Research ArticleMATERIALS SCIENCE

Giant electromechanical coupling of relaxor ferroelectrics controlled by polar nanoregion vibrations

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Science Advances  16 Sep 2016:
Vol. 2, no. 9, e1501814
DOI: 10.1126/sciadv.1501814
  • Fig. 1 Phonon dispersion along Q = [2 + H, −2 + H, 0] (L = 0 ± 0.05) in PMN-30%PT comparing temperature and poling effects.

    (A) Unpoled crystal measured above TC at 488 K showing a single TA mode. (B) Unpoled crystal measured below TC at 300 K showing splitting of the TA phonon. (C and D) Sketches of the diffuse elastic scattering around (HH0) reflections in the (HK0) plane, above and below TC (7, 28). (E) Inelastic scattering intensity map at the energy of the lower branch of the split TA phonon (E = [2, 4] meV) near the (2, −2, 0) reflection in the (HK0) plane. (F) [100]-poled PMN-30%PT showing a marked softening of the lower section of the TA branch (left) and an increase in the splitting of the TA mode from 1.5 to 2 meV (right). Data points overlaying the images of the TA phonon [center in (A), (B), and (F)] are peak positions from fits to the data, and the white lines running through these points are guides to the eye. (G) Confirmation of features in the (1, −1, 0) zone for the same direction, Q = [1 + H, −1 + H, 0]. The transverse optic (TO) and upper TA branch appear relatively weaker in the (1, −1, 0) zone, but the same features appear. All measurements were made on the time-of-flight angular-range chopper spectrometer (ARCS) at the Spallation Neutron Source, Oak Ridge National Laboratory.

  • Fig. 2 Simple model for coupling lattice modes to PNRs.

    (A) Average crystal structure of PMN-PT. (B) The TO and TA phonons approximated as one-dimensional displacements of planes of atoms. (C) Model for coupling PNR clusters to the lattice, where MO is the atomic mass of 2O, 32 u; MABO is the average mass on the alternate plane containing 1A, 1B, and 1O atoms, 286.4 u; and MPNR is the fractional mass of the PNR clusters, 200 u (see Supplementary calculations). The force constants are KAA = 14,000 u-meV2 and KAO = 500 u-meV2. The PNRs are assumed to be internally rigid, and c accounts for the coupling between the lattice and PNRs. (D) The solution for zero coupling, c/KAA = 0, exhibiting TO and TA modes and zero-energy PNR cluster dynamics that cross the TA mode at k = 0. Solution with coupling, c/KAA = 0.1, exhibits anticrossing with low-energy dynamics. At k = 0, the lower symmetric branch has PNRs moving in phase, and the upper antisymmetric branch has them moving out of phase with the lattice. (E) Sketch of the symmetric and antisymmetric TA-PNR motions in a lattice partially occupied with PNRs.

  • Fig. 3 Time-of-flight neutron scattering measurements of [100]-poled and unpoled PMN-30%PT at 300 K.

    (A) Phonon dispersion measured along Q = [2, K, 0] (H = 2 ± 0.025 and L = 0 ± 0.025). The PNR mode appears enhanced in this direction. (B) Phonon dispersion measured along Q = [H, −2, 0] (K = −2 ± 0.025 and L = 0±0.025). The PNR mode does not appear in this direction. The data points overlaying the images to the left of (A) and (B) are from peak fits, and the white lines running through these points are guides to the eye. (C and D) Diffuse elastic scattering (E = 0 ± 0.5 meV) measured with Q approximately parallel to the [100] poling direction on the (H, −1 ± 0.025, L) and (H, −0.5 ± 0.025, L) planes. (E and F) Diffuse elastic scattering on the (1 ± 0.025, K, L) and (0.5 ± 0.025, K, L) scattering planes, which are the equivalent to (C) and (D) except along directions approximately perpendicular to the [100] poling direction (see diagram for geometries). (G and H) Difference images created by subtracting (E) from (C), and (F) from (D) revealing vertical bands of diffuse scattering. The inset data points in (H) were obtained by integrating the difference image over L = [−1, 1]. The fit is described in the text. All measurements were made on the time-of-flight ARCS at the Spallation Neutron Source, Oak Ridge National Laboratory.

  • Fig. 4 Relationship between the soft [110]-TA phonon and the giant electromechanical coupling.

    (A) The [110]-TA phonon displacements include a shear deformation that tilts the [110] axis around the nonpolar [001] axis. The softening of this phonon at long wavelengths (near the zone center in Fig. 1) implies a softening of the indicated shear distortion. (B) The tilting of the [110] axis around [001] also results in the tilting of the [111] axis around [001] because it is in the same tilting plane [the (1, −1, 0) plane]. (C) An equivalent soft TA phonon involving the tilting of the [111] axis around [010] (the other nonpolar axis) must also exist by symmetry. (D) Combination of the soft distortions in (B) and (C) rotates the [111] axis toward the [100] polar axis. (E) Equivalent distortions in all four rhombohedral domain variants (4R) (31) distort the domains toward the [100] poling direction under the application of an electric field, E. The [100] poling aligns the PNR modes along the poling direction (red arrow).

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/2/9/e1501814/DC1

    Supplementary calculations

    fig. S1. Phonon dispersion curves measured along Q = [2, K, 0] in PZN-5%PT and PMN-38%PT, both above and below TC.

    fig. S2. Photograph of poled PMN-30%PT crystals.

    References (52, 53)

  • Supplementary Materials

    This PDF file includes:

    • Supplementary calculations
    • fig. S1. Phonon dispersion curves measured along Q = 2, K, 0 in PZN-5%PT and PMN-38%PT, both above and below TC.
    • fig. S2. Photograph of poled PMN-30%PT crystals.
    • References (52, 53)

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