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Ice Carbons Hui-Yan Zhao, Jing Wang, Xiu-Jie Su, Dong-Bo Zhang, and Ying Liu J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/jp5080048 • Publication Date (Web): 04 Nov 2014 Downloaded from http://pubs.acs.org on November 9, 2014

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The Journal of Physical Chemistry

Ice Carbons Hui-Yan Zhao,†,‡ Jing Wang,†,¶ Xiu-Jie Su,†,¶ Dong-Bo Zhang,‡ and Ying Liu∗,†,¶ Department of Physics and Hebei Advanced Thin Film Laboratory, Hebei Normal University, Shijiazhuang 050024, Hebei, China, Beijing Computational Science Research Center, Beijing 100084, China, and National Key Laboratory for Materials Simulation and Design, Beijing 100083, China E-mail: [email protected]

∗ To

whom correspondence should be addressed of Physics and Hebei Advanced Thin Film Laboratory, Hebei Normal University, Shijiazhuang 050024, Hebei, China † Department ‡

Beijing Computational Science Research Center, Beijing 100084, China ¶

National Key Laboratory for Materials Simulation and Design, Beijing 100083, China

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Abstract Based on the topologically-distinct oxygen nets of crystalline ice phases, a series of carbon structures with sp3 bonding are constructed. Five new low-energy polymorphous phases of carbon, named “Ice Carbons", are predicted by using the first-principles calculations. Their hardnesses are about 88.5∼98.5% that of diamond, indicating that these new carbon phases are superhard materials. In particular, the new “IceIII -Carbon" has the highest hardness 94.1 GPa that only 1.4 GPa smaller than that of diamond. Moreover, it also has slightly lower bulk modulus, which display similar properties with hP3, tI12, and tP12 superdense carbon allotropes.

Keywords: Hardness of solid, Metastable phases, Density-functional theory, Band structure of semiconductors

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Introduction Water is, without a doubt, an essential part of our world, playing an important role in many biological and chemical processes. The water molecule H2 O is the third most abundant molecular species in the universe following H2 and CO. 1 Water has many solid phases, i.e. ices. Currently there are sixteen or so crystalline phases and three amorphous phases. In all known crystalline ices except for ice X, the water molecules are fully hydrogen bonded to four neighboring water molecules, resulting in a four-fold coordination of the molecules. 2,3 Four hydrogen bonds in each water are directed towards vertices of an ideal or slightly distorted tetrahedron composed of water molecules. As a fundamental element on earth, carbon appears in a variety of forms due to its ability to form sp-, sp2 -, and sp3 -hybridized bonds. This results in forms of carbon such as graphite, lonsdaleite, diamond, nanotubes, fullerenes, and amorphous carbon. 4 People have had great interest in synthesizing new carbon allotropes. Recent cold compression experiments have indicated that new allotropes of carbon exist that exhibit exceptionally high indentation strength sufficient to indent diamond anvils. 5,6 More recently, an ultrahard nanotwinned cubic boron nitride, with an average twin thickness of 3.8 nm, has been synthesized under high pressure and high temperature conditions, using special turbostratic onion-like BN nanoparticle precursor materials. 7 Inspired by these experimental findings, much effort has been made in the quest for superhard materials. On the basis of a good match with the experimental X-ray diffraction (XRD) patterns for the superhard intermediate phase of the cold-compressed graphite, 6 several low-energy carbon structures have been proposed. Several of the proposed structures are: a monoclinic C2/m structure (M-carbon), 8 a body-centered tetragonal C4 phase (bct-C4 ), 9,10 a sp3 -orthorhombic Pnma structure (W-carbon), 11 an orthorhombic carbon (O-carbon) in Pbam symmetry, 12 an allotrope of carbon with Cmmm symmetry (Z-carbon), 13 a simple monoclinic P2/m F-carbon, 14 and Pcarbon. 15 In 2012 it was reported by Boulfelfel et al. and by Wang et al. that the experimentally observed superhard post-graphite phase, 6 is consistent with M-carbon. 16,17 Furthermore, Z-carbon and P-carbon, have also been proposed to account for a quenched product recovered from cold3



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compressed nanotube bundles. 5 In addition, other sp3 -hybridized carbon phases, including a chiral framework structure (CFS), 18 a very light and hard carbon allotrope (T-carbon), 19 superdense carbons hP3, tI12, and tP12, 20 amorphous diamond, 21 and a tetragonal carbon allotrope, 22 have also been proposed. In our previous work, based on possible solutions to the Kelvin problem, 11 new carbon phases have been predicted, and named “Kelvin carbons". 23 Note that in normal-pressure crystalline phases (Ih, Ic, and XI), each water molecule forms a nearly ideal tetrahedron with neighbouring molecules through four hydrogen bonds. Meanwhile, high-pressure crystalline ice phases are characterized by distorted tetrahedral closest environment of water molecules. The O-O-O angles are mainly in the range of 100-120◦ , which are close to the ideal tetrahedral angle of 109.47◦ found in cubic diamond. Both ice and carbon with sp3 bonding thus crystallize into solid-state structures composed of tetrahedral building units that are joined together to form an infinite four-connected net. The existing topological relationships between crystalline ices and carbon phases with sp3 bonding see Table I. 24–26 Tribello et al. 2 outlined that ice forms only 8 topologically-distinct oxygen nets under the pressure and temperature conditions that have been reported thus far. The oxygen nets in ice Ih and ice Ic are known to be structurally analogous to the lonsdaleite and diamond of carbon (See Table I). In this letter, six hypothetical carbon phases are obtained by replacing each oxygen atom in the remaining six oxygen nets of ices by a carbon atom. The structural stability of these hypothetical carbon phases are verified, and compared with that of carbon structures reported in previous literatures.

Computation Details Structural and property predictions for these carbon allotropes studied in this letter were performed within the Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation (GGA), 27 as implemented in the VASP code. 28 An energy cutoff of 800 eV and all-electron plane-wave basis sets

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within the projector augmented wave (PAW) 29 method were chosen. A dense k-point sampling with the grid spacing less than 2π ×0.02 Å−1 in the Brillouin zone was used. For all calculations, convergence in total energy was set to 1 meV/atom between two self-consistent iterations. Forces on the ions are calculated through the Hellmann-Feynman theorem allowing a full geometry optimization. To assess the accuracy of our first-principles total energy methods, we also calculated the structural parameters and total energies of these carbon structures using two exchange correlation functionals: a density functional constructed with a long-range dispersion correction (D2) 30 and the van der Waals density functional (vdW-DF). 31 The computed results are compared with that of DFT/PBE in Table II. It is found that the calculations with D2 and vdW-DF give the similar structural information with that using PBE exchange correlation functional. Considering the accuracy in the calculation of structures and total energies as well as the computational time, 32 the PBE functional for the rest of all first-principles calculations was used in this paper. The hardnesses of the optimized carbon allotropes were estimated using three most popular microscopic hardness models: bond resistance model, 33 bond strength model, 34 and electronegativity model. 35 The simulated X-ray diffraction (XRD) pattern is calculated using the REFLEX program implemented in the Materials Studio package. 36

Results and Discussion After minimizing its energy, a carbon phase based on the structure of ice IV evolves into the known diamond lattice structure while other five carbon structures, named “Ice Carbons", have not been reported thus far. Figure 1 shows the five new low-energy polymorphic phases of sp3 -hybridized carbon remaining in this letter, including a phase of carbon based on ice II, a carbon isomorph of the oxygen net in ice III, a carbon structure derived from ice V, a carbon analogue of ice VI, and a carbon phase based on the structure of ice XII. The structural data and properties of these new carbon phases are listed in Table III and Table IV, respectively.

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Like diamond, the IceII -Carbon structure, a carbon analogue of ice II, is a cubic crystal. It has ¯ space group different from that (R3) ¯ of the oxygen framework in ice II. The C-C-C angles a Ia3d in the IceII -Carbon are 99.59◦ and 131.81◦ . Along its body diagonal direction, IceII -Carbon can actually be thought of as six-coordinate close-packed structure composed of distorted (3,0) carbon nanotubes. Moreover, these nanotubes are linked together by chemical bonds, and the distances among the centers of these nanotubes are about 4.108-4.390 Å. It just corresponds to the well known S* net according to the terminology of Fisher and Koch. 37 Based on the oxygen framework of ice III, new tetragonal phase IceIII -Carbon contains the C-C-C angles ranging from 90.00◦ to 140.00◦ . As shown from Fig. 1, it contains two same parts with different orientation arrangements. Each part contains five membered rings joined as bicycloheptamers. However, though starting with a similar framework to that of the oxygen in ice V, IceV -Carbon shows differences. Its unit cell, which forms monoclinic crystals with a new space group of P21 /c, is shown opposite. IceV -Carbon contains four-, five-, six- and eight-membered rings. The opposite sub-structure with four-, five-, six-membered rings are connected by a distorted eight-membered ring. There is a new orthorhombic carbon phase IceVI -Carbon that has a space group of P2221 . Again, although IceVI -Carbon has a similar framework to the oxygen net in ice VI, its space group is different from the ice VI P42 /nmc space group. IceVI -Carbon contains five- and six-membered rings while ice VI only includes four-membered rings. Along its b axis direction, IceVI -Carbon shows the existence of holes, the cross section of which is five-membered ring. Finally, there is also a new carbon phase IceXII -Carbon, analogous to the ice XII, that has an ¯ space group. Its unit cell contains five- and seven-membered rings. Along its c axis direction, I 42d five-membered rings are polymerized to holes. To assess relative stabilities of the five new carbon phases with respect to the known polymorphic phases of sp3 -hybridized carbon, Fig. 2 shows the total energy per atom as a function of volume per atom at zero temperature and zero pressure. The lowest point for each energy curve cor-

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responds to that of the equilibrium structures of the respective carbon phases at zero pressure. As is well known, diamond and lonsdaleite structures are stable polymorphic phases of sp3 -hybridized carbon and are analogous to the respective ice Ic and ice Ih polymorphic phases. By inspection of Fig. 2 and Table IV, the carbon phase IceVI -Carbon was identified as low-energy sp3 -hybridized carbon form near that of diamond and its energy per atom is only 0.205 eV per atom higher than that of diamond. In comparison with the low-lying IceVI -Carbon phase, the energy differences per atom for the other new carbon phases are 0.686 eV for the IceII -Carbon phase, 0.682 eV for the carbon phase IceIII -Carbon, 0.475 eV for the IceV -Carbon structure, and 0.880 eV for the IceXII Carbon phase, respectively. As shown in Table IV, the volumes per atom at equilibrium of the five new carbon phases are between 5.645 Å3 and 6.339 Å3 . Note that the volumes per atom of the IceII -Carbon and IceIII -Carbon are approximately those of the diamond and lonsdaleite phases. Meanwhile, the IceV -Carbon and IceVI -Carbon have similar volumes per atom as guest-free carbon clathrates and CFS. The volume per atom for IceXII -Carbon is very close to that of the M-carbon phase. The stabilities of these Ice-Carbon structures are also confirmed by the density of phonon states curves in Fig. 3, where there are no appreciable imaginary phonon modes. So these Ice-Carbon structures are kinetically stable. Recently Sun et al. 38 conducted molecular dynamics calculations, and determined the equilibrium structure of CaSiO3 at relevant temperatures by inspecting the probability distribution of atomic displacements. Similarly, in this work, molecular dynamics calculations for these Ice-Carbon structures are performed using the DFTB+ program. 36 Resultly, the stability of these Ice-Carbon structures were again confirmed, see Supporting Information. The calculated densities, bulk moduli, and hardnesses of the five new carbon phases found in this letter are listed in Table IV. For comparison, the properties of cubic diamond, lonsdaleite, graphite, carbon clathrates, CFS, M-carbon, and T-carbon are computed using the same method as the five new carbon phases. Note that the densities of IceVI -Carbon and IceXII -Carbon, are quite comparable to that of M-carbon, which are intermediate between cubic diamond and guestfree carbon clathrates. By fitting the calculated total energy as a function of volume to third-order

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Birch-Murnaghan equations of state, the bulk moduli of these new carbon phases are in the range of 373.5-406.1 GPa, suggesting that these structures studied in this letter are not compressed easily. As seen in Table IV, the bulk modulus of the IceII -Carbon is quite comparable to that of cubic and hexagonal diamond, M-carbon, while larger than that of other known phases of sp3 -hybrized carbon. The calculated hardnesses show that these new carbon phases are promising superhard ˘ unek, the values materials. In the micro-hardness model based on bond strength proposed by Sim˚ of these new phases are about 88.5∼98.5% that of diamond. Note that the IceIII -Carbon phase has the highest hardness of 94.1 GPa and is a little less than that of the cubic diamond (for which the same model gives the hardness of 95.5 GPa), making this phase nearly as hard as diamond. Moreover, it displays higher density than that of diamond, whose properties are just as that of superdense carbon phases (hP3, tI12, and tP12). So the IceIII -Carbon phase is a superdense carbon phase. The electronic band structures of the five new carbon phases found in this letter are plotted in Fig. 4. The corresponding band gaps of these carbon structures are listed in Table IV. IceIII Carbon has an indirect band gap of 4.96 eV, which is 0.84 eV larger than that of cubic diamond. As inspection of Fig. 4 and Table IV shows, it can be easily deduced that other new carbon phases are semiconductors with band gaps in the range of 1.92-3.78 eV. A direct band gap of 1.92 eV at the Γ point is seen for the IceII -Carbon phase. The IceV -Carbon and IceVI -Carbon phases are indirect wide bandgap semiconductors with the value of the gaps larger than 3.50 eV. They should thus be optically transparent superhard material just as the post-graphite phase in cold-compressed graphite experiments displays. 6 For the IceXII -Carbon phase, the value of the band gap is located in visible range, and since the band gap is indirect, this carbon phase may be colorless. To provide more information and characteristies for possible experimental observations, the XRD patterns for the five new phases at the wavelength of 1.54059 Å have been simulated and are provided in Fig. 5. The five new carbon phases display more peaks in their XRD spectra, and with different intensities, than the three observed for diamond. For the IceII -Carbon, the strongest diffraction peak is seen at 2θ ≈ 42.80◦ that is very close to that of the strongest diffraction peak of

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diamond. Another larger intensity peak is found at 2θ ≈ 67.70◦ . It appears that the IceII -Carbon spectra is a distorted, or shifted version of the diamond spectra, but with additional secondary peaks. For the IceIII -Carbon, four sharp peaks are seen in the range of 2θ ≈ 30.00 − 52.00◦ . Different from other Ice-Carbon structures, a sharp peak below 2θ ≈ 30.00◦ is found in the IceV Carbon. For the low-energy IceVI -Carbon structure, there is an obvious peak at 2θ ≈ 40.00◦ but has many smaller peaks similar to that seen in IceIII -Carbon. The IceXII -Carbon structure has the strongest diffraction peaks at 2θ ≈ 38.00◦ , and in the range of 50.00 − 56.00◦ , there are three diffraction peaks with successively decreasing intensities.

Conclusions In summary, based on the topologically-distinct oxygen nets of crystalline ice phases, a series of carbon structures with sp3 bonding were constructed. By using the first-principles calculations, five new polymorphous phases of sp3 -hybridized carbon have been proposed and named “Ice Carbons". The new carbon phases, IceII -Carbon, IceV -Carbon, IceVI -Carbon, and IceXII -Carbon, are semiconductors with band gaps in the range of 1.92-3.78 eV, while the IceIII -Carbon structure is ˘ unek, an insulator with an indirect band gap of 4.96 eV. Using the hardness model proposed by Sim˚ their hardnesses are about 88.8∼98.5% that of diamond, suggesting that these new carbon phases are superhard materials. Notably, the new “IceIII -Carbon" has the highest hardness with the value of 94.1 GPa, making this phase nearly as hard as diamond (95.5 GPa in the same hardness model), and slightly lower bulk modulus, which display similar properties as three superdense carbon allotropes (hP3, tI12, and tP12). The new carbon phase IceVI -Carbon was identified as another low-energy sp3 -hybridized carbon form with only 0.205 eV higher in total energy per atom than diamond. Since the band gap is indirect with the value of 3.59 eV, the IceVI -Carbon should be an optically transparent superhard material just as is the post-graphite phase in the cold-compressed graphite experiments. The simulated XRD patterns of these new carbon phases should provide useful information for possible experimental observations and synthesis.

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Acknowledgement We would like to thank Dr. S. C. Sahyun for his help with the language. This work was supported by the National Natural Science Foundation of China (Grant Nos. 11274089, U1331116, and 11304076), National Science Foundation of Hebei Province (Grant Nos. A2012205066 and A2012205069), and the Start-up Funding from Young Thousand-Talent Program of China. We gratefully acknowledge the financial support from the 973 Project in China under Grant No. 2011CB606401.

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(38) Sun, T.; Zhang, D. B.; Wentzcovitch, R. M. Dynamic stabilization of cubic CaSiO3 perovskite at high temperatures and pressures from ab initio molecular dynamics. Phys. Rev. B 2014, 89,

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Figure 1: (color online). View of new polymorphic phases of carbon based on ice phases of water, showing (A) the IceII -Carbon based on ice II and (B) the IceIII -Carbon analogous to ice III, (C) the IceV -Carbon based on ice V, (D) the IceVI -Carbon isomorphic to ice VI, and (E) the IceXII -Carbon )LJ&RORURQOLQH &U\VWDOVWUXFWXUHVRIQHZSRO\PRUSKLFSKDVHVRIFDUERQ based on ice XII. In addition, (F) the lonsdaleite structure is analogous to ice Ih with hexagonal symmetry. EDVHGRQLFHSKDVHVRIZDWHUVKRZLQJ$ WKH,FH&DUERQ,EDVHGRQLFH,,DQG%

WKH,FH&DUERQ,,DQDORJRXVWRLFH,,,& WKH,FH&DUERQ,,,EDVHGRQLFH9' WKH ,FH&DUERQ,9LVRPRUSKLFWRLFH9,DQG( WKH,FH&DUERQ9EDVHGRQLFH;,,,Q DGGLWLRQ) WKHORQVGDOHLWHVWUXFWXUHLVDQDORJRXVWRLFH,

14


Page 15 of 22

DiamondLFH,c LonsdaleiteLFH,h &V,

&V,,

&)6 MFDUERQ TFDUERQ ,, Ice &DUERQ ,,, Ice &DUERQ 9 Ice &DUERQ 9, Ice &DUERQ ;,, Ice &DUERQ

(QHUJ\H9DWRP

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


9ROXPHc DWRP

)LJ&RORURQOLQH 7RWDOHQHUJ\SHUDWRPDVDIXQFWLRQRIYROXPHSHUDWRPIRUWKH Figure 2: (color online). energy atom asLQaWKLVfunction of volume PRVWTotal LPSRUWDQW FDUERQper VWUXFWXUHV IRXQG OHWWHU )RU FRPSDULVRQ ZH DOVRper atom for the most 3 important sp carbon structures in this letter. ForHJ comparison we also LQFOXGH VRPH found DOUHDG\ NQRZQ VWUXFWXUHV RI FDUERQ FXELF GLDPRQG DQDORJRXV WR include some already known structures of carbon, e.g., cubic diamond to ice lonsdaleite isostructural to LFH , ORQVGDOHLWH LVRVWUXFWXUDO WR LFH , analogous JXHVWIUHH FODWKUDWHV EDVHGIc, RQ FODWKUDWH K\GUDWHV&)6 FDUERQ ice Ih, guest-free clathrates based FDUERQDQG on clathrate hydrates, CFS, M-carbon, and T -carbon. The wellknown carbon structures are indicated by lines and the new phases by symbols and lines, respectively.

15


Page 16 of 22

1400

1400

1200

1200

1200

1000

1000

1000

800

800

800

600

600

600

400

400

400

-1

1400

200

200

200

II

0

Ice -Carbon

V

III

Ice -Carbon

0

0

1400

1400

1400

1200

1200

1200

1000

1000

1000

800

800

800

600

600

600

400

400

400

200

200

200

Ice -Carbon

-1

Frequency (cm )

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Frequency (cm )


0

VI

Ice -Carbon Density of Phonon States

XII

Ice -Carbon

0

Density of Phonon States

0

Lonsdaleite Density of Phonon States

Figure 3: (color online). The density of phonon states of the Ice-Carbon structures and lonsdaleite.

16


Page 17 of 22

,,

,,,

Ice &DUERQ

9

Ice &DUERQ

Ice &DUERQ

(QHUJ\H9

Γ+13

9,

Ice &DUERQ

Γ1=$0

Γ=5;

;,,

Γ =

Ice &DUERQ

Γ

Ice Carbons - American Chemical Society

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