Compression behavior of dense ${\mathrm{H}}_2\text{−}\mathrm{He}$ mixtures up to 160 GPa

We have studied the compression behavior of ${\mathrm{H}}_2\text{−}\mathrm{He}$ mixtures in comparison with pure ${\mathrm{H}}_2$ and He using powder synchrotron x-ray diffraction, and we present the pressure-volume (PV) compression data of ${\mathrm{H}}_2\text{−}\mathrm{He}$ mixtures to 160 GPa. The results indicate that both ${\mathrm{H}}_2$ and He in ${\mathrm{H}}_2\text{−}\mathrm{He}$ mixtures remain in hcp to the maximum pressure studied, yet they develop a substantial level of lattice distortion in the (100) plane, most profound in He-rich solids and below 66 GPa. The measured PV data also indicate the softening of an He (or ${\mathrm{H}}_2$) -rich lattice upon increasing the level of the guest ${\mathrm{H}}_2$ (or He) concentration. We suggest that the observed softening and lattice distortion are due to a substitutional incorporation of ${\mathrm{H}}_2$ (guest) molecules into the basal plane of the hcp-He (host) lattice, and thereby reflect the miscibility between ${\mathrm{H}}_2$ and He in ${\mathrm{H}}_2\text{−}\mathrm{He}$ mixtures. Interestingly, solid He exhibits a lesser degree of preferred orientation in ${\mathrm{H}}_2\text{−}\mathrm{He}$ mixtures than in pure He, likely due to the presence of solid ${\mathrm{H}}_2$ disturbing the crystalline ordering of He-rich solids. Finally, the present PV compression data of ${\mathrm{H}}_2$-rich and He-rich solids to 160 GPa deviate from those of pure ${\mathrm{H}}_2$ and pure He above ∼70 and 45 GPa respectively, providing new constraints for the development of the equation of state for ${\mathrm{H}}_2\text{−}\mathrm{He}$ mixtures for planetary models.

Figure 1

Binary phase diagram of ${\mathrm{H}}_2\text{−}\mathrm{He}$, reproduced from Ref. [22]. $F_1$, $F_2$, $S_1$, and $S_2$ signify ${\mathrm{H}}_2$-rich fluid, He-rich fluid, ${\mathrm{H}}_2$-rich solid, and He-rich solid, respectively. $S_1^{\prime }$ and $S_3$ signify ${\mathrm{H}}_2$-rich solid grown in He-rich fluid above the vertical dotted line, whereas $S_3$ refers to deformed $S_2$ (or a potential new structure) above 52 GPa or the horizontal dotted line.

Figure 2

Representative high-pressure XRD patterns of hcp ${\mathrm{H}}_2$ in ${\mathrm{H}}_2\text{−}\mathrm{He}$ mixtures with three compositions: (a) 99%, (b) 90%, and (c) 50% ${\mathrm{H}}_2$ mole fractions at room temperature. The inset in (b) shows the selected XRD patterns of pure ${\mathrm{H}}_2$ under high pressures for comparison. Note that the diffraction patterns of ${\mathrm{H}}_2$ in the 50% mixture are colored in red in (c), whereas those of He are shown in gray. Bragg peaks from Re gaskets are marked with * symbols.

Figure 3

The 300 K PV isotherm of hcp ${\mathrm{H}}_2$ in ${\mathrm{H}}_2$-rich ${\mathrm{H}}_2\text{−}\mathrm{He}$ mixtures along with pure ${\mathrm{H}}_2$, plotted in terms of (a) unit cell volume and (b) relative $a$ and $c$ lattice parameters as a function of pressure. Solid lines in red, green, blue, and magenta in (a) represent the Vinet EOS fits to the present data comparing with pure ${\mathrm{H}}_2$ (other solid lines) from Refs. [6, 8, 9, 10]. Black and orange lines in (b) are drawn as guides to the eye. Error bars for the volume are within the symbol sizes. Insets in (a) and (b) show a magnified view of the 0–2 GPa region of relative volume and pressure-dependent $c/a$ ratio, respectively.

Figure 4

Selected high-pressure XRD patterns of hcp He in ${\mathrm{H}}_2\text{−}\mathrm{He}$ mixtures with three compositions of (a) 99%, (b) 90%, and (c) 50% in He mole fractions at room temperature. Insets in (a) and (b) represent high-pressure XRD patterns of pure He and the diffraction image plate of hcp He in a 1:9 mixture at 161 GPa (the highest pressure reached; also see Fig. S1 [29]), respectively. The 99% He mixture shows the most diffraction lines, including (100), (002), (101), (102), and (110), in comparison with other concentrations. Solid blue lines in (c) remark Bragg peaks from hcp He in a 1:1 mixture to distinguish other contributions (gray solid lines) such as hcp ${\mathrm{H}}_2$ and the Re gasket. The contribution from the Re gasket is marked with a * symbol.

Figure 5

The 300 K PV-isotherm of hcp He in He-rich ${\mathrm{H}}_2\text{−}\mathrm{He}$ mixtures along with pure He, plotted in terms of (a) unit-cell volume, (b) relative $a$ lattice parameter, and (c) relative $c$ lattice parameter, as a function of pressure. Solid lines in red, green, blue, and magenta in (a) represent the Vinet EOS fits to the present data compared with pure He (other solid lines) from Refs. [7, 11, 30]. The distorted lattice of hcp He in a 90% He-rich mixture is denoted by a light blue triangle symbol. Black lines in (b) and (c) are drawn as guides to the eye. Error bars for the volume are within the symbol sizes. Insets in (a) and (c) show a magnified view of the 0–2 GPa region of relative volume and pressure-dependent $c/a$ ratio, respectively.

Figure 6

The XRD patterns of the distorted lattice (denoted by solid red lines) of hcp He in 90% He-rich mixture compared with those of other sample areas without lattice distortion (solid black lines) at (a) 32 GPa and (b) 53 GPa, respectively. The corresponding diffraction images are also shown on the right to compare the distorted [red box, labeled as (2) and (4)] and undistorted [black box, labeled as (1) and (3)] diffraction images.

Figure 7

${\mathrm{H}}_2$ molar volumes of noble-gas solid hydrides, $\mathrm{Xe}{\left({\mathrm{H}}_2\right)}_8$, $\mathrm{Ar}{\left({\mathrm{H}}_2\right)}_4$, and $\mathrm{Kr}{\left({\mathrm{H}}_2\right)}_2$, plotted as a function of the interstitial volumes, illustrating an interstitial filled mixing of ${\mathrm{H}}_2$ in Xe, Ar, and Kr, and maybe Ne—not in He. The specific volume of solid ${\mathrm{H}}_2$ is larger than that of the largest octahedral interstitial site of hypothetical fcc He at 12 GPa. It is likely that the mixing of ${\mathrm{H}}_2\text{−}\mathrm{He}$ occurs via a substitutional ${\mathrm{H}}_2$ inclusion into the basal plane of hcp-He.