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A study of density fluctuations near the critical point of fluid Se by small angle X-ray scattering
Journal of Non-Crystalline Solids 312–314 (2002) 279–283 www.elsevier.com/locate/jnoncrysol
A study of density fluctuations near the critical point of fluid Se by small angle X-ray scattering Moynul Huq Kazi a, Masanori Inui
b,*
, Kozaburo Tamura
b
a b
Graduate School of Biosphere Science, Hiroshima University, Higashi-Hiroshima 739-8521, Japan Faculty of Integrated Arts and Sciences, Hiroshima University, Higashi-Hiroshima 739-8521, Japan
Abstract Small angle X-ray scattering (SAXS) measurements for dense Se vapour have been carried out to investigate the characteristics of the density fluctuations near the critical density region. For this reason the correlation lengths of the density fluctuations and the number-density fluctuations have been measured precisely at different temperatures and pressures near the critical point. In this experiment a new spectrometer with a high brilliance source is used and SAXS spectra are detected using an imaging plate. Less noisy spectra with better fitting conditions to calculate correlation lengths of density fluctuations are found. Larger values of the correlation length of density fluctuations (and also the number-density fluctuations) are obtained near the critical density region, which agrees with the results of our previous experiments [J. Non-Cryst. Solids 250–252 (1999) 531]. The correlation length of the density fluctuations increases as we approach to the critical point of fluid Se along the path of critical density region. Ó 2002 Elsevier Science B.V. All rights reserved. PACS: 61.10.Eq; 61.25.MV; 62.50.+P; 64.60.Fr
1. Introduction Elemental Se in its liquid form is a semiconductor with a twofold coordinated chain structure in which the atoms are covalently bonded. From the measurements of viscosity [2], magnetic susceptibility [3] and nuclear magnetic resonance (NMR) [4] near the melting point, an average chain length of 104 –105 atoms can be estimated. With increasing temperature and pressure the
*
Corresponding author. Tel.: +81-824 24 6555; fax: +81-824 24 0757. E-mail address: [email protected] (M. Inui).
average chain length becomes shorter and near the critical point (critical constants: Tc ¼ 1615 °C, Pc ¼ 385 bar and qc ¼ 1:85 g/cm3 [5]) it approaches only about 10 atoms, estimated by an NMR study [4]. At the same time, the electrical conductivity increases gradually with increasing temperature and pressure [6,7] and a high conductivity region appears in the immediate vicinity of the critical point. Structural studies show that the twofold-coordinated structure is largely preserved in the metallic fluid Se [8–11], and the nearest-neighbour distance decreases slightly when the SC–M transition occurs. The SC–M transition in fluid Se has two characteristic features; the dc conductivity increases with the volume expansion
0022-3093/02/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 3 0 9 3 ( 0 2 ) 0 1 6 8 5 - X
280
M.H. Kazi et al. / Journal of Non-Crystalline Solids 312–314 (2002) 279–283
and the transition occurs when the chain length becomes very short, which seems to correlate with the instability of the chain structure. Recent experimental studies have suggested that a transition happens near a dc conductivity of 30 X1 cm1 [9]. When the metallic fluid is further expanded, the conductivity decreases, and the fluid finally becomes an insulating vapour consisting of Se dimers, which suggests that a metal–non-metal (M–NM) transition occurs in the further expansion process around the critical point. It is an important point to emphasize that Se experiences a SC–M-NM transition near the critical point. So it is plausible to think that the electronic properties of fluid Se are very sensitive to the density fluctuations. To make the mechanism of the SC–M-NM transition clear, it is interesting to study how the electronic properties of fluid Se correlate with the density fluctuations near the critical point. For this purpose we should first investigate the nature of the density fluctuations near the critical point of fluid Se. To understand the properties of density fluctuations of fluid Se we have performed a SAXS measurement for super critical fluid Se near the critical point and have measured the correlation lengths of the density fluctuations and the number density fluctuations at different temperatures and pressures. At the same time densities of fluid Se at those temperatures and pressures were estimated by the absorption method of X-ray intensities. In this paper new results of our SAXS measurements are presented.
2. Experimental SAXS measurements for the supercritical fluid Se have been carried out using a newly installed spectrometer of a slit collimation system with a high brilliance source. The SAXS spectrometer has two slits and the second slit eliminates parasitic scattering from the first one. The MoKa line is focussed and monochromatized by using a side by side multi-layered mirror produced by Osmic Co. Ltd. for the first time. The SAXS intensity is detected by an imaging plate with a camera length of 384 mm.
A high-pressure vessel made of super-high tension steel (SNCM-439) is used for the SAXS measurements. The vessel permits the measurements up to 1700 °C and 800 bar. The incident and scattered X-ray beam pass through diamond and Be windows respectively. The maximum scattering angle is limited by the diameter of the Be window for the scattered X-rays. The observable wavenumber, k [where k ¼ ð4p=kÞ sin h] in this study 1 . ranges from 0.05 to 0.25 A The high-purity grade (99.999%) Se sample is contained in a cell made of polycrystalline sapphire which is resistant to chemical reaction with Se at high temperatures. The sample thickness is 75 lm for the present measurements. The temperature is measured at three locations by two W– Re thermocouples (Re/W 5%, Re/W 26%) and one B-type thermocouple (Pt/Rh 30%, Pt/Rh 6%) and the difference of the temperatures is within 10 °C. The vessel is pressurized by high-purity grade (99.9999%) He gas and the pressure is measured with a Heise gauge, having an accuracy of 2 bar. The construction of the vessel is described in the literature [1].
3. Results The pressure and temperature dependence of the SAXS intensity from an empty cell was investigated in the previous experiments [1] and no parasitic scattering from the cell was observed, even at high temperature. We have investigated the scattering intensity of He gas from the vessel with the sapphire cell at room temperature and at pressures of 199, 400 and 595 bar. We obtain the calculated spectra using the scattering intensity of X-rays given by the equa2 tion: IðkÞ ¼ CNf ðkÞ SðkÞ, where f ðkÞ is the atomic form factor. We can obtain the constant C from the observed IðkÞ if the number of atoms, N and the structure factor, SðkÞ, of the pressurized He gas are estimated. The procedure for getting the constant C and the calculated spectra is described in the literature [1]. The constant C is determined to be (1:04 0:02Þ 1019 by adjusting the experimental and calculated spectra in the present experiment. We have deduced SðkÞ of fluid Se by
M.H. Kazi et al. / Journal of Non-Crystalline Solids 312–314 (2002) 279–283
281
using the calculated C after subtracting the scattering intensity of pressurized He gas. The SAXS spectra of liquid and fluid Se at different temperatures and pressures are obtained after absorption correction. The spectrum at 600 °C and 400 bar of liquid Se is used as the baseline to deduce the critical scattering of fluid Se. The larger scattering intensities of fluid Se are found near the critical density region. It is also observed that the intensity of critical scattering becomes larger as we approach to the critical point by decreasing temperature and reaches a maximum at 1647 °C and 415 bar in our present measurement. The isochore near the critical point of fluid Se in a pressure–temperature plane [5] is shown in Fig. 1, together with the measured points in the present work, where the circles denote the measured points and solid circles denote the points whose spectra are presented in this paper. Figs. 2 and 3 show the deduced SðkÞ of fluid Se at temperatures 1647, 1662 and 1667 °C with various pressures together with the estimated density q, correlation lengths of density fluctuations n, and the number density fluctuations Sð0Þ, obtained from the procedure described in the next section (Table 1). Fig. 2. SðkÞ of fluid Se at 1662 and 1647 °C at various pressures.
4. Discussion To investigate n and the number density fluctuations, Sð0Þ, for fluid Se near qc , the Ornstein– Zernike equation SðkÞ ¼
Fig. 1. The isochore of fluid Se near the critical point in the pressure–temperature plane.
Sð0Þ 1 þ n2 k 2
is used. We have obtained the larger value of n as well as Sð0Þ near the critical density region, which is consistent with our previous work [1,2]. At the temperature 1662 °C larger values of n and Sð0Þ and 10:0 4:2 respectively are found, 24:4 5:9 A at 434 bar, where the density is estimated to be 1.66 g/cm3 . At 1647 °C and 415 bar; n and Sð0Þ and 12:7 6:1 respectively become 26:5 7:4 A where the density is 1.44 g/cm3 . We see that the larger value of n as well as Sð0Þ increases with decreasing temperature, i.e. as we approach nearer to the critical point along the path of critical
282
M.H. Kazi et al. / Journal of Non-Crystalline Solids 312–314 (2002) 279–283 Table 1 The correlation length of density fluctuations, n and the fluctuation of number density, Sð0Þ, obtained from the Ornstein– Zernike equation for fluid Se together with estimated density q at different temperatures and pressures whose spectra are shown in Figs. 2 and 3 ) P T (°C) q (g/cm3 ) n (A Sð0Þ (bar)
Fig. 3. SðkÞ of fluid Se at 1667 °C at various pressures.
density region. This behavior may agree with the fact that the density fluctuations becomes larger as the critical point is approached. In the present experiment we successfully measured the SAXS spectra up to a temperature of 1647 °C, near the critical point. As is well known Sð0Þ ¼ DN 2 =hN i, where hN i and DN are the average number and its fluctuation, respectively. At a temperature of 1647 °C, it is found from the Gaussain fitting curves that the and 14.4 maximum values of n and Sð0Þ are 25.8 A respectively, where the density is 1.70 g/cm3 . These results mean that the density fluctuations induce a . few dense regions with an average size of 25.8 A is When a cubic cell with a side length of 25.8 A considered, the average Se dimers N and its fluctuation DN are estimated to be 111 and 40 respectively. The average distance between the at 1.70 g/cm3 . In the dense state the dimers is 5.4 A cubic cell contains 151 dimers and the average
480 471 461 454 442 436 433 433 423
1667 1667 1667 1667 1667 1667 1667 1667 1667
2.52 2.49 2.43 2.40 2.34 2.26 1.84 1.49 1.30
5.1 2.0 9.0 3.2 9.7 2.7 10.4 1.8 12.4 1.5 15.9 5.1 22.3 6.9 23.1 4.9 18.5 4.8
0.5 0.2 0.8 0.2 1.0 0.3 1.2 0.2 1.9 0.3 2.6 1.2 6.0 2.9 9.9 3.5 7.9 2.8
445 441 435 434 431
1662 1662 1662 1662 1662
2.32 2.28 2.18 1.66 1.41
16.6 3.3 16.9 5.7 18.2 8.0 24.4 5.9 19.0 6.1
2.6 0.7 2.6 1.3 2.4 1.5 10.0 4.2 6.8 3.4
490 461 441 429 415 415 415 402
1647 1647 1647 1647 1647 1647 1647 1647
2.64 2.57 2.50 2.44 1.53 1.44 1.35 1.18
7.2 2.5 8.7 3.1 9.0 2.4 12.8 1.5 20.0 1.7 26.5 7.4 18.0 4.6 13.2 0.4
0.3 0.1 0.6 0.2 0.5 0.1 1.0 0.1 10.6 1.6 12.7 6.1 6.2 2.3 2.2 0.1
. The density distance between the dimers is 4.8 A in the dense state becomes 2.3 g/cm3 . On the other hand, in the rare state the average distance is 6.2 , corresponding to a density of 1.08 g/cm3 . It is, A however, difficult to believe that most of the molecules are Se dimers in the dense state; chain molecules are expected to be formed because of strong intermolecular interactions between the dimers. The results of an ab initio moleculardynamics simulation by Shimojo et al. [12] for fluid Se, with densities 1 g/cm3 and 2 g/cm3 , where spin effects are taken into account, support our idea. The results show that in fluid Se with 1 g/cm3 most molecules are Se dimers and the fraction of chain molecules is small, while with 2 g/cm3 most Se atoms form chain molecules. The results support our speculation that chain molecules are formed in the dense state under the density fluctuations. Our XAFS results [13], however, suggest that fluid Se
M.H. Kazi et al. / Journal of Non-Crystalline Solids 312–314 (2002) 279–283
is a mixture of Se dimers and other chain molecules above the critical density. This result can be explained by the fact that XAFS spectroscopy observes the superposition of the dense and rare regions under the density fluctuations.
283
Ministry of Education, Science and Culture of Japan under contract no. 11102004. The technical supports of Rigaku Co. Ltd. and High Pressure System Co. Ltd., are gratefully acknowledged.
References 5. Conclusion SAXS measurements for supercritical fluid Se near the isochore of critical density have been carried out and correlation lengths of the density fluctuations as well as the number density fluctuation of fluid Se are determined at different temperatures and pressures near the critical density. We are able to measure the SAXS spectra up to 1647 °C, near the critical point. To understand the correlation between the density fluctuations and the electronic properties we need a clear map of the density fluctuations around the critical point. So, it is necessary to develop our present experimental set up in order to measure spectra closer to critical point of fluid Se.
Acknowledgements This research is supported by the Grantin-Aid for Specially Promoted Research from the
[1] M. Inui, Y. Oh’ishi, I. Nakaso, M.H. Kazi, K. Tamura, J. Non-Cryst. Solids 250–252 (1999) 531. [2] J.C. Perron, J. Rabit, J.F. Railland, Philos. Mag. B 46 (1982) 321. [3] W. Freyland, M. cutler, J. Chem. Soc. Faraday Trans. 76 (1980) 756. [4] W.W. Warren Jr., R. Dupee, Phys. Rev. B 22 (1980) 2257. [5] S. Hosokawa, T. Kuboi, K. Tamura, Ber Bunsenges. Phys. Chem. 101 (1997) 120. [6] H. Hoshino, R.W. Schmutzler, F. Hensel, Ber. Bunsenges. Phys. Chem. 80 (1976) 27. [7] H. Hoshino, R.W. Schmutzler, W.W. Warren Jr., F. Hensel, Philos. Mag. B 33 (1976) 255. [8] K. Tamura, S. Hosokawa, Ber. Bunsenges. Phys. Chem. 96 (1992) 681. [9] K. Tamura, J. Non-Cryst. Solids 205–207 (1996) 239. [10] M. Inui, T. Noda, K. Tamura, J. Non-Cryst. Solids 205207 (1996) 239. [11] M. Inui, T. Noda, K. Tamura, C. Li, J. Phys.: Condens. Matter 8 (1996) 261. [12] F. Shimojo, K. Hoshino, M. Watabe, Y. Zempo, J. Phys.: Condens. Matter 10 (1998) 1199. [13] M. Inui, K. Tamura, J.L. Hazemann, D. Raoux, Y. Soldo, R. Argoud, J.F. Jal, J. Non-Cryst. Solids 250–252 (1999) 525.
A study of density fluctuations near the critical point of fluid Se by small angle X-ray scattering Moynul Huq Kazi a, Masanori Inui
b,*
, Kozaburo Tamura
b
a b
Graduate School of Biosphere Science, Hiroshima University, Higashi-Hiroshima 739-8521, Japan Faculty of Integrated Arts and Sciences, Hiroshima University, Higashi-Hiroshima 739-8521, Japan
Abstract Small angle X-ray scattering (SAXS) measurements for dense Se vapour have been carried out to investigate the characteristics of the density fluctuations near the critical density region. For this reason the correlation lengths of the density fluctuations and the number-density fluctuations have been measured precisely at different temperatures and pressures near the critical point. In this experiment a new spectrometer with a high brilliance source is used and SAXS spectra are detected using an imaging plate. Less noisy spectra with better fitting conditions to calculate correlation lengths of density fluctuations are found. Larger values of the correlation length of density fluctuations (and also the number-density fluctuations) are obtained near the critical density region, which agrees with the results of our previous experiments [J. Non-Cryst. Solids 250–252 (1999) 531]. The correlation length of the density fluctuations increases as we approach to the critical point of fluid Se along the path of critical density region. Ó 2002 Elsevier Science B.V. All rights reserved. PACS: 61.10.Eq; 61.25.MV; 62.50.+P; 64.60.Fr
1. Introduction Elemental Se in its liquid form is a semiconductor with a twofold coordinated chain structure in which the atoms are covalently bonded. From the measurements of viscosity [2], magnetic susceptibility [3] and nuclear magnetic resonance (NMR) [4] near the melting point, an average chain length of 104 –105 atoms can be estimated. With increasing temperature and pressure the
*
Corresponding author. Tel.: +81-824 24 6555; fax: +81-824 24 0757. E-mail address: [email protected] (M. Inui).
average chain length becomes shorter and near the critical point (critical constants: Tc ¼ 1615 °C, Pc ¼ 385 bar and qc ¼ 1:85 g/cm3 [5]) it approaches only about 10 atoms, estimated by an NMR study [4]. At the same time, the electrical conductivity increases gradually with increasing temperature and pressure [6,7] and a high conductivity region appears in the immediate vicinity of the critical point. Structural studies show that the twofold-coordinated structure is largely preserved in the metallic fluid Se [8–11], and the nearest-neighbour distance decreases slightly when the SC–M transition occurs. The SC–M transition in fluid Se has two characteristic features; the dc conductivity increases with the volume expansion
0022-3093/02/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 3 0 9 3 ( 0 2 ) 0 1 6 8 5 - X
280
M.H. Kazi et al. / Journal of Non-Crystalline Solids 312–314 (2002) 279–283
and the transition occurs when the chain length becomes very short, which seems to correlate with the instability of the chain structure. Recent experimental studies have suggested that a transition happens near a dc conductivity of 30 X1 cm1 [9]. When the metallic fluid is further expanded, the conductivity decreases, and the fluid finally becomes an insulating vapour consisting of Se dimers, which suggests that a metal–non-metal (M–NM) transition occurs in the further expansion process around the critical point. It is an important point to emphasize that Se experiences a SC–M-NM transition near the critical point. So it is plausible to think that the electronic properties of fluid Se are very sensitive to the density fluctuations. To make the mechanism of the SC–M-NM transition clear, it is interesting to study how the electronic properties of fluid Se correlate with the density fluctuations near the critical point. For this purpose we should first investigate the nature of the density fluctuations near the critical point of fluid Se. To understand the properties of density fluctuations of fluid Se we have performed a SAXS measurement for super critical fluid Se near the critical point and have measured the correlation lengths of the density fluctuations and the number density fluctuations at different temperatures and pressures. At the same time densities of fluid Se at those temperatures and pressures were estimated by the absorption method of X-ray intensities. In this paper new results of our SAXS measurements are presented.
2. Experimental SAXS measurements for the supercritical fluid Se have been carried out using a newly installed spectrometer of a slit collimation system with a high brilliance source. The SAXS spectrometer has two slits and the second slit eliminates parasitic scattering from the first one. The MoKa line is focussed and monochromatized by using a side by side multi-layered mirror produced by Osmic Co. Ltd. for the first time. The SAXS intensity is detected by an imaging plate with a camera length of 384 mm.
A high-pressure vessel made of super-high tension steel (SNCM-439) is used for the SAXS measurements. The vessel permits the measurements up to 1700 °C and 800 bar. The incident and scattered X-ray beam pass through diamond and Be windows respectively. The maximum scattering angle is limited by the diameter of the Be window for the scattered X-rays. The observable wavenumber, k [where k ¼ ð4p=kÞ sin h] in this study 1 . ranges from 0.05 to 0.25 A The high-purity grade (99.999%) Se sample is contained in a cell made of polycrystalline sapphire which is resistant to chemical reaction with Se at high temperatures. The sample thickness is 75 lm for the present measurements. The temperature is measured at three locations by two W– Re thermocouples (Re/W 5%, Re/W 26%) and one B-type thermocouple (Pt/Rh 30%, Pt/Rh 6%) and the difference of the temperatures is within 10 °C. The vessel is pressurized by high-purity grade (99.9999%) He gas and the pressure is measured with a Heise gauge, having an accuracy of 2 bar. The construction of the vessel is described in the literature [1].
3. Results The pressure and temperature dependence of the SAXS intensity from an empty cell was investigated in the previous experiments [1] and no parasitic scattering from the cell was observed, even at high temperature. We have investigated the scattering intensity of He gas from the vessel with the sapphire cell at room temperature and at pressures of 199, 400 and 595 bar. We obtain the calculated spectra using the scattering intensity of X-rays given by the equa2 tion: IðkÞ ¼ CNf ðkÞ SðkÞ, where f ðkÞ is the atomic form factor. We can obtain the constant C from the observed IðkÞ if the number of atoms, N and the structure factor, SðkÞ, of the pressurized He gas are estimated. The procedure for getting the constant C and the calculated spectra is described in the literature [1]. The constant C is determined to be (1:04 0:02Þ 1019 by adjusting the experimental and calculated spectra in the present experiment. We have deduced SðkÞ of fluid Se by
M.H. Kazi et al. / Journal of Non-Crystalline Solids 312–314 (2002) 279–283
281
using the calculated C after subtracting the scattering intensity of pressurized He gas. The SAXS spectra of liquid and fluid Se at different temperatures and pressures are obtained after absorption correction. The spectrum at 600 °C and 400 bar of liquid Se is used as the baseline to deduce the critical scattering of fluid Se. The larger scattering intensities of fluid Se are found near the critical density region. It is also observed that the intensity of critical scattering becomes larger as we approach to the critical point by decreasing temperature and reaches a maximum at 1647 °C and 415 bar in our present measurement. The isochore near the critical point of fluid Se in a pressure–temperature plane [5] is shown in Fig. 1, together with the measured points in the present work, where the circles denote the measured points and solid circles denote the points whose spectra are presented in this paper. Figs. 2 and 3 show the deduced SðkÞ of fluid Se at temperatures 1647, 1662 and 1667 °C with various pressures together with the estimated density q, correlation lengths of density fluctuations n, and the number density fluctuations Sð0Þ, obtained from the procedure described in the next section (Table 1). Fig. 2. SðkÞ of fluid Se at 1662 and 1647 °C at various pressures.
4. Discussion To investigate n and the number density fluctuations, Sð0Þ, for fluid Se near qc , the Ornstein– Zernike equation SðkÞ ¼
Fig. 1. The isochore of fluid Se near the critical point in the pressure–temperature plane.
Sð0Þ 1 þ n2 k 2
is used. We have obtained the larger value of n as well as Sð0Þ near the critical density region, which is consistent with our previous work [1,2]. At the temperature 1662 °C larger values of n and Sð0Þ and 10:0 4:2 respectively are found, 24:4 5:9 A at 434 bar, where the density is estimated to be 1.66 g/cm3 . At 1647 °C and 415 bar; n and Sð0Þ and 12:7 6:1 respectively become 26:5 7:4 A where the density is 1.44 g/cm3 . We see that the larger value of n as well as Sð0Þ increases with decreasing temperature, i.e. as we approach nearer to the critical point along the path of critical
282
M.H. Kazi et al. / Journal of Non-Crystalline Solids 312–314 (2002) 279–283 Table 1 The correlation length of density fluctuations, n and the fluctuation of number density, Sð0Þ, obtained from the Ornstein– Zernike equation for fluid Se together with estimated density q at different temperatures and pressures whose spectra are shown in Figs. 2 and 3 ) P T (°C) q (g/cm3 ) n (A Sð0Þ (bar)
Fig. 3. SðkÞ of fluid Se at 1667 °C at various pressures.
density region. This behavior may agree with the fact that the density fluctuations becomes larger as the critical point is approached. In the present experiment we successfully measured the SAXS spectra up to a temperature of 1647 °C, near the critical point. As is well known Sð0Þ ¼ DN 2 =hN i, where hN i and DN are the average number and its fluctuation, respectively. At a temperature of 1647 °C, it is found from the Gaussain fitting curves that the and 14.4 maximum values of n and Sð0Þ are 25.8 A respectively, where the density is 1.70 g/cm3 . These results mean that the density fluctuations induce a . few dense regions with an average size of 25.8 A is When a cubic cell with a side length of 25.8 A considered, the average Se dimers N and its fluctuation DN are estimated to be 111 and 40 respectively. The average distance between the at 1.70 g/cm3 . In the dense state the dimers is 5.4 A cubic cell contains 151 dimers and the average
480 471 461 454 442 436 433 433 423
1667 1667 1667 1667 1667 1667 1667 1667 1667
2.52 2.49 2.43 2.40 2.34 2.26 1.84 1.49 1.30
5.1 2.0 9.0 3.2 9.7 2.7 10.4 1.8 12.4 1.5 15.9 5.1 22.3 6.9 23.1 4.9 18.5 4.8
0.5 0.2 0.8 0.2 1.0 0.3 1.2 0.2 1.9 0.3 2.6 1.2 6.0 2.9 9.9 3.5 7.9 2.8
445 441 435 434 431
1662 1662 1662 1662 1662
2.32 2.28 2.18 1.66 1.41
16.6 3.3 16.9 5.7 18.2 8.0 24.4 5.9 19.0 6.1
2.6 0.7 2.6 1.3 2.4 1.5 10.0 4.2 6.8 3.4
490 461 441 429 415 415 415 402
1647 1647 1647 1647 1647 1647 1647 1647
2.64 2.57 2.50 2.44 1.53 1.44 1.35 1.18
7.2 2.5 8.7 3.1 9.0 2.4 12.8 1.5 20.0 1.7 26.5 7.4 18.0 4.6 13.2 0.4
0.3 0.1 0.6 0.2 0.5 0.1 1.0 0.1 10.6 1.6 12.7 6.1 6.2 2.3 2.2 0.1
. The density distance between the dimers is 4.8 A in the dense state becomes 2.3 g/cm3 . On the other hand, in the rare state the average distance is 6.2 , corresponding to a density of 1.08 g/cm3 . It is, A however, difficult to believe that most of the molecules are Se dimers in the dense state; chain molecules are expected to be formed because of strong intermolecular interactions between the dimers. The results of an ab initio moleculardynamics simulation by Shimojo et al. [12] for fluid Se, with densities 1 g/cm3 and 2 g/cm3 , where spin effects are taken into account, support our idea. The results show that in fluid Se with 1 g/cm3 most molecules are Se dimers and the fraction of chain molecules is small, while with 2 g/cm3 most Se atoms form chain molecules. The results support our speculation that chain molecules are formed in the dense state under the density fluctuations. Our XAFS results [13], however, suggest that fluid Se
M.H. Kazi et al. / Journal of Non-Crystalline Solids 312–314 (2002) 279–283
is a mixture of Se dimers and other chain molecules above the critical density. This result can be explained by the fact that XAFS spectroscopy observes the superposition of the dense and rare regions under the density fluctuations.
283
Ministry of Education, Science and Culture of Japan under contract no. 11102004. The technical supports of Rigaku Co. Ltd. and High Pressure System Co. Ltd., are gratefully acknowledged.
References 5. Conclusion SAXS measurements for supercritical fluid Se near the isochore of critical density have been carried out and correlation lengths of the density fluctuations as well as the number density fluctuation of fluid Se are determined at different temperatures and pressures near the critical density. We are able to measure the SAXS spectra up to 1647 °C, near the critical point. To understand the correlation between the density fluctuations and the electronic properties we need a clear map of the density fluctuations around the critical point. So, it is necessary to develop our present experimental set up in order to measure spectra closer to critical point of fluid Se.
Acknowledgements This research is supported by the Grantin-Aid for Specially Promoted Research from the
[1] M. Inui, Y. Oh’ishi, I. Nakaso, M.H. Kazi, K. Tamura, J. Non-Cryst. Solids 250–252 (1999) 531. [2] J.C. Perron, J. Rabit, J.F. Railland, Philos. Mag. B 46 (1982) 321. [3] W. Freyland, M. cutler, J. Chem. Soc. Faraday Trans. 76 (1980) 756. [4] W.W. Warren Jr., R. Dupee, Phys. Rev. B 22 (1980) 2257. [5] S. Hosokawa, T. Kuboi, K. Tamura, Ber Bunsenges. Phys. Chem. 101 (1997) 120. [6] H. Hoshino, R.W. Schmutzler, F. Hensel, Ber. Bunsenges. Phys. Chem. 80 (1976) 27. [7] H. Hoshino, R.W. Schmutzler, W.W. Warren Jr., F. Hensel, Philos. Mag. B 33 (1976) 255. [8] K. Tamura, S. Hosokawa, Ber. Bunsenges. Phys. Chem. 96 (1992) 681. [9] K. Tamura, J. Non-Cryst. Solids 205–207 (1996) 239. [10] M. Inui, T. Noda, K. Tamura, J. Non-Cryst. Solids 205207 (1996) 239. [11] M. Inui, T. Noda, K. Tamura, C. Li, J. Phys.: Condens. Matter 8 (1996) 261. [12] F. Shimojo, K. Hoshino, M. Watabe, Y. Zempo, J. Phys.: Condens. Matter 10 (1998) 1199. [13] M. Inui, K. Tamura, J.L. Hazemann, D. Raoux, Y. Soldo, R. Argoud, J.F. Jal, J. Non-Cryst. Solids 250–252 (1999) 525.