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Origin of morphotropic phase boundaries in ferroelectrics


A piezoelectric material is one that generates a voltage in response to a mechanical strain (and vice versa). The most useful piezoelectric materials display a transition region in their composition phase diagrams, known as a morphotropic phase boundary1,2, where the crystal structure changes abruptly and the electromechanical properties are maximal. As a result, modern piezoelectric materials for technological applications are usually complex, engineered, solid solutions, which complicates their manufacture as well as introducing complexity in the study of the microscopic origins of their properties. Here we show that even a pure compound, in this case lead titanate, can display a morphotropic phase boundary under pressure. The results are consistent with first-principles theoretical predictions3, but show a richer phase diagram than anticipated; moreover, the predicted electromechanical coupling at the transition is larger than any known. Our results show that the high electromechanical coupling in solid solutions with lead titanate is due to tuning of the high-pressure morphotropic phase boundary in pure lead titanate to ambient pressure. We also find that complex microstructures or compositions are not necessary to obtain strong piezoelectricity. This opens the door to the possible discovery of high-performance, pure-compound electromechanical materials, which could greatly decrease costs and expand the utility of piezoelectric materials.

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Figure 1: Pressure dependence of energy dispersive and high-resolution angle-dispersive X-ray diffraction spectra at selected pressures at 10 K.
Figure 2: Raman spectra.
Figure 3: Lattice strain and monoclinic angle.
Figure 4: Phase diagram for lead titanate.


  1. 1

    Groth, P. Ueber Beziehungen zwischen Krystallform und chemische Constitution bei einigen organischen Verbindungen. Ann. Phys. Chem. 217, 31 (1870)

    ADS  Article  Google Scholar 

  2. 2

    Goldschmidt, V. M. Crystal structure and chemical constitution. A lecture delivered before the Faraday Society on Thursday, 14th March, 1929. Trans. Faraday Soc. 25, 253 (1929)

    CAS  Article  Google Scholar 

  3. 3

    Wu, Z. & Cohen, R. E. Pressure-Induced anomalous phase transitions and colossal enhancement of piezoelectricity in PbTiO3 . Phys. Rev. Lett. 95, 037601 (2005)

    ADS  Article  Google Scholar 

  4. 4

    Jaffe, B., Roth, R. S. & Marzullo, S. Piezoelectric properties of lead zirconate-lead titanate solid-solution ceramics. J. Appl. Phys. 25, 809–810 (1954)

    ADS  CAS  Article  Google Scholar 

  5. 5

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

    ADS  CAS  Article  Google Scholar 

  6. 6

    Guo, R. et al. Origin of the high piezoelectric response in PbZr1-xTixO3 . Phys. Rev. Lett. 84, 5423–5426 (2000)

    ADS  CAS  Article  Google Scholar 

  7. 7

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

    ADS  CAS  Article  Google Scholar 

  8. 8

    Cohen, R. E. Relaxors go critical. Nature 441, 941–942 (2006)

    ADS  CAS  Article  Google Scholar 

  9. 9

    Burns, G. & Scott, B. A. Raman studies of underdamped soft modes in PbTiO3. Phys. Rev. Lett. 25, 167–170 (1970)

    ADS  CAS  Article  Google Scholar 

  10. 10

    Sanjurjo, J. A., Lopez-Cruz, E. & Burns, G. High-pressure Raman study of zone-center phonons in PbTiO3 . Phys. Rev. B 28, 7260–7268 (1983)

    ADS  CAS  Article  Google Scholar 

  11. 11

    Feng, Y. et al. Energy dispersive x-ray diffraction of charge density waves via chemical filtering. Rev. Sci. Instrum. 76, 063913 (2005)

    ADS  Article  Google Scholar 

  12. 12

    Rutt, U. et al. Diffractometer for high energy X-rays at the APS. Nucl. Instrum. Meth. Phys. Res. A 467–468, 1026–1029 (2001)

    ADS  Article  Google Scholar 

  13. 13

    Sani, A. et al. High-pressure phases in highly piezoelectric PbZr0. 52Ti0. 48O3 . Phys. Rev. B 69, 020105 (2004)

    ADS  Article  Google Scholar 

  14. 14

    Noheda, B. et al. Stability of the monoclinic phase in the ferroelectric perovskite PbZr1-xTixO3 . Phys. Rev. B 63, 014103 (2000)

    ADS  Article  Google Scholar 

  15. 15

    La-orauttapong, D. et al. Phase diagram of the relaxor ferroelectric (1-x)Pb(Zn1/3Nb2/3)-xPbTiO3 . Phys. Rev. B 65, 144101 (2002)

    ADS  Article  Google Scholar 

  16. 16

    Noheda, B., Cox, D. E., Shirane, G., Guo, J. & Ye, Z.-G. Phase diagram of the ferroelectric relaxor (1-x)Pb(Mg1/3Nb2/3)-xPbTiO3 . Phys. Rev. B 66, 054104 (2002)

    ADS  Article  Google Scholar 

  17. 17

    Vanderbilt, D. & Cohen, M. H. Monoclinic and triclinic phases in higher-order Devonshire theory. Phys. Rev. B 63, 94108–94117 (2001)

    ADS  Article  Google Scholar 

  18. 18

    Kornev, I. A. et al. Ferroelectricity of perovskites under pressure. Phys. Rev. Lett. 95, 196804 (2005)

    ADS  Article  Google Scholar 

  19. 19

    Cohen, R. E. Origin of ferroelectricity in oxide ferroelectrics. Nature 358, 136–138 (1992)

    ADS  CAS  Article  Google Scholar 

  20. 20

    Waghmare, U. V. & Rabe, K. M. ab initio statistical mechanics of the ferroelectric phase transition in PbTiO3 . Phys. Rev. B 55, 6161–6173 (1997)

    ADS  CAS  Article  Google Scholar 

  21. 21

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

    ADS  Article  Google Scholar 

  22. 22

    Ghita, M., Fornari, M., Singh, D. J. & Halilov, S. V. Interplay between A -site and B -site driven instabilities in perovskites. Phys. Rev. B 72, 054114 (2005)

    ADS  Article  Google Scholar 

  23. 23

    Jin, Y. M., Wang, Y. U., Kachaturyan, A. G., Li, J. F. & Vielhland, D. Conformal miniaturization of domains with low domain wall energy: Monoclinic ferroelectric states near morphotropic phase boundaries. Phys. Rev. Lett. 91, 197601 (2003)

    ADS  CAS  Article  Google Scholar 

  24. 24

    Schonau, K. et al. Nanodomain structure of Pb[Zr1-xTi]O3 at its morphotropic phase boundary: Investigations from local to average structure. Phys. Rev. B 75, 184117 (2007)

    ADS  Article  Google Scholar 

  25. 25

    Rao, W.-F. & Wang, Y. U. Microstrutures of coherent phase decomposition near morphotropic phase boundary in lead zirconate titanate. Appl. Phys. Lett. 91, 052901 (2007)

    ADS  Article  Google Scholar 

  26. 26

    Ahart, M. et al. Single-domain electromechanical constants for Pb(Zn1/3Nb2/3)O3-4.5%PBTiO3 from micro-Brillouin scattering. Appl. Phys. Lett. 88, 042908 (2006)

    ADS  Article  Google Scholar 

  27. 27

    Gonze, X. et al. First-principles computation of material properties: the ABINIT software project. Comput. Mater. Sci. 25, 478–492 (2002)

    Article  Google Scholar 

  28. 28

    Ramirez, R., Lapena, M. F. & Gonzalo, J. A. Pressure dependence of free-energy expansion coefficients in PbTiO3 and BaTiO3 and tricritical-point behavior. Phys. Rev. B 42, 2604–2606 (1990)

    ADS  CAS  Article  Google Scholar 

  29. 29

    Heinz, D. & Jeanloz, R. The equation of state of the gold calibration standard. J. Appl. Phys. 55, 885–893 (1984)

    ADS  CAS  Article  Google Scholar 

  30. 30

    Goncharov, A. F. & Struzhkin, V. Raman spectroscopy of metals, high-temperature superconductors and related materials under high pressure. J. Raman Spectrosc. 34, 532–548 (2003)

    ADS  CAS  Article  Google Scholar 

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We thank D. Rytz for the PbTiO3 crystals. We thank B. Noheda and E. Salje for discussions. We also thank our GL colleagues R. Caracas, K. P. Esler Jr. and S. Gramsch for discussions. This work was sponsored by the Office of Naval Research. Support was also received from the Carnegie/Department of Energy Alliance Center (CDAC). High-pressure X-ray diffraction at the HPCAT facility of Advanced Photon Source was supported by DOE-BES, DOE-NNSA (CDAC), and the W. M. Keck Foundation. Use of the Advanced Photon Source was supported by the US Department of Energy, Office of Science, Office of Basic Energy Sciences.

Author Contributions M.A., M.S., H.-k.M., R.E.C. and R.J.H. conceived the project as a part of previous work3. M.A., M.S., H.-k.M. and R.J.H. executed the sample loading, Raman scattering and X-ray diffraction studies. P.D., Y.R. and P.L. helped in synchorotron X-ray diffraction experiments. P.G., Z.W. and R.E.C. carried out first-principles simulations.

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Correspondence to R. E. Cohen.

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Supplementary Information

This file contains Supplementary Methods, Supplementary Table 1 and Supplementary Figures 5-9 with Legends. (PDF 555 kb)

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Ahart, M., Somayazulu, M., Cohen, R. et al. Origin of morphotropic phase boundaries in ferroelectrics. Nature 451, 545–548 (2008).

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