Mechanically ductile 3D spsp 2 microporous carbon


A new spsp 2-hybridized tetragonal carbon allotrope, namely Tetra-carbon, is predicted through the evolutionary particle swarm structural search. Tetra-carbon has a 3D framework composed of sp 2 carbon helixes connected by linear sp carbon chains, similar to the interconnected network of propadienyl groups, which forms the well-proportioned microporous structure. Tetra-carbon is thermodynamically more stable than known graphdiyne and carbyne carbon and also shows mechanical and dynamic stabilities at ambient pressure. Tetra-carbon is a semiconductor with an indirect band gap of 3.27 eV and has anisotropic tensile strengths with an unexpected large tensile strain of 0.64 along the [001] direction. Base on the analysis of Poisson’s ratios as well as the tensile strains, it is significantly revealed that Tetra-carbon is a mechanically ductile microporous carbon allotrope in contrast with the known brittle carbons such as diamond, potentially applied in the fields where the ductile metals are available.

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  1. 1

    Hu M, Pan Y, Luo K, He J, Yu D, Xu B (2015) Three dimensional graphdiyne polymers with tunable band gaps. Carbon 91:518–526

    Article  Google Scholar 

  2. 2

    Pan Y, Hu M, Ma M, Li Z, Gao Y, Xiong M, Gao G, Zhao Z, Tian Y, Xu B (2017) Multithreaded conductive carbon: 1D conduction in 3D carbon. Carbon 115:584–588

    Article  Google Scholar 

  3. 3

    Li G, Li Y, Liu H, Guo Y, Li Y, Zhu D (2010) Architecture of graphdiyne nanoscale films. Chem Commun 46:3256–3258

    Article  Google Scholar 

  4. 4

    Kang B, Lee JY (2015) Electronic properties of α-graphyne nanotubes. Carbon 84:246–253

    Article  Google Scholar 

  5. 5

    Hu M, Jing Y, Zhang X (2015) Low thermal conductivity of graphyne nanotubes from molecular dynamics study. Phys Rev B 91:155408

    Article  Google Scholar 

  6. 6

    Wang J-T, Chen C, Li H-D, Mizuseki H, Kawazoe Y (2016) Three-dimensional carbon allotropes comprising phenyl rings and acetylenic chains in sp + sp2 hybrid networks. Sci Rep 6:24665-1–24665-9

    Google Scholar 

  7. 7

    Hongxia B, Mingwen Z, Yan X, Xiaopeng W, Hua P, Chunlei W, Xiangdong L (2012) Is yne-diamond a super-hard material? EPL 100:56003-p1–56003-p6

    Google Scholar 

  8. 8

    Hu M, Huang Q, Zhao Z, Xu B, Yu D, He J (2014) Superhard and high-strength yne-diamond semimetals. Diam Relat Mater 46:15–20

    Article  Google Scholar 

  9. 9

    Weimer M, Hieringer W, Della Sala F, Görling A (2005) Electronic and optical properties of functionalized carbon chains with the localized Hartree–Fock and conventional Kohn-Sham methods. Chem Phys 309:77–87

    Article  Google Scholar 

  10. 10

    Tabata H, Fujii M, Hayashi S, Doi T, Wakabayashi T (2006) Raman and surface-enhanced Raman scattering of a series of size-separated polyynes. Carbon 44:3168–3176

    Article  Google Scholar 

  11. 11

    Lucotti A, Tommasini M, Del Zoppo M, Castiglioni C, Zerbi G, Cataldo F, Casari C, Bassi AL, Russo V, Bogana M (2006) Raman and SERS investigation of isolated sp carbon chains. Chem Phys Lett 417:78–82

    Article  Google Scholar 

  12. 12

    Wang Y, Lv J, Zhu L, Ma Y (2010) Crystal structure prediction via particle-swarm optimization. Phys Rev B 82:094116-1–094116-8

    Article  Google Scholar 

  13. 13

    Kohn W, Sham LJ (1965) Self-consistent equations including exchange and correlation effects. Phys Rev 140:A1133–A1138

    Article  Google Scholar 

  14. 14

    Hohenberg P, Kohn W (1964) Inhomogeneous electron gas. Phys Rev 136:B864–B871

    Article  Google Scholar 

  15. 15

    Segall M, Lindan PJ, Probert MA, Pickard C, Hasnip P, Clark S, Payne M (2002) First-principles simulation: ideas, illustrations and the CASTEP code. J Phys Condens Matter 14:2717–2744

    Article  Google Scholar 

  16. 16

    Jones RO, Gunnarsson O (1989) The density functional formalism, its applications and prospects. Rev Mod Phys 61:689–746

    Article  Google Scholar 

  17. 17

    Monkhorst HJ, Pack JD (1976) Special points for Brillouin-zone integrations. Phys Rev B 13:5188–5192

    Article  Google Scholar 

  18. 18

    Fischer TH, Almlof J (1992) General methods for geometry and wave function optimization. J Phys Chem 96:9768–9774

    Article  Google Scholar 

  19. 19

    Heyd J, Scuseria GE, Ernzerhof M (2003) Hybrid functionals based on a screened Coulomb potential. J Chem Phys 118:8207–8215

    Article  Google Scholar 

  20. 20

    Heyd J, Scuseria GE, Ernzerhof M (2006) Erratum: “Hybrid functionals based on a screened Coulomb potential”[J. Chem. Phys. 118, 8207 (2003)]. J Chem Phys 124:219906-1

    Article  Google Scholar 

  21. 21

    Ducéré J-M, Lepetit C, Chauvin R (2013) Carbo-graphite: structural, mechanical, and electronic properties. J Phys Chem C 117:21671–21681

    Article  Google Scholar 

  22. 22

    Wu Z-J, Zhao E-J, Xiang H-P, Hao X-F, Liu X-J, Meng J (2007) Crystal structures and elastic properties of superhard Ir N 2 and Ir N 3 from first principles. Phys Rev B 76:054115-1–054115-15

    Google Scholar 

  23. 23

    Li Z, Hu M, Ma M, Gao Y, Xu B, He J, Yu D, Tian Y, Zhao Z (2016) Superhard superstrong carbon clathrate. Carbon 105:151–155

    Article  Google Scholar 

  24. 24

    Becke AD, Edgecombe KE (1990) A simple measure of electron localization in atomic and molecular systems. J Chem Phys 92:5397–5403

    Article  Google Scholar 

  25. 25

    Lee C, Wei X, Kysar JW, Hone J (2008) Measurement of the elastic properties and intrinsic strength of monolayer graphene. Science 321:385–388

    Article  Google Scholar 

  26. 26

    Pugh SF (1954) XCII. Relations between the elastic moduli and the plastic properties of polycrystalline pure metals. Philos Mag 45:823–843

    Article  Google Scholar 

  27. 27

    Xiaoju G, Li-Min W, Bo X, Zhongyuan L, Dongli Y, Julong H, Hui-Tian W, Yongjun T (2009) Unbinding force of chemical bonds and tensile strength in strong crystals. J Phys Condens Matter 21:485405-1–485405-5

    Article  Google Scholar 

  28. 28

    Lott WA, Christiansen WG (2010) Propadiene. J Pharm Sci 20:207–209

    Google Scholar 

  29. 29

    Scholten JP, Ploeg HJVD (1973) Polymerization of propadiene. IV. Kinetics and mechanism of polymerization under the influence of rhodium(I) complexes. J Polym Sci A 11:3205–3213

    Google Scholar 

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This work was supported by National Natural Science Foundation of China (NSFC) (51421091, 51472213, 51332005, 51525205, and 51672238).

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Correspondence to Zhisheng Zhao.

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Liu, L., Hu, M., Pan, Y. et al. Mechanically ductile 3D spsp 2 microporous carbon. J Mater Sci 53, 4316–4322 (2018).

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  • Butatriene
  • Graphdiyne
  • Carbon Allotropes
  • Carbyne Carbon
  • Large Tensile Strains