with noise at a high-K range, the d(r) functions were ˚ −1 for both data computed taking the value of Kmax = 20 A sets. The functions agree very well; however, the slight phase ˚ and differences in peaks amplitudes shift (of about 0.005 A)
Fig. 3. K[S(K) − 1] sin(πK/Kmax )/(πK/Kmax ) functions of the carbon nanotubes determined from data measured using image plate and Ge solid state detector.
Fig. 4. Reduced radial distribution functions computed from the data shown in Fig. 3.
54
L. Hawelek et al. / Journal of Alloys and Compounds 401 (2005) 51–54
between them are observed. These discrepancies can be explained by artificial ripples going through the reduced radial distribution function, obtained from the Ge solid state detector data set, and due to a noisy part of the diffraction data. Moreover, the presence of a small amount of remaining alumina in the sample cannot be ruled out because both samples measured using the Ge and 2D detectors were taken sepa˚ rately from the purified material. The small peak seen at 2 A for the Ge detector data can be attributed to the Al–O distance. Remaining non-structural ripples leading to splitting ˚ of the radial distribution function peaks observed for r > 6 A are clearly related to noisy part of the diffraction data at the high-K range. The present image plate data are of very good quality and yield a radial distribution function that can be analysed quantitatively.
4. Conclusions In the present work, high-energy X-ray scattering experiments using synchrotron radiation have been performed on the carbon nanotubes deposited into the channels of the alumina membrane. The use of the image plate technique opens the possibility for application of this method to the study of non-crystalline materials with low atomic numbers. Analysis of the obtained radial distribution functions shows promising results. The main advantages of the present approach are the short data-acquisition time and good counting statistics. This combination opens up a broad field for future applications to materials undergoing fast chemical reactions and also to biological materials. Acknowledgment
3. Discussion Previous image plate measurements of the diffraction patterns of disordered materials have been limited to ˚ −1 for ␣-Bi4 V2 O11 and ␣-AlF3 [8], 18 A ˚ −1 Kmax = 18.5 A ˚ −1 for aqueous solutions of CaCl2 and CaBr2 [10] and 20 A for glassy GeSe2 [11]. The materials studied and described in the above-mentioned papers consisted of atoms with medium- or high-Z number. The authors have shown that the use of the image plate as the detector provides a radial distribution function of good quality confirming that this approach will be possible for studies of low-Z materials [8]. In the present work, the diffraction data for the carbon ˚ −1 , yielding the nanotubes are extended up to about 25 A radial distribution function of high quality comparable with previous achievements. This K-value is the upper limit for carbon as its atomic scattering factor approaches zero at ˚ −1 . K = 25 A The nearest neighbour distance, defined by the position ˚ and is very close to the value of the first d(r) peak, is 1.41 A ˚ found for graphite. The positions of the second and 1.42 A, ˚ and 2.84 A ˚ are practically the same as third peaks at 2.45 A those of the perfect hexagonal network structure. However, the amplitude of the third peak is clearly lower in comparison with our previous neutron diffraction studies [16,17], suggesting a highly defective structure for these nanotubes. The possible source of such kind of disorder may be the presence of the five-membered rings which causes the curvature of the nanotube walls and an observed increase in the interlayer stacking.
This work is supported by Polish Ministry of Scientific Research and Information Technology through grant 1 PO3B 01227. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18]
S. Iijima, Nature 354 (1991) 56. T. Kyotani, L. Tsai, A. Tomita, Chem. Mater. 8 (1996) 2109. P.A. Egelstaff, Adv. Chem. Phys. 53 (1983) 1. H.F. Poulsen, J. Neuefeind, H.B. Neumann, J.R. Schneider, M.D. Zeidler, J. Non-Cryst. Solids 188 (1995) 63. J. Neuefeind, M.D. Zeidler, H.F. Poulsen, Mol. Phys. 87 (1996) 189. J. Neuefeind, K.-D. Liss, Ber. Bunsenges. Phys. Chem. 100 (1996) 1341. K.-D. Liss, A. Bartels, A. Schreyer, H. Clemens, Textures Microstruct. 35 (2003) 219. P.J. Chupas, X. Qiu, J.C. Hanson, P.L. Lee, C.P. Grey, S.J.L. Billinge, J. Appl. Cryst. 36 (2003) 1342. A. Szczygielska, A. Burian, J.C. Dore, V. Honkim¨aki, S. Duber, J. Alloys Compd. 362 (2004) 307. A.M. Gaspar, M.A. Marques, M.I. Cabaco, M.I. de Barros Marques, T. Buslaps, V. Honkim¨aki, J. Mol. Liquids 110 (2004) 15. V. Petkov, D. Qadir, S.D. Shastri, Solid State Commun. 129 (2004) 239. A.P. Hammersley, S.O. Svenson, M. Hanfland, D. H¨ausermann, High Press. Res. 14 (1996) 235. A.P. Hammersley, ESRF Internal Report, ESRF98HA01T, 1998. D. Wassmaier, A. Kirfel, Acta Cryst. A 51 (1995) 416. H.H.M. Balyuzi, Acta Cryst. A 31 (1975) 600. J. Koloczek, A. Burian, J.C. Dore, A.C. Hannon, Diamond Relat. Mater. 13 (2004) 1218. A. Burian, J. Koloczek, J.C. Dore, A.C. Hannon, J.B. Nagy, A. Fonseca, Diamond Relat. Mater. 13 (2004) 1261. E.A. Lorch, J. Phys. C 2 (1969) 229.