Structural and vibrational properties of methane up to 71 GPa

Single-crystal synchrotron x-ray diffraction, Raman spectroscopy, and first principles calculations have been used to identify the structure of the high-pressure (HP) phase of molecular methane above 20 GPa up to 71 GPa at room temperature. The structure of the HP phase is trigonal $R3$, which can be represented as a distortion of the cubic phase B, previously documented at 7–15 GPa and confirmed here. The positions of hydrogen atoms in the HP phase have been obtained from first principles calculations, which also demonstrated the stability of this structure above 260 K at 25 GPa. The molecules occupy four different crystallographic sites in phase B and 11 sites in the HP phase, which result in splitting of molecular stretching modes detected in Raman spectroscopy and assigned here based on a good agreement with the Raman spectra calculated from the first principles. Our study points out to a single HP phase unlike up to three HP phases proposed previously based on the Raman spectroscopy results only.

Figure 1

Reconstructed reciprocal lattice plane of methane visualized by crysalispro software package [24] at 7.07 GPa (left), 35.6 GPa (middle), and 63.2 GPa (right). D stands for diamond reflections. The observed diffraction spots from the sample have been indexed and used to determine the structure of phases B (left panel) and high-pressure (HP) phase (middle and right panels) (Table S1 and Tables 1 and 2, respectively).

Figure 2

Raman spectra of the C-H stretching modes of methane in HP phase at various pressures. The dots are the data and the lines are the fits to the Voigt oscillator model with eight (nine for the 36-GPa spectrum) peaks; variable color lines show the individual ${\nu }_1$ (dashed) and ${\nu }_3$ (solid) components. Note a change in the frequency scale in different panels due to a pressure shift.

Figure 3

(a) Theoretically calculated relative enthalpy of the most stable methane phases. The results for HP phase ($R3$-II) are shown by a thick red line. Other orientationally ordered phases are shown by thin lines of various colors. The vertical dashed line correspond to the pressure at which the temperature effects were taken into account. (b) Relative Gibbs free energies of the most stable methane phases as a function of temperature at 25 GPa. The symbols at $T=0\mathrm{K}$ represent relative classical enthalpies as computed with norm-conserving pseudopotentials.

Figure 4

Crystal structure of $\mathrm{HP}\text{−}{\mathrm{CH}}_4$ at 35 GPa. Black, red, green, and blue balls represent the positions of C1, C2, C3, and C4 carbon atoms, respectively; small pinkish circles are hydrogen atoms. Left panel shows C atoms only; gray lines connect the nearest C atoms with a cutoff of 3.08 Å.

Figure 5

Raman spectra of ${\nu }_1$ (left panels) and ${\nu }_3$ (right panels) stretching modes. The top panels are the spectrum measured at 25 GPa (488 nm excitation). Crosses are the data and gray line is the best fit to the Voigt oscillator model; variable color lines show the individual ${\nu }_1$ and ${\nu }_3$ components. The bottom panel shows the theoretically computed spectra at the same pressure. The labels (carbon atom sites) show the assignment of the peaks to the molecules of different kind. The experimental and theoretical peaks in the top and the bottom panels only slightly mismatch demonstrating a good correspondence of experiment and theory.

Figure 6

Lattice parameters (a) and volumes per formula unit (b) of methane as a function of pressure. Note two vertical scales in the panel (a) for phases B (blue) and HP (red) which are scaled by a factor of $\sqrt{3}/2$ reflecting the difference in the unit cell dimensions. Also, the parameter $a$ of the HP phase is divided by a factor of $1.633$. Our experimental and theoretical volumes (b) are compared to previous experiments in phases I, A, B, pre-B, and HP [12, 13, 15, 19, 20]. The unit cell volume of pre-B methane of Ref. [20] was assumed to contain 21 formula units. The lines are guides to the eye.

Figure 7

Raman frequencies of the C-H stretching modes of methane as a function of pressure. Vertical dashed lines mark the phase transitions following Ref. [16]. The symbols are the results of two experiments of this work (solid line is the guide to the eye), while dashed and dotted lines represent the results of previously published works [16, 17]. The data between 36 and 63 GPa could not be taken because the experiment to 63 GPa was performed at the x-ray synchrotron beamline, so the Raman spectra could be only measured at the last pressure point.