Multishock compression of dense cryogenic hydrogen-helium mixtures up to 60 GPa: Validating the equation of state calculated from first principles

Zhi-Guo Li, Qi-Feng Chen, Yun-Jun Gu, Jun Zheng, Wei Zhang, Lei Liu, Guo-Jun Li, Zhao-Qi Wang, and Jia-Yu Dai

Phys. Rev. B 98, 064101 – Published 9 August 2018

Abstract

Multishock compression experiments on hydrogen-helium ( $H_{2}$ -He) mixtures have been performed via a two-stage light-gas gun for providing equations of state (EOS) covering a wide pressure range. The initial gaseous $H_{2}$ -He sample was precompressed to 20–30 MPa and cooled down to around 90 K to gain high initial sample density. Up to three shock compressions were clearly observed from the time-resolved light radiance of the shocked sample recorded by a multichannel optical pyrometer. The measured EOS data of the $H_{2}$ -He mixture reached an unexplored range of pressure up to 60 GPa, which is well in the molecular-to-atomic transition regime. The wide-range experimental data are used to validate the state-of-the-art first-principles simulation methods. It is found that the density functional theory molecular dynamics (DFT-MD) simulations underestimate the dissociation of hydrogen and therefore predict the $H_{2}$ -He EOS to be stiffer than the experimental data in the molecular-to-atomic transition regime. A careful analysis of the pair correlation functions and comparison with the results of pure hydrogen revealed that DFT-MD might overestimate the effects of helium on the bond of the hydrogen molecule when hydrogen is mixed with helium. Finally, the current measurements validate a linear-mixing ab initio EOS [Astrophys. J. Suppl. S. 215, 21 (2014)] widely used in astrophysics.

Received 29 March 2018
Revised 14 June 2018

DOI:https://doi.org/10.1103/PhysRevB.98.064101

Physics Subject Headings (PhySH)

Chemical bonding Equations of state Structural properties

Warm-dense matter

First-principles calculations Pressure techniques

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Zhi-Guo Li¹, Qi-Feng Chen^1,*, Yun-Jun Gu^1,†, Jun Zheng¹, Wei Zhang², Lei Liu^1,3, Guo-Jun Li^1,3, Zhao-Qi Wang^1,3, and Jia-Yu Dai^4,‡

¹National Key Laboratory for Shock Wave and Detonation Physics, Institute of Fluid Physics, P. O. Box 919-102, Mianyang, China
²School of Science, Southwest University of Science and Technology, Mianyang 621010, China
³Institute of Atomic and Molecular Physics, Sichuan University, Chengdu 610064, China
⁴Department of Physics, National University of Defense Technology, Changsha 410073, China

^*chenqf01@gmail.com
^†guyunjun01@163.com
^‡jydai@nudt.edu.cn

Article Text (Subscription Required)

Click to Expand

Supplemental Material (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 98, Iss. 6 — 1 August 2018

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
Schematic diagram of the cryogenic target. The sample is sealed in a cell made up of a steel baseplate, sapphire window, and steel support. A cooling system with a working medium of liquid nitrogen surround the steel sample cell to decrease the initial temperature of the sample, which is measured through a thermocouple thermometer. A fiber bundle, protected by a heat insulation tube from low temperatures, is used to record the self-emission of the shocked sample.
Reuse & Permissions
Figure 2
Upper panel: The measured time-resolved self-emission of the shocked sample by MCOP at a wavelength of 600 nm, which provides clearly the time that the shock wave breaks into sample ( $t_{0}$ ) and shock reverberation times at sample/sapphire interface ( $t_{1}$ , $t_{3}$ ) and baseplate/sample interface ( $t_{2}$ ). Lower panel: Position-time diagram by 1D hydrodynamic simulations indicating the trajectories of the shock wave front (solid black lines labeled by $U_{s, 1}$ , $U_{s, 2}$ , $U_{s, 3}$ , ...) and interfaces (solid gray lines) of baseplate/sample and sample/sapphire.
Reuse & Permissions
Figure 3
Impedance matching solution to determine the multiple shock pressures and particle velocities for shot 051209. The open circle symbols indicate the multiple shock states of the current dense cryogenic $H_{2}$ -He mixture. The blue dash-dot-dot lines represent the first, second, and third shock compression curves of the $H_{2} − He$ mixture, respectively. The insert shows the situation above 100 GPa.
Reuse & Permissions
Figure 4
The first to third shock experimental $P − ρ$ data for shots 051209 and 050914. Open circles represent our experimental data for the dense cryogenic $H_{2}$ -He mixture. Dashed, dash-dot, dash-dot-dot, and dotted lines are DFT-MD results using PBE, vdW-DF1, DFT-D2, and rVV10 functionals, respectively. The solid circle represents the result by PBE with elevated electronic temperature $T_{e}$ . The PIMD results are displayed as a times sign ( $\times$ ) symbol. Chemical models of REOS.3, SCVH, and SFVT are displayed as solid, short-dotted, and short-dashed lines, respectively. The SFVT model without the consideration of dissociation is shown by a plus sign (+) symbol. Also shown are the experimental data by Gu et al. [23] for gaseous $H_{2}$ -He mixture with a mole component of $H_{2} : He = 1 : 1.2$ (open squares), and the orange-colored numbers in circles correspond to the shock index in their experiments.
Reuse & Permissions
Figure 5
Pair correlation functions of H-H in the $H_{2}$ -He mixture at 0.5 $g / {cm}^{3}$ and 6000 K using the trajectories of PBE, vdW-DF1, rVV10, DFT-D2, and PIMD simulations. The black short-dotted line represents the result by PBE with elevated electronic temperature $T_{e}$ . The magenta short-dashed line is derived from data of pure hydrogen.
Reuse & Permissions

Physical Review B

covering condensed matter and materials physics