Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Letter
  • Published:

Relationship between local structure and phase transitions of a disordered solid solution


The Pb(Zr,Ti)O3 (PZT) disordered solid solution is widely used in piezoelectric applications owing to its excellent electromechanical properties. Six different structural phases have been observed for PZT at ambient pressure, each with different lattice parameters and average electric polarization. It is of significant interest to understand the microscopic origin of the complicated phase diagram and local structure of PZT1,2,3,4,5,6,7,8. Here, using density functional theory calculations, we show that the distortions of the material away from the parent perovskite structure can be predicted from the local arrangement of the Zr and Ti cations. We use the chemical rules obtained from density functional theory to create a phenomenological model to simulate PZT structures. We demonstrate how changes in the Zr/Ti composition give rise to phase transitions in PZT through changes in the populations of various local Pb atom environments.

This is a preview of subscription content, access via your institution

Access options

Buy this article

Prices may be subject to local taxes which are calculated during checkout

Figure 1: Pair distribution functions (PDFs) for PZT with 50% Zr/50% Ti.
Figure 2: Projection of the 4 × 2 × 1 50/50 supercell DFT PZT structure on the xy plane.
Figure 3

Similar content being viewed by others


  1. Bellaiche, L., Garcia, A. & Vanderbilt, D. Finite-temperature properties of Pb(Zr1-xTix)O3 alloys from first principles. Phys. Rev. Lett. 84, 5427–5430 (2000)

    Article  ADS  CAS  Google Scholar 

  2. Noheda, B. et al. A monoclinic ferroelectric phase in the Pb(Zr1-xTix)O3 solid solution. Appl. Phys. Lett. 74, 2059–2061 (1999)

    Article  ADS  CAS  Google Scholar 

  3. Cohen, R. E. Origin of ferroelectricity in perovskite oxides. Nature 358, 136–138 (1992)

    Article  ADS  CAS  Google Scholar 

  4. Fu, H. & Cohen, R. E. Polarization rotation mechanism for ultrahigh electromechanical response in single-crystal piezoelectrics. Nature 403, 281–283 (2000)

    Article  ADS  CAS  Google Scholar 

  5. Ghosez, P., Cockayne, E., Waghmare, U. V. & Rabe, K. M. Lattice dynamics of BaTiO3, PbTiO3, and PbZrO3: A comparative first-principles study. Phys. Rev. B 60, 836–843 (1999)

    Article  ADS  CAS  Google Scholar 

  6. Saghi-Szabo, G., Cohen, R. E. & Krakauer, H. First-principles study of piezoelectricity in tetragonal PbTiO3 and PbZr1/2Ti1/2O3 . Phys. Rev. B 59, 12771–12776 (1999)

    Article  ADS  CAS  Google Scholar 

  7. Fornari, M. & Singh, D. J. Possible coexistence of rotational and ferroelectric lattice distortions in rhombohedral PbZrxTi1-xO3 . Phys. Rev. B 63, 092101 (2001)

    Article  ADS  Google Scholar 

  8. Dmowski, W., Egami, T., Farber, L. & Davies, P. K. in Fundamental Physics of Ferroelectrics—Eleventh Williamsburg Ferroelectrics Workshop (ed. Cohen, R. E.) 33–44 (AIP, Woodbury, New York, 2001)

    Google Scholar 

  9. Egami, T., Dmowski, W., Akbas, M. & Davies, P. K. in First-Principles Calculations for Ferroelectrics—Fifth Williamsburg Workshop (ed. Cohen, R. E.) 1–10 (AIP, Woodbury, New York, 1998)

    Google Scholar 

  10. Brese, N. E. & O'Keeffe, M. Bond-valence parameters for solids. Acta Crystallogr. B 47, 192–197 (1991)

    Article  Google Scholar 

  11. Brown, I. D. in Structure and Bonding in Crystals II (eds O'Keeffe, M. & Navrotsky, E.) 1–30 (Academic, New York, 1981)

    Book  Google Scholar 

Download references


We thank T. Egami, W. Dmowski and P. K. Davies for discussions and for sharing PDF data. This work was supported by the Office of Naval Research and the National Science Foundation. Computational support was provided by the High-Performance Computing Modernization Office of the Department of Defense and the Center for Piezoelectric Design. A.M.R. thanks the Camille and Henry Dreyfus Foundation for support.

Author information

Authors and Affiliations


Corresponding author

Correspondence to Andrew M. Rappe.

Ethics declarations

Competing interests

The authors declare that they have no competing financial interests.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Grinberg, I., Cooper, V. & Rappe, A. Relationship between local structure and phase transitions of a disordered solid solution. Nature 419, 909–911 (2002).

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI:

This article is cited by


By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing