X-RAY DIFFRACTION MEASUREMENTS FOR EXPANDED FLUID MERCURY A substantial and continuous volume expansion from liquid to rarefied vapor occurs by the change of temperature and pressure around the liquid- vapor critical point without crossing the saturated vapor pressure curve. In the expansion process the mean interatomic distance increases by up to ten times compared with that under standard conditions. In metallic or semiconducting liquids, physical properties can drastically change. Liquid Hg, well known as a prototype of liquid metals, transforms into an insulating state when it is expanded up to the liquid-gas critical point (critical data of Hg [1] : T c = 1478 C, p c = 1673 bar, ρ c = 5.8 g/cm 3 ). The first indication of the metal- nonmetal (M-NM) transition, which occurs around 9 g/cm 3 , was found in the electrical conductivity, thermoelectric power obtained by Hensel and Frank [2]. Many experimental and theoretical investigations focused on the M-NM transition have been made over the past few decades. The information on the atomic arrangement of expanded fluid Hg is quite important for understanding the mechanism of the M-NM transition. However, the diffraction experiments for expanded fluid Hg are not easy because the critical pressure is very high. Tamura and Hosokawa [3] succeeded in measuring the X-ray diffraction pattern of expanded liquid Hg both in the metallic and critical regions using an in-house X-ray source. We present new results of X-ray diffraction measurements using synchrotron radiation at SPring-8. These measurements extend from the liquid to the dense vapor region, which is beyond the liquid-vapor critical point. Energy-dispersive X-ray diffraction measurements for expanded fluid Hg were performed using a diffractometer and high-pressure apparatus installed at the beamline BL04B1 . White X-rays were used as the primary beam, and the scattered photons were detected by a solid state detector (SSD). The experimental conditions of high- temperatures up to 1520 C and of high-pressures up to 1765 bar were achieved with an internally heated high-pressure vessel made of a super- high-tension steel. Fluid Hg was contained in a single crystal sapphire cell. Figure 1 shows the density isochores of fluid Hg plotted in the pressure-temperature plane [1]. Figure 2 shows the pair distribution function g(r) for expanded fluid Hg under the different temperature and pressure conditions. To obtain the definite coordination number from the diffusive and broad atomic distribution in the non- crystalline state, we employed two different methods to integrate the first-neighboring atoms. In method A , 4 π r 2 ρ 0 g(r) is integrated up to the maximum position of g(r), r 1 , and doubled. Here ρ 0 denotes the average number density of Hg. In method B , 4 π r 2 ρ 0 g(r) is integrated up to the first minimum position of g(r), r min . We fixed r min as 4.5 in the entire density range because r min does not change so much except in the dense vapor region. 18 Fig. 1: Density isochores of fluid Hg plotted in the pressure- temperature plane [1]. Solid line indicates the saturated vapor- pressure curve and the cross shows the critical point. Open circles show the pressures and temperatures at which the X-ray diffraction measurements were performed [#]. The coordination numbers N A and N B obtained by methods A and B are plotted in Figure 3 as a function of density together with the nearest- neighbor distance r 1 at the bottom of the figure. N B decreases substantially and linearly with decreasing density in the wide region from liquid to dense vapor. N A also decreases almost linearly with decreasing density in the metallic region, but when the M-NM transition region is approached ( i.e., around 9-10 g/cm 3 ), the deviation from the linear dependence appears. It seems that as the density deviation starts, the M-NM transition starts to occur. In contrast to the N A case, no anomalous behavior is observed in the behavior of N B around this density region. In the dense vapor region the density variation of N A changes again. As seen in the figure, r 1 in the metallic region remains almost unchanged with decreasing density, but when the M-NM transition region is approached r 1 starts to slightly increase. Such behavior coincides with that of N A . In the dense vapor region r 1 substantially increases. The r 1 seems close to the interatomic distance of a Hg dimer in the rarefied vapor. From 19 Fig. 2: Pair distribution function g(r) for expanded fluid Hg. Temperature, pressure and density are indicated on the upper right hand side of each data plot [*]. Fig. 3: Coordination numbers N A , N B and nearest-neighbor distance r 1 of expanded fluid Hg as a function of density. Circles and triangles denote N A and N B obtained using methods A and B , respectively. Squares show variation of r 1 [*]. these results, we can conclude that the density decrease of fluid Hg is essentially caused by the reduction of the coordination number through the entire density region as seen in the behavior of N B . The variation in N A gives more detailed information about the structural change accompanied by the M- NM transition. N A represents the coordination number at the shortest distance in the first coordination shell, so the density variation of N A suggests that the change in the nearest part of the first coordination shell is strongly related to the M-NM transition. As the most important observation, the gross feature of the density variation in N A and r 1 in Figure 3 suggests that there exist three different regions in the density: the metallic region from 13.6 to about 10 g/cm 3, the M-NM transition region from 10 to the critical density of about 6 g/cm 3 and the dense vapor region. Kozaburo Tamura and Masanori Inui Hiroshima University E-mail: tamura@mls.ias.hiroshima-u.ac.jp References [1] W. Gözlaff et al., Z. Phys. Chem. NF 156 (1988) 219; W. Gözlaff, Ph.D Thesis, University of Marburg (1988). [2] F. Hensel and E. U. Frank, Ber. Bunsenges. Phys. Chem. 70 (1966) 1154. [3] K. Tamura and S. Hosokawa, Phys. Rev. B 58 (1998) 9030. [#] K. Tamura, M. Inui, I. Nakaso, Y. Oh'ishi, K. Funakoshi and W. Utsumi, J. Phys. Condens. Matter 10 (1998) 11405; [*] Jpn. J. Appl. Phys., in press. CRYSTAL STRUCTURE ANALYSIS OF THE FULLERENE COMPOUNDS BY THE MAXIMUM ENTROPY METHOD Alkali metal doped fullerenes in the form of A 2 BC 60 are fascinating substances. Many of them show superconductivity while a few others show no superconductivity. As the fundamental crystal structure, it is well known that C 60 molecules form an fcc lattice and alkali metal atoms locate at both the tetrahedral and octahedral sites [1] . There is a close relation between the lattice constant of the compounds and their superconducting transition temperature, Tc [2,3]. For example, Rb 2 CsC 60 has a relatively high Tc. On the other hand, Li 2 CsC 60 shows no superconductivity. It has been suggested that different bonding natures exist depending on their lattice constants and that they are closely related to the superconducting property [4]. Bonding nature may be divided into two regions, i.e., the interatomic region between the doped metal atoms and the carbon-carbon region on C 60 molecules. So far, there has been no definite experimental evidence on bonding nature. In this study, at the beamline BL02B1 , the fine structure of Rb 2 CsC 60 and Li 2 CsC 60 are revealed [5], including the bonding nature for alkali metal doped fullerenes by the Maximum Entropy Method (MEM), which is an advanced imaging technique using diffraction data [6]. The MEM charge densities of Rb 2 CsC 60 and Li 2 CsC 60 are shown for a (110) plane in Figures 1 (a) and (b) , respectively. At a glance, it can be easily seen that there are distinct structural differences between Rb 2CsC 60 and Li 2 CsC 60 . A non-superconducting alkali metal doped fullerene, Li 2 CsC 60 , has uniform charge densities of the C 60 molecule due to nearly free rotation of C 60 . In contrast, a superconducting alkali metal doped fullerene, Rb 2 CsC 60 , has some kinds of disorder. To visualize three-dimensional distributions of the charge on the carbon cage in Rb 2 CsC 60 , the MEM electron density distribution of C 60 and Rb atoms are shown by an equi-contour surface at 2.0 e Å -3 in Figures 2( a ). In this figure, the characteristic features of the merohedral disorder, the hexagons facing toward Rb atoms and cloverleaf features, 20
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