Noble-Gas Solubility in Solid and Fluid Metallic Hydrogen

Abstract

Metallic hydrogen dominates the deep interiors of giant planets, where trace elements interact with dense quantum matter under extreme pressure. We investigate the thermodynamic stability of noble-gas impurities (He, Ne, Ar, Kr, Xe) in metallic hydrogen at 500 GPa using ab initio molecular dynamics combined with first-principles free-energy calculations. In the solid metallic phase, all noble gases exhibit positive formation free energies, driven by unfavorable electronic enthalpy and zero-point vibrational contributions. By contrast, heavier noble gases (Ar, Kr, Xe) appear soluble in liquid hydrogen, while He and Ne phase separate. This crossover reflects a competition between electronic repulsion and disorder-driven stabilization intrinsic to the liquid phase. Our results reveal noble-gas retention in metallic hydrogen, providing a microscopic mechanism for noble-gas fractionation in giant-planet interiors.

Figures (4)

• Figure 1: (a) Substitutional structure of a noble-gas impurity in solid metallic hydrogen. (b–f) Time evolution of the mean-square displacement (MSD) averaged over all atoms in alloyed solid metallic hydrogen for He, Ne, Ar, Kr, and Xe systems with different numbers of removed hydrogen atoms. For the configurations exhibiting the most stable MSD behavior—HeH$_{199}$, NeH$_{196}$, ArH$_{192}$, KrH$_{192}$, and XeH$_{192}$—the ab initio molecular dynamics simulations were extended to 10.0 ps to ensure convergence of the enthalpy.
• Figure 2: Optimized atomic configurations obtained from the final step of ab initio molecular dynamics simulations at 500 GPa for (a) pristine metallic hydrogen (H$_{200}$) and noble-gas–substituted systems: (b) HeH$_{199}$, (c) NeH$_{196}$, (d) ArH$_{192}$, (e) KrH$_{192}$, and (f) XeH$_{192}$. Hydrogen atoms are shown in pink, while noble-gas impurities are highlighted in distinct colors.
• Figure 3: (a) Radial distribution functions (RDFs) of hydrogen in solid metallic $X\mathrm{H}_{Y}$ systems ($X = \mathrm{He}, \mathrm{Ne}, \mathrm{Ar}, \mathrm{Kr}, \mathrm{Xe}$). (b) Corresponding cumulative distribution functions (CDFs) describing the radial cumulative number of hydrogen atoms surrounding the noble-gas impurities. (c) RDFs of hydrogen around the impurity atoms $g_{X-H}(r)$. (d) Corresponding cumulative radial coordination numbers $N_{X-H}(r)$. (e) Crystal orbital Hamilton population (COHP) analysis for impurity--hydrogen interactions. (f) Phonon density of states (PhDOS) for pristine $I4_{1}/amd$ hydrogen and noble-gas-substituted systems.
• Figure 4: Mean-square displacement (MSD) and structural correlations in noble-gas–alloyed liquid metallic hydrogen at 500 GPa and 600 K within the $NPT$ ensemble. (a) Time evolution of the hydrogen MSD, $\mathrm{MSD}_H$, for HeH$_{192}$, NeH$_{192}$, ArH$_{192}$, KrH$_{192}$, and XeH$_{192}$. (b) Time evolution of the noble-gas impurity MSD, $\mathrm{MSD}_X$. (c) Radial distribution functions of hydrogen–hydrogen pairs, $g_{H-H}(r)$. (d) Corresponding cumulative coordination numbers $N_{H-H}(r)$. (e) Radial distribution functions of impurity–hydrogen pairs, $g_{X-H}(r)$. (f) Corresponding cumulative coordination numbers $N_{X-H}(r)$.