66 Physical Science Research Frontiers 2020 High-pressure X-ray diffraction studies of the supercritical fluid of hydrogen Hydrogen has high potential as a next-generation clean energy source. One of the challenges facing the realization of a hydrogen society is the establishment of safe and efficient hydrogen transportation and storage technology. For this purpose, it is important to have information on the basic physical properties of high-pressure hydrogen (H 2 ) gas, such as its aggregation state and density. Normal hydrogen (n-H 2 ) has a critical point at 32.97 K and 1.293 MPa and solidifies under a high pressure of 5.4 GPa at room temperature. Up to now, Mills et al . [1] have proposed an equation of state up to 2 GPa through volume compression and ultrasonic velocity measurements using a piston cylinder device. Pratesi et al . [2] have proposed a pressure dependence of density up to 5.4 GPa at room temperature on the basis of Brillouin scattering experiments. In this study, synchrotron radiation X-ray diffraction experiments were performed to collect halo patterns within a wide pressure range (0.1 to 5 GPa) to obtain information on the density and structure of the supercritical fluid phase [3]. A diamond anvil cell (DAC) was used to generate high pressure. The sample was n-H 2 and high-pressure H 2 gas of 180 MPa (or 50 MPa) was loaded into the DAC using a high-pressure gas filling apparatus. High-pressure X-ray diffraction experiments were performed at room temperature at SPring-8 BL10XU . The incident X-ray energy was 30 keV and an image plate was used as a two-dimensional detector. In these one-dimensional data, the halo pattern from the fluid H 2 was overlaid by the relatively strong Compton scattered X-ray background from the diamond anvil. To subtract this background numerically, the background pattern of an empty cell containing no sample was measured. During this X-ray diffraction experiment, we succeeded in observing the halo pattern of the hydrogen supercritical fluid phase within a wide pressure range from 0.12 to 5.1 GPa. Figure 1 shows the pressure change of a typical diffraction pattern. The first halo was observable, but the second was undetectable. A spectral analysis was performed to estimate the 2 q value and FWHM of the first halo peak. The d H value was calculated from the 2 q value. The d H value and FWHM decreased as the pressure increased (Fig. 2). The FWHM corresponds to a measure of the correlation of intermolecular distance in fluid. We considered d H to be the average nearest- neighbor intermolecular distance and assumed a packing of a hard sphere with diameter d H . Herein, the molar volume was estimated using the equation of state proposed on the basis of the ultrasonic measurement by Mills et al . [1] That is, assuming that the cube of the d H value at 2 GPa is proportional to the molar volume reported by Mills et al ., i.e., 11.593 cm 3 /mol. At this pressure, the proportional constant A of the following formula was determined to estimate the molar volume V m . V m ( P ) = A • N A • [ d H ( P )] 3 Here, N A is Avogadro’s number and A is 1.37, which corresponds to the reciprocal of the packing factor. If A was 1.0, it would correspond to the hexagonal coordinate of a simple cubic lattice. In our previous study on supercritical fluid phases of O 2 and N 2 , A was 1.47, indicating that the filling rate of H 2 is higher than those of O 2 and N 2 . Figure 3 shows the pressure dependence of the molar volume together with the results of previous studies. Fig. 1. Pressure evolution of the X-ray diffraction patterns for fluid H 2 . 4 8 12 16 2 (deg) 1.16 5.01 2.94 Fluid H 2 0.27 0.45 0.13 (GPa) Intensity (arb. units) θ θ 67 Research Frontiers 2020 The pressure dependence in this study was in good agreement with the data of Mills et al . up to 2 GPa and the data of Pratesi et al . above 1 GPa. Therefore, the validity of the hard sphere model assumed in this study was demonstrated. That is, it was considered that the d H value corresponded to the average intermolecular distance and that the average coordination number (packing factor: A ) of the molecules was constant and did not change in the pressure range of 0.1 to 5 GPa. There was a change in compressibility at around 1 GPa, i.e., the dependence followed the relational expression of P ~ V m –3.11 above 1 GPa. Fluid O 2 and N 2 , which are the same homonuclear diatomic molecules as H 2 , followed the relational expression of P ~ V m –4.32 at a pressure higher than 0.2 GPa. The repulsive term of the Lennard–Jones potential, which is applied to molecular solids, became dominant for fluid O 2 and N 2 . Therefore, it was found that fluid H 2 behaves differently from fluid O 2 and N 2 and is more easily compressed. The reason why H 2 and He are easily compressed is that the wave function of the 2 s electrons occupying the outer orbital of O 2 , N 2 , and Ne molecules is required to be orthogonal to the wave function of the 1 s electron, but the 1 s electron cloud surrounding H 2 and He molecules does not have this orthogonality constraint. However, in the pressure region lower than ~1 GPa, the pressure dependence of H 2 deviates from the relationship of P ~ V –3.11 . It seems that the repulsive term of the intermolecular potential becomes dominant in the pressure region higher than ~1 GPa. That is, the compressibility of the supercritical phase of hydrogen changes from gas-like to liquid- or solid- like at around 1 GPa. Fig. 2. Pressure dependence of the d H value and FWHM of the first halo peak. Fig. 3. Pressure dependence of V m for the supercritical fluid of H 2 together with previous data (a) and for supercritical fluids (solid line) and solids (broken line) of H 2 , He, Ne, N 2 , and O 2 (b). Yuichi Akahama Graduate School of Material Science, University of Hyogo Email: akahama@sci.u-hyogo.ac.jp References [1] R.L. Mills et al. : J. Chem. Phys. 66 (1977) 3076. [2] G. Pratesi et al. : J. Phys.: Condens. Matter 9 (1997) 10059. [3] Y. Akahama, R. Miyamoto, S. Nakano, S. Kawaguchi, N. Hirao and Y. Ohishi: J. Appl. Phys. 128 (2020) 135901. FWHM (deg) 0 1 2 3 4 5 2 3 4 0 2 4 6 Pressure (GPa) d H -Value (Å) 0.1 0.5 1 5 7 8 9 10 20 30 40 50 Pressure (GPa) V m (cm 3 /mol) V m (cm 3 /mol) 10 –2 10 –1 10 0 10 1 10 1 10 2 Pressure (GPa) Hydrogen RT (a) : Int. Critical Table : present V m ~ P – 0.321 ( P ~ V m –3.11 ) : Pratesi et al. : Mills et al. : N 2 : O 2 Supercritical Fluid solid P ∞ V –3.11 P ∞ V – 4.32 P ∞ V –1 : H 2 : He : Ne (b) ideal gas RT
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