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In situ high-temperature high-pressure Raman spectroscopy on single-crystal relaxor ferroelectrics PbSc1/2Ta1/2O3 and PbSc1/2Nb1/2O3

This content has been downloaded from IOPscience. Please scroll down to see the full text. 2013 J. Phys.: Condens. Matter 25 155902 (http://iopscience.iop.org/0953-8984/25/15/155902) View the table of contents for this issue, or go to the journal homepage for more

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IOP PUBLISHING

JOURNAL OF PHYSICS: CONDENSED MATTER

J. Phys.: Condens. Matter 25 (2013) 155902 (10pp)

doi:10.1088/0953-8984/25/15/155902

In situ high-temperature high-pressure Raman spectroscopy on single-crystal relaxor ferroelectrics PbSc1/2Ta1/2O3 and PbSc1/2Nb1/2O3 N Waeselmann1 , B Mihailova1 , M Gospodinov2 and U Bismayer1 1

Fachbereich Geowissenschaften, Universität Hamburg, Grindelallee 48, D-20146 Hamburg, Germany Institute of Solid State Physics, Bulgarian Academy of Sciences, Blvd. Tzarigradsko Chausse 72, 1784 Sofia, Bulgaria 2

E-mail: [email protected] and [email protected]

Received 18 December 2012, in final form 23 February 2013 Published 20 March 2013 Online at stacks.iop.org/JPhysCM/25/155902 Abstract The effect of temperature on the pressure-induced structural changes in perovskite-type (ABO3 ) relaxor ferroelectrics is studied by in situ high-temperature high-pressure Raman spectroscopy on single crystals of PbSc1/2 Ta1/2 O3 (PST) and PbSc1/2 Nb1/2 O3 (PSN), which allowed us to elucidate the interplay between the polar and antiferrodistortive order coexisting on the mesoscopic scale at ambient conditions. High-pressure experiments were carried out at elevated temperatures below and above the characteristic intermediate temperature T ∗ . The results were compared with those obtained at room temperature, which for PST is just above the paraelectric–ferroelectric phase transition TC , whereas for PSN is below TC . It is shown that the first critical pressure pc1 , at which a transition from a relaxor to a non-polar rhombohedral state with antiphase octahedral tilt ordering occurs, decreases at elevated temperatures due to the weakening of the polar coupling, which in turn facilitates the evolution of the preexisting medium-range antiferrodistortive order into a long-range order. The critical pressure pc2 of the second phase transition, involving a change in the type of the antiferrodistortive order, is not affected by temperature, i.e. it is independent of the state of polar coupling and is mainly related to the initial correlation length of antiferrodistortive order. The strong influence of temperature on pc1 , which occurs only when the mesoscopic polar order is suppressed, emphasizes the importance of coexisting ferroelectric and antiferrodistortive coupling for the occurrence of the relaxor states. (Some figures may appear in colour only in the online journal)

1. Introduction

existence of polar nanoregions (PNRs) flipping between different orientation states [4]. There are three different structure types which exhibit relaxor properties: (i) the tungsten bronze structure (A12 A24 B12 B28 C4 O30 ), (ii) the perovskite structure (ABO3 ), and (iii) the pyrochlore structure (A2 B2 O7 ). Tungsten–bronze-type relaxors are characterized by cation vacancies and compositional variations; hence the relaxor behaviour has been explained by quenched random electric

Due to their superb dielectric permittivity as well as excellent electro-elastic and electro-optical properties, relaxor ferroelectrics (relaxors) play an important role in our everyday life as actuators, capacitors and memory devices [1–3]. The defining property of relaxors is the broad frequencydependent maximum of the dielectric permittivity as a function of temperature, which has been attributed to the 0953-8984/13/155902+10$33.00

1

c 2013 IOP Publishing Ltd Printed in the UK & the USA

J. Phys.: Condens. Matter 25 (2013) 155902

N Waeselmann et al

tilt order. On a further pressure increase the octahedral tilts around the cubic [100], [010], and [001] directions become different from each other on the local scale at an intermediate pressure p∗2 , which precedes a second phase transition at pc2 . This phase transition involves a change in the BO6 -tilt pattern to antiphase tilts with unequal magnitude (a− b− b− , 0 ≤ a < b) or to a mixed tilt system (a+ b− b− ), as the latter is accompanied by compatible antipolar long-range ordering of the A-positioned Pb2+ cations [26]. All these pressure-induced changes have been observed in several Pb-based B-site complex perovskite-type relaxors at room temperature, which is close to Tm . The brief overview of structural transformations in relaxors shows that the decrease in temperature at ambient pressure enhances the coupling between cation polar shifts, whereas the increase in pressure at room temperature triggers the coupling between antiphase BO6 tilts and antipolar Pb shifts. To better understand the interplay between the intermediate-range ferroelectric and antiferrodistortive atomic ordering in relaxors we have applied in situ highpressure Raman spectroscopy to PbSc1/2 Ta1/2 O3 (PST) and PbSc1/2 Nb1/2 O3 (PSN) at fixed elevated temperatures that are close to T ∗ and to TB . Raman spectroscopy is highly sensitive to structural alterations on the short- and intermediate-range length scale. In addition, any dynamic atomic fluctuations slower than ∼10−12 s, which is approximately the phonon period, appear as static clustering to Raman spectroscopy. Therefore Raman spectroscopy is a very suitable method to study the transformation processes in relaxor materials. On the other hand, PST and PSN have been proved to be valuable model compounds [25, 26, 29], as they have the same stoichiometry (B01/2 B001/2 ) matching the ideal ratio for 1:1 chemical order, the same tolerance factor t = √ rA +rO = 2(rB +rO ) 0.977 (see table 1), and they both show an abundance of dynamic PNRs at ambient conditions, as revealed by the intense x-ray diffuse scattering along the cubic h110i∗ direction [20, 30]. In this paper we report on pressure-driven structural transformations in PST and PSN at T = 400 K, which for both compounds is between Tm and T ∗ , as well as at T = 600 K, which is between T ∗ and TB . We compare the results with those obtained under pressure at room temperature in order to clarify temperature renormalization of the pressure-driven phase transitions as well as the structural states of relaxors at different stages of development of PNRs.

fields associated with the local charge imbalance that hinder the development of a long-range ferroelectric order [5]. On the other hand, the relaxor properties of the pyrochlore-type relaxor Cd2 Nb2 O7 [6], with chemically homogeneous cation sites, have been attributed to structural order/disorder processes on the mesoscopic scale [7], leading to local elastic fields. The perovskite-type relaxors are perhaps the most challenging to understand because compositional disorder can lead to both charge imbalance and local strains due to the high flexibility of the structure to adopt more than one type of cation on the A and/or B site. Therefore both the concepts of quenched random electric fields and local elastic fields can be applied to perovskite-type relaxors. It is well known that Pb-based B-site complex perovskite relaxors exhibit frustrated chemical order of the NaCl type [8–10] and, as a consequence, the local structure appears to be double-perovskite (aristotype ¯ Fm3m). For these relaxors it has been recently shown that, near the temperature of the dielectric permittivity maximum Tm , the intermediate polar order coexists with intermediate antiferrodistortive order [11–14]. It was also proposed that the structural state of PNRs is frustrated ferrielectric [10], as a result of the coupling between the polar and antiferrodistortive order. The non-conventional V-shaped dependence of Tm on the bias electric field E observed for perovskite and non-perovskite relaxors [15–17] strongly supports the proposed ferrielectric nature of PNRs, which may play a key role in synthesizing novel smart ferroic materials with chemically tunable macroproperties. Competing ferroelectric and antiferroelectric interactions in canonical relaxors were also assumed on the basis of active Brillouin-zone-boundary soft modes along with the zone-centre soft TO mode [18]. Thus further studies of the nanoscale transformation processes in relaxors are required to elucidate the significance of the antiferrodistortive coupling for the development of PNRs. It is well known that dynamical PNRs are formed at the Burns temperature TB > Tm [19], at which off-centred cationic displacements couple to form small polar clusters [20, 21]. On a temperature decrease these clusters evolve and at the intermediate temperature T ∗ (TB > T ∗ > Tm ) they merge into larger clusters, while their flipping dynamics significantly slows down [20–22]. Below Tm the PNRs either are sufficiently enlarged to transform into normal ferroelectric domains at the Curie temperature TC , i.e. the dynamic intermediate-range polar order is developed into a static long-range ferroelectric order, or simply freeze at Tf , forming a static intermediate-range polar order. On the other hand, under pressure the intermediaterange antiferrodistortive order evolves into a long-range order [23–27], passing through several structural states [26]. Similar to the temperature-induced structural transformations, there is an intermediate pressure p∗1 , preceding the pressureinduced phase transition at pc1 from a relaxor to nonpolar rhombohedral state. At p∗1 the coupling between the off-centre displacements of the A- and B-site cations is suppressed in favour of dynamic antiferrodistortive order consisting of antiphase BO6 tilting of a− a− a− type (Glazer’s notation [28]), which at pc1 evolves into a static long-range

2. Experimental details Optically and chemically homogeneous single crystals of PST and PSN were synthesized by the high-temperature solution growth method. The chemical composition of the as-grown single crystals was determined by electron microprobe analysis (Cameca Microbeam SX100), averaging over 50 points from each specimen. Both samples have been thoroughly investigated by diffraction and Raman scattering analysis at different temperatures and ambient pressure, as well as at different pressures and room temperature [20, 2


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Table 1. Main characteristics of the studied single-crystal samples of PbSc0.5 B000.5 O3 , B00 = Ta, Nb. Ionic radius of B00 Tolerance factor Atomic mass of B00 B00 –O force constant Long-range chemical B-site orderb Mean size of chemically B-site ordered domainsc TB T∗ TC p∗1 pc1 p∗2 pc2

PST

PSN

Reference

˚ ri = 0.64 A t = 0.977 180.95 u 230 N m−1 204 N m−1 0.13

˚ ri = 0.64 A t = 0.977 92.91 u 210 N m−1 188 N m−1 Below detection limit

[31]

[29] [32]a [25]

6.4 nm

N.a.

[25]

750 K 550 K Between 368 and 378 Kd 2.5 GPa 4.1 GPa Between 7 and 10 GPa Between 13.5 and 16.6 GPa

[20, 30] [20, 30] [20, 34] [26] [35, 36] [26] [26]

700 K 450 K 270 K 1.2 GPa 1.9 GPa ∼3 GPa 5.5 GPa

a

Force constants determined for LiTaO3 and LiNbO3 ; note that the relative difference in the force constants is the nearly same as that for PST and PSN [29]. b Determined from the ratio ρ ¯ measured /ρfully ordered , ρ = I(111)/I(200) (Miller indices in Fm3m), according to [33]. c Determined from the Scherrer equation applied to the 111 diffraction peak in the powder XRD pattern. d Our in-house powder XRD data did not reveal deviation from cubic metric down to 10 K; Bragg peaks consistent with polar rhombohedral structure were detected at 150 K by single-crystal XRD with synchrotron radiation [30].

of the photoluminescence peak of SrB4 O7 :Sm2+ used as a pressure indicator during the pressure run confirmed that quasihydrostatic conditions were maintained within the experimental error. Prior to sample loading, NaCl was ground to a fine powder using a vibration mill and dried at 500 ◦ C for 24 h, in order to reduce the noise level during the Raman scattering experiments. Samples of approximate size 40 × 40 × 20 µm3 were placed in the sample chamber, ensuring that both the sample specimen and the pressure marker were surrounded by NaCl on all sides and did not touch the diamonds or the gasket. To prevent oxidation of the Re gasket at high temperatures, the DAC was purged with N2 gas. Raman spectra were collected using a Horiba Jobin–Yvon T64000 triple-grating spectrometer equipped with an Olympus BH41 microscope and a 50× long-working distance objective. The measurements were conducted in a backscattering geometry without an analyser on the scattered light, using the 514.5 nm line of an Ar+ laser and a spectral resolution of 2 cm−1 . PSN was measured at 400 K with an acquisition time of 30 s and 20 loops, at 600 K the acquisition time varied between 30 and 60 s averaging over 20 loops. PST was measured with an acquisition time of 15 s and 10 loops for 400 K and 30 s with 10 loops for 600 K. The as-measured spectra were baseline-corrected by subtracting a background spectrum measured from alongside the sample to eliminate the weak artificial contribution from the DAC and the pressure medium. The baseline-corrected spectra were then reduced by the Bose–Einstein phonon occupation factor to eliminate the effect of temperature on the peak intensities, using the relation Ireduced = Imeasured /(n(ω, T) + 1), where n(ω, T) = 1/(eh¯ ω/kT −

25, 26, 29, 30]. The main crystal–chemical parameters of PST and PSN, as well as their characteristic temperatures and pressures are summarized in table 1. Powder x-ray diffraction showed that the long-range chemical 1:1 B-site order in PST is very low [20], while for PSN the chemical B-site order is below the detection limit of powder x-ray diffraction [30]. Following the criterion proposed by Stenger and Burggraaf [33], the long-range chemical 1:1 B-site order in PST is ρmeasured /ρfully ordered = 0.13, where ρ = I(111)/I(200) and I(hkl) is the integrated area of the corresponding hkl Bragg diffraction peak with Miller indices ¯ given in Fm3m. In situ high-pressure high-temperature experiments were R µScopeDAC-HT(G) carried out using an easyLab Diacell gas-membrane-driven diamond anvil cell (DAC). The cell is equipped with a resistance gasket heater, ensuring temperature stability of ±10 K. The temperature was measured by a K-type thermocouple attached to the metal gasket. The pressure was determined from the shift of the 7 D0 –5 F0 photoluminescence line of SrB4 O7 :Sm2+ , which, in contrast to the commonly used ruby R1 photoluminescence line, has negligible temperature dependence [37]. The uncertainty in pressure determination was ∼0.1 GPa. Rhenium gaskets were prepared for all experiments to ensure the stability of the sample chamber at elevated temperatures. Sodium chloride was used as a pressure medium. As any solid medium, NaCl develops a certain anisotropic strain upon uniaxial mechanical load [38], which perturbs the hydrostaticity of the experiment. However, at high temperatures the anisotropic strain is considerably reduced [39], ensuring quasihydrostaticity up to 9 GPa, which was the highest pressure achieved at elevated temperatures with our setup. The constant width 3


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Figure 1. Raman scattering of PST and PSN measured in DAC at the same low pressure and different temperatures. The measured pressure was 0.4 GPa in all cases, except for PST at 600 K, for which the actual pressure was determined to be 0.3 GPa, i.e. within the experimental uncertainty all spectra were collected at ∼0.4 GPa.

1), ω, T, h, and k, are the phonon wavenumber, temperature, the reduced Planck constant, and the Boltzmann constant, respectively. None of these two procedures influence the Raman peak positions. The temperature-reduced spectra were fitted with Lorentzian functions to precisely determine the peak positions, full-widths-at-half-maximum (FWHMs) and integrated intensities.

different temperatures: 293 K, 400 K and 600 K (figure 1). The development of PNRs with temperature decrease is apparent from the enhancement of the anomalous Raman scattering near 140, 250, 430 and 700 cm−1 related to the cubic F1u modes [11, 29]. The characteristic temperatures T ∗ and TB can be deduced from the temperature dependences of the Raman peaks near 140 and 250 cm−1 , resulting from Pb–BO3 translations and vibrations of off-centred B-site cations, respectively [11, 20, 42]. In particular at T ∗ , the FWHM of the peak near 250 cm−1 considerably decreases on cooling due to the strong enlargement of the correlation length of coupled B-cation polar shifts. The peak near 350 cm−1 is related to the cubic silent F2u mode, which consists of Pb–O bond stretching within cubic {111} planes and can also be considered as antiphase BO6 rotation [11, 25, 29]. The anomalous Raman activity of this mode results from coupled ferroic Pb–O species. At ambient pressure the peak near 350 cm−1 is more pronounced for PST than for PSN due to the longer correlation length between the ferroic Pb–O species [29]. The Raman spectra of PST and PSN collected at different pressures at 400 and 600 K are shown in figure 2. Previous in situ high-pressure experiments at room temperature demonstrated that (i) pressure leads to the suppression of both Raman peaks at 140 and 250 cm−1 , indicating decoupling of the Pb and B-cation polar shifts and subsequent reduction of the B-cation off-centred displacements, i.e. suppression of the polar order; (ii) the pressure-induced phase transition at pc1 from a relaxor to a non-polar rhombohedral state containing long-range ordered antiphase BO6 tilts is accompanied by the appearance of a soft mode near 37 cm−1 ; (iii) the development

3. Results and discussion On the length scale of sensitivity of Raman spectroscopy Pb-based relaxors exhibit a double-perovskite structure, as clearly revealed by the strong peaks near 820 cm−1 and 50 cm−1 , arising from phonon modes existing only in the double-perovskite structure [11, 22, 29, 40, 41]. The prototype double-perovskite structure has face-centred cubic ¯ symmetry with occupied Wyckoff positions (4a), Fm3m (4b), (8c), (24e), and therefore the allowed optical phonon modes at the centre of the Brillouin zone are A1g (R) + Eg (R) + F1g (I) + 4F1u (IR) + 2F2g (R) + F2u (I), where (R), (IR) and (I) stand for Raman-active, infrared-active and inactive, respectively. By considering the mass and force-constant effects on the phonon wavenumbers, as well ¯ as the selection rules of the polarizability tensors for Fm3m, it was possible to discriminate the peaks originating from the cubic Raman-active A1g , Eg and F2g modes (see figure 1) from the Raman scattering related to ferroic (non-cubic) local structural distortions [11, 29]. The effect of temperature on the Raman spectra of PST and PSN collected in DAC can be seen from the spectra collected at the same low pressure 0.4 ± 0.1 GPa and three 4


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Figure 2. High-pressure Raman spectra of PST and PSN at 400 and 600 K.

of octahedral tilting with pressure increase is mirrored by the strong enhancement of the anomalous Raman scattering near 350 cm−1 [23, 25, 27, 43, 44]. As can be seen in figure 2, the same pressure-induced structural changes are observed at elevated temperatures. The peak near 350 cm−1 is apparently enhanced by high pressure for all temperatures, indicating the development of octahedral tilting. At low pressures the Raman scattering near 250 cm−1 is well pronounced at 400 K, but suppressed and broadened at 600 K, because the former temperature is still below T ∗ , whereas the latter temperature is well above T ∗ (see table 1). The same is valid for the peak near 140 cm−1 . At 400 K both peaks are suppressed

with increasing pressure, indicating a suppression of the polar order, similar to the high-pressure state at room temperature. First we analysed the effect of temperature on pc1 , at which the system undergoes a phase transition from a relaxor cubic to a non-polar rhombohedral state involving longrange antiphase octahedral tilting. Previous investigations on PST [23] as well as on A- and B-site doped PST and PSN [25, 45] using Raman spectroscopy and single-crystal XRD have shown that the first pressure-induced phase transition is associated with the appearance of a soft mode involving Pb vibrations. At room temperature the soft mode in PSN could not be resolved up to 7.5 GPa [45], which is 5


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The coexistence of two types of ferroic coupling at ambient conditions: polar and antiferrodistortive, explains why for relaxors the high-temperature state is different from the high-pressure state although the negative dpc1 /dT for both PST and PSN (see figure 3) implies that the high-symmetry phase is preferred at high temperature as well as at high pressure [47]. Our results about the negative dpc /dT are also consistent with the observed decrease in Tm with pressure increase [48, 49], which can be attributed to the suppression of the polar coupling on the account of the pressure-enhanced antiferrodistortive coupling. In order to study the influence of temperature on the second phase-transition pressure pc2 , as well as on the structural state between pc1 and pc2 and above pc2 , we compared the pressure dependences of the peak positions ω(p) of the Raman peaks related to the cubic F2g , F2u , A1g phonon modes as well as ω(p) of the soft mode for PST at room temperature, 400 K, and 600 K (see figure 4). Such a detailed comparison is not given for PSN, because for this compound pc2 is above 9 GPa, which is the limit of our experimental setup. Recent room-temperature high-pressure synchrotron XRD and Raman scattering experiments up to 30 GPa on several relaxor compounds revealed that the slope of ω(p) of the soft mode exhibits a kink at pc2 [45], regardless of the type of octahedral tilt pattern developed above pc2 and the length of coherence of antipolar Pb shifts. For PST the second pressure-induced phase transition is at pc2 ∼ 5.5 GPa, and the kink in dω/dp of the soft mode can hardly be deduced from the room-temperature data presented here because of the limited pressure range. However, a kink at 5.5 GPa is apparent in the data collected at elevated temperatures (figure 4), suggesting that the temperature increase does not affect the second pressure-induced phase transition. The same conclusion can be drawn if we consider the Raman scattering near 350 cm−1 generated by the O-localized Pb–O bond stretching mode within cubic {111} planes, which can be also considered as antiphase BO6 rotations [11, 25]. This mode was proved to be sensitive to the room-temperature intermediate pressures p∗1 and p∗2 (1.2 and 3.0 GPa for PST) of local structural changes preceding the corresponding phase transitions [26]. At p∗1 , ω(p) starts to increase considerably due to the evolving antiphase BO6 -tilt order (see figure 4), whereas at p∗2 the mode splits due to the locally developed unequal tilts [26]. If the splitting above p∗2 is neglected, ω(p) of the Pb–O bond stretching mode shows a remarkable resemblance to the pressure dependence of both the pseudocubic adiabatic and isothermal bulk moduli at room temperature in the pressure range up to 10 GPa [50], and pc2 can be deduced from the decrease in the ω(p)-slope. At elevated temperatures, splitting of the Raman peak near 350 cm−1 in the pressure range (pc1 , pc2 ) was not resolved, which most probably results from the temperature-induced broadening and subsequent overlapping of the peaks. Thus, from the Raman scattering near 350 cm−1 we cannot draw any conclusions about the effect of temperature on the second intermediate pressure p∗2 . However, the ω(p)-dependences measured at 400 ad 600 K exhibit a steady increase up to ∼5.5 GPa, which is the room-temperature pc2 for PST, and

Figure 3. Critical pressure pc1 versus temperature for PST (filled squares) and PSN (open circles) determined by the appearance of the soft mode. The characteristic temperatures at ambient pressure are marked on the top horizontal axis.

approximately 3 GPa higher than pc1 , due to the relatively small fraction of substance that undergoes a phase transition. For PSN the critical pressure pc1 was deduced from the Raman spectra by the maximum of the FWHM of the Pb-localized low-wavenumber mode near 50 cm−1 [46]. At elevated temperatures the soft mode is observed for both PST and PSN and appears at pressures lower than the corresponding room-temperature first critical pressure pc1 (figures 2–4(a)). At room temperature, pc1 is 1.9 GPa for PST. The increase in temperature to 400 K, which is 50 K below T ∗ , reduces pc1 to 1.5 GPa (see figures 2 and 3). On a further temperature increase up to 600 K, the soft mode was detected already at 0.3 GPa. The room temperature pc1 is 4.1 GPa for PSN [25], whereas at 400 K and 600 K a soft mode was detected at 3.8 GPa and 1.8 GPa, respectively. The fact that for PSN the soft mode can be resolved from the strong peak near 50 cm−1 at high temperatures suggests that the integrated intensity of the soft mode and, consequently, the fraction of the high-pressure phase is larger at 400 K, as well as at 600 K, than that at room temperature. It should be noted that the temperature-driven paraelectric–ferroelectric phase transition in PSN has been detected by neutron diffraction at ∼370 K [34], although at room temperature PSN is still in a relaxor state, i.e. there are abundant dynamic PNRs and the predominant structural component is cubic [30]. The coupling between polar cation displacements in both PNRs and ferroelectric domains is unfavoured by the temperature increase. This in turn facilitates the antiferrodistortive coupling and hence decreases the critical pressure, which may lead to a larger fraction of the material transforming under pressure into a non-polar rhombohedral phase with antiphase octahedral tilt order. The latter is supported by the fact that for PST the intensity of the soft mode at elevated temperatures is larger than the soft-mode intensity at room temperature. 6


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Figure 4. Pressure dependence of the positions of different Raman peaks for PST: the soft mode near 35 cm−1 , the Pb-localized mode near 50 cm−1 related to the cubic F2g , the Pb–O bond stretching vibrations near 350 cm−1 associated with the cubic F2u , and the BO6 symmetric stretching near 830 cm−1 related to the cubic A1g mode. The black filled squares represent the data at room temperature (), open blue triangles at 400 K (M), and red filled circles at 600 K ( •). The open grey squares () show the measured splitting of the peak near 350 cm−1 at room temperature above p∗2 . The error bars in the data collected at 400 and 600 K represent the uncertainties obtained from the spectrum fittings. The room-temperature data are after [23] and have been collected from several PST specimens to verify the trends; the uncertainties in ω obtained from the fittings are within the statistical deviations. The lines represent linear fits to the experimental data points in the corresponding pressure ranges. The kink in the soft-mode wavenumber near pc2 at room temperature was determined by considering experimental data up to 30 GPa [45].

then become almost constant (see figure 4). Therefore, based

one can conclude that the second pressure-induced phase

on the temperature renormalization of the pressure behaviour

transition is not, or negligibly, affected by the temperature

of the soft mode as well as of the Pb–O mode stretching,

increase, i.e. it is independent of the degree of polar order at 7


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Figure 5. Schematic presentation of the structural changes taking place in relaxors under temperature and pressure. Ellipsoids and rectangles with a single arrow denote polar nanoregions and long-range ordered ferroelectric domains, respectively, whereas ellipsoids and rectangles with a pair of opposite arrows represent antiferrodistortive nanoregions and long-range ordered antiferrodistortive domains, respectively. The red arrows designate uncoupled cation off-centred shifts. Differently coloured rectangles with a pair of opposite arrows designate the high-pressure long-range order below and above pc2 .

T < T ∗ are due to the competition between ferroelectric and antiferrodistortive coupling on the mesoscopic scale.

ambient pressure. Indeed, at pc2 the long-range octahedral tilt pattern is changed to better adopt the shrinking of the unit-cell volume under pressure increase and this process is solely related to the initial mesoscopic antiferrodistortive order. It should be mentioned that the pressure dependence of the wavenumber of the soft mode between pc1 and pc2 (figure 4) can also mirror the second intermediate pressure p∗2 (see figure 4). At room temperature, the soft-mode wavenumber remains approximately the same up to p∗2 , and then starts to increase with further pressure increase, similarly to the Pb–O mode stretching mode. The same trend is observed at T = 400 K, which is close but still below T ∗ , indicating that a temperature increase within the range (TC , T ∗ ) does not influence p∗2 . However at T = 600 K, which is ∼150 K above T ∗ , ω(p) of the soft mode gradually increases between pc1 and pc2 , indicating the absence of any intermediate characteristic pressure that would indicate the development of unequal octahedral tilts on the mesoscopic scale. This suggests that the stepwise pressure-induced transformation processes at

At T = 600 K the ω(p)-slopes of the two strong Raman peaks near 55 and 830 cm−1 , resulting from phonon modes ¯ structure, are reduced that exist in the prototype Fm3m above pc2 . Also, in the pressure range above pc2 , dω/dp at 600 K is smaller than dω/dp at 400 and 293 K. At first glance that latter fact is surprising, because in general at elevated temperatures the interatomic interactions weaken due to the overall volume expansion and the structure is supposed to be more compressible. However, relaxors are structurally heterogeneous materials and we attribute the observed decrease in dω/dp at p > pc2 with temperature increase to the suppression of polar nanoregions and the consequent enlargement of the material fraction that first develops a− a− a− long-range tilting at pc1 and then undergoes a phase transition to a mixed tilt system at pc2 . For the same reason, the second phase-transition pressure pc2 is much better 8


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(fourth column in figure 5). The second pressure-induced phase transition involving a change in the type of the antiferrodistortive long-range order seems to be negligibly affected by temperature.

revealed in the pressure trends of the phonon wavenumbers at elevated temperatures than at room temperature.

4. Conclusions The in situ high-pressure high-temperature Raman scattering data presented here unambiguously confirm the coexistence of mesoscopic polar and antiferrodistortive order in perovskitetype Pb-based relaxors [11–14, 51] and strongly support the proposed ferrielectric nature of the relaxor state [10]. Using temperature and pressure as two separate tuning mechanisms, one can select a structural state with a certain degree of polar order (by changing temperature) or of antiferrodistortive order (by applying pressure). At elevated temperatures the first pressure-induced phase transition from a relaxor cubic to a rhombohedral non-polar state comprising long-range ordered antiphase BO6 tilts of equal magnitude shifts towards lower pressures as the polar coupling is suppressed, which in turn facilitates the development of the mesoscopic antiferrodistortive order existing at ambient pressure into a long-range ordered antiferrodistortive state at high pressure. The second phase-transition pressure is negligibly affected by temperature, indicating that the energy barrier between the phases below and above pc2 depends mainly on the intrinsic mesoscopic-scale antiferrodistortive order. Figure 5 shows a sketch indicating the changes under temperature and pressure for Pb-based perovskite-type relaxors undergoing a phase transition. On the x-axis the evolution of dynamic PNRs (ellipsoids with single black arrow) with temperature is shown. Room-temperature high-pressure structural studies of PSN with TC ∼ 370 K and PST with TC ∼ 270 K as well as of doped PSN and PST with canonical relaxor behaviour have revealed the suppression of the polar order with pressure [25, 26]. The first two columns in figure 5 show the sequence of structural changes with pressure at temperatures close to Tm : at the first intermediate pressure p∗1 the large PNRs are reduced due to the decoupling between the polar shifts of the A- and B-site cations, and the correlation length of the mesoscopic antiferrodistortive order, which for ambient pressure exists at all temperatures (light grey ellipsoids with paired arrows), starts to enlarge. The first phase transition is associated with a static long-range order of antiphase octahedral tilts a− a− a− and the formation of non-polar rhombohedral domains (dark grey rectangles with paired arrows). At higher pressures a second phase transition occurs, which is also preceded by an intermediate pressure (not shown in sketch) and involves the occurrence of triclinic or monoclinic domains comprising long-range order of different BO6 -tilt pattern and matching antiferroelectric order of Pb2+ cations. At elevated temperatures (third column in figure 5) the PNRs are suppressed while the antiferrodistortive coupling is not significantly affected; hence, the development of antiferrodistortive long-range order is less hindered by the competitive mesoscopic polar order, which leads to a considerable decrease in the first critical pressure. We could not perform in situ high-pressure experiments at temperatures above TB , but the results obtained at 600 K suggest that pc1 should be just above ambient pressure

Acknowledgment Financial support by the Deutsche Forschungsgemeinschaft (MI 1127/2-2) is gratefully acknowledged.

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