Skip to main content
SpringerLink
Log in

Lattice dynamics and the incommensurability of the structures of hexagonal polytypes of diamond

  • Condensed-Matter Spectroscopy
  • Published:
Optics and Spectroscopy Aims and scope Submit manuscript

Abstract

In the density functional theory approximation, we have calculated the phonon dispersions and the densities of vibrational states of the 2H, 3C, 4H, 6H, and 8H hexagonal polytypes of diamond. We have found that a one-dimensional incommensurate modulation of the structure arises along the hexagonal axis, the parameter of which not only exceeds the parameters of basic translations of the crystal lattices of polytypes, but also is not a multiple of them. Based on the estimation of interactions between bilayers of carbon atoms in the structure of polytypes, we have assumed that competing interactions between bilayers are the main mechanism by which incommensurability arises. We have shown that optical measurements of vibrational frequencies in the center of the Brillouin zone of polytypes make it possible to retrieve the dispersion of acoustic branches of cubic diamond.

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.

Institutional subscriptions

Similar content being viewed by others

References

  1. K. E. Spear, A. W. Phelps, and W. R. White, J. Mater. Res. 5, 2277 (1990).

    Article  ADS  Google Scholar 

  2. F. P. Bundy and J. S. Kasper, J. Chem. Phys. 46, 3437 (1967).

    Article  ADS  Google Scholar 

  3. A. K. Sharma, H. G. Salunke, G. P. Das, P. Ayyub, and M. S. Multani, J. Phys.: Cond. Mater. 8, 5801 (1996).

    Article  ADS  Google Scholar 

  4. M. Frenklach, R. Kematick, D. Huang, W. Howard, K. E. Spear, A. W. Helps, and R. Koba, J. Appl. Phys. 66, 395 (1989).

    Article  ADS  Google Scholar 

  5. S. Bhargava, H. D. Bist, S. Sahli, M. Aslam, and H. B. Tripathi, Appl. Phys. Lett. 67, 1706 (1995).

    Article  ADS  Google Scholar 

  6. R. Kapil, B. R. Mehta, and V. D. Vankar, Thin Solid Films 312, 106 (1998).

    Article  ADS  Google Scholar 

  7. Z. Wang, Y. Zhao, C.-S. Zha, Q. Xue, R. T. Downs, R.-G. Duan, R. Carakas, and X. Liao, Adv. Mater. 20, 3303 (2008).

    Article  Google Scholar 

  8. D. S. Knight and W. B. White, J. Mater. Res. 4, 385 (1989).

    Article  ADS  Google Scholar 

  9. H. He, T. Sekine, and T. Kobayashi, Appl. Phys. Lett. 81, 610 (2002).

    Article  ADS  Google Scholar 

  10. D. C. Smith and G. Godard, Spectrochim. Acta, A 73, 428 (2009).

    Article  ADS  Google Scholar 

  11. A. T. J. Karczemska, Achiev. Mater. Manufact. Eng. 43, 94 (2010).

    Google Scholar 

  12. V. N. Denisov, B. N. Mavrin, N. R. Serebryanaya, G. A. Dubitsky, V. V. Aksenenkov, A. N. Kirichenko, N. V. Kuzmin, B. A. Kulnitskiy, I. A. Perezhogin, and V. D. Blank, Diamond Rel. Mater. 20, 951 (2011).

    Article  ADS  Google Scholar 

  13. A. A. Shiryaev, A. V. Fisenko, I. I. Vlasov, L. F. Semenova, P. Nagel, and S. Schuppler, http://arxiv.org/abs/1102.0880.

  14. E. Burgos, E. Halac, and H. Bonadeo, Chem. Phys. Lett. 298, 273 (1998).

    Article  ADS  Google Scholar 

  15. B. R. Wu and J.-A. Xu, Phys. Rev. 57, 13355 (1998).

    Article  Google Scholar 

  16. B. R. Wu, Diamond Rel. Mater. 16, 21 (2007).

    Article  ADS  Google Scholar 

  17. G. P. Das, Bull. Mater. Sci. 20, 409 (1997).

    Article  Google Scholar 

  18. B. Wen, J. Zhao, M. J. Bucknum, P. Yao, and T. Li, Diamond Rel. Mater. 17, 356 (2008).

    Article  ADS  Google Scholar 

  19. Z. Wang, F. Gao, N. Li, N. Qu, H. Gou, and X. Hao, J. Phys.: Cond. Mater. 21, 235401 (2009).

    Article  ADS  Google Scholar 

  20. www.abinit.org.

  21. G. N. Zhizhin, B. N. Mavrin, and V. F. Shabanov, Optical Vibrational Spectra of Crystals, Ed. by G. N. Zhizhin (Nauka, Moscow, 1984) [in Russian].

  22. G. R. Wilkinson, in Applications of Raman Scattering Spectra, Ed. by A. Anderson and K. I. Petrov (Mir, Moscow, 1977), pp. 408–578 [Russian translation].

  23. R. Currat and T. Jansen, Solid State Phys. 41, 201 (1988).

    Google Scholar 

  24. T. Janssen, Incommensurate Phases in Dielectrics: Part 1, Fundamentals, Ed. by R. Blinc and A. P. Levanyuk (North-Holland, 1986), Chap. 3.

  25. F. Bechstedt, P. Käckell, A. Zywietz, K. Karch, B. Adolph, K. Tenelsen, and J. Furthmuller,, Phys. Stat. Sol. (b) 202, 35 (1997).

    Article  ADS  Google Scholar 

  26. C. Raffy, J. Furthmuller, and F. Bechstedt, Phys. Rev. B 66, 075201 (2002).

    Article  ADS  Google Scholar 

  27. J. M. Ziman Principles of the Theory of Solids (Cambridge Univ. Press, London, 1972; Mir, Moscow, 1974).

    Book  Google Scholar 

  28. J. L. Warren, J. L. Yarnell, G. Dolling, and R. A. Cowley, Phys. Rev. 158, 805 (1967).

    Article  ADS  Google Scholar 

  29. W. Windl, P. Pavone, K. Karch, O. Schutt, D. Strauch, P. Giannozzi, and S. Baroni, Phys. Rev. B 48, 3164 (1993).

    Article  ADS  Google Scholar 

  30. J. Xie, S. P. Chen, J. S. Tse, S. De Gironcoli, and S. Baroni, Phys. Rev. B 60, 9444 (1999).

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute for Spectroscopy, Russian Academy of Sciences, Troitsk, Moscow, 142190, Russia

    T. A. Ivanova & B. N. Mavrin

  2. Technological Institute for Superhard and Novel Carbon Materials, Troitsk, Moscow, 142190, Russia

    T. A. Ivanova

Authors
  1. T. A. Ivanova
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. B. N. Mavrin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to B. N. Mavrin.

Additional information

Original Russian Text © T.A. Ivanova, B.N. Mavrin, 2014, published in Optika i Spektroskopiya, 2014, Vol. 117, No. 2, pp. 240–246.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ivanova, T.A., Mavrin, B.N. Lattice dynamics and the incommensurability of the structures of hexagonal polytypes of diamond. Opt. Spectrosc. 117, 228–234 (2014). https://doi.org/10.1134/S0030400X14080141

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0030400X14080141

Keywords

Search

Navigation