Skip to main content
SpringerLink
Log in

Negatively curved graphite and triply periodic minimal surfaces

  • Published:
Journal of Mathematical Chemistry Aims and scope Submit manuscript

Abstract

The Weierstrass representation has been used to construct negatively curved graphite in which atoms rest no a perfect triply periodic minimal surface. By applying the Bonnet transformation on a patch of the D surface decorated with graphite we have been able to construct the Gyroid and P minimal surfaces. Curvatures, densities and lattice parameters have been calculated. It has been found that the maximum Gaussian curvature for our negatively curved structures is less in magnitude than the Gaussian curvature ofC 60. In addition, a new periodic graphitic set with the same topology as the I-WP minimal surface has been obtained by introducing pentagonal and octagonal rings.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. O. Bonnet, Note sur la théorie générale des surfaces, C.R. Acad. Sci. Paris 37 (1853) 529.

    Google Scholar 

  2. E. Dubois-Violette and B. Pansu,Geometry and Interfaces, J. Phys. Colloq. 7, Paris (1990).

  3. T.W. Ebbesen and P.M. Ajayan, Nature 358 (1992) 220.

    Google Scholar 

  4. A. Fogden and S.T. Hyde, Acta Cryst. A48 (1992) 442.

    Google Scholar 

  5. A. Fogden and S.T. Hyde, Acta Cryst. A48 (1992) 575.

    Google Scholar 

  6. A.F. Hebard, M.J. Rosseinsky, R.C. Haddon, D.W. Murphy, S.H. Glarum, T.T.M. Palstra, A.P. Ramirez and A.R. Kortan, Nature 350 (1991) 600.

    Google Scholar 

  7. S.T. Hyde and S. Andersson, Z. Kristallogr. 170 (1985) 225.

    Google Scholar 

  8. S.T. Hyde and S. Andersson, Z. Kristallogr. 174 (1986) 225.

    Google Scholar 

  9. S.T. Hyde, Z. Kristallogr. 187 (1989) 165.

    Google Scholar 

  10. S. Iijima, Nature 354 (1991) 56.

    Google Scholar 

  11. S.P. Kelty, Chen Chia-Chun and C.M. Leiber, Nature 352 (1991) 223.

    Google Scholar 

  12. H.W. Kroto, J.R. Heath, S.C. O'Brien, R.F. Curl and R.E. Smalley, Nature 318 (1985) 162.

    Google Scholar 

  13. H.W. Kroto, Nature 239 (1987) 529.

    Google Scholar 

  14. H. Kroto, Science 242 (1988) 1139.

    Google Scholar 

  15. T. Lenosky, X. Gonze, M. Teter and V. Elser, Nature 355 (1992) 333.

    Google Scholar 

  16. S. Lidin and S.T. Hyde, J. Physique 48 (1987) 1585.

    Google Scholar 

  17. A.L. Mackay and H. Terrones, Nature 352 (1991) 762.

    Google Scholar 

  18. W.H. Meeks, Indiana Univ. Math. J. 39 (1990) 877.

    Google Scholar 

  19. J.C.C. Nitsche,Lectures on Minimal Surfaces, Vol. l (Cambridge University Press, 1989).

  20. R. Osserman,A Survey of Minimal Surfaces (Dover Pub1., 1986).

  21. A.H. Schoen, Infinite periodic minimal surfaces without self-intersections, NASA Technical Note D-5541(1970).

  22. H.A. Schwarz,Gesammelte Mathematische Abhandlungen, Vol. 1 (Springer, Berlin, 1890).

    Google Scholar 

  23. K. Tanigaki, T.W. Ebbesen, S. Saito, J. Mizuki, J.S. Tsai, Y. Kubo and S. Kuroshima, Nature 352 (1991) 222.

    Google Scholar 

  24. H. Terrones, Colloq. Physique C7, 51 (1990) 345.

    Google Scholar 

  25. H. Terrones, Mathematical surfaces and invariants in the study of atomic structures, Ph.D. Thesis, University of London (1992).

  26. H. Terrones, J. Math. Chem. 15 (1994) 143.

    Google Scholar 

  27. H. Terrones and A.L. Mackay, Carbon 30 (1992) 125.

    Google Scholar 

  28. S.J. Townsend, T.J. Lenosky, D.A. Muller, C.S. Nichols and V. Elser, Phys. Rev. Lett. 69 (1992) 92.

    Google Scholar 

  29. D. Vanderbilt and J. Tersoff, Phys. Rev. Lett. 68 (1992) 511.

    Google Scholar 

  30. K. Weierstrass, Untersuchungen über die Flächen, deren mittlere Krümmung überall gleich null ist, Monatsber. d. Berliner Akad. (1866) pp. 612–625.

Download references

Author information

Author notes

  1. H. Terrones

    Present address: Instituto de Fisica, UNAM, Apartado Postal 20-364, C.P. 01000, Mexico,D.F., Mexico

Authors and Affiliations

  1. Department of Crystallography, Birkbeck College, University of London, Malet Street, WCIE 7HX, London, UK

    H. Terrones & A. L. Mackay

Authors
  1. H. Terrones
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. L. Mackay
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Terrones, H., Mackay, A.L. Negatively curved graphite and triply periodic minimal surfaces. J Math Chem 15, 183–195 (1994). https://doi.org/10.1007/BF01277558

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01277558

Keywords

Search

Navigation