Two-phase coexistence for hydrogen-helium mixtures

We use our quantum Gibbs ensemble Monte Carlo algorithm to perform computer experiments for the two-phase coexistence of a hydrogen-helium mixture. Our results are in quantitative agreement with the experimental results of Sneed, Streett, Sonntag, and Van Wylen. The difference between our results and the experimental ones is in all cases less than 15% relative to the experiment, reducing to less than 5% in the low helium concentration phase. At the gravitational inversion between the vapor and the liquid phase, at low temperatures and high pressures, the quantum effects become relevant. At extremely low temperature and pressure, the first component to show superfluidity is the helium in the vapor phase.

Figure 1

Schematic pressure-composition phase diagram for six isotherms of the hydrogen-helium mixture at low temperatures and low pressures as obtained in the experimental work by Streett et al. [4]. The thick continuous black line is the mixture critical line.

Figure 2

Reproduction of Fig. 3 of Sneed et al. [3] for the $x$ line and the $g$ line [see Eq. (11)]. The inset shows the two lines in the temperature-composition plane.

Figure 3

Comparison between the results of our numerical experiments (points from Table 2) and of the laboratory experiments (lines from Table 1 in the Supplemental Material [21]) for the pressure-composition of three isotherms of the hydrogen-helium mixture phase diagram. A logarithmic scale is conveniently used on the ordinates. The double circled points at $T=15.5\text{K}$ denote the case in which we observed gravity inversion in the numerical experiment.

Figure 4

Fit of the histogram for the block averages of both $x_{\text{He}}^{\left(\text{I}\right)}$ and $x_{\text{He}}^{\left(\text{II}\right)}$ with the sum of two Gaussians with six parameters. This is the case $T=26\text{K},\rho =0.01{\text{Å}}^{-3}$, and $\chi =90/38$, where we had box identity exchanges.