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Fig. 8. (a) Temperature dependence of the Brillouin shift and FWHM of PMN-xPT crystals (x = 0, 0.15, 0.31, 0.35, 0.55) single crystals. (b) Relaxation time calculated from the data in (a) shown in the Arrhenius plot. The solid lines are the best-fitted results obtained by using the modified superparaelectric model. The inset of (b) shows the change in the activation barrier extrapolated to 0 K as a function of PT content. (see Ref. [38]) AINE AE EIDE ———————————eee ee eS eeeeeeeeeEeEeeeeEeEOeeeeEEeEeeeEeEeeee As the extraordinarily large piezoelectric properties have been noted for both the PMN-xPT and PZN-2PT single crystals, in partic- ular, at MPB, acoustic behaviors of these crystals near MPB have also been studied by Brillouin scattering intensively. The first systematic investigation was carried out on PMN-35%PT located near MPB [18,19]. Fig. 7 shows the temperature dependence of the Brillouin frequency shift and the full width at half maximum (FWHM) of the LA mode of PMN-352PT. This study revealed peculiar acoustic anomalies of PMN-35%PT: (1) LA mode frequency showed a substantial softening upon cooling toward the cubic-tetragonal phase transition temperature (Tc): (2) A strong central peak appeared at temperatures close to Tc_y. The central peak was explained by using the Eq.(4) to derive the temperature dependence of the relaxation time. The details of CP will be discussed in the next section. The Brillouin spectroscopy has later been applied to PMN- XPT single crystals covering a wide composition range including MPB [38]. Five PMN-xPT single crystals with 0 < x < 0.55 were investigated in a wide temperature range and the results are shown in Fig. 8(a). It can be noticed that all the LA modes of these single crystals exhibit softening at high temperatures below ~700 K accompanied by increasing damping upon further cooling. Since the onset temperature of this softening is systematically higher than Tp, the acoustic anomalies were attributed to the combined effects of the interactions between the acoustic phonon and the soft trans- verse optic phonon and the fluctuating PNRs. The temperature dependence of the relaxation time of the relaxation process coupled to the LA phonon can be quantitatively derived from acoustic dispersion relation based on a single-relaxation-time approxima- tion [48]. The obtained relaxation times are shown in the Arrhenius plot in Fig. 8(b). The relaxation time of all samples becomes larger The acoustic anomalies of typical relaxor behaviors observed from PMN and PZN become more complex as the PT content increases toward MPB. The LA mode frequencies of PZN-7%PT and PMN-312PT, located on the rhombohedral side but closer to MPB, exhibit step-like changes at the cubic-tetragonal phase transitions

Figure 8 (a) Temperature dependence of the Brillouin shift and FWHM of PMN-xPT crystals (x = 0, 0.15, 0.31, 0.35, 0.55) single crystals. (b) Relaxation time calculated from the data in (a) shown in the Arrhenius plot. The solid lines are the best-fitted results obtained by using the modified superparaelectric model. The inset of (b) shows the change in the activation barrier extrapolated to 0 K as a function of PT content. (see Ref. [38]) AINE AE EIDE ———————————eee ee eS eeeeeeeeeEeEeeeeEeEOeeeeEEeEeeeEeEeeee As the extraordinarily large piezoelectric properties have been noted for both the PMN-xPT and PZN-2PT single crystals, in partic- ular, at MPB, acoustic behaviors of these crystals near MPB have also been studied by Brillouin scattering intensively. The first systematic investigation was carried out on PMN-35%PT located near MPB [18,19]. Fig. 7 shows the temperature dependence of the Brillouin frequency shift and the full width at half maximum (FWHM) of the LA mode of PMN-352PT. This study revealed peculiar acoustic anomalies of PMN-35%PT: (1) LA mode frequency showed a substantial softening upon cooling toward the cubic-tetragonal phase transition temperature (Tc): (2) A strong central peak appeared at temperatures close to Tc_y. The central peak was explained by using the Eq.(4) to derive the temperature dependence of the relaxation time. The details of CP will be discussed in the next section. The Brillouin spectroscopy has later been applied to PMN- XPT single crystals covering a wide composition range including MPB [38]. Five PMN-xPT single crystals with 0 < x < 0.55 were investigated in a wide temperature range and the results are shown in Fig. 8(a). It can be noticed that all the LA modes of these single crystals exhibit softening at high temperatures below ~700 K accompanied by increasing damping upon further cooling. Since the onset temperature of this softening is systematically higher than Tp, the acoustic anomalies were attributed to the combined effects of the interactions between the acoustic phonon and the soft trans- verse optic phonon and the fluctuating PNRs. The temperature dependence of the relaxation time of the relaxation process coupled to the LA phonon can be quantitatively derived from acoustic dispersion relation based on a single-relaxation-time approxima- tion [48]. The obtained relaxation times are shown in the Arrhenius plot in Fig. 8(b). The relaxation time of all samples becomes larger The acoustic anomalies of typical relaxor behaviors observed from PMN and PZN become more complex as the PT content increases toward MPB. The LA mode frequencies of PZN-7%PT and PMN-312PT, located on the rhombohedral side but closer to MPB, exhibit step-like changes at the cubic-tetragonal phase transitions

Related Figures (13)

Fig. 1. Perovskite structure ABO3. In PMN, A-site is occupied by a Pb?* ion, and B-site is randomly occupied by Mg?* and Nb*+ ions.
Fig. 1. Perovskite structure ABO3. In PMN, A-site is occupied by a Pb?* ion, and B-site is randomly occupied by Mg?* and Nb*+ ions.
Fig. 2. Temperature evolution of PNRs and characteristic temperatures. angular frequency w is related to the imaginary part of the dynamic susceptibility y(q,w) via
Fig. 2. Temperature evolution of PNRs and characteristic temperatures. angular frequency w is related to the imaginary part of the dynamic susceptibility y(q,w) via
Fig. 4. Brillouin scattering spectrum of a PMN-35%PT crystal just above the Curie temperature. (see Ref. [19])
Fig. 4. Brillouin scattering spectrum of a PMN-35%PT crystal just above the Curie temperature. (see Ref. [19])
Fig. 3. Schematic illustration of broadband micro-Brillouin scattering spectroscopy. Archetypal RFEs such as PMN, Pb(Mgj/3Ta2/3)TiO3 (PMT) and Pb(Zn1/3Nb2/3)03 (PZN) are featured by the diffusive and broad dielectric peaks along with their significant frequency dispersion. Typical dielectric dispersion of RFEs is shown in Fig. 5, which exhibits temperature and frequency dependences of the complex dielectric constant ¢*(w,T) = €/(w,T)+ie”(w,T) of a PMT crystal with the B-site disorder [23]. The characteristic relaxation frequency of PMT, estimated from the peak position of either real or imaginary part of ¢*(w,T), normally obeys the Vogel-Fulcher law and reflects freezing process of PNR dynamics at low temperatures as shown in Fig. 5(c). Moreover, as Fig. 5(d) suggests, the leading edge of the
Fig. 3. Schematic illustration of broadband micro-Brillouin scattering spectroscopy. Archetypal RFEs such as PMN, Pb(Mgj/3Ta2/3)TiO3 (PMT) and Pb(Zn1/3Nb2/3)03 (PZN) are featured by the diffusive and broad dielectric peaks along with their significant frequency dispersion. Typical dielectric dispersion of RFEs is shown in Fig. 5, which exhibits temperature and frequency dependences of the complex dielectric constant ¢*(w,T) = €/(w,T)+ie”(w,T) of a PMT crystal with the B-site disorder [23]. The characteristic relaxation frequency of PMT, estimated from the peak position of either real or imaginary part of ¢*(w,T), normally obeys the Vogel-Fulcher law and reflects freezing process of PNR dynamics at low temperatures as shown in Fig. 5(c). Moreover, as Fig. 5(d) suggests, the leading edge of the
Fig. 5. The dielectric dispersion of PMT, BMT crystals ((a) and (b)) and the temperature dependence of the characteristic relaxation times of PMT ((c) and (d)). (see Ref. [23])
Fig. 5. The dielectric dispersion of PMT, BMT crystals ((a) and (b)) and the temperature dependence of the characteristic relaxation times of PMT ((c) and (d)). (see Ref. [23])
Fig. 6. A schematic phase diagram of PMN-xPT and PZN-xPT, where C, T, O, R, M denote cubic, tetragonal, orthorhombic, rhombohedral, and monoclinic phases, respectively. The first investigation into the temperature evolution of acoustic properties of PMN was studied either by the ultrasonic [34] or Brillouin scattering method [35,36]. These early results
Fig. 6. A schematic phase diagram of PMN-xPT and PZN-xPT, where C, T, O, R, M denote cubic, tetragonal, orthorhombic, rhombohedral, and monoclinic phases, respectively. The first investigation into the temperature evolution of acoustic properties of PMN was studied either by the ultrasonic [34] or Brillouin scattering method [35,36]. These early results
Fig. 7. Temperature dependence of Brillouin shift and FWHM of a PMN-35%PT crystal. (see Ref.s [18] and [19])
Fig. 7. Temperature dependence of Brillouin shift and FWHM of a PMN-35%PT crystal. (see Ref.s [18] and [19])
Fig. 9. Temperature dependence of (a) the LA mode frequency and (b) the FWHM of PZN-xPT crystals (x = 0.045.0.07, 0.09). (see Ref. [47])
Fig. 9. Temperature dependence of (a) the LA mode frequency and (b) the FWHM of PZN-xPT crystals (x = 0.045.0.07, 0.09). (see Ref. [47])
Fig. 10. Temperature dependence of the polarized (VV) and depolarized (VH) (a) CP intensity and (b) the width of a PZN-4.5%PT crystal measured at polarized and depolarized scattering geometries. The inset of (b) shows the temperature dependence of relaxation times estimated from the width of polarized and depolarized CPs. (see Ref. [49])
Fig. 10. Temperature dependence of the polarized (VV) and depolarized (VH) (a) CP intensity and (b) the width of a PZN-4.5%PT crystal measured at polarized and depolarized scattering geometries. The inset of (b) shows the temperature dependence of relaxation times estimated from the width of polarized and depolarized CPs. (see Ref. [49])
Fig. 11. Microheterogeneity of a PMN-35PT crystal. (see Ref. [18]) Additional feature revealed by BMBS is the microheterogeneity of RFEs. As the beam waist of the laser light at the focal point in BMBS is only a few um, inherent micrometer-scale inhomogeneity of condensed matters can be easily probed and systematically investigated by BMBS. Brillouin shift and FWHM of PMN-35%PT shown in Fig. 7 were found to be very sensitive to the chosen microarea in the ferroelectric phase while they did not show any positional dependence in the paraelectric phase [18]. This micro- heterogeneity induces the variation of local symmetry from one microarea to another in the ferroelectric phase. Fig. 11 clearly shows the micro areal dependence of the Brillouin spectrum of PMN-35%
Fig. 11. Microheterogeneity of a PMN-35PT crystal. (see Ref. [18]) Additional feature revealed by BMBS is the microheterogeneity of RFEs. As the beam waist of the laser light at the focal point in BMBS is only a few um, inherent micrometer-scale inhomogeneity of condensed matters can be easily probed and systematically investigated by BMBS. Brillouin shift and FWHM of PMN-35%PT shown in Fig. 7 were found to be very sensitive to the chosen microarea in the ferroelectric phase while they did not show any positional dependence in the paraelectric phase [18]. This micro- heterogeneity induces the variation of local symmetry from one microarea to another in the ferroelectric phase. Fig. 11 clearly shows the micro areal dependence of the Brillouin spectrum of PMN-35%
Fig. 12. (a) Temperature dependence of the LA mode frequency and the FWHM. (b) The relaxation time estimated from the data in (a) as a function of temperature. (see Ref. [28])
Fig. 12. (a) Temperature dependence of the LA mode frequency and the FWHM. (b) The relaxation time estimated from the data in (a) as a function of temperature. (see Ref. [28])
Fig. 13. The dependence of (a) the TA1 mode frequency and (b) the FWHM of PZN-9% PT on the applied electric field along the <001 > direction. (see Ref. [66]) As to the origin of the superior piezoelectric-response of PMN-xPT and PZN-xPT near MPB, special attention has been paid on the polarization rotation path during the field-induced phase transition from rhombohedral to tetragonal symmetry under an electric field along the <001 > direction [64]. The inset of Fig. 13 shows possible polarization vectors of various phases in the perovskite unit cell. The notations are adopted after Ref. [65]. The acoustic properties can be a good probe in revealing the mecha- nism of polarization rotations since the sound velocity and its
Fig. 13. The dependence of (a) the TA1 mode frequency and (b) the FWHM of PZN-9% PT on the applied electric field along the <001 > direction. (see Ref. [66]) As to the origin of the superior piezoelectric-response of PMN-xPT and PZN-xPT near MPB, special attention has been paid on the polarization rotation path during the field-induced phase transition from rhombohedral to tetragonal symmetry under an electric field along the <001 > direction [64]. The inset of Fig. 13 shows possible polarization vectors of various phases in the perovskite unit cell. The notations are adopted after Ref. [65]. The acoustic properties can be a good probe in revealing the mecha- nism of polarization rotations since the sound velocity and its
Fig. 14. The temperature dependence of (a) the LA mode frequency and (b) the FWHM of PZN-9%PT under the electric field along the <001 > direction. (see Ref. [68]) The field-induced effects on the temperature evolution of PZN-xPT single crystals were investigated by Kim et al. [60,68]. Fig. 14 shows the temperature dependence of the Brillouin shift and the FWHM of the LA mode of PZN-9%PT under an external field along the <001 > direction, which were compared to the zero- field-cooling data. As can be seen from this figure, the application of the electric field to this direction results in two major conse- quences: (1) The tetragonal phase is substantially extended in the temperature window. (2) The discontinuous change in the acoustic
Fig. 14. The temperature dependence of (a) the LA mode frequency and (b) the FWHM of PZN-9%PT under the electric field along the <001 > direction. (see Ref. [68]) The field-induced effects on the temperature evolution of PZN-xPT single crystals were investigated by Kim et al. [60,68]. Fig. 14 shows the temperature dependence of the Brillouin shift and the FWHM of the LA mode of PZN-9%PT under an external field along the <001 > direction, which were compared to the zero- field-cooling data. As can be seen from this figure, the application of the electric field to this direction results in two major conse- quences: (1) The tetragonal phase is substantially extended in the temperature window. (2) The discontinuous change in the acoustic
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