Chiral Pentagon Only Diamond-like Structures - The Journal of

Subscriber access provided by Binghamton University | Libraries

Article

Chiral Pentagon Only Diamond-like Structure Xi Zhu, and Haibin Su J. Phys. Chem. C, Just Accepted Manuscript • Publication Date (Web): 31 May 2017 Downloaded from http://pubs.acs.org on June 1, 2017

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

The Journal of Physical Chemistry C is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 17

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

The Journal of Physical Chemistry

Chiral Pentagon Only Diamond-like Structures Xi Zhu,† Haibin Su†,* †

Institute of Advanced Studies,

Nanyang Technological University, 60 Nanyang View, Singapore 639673, Singapore *

To whom correspondence should be addressed. Emails: [email protected];

Abstract Two novel full carbon chiral enantiomers, the CHiral Pentagon Only Diamond-like Structures (CHIPODS) are predicted with space groups P6122 and P6522. The enantiomers can be generated by interlayer covalent bonds in multi-layer penta-graphene. Both structures are energetically favorable than their precursor, penta-graphene. The crystal structures of CHIPODS exhibit intriguing 3D space filling only with pentagons. The mass density (3.24 g/cm3) of CHIPODS is lighter than that in diamond (3.51 g/cm3). CHIPODS is a semiconductor with a bandgap of 5.7 eV, comparable to diamond’s gap (5.5 eV). Moreover, the tensile and shear strain-stress simulation results demonstrate that CHIPODS are harder than the diamond in the means of ideal strength. This work highlights the importance of structural transformation from carbon layered structures to novel carbon allotropes, similar strategy can be applied to other two dimensional materials.

ACS Paragon Plus Environment


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

Introduction Carbon is one of the most versatile elements on earth1. Most of the carbon allotropes have six membered carbon rings due to the sp2 or sp3 carbon bonding character, like diamond, graphite, graphene, carbon nanotubs, fullerene etc, and these kinds of carbon structures are of great interests in both fundamental and applied research. The known full carbon of chiral symmetry materials include chiral fullerene2, chiral carbon nanotubes (CNTs) 3, which have attractive circular dichroism response properties. Many novel carbon allotropes are proposed with detail structures in the bulk form, such as carbon clathrates,4 monoclinic M-carbon,5 body-centered tetragonal C4-carbon,6 cubic T-carbon7, tetragonal T12-carbon,8 metallic K4 carbon,9 and other phases 10-19; as well as in nano structure forms including carbon nanocone20, carbon nanochain21 and graphdiyne22, etc. Recently, penta-graphene, penta-nanotubes, and related 3D structure of T12-carbon were reported by Zhang et al23. Inspired by high pressure enantiomeric phases of scandium (Sc) with space groups P61222 and P65222 at 240 GPa24, we would like to search carbon structures with chiral space groups to extend reported full carbon chiral structures.25-26 In this work, by introducing the inter-layer interaction in the multi-layer penta-graphene, we propose two novel enantiomeric CHIPODS material with space groups P61222 and P65222, by forming additional pentagons between the inter-layers of penta-graphene. The CHIPODS crystal is mechanically and kinetically stable and with a mass density 3.24 g/cm3. The tensile and shear strain-stress calculations demonstrate that this CHIPODS is even harder than diamond. Methods The calculations were carried out using the density functional theory (DFT)27 as implemented in the Abinit code28. We use Generalized Gradient Approximation (GGA) with Perdew-Burke-Ernzerhof (PBE) functional29 for exchange and correlation, and Norm-conserving pseudopotentials were used during the calculations. The plane wave basis set with kinetic energy cut-off of 40 Ha is used, a smallest allowed Kspacing 0.02 Åିଵ is used for the Gamma-centered K-points grid to sample Brillouin zone. The structure are fully optimized with lattice till the maximal force is converged to 1×10-5 eV/Å, the G0W0 methods30 is used to provide a better value of band gap which is usually underestimated by GGA. Results and discussion The penta-graphene23 is a mono-layer quasi-two dimensional carbon allotrope . There are two type of carbon atoms, 3-fold sp2 and 4-fold sp3 carbons as shown in gray and blue in Figure 1(a). Due to the existence of the 3-fold carbon atoms, the adjacent layers could be covalently bonded between multilayer penta-graphene. By sliding along direction in XY-plane from AA to AB stacking, the distance


Page 2 of 17

Page 3 of 17

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


between the 3-fold carbon atoms in the adjacent penta-graphene layers plane decreases, as shown in Figure 1(a). The subsequent formation of covalent bonds between 3-fold carbon atoms results in novel chiral carbon structures, CHIPODS with five-membered rings along the inter-layer direction, as shown in Figure 1(b). All pentagons of CHIPODS are identical with two sp3 bonds with lengths of 1.56 Å (red colored) and 1.54 Å (yellow colored) , This Peierls-like pattern by forming distorted sp3 bonds with two bond lengths gains 10 meV per unit cell with respect to the structure with equal bond length. The computed potential energy landscape of the aforementioned transformation is presented in Figure 1(c).The energy barrier of interlayer sliding is only 0.02 eV per atom which suggests CHIPODS can be obtained directly from multi-layer penta-graphene with proper stacking order. The electron localization function (ELF) of the CHIPODS is plotted in Figure 1(d), which is very close to the ELF of pure sp3 bonds in diamond (SI appendix S2). Interestingly, the sliding direction determines the chirality of the 3D bulk phases with space groups of P65222 and P61222 as shown in Figure 2(a). The unit cell contains 6 carbon atoms, and each carbon atom is shared by 5 different pentagons, as shown in the inserted figure in Figure 2(a). The 5 carbon atoms in each pentagon are not plenary, leading to observable variations in bond length and bond angles. It possesses two kinds of bond lengths (1.56 Å and 1.54 Å), and three kinds of bond angles (107.2º, 105.2º and 106.3º). Usually the pentagon carbon will suffer from the stress for untypical sp3 or sp2 hybridization, however, in this CHIPODS, both the bonds lengths and bond angles are close to the canonical sp3 hybridization in diamond, indicating the appreciable stability of this structure. Figure 2(b) shows the supercell of the CHIPODS structure (take the P65222 for example), where the helical carbon units illustrate the basic chirality in CHIPODS as presented in Figure 2(b1); and the pentagons of CHIPODS can be better viewed in Figure 2(b2). Mathematically, in 2D plane, only 15 convex pentagon types can cover the full plane, which the 15th pattern was reported by Casey et al in August 201531. The crystal structure of penta-graphene consists of nonplanar pentagons. Importantly, the pentagon only scheme cannot fully cover the 2D space. In penta-graphene the unit cell includes one pentagon plus an additional carbon (SI appendix S3). When the basic unit has the pentagon shape, due to the special property of 5-fold symmetry, 3D space cannot be fully filled. Figure 2(c) shows the adamantane like local structure in diamond32. The adamantane like local structure is made of 4 identical cyclohexanes with chair conformation. Thus, in diamond structure, the basic unit is 6-membered nonplanar ring. For the CHIPODS, the local structures inside the green boundary is a basic unit cell, as highlighted in red, the blue ones represent the nearby extensions. From the side view as shown in Figure 2(d), we can see this basic unit are composed of pentagons, which are tilted along the screw axis. This pentagon based local structure is not a closed object along the c axis. Along this screw axis direction, there is no truncated faces in the basic repeat unit cell, the size of hexagon pattern is comparable to that of



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

chair-cyclohexanes inside the diamond. We can see the basic repeat unit in CHIPODS is nanowire like with periodic screw structures along the c axis.

We summarize representative carbon structures, diamond, lonsdaleite, and CHIPODS, in Table 1, including space group, lattice constant, mass density, formation energy, energy gap, bulk and shear moduli. The lattice parameter of CHIPODS is very close to that of the diamond, and the mass density value is lower than that of the diamond and lonsdaleite. The formation energies among these three carbon structures are also very close. The bulk modulus of CHIPODS is about 391 GPa, smaller than that of the diamond and lonsdaleite Similar to the diamond, the CHIPODS is also a wide gap semiconductor (SI appendix S4). Figure 3(a) presents the formation energy per atom among reported carbon allotropes. The CHIPODS are energetic favorable than many other reported carbon allotropes (the detail information of all the structures are shown in SI appendix S5). Despite the penta-graphene and CHIPODS are stable phases, the penta-graphene phase is in a much higher energy state, about 0.91 eV/atom higher than graphite. Thus, this CHIPODS structure has good potential to be synthesized experimentally.36 Figure 3(b) plots the phonon band structure along the high-symmetry q-point paths in the first Brillouin zone (BZ) which shows no modes with imaginary frequency, indicating the excellent stability of CHIPODS (all the normal mode eigenvector are shown in SI appendix S6). Different from the diamond, in the zone center, the highest phonon mode with energy 1223cm-1 which is slightly redshifted as compared with that of the diamond (around 1303 cm-1). This is caused by the existence of longer C-C bonds involved in this vibration in CHIPODS. Figure 3(c) shows the energy-volume per atom curve for the diamond, graphite, penta-graphene and CHIPODS. The CHIPODS remains to be stable even it is compressed to half of its volume, where the pressure reaches as high as 800GPa. To check the structure stability under high temperature, we perform NVT molecular dynamics simulations at 1000K and 2000K, respectively (SI appendix S7). The CHIPODS keeps its structural integrity within 100ps, at both 1000K and 2000K, indicating the remarkable thermal stability of this CHIPODS material. Besides the inter-layer interaction of penta-graphene, the CHIPODS can be transformed from other carbon nanostructures as well. For example, the reported 8-membered rings defects in graphene (structure A) as shown in Figure 3(d),37 can be transformed into CHIPODS through several intermediate structures. The structure A is a bulk structure with 4-, 6-, and 8-membered rings. First, 4-6 rings is converted into 5-5 rings by the transition state (structure 2) possessing 0.15 eV/atom barrier height, resulting in a planar structure 3 (structure B) which consists of 5- and 8-membered rings only. Then through the inter-layer coupling, additional 5-membered rings are formed by adjoining 3-fold carbon atoms, as marked by the yellow lines in the transition state (structure 4) with 0.1 eV/per atom barrier height, leading to the CHIPODS structure with space groups of


Page 4 of 17

Page 5 of 17

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


P65222. From the structure transformations in both Figure 1 and Figure 3, the inter-layer interaction is critical to form the CHIPODS structures. Recently, there is also some work about synthesizing distortion of saddle-shaped isomer38, which could provide alternative transformation routes to bulk CHIPODS materials. Lastly, we characterize the ideal strength of the CHIPODS as compared with the diamond. The computed tensile stress-strain curves are presented in Figure 4(a). The calculated stress-strain curve of diamond along direction shows that when the tensile strain reaches about 0.15 with the critical stress value around 90 GPa, the diamond will collapse into graphite (structure T1). For the CHIPODS, the weakest direction in terms of mechanical strength is along direction, where the maximal tensile stress can reach 100 GPa at 0.18 tensile strain. And when the strain reaches 0.26, the structure breaks into pentagraphene (structure T4). The CHIPODS is harder than the diamond due to the fact that the inter-layer bonds in CHIPODS along is shorter in bond length and stronger in bond energy than that in diamond (SI appendix S9). Moreover, when deforming CHIPODS along and directions, the maximal stress can be even higher, as large as 115 GPa and 155 GPa, much larger than that of the diamond along and directions. For CHIPODS, the tensile beyond the threshold will break the structure into penta-graphene (structure T3) along the , and the 6-fold helical carbon atomic wires (structure T2) along the direction. If we focus on the helical chains in the CHIPODS crystal structure, as shown in Figure 2(b1), this tensile strain extends the length of the helical chain, breaks the inter-chain bonds, while keeping intra-chain bonds. Interestingly, this T2 structure can revert back to the bulk CHIPODS, just like a carbon spring as shown in SI appendix S10. Next, we calculated the shear stress-strain as shown in Figure 4(b). The computed shear stress-strain of (111) in diamond shows that the structure can maintain its integrity up to 0.23 shear strain with the maximal shear stress of 92 GPa, beyond which the structure breaks into layered structure, i.e. graphite (structure T1) as shown in Figure 4(c). In contrast, the critical shear strain of (210) in CHIPODS can reach 0.48 with the maximal shear stress 102 GPa. Subsequently, the bulk structures is sheared into the layered structure i.e. pentagraphene (structure T4) as shown in Figure 4(d). Therefore, CHIPODS exhibits more shear resistant than diamond. Under shear deformation of (210) in CHIPODS, the inter-layer bonds (the yellow colored bonds shown in Figure 2 (b2)) is 0.01Å shorter than that in diamond which determines the ideal shear strength. Interestingly, both bulk and shear moduli of CHIPODS are smaller than that of diamond. This seemingly contradictory can be also found in previous work.39 For instance, although the bulk modulus of wurtzite BN (374 GPa) is smaller than that of diamond (444 GPa)40 , the wurtzite BN can keep its structural stability at a pressure of 152 GPa, much higher than 97 GPa in diamond.39 Thus, stress-



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

strain simulations yield a better measure in terms of ideal mechanical strength as compared with the extrapolation from bulk and shear moduli values. Conclusion To summary, we propose that the AB stacked penta-graphene can form a novel chiral bulk carbon structure, CHIPODS, with space group P6522 and P6122, by promoting inter-layer covalent bonds. The CHIPODS has excellent mechanical properties, with higher ideal strength than diamond. This work sheds light on rational design of novel bulk materials through forming covalent bonds between building units in materials with low dimensions.

Supporting Information Electron localization function for the AA stacked of penta-graphene; electron localization function and projected density of states of CHIPODS and diamond; 2D space filling by graphene and penta-graphene; G0W0 corrected band structure of CHIPODS; Table of carbon allotropes studied in this work; eigenvectors and frequencies of phonons of CHIPODS; Potential energy of CHIPODS in NVT molecular dynamical simulations; XRD patterns of diamond, lansdaleite and CHIPODS; projected structures along direction of CHIPODS, and direction of diamond; reversible structural transformation under tensile deformation along direction of CHIPODS Acknowledgement We are grateful to Professors Yoshiyuki Kawazoe and Pulickel Ajayan for enlightening discussions. The work was supported in part by MOE Tier-2 grants (no. MOE2013-T2-2-049; MOE2013-T2-2-002) and Society of Interdisciplinary Research (SOIRÉE).


Page 6 of 17

Page 7 of 17

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


Table 1, The space group, lattice parameters, mass density (ߩ), formation energy (Eform), bulk modulus (B), and shear modulus (G) of Diamond, Lonsdaleite (wurtzite diamond), and CHIPODS. The data in parenthesis are from reference papers.

Structures

Space Group

Lattice parameters (Å)

Fd-3m

Lonsdaleite

P63/mmc

a=2.50,c=4.17

P6522

a=3.57,c=3.38

P6122

a=3.57,c=3.38

CHIPODS

(eV) 7.76

a=3.56

Diamond

(3.57)

Eform

33

(8.17)

34

ߩ (g/cm3)

B (GPa)

G (GPa)

3.52

464

501

(3.52)

7.73

3.52

7.65

3.24


33

(442)

33

(535)35

430

530

391

491

391

491


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

Figure 1: (a) Top and side views of the AA and AB stacked penta-graphene. The orange arrows in the side view indicates the 3-fold carbon atoms to form covalent bonds afterwards. (b) The structure formed by covalently bonded adjacent layers. (c) Transformation pathways from AA stacked penta-graphene to CHIPODS. (d) Electron localization function plot of CHIPODS. The grey balls represent carbon atoms, and electrons forming covalent bonds are distributed between adjacent carbon atoms.


Page 8 of 17

Page 9 of 17

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


Figure 2 (a) Enantiomer structures of CHIPODS with space groups of P6522 and P6122 structure; (b) supercell views with basic chiral unit (b1), inter-layer bonds (b2); (c) supercell structures of diamond (projected along direction) and CHIPODS (projected along direction).



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

Page 10 of 17

Figure 3: (a) Formation energy per carbon atom of carbon allotropes; (b) phonon dispersion in CHIPODS. (c) energy-volume relation of diamond, graphite, longsdaleite, CHIPODS and penta-graphene, together with two structures indicated in (d), i.e. A and B; (d) transformation pathways from one chiral carbon allotrope to CHIPODS. The 4-, 6-, 5- and 8-membered rings are colored by green, pink, red and blue. The red arrows show directions to form covalent bonds.


Page 11 of 17

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


Figure 4: (a, b) Tensile strain-stress relation along , and in diamond, and along , , in CHIPODS; (c) tensile deformation along , shear deformation of (111) in diamond; (d) tensile deformations along , , , and shear deformation of (210) in CHIPODS.



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

Page 12 of 17

Reference 1. Antonietti, M.; Müllen, K., Carbon: The Sixth Element. Adv. Mater. 2010, 22, 787-787. 2. Maroto, E. E.; Izquierdo, M.; Reboredo, S.; Marco-Martínez, J.; Filippone, S.; Martín, N., Chiral Fullerenes from Asymmetric Catalysis. Acc. Chem. Res. 2014, 47, 2660-2670. 3. Saito, R.; Dresselhaus, G. D.; Dresselhaus, M.; Physical Properties of Carbon Nanotubes. Imperial College Press 1998. 4. Wang, J.-T.; Chen, C.; Wang, D.-S.; Mizuseki, H.; Kawazoe, Y., Phase Stability of Carbon Clathrates at High Pressure. J. Appl. Phys. 2010, 107, 063507. 5. Li, Q.; Ma, Y.; Oganov, A. R.; Wang, H.; Wang, H.; Xu, Y.; Cui, T.; Mao, H.-K.; Zou, G., Superhard Monoclinic Polymorph of Carbon. Phys. Rev. Lett. 2009, 102, 175506. 6. Umemoto, K.; Wentzcovitch, R. M.; Saito, S.; Miyake, T., Body-Centered Tetragonal C4: A Viable Sp3 Carbon Allotrope. Phys. Rev. Lett. 2010, 104, 125504. 7. Sheng, X.-L.; Yan, Q.-B.; Ye, F.; Zheng, Q.-R.; Su, G., T-Carbon: A Novel Carbon Allotrope. Phys. Rev. Lett. 2011, 106, 155703. 8. Zhao, Z., et al., Tetragonal Allotrope of Group 14 Elements. J. Am. Chem. Soc. 2012, 134, 1236212365. 9. Itoh, M.; Kotani, M.; Naito, H.; Sunada, T.; Kawazoe, Y.; Adschiri, T., New Metallic Carbon Crystal. Phys. Rev. Lett. 2009, 102, 055703. 10. Jo, J. Y.; Kim, B. G., Carbon Allotropes with Triple Bond Predicted by First-Principle Calculation: Triple Bond Modified Diamond and T-Carbon. Phys.Rev.B 2012, 86, 075151. 11. Wang, J.-T.; Chen, C.; Wang, E.; Kawazoe, Y., A New Carbon Allotrope with Six-Fold Helical Chains in All-Sp2 Bonding Networks. Sci Rep 2014, 4, 4339. 12. Wang, J.-T.; Chen, C.; Kawazoe, Y., New Carbon Allotropes with Helical Chains of Complementary Chirality Connected by Ethene-Type Π-Conjugation. Sci Rep 2013, 3, 3077. 13. Johnston, R. L.; Hoffmann, R., Superdense Carbon, C8: Supercubane or Analog Of .Gamma.Silicon? J. Am. Chem. Soc. 1989, 111, 810-819. 14. Zhang, S.; Wang, Q.; Chen, X.; Jena, P., Stable Three-Dimensional Metallic Carbon with Interlocking Hexagons. Proc. Natl. Acad. Sci. 2013, 110, 18809-18813. 15. Rignanese, G. M.; Charlier, J. C., Hypothetical Three-Dimensional All-Sp2 Carbon Phase. Phys.Rev.B 2008, 78, 125415. 16. He, C.; Zhang, C. X.; Xiao, H.; Meng, L.; Zhong, J. X., New Candidate for the Simple Cubic Carbon Sample Shock-Synthesized by Compression of the Mixture of Carbon Black and Tetracyanoethylene. Carbon 2017, 112, 91-96. 17. Li, D., et al., Cubic C96: A Novel Carbon Allotrope with a Porous Nanocube Network. J. Mater. Chem. A 2015, 3, 10448-10452. 18. Wang, J.-T.; Chen, C.; Kawazoe, Y., Orthorhombic Carbon Allotrope of Compressed Graphite: Ab Initio Calculations. Phys.Rev.B 2012, 85, 033410. 19. Amsler, M., et al., Crystal Structure of Cold Compressed Graphite. Phys. Rev. Lett. 2012, 108, 065501. 20. Charlier, J.-C.; Rignanese, G.-M., Electronic Structure of Carbon Nanocones. Phys. Rev. Lett. 2001, 86, 5970-5973. 21. Jin, C.; Lan, H.; Peng, L.; Suenaga, K.; Iijima, S., Deriving Carbon Atomic Chains from Graphene. Phys. Rev. Lett. 2009, 102, 205501. 22. Zhou, J., et al., Synthesis of Graphdiyne Nanowalls Using Acetylenic Coupling Reaction. J. Am. Chem. Soc. 2015, 137, 7596-7599. 23. Zhang, S.; Zhou, J.; Wang, Q.; Chen, X.; Kawazoe, Y.; Jena, P., Penta-Graphene: A New Carbon Allotrope. Proc. Natl. Acad. Sci. 2015, 112, 2372-2377.


Page 13 of 17

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


24. Akahama, Y.; Fujihisa, H.; Kawamura, H., New Helical Chain Structure for Scandium at 240 Gpa. Phys. Rev. Lett. 2005, 94, 195503. 25. Deringer, V. L.; Csányi, G.; Proserpio, D. M., Extracting Crystal Chemistry from Amorphous Carbon Structures. ChemPhysChem 2017, 18, 873-877. 26. Pickard, C. J.; Needs, R. J., Hypothetical Low-Energy Chiral Framework Structure of Group 14 Elements. Phys. Rev. B 2010, 81, 014106. 27. Hohenberg, P.; Kohn, W., Inhomogeneous Electron Gas. Phys. Rev. 1964, 136, B864-B871. 28. Gonze, X., et al., Abinit: First-Principles Approach to Material and Nanosystem Properties. Comput. Phys. Commun. 2009, 180, 2582-2615. 29. Perdew, J. P.; Burke, K.; Ernzerhof, M., Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1996, 77, 3865-3868. 30. Onida, G.; Reining, L.; Rubio, A., Electronic Excitations: Density-Functional Versus Many-Body Green's-Function Approaches. Rev. Mod. Phys. 2002, 74, 601-659. 31. Casey Mann, J. M.-M., David Von Derau, Convex Pentagons That Admit I-Block Transitive Tilings. arXiv:1510.01186 [math.MG] 2015. 32. von R. Schleyer, P., A Simple Preparation of Adamantane. J. Am. Chem. Soc. 1957, 79, 3292-3292. 33. McSkimin, H. J.; Bond, W. L., Elastic Moduli of Diamond. Phys. Rev. 1957, 105, 116-121. 34. Kittel, C., Introduction to Solid State Physics. Wiley 1996. 35. McSkimin, H. J.; Jr., P. A., Elastic Moduli of Diamond as a Function of Pressure and Temperature. J. Appl. Phys. 1972, 43, 2944-2948. 36. Ewels, C. P.; Rocquefelte, X.; Kroto, H. W.; Rayson, M. J.; Briddon, P. R.; Heggie, M. I., Predicting Experimentally Stable Allotropes: Instability of Penta-Graphene. Proc. Natl. Acad. Sci. 2015, 112, 1560915612. 37. Robertson, A. W.; Allen, C. S.; Wu, Y. A.; He, K.; Olivier, J.; Neethling, J.; Kirkland, A. I.; Warner, J. H., Spatial Control of Defect Creation in Graphene at the Nanoscale. Nat Commun 2012, 3, 1144. 38. Fujikawa, T.; Segawa, Y.; Itami, K., Synthesis and Structural Features of Quadruple Helicenes: Highly Distorted Π Systems Enabled by Accumulation of Helical Repulsions. J. Am. Chem. Soc. 2016, 138, 3587-3595. 39. Pan, Z.; Sun, H.; Zhang, Y.; Chen, C., Harder Than Diamond: Superior Indentation Strength of Wurtzite Bn and Lonsdaleite. Phys. Rev. Lett. 2009, 102, 055503. 40. Kim, E.; Chen, C., First-Principles Study of Phase Stability of BN under Pressure. Phys. Lett. A 2003, 319, 384-389.



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

423x226mm (72 x 72 DPI)


Page 14 of 17

Page 15 of 17

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


127x58mm (300 x 300 DPI)



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

127x81mm (300 x 300 DPI)


Page 16 of 17

Page 17 of 17

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


127x84mm (300 x 300 DPI)


Chiral Pentagon Only Diamond-like Structures - The Journal of

Recommend Documents