Dense Hydrocarbon Structures at Megabar Pressures - American ...

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Dense Hydrocarbon Structures at Megabar Pressures Hanyu Liu,† Ivan I. Naumov,† and Russell J. Hemley*,‡,§ †

Geophysical Laboratory, Carnegie Institution of Washington, Washington, D.C. 20015, United States Department of Civil and Environmental Engineering, The George Washington University, Washington, D.C. 20052 United States § Lawrence Livermore National Laboratory, Livermore, California 94550 United States ‡

ABSTRACT: The structure, bonding, and other properties of phases in the carbon− hydrogen system over a range of conditions are of considerable importance to a broad range of scientific problems. However, the phase diagram of the C−H system at high pressures and temperatures is still not known. To search for new low-energy hydrocarbon structures, we carried out systematic structure prediction calculations for the C−H system from 100 to 300 GPa. We confirmed several previously predicted structures but found additional compositions that adopt more stable structures. In particular, a C2H4 structure is found that has an indirect band gap, and phonon calculations confirm that it is dynamically stable over a broad pressure range. We also identify more carbon-rich structures that are energetically favorable. The results are important for understanding carbon−hydrogen interactions in high-pressure experiments, dense astrophysical environments and the deep carbon cycle in planetary interiors.

ydrogen and carbon rank first and fourth as the most abundant elements in the cosmos. The diversity of chemical bonding in the carbon−hydrogen (C−H) system at or near ambient conditions forms the basis of organic chemistry, is a key component of biochemistry, and gives rise to compounds that are the predominant fuels in current energy systems.1 Despite its importance, the behavior of the C−H system under extreme conditions, including the pressures and temperatures found naturally within large carbon-rich extrasolar planets,2 is poorly understood. The conventional view for decades has been that all hydrocarbons break down to form hydrogen and diamond at pressures in the 10 GPa pressure range.3 Studies at more extreme conditions, such as megabar (>100 GPa) pressures found in planetary and astrophysical environments to date, have focused on the behavior of the endmembers, that is, hydrogen and carbon. These studies have indicated the existence of transitions to novel metallic forms of these elements.4,5 A major unexplored area is the behavior of intermediate compositions at these pressures and the possibility that dense phases in the C−H system exist and also exhibit novel properties. The behavior of this system under extreme conditions is also of both fundamental and practical interest in view of the evidence for penetration of hydrogen into diamond in high-pressure diamond anvil cell experiments on hydrogen and hydrogen-containing samples.4 A starting point is the C−H stoichiometry of methane (CH4), the simplest alkane and the main component of natural gas. Not only is the material an important energy source but it is also critical to understanding planetary interiors at extreme conditions. Solid methane exhibits a variety of phase transitions at high pressures.6−10 CH4 adopts a partially orientationally ordered cubic Fm3c structure (phase II)11 at low temperature and pressure. At 0.02 GPa, it transforms to an orientationally ordered orthorhombic Cmca phase (phase III).6 At higher

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pressure, CH4 then transforms to phases identified as IV, V, and VI,8,9 but the structures of these phases have not been unambiguously determined. On the other hand, high P−T shock compression studies indicate that methane dissociates to form hydrogen and diamond near 20 GPa and 2000 K.12 Static high P−T experiments carried out with laser-heated diamond anvil cells have provided some indications of phase behavior, though the results have not been definitive. Early experiments confirmed that methane is indeed unstable at high pressures and temperatures and forms diamond between 10 and 50 GPa at temperatures of 2000−3000 K, but other reaction products were not identified.13 Subsequent laser heating of methane at pressures below 100 GPa result in the formation of different hydrocarbon species.14 A later study showed evidence that both methane and ethane decomposed to form hydrogen and diamond.15 On the other hand, methane is reported to persist as a molecular solid upon compression at room temperature up to 200 GPa,16 and a static compression study provided constraints on the methane curve up to 80 GPa and 2000 K.17 An optical study up to 288 GPa reported changes in refractive index that were identified as a transformation to a new semiconducting phase.18 Thus, the existence of denser hydrocarbon structures, as well as distinguishing between stable and metastable species, has remained unresolved experimentally. Ab initio molecular dynamics calculations indicate that the interaction of methane with a transition metal facilitates the formation of these hydrocarbons in a range of temperatures Received: September 2, 2016 Accepted: October 5, 2016 Published: October 5, 2016 4218

DOI: 10.1021/acs.jpclett.6b02001 J. Phys. Chem. Lett. 2016, 7, 4218−4222

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The Journal of Physical Chemistry Letters where otherwise pure methane would be metastable.19 The local geometry and optical properties of hydrogen defects in diamond were explored using ab initio cluster and supercell methods.20 Crystal structure calculations employing an evolutionary algorithm approach predicted that CH4 is unstable at these pressures and dissociates into ethane and hydrogen (C2H6 + H2) at 95 GPa and butane and hydrogen (C4H10 + H2) at 158 GPa.21 In the present study, we extend these calculations using unbiased structure prediction methods to explore the structures of C−H phases at high pressures. We find that at 100 GPa, CH4 and C2H6 are stable phases, whereas a solid form of C2H4 is a metastable phase. With increasing pressure, C2H4 becomes the most stable phase above 200 GPa. At 300 GPa, no other thermodynamically stable phases are found. However, structures with compositions C4H4, C2H6, and C8H2 are found to be metastable but dynamically stable phases. On the basis of harmonic lattice dynamics, C2H4 is found to be the most stable phase up to 1000 K. The results are discussed in detail below. At 100 GPa, the C2H6 is found to be the most stable composition (Figure 1a). This qualitatively agrees with previous structure predictions.21 At this pressure, CH4 still retains a molecular structure. In addition, we have found C2H4 to become stable at 100 GPa (Figure 1a). For C2H6, we identify a lower-enthalpy phase with space group P21/c (Figure 2b) that is lower than the previously predicted P-1 structure.21 This C2H6 structure is the most stable one at 100 GPa. We find that C2H6 becomes less stable with increasing pressure. At 200 GPa, CH4 is a metastable phase (Figure 1b) and has a molecular form. Interestingly, at 300 GPa, only C2H4 is stable and both CH4 and C2H6 are unstable (Figure 1c). Here, the C2H4 phase adopts Cmcm symmetry with eight H atoms and four C atoms per unit cell (Figure 2a), which is in agreement with the previous theoretical prediction.21 In this structure, the C atoms form a zigzag chain along the c direction and each C atom bonds with two H atoms. This structure can thus be viewed as consisting of chains running in two dimensions. At 100 GPa, our calculations predict a C−C bond length of 1.38 Å and C− H bond length of 1.01 Å. At the same pressure, it is found that the C−H bond length in the Cmcm phase of CH4 is 1.01 Å. The zero-point energy (ZPE) plays an important role in determining the stability of hydrogen-rich materials. At 300 GPa, the ZPE of C2H4 is quite large at 2.08 eV/formula unit. Given this finding, we calculated the vibrational energy at finite temperatures using the harmonic approximation to explore the stabilities of C−H structures. We found that the vibrational energy does not modify the stability of C2H4 even up to 1000 K at 300 GPa. We also calculated the density of states and band structure of the C2H4 phase at 300 GPa (Figure 3a). The valence band maximum and the conduction band minimum are located at S and Γ points, respectively. Correcting for the deficiencies in DFT discussed below, this structure has a predicted indirect band gap of 3.7 eV at 300 GPa. We also examined the band gap of C2H4, employing this hybrid functional, which gives a result of 4.85 eV. The results indicate that C2H4 is a large-band-gap insulator even at 300 GPa. It is not unreasonable that C and H form strong covalent bonds and that electrons in this structure are localized. We also investigated the vibrational dynamics of C2H4 (Figure 3b). The phonon calculations predicted no imaginary frequencies, indicating dynamical stability of the predicted C2H4 structure over the range of pressures studied here. We note that the

Figure 1. Formation enthalpy of predicted structures in the C−H system at (a) 100, (b) 200, and (c) 300 GPa. The enthalpies are calculated relative to the ground states of H and C at each pressure (in the case of C, such a state is simply diamond).

phonon frequencies at around 110 THz are associated with the C−H stretching vibration. Previously reported calculations found that C2H6 and C4H10 are stable at 95−158 and 158−287 GPa, respectively.21 However, we did not find C4H10 to be stable at any of the pressures considered in our calculations. Including the ZPE, the formation enthalpy at 300 GPa becomes positive (3 meV/ atom). The result is qualitatively consistent with the previous prediction of the dissociation of CH4.21 Considering more carbon-rich compositions, we found several interesting lowenthalpy structures with C4H4, C6H2, and C8H2 stoichiometries (Figure 4). In each of these, the C−H and C−C bond lengths are 1.01 and 1.37−1.42 Å, respectively. The atom contacts in these structures suggest the possibility of C−H···C hydrogen bonding. On the other hand, the calculated C−H bond lengths (1.01 Å) are not unreasonable for such a dense structure; therefore, the calculations imply that the “nonbonded” H···C interactions is largely repulsive. It will be of considerable interest to search for such structures experimentally as well as consider them in natural environments, as discussed below. 4219


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Figure 2. Lowest-enthalpy predicted structures of (a) Cmcm-C2H4 (ethylene composition) and (b) P21/c-C2H6 (ethane composition). The lattice parameters for C2H4 are a = 5.18 Å, b = 3.09 Å, and c = 2.43 Å at 100 GPa. The H atoms sit at the 8g Wyckoff position (0.16, 0.84, 0.25) and the C atoms at the 4c position (0, 0.37, 0.25). The lattice parameters for C2H6 are a = 4.14 Å, b = 4.10 Å, and c = 5.05 Å at 100 GPa and alpha = 90°, beta = 145.15°, and gamma = 90°. The H atoms sit at the 4e Wyckoff position (1.07, 0.36, 0.43), (0.51, 0.85, 0.06), (0.78, 0.43, −0.07) and the C atoms at the 4e positions (−0.32, 0.12, −0.43).

Figure 4. Predicted structures at 300 GPa for (a) C4H4, (b) C6H2, and (c) C8H2. In the C4H4-P21/m structure, the C−C bond lengths are 1.38 Å, whereas in C6H2-C2/m they vary from 1.38 to 1.42 Å, and in C8H2-R3m they are shorter and have values of 1.37−1.38 Å. In all structures, the C−H bond lengths are 1.01 Å.

possible that these structures could form as metastable phases under hydrostatic conditions or be stabilized by nonhydrostatic stresses such as those produced in diamond anvil cell experiments. The present results could thus be very important for understanding the diamond−hydrogen interactions in highpressure diamond anvil cell experiments on hydrogen. Indeed, there is evidence for chemical interactions between hydrogen samples and diamond anvils in experiments going back many years.23,24 It is plausible that these or related structures form at the sample−diamond interface. Further investigations are needed to identify these structures experimentally. The reactivity of hydrogen with diamond is also an important question for the interpretation of the results of other highpressure experiments that involve hydrogen such as studies of hydride superconductors. Finally, the new structures should be considered in models of dense carbon-rich natural environments such as the interiors of carbon-rich exoplanets.2 The present results are thus expected to stimulate further studies of the high P−T physical chemistry of the C−H system needed to understand the nature of carbon in dense astrophysical environments.

Figure 3. (a) Calculated electronic band structure and (b) phonon dispersion for C2H4 at 300 GPa.

We summarize the implications of these calculations. Our simulations reveal new crystal structures in the C−H system up to 300 GPa, including a new phase of C2H4 that is predicted to be stable above 100 GPa. The electronic properties are of interest in view of the evidence that certain dense hydrides exhibit high-temperature superconductivity at high pressure (e.g., ref 22). Notably, the new C−H structures found here remain insulating (e.g., C2H4, which has an indirect band gap under the conditions investigated). The calculations for carbonrich compositions reveal energetically competitive but metastable structures that are similar to diamond. Indeed, it is

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METHODS Structure searches for low-energy crystalline phases in the C−H system at high pressure were performed using the particle swarm optimization method implemented in the CALYPSO code.25 This method has been successfully applied to a broad range of systems ranging from elemental solids to binary 4220


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AUTHOR INFORMATION

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS

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REFERENCES

This research was supported by EFree, an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences under Award DE-SC0001057. The infrastructure and facilities used are supported by the U.S. Department of Energy/National Nuclear Security Administration (Grant DE-NA-0002006, CDAC). Work at LLNL was performed under the auspices of the DOE under Contract No. DE-AC52-07NA27344. This is a contribution to the Deep Carbon Observatory.

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