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Crystal structures of C3N6H6 under high pressure
Chemical Physics Letters 368 (2003) 668–672 www.elsevier.com/locate/cplett
Crystal structures of C3N6H6 under high pressure H.A. Ma a, X. Jia a,*, Q.L. Cui a, Y.W. Pan a, P.W. Zhu a, B.B. Liu a, H.J. Liu a, X.C. Wang a, J. Liu b, G.T. Zou a a
National Laboratory of Superhard Materials, Jilin University, 10 Qianwei Road, Changchun 130012, PR China b Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100039, PR China Received 20 September 2002; in final form 6 December 2002
Abstract In situ high-pressure energy-dispersive X-ray diffraction (EDXRD) experiments on melamine ðC3 N6 H6 Þ have been carried out using diamond anvil cell (DAC) with synchrotron radiation source. In the pressure range from ambient pressure up to 14.7 GPa, two pressure-induced structure phase transitions, from monoclinic to triclinic structure at about 1.3 GPa and from triclinic to orthorhombic structure at about 8.2 GPa, are observed. The crystal structures of melamine at different pressures are built by using Materials Studio (MS) based on the principle of energy minimization. Ó 2002 Elsevier Science B.V. All rights reserved.
1. Introduction A single melamine molecule is D3h symmetry with a six-member CN aromatic ring and three amino groups [1,2]. The CN ring is quite similar to hexagonal C3 N4 predicted by theoretical research, whose hardness might exceed that of diamond [3–6]. The molecule crystal structure of melamine at ambient condition has been studied thoroughly since 1941 by many methods, such as X-ray diffraction, Raman and IR spectroscopy, etc. [1,2,7– 10]. The melamine crystallizes in a monoclinic phase, in which each molecule is linked to its neighbors by eight hydrogen bonds [7–10].
*
Corresponding author. Fax: +86-431-5168858. E-mail address: [email protected] (X. Jia).
Because of the special single molecule structure and the existence of weak hydrogen bonds in molecule crystal, high pressure is expected to easily cause the rearrangement of melamine molecule, and induce the structural phase transition. Thus, melamine, served as a starting material for the synthesis of superhard structure C3 N4 by using high pressure and high temperature (HPHT) method [11–14], has attracted much attention. The structure of melamine under high pressure up to 8.7 GPa has been studied by Raman spectra and gave indication for the structural phase transitions [15,16]. However, the studies of the detailed crystal structure at high pressure have not been reported. In the present Letter, we have carried out in situ high-pressure EDXRD experiments up to 14.7 GPa. The pressure-induced structural phase transitions of melamine are studied, and the crystal structures of melamine at different pressure are built by using Materials Studio (MS) [17].
0009-2614/02/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved. doi:10.1016/S0009-2614(02)01965-6
H.A. Ma et al. / Chemical Physics Letters 368 (2003) 668–672
2. Experiments The sample is a colorless melamine powder with high purity of 99.9% (Beijing Chemical Industry Group). The original structure of melamine was studied by an ordinary angle dispersive X-ray diffraction (ADXRD) method. The data were collected on a REGAKU diffractometer with monochromatic Cu-Ka radiation. The XRD results indicate that our sample is consistent with the standard X-ray diffraction card 24-1923, which is typical monoclinic structure. The X-ray diffraction of melamine under high pressure was studied by an energy-dispersive method. The experiment was carried out on the wiggler beam line (3W1A) of Beijing Synchrotron Radiation Laboratory (BSRL). The polychromatic X-ray beam was collimated to a 30 30 lm sized spot with the storage ring operating at 2.8 GeV, and the diffracted beam was collected between 5 and 40 keV. A diamond anvil cell (DAC) was driven by an accurately adjustable gear-wormlevel system. The DAC consists of a pair of type-I diamonds with a culet of 410 lm and a stainless steel gasket with a 200 lm hole serving as the sample chamber. The detailed experimental facility is described in the literature [18]. A mixture of methanol:ethanol:water ¼ 16:3:1 was used as the pressure medium, and very fine NaCl powder was employed as the inner pressure calibration. The pressure was determined from the strongest diffraction peak (200) of NaCl along with the equation of state under high pressure. We can obtain the d values of the sample according to the energydispersion equation: E:d ¼
0:619927 ðkeV nmÞ: sin h
The 2h angle between the direct beam and the detector was set at 9.6°.
3. Results and discussion The spectra of in situ EDXRD at various pressures are shown in Fig. 1. We can see that with pressure increasing the relative intensity and the widths of different diffraction lines change largely,
669
and all the diffraction lines shift to higher energy. It is obvious that the melamine molecule crystal is influenced by high pressure. We first analyzed the EDXRD pattern at ambient condition by using MS. The indexing and refinement of the powder X-ray diffraction pattern was carried out using DI C V O L 91 [19] and Rietveld refinement [20] of MS, respectively, for extracting the detailed structural information. DI C V O L 91 indexing program is widely used to the indexing of experimental powder X-ray diffraction pattern. Rietveld refinement was used to further refine a trial crystal structure against experimental X-ray diffraction data. At ambient condition, except for the fluorescence lines at lower energies, all the diffraction lines can be well indexed as typical monoclinic structure (see Fig. 1a) by using MS and being compared with the standard card 24-1923. The unit cell contains four molecules. The space group is P21/a, Z ¼ 14 and the lattice pa, b ¼ 7:53 A , c ¼ 7:36 A , rameters are a ¼ 10:69 A b ¼ 111:9°. In order to build the molecule crystal structure of melamine, we first built a single melamine molecule (see Fig. 2). The structure of single melamine molecule was built and optimized by using Materials Visualizer and DiscoverÕs Minimizer of MS. We used the smart minimization so that the energy of the structure is minimum, which results in a modeled structure with a close resemblance to a real physical structure. The smart minimization automatically combines appropriate features of several methods, which starts with the steepest descent method [21], followed by the conjugate gradient method [22], and ending with a Newton method [23]. Then, we further built the crystal structure by Material Visualizer of MS based on our experimental data of diffraction pattern. After the refinement of the trial structure, we got a final crystal structure (see Fig. 3a). We also tentatively determine the H bonds configuration linked to the molecules. We choose the appropriate parameters by adjusting the hydrogen-acceptor distance and donor-hydrogen-acceptor angle to get the H bonds geometry, which is close to the results in the literatures [7–10]. We then analyzed the EDXRD patterns at various pressures and build the crystal structures
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H.A. Ma et al. / Chemical Physics Letters 368 (2003) 668–672
Fig. 1. Energy-dispersive X-ray diffraction patterns of melamine at various pressures.
Fig. 2. A single molecule of melamine.
by repeating the same procedure. At about 1.3 GPa, some new diffraction lines appear (marked with the arrows in Fig. 1b), while the (0 0 1) line
merges with the background. The changes in the diffraction peaks show that the original monoclinic structure has been damaged under high pressure, and a new phase has formed. The patterns could be well indexed as triclinic phase (space group: P 1, Z ¼ 2) by using MS. The unit cell contains two molecules. The lattice parameters are: , b ¼ 6:47 A , c ¼ 9:84 A , a ¼ 99:52°, a ¼ 6:94 A b ¼ 91:07°, c ¼ 111:12°. Fig. 3b shows the crystal structure of melamine at about 1.3 GPa. In the same pressure region, the Raman data showed an inflexion in the frequencies of the external modes [15,16], which also suggested a structure phase transition in this pressure region. At about 8.2 GPa, a new diffraction peak appears at 35.66 keV, which continues up to 14.7 GPa. The patterns could be indexed as orthorhombic phase by using MS. The unit cell contains
H.A. Ma et al. / Chemical Physics Letters 368 (2003) 668–672
671
pressure region from 8.2 GPa to the highest pressure 14.7 GPa, the crystal keeps a relative stable orthorhombic structure. As to the second phase transition, we think, under pressure, the weak H bonds separations will decrease and ultimately reach the limiting value. These reduced H bonds separations will make a repulsive contribution to the total energy. To relieve these repulsive strains, the second structure phase transition is expected to occur. Based on the above results, the lattice parameters decrease with the pressure increasing, which induces the more condensed phases of melamine and the stronger interactions among the molecules. From the Raman data [15,16], we also can see that with the increasing of pressure, the external modes spectrum move to the high frequency and be close to the internal mode gradually. All these show that with the pressure increasing, the interactions among molecules become strong and close to that of inner-molecule gradually. Maybe, at sufficient high pressure molecule crystal will become covalent crystal, just like that H2 may be transformed to metal [24]. Fig. 4 shows the equation of state (P –V ) curve for melamine up to the pressure of 14.7 GPa. There are two inflexions at 1.3 and 8.2 GPa, respectively, in the whole pressure region. At the pressure lower than 1.3 GPa, the slope of the curve is larger, which showed that the original melamine
Fig. 3. X-ray crystal structure for melamine at different pres, b ¼ 7:53 A , sure: (a) monoclinic structure (a ¼ 10:69 A , b ¼ 111:9°) at ambient pressure; (b) triclinic c ¼ 7:36 A , b ¼ 6:47 A , c ¼ 9:84 A , a ¼ 99:52°, structure (a ¼ 6:94 A b ¼ 91:07°, c ¼ 111:12°) at about 1.3 GPa; (c) orthorhombic , b ¼ 7:09 A , c ¼ 5:76 A ) at about 8.2 structure (a ¼ 8:68 A GPa.
four molecules. The space group is P21212, Z ¼ 4, , and the lattice parameters are: a ¼ 8:68 A b ¼ 7:09 A, c ¼ 5:76 A. Fig. 3c shows the crystal structure of melamine at about 8.2 GPa. In the
Fig. 4. The equation of state (P –V ) curve for melamine up to the pressure of 14.7 GPa. The stars (I) are our experimental data points.
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H.A. Ma et al. / Chemical Physics Letters 368 (2003) 668–672
molecule crystal is easy to be compressed under pressure. At 1.3 GPa, the value of V =V0 is 73.8%. With the pressure increasing, the slope decreases gradually. At 8.2 GPa, the value of V =V0 is 64.4%. Above 8.2 GPa, the variation of V with P is slight, which shows melamine molecule crystal keeps a condensed and stable phase. At 14.7 GPa, the V =V0 is 61.6%. From the curve of P –V , we can see that with the pressure increasing, the lattice volume decreases, which also accounts for the condensability of melamine molecule crystal under high pressure.
4. Conclusions In situ high-pressure EDXRD experiments on melamine show that melamine undergoes two structural phase transitions under high pressure. At about 1.3 GPa, a pressure-induced structural phase transition from monoclinic to triclinic phase takes place. At about 8.2 GPa, a second structure phase transition occurs from triclinic to orthorhombic phase. The structures of melamine at different pressures are built using MS.
Acknowledgements The present work was carried out in BSRL. The authors would like to thank Dr. Liu Jing and her colleagues for the kind help in synchrotron radiation technique. Computational results are obtained using software programs from Accelrys Inc. and graphical displays generated with the Materials Visualizer. This work is partly supported by international cooperation funds of Chinese Science and Technology Department, Natural Science Funds of China, Plan of Skeleton Teacher in
University for Changjiang Scholar, Doctor Funds of Educational Department in China.
References [1] E.W. Hughes, J. Am. Chem. Soc. 63 (1941) 1737. [2] W. Sawodny, K. Niedenzu, J. Dawson, J. Chem. Phys. 45 (1966) 3155. [3] M.L. Cohen, Phys. Rev. B 32 (1985) 7988. [4] A.Y. Liu, M.L. Cohen, Science 245 (1989) 841. [5] A.Y. Liu, M.L. Cohen, Phys. Rev. B 41 (1990) 10727. [6] C.-M. Sung, M. Sung, Mater. Chem. Phys. 43 (1996) 1. [7] A.C. Larson, D.T. Cromer, J. Chem. Phys. 60 (1974) 185. [8] J.R. Schneider, B. Schrader, J. Mol. Struct. 29 (1975) 1. [9] J. Meier, J.R. Maple, M.J. Hwang, A.T. Hagler, J. Phys. Chem. 99 (1995) 5445. [10] M.P. Fernandez-Liencres, A. Navarro, J.J. Lopez-Gonzalez, et al., Chem. Phys. 266 (2001) 1. [11] P. Kroll, R. Hoffmann, J. Am. Chem. Soc. 121 (1999) 4696. [12] H. Montigaud, B. Tanguy, G. Demazeau, et al., Diam. Relat. Mater. 8 (1999) 1707. [13] H.A. Ma, X.P. Jia, L.X. Chen, et al., J. Phys. Condens. Mat. 14 (2002) 11269. [14] Z. Zhang, K. Leinenweber, M. Bauer, et al., J. Am. Chem. Soc. 123 (2001) 7788. [15] Y.N. Zhao, G.T. Zou, Chin. J. High Pressure Phys. 3 (1989) 269. [16] Y.N. Zhao, Q.L. Cui, G.T. Zou, et al., Chem. J. Chin. Universities 11 (1990) 720. [17] Materials Studio, Version 2.0, Accelrys Inc., Web page: www.materials-studio.com. [18] J. Liu, J. Zhao, R.Z. Chen, et al., Chin. J. High Pressure Phys. 14 (2000) 247. [19] A. Boultif, D. Louf, J. Appl. Cryst. 24 (1991) 987. [20] R.A. Young, The Rietveld Method, IUCr Monographies of Crystallography 5, Oxford University Press, Oxford, 1993. [21] M. Levitt, S. Lifson, J. Mol. Biol. 46 (1969) 269. [22] R. Fletcher, Practical Methods of Optimization, Vol. 1, Unconstrained Optimization, Wiley & Sons, New York, 1980. [23] O. Ermer, Struct. Bonding 27 (1976) 161. [24] W.J. Nellis, S.T. Weir, A.C. Mitchell, Science 273 (1996) 936.
Crystal structures of C3N6H6 under high pressure H.A. Ma a, X. Jia a,*, Q.L. Cui a, Y.W. Pan a, P.W. Zhu a, B.B. Liu a, H.J. Liu a, X.C. Wang a, J. Liu b, G.T. Zou a a
National Laboratory of Superhard Materials, Jilin University, 10 Qianwei Road, Changchun 130012, PR China b Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100039, PR China Received 20 September 2002; in final form 6 December 2002
Abstract In situ high-pressure energy-dispersive X-ray diffraction (EDXRD) experiments on melamine ðC3 N6 H6 Þ have been carried out using diamond anvil cell (DAC) with synchrotron radiation source. In the pressure range from ambient pressure up to 14.7 GPa, two pressure-induced structure phase transitions, from monoclinic to triclinic structure at about 1.3 GPa and from triclinic to orthorhombic structure at about 8.2 GPa, are observed. The crystal structures of melamine at different pressures are built by using Materials Studio (MS) based on the principle of energy minimization. Ó 2002 Elsevier Science B.V. All rights reserved.
1. Introduction A single melamine molecule is D3h symmetry with a six-member CN aromatic ring and three amino groups [1,2]. The CN ring is quite similar to hexagonal C3 N4 predicted by theoretical research, whose hardness might exceed that of diamond [3–6]. The molecule crystal structure of melamine at ambient condition has been studied thoroughly since 1941 by many methods, such as X-ray diffraction, Raman and IR spectroscopy, etc. [1,2,7– 10]. The melamine crystallizes in a monoclinic phase, in which each molecule is linked to its neighbors by eight hydrogen bonds [7–10].
*
Corresponding author. Fax: +86-431-5168858. E-mail address: [email protected] (X. Jia).
Because of the special single molecule structure and the existence of weak hydrogen bonds in molecule crystal, high pressure is expected to easily cause the rearrangement of melamine molecule, and induce the structural phase transition. Thus, melamine, served as a starting material for the synthesis of superhard structure C3 N4 by using high pressure and high temperature (HPHT) method [11–14], has attracted much attention. The structure of melamine under high pressure up to 8.7 GPa has been studied by Raman spectra and gave indication for the structural phase transitions [15,16]. However, the studies of the detailed crystal structure at high pressure have not been reported. In the present Letter, we have carried out in situ high-pressure EDXRD experiments up to 14.7 GPa. The pressure-induced structural phase transitions of melamine are studied, and the crystal structures of melamine at different pressure are built by using Materials Studio (MS) [17].
0009-2614/02/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved. doi:10.1016/S0009-2614(02)01965-6
H.A. Ma et al. / Chemical Physics Letters 368 (2003) 668–672
2. Experiments The sample is a colorless melamine powder with high purity of 99.9% (Beijing Chemical Industry Group). The original structure of melamine was studied by an ordinary angle dispersive X-ray diffraction (ADXRD) method. The data were collected on a REGAKU diffractometer with monochromatic Cu-Ka radiation. The XRD results indicate that our sample is consistent with the standard X-ray diffraction card 24-1923, which is typical monoclinic structure. The X-ray diffraction of melamine under high pressure was studied by an energy-dispersive method. The experiment was carried out on the wiggler beam line (3W1A) of Beijing Synchrotron Radiation Laboratory (BSRL). The polychromatic X-ray beam was collimated to a 30 30 lm sized spot with the storage ring operating at 2.8 GeV, and the diffracted beam was collected between 5 and 40 keV. A diamond anvil cell (DAC) was driven by an accurately adjustable gear-wormlevel system. The DAC consists of a pair of type-I diamonds with a culet of 410 lm and a stainless steel gasket with a 200 lm hole serving as the sample chamber. The detailed experimental facility is described in the literature [18]. A mixture of methanol:ethanol:water ¼ 16:3:1 was used as the pressure medium, and very fine NaCl powder was employed as the inner pressure calibration. The pressure was determined from the strongest diffraction peak (200) of NaCl along with the equation of state under high pressure. We can obtain the d values of the sample according to the energydispersion equation: E:d ¼
0:619927 ðkeV nmÞ: sin h
The 2h angle between the direct beam and the detector was set at 9.6°.
3. Results and discussion The spectra of in situ EDXRD at various pressures are shown in Fig. 1. We can see that with pressure increasing the relative intensity and the widths of different diffraction lines change largely,
669
and all the diffraction lines shift to higher energy. It is obvious that the melamine molecule crystal is influenced by high pressure. We first analyzed the EDXRD pattern at ambient condition by using MS. The indexing and refinement of the powder X-ray diffraction pattern was carried out using DI C V O L 91 [19] and Rietveld refinement [20] of MS, respectively, for extracting the detailed structural information. DI C V O L 91 indexing program is widely used to the indexing of experimental powder X-ray diffraction pattern. Rietveld refinement was used to further refine a trial crystal structure against experimental X-ray diffraction data. At ambient condition, except for the fluorescence lines at lower energies, all the diffraction lines can be well indexed as typical monoclinic structure (see Fig. 1a) by using MS and being compared with the standard card 24-1923. The unit cell contains four molecules. The space group is P21/a, Z ¼ 14 and the lattice pa, b ¼ 7:53 A , c ¼ 7:36 A , rameters are a ¼ 10:69 A b ¼ 111:9°. In order to build the molecule crystal structure of melamine, we first built a single melamine molecule (see Fig. 2). The structure of single melamine molecule was built and optimized by using Materials Visualizer and DiscoverÕs Minimizer of MS. We used the smart minimization so that the energy of the structure is minimum, which results in a modeled structure with a close resemblance to a real physical structure. The smart minimization automatically combines appropriate features of several methods, which starts with the steepest descent method [21], followed by the conjugate gradient method [22], and ending with a Newton method [23]. Then, we further built the crystal structure by Material Visualizer of MS based on our experimental data of diffraction pattern. After the refinement of the trial structure, we got a final crystal structure (see Fig. 3a). We also tentatively determine the H bonds configuration linked to the molecules. We choose the appropriate parameters by adjusting the hydrogen-acceptor distance and donor-hydrogen-acceptor angle to get the H bonds geometry, which is close to the results in the literatures [7–10]. We then analyzed the EDXRD patterns at various pressures and build the crystal structures
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H.A. Ma et al. / Chemical Physics Letters 368 (2003) 668–672
Fig. 1. Energy-dispersive X-ray diffraction patterns of melamine at various pressures.
Fig. 2. A single molecule of melamine.
by repeating the same procedure. At about 1.3 GPa, some new diffraction lines appear (marked with the arrows in Fig. 1b), while the (0 0 1) line
merges with the background. The changes in the diffraction peaks show that the original monoclinic structure has been damaged under high pressure, and a new phase has formed. The patterns could be well indexed as triclinic phase (space group: P 1, Z ¼ 2) by using MS. The unit cell contains two molecules. The lattice parameters are: , b ¼ 6:47 A , c ¼ 9:84 A , a ¼ 99:52°, a ¼ 6:94 A b ¼ 91:07°, c ¼ 111:12°. Fig. 3b shows the crystal structure of melamine at about 1.3 GPa. In the same pressure region, the Raman data showed an inflexion in the frequencies of the external modes [15,16], which also suggested a structure phase transition in this pressure region. At about 8.2 GPa, a new diffraction peak appears at 35.66 keV, which continues up to 14.7 GPa. The patterns could be indexed as orthorhombic phase by using MS. The unit cell contains
H.A. Ma et al. / Chemical Physics Letters 368 (2003) 668–672
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pressure region from 8.2 GPa to the highest pressure 14.7 GPa, the crystal keeps a relative stable orthorhombic structure. As to the second phase transition, we think, under pressure, the weak H bonds separations will decrease and ultimately reach the limiting value. These reduced H bonds separations will make a repulsive contribution to the total energy. To relieve these repulsive strains, the second structure phase transition is expected to occur. Based on the above results, the lattice parameters decrease with the pressure increasing, which induces the more condensed phases of melamine and the stronger interactions among the molecules. From the Raman data [15,16], we also can see that with the increasing of pressure, the external modes spectrum move to the high frequency and be close to the internal mode gradually. All these show that with the pressure increasing, the interactions among molecules become strong and close to that of inner-molecule gradually. Maybe, at sufficient high pressure molecule crystal will become covalent crystal, just like that H2 may be transformed to metal [24]. Fig. 4 shows the equation of state (P –V ) curve for melamine up to the pressure of 14.7 GPa. There are two inflexions at 1.3 and 8.2 GPa, respectively, in the whole pressure region. At the pressure lower than 1.3 GPa, the slope of the curve is larger, which showed that the original melamine
Fig. 3. X-ray crystal structure for melamine at different pres, b ¼ 7:53 A , sure: (a) monoclinic structure (a ¼ 10:69 A , b ¼ 111:9°) at ambient pressure; (b) triclinic c ¼ 7:36 A , b ¼ 6:47 A , c ¼ 9:84 A , a ¼ 99:52°, structure (a ¼ 6:94 A b ¼ 91:07°, c ¼ 111:12°) at about 1.3 GPa; (c) orthorhombic , b ¼ 7:09 A , c ¼ 5:76 A ) at about 8.2 structure (a ¼ 8:68 A GPa.
four molecules. The space group is P21212, Z ¼ 4, , and the lattice parameters are: a ¼ 8:68 A b ¼ 7:09 A, c ¼ 5:76 A. Fig. 3c shows the crystal structure of melamine at about 8.2 GPa. In the
Fig. 4. The equation of state (P –V ) curve for melamine up to the pressure of 14.7 GPa. The stars (I) are our experimental data points.
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H.A. Ma et al. / Chemical Physics Letters 368 (2003) 668–672
molecule crystal is easy to be compressed under pressure. At 1.3 GPa, the value of V =V0 is 73.8%. With the pressure increasing, the slope decreases gradually. At 8.2 GPa, the value of V =V0 is 64.4%. Above 8.2 GPa, the variation of V with P is slight, which shows melamine molecule crystal keeps a condensed and stable phase. At 14.7 GPa, the V =V0 is 61.6%. From the curve of P –V , we can see that with the pressure increasing, the lattice volume decreases, which also accounts for the condensability of melamine molecule crystal under high pressure.
4. Conclusions In situ high-pressure EDXRD experiments on melamine show that melamine undergoes two structural phase transitions under high pressure. At about 1.3 GPa, a pressure-induced structural phase transition from monoclinic to triclinic phase takes place. At about 8.2 GPa, a second structure phase transition occurs from triclinic to orthorhombic phase. The structures of melamine at different pressures are built using MS.
Acknowledgements The present work was carried out in BSRL. The authors would like to thank Dr. Liu Jing and her colleagues for the kind help in synchrotron radiation technique. Computational results are obtained using software programs from Accelrys Inc. and graphical displays generated with the Materials Visualizer. This work is partly supported by international cooperation funds of Chinese Science and Technology Department, Natural Science Funds of China, Plan of Skeleton Teacher in
University for Changjiang Scholar, Doctor Funds of Educational Department in China.
References [1] E.W. Hughes, J. Am. Chem. Soc. 63 (1941) 1737. [2] W. Sawodny, K. Niedenzu, J. Dawson, J. Chem. Phys. 45 (1966) 3155. [3] M.L. Cohen, Phys. Rev. B 32 (1985) 7988. [4] A.Y. Liu, M.L. Cohen, Science 245 (1989) 841. [5] A.Y. Liu, M.L. Cohen, Phys. Rev. B 41 (1990) 10727. [6] C.-M. Sung, M. Sung, Mater. Chem. Phys. 43 (1996) 1. [7] A.C. Larson, D.T. Cromer, J. Chem. Phys. 60 (1974) 185. [8] J.R. Schneider, B. Schrader, J. Mol. Struct. 29 (1975) 1. [9] J. Meier, J.R. Maple, M.J. Hwang, A.T. Hagler, J. Phys. Chem. 99 (1995) 5445. [10] M.P. Fernandez-Liencres, A. Navarro, J.J. Lopez-Gonzalez, et al., Chem. Phys. 266 (2001) 1. [11] P. Kroll, R. Hoffmann, J. Am. Chem. Soc. 121 (1999) 4696. [12] H. Montigaud, B. Tanguy, G. Demazeau, et al., Diam. Relat. Mater. 8 (1999) 1707. [13] H.A. Ma, X.P. Jia, L.X. Chen, et al., J. Phys. Condens. Mat. 14 (2002) 11269. [14] Z. Zhang, K. Leinenweber, M. Bauer, et al., J. Am. Chem. Soc. 123 (2001) 7788. [15] Y.N. Zhao, G.T. Zou, Chin. J. High Pressure Phys. 3 (1989) 269. [16] Y.N. Zhao, Q.L. Cui, G.T. Zou, et al., Chem. J. Chin. Universities 11 (1990) 720. [17] Materials Studio, Version 2.0, Accelrys Inc., Web page: www.materials-studio.com. [18] J. Liu, J. Zhao, R.Z. Chen, et al., Chin. J. High Pressure Phys. 14 (2000) 247. [19] A. Boultif, D. Louf, J. Appl. Cryst. 24 (1991) 987. [20] R.A. Young, The Rietveld Method, IUCr Monographies of Crystallography 5, Oxford University Press, Oxford, 1993. [21] M. Levitt, S. Lifson, J. Mol. Biol. 46 (1969) 269. [22] R. Fletcher, Practical Methods of Optimization, Vol. 1, Unconstrained Optimization, Wiley & Sons, New York, 1980. [23] O. Ermer, Struct. Bonding 27 (1976) 161. [24] W.J. Nellis, S.T. Weir, A.C. Mitchell, Science 273 (1996) 936.