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Low energy three-dimensional hydrocarbon crystal from cold compression of benzene
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2013 J. Phys.: Condens. Matter 25 205403
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IOP PUBLISHING JOURNAL OF PHYSICS: CONDENSED MATTER
J. Phys.: Condens. Matter 25 (2013) 205403 (5pp) doi:10.1088/0953-8984/25/20/205403
Low energy three-dimensionalhydrocarbon crystal from coldcompression of benzene
Chaoyu He, L Z Sun, C X Zhang and Jianxin Zhong
Hunan Key Laboratory for Micro-Nano Energy Materials and Devices, Xiangtan University, Hunan411105, People’s Republic of ChinaLaboratory for Quantum Engineering and Micro-Nano Energy Technology, Faculty of Materials andOptoelectronic Physics, Xiangtan University, Hunan 411105, People’s Republic of China
E-mail: [email protected] and [email protected]
Received 18 January 2013, in final form 2 March 2013Published 23 April 2013Online at stacks.iop.org/JPhysCM/25/205403
AbstractWe demonstrate an interesting phase transition from cold compressed benzene to a fullysaturated three-dimensional hydrocarbon crystal, Hex-CH. The very low transition pointpressure, remarkable energetic stability and positive dynamical stability indicate that Hex-CHis a promising three-dimensional hydrocarbon crystal. As a transparent insulator and potentialhard hydrocarbon material, Hex-CH is expected to be of general interest in organic chemistry,condensed matter physics and material science.
S Online supplementary data available from stacks.iop.org/JPhysCM/25/205403/mmedia
(Some figures may appear in colour only in the online journal)
1. Introduction
Carbon and hydrogen are fundamental elements for life onEarth. The element carbon has a wide ability to form sp,sp2 and sp3 hybridization and bond to itself and many otherelements. Hydrogen is the lightest in the periodic table ofelements and it does form compounds with most elements.The binary compounds of hydrogen and carbon, namelyhydrocarbons, have five fundamental forms, alkyne, alkene,alkane, cyclic hydrocarbons and aromatic hydrocarbons.Usually, most of these hydrocarbons are zero-dimensional(0D) molecules, one-dimensional (1D) chains and complexpolymers (e.g. polyethylene, polypropylene and polystyrene).A few years ago, by hydrogenating graphene [1], a perfecttwo-dimensional (2D) crystalline phase of hydrocarbon(graphane) was produced [2]. This novel 2D hydrocarbonwith an equal carbon–hydrogen ratio (1:1) was suggested [3]first by Sluiter and Kawazoe in 2003 and synthesized [2]in 2009 through exposure of a single-layer graphene to ahydrogen plasma. Since then, many low energy 2D crystalsfor hydrocarbon with a stoichiometry of 1:1 have beenproposed [3–9]. However, less attention has been paid to
the three-dimensional (3D) hydrocarbon crystals than to the2D graphane allotropes. In 2011, by stacking the previouslyproposed 2D graphane allotropes in different ways, Wen et alpredicted [6] some graphite-like 3D graphane crystals. Veryrecently, a diamond-like 3D hydrocarbon crystal (K4-CH)was proposed [10] through hydrogenating the hypotheticalK4-carbon [11, 12]. Inspired by this initial search for 3Dhydrocarbon crystals, we try to predict some 3D hydrocarboncrystals and design potential pathways to their formation.
High pressure technology is very successful in producingnew compounds, especially in inducing phase transitionsfrom the unsaturated C–C triple and double bonds tothe fully saturated C–C single bonds. For example, bycold compressing graphite [13] and carbon nanotubes [14],two new superhard carbon phases different from bothcubic diamond and hexagonal diamond can be obtained.Theoretically, Wen et al systematically studied [15] thepreviously proposed benzene phases [16–18] (benzene I, I′,II, III, III′, IV, V) at high pressure up to 300 GPa anddiscovered two interesting phase transitions from benzeneV to polymer I and benzene III to polymer II. Theyfound that the two saturated hydrocarbon polymers are more
10953-8984/13/205403+05$33.00 c© 2013 IOP Publishing Ltd Printed in the UK & the USA
J. Phys.: Condens. Matter 25 (2013) 205403 C He et al
Figure 1. The phase transition process from benzene VI to Hex-CH under pressure. In the left panel are the perspective views from the[001] and [110] directions of the initial benzene VI at zero pressure, which possesses a hexagonal lattice with constants of a = b = 7.815 Aand c = 9.125 A and two inequivalent hydrogen and carbon atoms located at 18h (0.149, −0.149, −0.333) and 18h (0.230, −0.230,−0.333), respectively. In the right panel are the perspective views from the [001] and [110] directions of the final crystalline Hex-CH phaseat 45.5 GPa, which possesses a hexagonal lattice with constants of a = b = 5.626 A and 5.642 A and two inequivalent hydrogen and carbonatoms located at 18h (−0.091, −0.181, 0.389) and 18h (−0.186, −0.372, 0.296), respectively.
favorable than all the benzene phases and are confirmedto be dynamically stable. Their results provide a promisingdirection for designing 3D hydrocarbons.
According to the above-mentioned background, wepropose a promising diamond-like 3D crystalline condensedhydrocarbon phase which can be potentially produced by coldcompressing benzene. Such a new 3D hydrocarbon phase(named as Hex-CH) possesses remarkable stability exceedingboth polymer I and polymer II. Its critical pressure is about45.5 GPa which is very low in comparison with those ofthe transitions from benzene V to polymer I (125 GPa)and from benzene III to polymer II (210 GPa) (see ourdiscussions about polymer I and polymer II in supplementaryinformation available at stacks.iop.org/JPhysCM/25/205403/mmedia). Calculations of the vibrational properties show thatHex-CH is dynamically stable at pressures up to 100 GPa.Our results suggest that Hex-CH is a promising 3D solidhydrocarbon crystal of general interest in organic chemistry,condensed matter physics and material science.
2. Model and method
We relate the hexagonal Hex-CH proposed in the presentwork to a simple arrangement of benzene molecules (we callit benzene VI) according to the structural relations betweenthem. Benzene VI is a promising precursor for synthesizingcrystalline Hex-CH. We believe that there is a probabilityof the existence of such an arrangement state of benzene (afully periodic crystalline arrangement is difficult but a localbenzene VI phase is possible). In figure 1 the left panelillustrates the [001] and [110] views of the initial benzene VIand the right panel shows the corresponding [001] and [110]views of the final Hex-CH phase. Both the initial benzene VIand the final Hex-CH belong to the same space group of R3m
(166). At zero pressure, benzene VI is less stable than all thepreviously proposed benzene phases and the phase transitionfrom benzene VI to Hex-CH spontaneously occurs when theexternal pressure increase up to 45.5 GPa.
Structure optimizations and properties were studied usingthe density-functional theory (DFT) based first-principlesmethod as implemented within the Vienna ab initio simulationpackage (VASP) [19, 20]. Dynamical stability was evaluatedthrough simulating the vibration properties by the phononpackage [21] with the forces calculated from VASP. In allcalculations, the interactions between the nucleus and thevalence electrons are described by the projector augmentedwave (PAW) method [22, 23] and the exchange and correlationeffect is considered according to the general gradientapproximation (GGA) [24]. Wavefunctions are solved byapproximation in the plane-wave basis with a cut-off energyof 500 eV. The Brillouin zone sampling mashes are set tobe dense enough (less than 0.25 A
−1) to ensure accuracy.
Before the calculation of properties and dynamical stabilityevaluation, the crystal lattices and atom positions are fullyoptimized until the residual force on every atom is less than0.005 eV A
−1and the residual stress is less than 0.3 GPa.
3. Results and discussion
The proposed initial benzene VI is a simple arrangementof benzene molecules. It has one inequivalent CH pairin its hexagonal crystal cell with lattice constants of a =b = 7.815 A and c = 9.125 A. At zero pressure, itstwo inequivalent positions for hydrogen and carbon are18h (0.149, −0.149, −0.333) and 18h (0.230, −0.230,−0.333), respectively. As shown in figure 2(a), at zeropressure, benzene VI is less stable than benzene I, II, III,IV and V. When the pressure increases up to 45.5 GPa,
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J. Phys.: Condens. Matter 25 (2013) 205403 C He et al
Figure 2. Enthalpy–pressure curves of benzene phases (I, II, III, IV, V and X) and previously proposed graphite-like graphane III [6] andK4-CH [10] relative to reference line1 (a). Phonon band structure and electronic band structure for Hex-CH at the critical pressure of45.5 GPa (b).
benzene VI undergoes a spontaneous phase transition to afully saturated phase (Hex-CH), which possesses remarkablestability exceeding benzene I, II, III, IV and V (includingpolymer I and polymer II) in a wide pressure range.Furthermore, our ab initio molecular dynamic (AIMD)simulation under the condition of 45.5 GPa and 273.5 Kshows that such a phase transition also occurs and finishesin the first 2 ps of our 10 ps simulation (we consider an NPTensemble with fixed atoms at fixed pressure and temperatureconditions, see the supplementary movie available at stacks.iop.org/JPhysCM/25/205403/mmedia). After we found suchan interesting phase transition of benzene VI, we examinedthe dynamical stability of Hex-CH in a wide pressure rangeup to 200 GPa (see supplementary information available atstacks.iop.org/JPhysCM/25/205403/mmedia) and the phononband structure of Hex-CH at the transition point of 45.5 GPais shown in figure 2(b). Our results show that Hex-CH isdynamically stable at pressures up to 100 GPa. In addition, thesimulated process of decompression (see the red solid circlefrom 45.5 to 0 GPa in figure 2(a)) indicates that Hex-CH ismore stable than all the benzene phases (I–V) at the pressurerange from 45.5 to 5 GPa. From figure 2(a) we know that thepreviously proposed graphite-like graphane III [6] is alwaysmore favorable than all the benzene phases and Hex-CH, butwe still believe that, as a metastable state of hydrocarbon withremarkable energetic stability and positive dynamical andmechanical stability, Hex-CH is a promising 3D hydrocarboncrystal. From the comparison with the recently proposedK4-CH [10], we can see that He-CH is more favorable thanK4-CH in the pressure range from 0 to 157.7 GPa. In ourstudy, we also found two phase transitions of benzene IV at160 GPa and 180 GPa, respectively (see the supplementary
information available at stacks.iop.org/JPhysCM/25/205403/mmedia).
To better realize the phase transition of benzene VIunder pressure, we summarize the structural information forbenzene VI (Hex-CH), including lattice constants, intra-C6C–C bonds, inter-C6 C–C bonds, C–H bonds and theminimum H–H distances, as functions of pressure in figure 3.From the lattice constants, we can see that benzene VIundergoes a fast compression when the pressure increasesfrom 0 to 45.5 GPa. The spontaneous phase transition canbe noticed from the transilient decreases of lattice constant cand inter-C6 C–C distances, as well as the transilient increaseof intra-C6 C–C bonds and C–H bonds at 45.5 GPa. Thetransilient decrease of inter-C6 C–C distances indicates theformation of the inter-C6 C–C bonds, which connect thebenzene molecules together forming a 3D crystal, and thetransilient increases of intra-C6 C–C bonds and C–H bondsindicate the transformation of the manner of hybridization ofthe carbon atoms from sp2 to sp3. After the phase transition,the change rates of lattice constants and bond lengths withthe increase of pressure are slowing down, indicating that theformed Hex-CH is less compressible.
Our calculations show that the formed Hex-CH crystalwith the same space group R3m as benzene VI is dynamicallystable and the energy more favorable than all the benzenephases (I–V) and polymers (I and II) in the pressure range
1 The absolute enthalpy–pressure curves integrated in a limited picture aretoo close to each other to be distinguished, so we chose a reference linewith proper slope and close to all the absolute enthalpy–pressure curves toavoid this difficulty. The reference line is set to be −5.15+ 0.0035 ∗Pressure(in GPa), where the value of pressure used to calculated the line is in GPa.This means nothing in physics terms but is very useful. The recalculatedrelative enthalpy–pressure curves are separated from each other and are easyto distinguish.
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J. Phys.: Condens. Matter 25 (2013) 205403 C He et al
Figure 3. Structural information for benzene VI during the compressing process, including lattice constants (a), inter-C6 C–C bond (b),intra-C6 C–C bond (c), C–H bond (d) and the minimum H–H distance (b).
from 5 to 200 GPa. The remarkable energetic stabilityand positive dynamical stability indicate that Hex-CH is apromising 3D hydrocarbon crystal. Decompressed back tozero pressure, its optimized lattice constants are a = b =6.178 A and 5.623 A. The two inequivalent positions forhydrogen and carbon in this crystal are 18h (−0.108, −0.215,0.405) and 18h (−0.192, −0.385, 0.298), respectively. Thelengths for intra-C6 C–C bonds, inter-C6 C–C bonds andC–H bonds in Hex-CH are 1.559 A, 1.581 A and 1.087 Arespectively. For the purpose of experimental identificationof this novel phase transition from benzene VI to Hex-CH,we simulated the x-ray diffraction (XRD) patterns based onour optimized crystal structures of benzene VI (Hex-CH) atdifferent pressures. The simulated XRD patterns are shownin the supplementary information (available at stacks.iop.org/JPhysCM/25/205403/mmedia).
Finally, we discuss the electronic and mechanicalproperties of Hex-CH. The calculated electronic propertiesshow that Hex-CH is a transparent insulator with an indirectbandgap of 5.52 eV at zero pressure and its bandgap willreduce to 4.73 eV at the transition point of 45.5 GPa.The simulated band structure at 45.5 GPa is shown infigure 2(b). The elastic constants of Hex-CH are calculatedas the second-order coefficient in the polynomial functionof the distortion parameter δ used to fit the total energyaccording to Hooke’s law. Based on the simulated elasticconstants of Hex-CH at zero pressure (see supplementary
information available at stacks.iop.org/JPhysCM/25/205403/mmedia), we can evaluate its bulk modulus (B0) and shearmodulus (G) [25]. The calculated B0 and G for Hex-CH are188.91 GPa and 129.53 GPa, respectively. To further analyzethe hardness of Hex-CH, we adopt the recently introducedempirical scheme [26] to evaluate its Vicker’s hardness (Hv)determined by the B0 and G as Hv = 2(G3/B2
0)0.585− 3.
Our results show that Hex-CH is a potential hard hydrocarbonmaterial with a hardness of 19.13 GPa.
4. Conclusion
We have demonstrated an interesting phase transition frombenzene VI to a fully saturated 3D crystalline phase, Hex-CH.The critical pressure for this phase transition is about 45.5 GPawhich is very low in comparison with those transitions frombenzene V to polymer I (125 GPa) and from benzene IIIto polymer II (210 GPa). The remarkable energetic stabilityand positive dynamical stability at ambient pressure indicatethat Hex-CH is a promising new hydrocarbon crystal whichcan be potentially formed by compressing benzene underpressure. As a transparent insulator and potential hardmaterial, crystalline hydrocarbon Hex-CH is expected to beof general interest in organic chemistry, condensed physicsand material science. We believe that our results will provideuseful indications for future experimental explorations.
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J. Phys.: Condens. Matter 25 (2013) 205403 C He et al
Acknowledgments
This work is supported by the National Natural Science Foun-dation of China (Grant Nos 51172191 and 11074211), theNational Basic Research Program of China (2012CB921303),the Program for New Century Excellent Talents in University(Grant No. NCET-10-0169), the Scientific Research Fund ofHunan Provincial Education Department (Grant Nos 09K033,10K065, 10A118) and the Hunan Provincial InnovationFoundation for Postgraduates (Grant No. CX2012A011).
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