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Lattice dynamics and dielectric spectroscopy of BZT and NBT lead-free perovskite relaxors – comparison with lead-based relaxors
Abstract
Appearance of the polar nanoregions (PNR) and their manifestation in the dielectric spectra is discussed for lead-free Ba(ZrxTi1−x)O3 (BZT-x) and (Na1/2Bi1/2)TiO3 (NBT) ceramics. Phonon softening is not as pronounced as in the lead-based relaxors, but the relaxation contribution is dominating in all cases, caused by the dynamics of the off-centred ions (Ti4+, Bi3+, Pb2+). In the lead-based relaxors, where there is no relation between the quenched chemical clusters at the B-sites and PNR, which concern the A-site Pb-ion correlations, the relaxation dynamics follows the Vogel-Fulcher behaviour with a clear freezing. However, in BZT and NBT, the PNR are smaller, since they are localised within the small quenched chemical clusters of BaTiO3 and BiTiO3, respectively. Their dynamics is Arrhenius-like, which indicates hopping of the off-centred Ti4+ and Bi3+ ions, respectively, without their complete freezing. BZT can be classified as a dipolar glass and NBT as a nanoscopic ferroelectric with peculiar Bi-ion dynamics.
... Let us now discuss in more detail the relation of our results to the published experimental data on Ba(Zr x Ti 1−x )O 3 system. While no high-frequency measurements of the samples of exactly the same composition (x = 0.5) we theoretically investigate have been reported, the comparison with the available data of similar compositions (x = 0.4 and x = 0.6) is meaningful, as it is known that the characteristic relaxation frequencies and their temperature behaviour are similar for all the compositions with 0.2 ≤ x ≤ 0.8 (see Figure 2 of Ref. [7] which shows the experimental results obtained for BZT ceramics). Significant differences only concern the magnitude and temperature variation of the static susceptibility [5,6]. ...
... Similar to the MD results, two relaxation-related excitations were revealed in the THz and sub-THz ranges experimentally. The first one is an excitation with the characteristic frequency of ∼ 3 THz (∼ 100 cm −1 ) which is practically temperature-independent (upper curve in Figure 2 of Ref. [7]). It was successfully simulated with the coupled oscillator-relaxator (COR) at T > 70 K and the overdamped harmonic oscillator at lower temperatures (their frequencies ν CR and ν CO are shown in Supplementary Figure 1(d) ). ...
... The characteristic frequency of this relaxation has not been determined accurately because of insufficiency of available experimental data points, but it has been found to remain within the range of 10 -100 GHz at all studied temperatures (see Figure 2 of Ref. [7]). This experimental result is in agreement with our prediction that reveals the Arrhenius law at T > 70 K and the saturation of ν m at lower temperatures (see Figure 3 (c) in the main text). ...
Supplementary Figures 1-3, Supplementary Notes 1-3 and Supplementary References
... There have been several experimental investigations of BZT ceramics so far [7][8][9][10][11][12][13][14][15][16][17]. Maiti et al. studied the structure of BZT for a number of compositions with different Zr content x, and found that BZT is a relaxor for 0.25 x 0.75 [8,11]. ...
... Maiti et al. studied the structure of BZT for a number of compositions with different Zr content x, and found that BZT is a relaxor for 0.25 x 0.75 [8,11]. Petzelt et al. [12,13] carried out an extensive broadband spectroscopy study of BZT and found that for a set of concentrations in the above range the relaxation time follows the Arrhenius rather than the Vogel-Fulcher law, and concluded that BZT should be classified as a dipolar glass rather than a relaxor. Similarly, Kleemann et al. [15] studied the nonlinear permittivity of BZT for 0.25 x 0.35 and described the crossover from ferroelectric to relaxor and cluster glass behavior. ...
... Since BZT50 has many features which are characteristic for relaxors, we can tentatively describe the system in terms of the spherical random bond-random field (SRBRF) model of relaxors [34]. This could be justified microscopically by assuming that the elementary dipolar units are not just isolated off-center Ti 4+ ions, but some clustering of the elementary dipoles may occur [12,13]. Hence, unlike the case of typical dipolar glasses, the dipolar degrees of freedom cannot be described by fixed-length pseudospins, but rather as vectors of variable length as in the SRBRF model. ...
Glassy freezing dynamics was investigated in BaZr0.5Ti0.5O3 (BZT50) ceramic samples by means of dielectric spectroscopy in the frequency range 0.001 Hz–1 MHz at temperatures 10<T<300 K. From measurements of the quasistatic dielectric polarization in bias electric fields up to ∼28 kV/cm it has been found that a ferroelectric state cannot be induced, in contrast to the case of typical relaxors. This suggests that—at least for the above field amplitudes—BZT50 effectively behaves as a dipolar glass, which can be characterized by a negative value of the static third order nonlinear permittivity. The relaxation spectrum has been analyzed by means of the frequency-temperature plot, which shows that the longest relaxation time obeys the Vogel-Fulcher relation τ=τ0exp[E0/(T−T0)] with the freezing temperature of 48.1 K, whereas the corresponding value for the shortest relaxation time is ∼0 K, implying an Arrhenius type behavior. By applying a standard expression for the static linear permittivity of dipolar glasses and/or relaxors the value of the Edwards-Anderson order parameter q(T) has been evaluated. It is further shown that q(T) can be described by the spherical random bond-random field model of relaxors.
... 27,[29][30][31][32] Thus, depolarization is closely related to the crystal structure. Furthermore, BNT-based ceramics are known as relaxors-ferroelectrics. 13,33,34) Specifically, in the case of relaxors, the ferroelectric phase returns to the relaxors with an increase in temperature. This phase transition temperature from the ferroelectric phase to the relaxor corresponds to T d . ...
... The frequency dispersion in the dielectric constant can be measured by increasing the frequency range, this is because BNT based ceramics are known as relaxor ferroelectrics. 13,33,34) Moreover, we observed that in the unpoled BNT, quenching generates tan δ peaks in the temperature dependence at each frequency, as shown in Figs. 10(b) and 10(d). ...
... The presence of charge, chemical, and structural heterogeneities in relaxor ferroelectrics enhances the polar and elastic susceptibilities of the system [37]. Although no serious attention has so far been given on the possibility of relaxor ferroelectricity in the BCTZ, this possibility cannot be ruled out in view of the fact that a normal to relaxor-ferroelectric crossover happens in Zr-modified BaTiO 3 and that this relaxor-ferroelectric system has been extensively studied as a model to understand the mechanisms associated with relaxor ferroelectricity [38][39][40][41][42][43][44][45][46]. Motivated by the possible correlation between the relaxor ferroelectricity and the very large piezoelectric response in soft PZT, Pb(Mg 1/3 Nb 2/3 )O 3 − PbTiO 3 (PMN-PT), and Pb(Zn 1/3 Nb 2/3 )O 3 − PbTiO 3 (PZN-PT) alloys, we probed for such a correlation in the BCTZ system. ...
... Xu et al. have shown that the polar nanoregions survive even in the nonergodic ferroelectric state of relaxor ferroelectrics [70]. Petzelt and co-workers [44,45] and Nuzhnyy et al. [71] have reported that the Ti 4+ dynamics does not freeze completely in the nonergodic state of Ba(Ti 1−x Zr x )O 3 . Detailed firstprinciples-based computational studies have shown that the relaxor state in BZT is caused by the difference in the ferroelectric strengths of the Ti 4+ and Zr 4+ ions [46,72,73]. ...
There is great interest in lead-free (Ba0.85Ca0.15)(Ti0.90Zr0.10)O3 (15/10BCTZ) because of its exceptionally large piezoelectric response [Liu and Ren, Phys. Rev. Lett. 103, 257602 (2009)]. In this paper, we have analyzed the nature of: (i) crystallographic phase coexistence at room temperature, (ii) temperature- and field-induced phase transformation to throw light on the atomistic mechanisms associated with the large piezoelectric response of this system. A detailed temperature-dependent dielectric and lattice thermal expansion study proved that the system exhibits a weak dielectric relaxation, characteristic of a relaxor ferroelectric material on the verge of exhibiting a normal ferroelectric-paraelectric transformation. Careful structural analysis revealed that a ferroelectric state at room temperature is composed of three phase coexistences, tetragonal (P4mm)+orthorhombic(Amm2)+rhombohedral(R3m). We also demonstrate that the giant piezoresponse is associated with a significant fraction of the tetragonal phase transforming to rhombohedral. It is argued that the polar nanoregions associated with relaxor ferroelectricity amplify the piezoresponse by providing an additional degree of intrinsic structural inhomogeneity to the system.
... The lead-free BaZr x Ti 1−x O 3 (BZT) solid solution recently came into focus because of its possible conceptual proximity to magnetic spin glasses; since zirconium is isovalent to titanium, the random fields should be suppressed [11]. Structural investigations of BZT ceramics with various Zr concentrations, x, showed relaxor properties for 0.25 ≤ x ≤ 0.75 [12][13][14][15][16][17][18][19][20][21][22][23]. In a recent review paper, Petzelt et al. [23] presented an infrared-range broadband dielectric study of a whole concentration range of the (1 − x)BaTiO 3−x BaZrO 3 (BZT-x) solid solution. ...
Glassy dielectric properties were investigated in lead-free BaZr0.4Ti0.6O3 (BZT40) ceramic samples using dielectric spectroscopy in the frequency range of 0.003 Hz–1 MHz and at temperatures of 10 K < T < 300 K. Measurements of the quasistatic dielectric polarization in bias electric fields up to ~28 kV/cm suggested that a ferroelectric state could not be induced, in contrast to the case of canonical relaxors such as PMN. The quasistatic dielectric and freezing dynamics results for the above field amplitudes showed that BZT40 effectively behaves as a dipolar glass. The relaxation spectrum was analyzed employing a frequency–temperature plot, which showed that the longest relaxation time obeyed the Vogel–Fulcher relation τ=τ0expE0/T−T0, with a freezing temperature of 76.7 K. The shortest relaxation time, in contrast, was characterized by a freezing temperature value close to 0 K, implying an Arrhenius-type behavior. The higher value of the polarization and the nonlinear third-order dielectric coefficient ε3 indicated a shift from a pseudospin glass behavior observed for BaZr0.5Ti0.5O3 (BZT50) toward a classical relaxor ferroelectric state.
... Fanoresonance and the thermally activated THz relaxation mode [68] due to the difference in offcentering of Zr 4+ and Ti 4+ is attributed as the cause of PNRs or relaxor behavior in BZT [69]. The Ti 4+ dynamics are reported to exist even in the non-ergodic relaxor phase of BZT [70,71]. ...
Environmentally benign (1-x)Ba(Ti$_{0.8}$Zr$_{0.2}$)O$_3$-x(Ba$_{0.7}$Ca$_{0.3}$)TiO$_3$ (BZT-BCT) ceramics are promising materials due to their remarkable high piezoresponse [Liu and Ren, Phys. Rev. Lett. \textbf{103}, 257602 (2009)]. In this Letter, by focusing on local and average structure in combination with macroscopic electromechanical and dielectric measurements we demonstrate the structure property relationship in the tetragonal BZT-BCT ceramic. During high-temperature cubic to tetragonal phase transformation, polar nanoregions are manifested through the spontaneous volume ferroelectrostriction at temperatures below $\sim$ 477 K. Temperature-dependent local structural investigations across the Zr K edge extended x-ray absorption fine structure spectroscopy reveal an anomalous collaboration between the ZrO$_{6}$ and TiO$_6$ octahedra. These octahedra compromise their individuality during polarization development. The presence of domains of submicron size embedded inside the macroscopic ferroelectric regions below T$_{m}$, as well as their hierarchical arrangement, is observed by piezo-response force microscopy. Effects of the existence of the structural/polar heterogeneities below T$_{m}$ are observed also when polarizibilities of the poled and the unpoled samples are compared; the poled sample is found to be more susceptible to the electric field. In addition, by using electric field dependent x-ray diffraction studies we also show that this ceramic under field exhibits reduction of tetragonal distortion, which is consistent with earlier reports.
... Fanoresonance and the thermally activated terahertz relaxation mode [68] due to the difference in off centering of Zr 4+ and Ti 4+ are attributed as the cause of PNRs or relaxor behavior in BZT [69]. The Ti 4+ dynamics are reported to exist even in the nonergodic relaxor phase of BZT [70,71]. ...
Environmentally benign (1-x)Ba(Ti 0.8 Zr 0.2)O 3-x(Ba 0.7 Ca 0.3)TiO 3 (BZT-BCT) ceramics are promising materials due to their remarkable high piezoresponse [Liu and Ren, Phys. Rev. Lett. 103, 257602 (2009)]. In this Letter, by focusing on local and average structure in combination with macroscopic electromechanical and dielectric measurements we demonstrate the structure property relationship in the tetragonal BZT-BCT ceramic. During high-temperature cubic to tetragonal phase transformation, polar nanoregions are manifested through the spontaneous volume ferroelectrostriction at temperatures below ∼477 K. Temperature-dependent local structural investigations across the Zr K edge extended x-ray absorption fine-structure spectroscopy reveal an anomalous collaboration between the ZrO 6 and TiO 6 octahedra. These octahedra compromise their individuality during polarization development. The presence of domains of submicron size embedded inside the macroscopic ferroelectric regions below T m , as well as their hierarchical arrangement, is observed by piezoresponse force microscopy. Effects of the existence of the structural/polar heterogeneities below T m are observed also when polarizabilities of the poled and unpoled samples are compared; the poled sample is found to be more susceptible to the electric field. In addition, by using electric field dependent x-ray diffraction studies we also show that this ceramic under field exhibits a reduction of tetragonal distortion, which is consistent with earlier reports.
... In the second scenario, the PNRs grow in size on cooling and percolate the sample, resulting in a spontaneous transition from the short-range relaxor to long-range ferroelectric order (e.g., PbSc 1/2 Ta 1/2 O 3 ). 11,12 (1-x)Na 1/2 Bi 1/2 TiO 3 -xBaTiO 3 (NBT-BT) is a wellknown lead-free relaxor ferroelectric [13][14][15] with the compositions in the range of 6-11 mol.% BaTiO 3 exhibiting non-ergodic relaxor characteristics. ...
Recently, quenching lead-free non-ergodic relaxor Na1/2Bi1/2TiO3-BaTiO3 (NBT-BT) materials has been reported to increase the thermal depolarization temperature and enhance the lattice distortion. Driven by the conjecture that enhanced lattice distortion is typically associated with the onset of ferroelectric order, two non-ergodic relaxor NBT-BT compositions at the morphotropic phase boundary were investigated. As evident from the temperature-dependent permittivity, both compositions exhibit a stabilization of ferroelectric order upon quenching. An increase in the depolarization temperature by 40-60 °C is observed. Moreover, the composition with higher tetragonality undergoes a spontaneous relaxor-ferroelectric transition upon quenching. Annealing in oxygen atmosphere is shown to revert back the quenching-induced ferroelectric order to the relaxor state.
... The tetragonal and rhombohedral phases coexist in a broad temperature range »260-330 C. In addition, two characteristic temperatures exist in this material: T d D 180-200 C at which the ferroelectric phase disappeared and a relaxor-like shallow hump of electric permittivity (e) was observed, and T m 320 C at which e reaches the maximum value (not related to any phase transition) [8]. According to the analysis of the lattice dynamics of NBT ceramics based on their THz and microwave dielectric spectroscopy [9,10], the main dielectric contributions to the high-permittivity maximum T m are caused by THz and relaxation modes assigned to the strongly anharmonic Bi ion vibration and hopping, and NBT represents a hybrid between standard and relaxor ferroelectric behavior. ...
Lead-free (Na0.5Bi0.5)1-xSrxTiO3 ceramics (x = 0–0.04) were synthesized by a conventional mixed-oxide technique. The microstructure study showed a dense structure, in good agreement with that of above 96% relative density determined by Archimedes method. X-ray diffraction measurements showed that the obtained specimens possess a pure perovskite structure with rhombohedral symmetry. The dielectric and ferroelectric behavior of these ceramics were examined. The temperature dependence of the dielectric spectra revealed a frequency dependence near the depolarization temperature Td, which is characteristic of a relaxor mechanism. This suggests that the ceramics lacked long-range ferroelectric order about temperature Td, which was evidenced by observation of deformed and pinched hysteresis loops, and significant decrease of remnant polarization Pr and coercive field Ec near this temperature.
... [51][52][53][54][55][56] However, various studies have come to the conclusion that the fundamental mechanisms leading to the relaxor behavior of lead-free materials such as NBT-BT differ from those found in classical lead-based relaxors. 22,57,58 As a first step towards elucidating the structural origins of the high permittivity of NBT-BT, electric field-dependent features could be identified by means of in situ diffuse scattering experiments. 59,60 The results indicate that the origin of the high permittivity can be found in the atomic structure or on the nanometer scale. ...
The local dynamics of the lead-free relaxor $0.964\mathrm{Na}_{1/2}\mathrm{Bi}_{1/2}\mathrm{TiO}_3-0.036\mathrm{BaTiO}_3$ (NBT-3.6BT) have been investigated by a combination of quasielastic neutron scattering (QENS) and ab initio molecular dynamics simulations. In a previous paper, we were able to show that the tetragonal platelets in the microstructure are crucial for understanding the dielectric properties of NBT-3.6BT [F. Pforr et al., Phys. Rev. B 94, 014105 (2016)]. To investigate their dynamics, ab initio molecular dynamics simulations were carried out using $\mathrm{Na}_{1/2}\mathrm{Bi}_{1/2}\mathrm{TiO}_3$ with 001 cation order as a simple model system for the tetragonal platelets in NBT-3.6BT. Similarly, 111-ordered $\mathrm{Na}_{1/2}\mathrm{Bi}_{1/2}\mathrm{TiO}_3$ was used as a model for the rhombohedral matrix. The measured single crystal QENS spectra could be reproduced by a linear combination of calculated spectra. We find that the relaxational dynamics of NBT-3.6BT are concentrated in the tetragonal platelets. Chaotic stages, during which the local tilt order changes incessantly on the timescale of several picoseconds, cause the most significant contribution to the quasielastic intensity. They can be regarded as an excited state of tetragonal platelets, whose relaxation back into a quasistable state might explain the frequency dependence of the dielectric properties of NBT-3.6BT in the 100 GHz to THz range. This substantiates the assumption that the relaxor properties of NBT-3.6BT originate from the tetragonal platelets.
... This difference in the off centering of Zr and Ti ions gives rise to Fano resonance and thermally activated THz relaxation [29]. Petzelt [30][31][32]. The persistence of the dielectric dispersion below the dielectric maximum down to 30°C, i.e., until the P 4mm-Amm2 transformation, however, suggests that the tetragonal ferroelectric regions are still small in size. ...
The exceptionally large piezoelectric response of the morphotropic-phase-boundary (MPB) composition of the lead-free piezoelectric system (1−x)Ba(Ti0.8Zr0.2)O3−x(Ba0.7Ca0.3)TiO3 has attracted great attention in recent years. Here in this paper we report a detailed investigation of the structural phase transformation behavior of the MPB composition (x=0.50) driven by electric field, stress, and temperature. We show that the system exhibits metastable phases in a wide temperature range, and that the large piezoresponse at room temperature has a significant contribution from the increased fraction of the metastable phases induced by the poling field. Using a “powder poling” technique we also demonstrate the equivalence of stress and electric field with regard to the nature of the structural transformation. The fundamental significance of this interesting observation is discussed.
... Nevertheless, some changes and peculiaritis of the low-frequency phonon dynamics were observed near T m . [12,13] Below T m , coupling between the overdamped sub-THz phonon and relaxation modes, assigned to the strongly anharmonic Bi ion vibration and hopping respectively, reduces on cooling and additional relaxation mode, assigned to quasi-Debye losses, appears in the 10 11 Hz range. Accounting for coexistance of the tetragonal and rhombohedral phases in a broad temperature interval around T m , »260À400 C for NBT [14] and increase of the rhombohedral phase fraction on cooling, the observed changes of phonon dynamics were related to the predominance of rhombohedral phase below T m . ...
Thermal expansion, Raman and dielectric properties of the lead-free (1−x)Na0.5Bi0.5TiO3-xSrTiO3 (x = 0, 0.08 and 0.1) ceramic solid solutions, fabricated by the conventional solid-state reaction method, were investigated. The Sr-doping results in an increase of the dielectric permittivity, broadening of the permittivity maximum, enhancement of the relaxation near depolarization temperature, broadening of the Raman bands and shift of all anomalies toward lower temperatures. The observed effects are attributed to an increase of the degree of cationic disorder and enhancement of the relaxor-like features. Anomalies in the thermal expansion strain were observed at the temperatures corresponding to the dielectric anomalies but not related to any phase transitions. These anomalies are supposed to follow changes of the averaged unit cell volume in the temperature interval of tetragonal and rhombohedral phase coexistence.
... depolarization temperature, T d % 190 C, which shows weak relaxation behavior and appears as a shallow hump in e(T), [5] followed by a broad peak in the loss tangent tan d(T). [6] According to the analysis of the lattice dynamics of NBT ceramics based on their THz and microwave dielectric spectroscopy, [7,8] the main dielectric contributions to the high-permittivity maximum at T m are caused by THz and relaxation modes assigned to the strongly anharmonic Bi ion vibration and hopping, and NBT represents a hybrid between standard and relaxor ferroelectric behavior. SrTiO 3 (ST) is a well-studied incipient ferroelectric with perovskite structure and antiferrodistortive structural phase transition from cubic to tetragonal symmetry at about 168 C. [9,10] It is characterized by increasing permittivity on cooling due to the softening of the lowest frequency polar optical phonon. ...
Lead-free (Na0.5Bi0.5)1−xSrxTiO3 (x = 0, 0.04 and 0.06) ceramics with relative densities above 97% were prepared by solid-state synthesis process. Their dielectric, thermal and Raman properties were studied. X-ray diffraction analysis shows perovskite structure with rhombohedral symmetry at room temperature. Sr doping of Na0.5Bi0.5TiO3 (NBT) results in an increase of the dielectric permittivity, diffusing of the permittivity maximum and its shift toward lower temperatures. The temperature of the rhombohedral–tetragonal phase transition indicated by the differential scanning calorimetry (DSC) peak and relaxational dielectric anomaly near the depolarization temperature are also shifted toward lower temperatures. The observed increase and broadening of the permittivity maximum, enhancement of the dielectric relaxation near the depolarization temperature, broadening of the DSC anomaly related to the rhombohedral–tetragonal phase transition and broadening of the Raman bands with increasing Sr content are attributed to the increase of the degree of cationic disorder and evident enhancement of the relaxor-like features in NBT–xST. This enhancement could play a positive role in the improvement of the piezoelectric performance of NBT-based ceramics.
... The diffuse scattering intensity does not exhibit anomalous rise on approaching T m from the paraelectric side in NBT whereas it exhibits abrupt rise on approaching T m in PMN [6]. Petzelt et al. [7] have recently compared the behavior of PMN and NBT from the lattice dynamical perspective. An obvious difference between PMN and NBT, which adds to the complications with regard to the understanding of the relaxor behavior of NBT vis-à-vis the PMN, is related to the fact that rhombohedral ground state in PMN emerges directly from the most symmetric cubic paraelectric phase, whereas the structure of the immediate paraelectric state of NBT is tetragonal P 4/mbm comprising in-phase tilted octahedra [8]. ...
The highly complex structure-property interrelationship in the lead-free piezoelectric (x)Na1/2Bi1/2TiO3 - (1 −
x) BaTiO3 is a subject of considerable contemporary debate. Using comprehensive x-ray, neutron diffraction,
dielectric, and ferroelectric studies, we have shown the existence of a new criticality in this system at x = 0.80,
i.e., well within the conventional tetragonal phase field. This criticality manifests as a nonmonotonic variation of the tetragonality and coercivity and is shown to be associated with a crossover from a nonmodulated tetragonal phase (forx < 0.8) to a long-period modulated tetragonal phase (forx > 0.80). It is shown that the stabilization of long-period modulation introduces a characteristic depolarization temperature in the system. While differing qualitatively from the two-phase model often suggested for the critical compositions of this system, our results support the view with regard to the tendency in perovskites to stabilize long-period modulated structures as a result of complex interplay of antiferrodistortive modes [Bellaiche and Iniguez, Phys. Rev. B 88, 014104 (2013);Prosandeev, Wang, Ren, Iniguez, ands Bellaiche, Adv. Funct. Mater. 23, 234 (2013)].
... The tetragonal and rhombohedral phases coexist in a broad temperature range »260-330 C. In addition, two characteristic temperatures exist in this material: T d D 180-200 C at which the ferroelectric phase disappeared and a relaxor-like shallow hump of electric permittivity (e) was observed, and T m 320 C at which e reaches the maximum value (not related to any phase transition) [8]. According to the analysis of the lattice dynamics of NBT ceramics based on their THz and microwave dielectric spectroscopy [9,10], the main dielectric contributions to the high-permittivity maximum T m are caused by THz and relaxation modes assigned to the strongly anharmonic Bi ion vibration and hopping, and NBT represents a hybrid between standard and relaxor ferroelectric behavior. ...
A (Na0.5Bi0.5)0.70Ba0.30TiO3 ceramic has been studied by X-ray diffraction and by measurements of dielectric and ferroelectric properties between room temperature and 450 °C. A sharp increase in the electric permittivity and dielectric loss near 200 °C has been observed. This sharp increase in dielectric responses indicates a transformation between normal and relaxor ferroelectric states. It is found that polar regions can exist at higher temperatures. The X-ray diffraction study shows that the transformation corresponds to the first order phase transition from tetragonal to cubic. The use of the (Na0.5Bi0.5)0.70Ba0.30TiO3 ceramic for device application has also been indicated.
The article reviews and complements the properties of broadband dielectric spectra up to THz-IR range of the (1−x)BaTiO3-xBaZrO3 (BZT-x) solid solution. This includes the proper ferroelectric (x = 0), diffuse ferroelectrics (0 < x ≤ 0.2), relaxor ferroelectrics (0.4 ≤ x ≤ 0.8), dipolar glasses (x > 0.8) and the normal dielectric (x = 1). The spectra are characterized by an overdamped central mode in the microwave range which weakens on cooling. Except for BaTiO3, the soft and central modes do not soften appreciably and do not contribute substantially to the low-frequency permittivity maximum. The most important dielectric contribution is brought by Cole-Cole relaxation assigned to hopping of Ti ions in the BaTiO3 clusters, which obeys the Arrhenius law with a common activation energy for the whole relaxor range of Ea ≈ 181+/-17 meV and broadens on cooling as described by a temperature-independent distribution of activation energies. It follows that the polar nanoregions within the BaTiO3 clusters remain very small with temperature independent size and frozen boundaries, even if the Ti ions inside them are hopping. This differs from the usual lead-containing relaxors, in which the polar nanoregions grow on cooling and follow the glass-like freezing.
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This article summarizes the results of the investigations of the dynamics of ferroelectric (FE) phase transitions (PTs) obtained in Prague during the last 25 years. After a short introduction, explaining differences between displacive and order-disorder types of FE PTs, the results of the broadband dielectric, THz, and mainly IR spectroscopic investigations of hydrogen-bonded FEs, BaTiO3, relaxor FEs, strained incipient FEs, and various multiferroics are reviewed. The high sensitivity of the IR spectroscopy to polar phonons was demonstrated in ultrathin films, which allowed us to reveal strain-induced FE PTs. Electrically active magnons (i.e., electromagnons) can be observed in the IR and Raman spectra of multiferroics. Their frequencies soften on heating toward temperatures of magnetic PTs similarly as phonons in displacive FEs. As expected, the electromagnons can be dependent on the external magnetic field. This behavior has been demonstrated in BiFeO3, SrMn7O12, and multiferroics with Y- and Z-type hexaferrite crystal structures.
An extensive broadband dielectric spectroscopy study of BaCe0.3Ti0.7O3 ceramics is presented. The distribution of relaxation times of the system derived from the frequency dependence of complex dielectric permittivity are similar to the ones observed in dipolar glasses. Therefore, it is demonstrated that the dipolar glass model, which is applied here for the first time for disordered perovskite oxides is able to properly describe the dielectric behavior of BaCe0.3Ti0.7O3 solid solution. The observed dipolar glass behavior in such BaTiO3-based solid solution is clearly different than one of canonical Pb-based relaxors and the two types of dielectric behavior are comparatively discussed.
Acoustic anomalies of relaxor ferroelectric Na1/2Bi1/2TiO3 single crystals were investigated over a wide temperature range from −196oC to 900oC by using Brillouin spectroscopy. The longitudinal sound velocity, the acoustic absorption coefficient and the elastic constant C11 were determined for the acoustic phonon mode propagating in the [100] direction. Two acoustic anomalies, weaker ones at the cubic-tetragonal phase transition temperature of ∼540oC and more pronounced ones at temperatures near 315oC near the dielectric maximum temperature, were investigated and discussed in relation with the relevant order parameters coupled to the acoustic waves. The relaxation dynamics in the cubic phase were studied based on the flattening of the mode frequency and the half width, which was observed for the first time, and a modified Arrhenius law.
Na0.5Bi0.5TiO3 ceramics were synthesized by the conventional solid-state reaction method. The influence of polarizing electric field strength, polarization time, and temperature on the depolarization currents of these ceramics was studied. The measurements were made in both the rhombohedral (ferroelectric) and rhombohedral/tetragonal (nonpolar or weakly polar) phases coexistence. The results indicate that depolarization currents follow the Id∼t-s formula. The value of the s parameter depends on the electric field strength, the polarization time, and the temperature. The calculated activation energy is close to that obtained from electric conductivity measurements.
Ceramic (1–x)Ba(Ti1–yZry)O3 · xPbTiO3 (0 ≤ x, у ≤ 1) samples have been characterized by X-ray diffraction and dielectric measurements. The results have been used to map out the phase diagram of the system, which demonstrates the variation in the phase composition of the samples. It has been shown that, in the composition regions adjacent to the BaTiO3–PbTiO3 side and BaZrO3 corner of the composition triangle, the samples consist of perovskite solid solutions that have tetragonal and cubic structures, respectively, at room temperature. In the intermediate composition region, the samples consist of different perovskite solid solutions similar in composition and structure. We have obtained composition dependences of the unit-cell symmetry and parameters for the solid solutions, their ferroelectric Curie temperature TC, characteristic dielectric relaxation temperatures, dielectric permittivity ε, and dielectric loss tangent tanδ (at temperatures from 100 to 800 K and frequencies from 25 to 106 Hz) and analyzed the evolution of their dielectric properties with increasing BaZrO3 content: from ferroelectric to properties of ferroelectric relaxors, reentrant relaxors, and dielectric relaxors of the dipole glass type.
(1-y)Na0.5Bi0.5TiO3-(y)BaTiO3 (NBT-BT) is one of the most investigated lead-free piezoelectric system in the recent past. Unlike the conventional piezoelectric alloys wherein the morphotropic phase boundary (MPB) compositions exhibiting maximum piezoelectric response, exhibit coexistence of ferroelectric phases with different symmetries on the global scale, the MPB composition (y = 0.06) of NBT-BT shows a cubic-like phase in the unpoled state. On poling it transforms to a non-cubic ferroelectric phase. Here we exploit the sensitivity of the photoluminescence (PL) property of doped rare-earth ions with regard to the local symmetry of the host crystal to investigate the local structure of the cubic-like phase of the MPB composition of NBT-BT. We performed a comparative study of the PL response by doping separately Er and Eu in very dilute concentration in the (i) MPB composition (y = 0.06) exhibiting a cubic-like phase, (ii) a sub-MPB composition (y = 0.03) exhibiting rhombohedral phase, and (iii) above the MPB composition (y = 0.10) exhibiting tetragonal phase. We found that both the Er and the Eu PL spectra of the MPB composition (y = 0.06) exhibits more number of Stark lines in its unpoled cubic-like phase as compared to that in the field-stabilized rhombohedral phase. The additional Stark lines in the cubic-like global phase are identified to be that of the tetragonal structure. Our study therefore confirms that what appears as a cubic-like phase on the global scale has intimately connected tetragonal and rhombohedral local structures. The success of our experiments suggests that rare-earth PL can be used as a simple yet powerful tool to investigate local structures in scenarios wherein the global structure need not comply with the local structure.
The local dynamics of the lead-free relaxor 0.964Na1/2Bi1/2TiO3−0.036BaTiO3 (NBT-3.6BT) have been investigated by a combination of quasielastic neutron-scattering (QENS) and ab initio molecular dynamics simulations. In a previous paper, we were able to show that the tetragonal platelets in the microstructure are crucial for understanding the dielectric properties of NBT-3.6BT [Pforr et al., Phys. Rev. B 94, 014105 (2016)]. To investigate their dynamics, ab initio molecular dynamics simulations were carried out using Na1/2Bi1/2TiO3 with 001 cation order as a simple model system for the tetragonal platelets in NBT-3.6BT. Similarly, 111-ordered Na1/2Bi1/2TiO3 was used as a model for the rhombohedral matrix. The measured single-crystal QENS spectra could be reproduced by a linear combination of calculated spectra. We find that the relaxational dynamics of NBT-3.6BT are concentrated in the tetragonal platelets. Chaotic stages, during which the local tilt order changes incessantly on the time scale of several picoseconds, cause the most significant contribution to the quasielastic intensity. They can be regarded as an excited state of tetragonal platelets, whose relaxation back into a quasistable state might explain the frequency dependence of the dielectric properties of NBT-3.6BT in the 100 GHz to THz range. This substantiates the assumption that the relaxor properties of NBT-3.6BT originate from the tetragonal platelets.
In this work, we attribute the ferroelectric-relaxor crossover in BaTiO3-based solid solution to the percolation of the BO6 octahedra occupied by solute atoms. BaTiO3-based solid solutions which are favorable for electrocaloric applications possess then a composition in the vicinity of the ferroelectric-relaxor crossover. For the first time, we consider a beneficial range of operational temperatures of EC devices based on these materials.
We have prepared ceramic samples of (1–x)Ba(Ti1–yZry)O3 ∙ xPbTiO3, (у = 0–0.10, x = 0–0.67) ferroelectric perovskite solid solutions and characterized them by X-ray diffraction and dielectric and pyroelectric measurements. The composition dependences of the unit-cell parameters for the solid solutions have been obtained; their Curie temperature TC, relative dielectric permittivity ε, and loss tangent tan δ have been measured at temperatures from 100 to 700 K and frequencies from 25 Hz to 1 MHz; and characteristics of their dielectric hysteresis loops and pyroelectric effect have been assessed. With increasing PbTiO3 content, the TC of the samples increases from 400 (x = 0) to 670 K (x = 0.67), the temperatures of their low-temperature phase transitions decrease (to the point that they disappear for x > 0.15), and ε(T = 296 K) decreases at x > 0.1.
A conventional solid-phase sintering process was used to fabricate the (1 − x)Na0.5Bi0.5TiO3-xBaTiO3 ceramics (x = 0, 0.04, 0.06, 0.08 and 0.1). X-ray measurements showed that all samples have a perovskite structure. The bulk density of the obtained samples exceeds 95% of the theoretical density. The thermal (DSC, dilatometry) and dielectric properties of these ceramics were investigated in a wide temperature range. Anomalies of the thermal expansion strain were observed at the temperatures which are not related to any phase transitions. The transition temperatures observed by means of thermal measurements are in good agreement with those obtained from dielectric studies.
Relaxor ferroelectrics are promsing in EC cooling devices due to a new upper bound of the electrocaloric (EC) effect combined with a corresponding novel figure of merit of EC materials performance. In general, the performance of EC coolers is limited either by the thermal time constants of heat switches or by the heat transfer coefficient to the gaseous or liquid heat transfer agent of active EC regenerators. Cooling power densities of a few W/cm 2 are achievable at cycle times of 100 ms.
Relaxor ferroelectrics were discovered almost 50 years ago among the complex oxides with perovskite structure. In recent years this field of research has experienced a revival of interest. In this paper we review the progress achieved. We consider the crystal structure including quenched compositional disorder and polar nanoregions (PNR), the phase transitions including compositional order-disorder transition, transition to nonergodic (probably spherical cluster glass) state and to ferroelectric phase. We discuss the lattice dynamics and the peculiar (especially dielectric) relaxation in relaxors. Modern theoretical models for the mechanisms of PNR formation and freezing into nonergodic glassy state are also presented. (c) 2006 Springer Science + Business Media, Inc.
The concept of polar nanoregions (PNRs) in relaxor ferroelectrics has recently been discussed in several numerical and theoretical studies for the special case of barium zirconate-titanate Ba(Zr${}_{x}$Ti${}_{1$-${}x})$O${}_{3}$ (BZT). Here we present a semiphenomenological model of relaxation in BZT and related systems in order to show that the correlation radius of a PNR is determined by the condition that the surrounding medium undergoes a local phase transformation into a correlated polar state. The model describes the growth and percolation of the PNRs on lowering the temperature or under the application of an electric field, leading to a generalized Vogel-Fulcher-type dielectric relaxation time. It is suggested that the above condition might be applied to discriminate between the relaxor state and the analogous dipolar glass state.
Fano resonance is a phenomenon in which a discrete state interferes with a continuum of states and has been observed in many areas of science. Here, we report on the prediction of a Fano resonance in ferroelectric relaxors, whose properties are poorly understood: an ab initio molecular dynamic scheme reveals such resonance between the bare optical phonon mode of the Zr sublattice (the discrete state) and the bare optical phonon mode of the Ti sublattice (the continuum of states) in disordered lead-free Ba(Zr,Ti)O3. The microscopic origins of the discrete state and continuum of states are discussed in the context of relaxor properties. Furthermore, our simulations suggest that the T* characteristic temperature of relaxor is related to a hardening of the vibrational frequencies associated with fluctuation of the Ti sublattice. Finally, a terahertz relaxation mode reflecting reorientations of Ti dipoles and showing a thermally activated behaviour is predicted, in agreement with previous experiments.
Dynamics of the main dielectric anomaly in Na1/2Bi1/2TiO3 (NBT) was studied
by time-domain THz and microwave spectroscopy, using also previously published
data and their new overall fits. Above the dielectric maximum temperature Tm ~
600 K, the response consists of coupled sub-THz oscillator and a relaxation
mode, assigned to strongly anharmonic Bi-ion vibrations and hopping, whose
slowing down explains the paraelectric-like permittivity increase to Tm. Below
Tm, the main relaxation continues slowing down and additional relaxation,
assigned to quasi-Debye losses, appears in the 10^11 Hz range. The oscillator
hardens on cooling and takes over the whole oscillator strength. The
permittivity decrease below Tm is caused by the reduced strength of the
relaxations due to dominance of the rhombohedral phase within the coexistence
region with the tetragonal phase. The anharmonic dynamics of Bi is supported by
previous structural studies. NBT represents a hybrid between standard and
relaxor ferroelectric behaviour.
With strong dependences of dielectric constant on external applied electric fields, relaxor barium zirconium titanate (BaZrxTi1-xO3 or BZT) and barium stannate titanate (BaSnxTi1-xO3 or BTS), in both bulk ceramic and thin film forms, are increasingly being recognized as potential candidates of microwave tunable materials for device applications. This paper is aimed to review the recent progress in understanding the dielectric properties (such as tunability, dielectric loss and dielectric constant) of these relaxor materials. However, due to their relatively high dielectric constant and loss tangent, pure Ba(Zr,Ti)O3 and Ba(Sn,Ti)O3 do not fully satisfy the requirements of practical device applications. Therefore, various strategies have been developed to improve the dielectric properties of these two groups of relaxor materials. In this paper, we first discussed the dielectric tunability characteristics of pure Ba(Zr,Ti)O3 and Ba(Sn,Ti)O3 and then summarized the strategies that have been used, including (i) small amount acceptor or donor doping (such as rare-earth ions and transition metal ions) and (ii) forming composites with low loss and low dielectric constant microwave dielectric materials (such as MgO, MgTiO3 and so on). At the same time, the relationship between relaxor behavior and dielectric tunability was also discussed.
This paper reviews the recent progress in the understanding of the dynamics of Pb(B1/2B′1/2)O3-type relaxor ferroelectrics using of broadband micro-Brillouin scattering spectroscopy, which covers a large frequency range from 1 to 1000 GHz by a tandem multi-pass Fabry–Perot interferometer. In contrast to Pb(B1/3B′2/3)O3-type relaxors, there is no frustration on the B-site of perovskite structure and the degree of order of B-site cations depends on heat treatment. Remarkable softening of sound velocity and an intense central peak are observed above the Curie temperature TC owing to the polarization fluctuations in polar nanoregions (PNRs). Unlike the Pb(B1/3B′2/3)O3 relaxors, Pb(B1/2B′1/2)O3 does not undergoes a typical diffuse phase transition without lead vacancies on A-site which enhances random fields. For the (1-x)Pb(B1/2B′1/2)O3–xPbTiO3 solid solutions, the long range polar order increases as the PbTiO3 content increases. Nevertheless, a central peak owing to dynamic PNRs still remains even for the composition near the MPB, and a critical slowing down is clearly observed in the vicinity of TC.
Broadband dielectric spectroscopy from Hz up to the infrared (IR) range and
temperature interval 10-300 K was carried out for xBaZrO3-(1-x)BaTiO3 (BZT-x, x
= 0.6, 0.7, 0.8) solid solution ceramics and compared with similar studies for
x = 0, 0.2, 0.4, 1 ceramics published recently (Phys. Rev. B 86, 014106
(2012)). Rather complex IR spectra without appreciable mode softening are
ascribed to Last-Slater transverse optic (TO) phonon eigenvector mixing and
possible two-mode mixed crystal behavior. Fitting of the complete spectral
range requires a relaxation in the 100 GHz range for all the samples. Below 1
GHz another relaxation appears, which is thermally activated and obeys the same
Arrhenius behavior for all the relaxor BZT samples. The frequently reported
Vogel-Fulcher behavior in BZT relaxors is shown to be an artifact of the
evaluation from the permittivity or loss vs. temperature dependences instead of
its evaluation from loss vs. frequency maxima. The relaxation is assigned to
local hopping of the off-centered Ti4+ ions in the frozen BTO clusters, whose
size is rather small and cannot grow on cooling. Therefore BZT is to be
considered as a dipolar glass rather than relaxor ferroelectric.
We use a combination of first-principles density functional theoretical analysis and experimental characterization to understand the lattice dynamics, dielectric and ferroelectric properties of lead-free relaxor ferroelectric Na0.5Bi0.5TiO3 (NBT) system. Vibrational spectrum determined through our calculations agrees well with the observed Raman spectrum, and allows assignment of symmetry labels to modes. The calculated Born effective charges reveal (a) two distinct types of Ti ions at the B-site with anomalous dynamical charges differing by up 1.6e, and (b) Na and Bi ions at the A-site exhibit disparate dynamical charges of about 1 and 5.5e, respectively. Thus, there exist hetero-polar activity at both A and B-sites in NBT, and disorder associated with these hetero-polar ions is responsible for its relaxor behaviour. Large dielectric response of NBT arises primarily from phonons, and specifically the modes involving Bi-O (109 cm−1) and Ti-O (246, 276 cm−1) vibrations, respectively.
Rietveld neutron powder profile analysis of the compound Na0.5Bi0.5TiO3 (NBT) is reported over the temperature range 5–873 K. The sequence of phase transitions from the high-temperature prototypic cubic structure (above 813 K), to one of tetragonal (673–773 K) and then rhombohedral structures (5–528 K) has been established. Coexisting tetragonal/cubic (773–813 K) and rhombohedral/tetragonal (with an upper temperature limit of 145 K between 528 and 673 K) phases have also been observed. Refinements have revealed that the rhombohedral phase, space group R3c, with aH = 5.4887 (2), cH = 13.5048 (8) Å, V = 352.33 (3) Å3, Z = 6 and Dx = 5.99 Mg m−3, exhibits an antiphase, a−a−a− oxygen tilt system, ω = 8.24 (4)°, with parallel cation displacements at room temperature. The tetragonal phase, space group P4bm, with aT = 5.5179 (2), cT = 3.9073 (2) Å, V = 118.96 (1) Å3, Z = 2 and Dx = 5.91 Mg m−3, possesses an unusual combination of in-phase, a0a0c+ oxygen octahedra tilts, ω = 3.06 (2)°, and antiparallel cation displacements along the polar axis. General trends of cation displacements and the various deviations of the octahedral network from the prototypic cubic perovskite structure have been established and their systematic behaviour with temperature is reported. An investigation of phase transition behaviour using second harmonic generation (SHG) to establish the centrosymmetric or non-centrosymmetric nature of the various phases is also reported.
The dielectric response of PbMg1/3Nb2/3O3-35%PbTiO3 ceramics (close to the morphotropic phase boundary) from 100 Hz up to 100 THz was determined in a broad temperature range of 5-900 K. Two ceramics were studied and compared: coarse grain ceramics (CGC) (grain size ˜4mum ) and fine grain ceramics (FGC) (grain size ˜150nm ). Both ceramics showed similar polar-phonon response and the ferroelectric transition near TC=440K that was manifested by partial softening of the overdamped lowest-frequency phonon using the time-domain THz spectroscopy. However, the dielectric response was dominated by a complex relaxational dispersion in the microwave range due to relaxorlike dynamics of the polar nanoclusters, which strongly differed in both the ceramics. Whereas the CGC undergoes a well-defined ferroelectric transition such as a single crystal, FGC exhibits a relaxor behavior with substantially smaller permittivity showing partial clamping of the polar nanocluster dynamics by grain boundaries. The pronounced difference was also revealed in a second-harmonic generation showing much larger paraelectric signal in the FGC with a much smeared ferroelectric transition only. Due to contributions of both the soft phonon mode and dielectric relaxations into the dielectric constant near its maximum even in the paraelectric phase, the ferroelectric transition corresponds to a percolation threshold of the polar nanoclusters into macroscopic domains. Such a type of phase transition can be considered as a special case of crossover between the displacive and order-disorder types, where the ordering process concerns a mesoscopic range.
In this review we describe and discuss recent results on the linear dielectric response of high-permittivity dielectric crystals and ceramics in the wide frequency range 10–10Hz. Our attention is paid to materials which exhibit some interesting low-frequency polar-phonon anomalies in combination with some additional dielectric dispersion below the polar phonon region. The following compounds are discussed: microwave ceramics Bi1.5Zn1.0Nb1.5O7, antiferroelectric PbZrO3ceramics and AgNbO3crystals, ferroelectric LiNaGe4O9, LaBGeO5, Cd2Nb2O7and SrBi2Ta2O9crystals, incommensurate ferroelectric Sr2Nb2O7, Ba2NaNb5O15and BCCD crystals, dipolar-glass crystal of Rb1/2(ND4)1/2D2PO4, relaxor ferroelectric Pb(Sc1/2Ta1/2)O3and PLZT ceramics and PMN crystals, antiferroelectric PLZT 2/95/5 ceramics and relaxor-based PMN-PT, PZN-PT and BiScO3-PT crystals and ceramics. For these materials the polar phonon spectra are discussed together with their flow-frequency dielectric response and dispersion regions in between, in the 10–300 K or higher temperature range, depending on the existing phase transitions of interest. Some universal features of the disorder and anharmonicities are pointed out: central-mode phenomena near displacive phase transitions and polar nano-clusters which appear at rather high temperatures and remain present down to low temperatures if the material remains structurally disordered. The manifestation of the latter in the dielectric spectra consists in extreme broadening of the relaxation region on cooling which at low temperatures results in constant loss spectra (1/fnoise).
Relaxor ferroelectrics were discovered in the 1950s but many of their properties are not understood. In this review, we shall concentrate on materials such as PMN (PbMg1/3Nb2/3O3), which crystallize in the cubic perovskite structure but with the Mg ion, charge 2+, and the Nb ion, charge 5+, randomly distributed over the B site of the perovskite structure. The peak of the dielectric susceptibility for relaxors is much broader in temperature than that of conventional ferroelectrics, while below the maximum of the susceptibility most relaxors remain cubic and show no electric polarization, unlike that observed for conventional ferroelectrics. Because of the large width of the susceptibility, relaxors are often used as capacitors. Recently, there have been many X-ray and neutron scattering studies of relaxors and the results have enabled a more detailed picture to be obtained. An important conclusion is that relaxors can exist in a random field state, as initially proposed by Westphal, Kleemann and Glinchuk, similar to that which has been studied for diluted antiferromagnets. If a relaxor is cooled from a high temperature, then the Burns temperature is a measure of when slow fluctuations become evident. These fluctuations are connected with the disorder and are known as nano-domains. The Burns temperature is not a well-defined transition temperature. At a lower temperature, there is a well-defined boundary to a so-called random field state when the nano-domains become static but there is no long-range periodic order. This phase may have both history-dependent properties and a skin effect in which the surface of the sample is different from that of the bulk material, as also found in experiments on magnetic systems. Section 1 is an introduction to the review, to ferroelectricity and to relaxors. Section 2 gives a description of the results obtained by dielectric, optical, specific heat and other macroscopic properties. These long-wavelength properties give a variety of different characteristic temperatures and do not directly probe the random field state. In Section 3, we describe the results of neutron and X-ray scattering and show that they strongly support the interpretation that relaxors have a random field state. In Section 4, we briefly describe the results for other relaxor systems such as (PMN)1−x(PT)x for which PMN is mixed with different amounts of the ferroelectric lead titanate (PT), and we show that the existence of a random field state enables us also to describe the experimental results for these mixed materials. We hope that this review will inspire further theoretical and experimental work to understand the nature of the random field states and to compare the experimental results more satisfactorily with theory.
In the article we discuss the dielectric response of relaxor-type complex perovskites in the phonon-frequency region on the basis of a rich collection of experimental data accumulated in our laboratory by numerous infrared spectroscopy investigations over the past decade. The effect of the cation occupational disorder and of the nanoscopic inhomogeneous polarisation on the infrared response is considered in the framework of the factor-group symmetry analysis and the effective-medium approach. Polar mode assignment and comparison of the mode parameters of different materials is facilitated by systematic evaluation of mode-plasma frequencies. Whenever possible, the results are presented in form of tables convenient for further analysis or by comparison with results of other techniques, including ab-initio calculations. Infrared properties of other non-perovskite relaxors are briefly mentioned.
In this review the dielectric properties of relaxor ferroelectrics are discussed and compared with the properties of normal dielectrics and ferroelectrics. We try to draw a general picture of dielectric relaxation starting from a textbook review of the underlying concepts and pay attention to common behavior of relaxors rather than to the features observed in specific materials. We hope that this general approach is beneficial to those physicists, chemists, material scientists and device engineers who deal with relaxors. Based on the analysis of dielectric properties, a comprehensive definition of relaxors is proposed: relaxors are defined as ferroelectrics in which the maximum in the temperature dependence of static susceptibility occurs within the temperature range of dielectric relaxation, but does not coincide with the temperature of singularity of relaxation time or soft mode frequency.
Substitutional charge disorder as in PbMg1/3Nb2/3O3, structural cation vacancies as in SrxBa1-xNb2O6 and isovalent substitution of off-centered cations as in BaTi1-xSnxO3 and BaTi1-xZrxO3 give rise to quenched electric random-fields (RFs), which we proposed to be at the origin of the peculiar behavior of relaxor ferroelectrics 20 years ago. These are, e.g. a strong frequency dispersion of the dielectric response and an apparent lack of macroscopic symmetry breaking in the low temperature phase. Both are related to mesoscopic RF-driven phase transitions, which give rise to irregularly shaped quasi-stable polar nanoregions below the characteristic temperature T*, but above the global transition temperature Tc. Their co-existence with the paraelectric parent phase can be modeled by time-dependent field equations under the control of quenched RFs and stress-free strain (in the case of order parameter dimension n ≥ 2). Transitions into global polar order at Tc may occur in uniaxial relaxors as observed on the uniaxial relaxor ferroelectric Sr0.8Ba0.2Nb2O6 and come close to RF Ising model criticality. Re-entrant relaxor transitions as observed in solid solutions of Ba2Pr0.6Nd0.4(FeNb4)O15 are proposed to evidence the coexistence of distinct normal and relaxor ferroelectric phases within the framework of percolation theory.
Local structures in BaTi1-xZrxO3 solid solutions were analyzed using x-ray absorption fine structure (XAFS) measurements and density-functional theory (DFT) calculations. We demonstrate that for low concentrations of Ti, isolated Ti atoms in the relatively large octahedral sites of the BaZrO3 lattice acquire centrosymmetric coordination with average Ti-O distances shorter than those in BaTiO3. In contrast for higher concentrations of Ti, Ti atoms having one or more Ti as their B-site nearest neighbors undergo polar off-center displacements. Our DFT calculations confirm both effects. These results combined with the previously published data suggest that isolated polarizable ions on the B sites of a relatively expanded host perovskite lattice remain nonpolar by symmetric relaxation of the nearest-neighbor oxygen atoms to yield nearly ideal bond lengths around the dopant species. For neighboring Ti atoms, such symmetric relaxation is impossible, and these atoms are displaced off center. Our XAFS measurements did not detect any significant deviations from a random distribution of Ti and Zr in the present samples except for compositions close to BaTiO3. The DFT calculations suggest that the dominant effect of the local displacements on band-gap values for this system is determined by the shortest Ti-O bonds due to strong Ti 3d–O 2p hybridization; however, local displacements have only a secondary effect on the band-gap behavior.
Dielectric response of [Pb(Zn1/3Nb2/3O3]0.92-[PbTiO3]0.08 single crystal was investigated in a broad frequency (100 Hz–600 GHz) range. Near stepwise anomaly at Tc≈ 415 K, characteristic of the ferroelectric phase transition, and a diffuse relaxational maximum of permittivity above 415 K, characteristic of the relaxor ferroelectrics, were observed. Broad dielectric dispersion takes place both above and below Tc, resulting in the decrease in permittivity down to values of ∼ 100 at 600 GHz. The Tc value shows a temperature hysteresis of ∼ 15 K, while no remarkable temperature hysteresis of the diffuse maximum is observed. Both the stepwise dielectric anomaly at Tc and the diffuse maximum above Tc are considered to be caused by contributions of polar nanoclusters, similar to the model relaxor ferroelectrics. The ferroelectric phase transition can be considered as a result of a stepwise increase in the nanocluster size, i.e. nanoclusters transform into domains below Tc.
The phase transition from tetragonal to rhombohedral phase in sodium bismuth titanate (NBT) is studied by means of neutron scattering. It is found that the rhombohedral phase has incommensurate modulation along the four-fold axis of the precursor tetragonal phase. The appearance of the incommensurate modulation is discussed on the symmetry grounds in the framework of the phenomenological theory of phase transitions.
Infrared reflectivity, time-domain terahertz transmission, high-frequency dielectric measurements and Raman spectroscopy of Na0.5Bi0.5TiO3 complex ferroelectric perovskite were performed in a broad temperature range. The results were analysed considering the macroscopic symmetry as well as symmetry resulting from local Na–Bi ordering in all three known phases. An overdamped infrared soft mode was revealed in the THz range which, together with central-mode type dispersion in the GHz range, contribute to the strong and broad dielectric permittivity maximum around 600 K. Anharmonic Bi and/or Na vibrations and local hopping, respectively, are suggested to be the main origins of these excitations. The broad phonon spectra and the frequency independent dielectric losses at low temperatures are compatible with the existence of nanoscopic polar regions and disorder to liquid He temperatures similar to relaxor ferroelectrics.
Relaxor ferroelectrics were discovered almost 50 years ago among the complex oxides with perovskite structure. In recent years
this field of research has experienced a revival of interest. In this paper we review the progress achieved. We consider the
crystal structure including quenched compositional disorder and polar nanoregions (PNR), the phase transitions including compositional
order-disorder transition, transition to nonergodic (probably spherical cluster glass) state and to ferroelectric phase. We
discuss the lattice dynamics and the peculiar (especially dielectric) relaxation in relaxors. Modern theoretical models for
the mechanisms of PNR formation and freezing into nonergodic glassy state are also presented
Far-infrared reflectivity spectra of [ Pb ( Zn <sub>1/3</sub> Nb <sub>2/3</sub>) O <sub>3</sub>]<sub>0.92</sub>–[ PbTiO <sub>3</sub>]<sub>0.08</sub> and [ Pb ( Mg <sub>1/3</sub> Nb <sub>2/3</sub>) O <sub>3</sub>]<sub>0.71</sub>–[ PbTiO <sub>3</sub>]<sub>0.29</sub> single crystals were investigated between 10 and 530 K, micro-Raman spectra were recorded between 300 and 800 K. No phonon softening was observed near either of the ferroelectric phase transitions. The low-frequency dielectric anomaly in the paraelectric phase is caused by contribution of dynamic polar nanoclusters with the main dispersion in the microwave range. Infrared and Raman spectra confirm the locally doubled unit cell (Z<sub> prim </sub>=2) in the paraelectric and ferroelectric phases due to the ordering in the perovskite B sites and occurrence of polar nanoclusters in the paraelectric phase. The lowest-frequency transverse optical ( TO <sub>1</sub>) phonon mode active in the infrared spectra is underdamped in contrast to the recent result of inelastic neutron scattering, where no TO <sub>1</sub> mode could be observed for the wave vectors q≤0.2 Å<sup>-1</sup>. This discrepancy was explained by different q vectors probed in infrared and neutron experiments. The infrared probe couples with very long-wavelength phonons (q≈10<sup>-5</sup> Å<sup>-1</sup>) which see the homogeneous medium averaged over the nanoclusters, whereas the neutron probe couples with phonons whose wavelength is comparable to the nanocluster size (q≥10<sup>-2</sup> Å<sup>-1</sup>). © 2003 American Institute of Physics.
Relaxor ferroelectric PbMg <sub>1/3</sub> Ta <sub>2/3</sub>O<sub>3</sub> ceramics and thin films were investigated by means of broad-band dielectric, time-domain terahertz (THz), and Fourier-transform infrared (IR) spectroscopy in the frequency range 100 Hz–90 THz at temperatures 100–490 K; the THz and IR spectra were studied from 20 to 900 K. A diffused and strongly temperature dependent peak in the complex permittivity is caused by a dielectric relaxation due to the dynamics of polar clusters. The relaxation appears below the Burns temperature T<sub>d</sub> in the THz range; it slows down on cooling through the microwave and MHz range and anomalously broadens. The shortest and longest relaxation times of the distribution of relaxation times follow Arrhenius and Vogel–Fulcher laws, respectively. The degree of the B-site order has only a small influence on the parameters of the dielectric relaxation and almost no influence on the phonon parameters. Below T<sub>m</sub>≅180 K the distribution of relaxation frequencies becomes broader than our experimental spectral range, and frequency independent dielectric losses develop below 100 GHz in the spectra. Although the macroscopic crystal structure is cubic, IR spectra give evidence about the lower local symmetry, which can be assigned to the presence of the polar clusters below T<sub>d</sub> . Infrared spectra above T<sub>d</sub> still reveal more modes than predicted by selection rules in the paraelectric phase of the Fm 3 m space group so that we suggest selection rules which take into account chemical inhomogeneity in the β<sup>″</sup> -perovskite sublattice.
The relaxor ferroelectric PbMg(1/3)Nb(2/3)O(3) (PMN) is investigated by means of dielectric and Fourier transform far infrared transmission spectroscopy in the frequency range from 10 kHz to 15 THz at temperatures between 20 and 900 K using mostly thin films on infrared transparent sapphire substrates. While the thin film relaxors display reduced dielectric permittivity at low frequencies, their high frequency lattice response is shown to be the same as for single-crystal/ceramic specimens. In contrast to the results of inelastic neutron scattering, the optic soft mode is found to be underdamped at all temperatures. On heating, the TO1 soft phonon follows the Cochran law with an extrapolated critical temperature of 670 K near to the Burns temperature. Above 450 K the soft mode frequency levels off near 50 cm(-1) and above the Burns temperature it slightly hardens. Central-mode-type dispersion assigned to the dynamics of polar nanoclusters appears below the Burns temperature at frequencies near to but below the soft mode and slows down and broadens dramatically on cooling, finally, below the freezing temperature of 200 K, giving rise to frequency independent losses from the microwave range down. A new explanation of the phonon 'waterfall' effect in inelastic neutron scattering spectra is proposed.
A large body of work has been reported in the last 5 years on the development of lead-free piezoceramics in the quest to replace lead–zirconate–titanate (PZT) as the main material for electromechanical devices such as actuators, sensors, and transducers. In specific but narrow application ranges the new materials appear adequate, but are not yet suited to replace PZT on a broader basis. In this paper, general guidelines for the development of lead-free piezoelectric ceramics are presented. Suitable chemical elements are selected first on the basis of cost and toxicity as well as ionic polarizability. Different crystal structures with these elements are then considered based on simple concepts, and a variety of phase diagrams are described with attractive morphotropic phase boundaries, yielding good piezoelectric properties. Finally, lessons from density functional theory are reviewed and used to adjust our understanding based on the simpler concepts. Equipped with these guidelines ranging from atom to phase diagram, the current development stage in lead-free piezoceramics is then critically assessed.
The dielectric response to infrared waves polarized along the tetragonal axis of a ferroelectric single-domain crystal of BaTiO3 was determined by time-domain THz spectroscopy and Fourier-transform infrared reflectivity techniques. In addition to the three well-known polar lattice modes, the experiment shows an additional mode of the relaxation type in the THz spectral region, which accounts for the Curie-Weiss behavior of the c-axis dielectric constant. A comparison of experimental results with ab initio based effective-Hamiltonian simulations allows us to elucidate its relation to the order-disorder model of Comes, Lambert, and Guinier [Solid State Commun. 6, 715 (1968)10.1016/0038-1098(68)90571-1].
ABO3 perovskite-type solid solutions display a large variety of structural and physical properties, which can be tuned by chemical composition or external parameters such as temperature, pressure, strain, electric, or magnetic fields. Some solid solutions show remarkably enhanced physical properties including colossal magnetoresistance or giant piezoelectricity. It has been recognized that structural distortions, competing on the local level, are key to understanding and tuning these remarkable properties, yet, it remains a challenge to experimentally observe such local structural details. Here, from neutron pair-distribution analysis, a temperature-dependent 3D atomic-level model of the lead-free piezoelectric perovskite Na0.5Bi0.5TiO3 (NBT) is reported. The statistical analysis of this model shows how local distortions compete, how this competition develops with temperature, and, in particular, how different polar displacements of Bi3+ cations coexist as a bifurcated polarization, highlighting the interest of Bi-based materials in the search for new lead-free piezoelectrics.
Bismuth sodium titanate (BNT)-derived materials have seen a flurry of research interest in recent years because of the existence of extended strain under applied electric fields, surpassing that of lead zirconate titanate (PZT), the most commonly used piezoelectric. The underlying physical and chemical mechanisms responsible for such extraordinary strain levels in BNT are still poorly understood, as is the nature of the successive phase transitions. A comprehensive explanation is proposed here, combining the short-range chemical and structural sensitivity of in situ Raman spectroscopy (under an applied electric field and temperature) with macroscopic electrical measurements. The results presented clarify the causes for the extended strain, as well as the peculiar temperature-dependent properties encountered in this system. The underlying cause is determined to be mediated by the complex-like bonding of the octahedra at the center of the perovskite: a loss of hybridization of the 6s2 bismuth lone pair interacting with the oxygen p-orbitals occurs, which triggers both the field-induced phase transition and the loss of macroscopic ferroelectric order at the depolarization temperature.
Neutron-scattering studies of (Bi1/2Na1/2)TiO3 (BNT) have been performed to elucidate the microscopic mechanism of the broad maximum in the temperature dependence of the dielectric constant at Tm∼600 K and the reduction in the piezoelectric properties above the depolarization temperature, 460∼480 K. We observed diffuse scattering near the Γ point below 700 K, which competes with the superlattice peak at the M point of the tetragonal phase but coexists with the superlattice peak at the R point of the rhombohedral phase. The diffuse scattering shows an anisotropic Q shape extending along the 〈100〉 direction transverse to the scattering vector Q, which is explained by atomic shifts bridging the tetragonal and rhombohedral structures. We propose that the broad maximum in the dielectric constant is associated with a diffusive first-order transition between the competing tetragonal and rhombohedral phases. In addition, we found that the diffuse scattering is reduced for single crystals grown under high oxygen pressure, which suggests an analogy with the central peak in hydrogen-reduced SrTiO3. Inelastic neutron scattering near the Γ point reveals a heavily overdamped soft mode similar to those reported in lead-based relaxors, the “waterfall” feature. Moreover, a damped soft transverse acoustic mode is observed for the 〈100〉 direction as the anisotropic diffuse scattering, indicating phase instabilities with the same origin as that of the diffuse scattering. The recovery of the soft mode is observed near the depolarization temperature, which coincides with the disappearance of the superlattice peak at the M point. These results indicate that the depolarization and the waterfall feature originate in the dynamic nature of ferroelectric clusters in the coexisting tetragonal/rhombohedral phase.
In the course of searching environmental friendly lead-free relaxor ferroelectrics a complete phase diagram of barium zirconate titanate, Ba(ZrxTi1-x)O-3 system with compositions 0. 00 <= x <= 1.00 has been developed based on their dielectric behavior. It has been shown that BaZrxTi1-xO3 system depending on the composition, successively depicts the properties extending from simple dielectric (pure BaZrO3) to polar cluster dielectric, relaxor ferroelectric, second order like diffuse phase transition, ferroelectric with pinched phase transitions and then to a proper ferroelectric (pure BaTiO3). A comprehensive structure-property correlation of BaZrxTi1-xO3 ceramics has been studied to understand the various ferroelectrie phenomena in the whole phase diagram.
IR reflectivity of B-site ordered and disordered Pb(Sc1/2Ta1/2)O3 ceramics was measured and evaluated between 20 and 500 K. All the IR modes were assigned and their parameters and temperature dependences determined and discussed. No softening of any phonon mode was observed near the ferroelectric transition. Therefore, the transition is of order–disorder type and Pb vibrational anharmonicity seems to be the most important cause of disorder. To our knowledge, this represents the first case of prevailingly order–disorder ferroelectric phase transition among perovskite ferroelectrics. The comparison of ordered and disordered samples shows that the strength of the weak mode near 315 cm−1 assigned to Sc–Ta vibrations can be used to estimate the degree of local order in the disordered sample. This was estimated to be 21 vol.% in good agreement with 18 vol.% estimated from X-ray diffraction.
Since approximately 1950 an increasing portion of experimental solid state physics research has been concerned with studying defects in crystals. This trend might appear to be a rather belated recognition that most of the materials we come into contact with have a random structure. In fact the theoretical understanding and controlled preparation of compounds with defects or random structure has been very slow in developing. The present paper examines and reviews our knowledge of the lattice vibrations associated with defects. The coverage is extremely broad, as shown by the table of contents. It includes localized and resonant modes of isolated defects as well as the modes in highly disordered mixed crystals and glasses. It is primarily a review of experimental work but theoretical results are included where the latter explain or predict significant features. In order to be self-contained several sections of the paper deal entirely with theoretical matters. There is a chapter on explicit solutions of the linear chain vibration problem and a short chapter on Green's function methods. The review emphasizes the infrared absorption and Raman scattering of defects. This is simply because other techniques have not yielded nearly so much information. Neutron scattering and electron tunneling are referred to only where they have shed light on certain systems. Extensive tables of defects and mode frequencies are included for each type of solid. The major solids which are reviewed include semiconductors, ionic compounds, organic compounds, and amorphous insulators.
Wide range dielectric response (10–1014Hz) of three relaxor ferroelectrics: PMN, PLZT and PST is analyzed. The common features are: low phonon contribution to the high static permittivity; dielectric relaxation in a wide frequency range; widening of the relaxation times distribution with decreasing temperature down to the freezing temperature Tf, where extrapolated divergence of the mean relaxation time takes place; change of dielectric behaviour at the Burns temperature TB. Dynamics of polar nanoclusters, which appear below TB, is considered to be responsible for the relaxor behaviour. It enables us to define the general structure of the dielectric spectrum of relaxor ferroelectrics. Only above TB the fundamental dielectric contribution is due to polar phonons. Below TB the contributions caused by polar clusters dynamics prevail: both dipole reversal of polar cluster and fluctuations of their boundaries contribute to the dielectric response.
Dielectric responses of ceramics from the lead-free isovalent BaZrO3-BaTiO3 (BZT) system were investigated from Hz frequencies up to the infrared in a broad temperature range, 10–700 K. Pure BaZrO3 is a displacive weak-incipient ferroelectric with a simple cubic perovskite structure down to low temperatures, whose dielectric response is fully determined by polar phonons, the lowest-frequency one being of the Last type, unlike BaTiO3, where it is of the Slater type. BaZr0.4Ti0.6O3 is a relaxor ferroelectric whose dielectric anomaly is caused by a strong, overdamped excitation, which softens from the THz down to MHz range according to the Arrhenius law and merges into a constant-loss background at low temperatures. Such a reponse is similar to lead-containing and heterovalent relaxors, but unlike them, the lowest-frequency TO1 polar phonon does not soften appreciably. In the case of BaZr0.2Ti0.8O3 we have investigated the dynamic response connected with a diffuse ferroelectric phase transition. The main dielectric anomaly is again due to similar overdamped THz-microwave excitation, which, however, softens only to the GHz range near the transition temperature and below it merges with a near-constant-loss background. The picture of polar nanoregions in BZT differs from that in heterovalent relaxors, because they are pinned to the regions of the off-centered Ti4+ ions, which are frozen in our temperature range. Therefore we assign the soft relaxations to hopping of the off-centered Ti4+ ions. This is compared with the behavior of pure BaTiO3 ceramics, in which the hopping of the off-centered Ti4+ ions also substantially contributes to the phase transition dynamics. Unlike BaTiO3, the dynamic instability, which is responsible for the diffuse ferroelectric and relaxor behavior in BZT, is fully due to the hopping dynamics of the off-centered Ti4+ ions rather than due to soft phonons, and therefore the diffuse transition is of the order-disorder type.
The local environment of Bi and Ti atoms in the lead-free relaxor ferroelectric solid-solution (KxNa1−x)0.5Bi0.5TiO3 has been studied as a function of K concentration and as a function of temperature for the x=0 end member by x-ray absorption fine structure (XAFS). It is found that the local environment of Bi is much more distorted than that determined from conventional diffraction experiments. The shortest Bi-O distances are determined to be 2.22 Å, and are 0.3 Å shorter than those calculated from the crystallographic data. Several possible models of the Bi coordination environment, which are consistent with the XAFS data and provide bond-valence sums for Bi that are closer to the theoretical values, are proposed. The Ti displacement from the center of the oxygen octahedron increases with K concentration while the shortest Bi-O distance shows no compositional dependence. In K0.5Bi0.5TiO3 the value of the Ti displacement is determined to be 0.18 Å. The changes of the macroscopic symmetry at the phase transition points in Na0.5Bi0.5TiO3 do not lead to changes of the radial atomic distribution around Ti, which is well off-center over the whole temperature range up to and including the paraelectric cubic phase. The results can be explained by assuming the presence of structural disorder.
Comprehensive structural studies on normal ferroelectric to relaxor crossover in Ba(Ti1−xZrx)O3 (BTZ) are performed using neutron total scattering measurements analyzed by reverse Monte Carlo modeling. In BTZ solid solution, we estimated the degree of the displacement correlation between Ti ions and found that it is stronger and extends much longer for ferroelectric state than relaxor state. In addition, we present evidence that the overall off-centering behavior of Ti ion changes from directional to random displacements between ferroelectric and relaxor phases, and thus provide atomistic picture for ferroelectric-relaxor crossover with increasing Zr concentration.
A first-principles-based approach is developed to study the dielectric response of paraelectric BaTiO3, as a function of frequency and temperature. Two different overdamped modes of comparable strengths are found to contribute to such response, in the ≃1–150 cm−1 frequency range for temperatures up to ≃750 K. The lower frequency mode softens toward the Curie point, while the higher-frequency mode stays in the 60–100 cm−1 range and is associated with temperature-independent short-range correlations. Our far-infrared reflectivity measurements confirm the existence of these two modes, and yield a very good agreement with calculations.
Classical soft-mode behaviour above the phase-transition temperatures is discussed phenomenologically and the discussion is applied to paraelectric phases of sixteen well known and most investigated ferroelectrics of both displacive and order-disorder type. The experimental dielectric spectra ε'(v) and ε''(v) are obtained using BWO spectromctry in the 3-30 cm-1 region. In nearly all cases, the Cochran law is fulfilled in the whole region where the soft mode is underdamped and the classical critical-slowing-down law holds in regions of overdamping with the same critical temperature. As a rule, damping and oscillator strength are not critically temperature dependent. An unusual behaviour is found for Rochelle salt where below the lower transition temperature the relaxational behaviour develops into a well underdamped oscillator. A comparison with properly evaluated low-frequency dielectric data showed that in six cases, additional central-mode type dispersion near Te is expected and in some cases actually observed (TGS, SbSI, TSCC). A coupled mode analysis makes it possible to estimate the central mode parameters and the real coupling constant between the soft and central mode even if the central mode is not directly seen. In the case of BaTiO3, our new results show no soft mode stabilization and exclude any central-mode type dispersion.
Microwave dielectric properties at ∼35 GHz of B-site ordered (PST-O) and disordered with Pb-vacancies (PST-DV) relaxor ceramics Pb(Sc½Ta½)O3 were investigated in the temperature range 100 ÷ 550 K. The results were compared and fitted together with the new and earlier data in the 100 Hz ÷ 1 GHz range and recent data on infrared and submillimetre response (3·10 ÷ 10 Hz). The dielectric response below polar phonon frequencies comprises two separate dispersion regions in both types of samples from which only the lower frequency one (10 ÷ 10Hz) shows partial critical slowing down. The basic role of the Pb disorder and ordered nano-clusters in the paraelectric phase is emphasized.
We report an investigation of the local structure in homovalent-substituted BaTi1−x Zr x O3 relaxors by a combination of experimental and theoretical methods, namely neutron total scattering, X-ray absorption spectroscopy, and supercell ab-initio calculations. It is shown that unlike Zr atoms, Ti atoms are largely displaced in their octahedra, and are thus associated with strong local dipole moments. Besides, we give evidence that the difference in the size of Ti4+ and Zr4+ cations leads to a significant size mismatch of the Ti–O6 and Zr–O6 octahedra. When they link to form the perovskite structure of BaTi1−x Zr x O3, the O6 octahedra undergo slight distortions in order to accommodate their different sizes. It is shown that they are compressed in the direction of Zr neighbors, and expanded in the direction of Ti neighbors. The polar Ti displacements, which are sensitive to the octahedral distortions, then become constrained in their orientation according to the local Zr/Ti distribution. Such constraints impede a perfect alignment of all the Ti displacements as existing in the classic ferroelectric BaTiO3. Our results shed light on the structural mechanisms that lead to disordered Ti displacements in BaTi1−x Zr x O3 relaxors, and probably in other BaTiO3-based relaxors with homovalent substitution.
In this paper we report the mechanism and nature of relaxor ferroelectric behavior in the environmental friendly lead free Barium Zirconate Titanate (BZT) system. A revised complete (Structure:Property) phase diagram of Ba(ZrxTi1-x)O3, with compositions 0.00≤ × ≤1.00 has been developed based on their electrical properties. Two different kinds of relaxor behaviors have been observed in the BZT system; one is dominated by polar Ti-rich regions and another by non-polar Zr-rich regions. All the BZT relaxor compositions are characterized by dielectric properties with and without bias, pyroelectric and thermal expansion measurements in the wide range of temperatures. The structure of the BZT compositions has been evaluated by XRD, Neutron diffraction study. Further the local structure of the BZT compositions has been probed by micro-Raman spectra. Although the global structure of BZT relaxors is cubic as observed in Neutron diffraction studies, the local symmetry is non-cubic as evident in the micro-Raman spectra of BZT relaxors as well as in their thermal strain measurement, dielectric and pyroelectric behavior.
Dielectric properties of the relaxor ferroelectric ceramics PLZT 8/65/35 and 9.5/65/35 were studied in the broad frequency range of 100 Hz–1 THz at low temperatures below the freezing temperature. Nearly frequency-independent dielectric losses were observed up to 1 GHz on cooling down to 10 K. Their magnitude decreases exponentially with temperature, but remains remarkable high down to 10 K. A Landau-type thermodynamic model based on the perovskite structure near the morphotropic phase boundary is proposed for calculating the energy barriers for polarization reversal near the polar cluster boundaries and explaining the broad distribution function of relaxation times, which fits the observed frequency dependences of permittivity and losses below 1 GHz. High dielectric losses in the submillimetre region were explained by shear wave emission of vibrating polar cluster walls in an ac electric field and by piezoelectric resonances on polar clusters.
The dielectric dispersion of the transparent relaxor ferroelectric ceramics PLZT 8/65/35 and 9.5/65/35 was determined in a wide frequency range including the microwave and infrared range. The number of observed polar phonons in infrared spectra gives evidence about the locally broken cubic symmetry and the presence of polar nanoclusters in the whole investigated temperature range up to 530 K. A single broad and symmetric dispersion that occurs below the polar phonon frequencies was fitted with the Cole-Cole formula and a uniform distribution of Debye relaxations. On decreasing temperature, the distribution of relaxation times becomes extremely broad which indicates increasing correlation among the clusters. The mean relaxation time diverges according to the Vogel-Fulcher law with the same freezing temperature 230±5 K for both ceramics, but different activation energies 1370 K and 1040 K for the 8/65/35 and 9.5/65/35 sample, respectively. The shortest relaxation time is about 10-12 s and remains almost temperature independent. Below room temperature, the loss spectra become essentially frequency independent and the permittivity increases linearly with decreasing logarithm of frequency. The slope of this dependence is proportional to T 4 in the investigated temperature range (above 210 K) which indicates appreciable anharmonicity of the potential for polarization fluctuations.
Feature size is a natural determinant of material properties. Its design offers the technological perspectives for material improvement. Grain size, crystallite size, domain width, and structural defects of different nature constitute the classical design elements. Common ferroelectric ceramics contain micrometer grain sizes and submicrometer domain widths. Domain wall mobility is a major contribution to their macroscopic material properties providing approximately half of the macroscopic output in optimized materials. The extension into the dynamic nanoworld is provided by relaxor ferroelectrics. Ionic and nanoscale field disorders form the base to a state with natural nanometer-size polar structures even in bulk materials. These polar structures are highly mobile and can dynamically change over several orders of magnitude in time and space being extremely sensitive to external stimuli. This yields among the largest dielectric and piezoelectric constants known. In this feature article, we want to outline how lead-free relaxors will offer a route to an environmentally safer option in this outstanding material class. Properties of uniaxial, planar, and volumetric relaxor compositions will be discussed. They provide a broader and more interesting scope of physical properties and features than the classical lead-containing relaxor compositions.
This article reviews the polarizability model and its applications to
ferroelectric perovskite oxides. The motivation for the introduction of the
model is discussed and nonlinear oxygen ion polarizability effects and their
lattice dynamical implementation outlined. While a large part of this work is
dedicated to results obtained within the self-consistent-phonon approximation
(SPA), also nonlinear solutions of the model are handled which are of interest
to the physics of relaxor ferroelectrics, domain wall motions, incommensurate
phase transitions. The main emphasis is to compare the results of the model
with experimental data and to predict novel phenomena.
A first-principles-based technique is developed to investigate properties of
Ba(Zr,Ti)O$_3$ relaxor ferroelectrics as a function of temperature. The use of
this scheme provides answers to important, unresolved and/or controversial
questions, such as: what do the different critical temperatures usually found
in relaxors correspond to? Do polar nanoregions really exist in relaxors? If
yes, do they only form inside chemically-ordered regions? Is it necessary that
antiferroelectricity develops in order for the relaxor behavior to occur? Are
random fields and random strains really the mechanisms responsible for relaxor
behavior? If not, what are these mechanisms? These {\it ab-initio-based}
calculations also leads to a deep microscopic insight into relaxors.
Data of the extensive study of dielectric response of relaxor PbMg1/3Nb2/3O3 (PMN) single crystals, ceramics (standard and textured) and thin films (thickness 500 nm, sapphire substrate) in the broad frequency range (3 × 10−3 to 1014 Hz) were combined, summarized and analyzed. Influence of the mesoscopic structure, possible strain and defects in ceramics and thin film on both relaxational and phonon dynamics is discussed. The phonon response of PMN single crystal and thin film appears to be very similar, including the soft mode behaviour. Similar to PMN crystals, the dielectric response of PMN ceramics and films is mainly determined by relaxational dynamics of polar nanoclusters. Flipping and breathing of the clusters are assumed to be the dominant mechanisms, which can be resolved in the frequency spectra of the complex permittivity. The mesoscopic structure and defects in the ceramics do not result in any significant contribution to additional mechanisms, but influence the dynamics of nanoclusters and lead to pinning of the flipping contribution. In thin films the dielectric response due to cluster dynamics is much more reduced.
Hyper-Raman scattering experiments suggest that a splitting of the lowest F1u-symmetry mode of PbMg1/3Nb2/3O3 crystal occurs in a wide temperature range around its Burns temperature Td≈630 K. The upper-frequency component, earlier investigated by inelastic neutron scattering experiments above Td, appears to be underdamped even hundred of degrees below Td. The lower-frequency component, known below Td from far-IR spectroscopy, actually becomes underdamped above Td. This suggests that the lower-frequency mode is the “primary” polar soft mode of PbMg1/3Nb2/3O3, responsible for the Curie-Weiss behavior of its dielectric permittivity above Td.
Hyper-Raman scattering experiments suggest that a splitting of the lowest F{1u}-symmetry mode of PbMg{1/3}Nb{2/3}O{3} crystal occurs in a wide temperature range around its Burns temperature T{d}≈630 K. The upper-frequency component, earlier investigated by inelastic neutron scattering experiments above T{d}, appears to be underdamped even hundred of degrees below T{d}. The lower-frequency component, known below T{d} from far-IR spectroscopy, actually becomes underdamped above T{d}. This suggests that the lower-frequency mode is the "primary" polar soft mode of PbMg{1/3}Nb{2/3}O{3}, responsible for the Curie-Weiss behavior of its dielectric permittivity above T{d}.
We review the current theory of intrinsic dielectric loss, that is the loss in a perfect crystal due to anharmonic interaction of a.c. electric field with the phonon system of the crystal. Both ordinary dielectrics and displacive ferroelectrics are considered. The theory predicts dependence of the loss on frequency omega and temperature T. This dependence is very sensitive to the symmetry of the crystal. For ordinary dielectrics, the results are presented and tabulated for all 32 symmetry groups, except for non-symmorphic groups. The existing experimental date are analysed and explained on the basis of the theory.