Journal of Materials Science

, Volume 27, Issue 10, pp 2589–2594 | Cite as

Phenomenological analysis of tetragonal tungsten bronze ferroelectrics

  • L. E. Cross
  • R. R. Neurgaonkar


A simple Devonshire form has been derived for the phenomenological elastic Gibbs function to describe the elasto-dielectric parameters of simple proper ferroelectrics in the tungsten bronze structure family which has 4/mmm prototypic point symmetry. For the assumption that all temperature dependence is carried by the Curie-Weiss behaviour implicit in the quadratic term and that the expansion may be terminated at the first sixth-order term, reasonable agreement between calculated and derived Ps against T curves in the ferroelectric phase can be obtained for a wide range of bronze compositions. From the fitting it is clear that second and sixth rank terms are remarkably constant over a very wide range of bronze compositions. Variation in the negative fourth rank term is larger, but this is to be expected since it contains large contributions from electrostrictive and elastic terms which will depend on boundary conditions. These initial studies suggest that the phenomenological method may be used to derive expectation values for tensor parameters across the whole family of ferroelectric bronzes. The study also points up the need for more careful detailed studies of lattice strain, birefringence and permittivity as a function of temperature in model bronze compounds to provide more detailed checks of the method.


Gibbs Function Ferroelectric Phase Phenomenological Analysis Tungsten Bronze Phenomenological Method 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    L. E. Cross, R. Betsch, H. Mckinstry, T. Shrout and R. R. Neurgaonkar, in Proceedings of the 34th Frequency Control Symposium, May 1980 (IEEE).Google Scholar
  2. 2.
    T. R. Shrout, L. E. Cross, P. Moses, H. A. Mckinstry and R. R. Neurgaonkar, in Proceedings of the 1980 Ultrasonics Symposium, 1980, (IEEE) p. 414.Google Scholar
  3. 3.
    T. R. Shrout, PhD thesis, The Pennsylvania State University (1981).Google Scholar
  4. 4.
    L. E. Cross and R. C. Pohanka, J. Appl. Phys. 39 (1968) 3992.Google Scholar
  5. 5.
    L. A. Shuvalov, J. Phys. Soc. Suppl. (Jap.) 28 (1970) 38.Google Scholar
  6. 6.
    T. R. Shrout, D. A. Hukin and L. E. Cross, Ferroelectric Lett. 44 (1983) 325.Google Scholar

Copyright information

© Chapman & Hall 1992

Authors and Affiliations

  • L. E. Cross
    • 1
  • R. R. Neurgaonkar
    • 2
  1. 1.Materials Research LaboratoryThe Pennsylvania State UniversityUniversity ParkUSA
  2. 2.Rockwell Science CenterThousand OaksUSA

Personalised recommendations