High Pressure Synthesis of the Carbon Allotrope Hexagonite with Carbon Nanotubes in a Diamond Anvil Cell
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.
KeywordsDensity Functional Theory Diamond Anvil Cell Infinite Family Carbon Allotrope Ultrasoft Pseudopotentials
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.
- Bucknum MJ, Castro EA (2005) MATCH Commun Math Comput Chem 54:89–119Google Scholar
- Cotton FA (1990) Chemical applications of group theory, 3rd edn. Wiley, New York, pp 166–172Google Scholar
- 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
- Wells AF (1977) Three dimensional nets and polyhedra, 1st edn. Wiley, New York, pp 1–150Google Scholar
- Wells AF (1979) Further studies of three-dimensional nets, ACA monograph #8. ACA Press, Pittsburgh, pp 1–75Google Scholar