Correlating electromechanical and dielectric properties with nanometre-scale order is the defining challenge for the development of piezoelectric oxides. Current lead (Pb)-based relaxor ferroelectrics can serve as model systems with which to unravel these correlations, but the nature of the local order and its relation to material properties remains controversial. Here we employ recent advances in diffuse scattering instrumentation to investigate crystals that span the phase diagram of PbMg1/3Nb2/3O3-xPbTiO3 (PMN-xPT) and identify four forms of local order. From the compositional dependence, we resolve the coupling of each form to the dielectric and electromechanical properties observed. We show that relaxor behaviour does not correlate simply with ferroic diffuse scattering; instead, it results from a competition between local antiferroelectric correlations, seeded by chemical short-range order, and local ferroic order. The ferroic diffuse scattering is strongest where piezoelectricity is maximal and displays previously unrecognized modulations caused by anion displacements. Our observations provide new guidelines for evaluating displacive models and hence the piezoelectric properties of environmentally friendly next-generation materials.

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Work at the Materials Science Division at Argonne National Laboratory was supported by the US Department of Energy, Office of Science, Materials Sciences and Engineering Division. Research conducted at ORNL’s Spallation Neutron Source was sponsored by the Scientific User Facilities Division, Office of Basic Energy Sciences, US Department of Energy. Research conducted at the Cornell High Energy Synchrotron Source (CHESS) was supported by the NSF and NIH/NIGMS via NSF award DMR-1332208. The work at Simon Fraser University was supported by the US Office of Naval Research (ONR grant numbers N00014-12-11045 and N00014-16-1-3106) and the Natural Sciences and Engineering Research Council of Canada (NSERC grant number 203773). We acknowledge the support of the National Institute of Standards and Technology, US Department of Commerce, in providng access to the neutron Prompt Gamma Activation Analysis (PGAA) research facilities used in this work. We also acknowledge the assistance of R. Paul in performing the PGAA measurements and data analysis.

Author information


  1. Materials Science Division, Argonne National Laboratory, Argonne, IL, USA

    • M. J. Krogstad
    • , S. Rosenkranz
    • , R. Osborn
    • , O. Chmaissem
    •  & D. Phelan
  2. Department of Physics, Northern Illinois University, DeKalb, IL, USA

    • M. J. Krogstad
    •  & O. Chmaissem
  3. NIST Center for Neutron Research, National Institute of Standards and Technology, Gaithersburg, MD, USA

    • P. M. Gehring
  4. Neutron Scattering Division, Oak Ridge National Laboratory, Oak Ridge, TN, USA

    • F. Ye
    •  & Y. Liu
  5. CHESS, Cornell University, Ithaca, NY, USA

    • J. P. C. Ruff
  6. Department of Chemistry and 4D LABS, Simon Fraser University, Burnaby, British Columbia, Canada

    • W. Chen
    •  & Z.-G. Ye
  7. Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, IL, USA

    • J. M. Wozniak
  8. Computation Institute, University of Chicago and Argonne National Laboratory, Chicago, IL, USA

    • J. M. Wozniak
  9. Shanghai Institute of Ceramics, Chinese Academy of Sciences, Shanghai, China

    • H. Luo


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D.P. directed the project with guidance from P.M.G. M.J.K., P.M.G., S.R., F.Y., Y.L. and D.P. performed the diffuse neutron scattering experiments. M.J.K., S.R., J.P.C.R., R.O. and D.P. performed the X-ray diffuse scattering experiments. J.M.W. and R.O. developed the infrastructure to transform X-ray data into reciprocal space. W. Chen, Z.-G.Y. and H.L. grew single crystals. P.M.G. performed neutron prompt gamma measurements and analysis. M.J.K. performed the diffuse scattering analysis. D.P., M.J.K., P.M.G. and S.R. wrote the manuscript, with contributions from R.O., Z.-G.Y., Y.L., F.Y. and J.P.C.R. O.C. provided guidance to M.J.K.

Competing Interests

The authors declare no competing interests.

Corresponding author

Correspondence to D. Phelan.

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    Supplementary Notes 1–5, Supplementary References 1,2, Supplementary Figures 1–6

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