Formation and Stability of Dense Methane-Hydrogen Compounds

Through a series of x-ray diffraction, optical spectroscopy diamond anvil cell experiments, combined with density functional theory calculations, we explore the dense ${\mathrm{CH}}_4\text{−}{\mathrm{H}}_2$ system. We find that pressures as low as 4.8 GPa can stabilize ${\mathrm{CH}}_4({\mathrm{H}}_2{)}_2$ and $({\mathrm{CH}}_4{)}_2{\mathrm{H}}_2$, with the latter exhibiting extreme hardening of the intramolecular vibrational mode of ${\mathrm{H}}_2$ units within the structure. On further compression, a unique structural composition, $({\mathrm{CH}}_4{)}_3({\mathrm{H}}_2{)}_{25}$, emerges. This novel structure holds a vast amount of molecular hydrogen and represents the first compound to surpass 50 wt % ${\mathrm{H}}_2$. These compounds, stabilized by nuclear quantum effects, persist over a broad pressure regime, exceeding 160 GPa.

Figure 1

Pressure-composition phase diagram of the ${\mathrm{CH}}_4\text{−}{\mathrm{H}}_2$ binary system. Filled square symbols indicate the formation pressures of each compound: $({\mathrm{CH}}_4{)}_2{\mathrm{H}}_2$ (orange), ${\mathrm{CH}}_4({\mathrm{H}}_2{)}_2$ (purple), and $({\mathrm{CH}}_4{)}_3({\mathrm{H}}_2{)}_{25}$ (green). The green open squares represent the pressures at which $({\mathrm{CH}}_4{)}_3({\mathrm{H}}_2{)}_{25}$ is first observed. The black squares, black triangle, and blue circle represent the formation pressure of ${\mathrm{CH}}_4\text{-I}$, ${\mathrm{CH}}_4\text{-A}$, and ${\mathrm{H}}_2\text{-I}$, respectively. The gray line represents the liquidus curve and is adapted from Ref. [21]. Below 7 GPa, the error in pressure is $\pm 0.2\mathrm{GPa}$ and smaller than the size of the symbol. Initial gas mixtures have a tolerance of 1%.

Figure 2

(a) Representative x-ray diffraction patterns of the three compounds plotted as a function of exchanged wave vector and their Le Bail refinements. Refinements include $({\mathrm{CH}}_4{)}_3({\mathrm{H}}_2{)}_{25}\text{−}R\overline{3}m$ ($a=7.804\AA$ and $c=11.199\AA$), $({\mathrm{CH}}_4{)}_2{\mathrm{H}}_2\text{−}I4/mcm$ ($a=7.195\AA$ and $c=5.909\AA$), ${\mathrm{CH}}_4\text{−}A\text{−}R3$ ($a=12.306\AA$ and $c=15.520\AA$), ${\mathrm{CH}}_4({\mathrm{H}}_2{)}_2\text{−}P{6}_3/mmc$ ($a=4.981\AA$ and $c=8.125\AA$), and $\mathrm{Au}\text{−}Fm\overline{3}m$ ($a=3.976\AA$). Excluded regions in the pattern of $({\mathrm{CH}}_4{)}_3({\mathrm{H}}_2{)}_{25}$ correspond to rhenium (gasket material) and rhenium hydride (*) and excess ${\mathrm{H}}_2$ (#). (b) Volumes per formula unit as a function of pressure. Symbols represent experimental data (the error bars are smaller than the symbol size), and black full lines represent their best second-order Birch-Murnaghan fits: ${\mathrm{CH}}_4({\mathrm{H}}_2{)}_{8.33}$, $V_0=246\pm 17{\AA }^3$ and $K=3.0\pm 0.6\mathrm{GPa}$; $({\mathrm{CH}}_4{)}_2{\mathrm{H}}_2$, $V_0=101\pm 2{\AA }^3$ and $K=10.2\pm 0.8\mathrm{GPa}$; ${\mathrm{CH}}_4({\mathrm{H}}_2{)}_2$, $V_0=90\pm 3$ ų and $K=5.0\pm 0.4\mathrm{GPa}$. Dashed lines represent volumes derived from our DFT calculations, and gray dotted lines represent the volumes of ideal mixtures of ${\mathrm{CH}}_4\text{−}A/{\mathrm{CH}}_4\text{−}B$ and ${\mathrm{H}}_2\text{−}I$ using the previously determined equations of state [14, 17, 69]. The experimental volumes given in Ref. [21] are represented by gray circles. (c) Structural models of the three compounds, where ${\mathrm{CH}}_4$ and ${\mathrm{H}}_2$ are represented by brown and white spheres, respectively, and lines indicate ${\mathrm{CH}}_4\text{−}{\mathrm{H}}_2$ nearest neighbors.

Figure 3

Representative vibrational Raman spectra of (a) 70% ${\mathrm{H}}_2$, (b) 50% ${\mathrm{H}}_2$, and (c) 30% ${\mathrm{H}}_2$ mixtures. Colors indicate the modes assigned to ${\mathrm{CH}}_4({\mathrm{H}}_2{)}_2$ (purple), $({\mathrm{CH}}_4{)}_3({\mathrm{H}}_2{)}_{25}$ (green), $({\mathrm{CH}}_4{)}_2{\mathrm{H}}_2$ (orange), and excess ${\mathrm{H}}_2$ (black).

Figure 4

Raman shift as a function of pressure of the ${\mathrm{H}}_2$ vibrational modes and C-H stretching modes of ${\mathrm{CH}}_4({\mathrm{H}}_2{)}_2$ and $({\mathrm{CH}}_4{)}_3({\mathrm{H}}_2{)}_{25}$ (left panel, purple and green symbols, respectively), and $({\mathrm{CH}}_4{)}_2{\mathrm{H}}_2$ (right panel, orange symbols). Frequencies are collated from 30% (squares), 50% (circles), 70% (triangles), 80% (diamonds), and 90% (hexagons) ${\mathrm{H}}_2$ mixtures, with the most intense modes represented by larger symbols. Raman frequencies of individual mixtures are given in Supplemental Material [45]. The dot-dashed lines represent the calculated frequencies of the ${\mathrm{H}}_2$ modes and C-H stretching bands of each compound, with the thickest line representing the most intense modes. Black and gray solid lines represent pure ${\mathrm{H}}_2$ [6] and ${\mathrm{CH}}_4$ [15], respectively. The black dotted line represents the frequency of ${\mathrm{H}}_2$ in a Ne matrix [70]. The error in pressure ranges from $\pm 0.2$ GPa below 50 GPa, $\pm 1$ GPa below 150 GPa, and $\pm 5$ GPa above. The error bars in frequency are smaller than the symbol size. Photomicrographs show examples of morphology of synthesised samples within the DAC sample chamber.