Acta Scientific Applied Physics

Review Article Volume 2 Issue 12

Novel Ultrahard Carbon Allotrope C5 with Mixed sp2/sp3 Carbon Hybridizations. Crystal chemistry and First Principles Investigations

Samir F Matar*

Lebanese German University (LGU), Sahel-Alma, Jounieh, Lebanon

*Corresponding Author: Samir F Matar, Lebanese German University (LGU), Sahel-Alma, Jounieh, Lebanon.

Received: November 28, 2022; Published: December 06, 2022


From crystal chemistry rationale and first principles investigations, novel tetragonal carbon allotrope C5 with mixed sp2/sp2–like carbon sites hybridizations is identified as cohesive and stable both dynamically and mechanically with metallic behavior. Charge density distribution is localized at tetrahedral C-sp3 and delocalized with π-like electrons between trigonal C-sp2 leading to metallic like electronic behavior The anisotropic structure resulting from vertically aligned C=C (ethylene –like) along the tetragonal c-axis provide large C33 elastic constant and high Vickers hardness with a magnitude slightly below diamond. The properties of novel simple allotrope should help assessing nanodiamonds with mixed sp2/sp3 C investigated in different fields of materials as electrochemical ones.

Keywords: Diamond; Hardness; Phonons; DFT; Crystal Chemistry


  1. VV Brazhkin and VL Solozhenko. “Myths about new ultrahard phases: Why materials that are significantly superior to diamond in elastic moduli and hardness are impossible”. Journal of Applied Physics 125, 130901 (2019).
  2. Shuang Shuang Zhang., et al. “Discovery of superhard materials via CALYPSO methodology”. Chinese Physics B 28 (2019): 106104.
  3. R Hoffmann., et al. “Homo Citans and Carbon Allotropes: For an Ethics of Citation”. Angewandte Chemie 55 (2016): 10962-10976. and SACADA database (Samara Carbon Allotrope Database).
  4. SF Matar., et al. “The simplest dense carbon allotrope: Ultra-hard body centered tetragonal C4”. Journal of Solid State Chemistry 314 (2022): 123424.
  5. AP Shevchenko., et al. “Topological representations of crystal structures: generation, analysis, and implementation in the TopCryst system”. Science and Technology of Advanced Materials: Methods1 (2022): 250-265.
  6. O'Keeffe M., et al. “The reticular chemistry structure resource (RCSR) database of, and symbols for, crystal nets. Acc. Chem. Res., , 41, 1782-1789 (2008).
  7. P Hohenberg and W Kohn. “Inhomogeneous electron gas”. Physical Review B 136 (1964): 864-871.
  8. Y Fujii., et al. “Pentadiamond: A Hard Carbon Allotrope of a Pentagonal Network of sp2 and sp3 C Atoms. Physical Review Letters 125 (2020): 016001 and Retraction: Physical Review Letters 125 (2020): 079901 (2020).
  9. Zhaofeng Zhai., et al. “Progress in electrochemistry of hybrid diamond/sp2-C nanostructures”. Current Opinion in Electrochemistry 32 (2022): 100884.
  10. G Kresse and J Furthmüller. “Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set”. Physical Review B 54 (1996): 11169.
  11. G Kresse and J Joubert. “From ultrasoft pseudopotentials to the projector augmented wave”. Physical Review B 59 (1999): 1758-1775.
  12. PE Blöchl. “Projector augmented wave method”. Physical Review B 50 (1994): 17953-17979.
  13. J Perdew., et al. “The Generalized Gradient Approximation made simple”. Physical Review Letter 77 (1996): 3865-3868.
  14. WH Press., et al. “Numerical Recipes”. 2nd Cambridge University Press: New York, USA, (1986).
  15. PE Blöchl., et al. “Improved tetrahedron method for Brillouin-zone integrations”. Physical Review B 49 (1994): 16223-16233.
  16. M Methfessel and AT Paxton. “High-precision sampling for Brillouin-zone integration in metals”. Physical Review B 40 (1989): 3616-3621.
  17. HJ Monkhorst and JD Pack. “Special k-points for Brillouin Zone integration”. Physical Review B 13 (1976): 5188-5192.
  18. A Togo and I Tanaka. “First principles phonon calculations in materials science”. Scripta Materialia 108 (2015): 1-5.
  19. V Eyert. “Basic notions and applications of the augmented spherical wave method”. International Journal of Quantum Chemistry 77 (2000): 1007-1031.
  20. SF Matar. CCDC 2208344: (Refcode NEQHUQ; name C6POLr) (2022).
  21. W Voigt. “Über die Beziehung zwischen den beiden Elasticitätsconstanten isotroper Körper”. Annals of Physics 274 (1889): 573-587.
  22. DC Wallace. “Thermodynamics of crystals”. New York, USA: John Wiley and Sons (1972).
  23. VA Mukhanov., et al. “The interrelation between hardness and compressibility of substances and their structure and thermodynamic properties”. Journal of Superhard Materials 30 (2008): 368-378.
  24. E Mazhnik and AR Oganov. “A model of hardness and fracture toughness of solids”. Journal of Applied Physics 126 (2019): 125109.
  25. AO Lyakhov and AR Oganov. “Evolutionary search for superhard materials: Methodology and applications to forms of carbon and TiO2”. Physical Review B 84 (2011): 092103.
  26. RS Krishnan. “Raman spectrum of diamond”. Nature 155 (1945): 171.


Citation: Samir F Matar. “Novel Ultrahard Carbon Allotrope C5 with Mixed sp2/sp3 Carbon Hybridizations. Crystal chemistry and First Principles Investigations". Acta Scientific Applied Physics 3.1 (2022): 02-09.


Copyright: © 2022 Samir F Matar. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

News and Events

  • Certification for Review
    Acta Scientific certifies the Editors/reviewers for their review done towards the assigned articles of the respective journals.
  • Submission Timeline for Upcoming Issue
    The last date for submission of articles for regular Issues is May 30, 2024.
  • Publication Certificate
    Authors will be issued a "Publication Certificate" as a mark of appreciation for publishing their work.
  • Best Article of the Issue
    The Editors will elect one Best Article after each issue release. The authors of this article will be provided with a certificate of "Best Article of the Issue"
  • Welcoming Article Submission
    Acta Scientific delightfully welcomes active researchers for submission of articles towards the upcoming issue of respective journals.

Contact US