High Pressure Synthesis of the Carbon Allotrope Hexagonite with Carbon Nanotubes in a Diamond Anvil Cell

  • Michael J. Bucknum
  • Eduardo A. Castro
Part of the Carbon Materials: Chemistry and Physics book series (CMCP, volume 5)


In a previous report, the approximate crystalline structure and electronic structure of a novel, hypothetical hexagonal carbon allotrope has been disclosed. Employing the approximate extended Hückel method, this C structure was determined to be a semi-conducting structure. In contrast, a state-of-the-art density functional theory (DFT) optimization reveals the hexagonal structure to be metallic in band profile. It is built upon a bicyclo[2.2.2]-2,5,7-octatriene (barrelene) generating fragment molecule, and is a Catalan network, with the Wells point symbol (66)2(63)3 and the corresponding Schläfli symbol (6, 3.4). As the network is entirely composed of hexagons and, in addition, possesses hexagonal symmetry, lying in space group P6/mmm (space group #191), it has been given the name hexagonite. The present report describes a density functional theory (DFT) optimization of the lattice parameters of the parent hexagonite structure, with the result giving the optimized lattice parameters of a = 0.477 nm and c = 0.412 nm. A calculation is then reported of a simple diffraction pattern of hexagonite from these optimized lattice parameters, with Bragg spacings enumerated for the lattice out to fourth order. Results of a synchrotron diffraction study of carbon nanotubes which underwent cold compression in a diamond anvil cell (DAC) to 100 GPa, in which the carbon nanotubes have evidently collapsed into a hitherto unknown hexagonal C polymorph, are then compared to the calculated diffraction pattern for the DFT optimized hexagonite structure. It is seen that a close fit is obtained to the experimental data, with a standard deviation over the five matched reflections being given by σx = 0.003107 nm/reflection.


Density Functional Theory Diamond Anvil Cell Infinite Family Carbon Allotrope Ultrasoft Pseudopotentials 
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MJB thanks his wife Hsi-cheng Shen for much love and patience in his work on C allotropy and the subtle structural issues of C. The authors wish to thank Norman Goldberg, PhD for producing the structural drawings of hexagonite while a post-doctoral associate in Professor Roald Hoffmann’s theoretical chemistry group at Cornell University. The authors wish to thank Chris J. Pickard, PhD of the Theoretical Condensed Matter (TCM) Group at Cambridge University, for his great help in carrying out the DFT-CASTEP optimization calculations of the hexagonite structure. The authors wish to thank Roald Hoffmann for his suggestions in writing this manuscript. Finally, the authors wish to thank D.M.E. (Marian) Szebenyi, PhD at Cornell High Energy Synchrotron Source (CHESS) for helpful discussions of the symmetry aspects of hexagonite.


  1. Balaban AT, Klein DJ, Folden CA (1994) Chem Phys Lett 217:266–270CrossRefGoogle Scholar
  2. Bucknum MJ, Castro EA (2004) J Math Chem 36(4):381–408CrossRefGoogle Scholar
  3. Bucknum MJ, Castro EA (2005) MATCH Commun Math Comput Chem 54:89–119Google Scholar
  4. Bucknum MJ, Castro EA (2006) J Math Chem 39(3–4):611–628CrossRefGoogle Scholar
  5. Bucknum MJ, Castro EA (2009) J Math Chem 42(1):117–138CrossRefGoogle Scholar
  6. Bucknum MJ, Hoffmann R (1994) J Am Chem Soc 116:11456–11464CrossRefGoogle Scholar
  7. Bucknum MJ, Stamatin I, Castro EA (2005) Mol Phys 103(20):2707–2715CrossRefGoogle Scholar
  8. Burroughes JH, Jones CA, Friend RH (1988) Nature(London) 335:137–141CrossRefGoogle Scholar
  9. Cohen ML (1994) Solid State Commun 92(1–2):45–52CrossRefGoogle Scholar
  10. Cotton FA (1990) Chemical applications of group theory, 3rd edn. Wiley, New York, pp 166–172Google Scholar
  11. Epstein AJ, Miller JS (1979) Sci Am 241:48–61CrossRefGoogle Scholar
  12. Hoffmann R (1963) J Chem Phys 39:1397–1407CrossRefGoogle Scholar
  13. Hoffmann R, Lipscomb WN (1962) J Chem Phys 37:2872–2878CrossRefGoogle Scholar
  14. Kaner RB, MacDiarmid AG (1988) Sci Am 258:60–72CrossRefGoogle Scholar
  15. Karfunkel HR, Dressler T (1992) J Am Chem Soc 114(7):2285–2288CrossRefGoogle Scholar
  16. Kroto HW, Heath JR, O’Brien SC, Curl RF, Smalley RE (1985) Nature(London) 318:162–163CrossRefGoogle Scholar
  17. Liu AY, Cohen ML (1989) Science 245:841–845CrossRefGoogle Scholar
  18. Merz KM Jr, Hoffmann R, Balaban AT (1987) J Am Chem Soc 109:6742–6751CrossRefGoogle Scholar
  19. Segall MD, Lindan PJD, Probert MJ, Pickard CJ, Hasnip PJ, Clark SJ, Payne MC (2002) J Phys Condens Matter 14(11):2717–2743CrossRefGoogle Scholar
  20. Wang Z, Zhao Y, Tait K, Liao X, Schiferl D, Zha C, Downs RT, Qian J, Zhu Y, Shen T (2004) P Natl A Sci (PNAS) 101(38):13699–13702CrossRefGoogle Scholar
  21. Warren BE (1990) X-ray Diffraction, 1st edition, Dover Publications, Inc., Mineola, NY: 21–22. The formula used to calculate Bragg spacings in the hexagonal crystal system of hexagonite is given in the book by B.E. Warren in the following format: 1/dhkl2 = (4/3)((h2 + hk + k2)/a 2) + l2/c 2 Google Scholar
  22. Wells AF (1977) Three dimensional nets and polyhedra, 1st edn. Wiley, New York, pp 1–150Google Scholar
  23. Wells AF (1979) Further studies of three-dimensional nets, ACA monograph #8. ACA Press, Pittsburgh, pp 1–75Google Scholar
  24. Whangbo MH, Hoffmann R (1978) J Am Chem Soc 100:6093–7002CrossRefGoogle Scholar
  25. Whangbo MH, Hoffmann R, Woodward RB (1979) P Roy Soc A 366:23–32CrossRefGoogle Scholar
  26. Wilcox CF Jr, Winstein S, McMillan WG (1960) J Am Chem Soc 82:5450–5453CrossRefGoogle Scholar
  27. Zimmerman HE, Paufler RM (1960) J Am Chem Soc 82:1514–1516CrossRefGoogle Scholar

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© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.INIFTA, Theoretical Chemistry Division, Suc. 4, C.C. 16Universidad de La PlataLa PlataArgentina

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