Skip to main content
SpringerLink
Log in

Group-Theoretical Classification of Aristotypes of Cation and Anion Orders in Perovskites

  • THEORY OF CRYSTAL STRUCTURES
  • Published:
Crystallography Reports Aims and scope Submit manuscript

Abstract

A group-theoretical classification of cation and anion orders of crystals with a perovskite structure is presented. Aristotypes are idealized structures (phases), from which the low-symmetry ordered modifications of perovskites are formed as a result of rotations and deformation of octahedra, as well as the cooperative Jahn–Teller effect and other physical phenomena. Seven aristotype classes have been distinguished, which are characterized by the atomic ordering in each of Wyckoff positions and simultaneous atomic ordering in several positions. The critical and secondary (improper) order parameters, describing the formation of ordered structures, are determined. The classification proposed makes it possible to systematize a variety of known phases, establish genetic structural links between low-symmetry ordered structures, and design new materials.

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

Fig. 1.
Fig. 2.

Similar content being viewed by others

REFERENCES

  1. K. S. Aleksandrov and B. V. Beznosikov, Perovskites: Present and Future. Variety of Parent Phases, Phase Transitions, Possibilities of Synthesis of New Compounds (Sib. Otd. Ross. Akad. Nauk, Novosibirsk, 2004) [in Russian].

    Google Scholar 

  2. K. M. Rabe, Ch. H. Ahn, and J.-M. Triscone, Physics of Ferroelectrics: A Modern Perspective (Springer Science and Business Media, 2007.

    Google Scholar 

  3. K. S. Aleksandrov and B. V. Beznosikov, Perovskite-Type Crystals (Nauka. Sibirskoe Predpriyatie RAN, Novosibirsk, 1997) [in Russian].

  4. R. H. Mitchel, Perovskites: Modern and Ancient (Almaz Press, Ontario, 2002).

    Google Scholar 

  5. E. G. Fesenko, Perovskite Family and Ferroelectricity (Atomizdat, Moscow, 1972) [in Russian].

    Google Scholar 

  6. G. King and P. M. Woodward, J. Mater. Chem. 20, 5785 (2010).

    Article  Google Scholar 

  7. P. K. Davies, Current Opinion Solid State Mater. Sci. 4, 467 (1999).

    Article  ADS  Google Scholar 

  8. A. Ourmazd and J. C. H. Spence, Nature (London) 329, 425 (1987).

    Article  ADS  Google Scholar 

  9. K. S. Aleksandrov and S. V. Misyul’, Kristallografiya 26 (5), 1074 1981).

    Google Scholar 

  10. C. J. Howard, B. J. Kennedy, and P. M. Woodward, Acta Crystallogr. B 59, 463 (2003).

    Article  Google Scholar 

  11. C. J. Howard and H. T. Stokes, Acta Crystallogr. B 60, 674 (2004).

    Article  Google Scholar 

  12. C. J. Howard and M. A. Carpenter, Acta Crystallogr. B 66, 40 (2010).

    Article  Google Scholar 

  13. H. D. Megaw, Ferroelectricity in Crystals (Methuen, London, 1957).

    Google Scholar 

  14. H. D. Megaw, Crystal Structures: A Working Approach (W.B. Saunders, Philadelphia, 1973).

    Google Scholar 

  15. K. S. Aleksandrov, A. T. Anistratov, B. V. Beznosikov, and N. V. Fedoseeva, Phase Transitions in Crystals of ABX3 Haloid Compounds (Nauka, Novosibirsk, 1981) [in Russian].

    Google Scholar 

  16. V. M. Talanov, M. V. Talanov, and V. B. Shirokov, Crystallogr. Rep. 59 (5), 650 (2014).

    Article  ADS  Google Scholar 

  17. M. V. Talanov, V. B. Shirokov, and V. M. Talanov, Crystallogr. Rep. 59 (5), 662 (2014).

    Article  ADS  Google Scholar 

  18. M. V. Talanov, V. B. Shirokov, and V. M. Talanov, Acta Crystallogr. A 72, 222 (2016).

    Article  Google Scholar 

  19. L. D. Landau and E. M. Lifshitz, Course of Theoretical Physics, Vol. 5: Statistical Physics (Nauka, Moscow, 1976; Pergamon, Oxford, 1980).

  20. E. B. Vinberg, Yu. M. Gufan, V. P. Sakhnenko, and Yu. I. Sirotin, Kristallografiya 19 (1), 21 (1974).

    Google Scholar 

  21. J. Dimmock, Phys. Rev. 130, 1337 (1963).

    Article  ADS  Google Scholar 

  22. Yu. A. Izyumov, V. E. Naish, and V. N. Syromyatnikov, Kristallografiya 24 (6), 1115 (1979).

    Google Scholar 

  23. Yu. I. Sirotin and M. P. Shaskolskaya, Fundamentals of Crystal Physics (Nauka, Moscow, 1975).

    Google Scholar 

  24. G. M. Chechin, T. I. Ivanova, and V. P. Sakhnenko, Phys. Status Solidi B 152, 431 (1989).

    Article  ADS  Google Scholar 

  25. V. P. Sakhnenko, V. M. Talanov, and G. M. Chechin, Fiz. Met. Metalloved. 62 (5), 847 (1986).

    Google Scholar 

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

    Google Scholar 

  27. K. S. Aleksandrov and S. V. Misyul’, Kristallografiya 26 (5), 1074 (1981).

    Google Scholar 

  28. M. V. Talanov, Cryst. Growth Des. 18, 3433 (2018).

    Article  Google Scholar 

  29. A. P. Levanyuk and D. G. Sannikov, Usp. Fiz. Nauk 112 (4), 561 (1974).

    Article  Google Scholar 

  30. O. V. Kovalev, Irreducible Representations of Space Groups (Izd-vo AN USSR, Kiev, 1961) [in Russian].

    Google Scholar 

  31. H. T. Stokes, D. M. Hatch, and B. J. Campbell, ISOTROPY Software Suite (2007); iso.byu.edu.

  32. C. J. Howard and H. T. Stokes, Acta Crystallogr. A 61, 93 (2005).

    Article  ADS  Google Scholar 

  33. V. B. Shirokov and V. I. Torgashev, Crystallogr. Rep. 49 (1), 20 (2004).

    Article  ADS  Google Scholar 

Download references

ACKNOWLEDGMENTS

This study was supported by the Russian Foundation for Basic Research, project no. 16-32-60025 mol_a_dk.

Author information

Authors and Affiliations

  1. Southern Federal University, 344006, Rostov-on-Don, Russia

    M. V. Talanov & V. B. Shirokov

  2. Platov South-Russian State Polytechnic University, 346428, Novocherkassk, Russia

    V. M. Talanov

  3. South Scientific Center, Russian Academy of Sciences, 344006, Rostov-on-Don, Russia

    V. B. Shirokov

Authors
  1. M. V. Talanov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. V. M. Talanov
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. V. B. Shirokov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. V. Talanov.

Additional information

Translated by Yu. Sin’kov

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Talanov, M.V., Talanov, V.M. & Shirokov, V.B. Group-Theoretical Classification of Aristotypes of Cation and Anion Orders in Perovskites. Crystallogr. Rep. 64, 386–391 (2019). https://doi.org/10.1134/S1063774519030258

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1063774519030258

Search

Navigation