Dielectric∕piezoelectric resonance in high-strain Pb ( Mg 1 ∕ 3 Nb 2 ∕ 3 ) 1 − x Ti x O 3 crystals Chi-Shun Tu, R. R. Chien, V. H. Schmidt, F.-T. Wang, W.-T. Hsu, C.-T. Tseng, and C. C. Shih Citation: Journal of Applied Physics 97, 126105 (2005); doi: 10.1063/1.1948523 View online: http://dx.doi.org/10.1063/1.1948523 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/97/12?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Effect of crystal orientation on the phase diagrams, dielectric and piezoelectric properties of epitaxial BaTiO3 thin films AIP Advances 6, 015309 (2016); 10.1063/1.4940205 Poling effect and piezoelectric response in high-strain ferroelectric 0.70 Pb ( Mg 1 / 3 Nb 2 / 3 ) O 3 – 0.30 PbTiO 3 crystal J. Appl. Phys. 108, 044101 (2010); 10.1063/1.3475150 Phase diagrams, dielectric response, and piezoelectric properties of epitaxial ultrathin (001) lead zirconate titanate films under anisotropic misfit strains J. Appl. 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Shih Department of Physics, Fu Jen University, Taipei 242, Taiwan, Republic of China Received 28 April 2005; accepted 18 May 2005; published online 24 June 2005 This work presents dielectric resonance in PbMg1/3Nb2/31−xTixO3 crystals after electric E-field poling, which is crucial for piezoelectric applications. Dielectric permittivity has been measured as functions of temperature, frequency, poling E-field strength, and Ti content x=25% and 34%. Frequency-dependent dielectric spectroscopy after poling exhibits multiple piezoelectric resonances between 0.2 and 1 MHz, and can be described by the forced-damped-oscillator model. The resonant spectra show significant changes while phase transitions are taking place. © 2005 American Institute of Physics. DOI: 10.1063/1.1948523 High-strain ferroelectric PbMg1/3Nb2/31−xTixO3 PMNT crystals have demonstrated piezoelectric effects much larger than conventional PbZr1−xTixO3 PZT ceramics.1 Physical properties of PMNT strongly depend on Ti content, poling electric E-field strength, and crystallo- graphic orientation.2–4 It was found that the monoclinic M phase plays an essential role in bridging higher symmetries rhombohedral R, tetragonal T, and cubic C while phase transitions are taking place.4 Though these crystals have been studied extensively in recent years, there are still many application issues and unclear physical origins to be addressed. To enhance piezoelectric performance, an E-field poling has usually been used on these materials before appli- cation. However, how an E-field poling affects dielectric spectroscopy still remains unclear, particularly for an operat- ing frequency above 100 kHz. Piezoelectric resonances have been observed in poled PZT ceramics5 and piezoelectric polymers.6 A field-induced piezoelectric resonance was seen in paraelectric BaTi0.8Sn0.2O3 ceramic, which vanished after removing the bias field.7 These dielectric resonances were found to be as- sociated with vibrations of microscopic ionic units and vari- ous extension modes. A detailed theoretical review of piezo- electric resonance for polymers can be found in Ref. 6. In this study, the PMNT crystals were cut perpendicular to the 111 direction. Hereafter, x% stands for 111-oriented PMNTx%. The Ti concentration x%  was determined by using the dielectric maximum temperature Tm upon heating.4 A Wayne–Kerr precision analyzer PMA3260A with four-lead connections was used to obtain real  and imaginary  parts of dielectric permittivity. A Janis CCS-450 cold head was used with a Lakeshore 340 temperature controller. Gold electrodes were deposited on sample surfaces by sputtering. The sample thicknesses are 1.0 and 0.6 mm for 25% and 34%, respectively. Two processes were used in the dielectric measurements. The first is called “zero-field heating” ZFH, in which the data were taken upon heating without any E-field poling. In the second process, FR-ZFH, the sample was poled at room temperature RT along 111 with a dc E field for about 1 h before ZFH was performed. The hyster- esis loop of electric field versus polarization was also mea- sured by using a Sawyer–Tower circuit at f =46 Hz. Figures 1a and 1b show the temperature-dependent  and  at several frequencies obtained from ZFH and FR-ZFH for 25% and 34%, respectively. For measuring fre- quencies below 100 kHz, besides a broad maximum at Tm 390 K, 25% shows an extra peak near 368 K in  FR- ZFH. For 34%, instead of a gradual anomaly near 325 K in  ZFH, a step-up anomaly is seen near 340 K in  FR- ZFH below 100 kHz. The dielectric maximum temperatures Tm of  ZFH and  FR-ZFH in 34% are, respectively, 434 and 438 K, where the tetragonal-cubic ferroelectric transition occurs. Dielectric spectra of  FR-ZFH above 100 kHz in both 25% and 34% exhibit irregular swinging anomalies, which vanish as temperature approaches Tm. Figures 2a and 2b illustrate dielectric spectra of  and  in 25% and 34% after various poling E fields at RT, in which multiple piezoelectric resonances occur between 0.2 and 1 MHz. Resonant spectra in 25% are similar for different poling fields. In 34%, resonant spectra are similar for E 5 kV/cm. The minimum E fields to induce resonant anomalies are 1.0 and 2.5 kV/cm for 25% and 34%, respectively, which are smaller than their coercive fields EC3.2 kV/cm for 25% and EC8.0 kV/cm for 34%. Electric hysteresis loops obtained at RT are given in Fig. 1. Figures 3a and 3b show temperature-dependent fre- quency spectra of  after poling for 25% and 34%, respec- tively. The resonant spectra of 25% exhibit an obvious split- ting of the resonant peak near 850 kHz and dramaticaElectronic mail: chien@physics.montana.edu JOURNAL OF APPLIED PHYSICS 97, 126105 2005 0021-8979/2005/9712/126105/3/$22.50 © 2005 American Institute of Physics97, 126105-1 Reuse of AIP Publishing content is subject to the terms at: https://publishing.aip.org/authors/rights-and-permissions. Download to IP: 153.90.170.56 On: Fri, 29 Apr 2016 16:58:23 changes of resonant intensity at 367 K, which corresponds to an extra peak in  FR-ZFH. The resonant anomaly van- ishes near 380 K which is lower than Tm390 K. With the above data and the phase diagram for poled PMNT crystals,4 the poled 25% crystal likely undergoes a RM→MR →C transition sequence near 367 and 390 K upon heating. “RM” represents the dominant R domains that coexist with a smaller fraction of M domains. The resonant spectra of  poled in 34% show significant changes of intensity and resonant frequency near 210 and 340 K as indicated by the solid and dashed arrows, respec- tively, in Fig. 3b. The resonance vanishes near 430 K, which is lower than Tm438 K. What are the physical ori- gins of this behavior near 210 and 340 K? In a pure PMN crystal an extra peak was seen at Tc212 K in a field- heating dielectric result, and was attributed to the percolating clusters due to the suppression of the random fields.8 An MT→TM transition associated with a step-down anomaly near 210 K in  FR-ZFH was evidenced in 001-cut PMNT35%.4 Note that the poling E field was along 111 which is the polar direction of the R phase. Thus the resonant anomaly near 210 K corresponds to a phase trans- formation, perhaps RM→MR, associated with a long- range percolation of microdomains. Near 340 K the crystal transforms into the tetragonal phase. What are the physical origins of piezoelectric reso- nances? It was found that resonant spectra can be described by the model of multiple force-damping oscillators, i.e., * =  − i = c + i=1 Ai 0i 2 − 2 − i2i 0i 2 − 22 + 42i 2 , 1 where 0id and Aid are the thickness-dependent resonant frequency and amplitude for the ith oscillator, id is the damping factor, and c is the “clamped” dielectric permittiv- FIG. 1. Color online Dielectric permittivities of ZFH and FR-ZFH for a 25% and b 34%. FIG. 2. Color online Resonant spectra after various E-field polings for a 25% and b 34%. FIG. 3. Color online Temperature-dependent frequency spectra of  after poling at 2.0 and 5.0 kV/cm for a 25% and b 34%, respectively. 126105-2 Tu et al. J. Appl. Phys. 97, 126105 2005 Reuse of AIP Publishing content is subject to the terms at: https://publishing.aip.org/authors/rights-and-permissions. Download to IP: 153.90.170.56 On: Fri, 29 Apr 2016 16:58:23 ity. The thickness dependence is included in the parameters because the piezoelectric resonance is a dimension- dependent macroscopic phenomenon, which associates with complex capacitance. To obtain Eq. 1, the ion motion was assumed to be like the one-dimensional forced damped os- cillation, i.e., d2z /dt2+2dz /dt+0 2z= q /mE0 Reeit, where d=bd /2m and 0 2d=Kd /m. Kd; bd, and m are restoring-force constant, damping coefficient, and effec- tive ion mass, respectively. The oscillating charges can be the Pb+2 and Mg1/3Nb2/31−xTixO3−2 ionic sublattices. A simi- lar mathematical analysis for induced dynamic polarizability appears in Ref. 9. The dotted lines in Fig. 4 are fitting curves of Eq. 1 with parameters given in Table I for resonant peaks I–IV in 34%. The consistent fittings indicate that these resonant phe- nomena correlate to microscopic vibrations of the ionic units. Peak “I” is expected to be the thickness extension TE mode, because its frequency increased as sample thickness was reduced. Manifold resonances are likely associated with phase segregation due to Ti variation, various extension modes, and their higher-order overtones. This work has revealed significant evidence of piezo- electric resonances in poled PMNT25% and 34% crystals, which occur in a wide temperature region. Similar resonant phenomena have also been observed in other poled PMNTx% crystals x=24, 26, 28, 29, 35, and 36. Piezoelec- tric resonance seems to be a regular phenomenon in poled PMNT crystals and can be easily induced with poling strength less than the coercive field, but it vanishes after annealing above Tm. The dielectric resonance is sensitive to microscopic structure, and is a valuable characterization method for the PMNT system. The authors would like to express sincere thanks to Dr. H. Luo and Y. Tang for the crystals. This work was supported by NSC Grant No. 93-2112-M-030-001 and DoD EPSCoR Grant No. N00014-02-1-0657. 1T. R. Shrout, Z. P. Chang, N. Kim, and S. Markgraf, Ferroelectr., Lett. Sect. 12, 63 1990. 2Z.-G. Ye, B. Noheda, M. Dong, D. Cox, and G. Shirane, Phys. Rev. B 64, 184114 2001. 3Z. Feng, H. Luo, Y. Guo, T. He, and H. Xu, Solid State Commun. 126, 347 2003. 4C.-S. Tu, R. R. Chien, F. T. Wang, V. H. Schmidt, and P. Han, Phys. Rev. B 70, 220103 2004. 5N. Cereceda, B. Noheda, J. R. Fdez.-del-Castillo, J. A. Gonzalo, J. De Frutos, and A. M. González, J. Eur. Ceram. Soc. 19, 1259 1999. 6A. Mellinger, IEEE Trans. Dielectr. Electr. Insul. 10, 842 2003. 7X. Wei, Y. Feng, and X. Yao, Appl. Phys. Lett. 84, 1534 2004. 8V. Westphal and W. Kleemann, Phys. Rev. Lett. 68, 847 1992. 9V. D. Barger and M. G. Olsson, Classical Electricity and Magnetism Al- lyn and Bacon, Boston, 1987, pp. 168–170. FIG. 4. Color online Resonant spectra of  between 450 and 720 kHz taken at 300 K. The dotted lines are fits of Eq. 1 for peaks I–IV with parameters in Table I. The solid line is the sum of fittings with c=2200. TABLE I. Fitting parameters of resonant peaks in Fig. 4. Peak o /2 kHz A /42 Hz2  /2 kHz I 640 3.21014 1.25104 II 550 3.31013 9.5103 III 522 2.41013 7.3103 IV 505 3.81013 6.0103 126105-3 Tu et al. J. Appl. Phys. 97, 126105 2005 Reuse of AIP Publishing content is subject to the terms at: https://publishing.aip.org/authors/rights-and-permissions. Download to IP: 153.90.170.56 On: Fri, 29 Apr 2016 16:58:23