Skip to main content
SpringerLink
Log in

Totally symmetric order parameter in the framework of the phenomenological theory of phase transitions: Ferroelastics

  • Low-Temperature Solid-State Physics
  • Published:
Journal of Experimental and Theoretical Physics Aims and scope Submit manuscript

Abstract

A new approach is proposed for constructing the phenomenological theory of phase transitions. The approach is based on the classical Landau theory with allowance made for the order parameter that corresponds to changes in the charge distribution probability density of a crystal and does not affect the symmetry of the high-symmetry phase. It is demonstrated that this approach makes it possible to describe phase transitions in terms of a nonequilibrium polynomial Landau potential of degree four in the components of the order parameters. The capabilities of the proposed approach are illustrated with three systems that undergo ferroelastic phase transitions.

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. L. D. Landau and E. M. Lifshitz, Course of Theoretical Physics, Vol. 5: Statistical Physics, 5th ed. (Fizmatlit, Moscow, 2001; Butterworth, London, 1999).

    Google Scholar 

  2. L. D. Landau, Collected Works (Nauka, Moscow, 1969), Vol. 1.

    Google Scholar 

  3. L. M. Mikhel’son and Yu. I. Sirotin, Kristallografiya 14, 573 (1969) [Sov. Phys. Crystallogr. 14, 485 (1969)].

    Google Scholar 

  4. Yu. M. Gufan, Structural Phase Transitions (Nauka, Moscow, 1982) [in Russian].

    Google Scholar 

  5. M. A. Krivoglaz and A. A. Smirnov, Theory of Orderable Alloys (Fizmatlit, Moscow, 1958) [in Russian].

    Google Scholar 

  6. V. P. Sakhnenko and V. M. Talanov, Fiz. Tverd. Tela (Leningrad) 21, 2435 (1979) [Sov. Phys. Solid State 21, 1401 (1979)]; Fiz. Tverd. Tela (Leningrad) 22, 785 (1980) [Sov. Phys. Solid State 22, 458 (1980)].

    Google Scholar 

  7. R. W. G. Wyckoff, Crystal Structures (Interscience, New York, 1963), Vol. 1.

    Google Scholar 

  8. B. R. Sahu and L. Kleinman, Phys. Rev. B 69, 193 101 (2004).

  9. Hirotsugu Ogi, Masashi Fukunaga, and Masahiko Hirao, Phys. Rev. B 69, 024104 (2004).

    Google Scholar 

  10. D. B. McWhan, R. J. Birgeneau, W. A. Bonner, et al., J. Phys. C 8, L81 (1975).

  11. P. S. Peercy, I. J. Fritz, and G. A. Samara, J. Phys. Chem. Solids 36, 1105 (1975).

    Article  Google Scholar 

  12. Hiromoto Uwe and Hiroshi Tokumoto, Phys. Rev. B 19, 3700 (1979).

    Article  ADS  Google Scholar 

  13. E. F. Skelton, J. L. Feldman, C. Y. Liu, and I. L. Spain, Phys. Rev. B 13, 2605 (1976).

    Article  ADS  Google Scholar 

  14. O. V. Kovalev, Irreducible Representations of the Space Groups (Naukova Dumka, Kiev, 1961; Gordon and Breach, New York, 1965).

    Google Scholar 

  15. Yu. I. Sirotin and M. P. Shaskolskaya, Fundamentals of Crystal Physics (Nauka, Moscow, 1975; Mir, Moscow, 1982).

    Google Scholar 

  16. A. V. Vinogradov, V. A. Lomonov, Yu. A. Pershin, and N. L. Sizova, Kristallografiya 47, 1105 (2002) [Sov. Phys. Crystallogr. 47, 1036 (2002)].

    Google Scholar 

  17. K. Brugger, J. Appl. Phys. 36, 759 (1965).

    Article  ADS  Google Scholar 

  18. G. Arilt and H. Schweppe, Solid State Commun. 6, 783 (1968).

    Article  Google Scholar 

  19. H. Ledbetter, R. G. Leisure, and H. Ogi, J. Appl. Phys. 96, 6201 (2004).

    Article  ADS  Google Scholar 

  20. A. M. Antonenko, M. D. Volnyanskiĭ, and A. Yu. Kudzin, Kristallografiya 24, 1071 (1979) [Sov. Phys. Crystallogr. 24, 613 (1979)].

    Google Scholar 

  21. R. N. Thurston and K. Brugger, Phys. Rev. A 133, 1604 (1964).

    Article  ADS  Google Scholar 

  22. T. G. Worlton and R. A. Beyerlein, Phys. Rev. B 12, 1899 (1975).

    Article  ADS  Google Scholar 

  23. J.-C. Toledano and P. Toledano, The Landau Theory of Phase Transitions (World Sci., Singapore, 1987; Mir, Moscow, 1994).

    Google Scholar 

  24. I. J. Fritz and P. S. Peercy, Solid State Commun. 16, 1197 (1975).

    Article  Google Scholar 

  25. A. Yu. Gufan, Kristallografiya 49, 515 (2004) [Crystallogr. Rep. 49, 450 (2004)].

    Google Scholar 

  26. A. Yu. Gufan and M. B. Stryukov, Izv. Ross. Akad. Nauk, Ser. Fiz. 66, 791 (2002).

    Google Scholar 

  27. P. T. Toledano, M. M. Fejer, and B. A. Auld, Phys. Rev. B 27, 5717 (1983).

    Article  ADS  Google Scholar 

  28. R. M. Hazen, Am. Mineral. 62, 528 (1977).

    Google Scholar 

  29. Tsien Hsue Shen, Physical Mechnics (Peking, 1962; Mir, Moscow, 1987).

  30. L. D. Landau and E. M. Lifshitz, Course of Theoretical Physics, Vol. 7: Theory of Elasticity, 4th ed. (Nauka, Moscow, 1987; Pergamon, Oxford, 1986).

    Google Scholar 

  31. Y. Ohmachi and N. Uchida, J. Appl. Phys. 41, 2307 (1970).

    Article  ADS  Google Scholar 

  32. R. M. Hazen and C. W. Burnaham, Am. Mineral. 59, 1166 (1975).

    Google Scholar 

  33. R. M. Hazen and L. W. Finger, Am. Mineral. 68, 595 (1983).

    Google Scholar 

  34. R. G. J. Stern, Chem. Commun. 21, 777 (1966).

    Google Scholar 

  35. A. Trister, W. Schranz, and R. Miletich, Phys. Rev. Lett. 88, 055503 (2002).

    Google Scholar 

  36. Yu. M. Gufan, V. I. Snezhkov, and S. B. Roshal’, The Landau Phases in Close-Packed Structures (Rostov. Gos. Univ., Rostov-on-Don, 1990) [in Rusian].

    Google Scholar 

  37. M. Kataoka and J. Kanamori, J. Phys. Soc. Jpn. 32, 113 (1972).

    Article  ADS  Google Scholar 

  38. H. J. Levinstein, M. Robbins, and C. Capio, Mater. Res. Bull. 7, 27 (1972).

    Article  Google Scholar 

  39. J. D. Axe and Y. Yamada, Phys. Rev. B 24, 2567 (1981).

    Article  ADS  Google Scholar 

  40. A. P. Levanyuk and D. G. Sannikov, Pis’ma Zh. Éksp. Teor. Fiz. 11, 68 (1970) [JETP Lett. 11, 43 (1970)].

    ADS  Google Scholar 

  41. A. Yu. Gufan, Izv. Ross. Akad. Nauk, Ser. Fiz. 68, 1652 (2004).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Research Institute of Physics, Rostov State University, pr. Stachki 194, Rostov-on-Don, 344002, Russia

    A. Yu. Gufan

Authors
  1. A. Yu. Gufan
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Original Russian Text © A.Yu. Gufan, 2007, published in Zhurnal Éksperimental’noĭ i Teoreticheskoĭ Fiziki, 2007, Vol. 132, No. 1, pp. 138–149.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gufan, A.Y. Totally symmetric order parameter in the framework of the phenomenological theory of phase transitions: Ferroelastics. J. Exp. Theor. Phys. 105, 120–131 (2007). https://doi.org/10.1134/S1063776107070266

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1063776107070266

PACS numbers

Search

Navigation