Frequency dependence of the characteristic

Frequency dependence of the characteristic temperatures in PbSc0.5Ta0.36Nb0.14O3 relaxor ferroelectrics crystals seen via acoustic emission E. Dul'kin, B. Mihailova, M. Gospodinov, and M. Roth Citation: Journal of Applied Physics 115, 084103 (2014); doi: 10.1063/1.4864036 View online: http://dx.doi.org/10.1063/1.4864036 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/115/8?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Optical properties of epitaxial relaxor ferroelectric PbSc0.5Nb0.5O3 films Appl. Phys. Lett. 103, 132901 (2013); 10.1063/1.4822108 Effect of A-site La, Ba, and Sr doping on the threshold field and characteristic temperatures of PbSc0.5Nb0.5O3 relaxor studied by acoustic emission J. Appl. Phys. 113, 054105 (2013); 10.1063/1.4790601 Influence of electric field on local phase transformations in relaxor ferroelectrics PbSc 0.5 Ta 0.5 O 3 and Pb 0.78 Ba 0.22 Sc 0.5 Ta 0.5 O 3 J. Appl. Phys. 112, 124111 (2012); 10.1063/1.4770479 Effect of A-site La and Ba doping on threshold field and characteristic temperatures of PbSc0.5Ta0.5O3 relaxor studied by acoustic emission J. Appl. Phys. 112, 064107 (2012); 10.1063/1.4752400 Acoustic emission and dielectric studies of phase transitions within the morphotropic phase boundary of x Pb ( Zr 1 / 2 Ti 1 / 2 ) O 3 - ( 1 − x ) Pb ( Ni 1 / 3 Nb 2 / 3 ) O 3 relaxor ferroelectrics Appl. Phys. Lett. 95, 252903 (2009); 10.1063/1.3275730

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JOURNAL OF APPLIED PHYSICS 115, 084103 (2014)

Frequency dependence of the characteristic temperatures in PbSc0.5Ta0.36Nb0.14O3 relaxor ferroelectrics crystals seen via acoustic emission E. Dul’kin,1 B. Mihailova,2 M. Gospodinov,3 and M. Roth1 1

Department of Applied Physics, The Hebrew University of Jerusalem, Jerusalem 91904, Israel Fachbereich Geowissenschaften, Universit€ at Hamburg, Grindelallee 48, D-20146 Hamburg, Germany 3 Institute of Solid State Physics, Bulgarian Academy of Sciences, Boulevard Tzarigradsko Chausse 72, 1784 Sofia, Bulgaria 2

(Received 8 December 2013; accepted 22 January 2014; published online 24 February 2014) PbSc0.5Ta0.36Nb0.14O3 relaxor ferroelectrics crystals were investigated in a wide temperature range of 200–700 K using acoustic emission. The intermediate temperature T* as well as the Burns temperature Td were successfully detected at 480 K and 581 K, respectively. Another acoustic emission burst was detected at Tnl 211 K, which is below the temperature of the dielectric-permittivity maximum Tm 257 K but it is accompanied by a slight anomaly in the dielectric permittivity. Tnl is attributed to the low-temperature boundary of an incommensurately modulated antiferroelectric phase transition taking place over a temperature range. All characteristic temperatures exhibit frequency dispersion in the range of 0.1–10 kHz, which is considerably stronger for T* and Td than for Tm and Tnl . In addition, Tnl depends linearly on frequency, whereas both T* and Td resemble the non-linear frequency dependence of Tm typical of relaxors. The nature of the frequency dispersion of T* and Td is discussed from the viewpoint of complex behavior of low-energy polar modes intrinsic of relaxor ferroelectrics. C 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4864036] V I. INTRODUCTION 0

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Perovskite Pb-based A(B 1/2B 1/2)O3 and A(B 1/3B 2/3) O3 relaxor ferroelectrics (RFEs) are nowadays generally recognized to be very perspective materials for a wide range of applications. The multifunctionality of relaxors is due to their intrinsic chemical inhomogeneity and related local structural distortions caused by the difference in ionic charges and radii between the different types of B-site cations, in contrast to chemically B-site ordered FEs.1 The spatial variations in the B0 - and B"-cation distribution result in an overall chemically disordered host matrix possessing local electric fields (often called random fields, RFs) and chemically short-range ordered regions on a length scale of 2–6 nm (5–15 unit cells of the aristotype structure Pm3m), giving rise to nanoscale heterogeneities. Coupling between RFs and the FE degrees of freedom of the chemically ordered regions is shown to generate polar nanoregions (PNRs), which consist of mesoscopic-scale coherent polar structural distortions and are responsible for the outstanding properties of RFEs, in particular for the giant dielectric permittivity (e) exhibiting a broad diffuse and frequencydispersive maximum at Tm.2 The PNRs are randomly dispersed within a paraelectric (PE) host matrix that appears to be in average non-polar, although it may contain abundant incoherent local polar structural distortions. Being highly dynamic, PNRs nucleate at the so-called Burns temperature Td, which is usually some hundred degrees above the temperature of the dielectric permittivity maximum Tm in the PE phase. Upon cooling, PNRs begin to couple, their flipping dynamics slows down, and at another characteristic temperature, called intermediate temperature T*, they undergo a structural martensite-like phase transition 0021-8979/2014/115(8)/084103/5/$30.00

on the mesoscopic scale and become long-lived. Finally, at a sufficiently low temperature called the freezing temperature Tf, the PNR dipoles in the RFEs become frozen into a nonergodic state, similar to polar-glass phases, or the mesoscopic polar order evolves into long-range ferroelectric order as in chemically ordered FEs.1 Thus, no structural phase transition occurs in canonical RFEs,1 whereas non-canonical RFEs possess a paraelectric-to-ferroelectric phase transition accompanied by pronounced acoustic emission (AE).3–5 However, for both canonical, e.g., pure PbMg1/3Nb2/3O3 (PMN), and non-canonical relaxors, e.g., B-site doped (1x)PbMg1/3Nb2/3O3xPbTiO3 (PMN-xPT), it was demonstrated that Tm possesses a non-trivial dependence on an external dc electric field E, namely, Tm initially decreases, attains a sharp minimum at a certain threshold field Eth, and then starts increasing,6 in contrast to normal FEs in which Tm monotonically increases with increasing the applied external field E. Moreover, for non-canonical relaxors, the electric-field dependence of the AE burst detected at Tm also exhibits a non-trivial behavior, while the phase-transition temperature Tc(E), which represents the long-range ferroelectric coupling, shows a linear trend.4 The latter observation indicates that the non-linear behavior of Tm(E) is related to mesoscopic-scale coupling processes in relaxors, similarly to the well-known frequency dispersion of Tm. Recently, it has been found that some RFEs, including pure and heavily A-site doped PbSc0.5Ta0.5O3 (PST),5,7,8 exhibit two AE bursts in the vicinity of Tm, one with a position showing a gradual increase with E and a second one, the position of which as a function of E possesses a non-trivial minimum at Eth. Since previous studies on PST revealed the presence of an incommensurately modulated antiferroelectric

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phase (IMAFE) within a temperature range around Tm,9–11 the additional AE signal exhibiting non-trivial behavior was ascribed to the high-temperature boundary of IMAFE phase transition (Tnh ). For these relaxors, the characteristic temperature T* detected by AE depends linearly on E,7 but Raman spectroscopic studies under an external electric field have revealed a non-trivial behavior of the wavenumber of the Pb-localized phonon mode near T*.12 Furthermore, RFEs that have a single AE burst near Tm, such as pure and heavily A-site doped PbSc0.5Nb0.5O3 (PSN),13 show a non-trivial behavior of the AE burst under E not only for Tm but also for T* and Td. Since both B-site- and A-site-doped RFEs exhibit the non-trivial dependence of Tm on E, the phenomenon has been previously assumed to be a consequence of the competition between the external field E and the intrinsic RFs and/or random elastic fields when affecting the PNRs.6,8,12 As mentioned above, the non-trivial E-dependence of the characteristic temperatures Tm, T*, and Td may stem from the same mesoscopic-scale coupling processes that are responsible for the frequency dispersion of Tm and hence, one may expect that T* and Td are also frequency dependent due to the presence of dynamic ferroic species. However, while the frequency dispersion of Tm is well established in RFEs, no investigations devoted to such a dispersion of both T* and Td have been performed so far. Thus, the main goal of this study was to comparatively analyze the frequency dispersions of Tm, T*, and Td. For the purpose we have performed AE analysis on single crystals of PbSc0.5(Ta1xNbx)0.5O3 (PSTN) with x ¼ 0.14. This compound was chosen as a solid solution between a relaxor exhibiting a single AE burst near Tm (PSN) and a relaxor with two AE bursts near Tm (PST). Complementary Raman scattering experiments were performed to shed light on the atomistic origin of the observed frequency dispersions. II. EXPERIMENTAL DETAILS

The optically homogeneous cube-shaped singe-crystal samples of PSTN with x ¼ 0.14 were synthesized by the high temperature solution growth method.14 Exact chemical composition was determined by electron microprobe analysis (Cameca microbeam SX100SEM system), averaging over 100 spatial points. Powder x-ray diffraction (XRD) analysis (Philips X-Pert diffractometer) showed negligible degree of chemical long-rage order. Synchrotron single-crystal XRD (DESY/HASYLAB F1 beamline with a MarCCD 165 detector) revealed the presence of PNRs at 300 K and 180 K and no PE-FE phase transition between 700 and 180 K. The compound was also studied by polarized Raman spectroscopy in the temperature range of 850–10 K (Horiba T64000 spectrometer with an Olympus microscope). Plate-like (100)-oriented samples with a size of approximately 1.8 1.2 0.2 mm3 were used for frequencydependent dielectric and AE experiments. The AE technique has been described previously.3 Silver contacts are prepared on both sides of the sample. The sample is pasted with a silver epoxy to the polished side of a fused silica acoustic rod waveguide. A PZT-19 disk piezoelectric sensor is attached to the rear end of the waveguide. The sensor is electrically

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coupled to a 500 kHz bandpass low noise variable (up to 40 dB) preamplifier connected to a detector-amplifier (40 dB). A Cu-K thermocouple junction is glued to the waveguide near the sample. For low temperature measurements, the higher part of the acoustic waveguide with the pasted sample is vertically mounted from below into the VPF-100 cryostat through a sealing washer, and for high temperature measurements, the waveguide with the pasted sample is vertically mounted from below into resistance element furnace. The dielectric data are measured using a HP4263A LCR meter wired to the sample. All the thermocouple, amplifier, and LCR meter outputs are interfaced with a PC for a coupled readout. Temperature dependences of e are measured in the temperature interval of 190–300 K, and the AE count rate dN/dT (s1) is measured in the temperature interval of 200–700 K with a rate of about 1–3 K/min at the measuring frequencies of 0.1, 1.0, and 10 kHz on heating. III. RESULTS AND DISCUSSION

Both the real part e0 and loss tangent tan d of the dielectric permittivity as well as dN/dT measured at all the above mentioned frequencies are shown in Fig. 1. e0 (T) exhibits a slightly distinguished anomaly near 211 K accompanied by pronounced AE and a main broad maximum at Tm which, as expected for RFEs, varies with frequency between 257 and 265 K. tan d shows a wide maximum spread out between approximately 200–240 K and a small sharp maximum at 286 K. Because no AE in a close vicinity of Tm was detected, in contrast to those previously observed in pure PST,5 PST doped with La,8 and PSN,13 PSTN is confirmed to be a canonical RFE,1 in according with suggestion of Ref. 14 based on XRD data. Both Td ¼ 480 K and T* ¼ 581 K (not shown in Fig. 1) were successfully detected by AE, similar to the previously reported observation of Td by AE in the wellknown canonical RFE PMN.15 The frequency dispersion of Tm is well-known to follow the Vogel–Fulcher law16 T0 ; (1) fm ¼ f0 exp Tm Tf

FIG. 1. Dielectric permittivity e0 (filled symbols), loss tan d (open symbols), and AE count rate (filled symbols) measured at 0.1 kHz (squares, 1), 1.0 kHz (circles, 2), and 10 kHz (diamonds, 3). The inset shows in a larger scale of AE count rate dN/dt temperatures at 0.1 and 1.0 kHz, respectively.


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where T0 ¼ E/kB is an equivalent temperature (E is the activation energy and kB is the Boltzmann constant), Tf is the freezing temperature, and f0 is the attempt frequency. The experimental Tm(f) data points for PSTN fulfill the VogelFulcher law, indicating that PSTN belongs to RFEs.1 The values obtained by the fittings suggest that Tf is near 225 K, while T0 and f0 may range between 630–700 K and 6 1010–3 1011 Hz, respectively; the unambiguous determination of T0 and f0 is hindered by the number of data points, which is restricted by the frequencies available in the set-up. Intriguingly, both Tf and Tm for PSTN are very close to those that well known for PMN.1 It should be noted that Tf 225 K lies slightly above the dielectric anomaly in e0 near 211 K accompanied by AE. However, it is well known that in canonical RFEs the Tf is not accompanied by AE in the absence of applied E inducing a FE phase transition.17 On the other hand, as it is mentioned above, PST possesses an IMAFE phase coexisting with the PE as well as FE phase in the corresponding temperature range. The temperature range of IMAFE state is extended above and below Tm and is wider for crystals with a higher degree of B-site ordering.9–11 Previously, the Tnh of IMAFE was observed in both the e0 and tan d as a slight anomaly accompanied by AE in non-canonical relaxor ferroelectric PST,5 which below Tm undergoes a spontaneous ferroelectric phase transition. In our present work, Tnh is observed as a slight anomaly only in tan d at 286 K (Fig. 1) and is not accompanied by AE as believed due to the canonical relaxor behavior of PSTN. However, the dielectric anomaly near 211 K is accompanied by pronounced AE at a temperature denoted, hereafter, as Tnl , assuming this AE corresponds to the low-temperature boundary of IMAFE, i.e., the temperature range of existence of IMAFE state in PSTN expands from 211 K to 286 K. The latter is in good agreement with the temperature range of 230–310 K of existing IMAFE state in pure PST determined by transmission electron microscopy analysis.9–11 Additionally, the shape of the tan d(T) (Fig. 1) looks similar to that observed in tungsten bronze RFE Sr1xBaxNb2O6 (SBN).18 In the latter paper, the wide maximum in tand(T) was explained to result from a modulated antiferrodistortive incommensurate-commensurate phase transition Tb below Tm, at that, this Tb shifts to higher temperatures as frequency enhances.18 This is another argument supporting our suggestion that Tnl indeed marks the range of existence of IMAFE phase in PSTN. The frequency dependence of Tnl as well as the corresponding acoustic rate dN/dT is shown in Fig. 2. Tnl depends linearly on frequency with a dispersion of 0.6 K/kHz, while dN/dT increases monotonically, seeks to saturation at high frequencies. Previously, when studying FEs phase transitions in PbTiO3 crystals by AE, the essential influence of arising of misfit dislocations was established.19 During multiple thermal cycling with a frequency of about 0.01 Hz, misfit dislocations arise on the domain walls and lead to the so-called work hardening of the crystals. This means that the dislocations are the pinning centers for domains and prevent a free movement of their walls. Hence, while •N is well known to be proportional to misfit dislocation density,20,21 it in fact initially increases, but then attains the maximum and

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FIG. 2. Frequency dependence of Tnl and corresponding AE count rate dN/dt. The inset shows the frequency dependence of Tm.

slowly decreases. Such a behavior is concluded to be a consequence of annihilation of both the misfit and post-grown dislocations of the crystals, confirmed by x-ray diffraction analysis.19 Recently, a similar behavior of the frequency dependence of dN/dT up to 5 Hz at room temperature was observed in PZT ceramic FEs.22 It was concluded that the decrease in dN/dT is caused by domain pinning, however, the annihilation mechanism of dislocations was not taken into account. In the present work, dN/dT tends to saturation as the frequency exceeds the 10 kHz, what is believed to be an evidence of perfection of our crystals. Figure 3 presents the frequency dispersion of T* and Td, detected by AE. They vary with frequency between 480–551 K and 581–625 K, respectively. These dispersions are similar to that of Tm presented in Fig. 2. Unfortunately, no parameters can be fitted for these dispersion curves to follow the Vogel-Fulcher law.16 Both T* and Td exhibit a considerably stronger dispersion in comparison to Tm (see Fig. 1). In the range of 0.1–1.0 kHz, dT*/df and dTd/df are almost the same but between 1.0 and 10 kHz the change in T* is approximately twice as strong than the change in Td, i.e., the frequency dispersion has a maximum near T*. The frequency dependence of the characteristic temperatures should be related to the difference in the relaxation times of the flipping structural species. So, our data suggest that the change

FIG. 3. Frequency dependencies of the intermediate temperature T* and Burns temperature Td.


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in the lifetimes of dynamic PNRs is strongest near T*. This conclusion is in accordance with Raman optical activity studies,23 implying that the local random fields might be quenched not only at low but also at high temperatures. Let us now consider the nature of frequency dispersion of both the T*and Td in more detail. For chemically ordered FEs undergoing a phase transition of displacive type, the socalled soft phonon mode (SM) is known to obey the famous Cochran law in the framework of thermodynamic Landau theory24 x2SM ðT Tc Þ;

(2)

where x2SM e1 is the square wavenumber of the soft mode. However, the development of non-ergodic polar state in relaxors is much more complex, it considerably involves order-disorder phenomena and coupling between preexisting polar species. The emergence of relaxation (central) mode below Td caused by intrinsic chemical inhomogeneity and related local structural distortions of RFEs influences the atomic vibrations and hence, one can better understand the underlying atomistic mechanism of the frequency dispersion of Tm, T*, and Td by analyzing the anomalies in the temperature dependences of the phonon modes. Figure 4 shows the temperature evolution of the lowest-energy phonon modes for PSTN, which involve cation vibrations and generate Raman scattering:14 (i) x1xx and x1xy denote the positions of the Raman peaks near 50 cm1 in ZðXXÞZ and ZðXYÞZ polarized spectra, which both result from the A-site Pb-localised Raman-active mode existing only in a double-perovskite structure and in the paraelectric state it is symmetry allowed in ZðXYÞZ and forbidden in ZðXXÞZ; (ii) x2xx and x3xx denote the Raman scattering near 75 and 135 cm1 resulting from vibrations of both Pb and B-site cations and correspond to the TO and LO component of the IR-active triply degenerate mode in the paraelectric state; and (iii) x4xx denotes the position of the Raman peak near 240 cm1 originating from a B-cation localised mode that exists only in double-perovskite structures and in the paraelectric state is only IR active, similar to x2xx and x3xx. The first three modes soften and from the kinks of in the temperature dependencies of the Raman signals x1xx, x2xx, x3xx which are anomalous (symmetry-forbidden) in the paraelectric state14,25 one can deduce T* to be between 450–500 K and Td to be between of 640–700 K. The T* can also be determined from the temperature dependence of the FWHM of the hard mode x4xx,25 and for PSTN it is around 450 K–480 K.14 In pure PST and PSN, x4xx(T) shows a clear kink at T*,25,26 but apparently the co-existence of two ferroelectrically active B-site cations smoothens the temperature dependence. However, if x4xx(T) is fitted with a growth function, e.g., Boltzmann, the obtained inflection point is 485 6 15 K. Hence, T* deduced from Raman data corresponds very well to T* detected by AE. The Burns temperature Td determined from Raman data is slightly higher that Td detected by AE, which can be due to the difference in the time scale sensitivities of the methods. The lifetime of PNRs between Td and T* is shorter than that below T* and hence, Td appears at higher temperatures in Raman experiments than in AE experiments because Raman can detect ferroic

FIG. 4. Temperature dependence of positions of Raman peaks generated by low-energy phonon modes in PSTN that involve cation vibrations: x1xx and x1xy generated from of Pb-localised Raman-active mode which is symmetry-forbidden (xx) and allowed (xy) in a cubic double-perovskite structure (a); x2xx and x3xx from Pb-BO3 translation modes, which are only IR active in a cubic single/double-perovskite structure (b), and x4xx from of B-cation-localised mode in a double-perovskite structure (a), which is only IR active in the cubic phase; superscripts xx and xy stand for ZðXXÞZ and ZðXYÞZ scattering geometry. The solid lines are linear fits to high-temperature data points; the dashed line in (a) is a Boltzmann fit to x4xx(T) data points over the entire temperature range.

formations on the time scale of 1012 s, while AE is expected to be a "slower" method. The anomalous Raman scattering at x1xx, x2xx, x3xx, and x4xx is caused by off-centered (polar) displacements of the corresponding cations and hence the temperature dependencies of these peaks reveal Pb–Pb (x1xx), Pb–B-cation (x2xx and x3xx), and B-cation–B-cation (x4xx) coupling processes. Therefore, the Raman data clearly show that the predominant coupling of all types of cations, including A-site and B-site cations, occurs at T*, implying that the strongest changes in the relaxation times of PNRs should be near T*, which explains the strongest frequency dispersion of T* detected by AE. IV. CONCLUSIONS

In summary, we have studied PSTN RFEs crystals in a wide temperature range using an acoustic emission method. The acoustic emission signals observed at Tnl < Tm were


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attributed to an incommensurate-commensurate modulated antiferroelectric phase transition, by analogy with other relaxor ferroelectrics. We also successfully detected the intermediate T* and Burns Td temperatures. We have observed that a lower temperature boundary of IMAFE Tnl behaves linearly in dependence on frequency, whereas the Tm as well as the T* and Td exhibit a non-linear frequency dispersion, at that such a dispersion of two last is stronger than that of Tm following the Vogel–Fulcher law. We have concluded that the reason of the frequency dispersion of T* and Td characteristic temperatures is the emergence of relaxation (central) mode below Td, caused by nucleation of polar nanoregions PNRs and their coupling via phonon modes localized in Asite and/or B-site cations below T*. 1

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