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New metallic carbon: Three dimensionally carbon allotropes comprising ultrathin diamond nanostripes
Accepted Manuscript New metallic carbon: Three dimensionally carbon allotropes comprising ultrathin diamond nanostripes Yinqiao Liu, Xue Jiang, Jie Fu, Jijun Zhao PII:
S0008-6223(17)31022-9
DOI:
10.1016/j.carbon.2017.10.066
Reference:
CARBON 12493
To appear in:
Carbon
Received Date: 14 September 2017 Revised Date:
8 October 2017
Accepted Date: 9 October 2017
Please cite this article as: Y. Liu, X. Jiang, J. Fu, J. Zhao, New metallic carbon: Three dimensionally carbon allotropes comprising ultrathin diamond nanostripes, Carbon (2017), doi: 10.1016/ j.carbon.2017.10.066. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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New Metallic Carbon: Three Dimensionally Carbon Allotropes Comprising Ultrathin Diamond Nanostripes Yinqiao Liu a, Xue Jiang a*, Jie Fu a, Jijun Zhao a Key Laboratory of Materials Modification by Laser, Ion and Electron Beams (Dalian University
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a
of Technology), Ministry of Education, Dalian 116024, China
Abstract
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Metallic carbon has received long-standing attentions for its fascinating applications in superconductivity, electronic devices and high-performance anode
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materials. Here we design two types of metallic carbon phases, namely O-type and T-type carbon, using self-assembling diamond nanostripes as building block and C=C bond as linkers. These O-type and T-type allotropes are energetically more favorable than most previously identified three-dimensional (3D) metallic carbon allotropies, while their stability is confirmed by a series of first-principles calculations. Excitingly,
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these all-carbon crystals not only exhibit ultrahigh Fermi velocity and anisotropic electrical conductivity, but also belong to superhard materials with good mechanical properties. By simulating the X-ray diffraction patterns, we propose that O-type and T-type carbon would be one of the unidentified carbon phases observed in recent
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detonation experiments or shock-compression of tetracyanoethylene (TCE) powder. The good electrical conductivity, high mechanical strength, tunable electronic
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properties might find applications in electromechanical systems and nanoelectronic devices.
*
Corresponding author. Email: [email protected]. (Xue Jiang) 1
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1. Introduction Diamond, londsdaleite, graphite, fullerenes and plenty of carbon allotropies are designed and synthesized because the carbon atom has flexible bond hybridization. Those carbon allotropes with different bond types reveal different dimensionalities
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(from 0D to 3D) and diverse electronic properties (from insulator to semiconductor to conductor) [1-5]. Among them, 3D metallic carbon have received long-standing attentions because of its fascinating properties, such as superconductivity[6], negative differential resistance[7], strong phonon plasmon coupling[8] and high lithium
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capacity[9].
The investigations of 3D metallic carbon can be traced back to thirteen years ago,
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Hoffmann et al. [10] proposed elemental carbon with both ThSi2 and 3,4-connected trigonal structure (T6 carbon) [11] showing metallic form. By adding more hexagons to T6 carbon, the latter one was expanded to the T14 carbon with larger unit cell [12]. Due to the same interlocking hexagons arrangements, the metallic character was also observed in T14 carbon. Wang et al. [12] suggested that T6 and T14 were stable at
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ambient conditions and may be chemically fabricated using benzene or polyacenes molecules. Four new superlattice-type carbon allotropes with layered sp2-bonding and sp3-bonding domains with the potential applications in 3D all-carbon devices have
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been constructed[13]. Three of them have the unique electronic properties and present huge electrical anisotropy. Besides those efforts, there have been also a few works in
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searching 3D metallic carbon allotropes. For instance, H18 carbon [14], GTs and CTs [15] with fully sp2 hybridized networks, K6 [16], Hex-C18[9], and Tri-C9 carbon [17] have been predicted to be metallic. Despite these theoretical efforts, all these 3D metallic carbon phases have not
been synthesized experimentally so far. That is to say, more efforts are still needed to screen the low-energy carbon allotropes on the complex potential energy surface. In addition,
many
previous
studies
have
demonstrated
that
self-assembling
low-dimensional carbon building blocks together is an effective strategy for the bottom-up synthesis of 3D carbon [15, 18-21]. For example, it was not long before 2
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Here we design two classes of carbon allotropies by self-assembling ultrathin diamond nanostripes. These allotropes can be regarded as bulk superlattices which compose of 2D diamond tripe and a sort of sp2 junction. According to our extensive first-principles calculations, these carbon allotropes are not only dynamically,
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thermally, and mechanically stable, but also energetically prevail the previously predicted 3D metallic carbon allotropes. Moreover, they are metallic with a very high
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Fermi velocity and anisotropic electrical conductivity. Theoretical calculations of their elastic modulus, ideal strength, and hardness demonstrate good mechanical properties. Under tensile strain, some of these carbon phases can transform from metal to semimetal or to semiconductor. All these merits together make them promising candidate materials for electromechanical systems and nanoelectronic
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devices.
2. Theoretical methods
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We performed density functional theory (DFT) [22] calculations implemented in the VASP code [23, 24]. The PAW pseudopotentials [25, 26] was used to treat 2s22p2
electrons
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outermost
as
valence
electrons
of
carbon
atoms.
The
Perdew−Burke−Ernzerh of (PBE) parameterization [27] within the generalized gradient approximation (GGA) was adopted to describe the exchange and correlation interactions.
Integrations
over
the
Brillouin
zone
were
performed
using
Monkhorst-Pack grids.[28] A k-point grid of spacing 2π×0.06 Å−1 was used for the Brillouin zone integrations, and the plane-wave cutoff energy was set to 600 eV. The dynamic stability of the constructed structures was examined by phonon dispersion calculations, which were carried out using a supercell approach as implemented in the PHONONPY code.[29] 3
ACCEPTED MANUSCRIPT For each carbon crystalline phase, its second-order elastic constants (Cij) were determined using a finite strain technique [30]. More specifically, elastic constant matrices were calculated using four amplitude steps and 800 eV of energy cutoff to obtain more accurate results. The calculations of stress-strain relations were
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performed using the method in Ref.[31] This approach with a relaxed loading path has been successfully applied to the calculation of the strength of several strong solids. Hardness calculations are based on two empirical models developed by Chen et al.[32] and Jiang et al.[33], respectively, as well as a microhardness model for covalent
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3. Results and Discussions
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crystals by Gao et al. [34].
As shown in Figure 1 and Figure 2, two series of 3D diamond nanostripe assemblies are constructed. The essential idea of designing these carbon allotropes is to integrate diamond nanostripes of different thickness as building blocks. The dangling bonds of neighboring diamond nanostripe are terminated by C=C double
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bond as linkers. According to the number of atomic layer is odd or even, these 3D diamond nanostripe assemblies fall into orthorhombic (Cmmm) and tetragonal (P42/mmc) symmetries, respectively. With fixed sp2 bond as junction nodes, one can
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easily tailor the thickness of diamond nanostripe. Based on their crystal system and total number of carbon atoms per unit cell, we name them as T10, T18, T26, O12,
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O20, and O20 carbon, respectively (Figure S1 in Supplementary Data). For example, the T18 carbon consists of 9-atomic layer thick diamond nanofilm as motif and the total number of carbon atoms per unit cell is 18, while the O20 carbon consists of 10-atomic layer thick diamond nanofilm as motif and 20 carbon atoms per unit cell. As a consequence, infinite 1-D channels along the <010> axis are formed in O12, O20, O28, while in T10, T18, and T26 carbon, half of infinite 1-D channels are along <010> axis and the other half along the <001> axis. That is to say, the plane of sp2 bond between two neighboring junction area in T-type carbon are perpendicular; while in the O-type carbon, the plane of sp2 bond between two neighboring junction 4
ACCEPTED MANUSCRIPT area are parallel. Note that T10, T18, T26, O12, O20, and O28 carbon are just representative models; they are symmetric with identical and specific thick diamond nanostripe. In principle, countless 3D diamond nanostripe assemblies can be constructed from diamond nanostripes of different thickness. T10 carbon have already
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been found by Xu et al. [35] very recently, and the other five carbon phases have not been reported so far [36].
The crystallographic information for optimized crystal structures of O12, O20, O28, T10, T18 and T26 carbon are listed in Table I, including their space group,
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lattice constant, mass density, ratio of sp3 carbon atoms, and formation energy relative to diamond. For comparison, the experiment data of diamond crystal [37] are also
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given. The detailed lattice parameters and coordinates are provided in Table S1 as well. Taking O20 carbon as an example (Figure 1 and Figure 2), the carbon atoms are located at the 4h (0.464, 0, 0.5), 4g (0.13, 0, 0), 4h (0.726, 0, 0.5), and 4g (0.178, 0.5, 0) sites. The 4h (0.464, 0, 0.5) carbon atoms on the surface of diamond nanostripe form sp2 junctions, whereas the rest of carbon atoms still retain sp3 hybridization.
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With fixed sp2 junction nodes, the percentage of sp3 atoms increases with the total number of atoms in the unit cell, i.e., 60% for T10 carbon, 66.7% for O12 carbon, 77.8 % for T18 carbon, 80% for O20 carbon, 84.6% for T26 carbon, and 85.7% for O28 carbon, respectively. Owing to their high sp3 ratio, the mass density of T10, O12,
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T18, O20, O28 and T26 carbon are 3.16, 3.18, 3.31, 3.32, 3.37, and 3.37 g/cm3, respectively, which are comparable to diamond (3.49 g/cm3) and much higher than
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graphite (2.20 g/cm3). Those carbon allotropes with high density and large portion of sp3 bonding are expected to possess good mechanical properties, as we will discuss in the following.
To check the stability of our proposed metallic carbon, we calculate their total
energy, phonon dispersion, and elastic constants. Figure 3(a) displays the equations of state for all six carbon allotropes, along with graphite and diamond. Along with the cohesive energies summarized in Table I, one can see that these carbon phases are slightly less stable than graphite and diamond by only 0.1–0.3 eV/atom. As the thickness of diamond nanostripe increases, the thermodynamic stability of both O5
ACCEPTED MANUSCRIPT and T-type carbon allotropes is further enhanced and gradually approaches to the limit of diamond. For further comparison, Table SII also lists the cohesive energies for some recently proposed metallic carbon allotropes, such as Bct-4 Carbon [38], H6 Carbon [38], sp2-diamond [39], T6 [12], H18 [14], K6 [16], Tri-C9 [17] and
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Hex-C18[9]. The relative cohesive energies of O28 and T26 carbon are 0.099 eV/atom and 0.108 eV/atom, respectively, which are energetically more favorable than all previous identified 3D metallic carbon so far. Remarkably, Our O- and T-type carbon allotropes possess ~1.06 eV/atom larger cohesive energies than T-carbon,
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which has been very recently produced from pseudo-topotactic conversion of multi-walled carbon nanotube by picosencond pulsed-laser irradiation [5].
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In addition, according to the pressure–enthalpy relationship of these carbon allotropes (Figure 3(b)), we can derive T10, T18, T26, O12, O20, and O28 carbon by applying 6.85-20.65 GPa pressure to graphite. Also note that, our O- and T-type carbon allotropes and the carbon-rich compounds [40][41] [42] have a big similarity in framework to each other, which also provide us a new idea to synthesize them. In
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short, their unique atomic arrangements and favorable energy suggest that our proposed carbon allotropes might be synthesized as an intermediate metastable phase between graphite and diamond [43].
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Phonon analysis is further performed to determine the dynamic stability of these carbon allotropies, which are shown in Figure 4. There is no imaginary frequency in the phonon dispersions of all six structures throughout the entire Brillioun zone,
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indicating their dynamical stability. The mechanical stability of our proposed O/T-type carbon allotropes are confirmed by calculating their single-crystal zero-pressure elastic constants (Table II). For a stable orthorhombic/tetragonal structure, its nine/six independent elastic constants Cij should satisfy the well-known Born stability criteria [44], which are given in the Supplementary Data. Clearly, these calculated elastic constants Cij satisfy the mechanical stability criteria, confirming that T10, T18, T26, O12, O20, and O28 carbon allotropes are mechanically stable at ambient conditions. We calculate the electronic band structures to explore their electrical properties, as 6
ACCEPTED MANUSCRIPT illustrated in Figure 5. One can see that the Fermi level crosses the highest occupied band in the neighbor of R-T path for O carbon (A-M for T carbon) in the Brillouin zone. At the same time, the Fermi level also crosses the bands near the Γ and Z points, giving rise to the presence of the hole pocket around Γ and Z. Thus, all six carbon
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allotropes exhibit metallic properties. The metallicity is confirmed by recalculated the electronic band structures using a more accurate HSE06 functional (see Figure S2). On the other hand, the electronic band structures of these carbon phases also imply a high Fermi velocity comparable to graphite (~105 m/s), which are show in Table SIII.
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To understand the origin of metallic feature in these two classes of carbon allotropies, we plot the band decomposed charge density (PBDC) of T18 and O20
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carbon allotropes as representative models, which is relevant to all the energy bands intersections at the Fermi level (Figure 6(a) and 6(b)). We find the distributions of PBDC at the Fermi level mainly come from electrons of sp2 carbon atoms, which form two kinds of delocalized charge 1D channels along the direction of the sp2 hybridized C=C bond plane, while the contribution from electronic orbitals of sp3
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carbon atoms can be completely ignored. Accordingly, the O-type carbon phases show the strongest electronic conduction along the z direction, but are insulating along the x or y direction. Similarly, the strongest electronic conduction directions of
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T-type carbon phases are z and y directions, while the electron transport in the x direction is almost forbidden.
Such electronic anisotropy is in line with the features of atomic arrangements of
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carbon atoms and their electronic band structures. For example, the 1D sp2 channels of T18 carbon are separated by the diamond nanostripe of 7.03 Å thickness. Also, a finite gap (2.7 eV) for T18 carbon is observed along the Γ-Z line (Figure 5). Remarkably, the conductivity of both O and T type carbon allotropes switches from conductive to electron transport forbid and then to conductive again (Figure 6(a) and 6(b)). Such highly anisotropic conductive behaviors are important for nanoelectronic switches. Similar results are also discovered in the other four systems. However, the thickness of the diamond nanostripe will further influence the electronic conductivity in z direction; that is, the wider the diamond nanostripes, the larger electronic 7
ACCEPTED MANUSCRIPT conductivity anisotropy. Diamond is known as the hardest material in nature determined by its sp3 bonding, while the layered graphite is a soft material with sp2 hybridization. Hence, it would be interesting to investigate the mechanical properties of these carbon phases
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consisting of sp2 and sp3 mixed bonds. On basis of the Voigt-Reuss-Hill approximation [45], we obtain their corresponding bulk modulus, shear modulus, Young modulus, and Poisson’s ratio, which are listed in Table II. Obviously, our calculated modulus and Poisson’s ratio of diamond are in good agreement with the
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experimental values [37]. The calculated bulk modulus, shear modulus, and Young modulus of O/T-type carbon superlattices are 357−407 GPa, 223−398 GPa, and
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553−899 GPa, respectively, which are more than half of those of diamond (433 GPa, 520 GPa, and 1113 GPa). In addition, the bulk modulus increases with the increasing of sp3 carbon atoms. For example, the Young modulus of O28 carbon reaches 899 GPa, which is higher than those of the other five carbon phases. In term of the bulk modulus, the six carbon phases are comparable to metals with high hardness (e.g., 230
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GPa for Mo, 200 GPa for Ta, 310 GPa for W) [46].Hence, they are expected to be surperhard metal with low compressibility.
The Vickers hardnesses (Hv) of these carbon phases are evaluated using three
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different empirical models developed by Chen et al. [32], Gao et al. [34], and Jiang et al. [33], respectively. All of them have been successfully applied to many covalent superhard materials. To eliminate the systematic error due to the choice of
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methodology, we use average value for each carbon phase by the three models. As listed in Table II, the average Hv values are 41 GPa, 56 GPa, 63 GPa, 48 GPa, 59 GPa, and 66 GPa for O10, O18, O26, T12, T20, and T28 carbon, respectively. Impressively, they are comparable to that of cubic BN (65 GPa) [47]. According to the generally accepted definition that a superhard material owns Hv > 40 GPa [48], both O-type and T-type carbon allotropes can be regarded as superhard materials. The bulk modulus and hardness of those carbon phases can be decomposed into the contributions from the sp3 bonding building blocks and sp2 bonding junctions. The existence of π-π interactions between different sp2 bonding junctions softens material strength. As the 8
ACCEPTED MANUSCRIPT ratio of sp3 hybridization carbon atoms increases, the sp2 bonding becomes less significant and the values of bulk modulus and hardness will gradually approach the bulk limit of diamond crystal (433 GPa and 96 GPa, respectively). In addition, ductility and brittleness are also important for the mechanical
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behaviors, which describe the ability to change shape without fracture of a material. Low ductility/high brittleness may affect their potential applications even though they possess extreme hardness. The brittleness and ductility can be estimated by the B/G value from Frantsevich’s rule[49], and the approximate criteria for ductile-brittle
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transition is 1.75. It is clearly seen from Table II that O/T-type carbon possesses a ratio of B/G in the range from 1.02−1.6, implying that their ductility are much better
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than diamond (0.84). After comparing the ductility of O/T-type carbon phases, one can deduce that decreasing the percentage of sp3 carbon atoms may improve the ductile properties of materials. In this regard, T10 carbon exhibits the highest ductility with B/G = 1.60, which is close to the critical value of 1.75 and comparable to the B/G value of 1.62, 1.92, 2.07 for Zn, Ta and Fe, respectively[46]. The Poisson’s ratios
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also give consistent conclusion.
To better understand the engineering applications of these superhard metallic carbon, here we calculate the stresses-strain curves for our proposed six carbon phases
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under tensile and shear strains along low-index directions, such as [100], [010], [001], [110], [101], [011]. Beyond these directions, we also define a new [111]* direction to compare with the [111] oriented diamond directly. The angles between [111]*
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direction and x, y, z axis are 0°, 90°, 54.73°, respectively, as shown in the Figure 2. The turning points on the stress–strain curves can be defined as ideal tensile/shear strengths and critical fractural strain. Our computed stress–strain curves for O20 carbon under tensile strain are shown
in Figure 7(a). The ideal strength and their corresponding critical fractural strains of all six carbon allotropies are summarized in Table III. First, the ideal strengths for diamond along [100] and [111] directions are 198.7 GPa and 82.3 GPa, respectively, in good agreement with previous theoretical results (203.9 GPa and 83.8 GPa) [50]. Second, one can see that tensile stress-strain curves along [010] and [001] for O20 9
ACCEPTED MANUSCRIPT carbon show a plastic deformation relation, which is consistent with above discussion of ductility. Third, the ideal strength of O20 carbon is also strongly anisotropic like diamond. O20 carbon with [011] orientation possess the largest ideal strength of 151 GPa and critical strains of 0.31; O20 carbon with [100], [010], [001], [110] and [101]
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orientations possess intermediate ideal strengths range from 126 GPa to 84 GPa; whereas O20 with [111]* direction have the smallest ideal strength and critical strain (68 GPa and 0.14). Similarly, the weakest direction of tensile strength of O12, O20, T10, T18, T26 are also [111]* orientation with corresponding ideal strengths of 54
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GPa, 70 GPa, 40 GPa, 40 GPa and 40 GPa, respectively.
Additionally, Figure 7(b) show the stress-strain curves for O20 and T18 carbon
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along (100)[010] and (100)[001] shear directions. A largely anisotropic shear strength is also observed in our proposed metallic carbon. As shown in Table III, the peak shear stresses are 90−100 GPa along (100)[010] direction for O-type carbon, while the values are only 9−14 GPa along (100)[001]. In other words, both O-type carbon and T-type carbon can resist large/small shear deformation along the direction
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parallel/vertical to the sp2 bond plane. Hence, the failure mode in O-type carbon is dominated by the shear type in the (100)[001] direction, and the failure mode in T-type carbon is dominated by the shear type in the (100)[001] and (100)[010]
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direction. To understand their intriguing deformation mechanism and anisotropic ideal strength, we examine the charge density of O/T-type carbon under the tensile/shear strain. O20 and T18 carbon is presented as an example to clarify such phenomenon
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(Figure 8(a) and Figure 8(b)). As the tensile deformation along the [100] direction increases, the sp2 C=C bond is continuously stretched from 1.342 Å to 1.616 Å, which could finally lead to the break of sp2 C=C bond after critical strain. However under tensile loading in [111]* for T18, both bond length and bond angle of sp2 C are continuously varied, which makes a transition from sp2 carbon to sp3 carbon rather than sp2 C=C bond breaking. Under shear loading in (100)[001] for T18, the sp2 C=C bond varies could makes a transition from sp2 carbon to sp3 carbon as well. Figure 8(a) suggest that both bond breaking and bonding state transition induced deformation could also be found in the O20 carbon. The two deformation mechanisms 10
ACCEPTED MANUSCRIPT simultaneously affect the values of ideal strength and critical strain, which further result in the anisotropy of ideal strength and the observable anomalous stress response. It is interesting to mention that the ideal tensile strength and shear strength for
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our predicted metallic carbon are in the ranges of 40−70 GPa and 10−14 GPa, respectively. The ideal tensile strengths are comparable to those of c-BN (55.3 GPa) [51], B6O (53.3 GPa) [52], and ReB2 (58.5 GPa) [53], which are generally accepted as intrinsically superhard materials. As a metal, the ideal shear strengths of those 3D
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diamond nanostripe assemblies are also higher than those of common metal Al (3.4 GPa) [54], Cu (4.0 GPa) [54], Fe (6.40 GPa) [55]. Such high values of bulk modulus,
wear-resistant metal coatings.
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hardness, and ideal strength make them promising for applications in cutting tool and
It is well known that shear/tensile deformation may play an important role in the electronic properties of materials. Hence, we investigate the variation of band structures of O/T-type carbon under uniaxial tensile strains. The band structures of
in
Figure
9.
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O12, O20, and O28 carbon under critical fractural strain as representatives are shown Strain
induced
metal-semimetal,
metal-semiconductor,
and
metal-semiconductor transitions are clearly observed in the O12, O20, and O28
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carbon, respectively. At the same time, the magnitude of band gap opening highly depends on the thickness of diamond nanostripe. Under the tensile strain of 0.143, 0.143, and 0.126, the band gap of O12, O20 and O28 carbon are 0 eV, 0.300 eV, and
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0.346 eV, respectively. The band gap open rates are 0.021 eV and 0.027 eV per 0.01 strain for O20 and O28 carbon, respectively. As discussed above, the origin of metallic behavior is predominantly contributed by the pz orbitals of sp2 carbon. Tensile strain along [111]* direction leads to slipping of the sp2 planes, which reduces the π-π orbital interaction. On the other hand, tensile strain along [111]* direction will stretch the sp3 bonds, which reduce the band gap of diamond as suggested by our previous paper[56]. Thus, the change of electronic structure in the O-type carbon is a coupled effect of reduced π-π orbitals interaction and electron delocalization of sp3 bonds. However, the strain-induced band opening is not found in the T-type carbon. 11
ACCEPTED MANUSCRIPT This can be ascribed to specific symmetry of the 1D channels arrangements of T-type carbon. As stated above, 1D channels in O-type carbon are along y axis only, while 1D channels in T-type carbon are along both z and y axis. In the latter case, the slipping of sp2 planes along z and y axis would compensate π-π orbitals interaction.
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Such tunable electronic properties open an avenue for strain sensitive nanodevices. To provide more information to identify the possible existence in experiment, the simulated X-ray diffraction (XRD) patterns of the O/T-type carbon phases along with diamond, graphite, and the experimental data from detonation soot [57] and
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shock-compressed tetracyanoethylene powder [58] are compared in Figure 10. Both previous experiments reported new diffraction lines with identified carbon phases. In
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these O/T-type carbon phases, the XRD peaks of ~45° and ~75° are clearly observed, which are very similar to that of bulk diamond of (111) and (022) because the diamond nanostripes serving as the building blocks. However, the two fingerprint XRD peaks of diamond shift to higher/lower angle as the diamond nanostripes thickness increases. For (111) peaks, the diffraction angle is 43.6°, 43.4°, and 43.1°
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for O12, O20, and O28 carbon, respectively. Besides the two strongly identified fingerprint peaks, those carbon allotropes also display several peaks in the range of 35°−45° and 65−80°. Hence, it is meaningful to compare them with the unidentified
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experimental observations. On one hand, the peaks of 34.2°, 37.8°, 47.1°, 65.8°, and 79.0° of O12 carbon match well with the experimental XRD spectra from detonation soot [57] located at 35.0°, 37.6°, 45.7°, 66.5°, and 80.1°, respectively. On the other
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hand, the main peaks of 42.2°, 44.5°, and 46.9° of T26 carbon also coincide well with the experimental XRD features from shock-compressed tetracyanoethylene powder [58] (42.2°, 44.3°, and 45.7°). Hence, we suggest those O/T-type carbon phases might be
the
unidentified
carbon
phases
in
detonation
and
shock-compressed
tetracyanoethylene experiments. We have to mention that our O/T-type carbon allotropies still lack the diffraction angles around 66° in detonation soot experiment and around 83° in shock-compressed tetracyanoethylene powder experiment.
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4. Conclusion Two types of carbon allotropies named O-type carbon and T-type carbon are designed by self-assembling diamond nanostripe as building block and C=C bond as linkers. First-principles calculations are performed to predict their mechanical and
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electronic properties. In these proposed structures, sp3 hybridized carbon atoms guarantee their mechanical and dynamical stability, while sp2 hybridized carbon atoms ensure their metallicity. These carbon phases are energetically more stable than most previously predicted metallic carbon allotropies. Moreover, the computed ideal
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strength and elastic modulus demonstrate superior mechanical strength, moderate ductility, and high hardness. More excitingly, electron structure calculations illustrate
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their anisotropic metallic conductivity, high Fermi velocity, and tunable electronic properties by strain. The origins of those unique mechanical/electronic properties have been thoroughly discussed. These new carbon allotropies with high stability, robust metallicity, high Fermi velocity and high hardness would stimulate applications in novel all-carbon devices, such as electromechanical devices under
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working condition of high stress, nanoelectronic switches, and nano-sensors.
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Acknowledgement
This work is supported by the National Natural Science Foundation of China
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(11404050) and the Fundamental Research Funds for the Central Universities of China (DUT16RC(4)50, DUT16JJ(G)05, DUT16LAB01, DUT17LAB19). We also acknowledge the Supercomputing Center of Dalian University of Technology for providing the computing resource.
Appendix A. Supplementary data
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Figure 1. Schematic illustration of the formation of the 3D diamond nanostripes
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assemblies.
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Figure 2. Crystallographic direction using O20 and T18 as representative models
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Figure 3. (a) The equations of state of O12, O20, O28, T10, T18, T26 carbon, graphite and diamond, respectively. (b) The enthalpies per atom of various carbon phases relative to graphite.
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at zero pressure.
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Figure 4. The phonon dispersion relations of (a) O-type carbon and (b) T-type carbon
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Figure 5. Electron band structures of (a) O-type and (b) T-type carbon structures. The
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valence bands and conduction bands are shown in black and blue lines, respectively.
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Figure 6. Band structures and PBDC of (a) O20 carbon and (b) T18 carbon. (The PBDC is distributions of partial band decomposed charge density with isovalue of 3e-5 level at various k-points around the Fermi level, which are directed by the blue arrows.)
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Figure 7. (a) Calculated stress versus tensile strain for O20 carbon (b) Calculated stress versus shear strain for O20/T18, in principal symmetry directions.
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(b)
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Figure 8. The charge density of (a) O20 at free strian (S0), at strain 0.18 (S1) during tensiling along the [100] path, at strain 0.14 (S2) during tensiling along the [111]*
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path and at strain 0.11 (S3) during shearing along the (100)[001] path; and (b) T18 carbon at free strian (S0), at strain 0.19 (S1) during tensiling along the [100] path, at strain 0.08 (S2) during tensiling along the [111]* path and at strain 0.06 (S3) during shearing along the (100)[001] path..
21
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Figure 9. The band structures of O12, O20, and O28 carbon under critical fractural
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strain.
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Figure 10. Simulated XRD patterns for O-type carbon allotropies, T-type carbon allotropies, diamond and graphite, comparing experimental XRD pattern for the detonation soot of TNT (sample Alaska B) [57] and shock-compressed tetracyanoethylene powder (TEC)[58]. The X-ray wavelength we adopted for simulation is 1.54 Å. 23
ACCEPTED MANUSCRIPT Table I. The space group, lattice constant (Å), density (g/cm3), ratio of sp3 atoms, and relative energy (eV) to diamond phase of O-type and T-type carbon allotropes at ambient pressure (values in parenthesis are the experimental data of diamond[37]). Space group Lattice constant Mass Density Ratio 3
(Å) Diamond Fd3തm
O12
Cmmm
(g/cm )
a=3.5757
3.490
(a=3.5682)
(3.512)
a=11.3650
3.183
c=2.62440 O20
Cmmm
(eV) 100%
0
66.7% 0.219
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b=2.5160
∆E
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Name
a=18.5192
3.316
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b=2.5206
80%
0.139
c=2.5696 O28
Cmmm
a=25.6762
3.370
85.7% 0.099
3.157
60%
3.310
77.8% 0.157
3.367
84.6% 0.108
b=2.5221 c=2.5513 T10
P42/mmc
a=9.6009
0.286
c=2.5577 P42/mmc
a=16.7595
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T18
c=2.5399
T26
P42/mmc
a=23.9055
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c=2.5347
24
ACCEPTED MANUSCRIPT Table II. Calculated elastic constants (Cij), bulk modulus (B), shear modulus (G) Young modulus(E), Poisson’s ratio(ν), ratio of B/G and hardness (Hv, based on average value by the three models of Chen et al.[32] , Jiang et al.[33] and Gao et al. [34], respectively.) of O-type carbon, T-type carbon and diamond. The values in
B/G are dimensionless). C12
1049
125
C13
C23
C22
C33
C44
C55
C66
558
(1067) (132)
B
G
433 520
(571)
E
ν
B/G
Hv
1113
0.07
0.84
96.1
(444) (527 (1133) (0.07) (0.84) (95.7)
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Diamond
C11
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parenthesis are the experimental data of diamond[37] (all in unit of GPa except ν and
1086
148
94
16
1141
647
215
101
523
362 294
695
0.18
1.23
48
O20
1048
131
179
43
1145
649
310
161
537
382 351
806
0.15
1.09
59.2
O28
1154
132
133
31
1069
T10
724
90
140
T18
919
28
158
T26
976
41
148
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O12
208
541
404 398
899
0.13
1.02
66
1093
150
183
357 223
553
0.24
1.6
41.3
1054
259
297
394 324
764
0.18
1.22
55.9
1055
317
347
407 369
851
0.15
1.1
62.6
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864
25
355
ACCEPTED MANUSCRIPT Table III. Calculated ideal strength for O-type and T-type carbon allotropes with the corresponding strain at which the maximum stress (GPa) occurs. [100]
[111]*
Stress(GPa)
Strain
Stress(GPa)
Strain
Stress(GPa)
Diamond
0.31
198.7
0.25
115.2
0.14
82.3
O12
0.19
136.4
0.28
121.9
0.14
54.4
O20
0.16
126.3
0.28
152.7
O28
0.16
129.8
0.31
169.0
T10
0.21
124.3
0.47
159.5
T18
0.16
127.9
0.41
176.8
T26
0.16
130.5
0.41
184.6
(100)[001]
(100)[010]
Stress(GPa)
Strain
Stress(GPa)
O12
0.16
14.2
0.25
105.7
O20
0.10
12.6
0.22
96.5
O28
0.08
12.6
0.22
94.1
T10
0.08
9.6
−
−
T18
0.06
11.1
−
−
T26
0.04
12.4
−
−
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Strain
Shear
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Strain
26
0.14
67.9
0.13
69.7
0.08
40.1
0.06
40.5
0.06
40.5
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Tensile
[011]
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S0008-6223(17)31022-9
DOI:
10.1016/j.carbon.2017.10.066
Reference:
CARBON 12493
To appear in:
Carbon
Received Date: 14 September 2017 Revised Date:
8 October 2017
Accepted Date: 9 October 2017
Please cite this article as: Y. Liu, X. Jiang, J. Fu, J. Zhao, New metallic carbon: Three dimensionally carbon allotropes comprising ultrathin diamond nanostripes, Carbon (2017), doi: 10.1016/ j.carbon.2017.10.066. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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New Metallic Carbon: Three Dimensionally Carbon Allotropes Comprising Ultrathin Diamond Nanostripes Yinqiao Liu a, Xue Jiang a*, Jie Fu a, Jijun Zhao a Key Laboratory of Materials Modification by Laser, Ion and Electron Beams (Dalian University
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a
of Technology), Ministry of Education, Dalian 116024, China
Abstract
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Metallic carbon has received long-standing attentions for its fascinating applications in superconductivity, electronic devices and high-performance anode
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materials. Here we design two types of metallic carbon phases, namely O-type and T-type carbon, using self-assembling diamond nanostripes as building block and C=C bond as linkers. These O-type and T-type allotropes are energetically more favorable than most previously identified three-dimensional (3D) metallic carbon allotropies, while their stability is confirmed by a series of first-principles calculations. Excitingly,
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these all-carbon crystals not only exhibit ultrahigh Fermi velocity and anisotropic electrical conductivity, but also belong to superhard materials with good mechanical properties. By simulating the X-ray diffraction patterns, we propose that O-type and T-type carbon would be one of the unidentified carbon phases observed in recent
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detonation experiments or shock-compression of tetracyanoethylene (TCE) powder. The good electrical conductivity, high mechanical strength, tunable electronic
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properties might find applications in electromechanical systems and nanoelectronic devices.
*
Corresponding author. Email: [email protected]. (Xue Jiang) 1
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1. Introduction Diamond, londsdaleite, graphite, fullerenes and plenty of carbon allotropies are designed and synthesized because the carbon atom has flexible bond hybridization. Those carbon allotropes with different bond types reveal different dimensionalities
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(from 0D to 3D) and diverse electronic properties (from insulator to semiconductor to conductor) [1-5]. Among them, 3D metallic carbon have received long-standing attentions because of its fascinating properties, such as superconductivity[6], negative differential resistance[7], strong phonon plasmon coupling[8] and high lithium
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capacity[9].
The investigations of 3D metallic carbon can be traced back to thirteen years ago,
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Hoffmann et al. [10] proposed elemental carbon with both ThSi2 and 3,4-connected trigonal structure (T6 carbon) [11] showing metallic form. By adding more hexagons to T6 carbon, the latter one was expanded to the T14 carbon with larger unit cell [12]. Due to the same interlocking hexagons arrangements, the metallic character was also observed in T14 carbon. Wang et al. [12] suggested that T6 and T14 were stable at
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ambient conditions and may be chemically fabricated using benzene or polyacenes molecules. Four new superlattice-type carbon allotropes with layered sp2-bonding and sp3-bonding domains with the potential applications in 3D all-carbon devices have
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been constructed[13]. Three of them have the unique electronic properties and present huge electrical anisotropy. Besides those efforts, there have been also a few works in
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searching 3D metallic carbon allotropes. For instance, H18 carbon [14], GTs and CTs [15] with fully sp2 hybridized networks, K6 [16], Hex-C18[9], and Tri-C9 carbon [17] have been predicted to be metallic. Despite these theoretical efforts, all these 3D metallic carbon phases have not
been synthesized experimentally so far. That is to say, more efforts are still needed to screen the low-energy carbon allotropes on the complex potential energy surface. In addition,
many
previous
studies
have
demonstrated
that
self-assembling
low-dimensional carbon building blocks together is an effective strategy for the bottom-up synthesis of 3D carbon [15, 18-21]. For example, it was not long before 2
ACCEPTED MANUSCRIPT our group reported 3D graphene monoliths (GMs) on the basis of 3D architectures comprising graphene sheets [18]. These GMs possess high surface areas, appreciable mechanical strength, and tunable band gaps, solving the problems of zero gap and dimensionality of graphene sheets simultaneously.
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Here we design two classes of carbon allotropies by self-assembling ultrathin diamond nanostripes. These allotropes can be regarded as bulk superlattices which compose of 2D diamond tripe and a sort of sp2 junction. According to our extensive first-principles calculations, these carbon allotropes are not only dynamically,
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thermally, and mechanically stable, but also energetically prevail the previously predicted 3D metallic carbon allotropes. Moreover, they are metallic with a very high
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Fermi velocity and anisotropic electrical conductivity. Theoretical calculations of their elastic modulus, ideal strength, and hardness demonstrate good mechanical properties. Under tensile strain, some of these carbon phases can transform from metal to semimetal or to semiconductor. All these merits together make them promising candidate materials for electromechanical systems and nanoelectronic
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devices.
2. Theoretical methods
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We performed density functional theory (DFT) [22] calculations implemented in the VASP code [23, 24]. The PAW pseudopotentials [25, 26] was used to treat 2s22p2
electrons
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outermost
as
valence
electrons
of
carbon
atoms.
The
Perdew−Burke−Ernzerh of (PBE) parameterization [27] within the generalized gradient approximation (GGA) was adopted to describe the exchange and correlation interactions.
Integrations
over
the
Brillouin
zone
were
performed
using
Monkhorst-Pack grids.[28] A k-point grid of spacing 2π×0.06 Å−1 was used for the Brillouin zone integrations, and the plane-wave cutoff energy was set to 600 eV. The dynamic stability of the constructed structures was examined by phonon dispersion calculations, which were carried out using a supercell approach as implemented in the PHONONPY code.[29] 3
ACCEPTED MANUSCRIPT For each carbon crystalline phase, its second-order elastic constants (Cij) were determined using a finite strain technique [30]. More specifically, elastic constant matrices were calculated using four amplitude steps and 800 eV of energy cutoff to obtain more accurate results. The calculations of stress-strain relations were
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performed using the method in Ref.[31] This approach with a relaxed loading path has been successfully applied to the calculation of the strength of several strong solids. Hardness calculations are based on two empirical models developed by Chen et al.[32] and Jiang et al.[33], respectively, as well as a microhardness model for covalent
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3. Results and Discussions
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crystals by Gao et al. [34].
As shown in Figure 1 and Figure 2, two series of 3D diamond nanostripe assemblies are constructed. The essential idea of designing these carbon allotropes is to integrate diamond nanostripes of different thickness as building blocks. The dangling bonds of neighboring diamond nanostripe are terminated by C=C double
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bond as linkers. According to the number of atomic layer is odd or even, these 3D diamond nanostripe assemblies fall into orthorhombic (Cmmm) and tetragonal (P42/mmc) symmetries, respectively. With fixed sp2 bond as junction nodes, one can
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easily tailor the thickness of diamond nanostripe. Based on their crystal system and total number of carbon atoms per unit cell, we name them as T10, T18, T26, O12,
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O20, and O20 carbon, respectively (Figure S1 in Supplementary Data). For example, the T18 carbon consists of 9-atomic layer thick diamond nanofilm as motif and the total number of carbon atoms per unit cell is 18, while the O20 carbon consists of 10-atomic layer thick diamond nanofilm as motif and 20 carbon atoms per unit cell. As a consequence, infinite 1-D channels along the <010> axis are formed in O12, O20, O28, while in T10, T18, and T26 carbon, half of infinite 1-D channels are along <010> axis and the other half along the <001> axis. That is to say, the plane of sp2 bond between two neighboring junction area in T-type carbon are perpendicular; while in the O-type carbon, the plane of sp2 bond between two neighboring junction 4
ACCEPTED MANUSCRIPT area are parallel. Note that T10, T18, T26, O12, O20, and O28 carbon are just representative models; they are symmetric with identical and specific thick diamond nanostripe. In principle, countless 3D diamond nanostripe assemblies can be constructed from diamond nanostripes of different thickness. T10 carbon have already
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been found by Xu et al. [35] very recently, and the other five carbon phases have not been reported so far [36].
The crystallographic information for optimized crystal structures of O12, O20, O28, T10, T18 and T26 carbon are listed in Table I, including their space group,
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lattice constant, mass density, ratio of sp3 carbon atoms, and formation energy relative to diamond. For comparison, the experiment data of diamond crystal [37] are also
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given. The detailed lattice parameters and coordinates are provided in Table S1 as well. Taking O20 carbon as an example (Figure 1 and Figure 2), the carbon atoms are located at the 4h (0.464, 0, 0.5), 4g (0.13, 0, 0), 4h (0.726, 0, 0.5), and 4g (0.178, 0.5, 0) sites. The 4h (0.464, 0, 0.5) carbon atoms on the surface of diamond nanostripe form sp2 junctions, whereas the rest of carbon atoms still retain sp3 hybridization.
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With fixed sp2 junction nodes, the percentage of sp3 atoms increases with the total number of atoms in the unit cell, i.e., 60% for T10 carbon, 66.7% for O12 carbon, 77.8 % for T18 carbon, 80% for O20 carbon, 84.6% for T26 carbon, and 85.7% for O28 carbon, respectively. Owing to their high sp3 ratio, the mass density of T10, O12,
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T18, O20, O28 and T26 carbon are 3.16, 3.18, 3.31, 3.32, 3.37, and 3.37 g/cm3, respectively, which are comparable to diamond (3.49 g/cm3) and much higher than
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graphite (2.20 g/cm3). Those carbon allotropes with high density and large portion of sp3 bonding are expected to possess good mechanical properties, as we will discuss in the following.
To check the stability of our proposed metallic carbon, we calculate their total
energy, phonon dispersion, and elastic constants. Figure 3(a) displays the equations of state for all six carbon allotropes, along with graphite and diamond. Along with the cohesive energies summarized in Table I, one can see that these carbon phases are slightly less stable than graphite and diamond by only 0.1–0.3 eV/atom. As the thickness of diamond nanostripe increases, the thermodynamic stability of both O5
ACCEPTED MANUSCRIPT and T-type carbon allotropes is further enhanced and gradually approaches to the limit of diamond. For further comparison, Table SII also lists the cohesive energies for some recently proposed metallic carbon allotropes, such as Bct-4 Carbon [38], H6 Carbon [38], sp2-diamond [39], T6 [12], H18 [14], K6 [16], Tri-C9 [17] and
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Hex-C18[9]. The relative cohesive energies of O28 and T26 carbon are 0.099 eV/atom and 0.108 eV/atom, respectively, which are energetically more favorable than all previous identified 3D metallic carbon so far. Remarkably, Our O- and T-type carbon allotropes possess ~1.06 eV/atom larger cohesive energies than T-carbon,
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which has been very recently produced from pseudo-topotactic conversion of multi-walled carbon nanotube by picosencond pulsed-laser irradiation [5].
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In addition, according to the pressure–enthalpy relationship of these carbon allotropes (Figure 3(b)), we can derive T10, T18, T26, O12, O20, and O28 carbon by applying 6.85-20.65 GPa pressure to graphite. Also note that, our O- and T-type carbon allotropes and the carbon-rich compounds [40][41] [42] have a big similarity in framework to each other, which also provide us a new idea to synthesize them. In
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short, their unique atomic arrangements and favorable energy suggest that our proposed carbon allotropes might be synthesized as an intermediate metastable phase between graphite and diamond [43].
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Phonon analysis is further performed to determine the dynamic stability of these carbon allotropies, which are shown in Figure 4. There is no imaginary frequency in the phonon dispersions of all six structures throughout the entire Brillioun zone,
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indicating their dynamical stability. The mechanical stability of our proposed O/T-type carbon allotropes are confirmed by calculating their single-crystal zero-pressure elastic constants (Table II). For a stable orthorhombic/tetragonal structure, its nine/six independent elastic constants Cij should satisfy the well-known Born stability criteria [44], which are given in the Supplementary Data. Clearly, these calculated elastic constants Cij satisfy the mechanical stability criteria, confirming that T10, T18, T26, O12, O20, and O28 carbon allotropes are mechanically stable at ambient conditions. We calculate the electronic band structures to explore their electrical properties, as 6
ACCEPTED MANUSCRIPT illustrated in Figure 5. One can see that the Fermi level crosses the highest occupied band in the neighbor of R-T path for O carbon (A-M for T carbon) in the Brillouin zone. At the same time, the Fermi level also crosses the bands near the Γ and Z points, giving rise to the presence of the hole pocket around Γ and Z. Thus, all six carbon
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allotropes exhibit metallic properties. The metallicity is confirmed by recalculated the electronic band structures using a more accurate HSE06 functional (see Figure S2). On the other hand, the electronic band structures of these carbon phases also imply a high Fermi velocity comparable to graphite (~105 m/s), which are show in Table SIII.
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To understand the origin of metallic feature in these two classes of carbon allotropies, we plot the band decomposed charge density (PBDC) of T18 and O20
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carbon allotropes as representative models, which is relevant to all the energy bands intersections at the Fermi level (Figure 6(a) and 6(b)). We find the distributions of PBDC at the Fermi level mainly come from electrons of sp2 carbon atoms, which form two kinds of delocalized charge 1D channels along the direction of the sp2 hybridized C=C bond plane, while the contribution from electronic orbitals of sp3
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carbon atoms can be completely ignored. Accordingly, the O-type carbon phases show the strongest electronic conduction along the z direction, but are insulating along the x or y direction. Similarly, the strongest electronic conduction directions of
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T-type carbon phases are z and y directions, while the electron transport in the x direction is almost forbidden.
Such electronic anisotropy is in line with the features of atomic arrangements of
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carbon atoms and their electronic band structures. For example, the 1D sp2 channels of T18 carbon are separated by the diamond nanostripe of 7.03 Å thickness. Also, a finite gap (2.7 eV) for T18 carbon is observed along the Γ-Z line (Figure 5). Remarkably, the conductivity of both O and T type carbon allotropes switches from conductive to electron transport forbid and then to conductive again (Figure 6(a) and 6(b)). Such highly anisotropic conductive behaviors are important for nanoelectronic switches. Similar results are also discovered in the other four systems. However, the thickness of the diamond nanostripe will further influence the electronic conductivity in z direction; that is, the wider the diamond nanostripes, the larger electronic 7
ACCEPTED MANUSCRIPT conductivity anisotropy. Diamond is known as the hardest material in nature determined by its sp3 bonding, while the layered graphite is a soft material with sp2 hybridization. Hence, it would be interesting to investigate the mechanical properties of these carbon phases
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consisting of sp2 and sp3 mixed bonds. On basis of the Voigt-Reuss-Hill approximation [45], we obtain their corresponding bulk modulus, shear modulus, Young modulus, and Poisson’s ratio, which are listed in Table II. Obviously, our calculated modulus and Poisson’s ratio of diamond are in good agreement with the
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experimental values [37]. The calculated bulk modulus, shear modulus, and Young modulus of O/T-type carbon superlattices are 357−407 GPa, 223−398 GPa, and
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553−899 GPa, respectively, which are more than half of those of diamond (433 GPa, 520 GPa, and 1113 GPa). In addition, the bulk modulus increases with the increasing of sp3 carbon atoms. For example, the Young modulus of O28 carbon reaches 899 GPa, which is higher than those of the other five carbon phases. In term of the bulk modulus, the six carbon phases are comparable to metals with high hardness (e.g., 230
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GPa for Mo, 200 GPa for Ta, 310 GPa for W) [46].Hence, they are expected to be surperhard metal with low compressibility.
The Vickers hardnesses (Hv) of these carbon phases are evaluated using three
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different empirical models developed by Chen et al. [32], Gao et al. [34], and Jiang et al. [33], respectively. All of them have been successfully applied to many covalent superhard materials. To eliminate the systematic error due to the choice of
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methodology, we use average value for each carbon phase by the three models. As listed in Table II, the average Hv values are 41 GPa, 56 GPa, 63 GPa, 48 GPa, 59 GPa, and 66 GPa for O10, O18, O26, T12, T20, and T28 carbon, respectively. Impressively, they are comparable to that of cubic BN (65 GPa) [47]. According to the generally accepted definition that a superhard material owns Hv > 40 GPa [48], both O-type and T-type carbon allotropes can be regarded as superhard materials. The bulk modulus and hardness of those carbon phases can be decomposed into the contributions from the sp3 bonding building blocks and sp2 bonding junctions. The existence of π-π interactions between different sp2 bonding junctions softens material strength. As the 8
ACCEPTED MANUSCRIPT ratio of sp3 hybridization carbon atoms increases, the sp2 bonding becomes less significant and the values of bulk modulus and hardness will gradually approach the bulk limit of diamond crystal (433 GPa and 96 GPa, respectively). In addition, ductility and brittleness are also important for the mechanical
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behaviors, which describe the ability to change shape without fracture of a material. Low ductility/high brittleness may affect their potential applications even though they possess extreme hardness. The brittleness and ductility can be estimated by the B/G value from Frantsevich’s rule[49], and the approximate criteria for ductile-brittle
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transition is 1.75. It is clearly seen from Table II that O/T-type carbon possesses a ratio of B/G in the range from 1.02−1.6, implying that their ductility are much better
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than diamond (0.84). After comparing the ductility of O/T-type carbon phases, one can deduce that decreasing the percentage of sp3 carbon atoms may improve the ductile properties of materials. In this regard, T10 carbon exhibits the highest ductility with B/G = 1.60, which is close to the critical value of 1.75 and comparable to the B/G value of 1.62, 1.92, 2.07 for Zn, Ta and Fe, respectively[46]. The Poisson’s ratios
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also give consistent conclusion.
To better understand the engineering applications of these superhard metallic carbon, here we calculate the stresses-strain curves for our proposed six carbon phases
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under tensile and shear strains along low-index directions, such as [100], [010], [001], [110], [101], [011]. Beyond these directions, we also define a new [111]* direction to compare with the [111] oriented diamond directly. The angles between [111]*
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direction and x, y, z axis are 0°, 90°, 54.73°, respectively, as shown in the Figure 2. The turning points on the stress–strain curves can be defined as ideal tensile/shear strengths and critical fractural strain. Our computed stress–strain curves for O20 carbon under tensile strain are shown
in Figure 7(a). The ideal strength and their corresponding critical fractural strains of all six carbon allotropies are summarized in Table III. First, the ideal strengths for diamond along [100] and [111] directions are 198.7 GPa and 82.3 GPa, respectively, in good agreement with previous theoretical results (203.9 GPa and 83.8 GPa) [50]. Second, one can see that tensile stress-strain curves along [010] and [001] for O20 9
ACCEPTED MANUSCRIPT carbon show a plastic deformation relation, which is consistent with above discussion of ductility. Third, the ideal strength of O20 carbon is also strongly anisotropic like diamond. O20 carbon with [011] orientation possess the largest ideal strength of 151 GPa and critical strains of 0.31; O20 carbon with [100], [010], [001], [110] and [101]
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orientations possess intermediate ideal strengths range from 126 GPa to 84 GPa; whereas O20 with [111]* direction have the smallest ideal strength and critical strain (68 GPa and 0.14). Similarly, the weakest direction of tensile strength of O12, O20, T10, T18, T26 are also [111]* orientation with corresponding ideal strengths of 54
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GPa, 70 GPa, 40 GPa, 40 GPa and 40 GPa, respectively.
Additionally, Figure 7(b) show the stress-strain curves for O20 and T18 carbon
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along (100)[010] and (100)[001] shear directions. A largely anisotropic shear strength is also observed in our proposed metallic carbon. As shown in Table III, the peak shear stresses are 90−100 GPa along (100)[010] direction for O-type carbon, while the values are only 9−14 GPa along (100)[001]. In other words, both O-type carbon and T-type carbon can resist large/small shear deformation along the direction
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parallel/vertical to the sp2 bond plane. Hence, the failure mode in O-type carbon is dominated by the shear type in the (100)[001] direction, and the failure mode in T-type carbon is dominated by the shear type in the (100)[001] and (100)[010]
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direction. To understand their intriguing deformation mechanism and anisotropic ideal strength, we examine the charge density of O/T-type carbon under the tensile/shear strain. O20 and T18 carbon is presented as an example to clarify such phenomenon
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(Figure 8(a) and Figure 8(b)). As the tensile deformation along the [100] direction increases, the sp2 C=C bond is continuously stretched from 1.342 Å to 1.616 Å, which could finally lead to the break of sp2 C=C bond after critical strain. However under tensile loading in [111]* for T18, both bond length and bond angle of sp2 C are continuously varied, which makes a transition from sp2 carbon to sp3 carbon rather than sp2 C=C bond breaking. Under shear loading in (100)[001] for T18, the sp2 C=C bond varies could makes a transition from sp2 carbon to sp3 carbon as well. Figure 8(a) suggest that both bond breaking and bonding state transition induced deformation could also be found in the O20 carbon. The two deformation mechanisms 10
ACCEPTED MANUSCRIPT simultaneously affect the values of ideal strength and critical strain, which further result in the anisotropy of ideal strength and the observable anomalous stress response. It is interesting to mention that the ideal tensile strength and shear strength for
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our predicted metallic carbon are in the ranges of 40−70 GPa and 10−14 GPa, respectively. The ideal tensile strengths are comparable to those of c-BN (55.3 GPa) [51], B6O (53.3 GPa) [52], and ReB2 (58.5 GPa) [53], which are generally accepted as intrinsically superhard materials. As a metal, the ideal shear strengths of those 3D
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diamond nanostripe assemblies are also higher than those of common metal Al (3.4 GPa) [54], Cu (4.0 GPa) [54], Fe (6.40 GPa) [55]. Such high values of bulk modulus,
wear-resistant metal coatings.
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hardness, and ideal strength make them promising for applications in cutting tool and
It is well known that shear/tensile deformation may play an important role in the electronic properties of materials. Hence, we investigate the variation of band structures of O/T-type carbon under uniaxial tensile strains. The band structures of
in
Figure
9.
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O12, O20, and O28 carbon under critical fractural strain as representatives are shown Strain
induced
metal-semimetal,
metal-semiconductor,
and
metal-semiconductor transitions are clearly observed in the O12, O20, and O28
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carbon, respectively. At the same time, the magnitude of band gap opening highly depends on the thickness of diamond nanostripe. Under the tensile strain of 0.143, 0.143, and 0.126, the band gap of O12, O20 and O28 carbon are 0 eV, 0.300 eV, and
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0.346 eV, respectively. The band gap open rates are 0.021 eV and 0.027 eV per 0.01 strain for O20 and O28 carbon, respectively. As discussed above, the origin of metallic behavior is predominantly contributed by the pz orbitals of sp2 carbon. Tensile strain along [111]* direction leads to slipping of the sp2 planes, which reduces the π-π orbital interaction. On the other hand, tensile strain along [111]* direction will stretch the sp3 bonds, which reduce the band gap of diamond as suggested by our previous paper[56]. Thus, the change of electronic structure in the O-type carbon is a coupled effect of reduced π-π orbitals interaction and electron delocalization of sp3 bonds. However, the strain-induced band opening is not found in the T-type carbon. 11
ACCEPTED MANUSCRIPT This can be ascribed to specific symmetry of the 1D channels arrangements of T-type carbon. As stated above, 1D channels in O-type carbon are along y axis only, while 1D channels in T-type carbon are along both z and y axis. In the latter case, the slipping of sp2 planes along z and y axis would compensate π-π orbitals interaction.
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Such tunable electronic properties open an avenue for strain sensitive nanodevices. To provide more information to identify the possible existence in experiment, the simulated X-ray diffraction (XRD) patterns of the O/T-type carbon phases along with diamond, graphite, and the experimental data from detonation soot [57] and
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shock-compressed tetracyanoethylene powder [58] are compared in Figure 10. Both previous experiments reported new diffraction lines with identified carbon phases. In
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these O/T-type carbon phases, the XRD peaks of ~45° and ~75° are clearly observed, which are very similar to that of bulk diamond of (111) and (022) because the diamond nanostripes serving as the building blocks. However, the two fingerprint XRD peaks of diamond shift to higher/lower angle as the diamond nanostripes thickness increases. For (111) peaks, the diffraction angle is 43.6°, 43.4°, and 43.1°
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for O12, O20, and O28 carbon, respectively. Besides the two strongly identified fingerprint peaks, those carbon allotropes also display several peaks in the range of 35°−45° and 65−80°. Hence, it is meaningful to compare them with the unidentified
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experimental observations. On one hand, the peaks of 34.2°, 37.8°, 47.1°, 65.8°, and 79.0° of O12 carbon match well with the experimental XRD spectra from detonation soot [57] located at 35.0°, 37.6°, 45.7°, 66.5°, and 80.1°, respectively. On the other
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hand, the main peaks of 42.2°, 44.5°, and 46.9° of T26 carbon also coincide well with the experimental XRD features from shock-compressed tetracyanoethylene powder [58] (42.2°, 44.3°, and 45.7°). Hence, we suggest those O/T-type carbon phases might be
the
unidentified
carbon
phases
in
detonation
and
shock-compressed
tetracyanoethylene experiments. We have to mention that our O/T-type carbon allotropies still lack the diffraction angles around 66° in detonation soot experiment and around 83° in shock-compressed tetracyanoethylene powder experiment.
12
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4. Conclusion Two types of carbon allotropies named O-type carbon and T-type carbon are designed by self-assembling diamond nanostripe as building block and C=C bond as linkers. First-principles calculations are performed to predict their mechanical and
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electronic properties. In these proposed structures, sp3 hybridized carbon atoms guarantee their mechanical and dynamical stability, while sp2 hybridized carbon atoms ensure their metallicity. These carbon phases are energetically more stable than most previously predicted metallic carbon allotropies. Moreover, the computed ideal
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strength and elastic modulus demonstrate superior mechanical strength, moderate ductility, and high hardness. More excitingly, electron structure calculations illustrate
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their anisotropic metallic conductivity, high Fermi velocity, and tunable electronic properties by strain. The origins of those unique mechanical/electronic properties have been thoroughly discussed. These new carbon allotropies with high stability, robust metallicity, high Fermi velocity and high hardness would stimulate applications in novel all-carbon devices, such as electromechanical devices under
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working condition of high stress, nanoelectronic switches, and nano-sensors.
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Acknowledgement
This work is supported by the National Natural Science Foundation of China
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(11404050) and the Fundamental Research Funds for the Central Universities of China (DUT16RC(4)50, DUT16JJ(G)05, DUT16LAB01, DUT17LAB19). We also acknowledge the Supercomputing Center of Dalian University of Technology for providing the computing resource.
Appendix A. Supplementary data
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Figure 1. Schematic illustration of the formation of the 3D diamond nanostripes
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assemblies.
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Figure 2. Crystallographic direction using O20 and T18 as representative models
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(b)
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(a)
Figure 3. (a) The equations of state of O12, O20, O28, T10, T18, T26 carbon, graphite and diamond, respectively. (b) The enthalpies per atom of various carbon phases relative to graphite.
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(a)
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(b)
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at zero pressure.
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Figure 4. The phonon dispersion relations of (a) O-type carbon and (b) T-type carbon
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(a)
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(b)
Figure 5. Electron band structures of (a) O-type and (b) T-type carbon structures. The
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valence bands and conduction bands are shown in black and blue lines, respectively.
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(a)
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(b)
Figure 6. Band structures and PBDC of (a) O20 carbon and (b) T18 carbon. (The PBDC is distributions of partial band decomposed charge density with isovalue of 3e-5 level at various k-points around the Fermi level, which are directed by the blue arrows.)
19
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(a)
(b)
Figure 7. (a) Calculated stress versus tensile strain for O20 carbon (b) Calculated stress versus shear strain for O20/T18, in principal symmetry directions.
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(a)
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(b)
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Figure 8. The charge density of (a) O20 at free strian (S0), at strain 0.18 (S1) during tensiling along the [100] path, at strain 0.14 (S2) during tensiling along the [111]*
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path and at strain 0.11 (S3) during shearing along the (100)[001] path; and (b) T18 carbon at free strian (S0), at strain 0.19 (S1) during tensiling along the [100] path, at strain 0.08 (S2) during tensiling along the [111]* path and at strain 0.06 (S3) during shearing along the (100)[001] path..
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Figure 9. The band structures of O12, O20, and O28 carbon under critical fractural
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strain.
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Figure 10. Simulated XRD patterns for O-type carbon allotropies, T-type carbon allotropies, diamond and graphite, comparing experimental XRD pattern for the detonation soot of TNT (sample Alaska B) [57] and shock-compressed tetracyanoethylene powder (TEC)[58]. The X-ray wavelength we adopted for simulation is 1.54 Å. 23
ACCEPTED MANUSCRIPT Table I. The space group, lattice constant (Å), density (g/cm3), ratio of sp3 atoms, and relative energy (eV) to diamond phase of O-type and T-type carbon allotropes at ambient pressure (values in parenthesis are the experimental data of diamond[37]). Space group Lattice constant Mass Density Ratio 3
(Å) Diamond Fd3തm
O12
Cmmm
(g/cm )
a=3.5757
3.490
(a=3.5682)
(3.512)
a=11.3650
3.183
c=2.62440 O20
Cmmm
(eV) 100%
0
66.7% 0.219
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b=2.5160
∆E
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Name
a=18.5192
3.316
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b=2.5206
80%
0.139
c=2.5696 O28
Cmmm
a=25.6762
3.370
85.7% 0.099
3.157
60%
3.310
77.8% 0.157
3.367
84.6% 0.108
b=2.5221 c=2.5513 T10
P42/mmc
a=9.6009
0.286
c=2.5577 P42/mmc
a=16.7595
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T18
c=2.5399
T26
P42/mmc
a=23.9055
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c=2.5347
24
ACCEPTED MANUSCRIPT Table II. Calculated elastic constants (Cij), bulk modulus (B), shear modulus (G) Young modulus(E), Poisson’s ratio(ν), ratio of B/G and hardness (Hv, based on average value by the three models of Chen et al.[32] , Jiang et al.[33] and Gao et al. [34], respectively.) of O-type carbon, T-type carbon and diamond. The values in
B/G are dimensionless). C12
1049
125
C13
C23
C22
C33
C44
C55
C66
558
(1067) (132)
B
G
433 520
(571)
E
ν
B/G
Hv
1113
0.07
0.84
96.1
(444) (527 (1133) (0.07) (0.84) (95.7)
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Diamond
C11
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parenthesis are the experimental data of diamond[37] (all in unit of GPa except ν and
1086
148
94
16
1141
647
215
101
523
362 294
695
0.18
1.23
48
O20
1048
131
179
43
1145
649
310
161
537
382 351
806
0.15
1.09
59.2
O28
1154
132
133
31
1069
T10
724
90
140
T18
919
28
158
T26
976
41
148
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O12
208
541
404 398
899
0.13
1.02
66
1093
150
183
357 223
553
0.24
1.6
41.3
1054
259
297
394 324
764
0.18
1.22
55.9
1055
317
347
407 369
851
0.15
1.1
62.6
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864
25
355
ACCEPTED MANUSCRIPT Table III. Calculated ideal strength for O-type and T-type carbon allotropes with the corresponding strain at which the maximum stress (GPa) occurs. [100]
[111]*
Stress(GPa)
Strain
Stress(GPa)
Strain
Stress(GPa)
Diamond
0.31
198.7
0.25
115.2
0.14
82.3
O12
0.19
136.4
0.28
121.9
0.14
54.4
O20
0.16
126.3
0.28
152.7
O28
0.16
129.8
0.31
169.0
T10
0.21
124.3
0.47
159.5
T18
0.16
127.9
0.41
176.8
T26
0.16
130.5
0.41
184.6
(100)[001]
(100)[010]
Stress(GPa)
Strain
Stress(GPa)
O12
0.16
14.2
0.25
105.7
O20
0.10
12.6
0.22
96.5
O28
0.08
12.6
0.22
94.1
T10
0.08
9.6
−
−
T18
0.06
11.1
−
−
T26
0.04
12.4
−
−
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Strain
Shear
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Strain
26
0.14
67.9
0.13
69.7
0.08
40.1
0.06
40.5
0.06
40.5
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Tensile
[011]
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