Skip to main content
Log in

Elastic constants and softening of acoustic modes in A2MX6-crystals observed by Brillouin scattering

  • Published:
Zeitschrift für Physik B Condensed Matter

Abstract

Room-temperature Brillouin-scattering measurements of the longitudinal and transverse sound velocities for the cubic crystals K2SnCl6, K2ReCl6, (NH4)2SnCl6 and (NH4)2SiF6 are presented. The elastic constantsc 11,c 12 andc 44 are determined from the angular variation of the Brillouin line shifts. Furthermore, for K2SnCl6 the sound velocities in the [100]- and [111]-direction are investigated as a function of temperature, 256K≦T≦330K. A strong softening of thec 11c 12 mode is observed in the para-distortive phase as the temperature approaches the phase transition temperatureT c1=262K from above, whilec 44 shows no anomaly within the experimental error. These acoustic anomalies are interpreted theoretically by a mechanism based on the coupling of the elastic strain field to the fluctuations of the soft-mode coordinates.

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

Access this article

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. Rössler, K., Winter, J.: Chem. Phys. Lett.46, 566 (1977)

    Google Scholar 

  2. Armstrong, R.L., von Driel, H.M., In: Adv. in nuclear quadrupole resonance. Vol. 2, p. 179. Smith, J.A. (ed.). London: Heyden 1975

    Google Scholar 

  3. Regelsberger, M., Pelzl, J.: Solid State Commun.28, 783 (1978)

    Google Scholar 

  4. Prager, M., Press, W., Alefeld, B., Hüller, A.: J. Chem. Phys.67, 5126 (1977)

    Google Scholar 

  5. O'Leary, G.P., Wheeler, R.G.: Phys. Rev. B1, 4409 (1970)

    Google Scholar 

  6. Lynn, J.W., Patterson, H.H., Shirane, G., Wheeler, R.G.: Solid State Commun.27, 859 (1978)

    Google Scholar 

  7. Kugler, W., Knorr, K., Ihringer, J., Prandl, W.: Diskussionstagung der AGKP, Aachen, 19.3.–21.3.1979 and priv. comm.

  8. Boysen, H., Hewat, A.W.: Acta Cryst. B34, 1412 (1978)

    Google Scholar 

  9. Boysen, H., Ihringer, J., Prandl, W., Yelon, W.: Solid State Commun.20, 1019 (1976)

    Google Scholar 

  10. Pelzl, J., Engels, P., Florian, R.: Phys. Stat. Sol. b82, 145 (1977)

    Google Scholar 

  11. Jeffrey, K.R.: J. Magn. Res.7, 184 (1972)

    Google Scholar 

  12. Strange, J.H., Terenzi, M.: J. Phys. Chem. Sol.33, 923 (1972)

    Google Scholar 

  13. Svare, I., Thorkildsen, G., Andersson, H.I., Skjaeveland, S.M., Trivijtkasem, P.: J. Phys. C, Solid State Phys.11, 997 (1978)

    Google Scholar 

  14. Blinc, R., Lahajnar, G.: J. Chem. Phys.47, 4146 (1967)

    Google Scholar 

  15. Schlemper, E.O., Hamilton, W., Rush, J.J.: J. Chem. Phys.44, 2499 (1966)

    Google Scholar 

  16. Pelzl, J., Florian, R., Lütgert, U. In: Proc. 6th. Int. Conf. on Raman Spectroscopy. Vol. 2, p. 246. Schmid, E.D., Krishnan, R.S., Kiefer, W., Schrötter, H.W. (eds.). London: Heyden 1978

    Google Scholar 

  17. Dimitropoulos, C., Pelzl, J. In: 5th Intern. NQRS Symposium. Toulouse, Sept. 1979, and J. Mol. Struct., in press

  18. Benedek, G.B., Fritsch, K.: Phys. Rev.149, 647 (1966)

    Google Scholar 

  19. Cummins, H.Z., Schoen, P.E. In: Laser Handbook. Arecchi, F.T., Schulz Du Bois, E.O. (eds.) p. 1031. Amsterdam: North Holland Publ. 1972

    Google Scholar 

  20. Landolt-Börnstein III/11., Hellwege, K.H., Hellwege, A.M. (eds.). Berlin, Heidelberg, New York: Springer 1979

  21. Pelzl, J., Miller, A.J., Ford, P., Saunders, G.A.: 17th Annual Solid State Conf., Jan. 1980, Warwick (U.K.) Pelzl, J., Höck, K.-H., Saunders, G.A.: Verh. DPG 1980, Frühjahrstagung Freudenstadt

  22. Landau, L.D., Lifshitz, E.M.: Lehrbuch der Theoretischen Physik, Bd. V, Statistische Physik. Berlin: Akademie Verlag 1966

    Google Scholar 

  23. Bradley, C., Cracknell, A.P.: The mathematical theory of symmetry in solids. Oxford: Clarendon Press 1972

    Google Scholar 

  24. Gufan, Y.M.: Sov. Phys. Solid State13, 175 (1971)

    Google Scholar 

  25. Ascher, E.: J. Phys. C, Solid State Phys.10, 1365 (1977)

    Google Scholar 

  26. Dvorak, V.: In preparation, will be published in “Topics in Modern Physics”, Springer Verlag

  27. Thomas, H., Müller, K.A.: Phys. Rev. Lett.17, 1256 (1968)

    Google Scholar 

  28. Slonczewski, J.C., Thomas, H.: Phys. Rev. B9, 3599 (1970)

    Google Scholar 

  29. Murata, K.K.: Phys. Rev. B13, 4015 (1976); Phys. Rev. B15, 4328 (1977) and the literature mentioned therein

    Google Scholar 

  30. Thomas, H.: Structural phase transitions and soft modes, in “Structural phase transitions and soft modes”. Samuelsen, E.J., Andersen, E., Feder, J. (eds.) p. 15. Oslo: Universitetsforlaget 1971

    Google Scholar 

  31. Thomas, H.: Mean-field theory of phase transitions, in Proceedings of the International School of Physics Enrico Fermi, Course LIX 1976 on “Local properties at phase transitions”. Müller, K.A., Rigamonti, A. (eds.) p. 3. Amsterdam: North-Holland 1976

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Work supported by the Deutsche Forschungsgemeinschaft and the Swiss National Science Foundation

Rights and permissions

Reprints and permissions

About this article

Cite this article

Henkel, W., Pelzl, J., Höck, K.H. et al. Elastic constants and softening of acoustic modes in A2MX6-crystals observed by Brillouin scattering. Z Physik B 37, 321–332 (1980). https://doi.org/10.1007/BF01352742

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01352742

Keywords

Navigation