Skip to main content
SpringerLink
Log in

Extreme values of the Poisson’s ratio of cubic crystals

  • Solid State
  • Published:
Technical Physics Aims and scope Submit manuscript

Abstract

The problem of determining the extrema of Poisson’s ratio for cubic crystals is considered, and analytical expressions are derived to calculate its extreme values. It follows from the obtained solution that, apart from extreme values at standard orientations, extreme values of Poisson’s ratio can also be detected at special orientations deviated from the standard ones. The derived analytical expressions are used to calculate the extreme values of Poisson’s ratio for a large number of known cubic crystals. The extremely high values of Poisson’s ratio are shown to be characteristic of metastable crystals, such as crystals with the shape memory effect caused by martensitic transformation. These crystals are mainly represented by metallic alloys. For some crystals, the absolute extrema of Poisson’s ratio can exceed the standard values, which are–1 for a standard minimum and +2 for a standard maximum.

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. I. L. Svetlov, A. I. Epishin, A. I. Krivko, A. I. Samoilov, I. N. Odintsev, and A. P. Andreev, Sov. Phys. Dokl. 33, 771 (1988).

    ADS  Google Scholar 

  2. U. Scharer and P. Wachter, Solid State Commun. 96, 497 (1995).

    Article  ADS  Google Scholar 

  3. M. Hayes and A. Shuvalov, Trans. ASME 65, 786 (1998).

    Article  MathSciNet  Google Scholar 

  4. T. C. T. Ting and D. M. Barnett, J. Appl. Mech. 72, 929 (2005).

    Article  ADS  MathSciNet  Google Scholar 

  5. A. N. Norris, Proc. R. Soc. A 462, 3385 (2006).

    Article  ADS  MathSciNet  Google Scholar 

  6. T. P. Hughes, A. Marmier, and K. E. Evans, Int. J. Solids Struct. 47, 1469 (2010).

    Article  Google Scholar 

  7. G. N. Greaves, A. L. Greer, R. S. Lakes, and T. Rouxel, Nat. Mater. 10, 823 (2011).

    Article  ADS  Google Scholar 

  8. A. C. Branka, D. M. Heyes, and K. W. Wojciechowski, Phys. Status Solidi B 248, 96 (2011).

    Article  ADS  Google Scholar 

  9. R. V. Goldstein, V. A. Gorodtsov, D. S. Lisovenko, and M. A. Volkov, Phys. Mesomech. 17 (2), 97 (2014).

    Article  Google Scholar 

  10. R. V. Goldstein, V. A. Gorodtsov, and D. S. Lisovenko, Phys. Dokl. 56, 399 (2011).

    Article  Google Scholar 

  11. R. V. Goldstein, V. A. Gorodtsov, and D. S. Lisovenko, Phys. Status Solidi B 250, 2038 (2013).

    Google Scholar 

  12. V. N. Belomestnykh and E. G. Soboleva, Vestn. Buryatsk. Gos. Univ., No. 3, 79 (2013).

    Google Scholar 

  13. K. E. Evans, M. A. Nkansah, I. J. Hutchinson, and S. C. Rogers, Nature 353 (6340), 124 (1991).

    Article  ADS  Google Scholar 

  14. Landolt–Börnstein: Group III Condensed Matter (Springer, Berlin, 1992), Vol. 29a, pp. 11–100.

  15. A. A. Nayeb-Hashemi, J. B. Clark, and A. D. Pelton, Bull. Alloy Phase Diagrams 5, 365 (1984).

    Article  Google Scholar 

  16. N. Stanford and P. S. Bate, Acta Mater. 53, 859 (2005).

    Article  Google Scholar 

  17. Landolt–Börnstein: Group IV Physical Chemistry (Springer, Berlin, 1992), Vol. 5a, pp. 1–7.

  18. S. Rosen and J. A. Gobel, Trans. Am. Inst. Min. Metall. Eng. 242, 722 (1968).

    Google Scholar 

  19. M. Ahlers, Mater. Sci. Eng. A 481–482, 500 (2008).

    Article  Google Scholar 

  20. S. Sathish, U. S. Mallik, and T. N. Raju, J. Miner. Mater. Charact. Eng. 2 (2), 71 (2014).

    Google Scholar 

  21. J. Perkins and W. E. Muesing, Metall. Trans. 14 (1), 33 (1983).

    Article  Google Scholar 

  22. L. Righi, F. Albertini, S. Fabbrici, and A. Paoluci, Mater. Sci. Forum 684, 105 (2011).

    Article  Google Scholar 

  23. O. Crottaz, F. Kubelb, and H. Schmida, J. Mater. Chem. 7 (1), 143 (1997).

    Article  Google Scholar 

  24. S. Kaufmann-Weiss, S. Hamann, M. E. Gruner, J. Buschbeck, A. Ludwig, L. Schultz, and S. Fähler, Adv. Eng. Mater. 14, 724 (2012).

    Article  Google Scholar 

  25. Z. P. Luo, Metallogr. Microstruct. Anal. 1 (6), 320 (2012).

    Article  Google Scholar 

  26. M. Stipcich, L. Mañosa, and A. Planes, Phys. Rev. B 70, 054115 (2004).

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Technische Universität Berlin, Berlin, 10587, Germany

    A. I. Epishin

  2. Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, Moscow, 119526, Russia

    D. S. Lisovenko

Authors
  1. A. I. Epishin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. D. S. Lisovenko
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to D. S. Lisovenko.

Additional information

Original Russian Text © A.I. Epishin, D.S. Lisovenko, 2016, published in Zhurnal Tekhnicheskoi Fiziki, 2016, Vol. 86, No. 10, pp. 74–82.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Epishin, A.I., Lisovenko, D.S. Extreme values of the Poisson’s ratio of cubic crystals. Tech. Phys. 61, 1516–1524 (2016). https://doi.org/10.1134/S1063784216100121

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1063784216100121

Search

Navigation