Nanotwins and phases in high-strain Pb ( Mg 1 / 3 Nb 2 / 3 ) 1 − x Ti x O 3 crystal C.-S. Tu, C.-M. Hsieh, R. R. Chien, V. H. Schmidt, F.-T. Wang, and W. S. Chang Citation: Journal of Applied Physics 103, 074117 (2008); doi: 10.1063/1.2904900 View online: http://dx.doi.org/10.1063/1.2904900 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/103/7?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Mapping bias-induced phase stability and random fields in relaxor ferroelectrics Appl. Phys. Lett. 95, 092904 (2009); 10.1063/1.3222868 Field-induced intermediate orthorhombic phase in (110)-cut Pb ( Mg 1 / 3 Nb 2 / 3 ) 0.70 Ti 0.30 O 3 single crystal J. Appl. Phys. 104, 094105 (2008); 10.1063/1.3009319 Nanotwin and phase transformation in tetragonal Pb ( Fe 1 / 2 Nb 1 / 2 ) 1 − x Ti x O 3 single crystal J. Appl. Phys. 104, 054106 (2008); 10.1063/1.2974791 Phase transformations in poled PZN-4.5%PT single crystal revealed by combined property measurements and high-resolution diffraction technique J. Appl. Phys. 104, 054102 (2008); 10.1063/1.2969782 Intermediate phases in rhombohedral Pb ( Mg 1 ∕ 3 Nb 2 ∕ 3 ) 1 − x Ti x O 3 crystal J. Appl. Phys. 104, 024110 (2008); 10.1063/1.2956611 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 18:21:56 Nanotwins and phases in high-strain Pb„Mg1/3Nb2/3…1−xTixO3 crystal C.-S. Tu,1,a C.-M. Hsieh,1 R. R. Chien,2 V. H. Schmidt,2 F.-T. Wang,1 and W. S. Chang3 1Department of Physics, Fu Jen Catholic University, Taipei 242, Taiwan 2Department of Physics, Montana State University, Bozeman, Montana 59717, USA 3Department of Mechanical Engineering, National University of Singapore, Singapore 112960, Singapore Received 24 January 2008; accepted 5 February 2008; published online 14 April 2008 This work is a study of the thermal stability of 001-cut PbMg1/3Nb2/31−xTixO3 x=0.30 single crystals before and after an electric E-field poling by means of dielectric permittivity, hysteresis loop, domain structure, polarization current, and x-ray diffraction. An RRNT-RRNT / TTNT-TTNT-C transition sequence was observed upon heating in the unpoled sample. R, RNT, T, TNT, and C are the rhombohedral, rhombohedral nanotwin, tetragonal, tetragonal nanotwin, and cubic phases, respectively. R /T indicates coexistence of the R and T phases. RRNT and TTNT indicate that the RNT and TNT structures mimic monoclinic phases in the R and T matrices, respectively. After a prior E-field poling, an RRNT-TTNT-C phase sequence takes place upon heating. The dielectric permittivity and current density evidenced an additional polarization at 355 K, which is associated with the vanishing of the dielectric dispersion, which reappears near 410 K and remains up to the Burns temperature TB=510 K. This study suggests that nanotwins RNT and TNT can play an important role in high-strain piezoelectric crystals while phase transition takes place. Under E=38 kV /cm, 001 T domains randomly appeared in the matrix, suggesting that the matrix consists of a glassy matrix and ferroelectric nanoclusters. © 2008 American Institute of Physics. DOI: 10.1063/1.2904900 I. INTRODUCTION An important feature of relaxor ferroelectrics is the ex- istence of polar nanoclusters or polar nanoregions PNRs, which are believed to be responsible for ferroelectric FE properties and giant piezoelectricity. Field-cooled and zero- field-cooled 207Pb nuclear-magnetic-resonance NMR spec- tra of the PbMg1/3Nb2/3O3 PMN prototype relaxor crystal showed the existence of two components—an isotropic spherical glass matrix and an anisotropic FE nanoclusters.1,2 Also, Pb nuclei are displaced in the spherical glass matrix at 290 K TC210 K, but there is no preferential frozen orientation or magnitude of displacement.2 The FE polar clusters, which can respond to an external E field greater than the threshold field Et, are embedded in the single- dipole-glass matrix, which does not appreciably respond to an E field.2 About 50% of the Pb nuclei reside in the spheri- cal glass matrix and 50% in the FE polar nanoclusters.2 An extra peak was observed near 210 K in the field-heated/field- cooled dielectric spectra, implying a first-order FE transition.3 A neutron analysis of unpoled PMN powder shows that the volume fraction of PNRs and their correlation lengths drastically increase below 200 K.4 Two different atomic displacements c.m and shift were proposed that are below the Burns temperature of a PMN crystal by neutron diffuse scattering.5 c.m is caused by soft-mode condensation and shift represents a uniform displacement of PNRs along their polar direction, which is relative to the surrounding cubic matrix or glassy matrix. These phenomena indicate that PMN is an incipient FE. Recent first-principles dynamic simulations for PbSc1/2Nb1/2O3 and PMN show the formation of nanoclusters in the quenched short-range- ordered regions below the Burns temperature.6 By dielectric and domain studies, an incipient FE nature was found in PbMg1/3Nb2/31−xTixO3 PMN-xPT crystals x=24%–38%, in which a “hidden” transition which was seen in unpoled samples but not as clearly as in the poled sample was enhanced by an E field.7 This hidden transition is associated with the appearance of monoclinic microdomains.7 High-strain PMN-PT and PbZn1/3Nb2/31−xTixO3 crys- tals have demonstrated their value in piezoelectric devices,8 and their physical properties are sensitive to the Ti content, E field, crystallographic orientation, thermal treatment, and other factors.7,9–11 The ultrahigh piezoelectric response has been theoretically attributed to polarization rotations be- tween the tetragonal T and rhombohedral R phases through monoclinic MA, MB, and MC or orthorhombic O phases.12 A C-T-MC-MA phase sequence was proposed for the field-cooled process under E=1.0 kV /cm in the 001- cut PMN-30%PT crystal.13 An R-M-T-C sequence was pro- posed to exist in the 001 poled PMN-30%PT crystal upon heating after the crystal was poled from the dielectric maxi- mum temperature with E=10 kV /cm.14 Polarizing micros- copy revealed an MC phase space group Pm in the domain structure of a 001-cut PMN-33%PT crystal.15 From syn- chrotron x-ray diffraction XRD, an MA phase space group Cm was observed in a 001 poled PMN-35%PT crystal, but the weakly poled sample exhibits an average R phase.16 High energy XRD results of PbZn1/3Nb2/31−x-TixO3 x=0, 4.5, and 8.0 crystals show that distinct outer layers 10–50 m are present in all of the samples.17 An R phase was found to develop in both the outer layer and the aAuthor to whom correspondence should be addressed. Electronic mail: 039611@mail.fju.edu.tw. JOURNAL OF APPLIED PHYSICS 103, 074117 2008 0021-8979/2008/1037/074117/8/$23.00 © 2008 American Institute of Physics103, 074117-1 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 18:21:56 crystal interior with increasing Ti content.17 The polarization of FE nanoclusters and boundary conditions near the surface are believed to play an essential role in the surface distortion.17 In PZN crystals, an X phase and an R phase were suggested for the inside crystal bulk and the outer layer, respectively.18 The X phase has a nearly cubic lattice with a slight tetragonal distortion.18 Similar phenomena be- tween the outer layer and bulk have been reported in PMN-PT crystals.19,20 High-resolution neutron scattering re- sults show that PMN-10%PT and PMN-20%PT transform to the X phase below TC.19 The R distortion is limited to the outer layer. However, in PMN-27%PT, the low-temperature phase was found to be R in both the outer layer and the bulk. Neutron diffraction of PMN crystals reveals a strong lattice distortion and depth dependence in the surface region over a length scale of 100 m.21 These results indicate that the ground state inside the bulk of PMN-PT crystals prefers the X phase for a small Ti content and transfers to the R phase as the Ti content increases. On the other hand, the R phase has been observed in PMN-PT even for a very small Ti content by conventional XRD, which apparently probes the outer layer.22 A nanotwin diffraction theory that was recently devel- oped by Wang23,24 shows that tetragonal nanotwins of the 101 twin plane can mimic the MC phase and rhombohedral nanotwins of the 001 and 110 twin planes can mimic the monoclinic MA and MB phases, respectively. Ferroelastic crystals usually consist of structural twins, accommodating the spontaneous lattice distortion and minimizing the elastic strain energy. Since the nanodomain size is much smaller than the coherent length of diffraction radiation, scattered waves from individual nanodomains coherently superimpose during diffraction, and thus, significant broadening of the reflection peak is expected.24 In experiments, the MA and MB phases are always observed to be associated with the R phase, while the MC phase is always observed to be associ- ated with the T phase. T-phase nanotwins with a domain size of about 10 nm have been observed by transmission electron microscopy in PMN-PT,25 which appear to have the MC phase in low-resolution diffraction and polarized light mi- croscopy. For piezoelectric performance, an E-field poling is usu- ally employed before application. However, how E-field pol- ing affects the FE polarization, thermal stability, and nano- structure of the relaxor FE crystals is still not fully understood, especially for the compounds near the morpho- tropic phase boundary. Both in this crystal and in other 001-cut relaxor FE crystals containing other B-site ele- ments, the dielectric permittivity upon zero-field heating af- ter a prior poling at room temperature often shows a dra- matic drop as seen in Fig. 1 at 355 K, which is followed by a large steep rise and re-entry of dielectric dispersion. No one had explained this dramatic dip before because of the following paradox: The dip appears to be similar to that seen for 001-cut crystals of higher Ti content for which polariz- ing microscopy indicated a T structure. However, in this crystal, the polarizing microscopy showed very little T phase but, instead, showed an apparent M phase, which would give a quite stronger dielectric response for measuring the field along 001. In this report, we propose the R- and T-phase nanotwins to reconcile the apparently contradictory results that were seen in relaxor FE crystals of several different compositions. The existence of nanotwins can be easily mis- taken as monoclinic phases MA, MB, MC due to the aver- aging effect in both polarizing microscopy and x-ray diffrac- tion. II. EXPERIMENTAL PROCEDURE The PMN-xPT with x=0.30 crystal was grown by us- ing a modified Bridgman method. A Wayne–Kerr analyzer PMA3260A was used to obtain the real part  of the dielec- tric permittivity. A sample with dimensions of 55 1 mm3 was cut perpendicular to the 001 direction, and its basal surfaces were coated with gold electrodes. Three processes were used in the dielectric studies. The first two are called “zero-field heated” ZFH and “zero-field cooled” ZFC processes, in which the data were taken upon heating and cooling without any poling. In “prior-poled zero-field heated” PP-ZFH process, the sample was poled at room temperature with a dc E field of 5 kV/cm along 001; then, ZFH was performed without an E field. An irregular piezo- electric resonance was observed for f100 kHz in the PP- ZFH dielectric spectra. The ZFH and PP-ZFH polarization FIG. 1. Color online a ZFH dielectric permittivity and polarization cur- rent density JZFH, b PP-ZFH dielectric permittivity, and c PP-ZFH polar- ization current density JPP-ZFH. The 1 / and ZFC after PP-ZFH were taken at f =10 kHz. 074117-2 Tu et al. J. Appl. Phys. 103, 074117 2008 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 18:21:56 current densities after poling at E=5 kV /cm were measured by using a Keithley 6517A electrometer. Hysteresis loops were taken by using a Sawyer–Tower circuit at f =46 Hz. A Janis CCS-450 cold head was used with a Lakeshore 340 controller for the above temperature-dependent measure- ments. Domain structures were observed by using a Nikon E600POL polarizing microscope with a crossed polarizer/ analyzer P/A pair. Transparent conductive films of indium tin oxide ITO were deposited on the 001 basal surfaces. The crystal thickness was about 70 m. The angles of the P/A pair were measured with regard to the 110 direction. The experimental setup and details for using optical extinc- tion to determine domain phases can be found in Ref. 10. A high-temperature Rigaku model MultiFlex x-ray dif- fractometer with Cu K1 =0.154 06 nm and Cu K2  =0.154 44 nm radiations was used for the structural study of the unit cell. The intensity ratio between K1 and K2 is about 2:1.26 To avoid surface stress caused by polishing, thin gold films thickness30 nm were deposited on the basal surfaces and were kept on the sample after poling. The sample thickness is 0.75 mm and the x-ray penetration depth is less than 10 m.17 The XRD spectra were fitted by using the PEAKFIT software with the sum of the Gaussian and Lorentzian equations. According to previous synchrotron XRD results,19,20 both the outer layer and the inner part of the PMN-xPT crystals x27% have the same structure. Therefore, the XRD spectra in this work can present the bulk structure. III. RESULTS AND DISCUSSION Figure 1 shows the Fig. 1a ZFH dielectric permittiv- ity and polarization current density JZFH, Fig. 1b PP-ZFH dielectric permittivity, and Fig. 1c PP-ZFH polarization current density JPP-ZFH after a prior poling at E=5 kV /cm. The dielectric maxima associated with frequency disper- sion and the corresponding temperatures Tm415 K are nearly the same for ZFH and PP-ZFH. The ZFH dielectric permittivity ZFH exhibits two continuous step-up-like anomalies near 350 and 380 K. The ZFH current density JZFH shows two clear responses in the regions of 350–360 and 405–415 K, which is consistent with the two thermal hystereses in the regions of 280–360 and 380–410 K, respec- tively, as shown in the inset of Fig. 1a, indicating two first- order transformations. Note from the scale at right that these currents indicate very small polarizations downward spikes and depolarizations upward spikes. The ZFH polarization current JZFH is mainly associated with spontaneous polariza- tion PS, i.e., JZFH=−PS /t. The PP-ZFH dielectric permittivity PP-ZFH exhibits a dramatic step-down near 355 K. The minimum E field to induce this step-down anomaly is about 1 kV/cm, which is smaller than the coercive field 2.2 kV /cm at room tem- perature, as shown in Fig. 2. The polarization current density JPP-ZFH shows an obvious negative response near 355 K, as seen in Fig. 1c, which is followed by a positive peak near 410 K. These two discontinuous current responses indicate two first-order transitions near 355 and 410 K and are con- sistent with the thermal hystereses seen in Fig. 1a. The PP-ZFH polarization current JPP-ZFH is mainly associated with E-field-induced polarization Pind, i.e., JPP-ZFH =−Pind /t. This pyroelectric effect is the inverse of the po- larocaloric or electrocaloric effect, which was investigated in PZN-8%PT crystals by Priya and Uchino.27 They found two negative peaks in the 315–345 K temperature range, which are followed by a positive peak near 435 K. The sign indi- cates whether the discontinuous change is stable or unstable. They attributed the negative peaks to a first-order R-O-T sequence because the O phase is metastable with respect to the R and T phases.27 How can these phenomena be explained? We start with a broad-brush explanation and fill in details as we discuss more experimental results. The prior poling develops some degree of FE order, which is probably the R phase that has polarization rotation under a 001 measuring field, and so has a relatively high permittivity compared to ZFH . This order enhances the degree to which a different type of order, perhaps the T phase, can suddenly arise at 355 K. The in- crease in polarization at 355 K could result from this ordered phase arising at the expense of previously disordered mate- rial. At and above 355 K, these T domains have little ten- dency to rotate in the weak 001 measuring field and, thus, have much lower permittivity, as observed. As the temperature increases above 355 K, as seen in Fig. 1b, the dielectric dispersion vanishes and then com- pletely reappears near Tre=410 K, which is associated with FIG. 2. Color online Temperature-dependent a hysteresis loop and b remanent polarization Pr and coercive field EC upon heating. 074117-3 Tu et al. J. Appl. Phys. 103, 074117 2008 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 18:21:56 a multiple-peak response in JPP-ZFH. Multiple jumps of polar- ization current can be interpreted as discrete changes in the size or rotation of FE microdomains or nanodomains. Here, we define Tre as the temperature above which the dielectric relaxation re-establishes in the crystal. Our PP-ZFH and po- larization current response are different from the result for the 001 poled PMN-30%PT crystal reported in Ref. 14, which shows three dielectric peaks and three current re- sponses upon heating. Both ZFH and PP-ZFH were found to follow the Curie– Weiss equation, =C / T-To, above 510 K, below which there is a noticeable deviation from the Curie–Weiss law. The dashed lines in Fig. 1 are fittings with C=1.8105 and To=465 K for both ZFH and PP-ZFH . We consider 510 K to be the Burns temperature TB, below which dipole glass attenuated dielectric response and polar nanoclusters begin to develop.5 The weaker dipole glass dielectric response causes deviation from the Curie–Weiss law and the polar nanoclus- ter dynamics are responsible for the dielectric dispersion.28 As given in Fig. 1b, the ZFC dielectric permittivity mea- sured after a prior poling at E=5.0 kV /cm shows a similar behavior as seen in ZFC above Tre and has the same Burns temperature. This indicates that the polarized state induced by an E field can be erased by thermal annealing. Figure 2a shows the temperature-dependent hysteresis loops and Fig. 2b shows the remanent polarization Pr and coercive field EC. At room temperature, PS, Pr, and EC are about 15.5 C /cm2, 14 C /cm2, and 2.2 kV/cm, respec- tively. This PS from the R phase is considerably smaller than the 18–19 C /cm2 values seen in the 340–380 K range, which could be attributed to the T phase. Accordingly, at least part of the increase in P as the temperature increases to 355 K, as evidenced by the negative depolarization current density, could result from the polarization rotation of some regions from R via MA to 001 T. The low permittivity above 355 K is consistent with T domains. Both Pr and EC reach a local maximum near 365 K and Pr exhibits a steep decline above Tre=410 K. A “double hys- teresis loop” was observed in the region of 400–420 K, as can be seen in Fig. 2a, which is the characteristic of a P-E loop near a first-order transition. The double hysteresis loop indicates a discontinuous jump from a field-induced FE state to a paraelectric state at zero field. These phenomena are consistent with the re-entry of dielectric dispersion in PP-ZFH and the positive depolarization current responses in Fig. 1c. The polarization appears to retain some finite magnitude even above Tm415 K, as commonly seen in disordered materials, but this could result from a field-induced transition or from the finite measuring frequency of 46 Hz. Figures 3a and 3b exhibit the room temperature ZFH domain structures with various micron-sized domains less than 10 m randomly distributed in the matrix. Most of the matrix has an optical extinction at P /A=0° but a small frac- tion exhibits an extinction at P /A0° 45°, indicating that a majority R phase mixes with M or rhombohedral nanotwin RNT phases which can mimic MA and MB phases.24 The coexistence of the R and M or RNT phases is confirmed by the 002 XRD, as shown in Fig. 4a, which shows a strong R and a minor broad peak. The lattice parameter of the R phase was estimated to be a=4.025 Å, which is fairly con- sistent with aR4.020 Å that was obtained in Ref. 13 but is larger, perhaps because of the partly disorganized nature of this R phase in the ZFH crystal. Figure 5 shows the 1 3 ratio between the room temperature spontaneous polarizations PS15.5 C/cm2 and PS27.0 C/cm2, which were taken along 001 and 111, respectively, which confirms that R is the majority phase at room temperature. Note that 1 3 is the projection fraction of the 111 polarization on the 001 axis. As the temperature increases, as shown in Figs. 3c and 3d, the domain matrix exhibits an obvious change in the region of 360–370 K. Besides some domains with an extinc- tion angle at P /A=0°, some domains rotate toward the T phase with extinction angles at 0 P /A 45°, indicating M or RNT and TTNT phases. Note that tetragonal nanotwins TNT can mimic the MC phase with extinction angles at P /A0°.23 TTNT represents T nanotwins that mimic the MC phase in the T matrix. The horizontal and vertical stria- tions in Fig. 3d resemble those seen from the 100 and 010 T domains. This rotation toward the T phase is con- firmed by the XRD in Fig. 4c, in which the diffraction FIG. 3. Color online ZFH domain structures taken at P /A=0° and 45°. The dashed lines are the boundaries of the ITO films. The dashed circle indicates the region of incomplete total extinction. 074117-4 Tu et al. J. Appl. Phys. 103, 074117 2008 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 18:21:56 shows an obvious change in contour and relative intensities and the right-hand peak becomes narrower and approaches the lattice parameter of the T phase found for PP-ZFH, as will be seen below. Note that the current density JZFH exhib- its a small random response with up and down components in the region of 350–360 K. The inset in Fig. 1a shows a thermal hysteresis near 355 K, indicating a first-order RRNT-TTNT transition near 355 K, where ZFH exhibits a step-up anomaly upon heating. Near 378 K, as seen in Figs. 3e and 3f, the domain matrix exhibits a significant evolu- tion, in which the area with an extinction at P /A=45° dra- matically increases, indicating a major T phase, even though the striations seen at P /A=0 show little change. Note that ZFH exhibits a gradual step-up-like anomaly near 380 K in Fig. 1a. However, there is no current response in JZFH Fig. 1a and the XRD shows only a gradual change in linewidth and lattice parameter, which corresponds to the appearance of the T phase. According to the eighth-order Devonshire theory analysis by Vanderbilt and Cohen,29 both MA-T and MC-T transitions should be of second order, which may ex- plain why no discontinuity appears in the current density and lattice parameter near 380 K, as seen in Figs. 1a and 6. Near 413 K, as seen in Figs. 3g and 3h, the cubic C phase with total extinction begins to develop, which is as- sociated with a partial T-phase matrix that does not show a total extinction. As the temperature increases above Tm415 K, as seen in Figs. 3i and 3j, the domain matrix does not immedi- ately go into a complete total extinction C phase, as indi- cated by the dotted circle in Fig. 3j. Instead, in addition to the C phase, a low-2 XRD shoulder, which remains up to about 450 K, was detected, as shown in Figs. 4d and 4e. The broad shoulder is possibly due to lattice distortions caused by a local residual stress from the T-C transition or polar nanocluster material. The narrow C peak corresponds to the dipole glass material. Figure 6 gives the temperature- dependent d spacings in the ZFH process. In brief, the unpoled crystal proceeds by an RRNT-RRNT / TTNT-TTNT-C transition sequence near 355, 380, and 410 K. The PP-ZFH domain structures after poling with E =5 kV /cm along 001 at room temperature are illustrated in Fig. 7. Percolating microdomains green interference were induced after poling with a size less than 30 m and FIG. 4. Color online ZFH 002 XRD spectra. The solid and short-dashed lines correlate to the K1 and K2 radiations, respectively. The red solid line is the sum of the fitting curves. FIG. 5. Color online Hysteresis loops obtained from 001- and 111-cut crystals at room temperature. FIG. 6. Color online d spacing vs temperature for various phases in the ZFH process. The dashed line is ZFH . The dotted lines indicate the various transition temperatures. The triangle corresponds to the low-2 lattice distortion. 074117-5 Tu et al. J. Appl. Phys. 103, 074117 2008 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 18:21:56 were randomly distributed in the matrix. The field-induced micrometric percolations were caused by rotating the polar- izations of much smaller microdomains or nanoclusters into alignment so that the boundaries disappear. As shown in Figs. 7a and 7b, most regions have an extinction angle at P /A=0°, indicating the coexistence of the R and RNT phases. The coexistence of R and RNT is confirmed by the 002 XRD in Fig. 8a with a sharper R peak and a broad peak. The broadening of the diffraction peak is due to coherent superimposition of scattered waves from individual nan- odomains. Note that this RNT assignment is to a peak to the left of the R peak, whereas in Figs. 4a and 4b, the RNT peak is to the right of the R peak. This only makes sense if the PP-ZFH RNT MA and/or MB peak corresponds to the T001 peak because the prior poling prefers that orientation. From the 2 fitting, the lattice parameter of the R phase was estimated to be a=4.019 Å. As the temperature increases, some of the percolating microdomains green gradually grow with a maximum size of 150 m, as shown in Fig. 7c. The extinction angle of most of the matrix stays at P /A=0° Figs. 7c–7h. How- ever, the domain matrix exhibits no obvious change in the extinction angle near 355 K, where both the dielectric per- mittivity Fig. 1b and the polarization current Fig. 1c show a discontinuous first-order transition. It is important to note that tetragonal nanotwins TNT can mimic an MC phase with extinction angles close to P /A=0°. Note that the opti- mal resolution of the polarizing microscope is about 1 m due to the optical diffraction limit. The low PP-ZFH permit- tivity above 355 K in the 001 measuring field evidences a first-order RRNT-TTNT transition. A rapid growth of the TNT phase is verified near 360 K, as seen in Figs. 8b and 8c, which shows a major broad TNT peak at low 2  with a T peak at high 2 . The d spacing also exhibits a discon- tinuous transition at 355 K, as shown in Fig. 9. Near 378 K Figs. 7g and 7h, the domain matrix radically turned to gray with extinction angles in the region of P /A=0–15°, which is likely associated with the break- down of percolations and rapid development of polar tetrag- onal nanotwins or polar tetragonal nanoclusters, as well as striations characteristic of T100 and T010 domains. The ap- pearance of polar nanotwins can reduce the averaged optical birefringence and their dynamics causes a complete recovery of the dielectric relaxation near Tre=410 K. The C phase with total extinction begins to develop FIG. 7. Color online PP-ZFH E=5 kV /cm domain structures taken at P /A=45° and 0°. FIG. 8. Color online PP-ZFH 002 XRD spectra after poling at E =5 kV /cm. The solid and short-dashed lines correlate to the K1 and K2 radiations, respectively. 074117-6 Tu et al. J. Appl. Phys. 103, 074117 2008 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 18:21:56 near Tre=410 K, as shown in Figs. 7i and 7j. This is consistent with the multiple-jump polarization current re- sponse in the region of 410–415 K Fig. 1c and the reap- pearance of the dielectric dispersion at Tre=410 K Fig. 1b. Above Tre=410 K, as indicated by the dotted circle in the inset of Fig. 7j, the domain matrix does not immedi- ately go into a complete total extinction C phase. Instead, a high-2 broad and weak shoulder was detected in the XRD, as shown in Figs. 8d and 8e. This weak high-2 broad peak is possibly attributed to lattice distortions caused by a local residual stress from the T-C transition or polar nano- cluster material. In brief, the crystal is in a cubic state above Tre=410 K with polar nanoclusters, which immerse in the glassy matrix and vanish above TB=510 K. Figure 9 is a summary of the RRNT-TTNT-C transition sequence taking place near 355 K and Tre=410 K in the PP-ZFH process. The XRD data are perhaps the most difficult results to understand, and their discussion is interspersed above with the discussion of results from other techniques, so we present here a separate interpretation of the XRD data. In Figs. 4 and 8, for ZFH and PP-ZFH spectra, respectively, the narrow peaks come from well-organized larger regions of a given phase R, T, or C, for which the K1 and K2 peaks are well resolved. Their separations obey the Bragg law 2 d sin =n. The broadening of the peaks is associated with nanot- wins and is caused by the coherent superimposition of scat- tered diffraction waves. Now, we consider the evolution of the XRD spectra with increasing temperature for both ZFH and PP-ZFH. At room temperature, the ZFH peak is broad, whereas the PP-ZFH spectrum has a narrow peak, which results from some well- organized R domains in addition to a broad peak from coher- ent diffractions of R nanotwins. As the temperature increases toward Tre=410 K, the ZFH peak gradually develops a structure, whereas the PP-ZFH spectrum exhibits a dramatic shift from a large narrow R peak at 355 K to a smaller but narrow T100/010 peak at 363 K, while the broad peak strength- ens from T nanotwins. The attribution of the sharp T peaks for both ZFH and PP-ZFH at 363 K is supported by both having the same d value of 4.009 Å. Above Tre=410 K, both the permittivity and the polar- izing microscopy results are similar for both ZFH and PP- ZFH, which indicates the gradual transformation of the re- maining T-phase material to the C phase, so it may seem surprising that the XRD spectra for ZFH and PP-ZFH are quite different above 410 K. At 418 K, the ZFH intensity is divided into a sharp C peak with d=4.016 Å and a slightly weaker broad peak with d=4.027 Å. We attribute this broad peak to disorganized tetragonal nanotwins of average C sym- metry because its d value is close to the value of d =4.035 Å for the single broad PP-ZFH peak at 418 K. The broad peaks can be attributed to the polar nanotwin or nano- cluster material and the narrow peak to the dipole glass material. The ZFH broad peak becomes much weaker at 453 K and disappears before 573 K. We can speculate that the less organized ZFH material below Tre=410 K contains considerable dipole glass mate- rial that easily transforms into a cubic dipole glass material at 410 K, giving the observed sharp C peak. By contrast, for PP-ZFH, the more ordered T material may transform at 410 K into mostly polar nanoclusters that then gradually trans- form into a cubic dipole glass and, finally, to an ordinary paraelectric C material above TB. Figure 10 shows the E-field-induced domain structures under E 38 kV /cm along 001 at room temperature. At E=0 kV /cm, most parts of the domain matrix have an ex- tinction angle of P /A=0°, indicating a majority R phase. As the E field increases Figs. 10c–10f, more domains have extinctions at P /A0°, implying the expansion of the TNT or MC phase in the matrix. Under E=38 kV /cm Figs. 10g and 10h, only a portion of the matrix became the 001 tetragonal phase, as indicated by “T001,” with an ex- tinction at all P /A angles. The field-induced domain matrix exhibits irregular-shaped percolating microdomains that are randomly distributed in the matrix. This phenomenon implies that only part of the domain matrix can respond to an exter- nal E field. An internal crack as indicated by the arrow started to notably expand at E10 kV /cm along the 100 direction from the initial crack initially caused by polish- ing. An irreversible E-field-induced effect was observed and the domain structures did not return to the original structures before poling after the E field was removed. Similar E-field-induced domain structures were observed in a 001- cut PMN-24%PT crystal, in which percolating microdomains randomly embedded in the matrix and only part of the matrix turned into the T001 phase under E=44 kV /cm.10 IV. CONCLUSIONS An RRNT-RRNT /TTNT-TTNT-C phase transforma- tion sequence near 355, 380, and Tre=410 K was observed in a ZFH process. After a prior poling at E=5.0 kV /cm at room temperature, the crystal proceeds by an RRNT-TTNT-C transition sequence near 355 K and Tre =410 K upon heating. Rhombohedral nanotwins RNT and tetragonal nanotwins TNT play an important role in high- strain piezoelectric PMN-PT crystals while phase transitions take place because they can accommodate the spontaneous lattice distortion and minimize the elastic strain energy. It FIG. 9. Color online d spacing vs temperature for various phases. The dashed line is PP-ZFH . The dotted lines indicate the various transition temperatures. 074117-7 Tu et al. J. Appl. Phys. 103, 074117 2008 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 18:21:56 was found that the RNT and TNT phases can be easily mis- taken as monoclinic phases MA, MB, or MC. For example, an R-M-T-C phase sequence was proposed to exist in a 001-cut PMN-30%PT crystal upon heating after the crystal was poled from the dielectric maximum temperature with E=10 kV /cm.14 E-field-induced percolations were observed after a prior poling at E=5 kV /cm. A dramatic drop in per- mittivity occurs in the 355–410 K range and confirms an intrinsic TTNT phase, whose nanotwins or nanoclusters play a key role in the re-establishment of the dielectric dis- persion above 410 K. This work suggests that an intermedi- ate E-field poling can induce microscopic percolations. Simi- lar field-induced percolation and breakdown were seen in a 001-cut rhombohedral PIN-30%PT crystal.30 The E-field-dependent domain study presents a partial confirmation of the 207Pb NMR result, which proposes two components in the prototype PMN crystal, i.e., spherical glassy matrix and polar nanoclusters.2 The FE nanoclusters are embedded in the glassy matrix and can be percolated into micrometric clusters by an external E field. The glassy ma- trix probably the material in local random fields less strongly responds to an E field than predicted by the Curie– Weiss law. ACKNOWLEDGMENTS The authors would like to thank Dr. H. Luo Shanghai Institute of Ceramics for the crystals. This work was sup- ported by National Science Council of Taiwan Grant No. 96-2112-M-030-001. 1R. Blinc, V. V. Laguta, and B. Zalar, Phys. Rev. Lett. 91, 247601 2003. 2R. Blinc, V. V. Laguta, B. Zalar, and J. Banys, J. Mater. Sci. 41, 27 2006. 3R. Sommer, N. K. Yushin, and J. J. van der Klink, Phys. Rev. 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