Nonergodic Relaxor Research Articles

Large strains accompanying field-induced ergodic phase-polar ordered phase transformations in Bi(Mg0.5Ti0.5)O3–PbTiO3–(Bi0.5Na0.5)TiO3 ternary system

A composition-induced pseudocubic–tetragonal structural transition was found to be accompanied by a relaxor phase transformation in xBi(Mg0.5Ti0.5)O3–(0.75 − x)PbTiO3–0.25(Bi0.5Na0.5)TiO3 ternary solid solutions. Dielectric and ferroelectric measurements suggest the coexistence of ergodic and nonergodic relaxor phases within a single pseudocubic phase zone for samples with 0.50 < x < 0.51 where large electromechanical strains of up to 0.43% (Smax/Emax = 621 pm/V) can be generated. The mechanism was mainly ascribed to the accumulated effects of field-modulated continuous and reversible transformations from a pseudocubic ergodic phase to a rhombohedral short-range ordered phase (but not nonergodic polar phase), and finally to a long-range ordered ferroelectric tetragonal phase. These procedures were found to be strongly dependent on the applied field magnitudes. These findings were reasonably approved by a couple of measurements such as dielectric–temperature–frequency spectrum, ferroelectric polarization/strain hysteresis loops, polarization current density curves and particularly ex situ Raman spectrum and in situ high-resolution synchrotron X-ray diffraction.

Dielectric Relaxor Evolution and Frequency‐Insensitive Giant Strains in (Bi0.5Na0.5)TiO3‐Modified Bi(Mg0.5Ti0.5)O3–PbTiO3 Ferroelectric Ceramics

The 0.45Bi(Mg0.5Ti0.5)O3–(0.55 − x)PbTiO3–x(Bi0.5Na0.5)TiO3 (BMT–PT–xBNT) ternary solid solution ceramics were prepared via a conventional solid‐state reaction method; the evolution of dielectric relaxor behavior and the electrostrain features were investigated. The XRD and dielectric measurements showed that all studied compositions own a single pseudocubic perovskite structure and undergo a diffuse‐to‐relaxor phase transition owing to the evolution of the domain from a frozen state to a dynamic state. The formation of the above dielectric relaxor behavior was further confirmed by a couple of measurements such as polarization loops, polarization current density curves, as well as bipolar strain loops. A large strain value of ~0.41% at a driving field of 7 kV/mm (normalized strain d33* of ~590 pm/V) was obtained at room temperature for the composition with x = 0.32, which is located near the boundary between ergodic and nonergodic relaxor. Moreover, this electric field‐induced large strain was found to own a frequency‐insensitive characteristic.

Dielectric, ferroelectric, and field-induced strain properties of Ta-doped 0.99Bi0.5(Na0.82K0.18)0.5TiO3–0.01LiSbO3 ceramics

Ta-doped 0.99Bi0.5(Na0.82K0.18)0.5TiO3–0.01LiSbO3 (BNKTT–LS) ceramics were prepared through a conventional mixed oxide solid-state sintering route. Partial substitution of Ta for Ti decreased the dielectric constant and depolarization temperature. The dielectric curves, polarization and strain hysteresis loops demonstrated that the incorporation of Ta stabilized the canonical relaxor phase of BNKT–LS ceramics leading to the degradation of piezoelectric and ferroelectric responses. The destabilization of field-induced ferroelectric order at x = 0.013 was accompanied by substantial enhancement in strain level. A unipolar field-induced strain of 0.39 % with a normalized strain (S max/E max = $$ d_{33}^{*} $$ ) of 650 pm/V was achieved at a driving field of 6 kV/mm. The observed large strain can be attributed to the non-ergodic relaxor phase at zero electric field that transformed into an ergodic relaxor phase under the influence of the applied electric field.

Structural, dielectric, ferroelectric and strain properties in CaZrO3-modified Bi(Mg0.5Ti0.5)O3–PbTiO3 solid solutions

The structural, dielectric, ferroelectric, strain properties of (0.89−x)Bi(Mg0.5Ti0.5)O3–xPbTiO3–0.11CaZrO3 ceramics (x=0.45–0.55) were investigated. A morphotropic phase boundary between rhombohedral relaxor and tetragonal normal ferroelectric phases was identified in the composition range of 0.49<x<0.51. Moreover, a phase transition from ergodic to nonergodic relaxor states was noticed in the composition range of 0.45<x<0.51 with increasing the PbTiO3 content, during which a giant electric field induced strain (∼0.32%, d33*∼640pm/V) was observed in the proximity of x=0.48. Such a giant strain is believed to originate from the field induced reversible phase transformation between ergodic relaxor and the long-range ferroelectric phase and this was further confirmed by the measurements of the temperature-dependent ferroelectric polarization/strain loops.

Tailoring Strain Properties of (0.94−x)Bi1/2Na1/2TiO3–0.06BaTiO3–xK0.5Na0.5NbO3 Ferroelectric/Relaxor Composites

A remarkable progress in the quest of lead‐free piezoceramics for actuator applications has been made with the development of incipient piezoceramics featured by giant strains. A drawback, however, is the high electric field required to generate this giant strain. A powerful approach to overcoming this drawback lies in relaxor/ferroelectric (FE) composites comprised such giant strain materials (matrix) and a FE or nonergodic relaxor (seed). In this study, we investigate the effect of K0.5Na0.5NbO3 content in the matrix and the volume ratio of seed to matrix using composites of 0.93Bi1/2Na1/2TiO3–0.07BaTiO3 as a seed and (0.94 − x)Bi1/2Na1/2TiO3–0.06BaTiO3–xK0.5Na0.5NbO3 as a matrix. The strain of all matrices, independent of their K0.5Na0.5NbO3 content, was found to be enhanced by adding a certain amount of seed. An optimum strain is achieved for the composite comprised of a matrix with x = 0.02 K0.5Na0.5NbO3 and 10% seed. By means of a differential analysis on the temperature‐dependent dielectric permittivity, it was shown that the seed phase is still present in the composites despite the naturally expected diffusion process during sintering.

Morphotropic Phase Boundary in Solution-Derived (Bi0.5 Na0.5 )1−x Ba x TiO3 Thin Films: Part II Functional Properties and Phase Stability

The analysis of the functional properties (ferroelectric, dielectric, and piezoelectric) of chemical solution deposited thin films of the lead-free (Bi0.5Na0.5)1−xBaxTiO3 (BNBT) solid solution prepared from solution precursors with and without Na+ and Bi3+ excesses has been performed in this work. At room temperature a nonergodic relaxor ferroelectric state has been found. The switched polarization of the films is not stable at room temperature, poor remnant polarization, associated with an enhancement of the induced domains randomization produced by the films constraints. The depolarization temperature for the switched polarization allowed us to build up a tentative phase diagram for these BNBT films. Both the better functional properties and the agreement of the depolarization temperature with the freezing temperature of the relaxor Volger–Fulcher behavior permit to locate the center of the morphotropic phase boundary region close to x = 0.055 in the stoichiometric films and x = 0.10 for the films with Na+ and Bi3+ excesses. Based on these results, the possible applications of these films are discussed.

Local structural disorder and its influence on the average global structure and polar properties in Na0.5Bi0.5TiO3

Na${}_{0.5}$Bi${}_{0.5}$TiO${}_{3}$ (NBT) and its derivatives have prompted a great surge in interest owing to their potential as lead-free piezoelectrics. In spite of five decades since its discovery, there is still a lack of clarity on crucial issues such as the origin of significant dielectric relaxation at room temperature, structural factors influencing its depoling, and the status of the recently proposed monoclinic ($Cc$) structure vis-\`a-vis the nanosized structural heterogeneities. In this work, these issues are resolved by comparative analysis of local and global structures on poled and unpoled NBT specimens using electron, x-ray, and neutron diffraction in conjunction with first-principles calculation, dielectric, ferroelectric, and piezoelectric measurements. The reported global monoclinic ($Cc$) distortion is shown not to correspond to the thermodynamic equilibrium state at room temperature. The global monocliniclike appearance rather owes its origin to the presence of local structural and strain heterogeneities. Poling removes the structural inhomogeneities and establishes a long-range rhombohedral distortion. In the process the system gets irreversibly transformed from a nonergodic relaxor to a normal ferroelectric state. The thermal depoling is shown to be associated with the onset of incompatible in-phase tilted octahedral regions in the field-stabilized long range rhombohedral distortion.

Electromechanical strain and bipolar fatigue in Bi(Mg1/2Ti1/2)O3-(Bi1/2K1/2)TiO3-(Bi1/2Na1/2)TiO3 ceramics

Lead-free ceramics of composition Bi(Mg1/2Ti1/2)O3-(Bi1/2K1/2)TiO3-(Bi1/2Na1/2)TiO3 were prepared using solid state synthesis techniques. The dielectric spectra showed a Tmax of more than 320 °C for all compositions, and the transitions became increasingly diffuse as the Bi(Mg1/2Ti1/2)O3 content increased. A lower temperature transition, indicating a transformation from an ergodic to a non-ergodic relaxor state, was also seen for all compositions, and this transition temperature decreased as the mole fraction of Bi(Mg1/2Ti1/2)O3 increased. The composition with 1% Bi(Mg1/2Ti1/2)O3 showed characteristic ferroelectric-like polarization and strain hysteresis. However, compositions with increased Bi(Mg1/2Ti1/2)O3 content became increasingly ergodic at room temperature with pinched polarization loops and no negative strain. Among these compositions, the magnitude of d33* increased with Bi(Mg1/2Ti1/2)O3 content, and the composition with 10% Bi(Mg1/2Ti1/2)O3 exhibited a d33* of 422 pm/V. Fatigue measurements were conducted on all compositions and while the 1% Bi(Mg1/2Ti1/2)O3 composition exhibited a measurable, but small loss in maximum strain after a million cycles; all the other compositions from 2.5% to 10% Bi(Mg1/2Ti1/2)O3 were essentially fatigue-free. Lastly, optical and alternating current impedance measurements were employed to identify intrinsic conduction as the dominant conduction mechanism. These compositions were also highly insulating with high resistivities (∼107 Ω-cm) at high temperatures (440 °C).

Incipient piezoelectrics and electrostriction behavior in Sn-doped Bi1/2(Na0.82K0.18)1/2TiO3 lead-free ceramics

Dielectric, ferroelectric, piezoelectric, and strain properties of lead-free Sn-doped Bi1/2(Na0.82K0.18)1/2TiO3 (BNKT) were investigated. A crossover from a nonergodic relaxor to an ergodic relaxor state at room temperature, accompanied by a giant electric-field-induced strain, was observed at 5 at. % Sn doping. Switching dynamics monitored during a bipolar poling cycle manifested that the observed giant strain originates from incipient piezoelectricity. When Sn doping level reached 8 at. %, BNKT exhibited an electrostrictive behavior with a highly temperature-insensitive electrostrictive coefficient of Q11 = 0.023 m4 C−2.

Electrical poling below coercive field for large piezoelectricity

Isotropic polycrystalline ferroelectric ceramics have to be electrically poled to develop a net macroscopic polarization and hence piezoelectricity. It is well accepted that a sufficient poling can only be realized under an electric field that is much higher than the coercive field. In this study, we observed in (Bi1/2Na1/2)TiO3-BaTiO3 ceramics that large piezoelectricity can develop at poling fields far below the measured coercive field. Using in situ transmission electron microscopy, such an unusual behavior, is interpreted with the polarization alignment of polar nanodomains in the non-ergodic relaxor phase.

Domain structures and dielectric properties resulting from tweed precursors of relaxor ferroelectric solid-solution single-crystal 24Pb(In1/2Nb1/2)O3-46Pb (Mg1/3Nb2/3)O3-30PbTio3

The domain structures of poled and depoled lead-based relaxor ferroelectric solid-solution single-crystal 24Pb(In(1/2)Nb(1/2))O(3)-46Pb (Mg(1/3)Nb(2/3))O(3)-30PbTio(3) are studied by polarized light microscopy, piezoresponse force microscopy (PFM), scanning electron microscopy (SEM), and dielectric spectroscopy. The domain structures in the nonergodic relaxor state are found by PFM to consist of tweed structures resulting from random fields from the competition between ferroelectric and antiferroelectric distortion, and planar defects found by SEM are treated as dislocations associated with strain accommodation, resulting in superior piezoelectric properties. This domain structure is found to be connected with hierarchical domain structures.

Asymmetric phase diagram of mixedCuInP2(SxSe1−x)6crystals

Mixed ${\text{CuInP}}_{2}{({\text{S}}_{x}{\text{Se}}_{1\ensuremath{-}x})}_{6}$ crystals were investigated by broadband dielectric spectroscopy (20 Hz--3 GHz). The complete phase diagram has been obtained. The phase diagram of investigated crystals is strongly asymmetric---the decreasing of ferroelectric phase-transition temperatures in ${\text{CuInP}}_{2}{({\text{S}}_{x}{\text{Se}}_{1\ensuremath{-}x})}_{6}$ is much more flat with small admixture of sulfur than with small admixture of selenium. In the middle part of the phase diagram $(x=0.4--0.9)$ the dipolar glass phase has been observed. In boundary region between ferroelectric order and dipolar glass disorder with small amount of sulfur $(x=0.2--0.25)$ at low temperatures, the nonergodic relaxor phase appears. The phase diagram was discussed in terms of random bonds and random fields.

High-temperature structural transformations in the relaxor ferroelectricsPbSc0.5Ta0.5O3andPb0.78Ba0.22Sc0.5Ta0.5O3

Temperature-driven structural transformations in Pb-based perovskite-type relaxors are studied by using polarized Raman spectroscopy, high-resolution powder, and synchrotron single-crystal x-ray diffraction applied to PbSc0.5 Ta0.5 O3 (PST) and Pb0.78 Ba0.22 Sc0.5 Ta0.5 O3 (PBST). The two compounds were chosen as model systems because PST is a relaxor that exhibits ferroelectric long-range order on cooling, whereas PBST shows canonical relaxor behavior. The temperature evolution of phonon anomalies and the pseudocubic unit-cell parameter for both PST and PBST reveals the existence of a characteristic temperature T between the Burns temperature TB and the temperature of the dielectric-permittivity maximum Tm. T is associated with the coupling of initially nucleated small polar clusters and their aggregation into larger polar clusters. The temperature range between TB and T is characterized by a coupling between adjacent off-centered BO6 octahedra to form initial polar clusters, while the range between T and Tm is characterized by a coupling between off-centered B cations from adjacent polar clusters. Off-centered Pb atoms exist even above the Burns temperature and their length of coherence governs the coupling between polar regions comprising B -cation off-center shifts and, consequently, directs the formation of the ferroelectric state to a normal, long-range ordered or nonergodic relaxor state.

Impossibility of pressure-induced crossover from ferroelectric to nonergodic relaxor state in aPb(Mg1∕3Nb2∕3)0.7Ti0.3O3crystal: Dielectric spectroscopic study

Relaxor behavior induced by hydrostatic pressure up to $0.95\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$ in the $\mathrm{Pb}({\mathrm{Mg}}_{1∕3}{\mathrm{Nb}}_{2∕3}{)}_{0.7}{\mathrm{Ti}}_{0.3}{\mathrm{O}}_{3}$ (PMN-30PT) ferroelectric crystal was studied using dielectric spectroscopy. With increasing pressure we observed the decrease of the ferroelectric phase transition temperature $({T}_{C})$, the suppression and smearing of the dielectric anomaly at ${T}_{C}$, and the appearance of strong relaxorlike dielectric dispersion below the temperature of the permittivity maximum $({T}_{m})$. Such kinds of pressure-induced alteration are inherent in compositionally disordered perovskite ferroelectrics. It is usually believed to signify a crossover from the ferroelectric ground state to the nonergodic relaxor ground state in which the dipole moments of polar nanoregions (PNRs) are frozen in a way characteristic of dipole glasses. Surprisingly, our analysis of the dielectric spectra in PMN-30PT at high pressure did not reveal any glassy freezing of dipole dynamics. This means that the nature of the high-pressure-induced ground state is different from the nonergodic relaxor state observed in canonical relaxors at ambient pressure. At $T&gt;{T}_{C}$ the dielectric spectra measured in PMN-30PT under different pressures are qualitatively similar. They are composed of two contributions that follow the Kohlrausch-Williams-Watts (KWW) and the Curie--von Schweidler (CS) relaxation patterns, respectively. The dielectric susceptibility related to the KWW relaxation provides the major contribution to the total dielectric constant. The shapes of the frequency and temperature dependences of this susceptibility remain practically unaffected by pressure. Contrary to the canonical relaxors the KWW relaxation time does not obey the Vogel-Fulcher law. On the other hand the CS-related susceptibility, which is significant only at low frequencies, considerably increases with increasing pressure and the shapes of its frequency and temperature dependences change radically. At $T&lt;{T}_{C}$ the KWW and CS relaxation processes are not observed at ambient pressure, but persist at $0.8\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$. The KWW characteristic relaxation time varies with temperature according to the Arrhenius law. We propose that the observed variation of properties results from the pressure-induced crossover from the sharp order-disorder-type ferroelectric phase transition, which is triggered by the cooperative interactions among dynamic (in the high-temperature phase) PNRs to the diffuse displacive-type ferroelectric transition, which is related to the growth of PNR dimensions.

Electric field-induced phase transitions in (111)-, (110)-, and (100)-orientedPb(Mg1∕3Nb2∕3)O3single crystals

Electric field-induced phase transitions were investigated in (111), (110), and (100) thin platelets of relaxor ferroelectric $\mathrm{Pb}({\mathrm{Mg}}_{1∕3}{\mathrm{Nb}}_{2∕3}){\mathrm{O}}_{3}$ single crystals with electric fields applied along the $⟨111⟩$, $⟨110⟩$, and $⟨100⟩$ directions, respectively. Temperature dependences of complex dielectric permittivity, pyroelectric current and dielectric hysteresis loops were investigated. Electric field-temperature $(E\text{\ensuremath{-}}T)$ phase diagrams were proposed for the different directions of the field. Alongside with the high-temperature ergodic relaxor phase and the low-temperature glassy nonergodic relaxor phase existing at $E=0$, the ferroelectric phase may appear in the diagram at the fields higher than the threshold field $({E}_{\mathrm{th}})$. The temperature of the first-order transition between ergodic relaxor and ferroelectric phases $({T}_{C})$ was located in field cooling and field heating after field-cooling regimes. For the $⟨111⟩$ field direction, ${T}_{C}$ is higher and ${E}_{\mathrm{th}}$ is lower than for the other directions. For the $⟨100⟩$ direction, ${T}_{C}$ is the lowest and ${E}_{\mathrm{th}}$ is the highest. The critical point bounding the ${T}_{C}(E)$ line when the field is applied in $⟨111⟩$ direction [Z. Kutnjak, J. Petzelt, and R. Blinc, Nature 441, 956 (2006)] is not observed in the $⟨110⟩$ and $⟨100⟩$ directions up to the highest applied field of $7.5\phantom{\rule{0.3em}{0ex}}\mathrm{kV}∕\mathrm{cm}$. Extrapolation of experimental data suggests that the critical point for the $⟨110⟩$ and $⟨100⟩$ directions (if any) can be expected only at much higher fields. In the hysteresis loops experiments performed after zero-field cooling, the lower temperature limit is determined above which a ferroelectric phase can be induced from the frozen glassy state at a given field strength or the polarization of the induced ferroelectric phase can be reversed. This limit is located at much lower temperatures in the (100) platelet than in the (110) or (111) platelets. An additional ferroelectric rhombohedral to ferroelectric orthorhombic phase transition occurs in the (110) platelet at high electric fields $(\ensuremath{\sim}20\phantom{\rule{0.3em}{0ex}}\mathrm{kV}∕\mathrm{cm})$. The mechanisms of the field-induced transformation from the glassy nonergodic relaxor phase or the ergodic relaxor phase to the ferroelectric phase are discussed.

Dielectric response of the relaxor ferroelectric Pb(Mg1/3Nb2/3)O3 in the nonergodic state after a DC electric field is turned off

The Pb(Mg1/3Nb2/3)O3 (PMN) relaxor system is used as an example to analyze the temperature dependences of the low-frequency dielectric permitivity (ɛ′(T)) measured during zero-field heating (ZFH) from T = 10 K to T = 300 K after using different field cooling (FC) conditions. No changes in the temperature dependences of the permittivity have been detected during the transition from a nonergodic relaxor state (NERS) into an ergodic relaxor state (ERS) (at T f ≈ 216 K). However, the difference Δɛ′(T) between the curves corresponding to different field cooling conditions in the same electric field has different shapes and different values below and above T → (T f + 9 K)− (for E dc = 1.52 kV/cm). The reduced permittivities ɛ′r(T, f) recorded under different cooling conditions are shown to change their behavior when passing through T = T f + 9 K. In NERS, these curves diverge: the stronger the field (0 ≤ E dc ≤ 3 kV/cm), the larger the divergence. In ERS, however, the ɛ′r(T, f) curves coincide under different cooling conditions irrespective of the field. The character of the changes in Δɛ′(T) and ɛ′r (T, f) during the NERS-ERS transition is frequency-independent. The difference in the behavior of the dielectric response during ZFH after cooling in different (ZFC, FC) modes (even in a weak field), for both transition through T f and cooling down to T = 10 K, indicates different NERSs forming under these conditions. The contribution to ɛ′(T) from slowly relaxing regions (ω ∼ 0.1 mHz), whose polarization is reoriented after the field is turned off, is responsible for the fact that, during the NERS-ERS transition, the ɛ′r(T, f) curves coincide at a temperature that is higher than T = T f.

Nano-Scale Frustrated Cd2Nb2O7 Ferroics

The dielectric response (100 Hz to 6 MHz), relaxation-time distribution, dielectric hysteresis loops and polarization obtained from pyroelectric current have been studied in the Cd 2 Nb 2 O 7 pyrochlore the ferroelectric (FE) state of which is frustrated due to embedded polar nanoregions of the nonergodic relaxor state (NERS). It is found that at frequencies below 1.5 MHz for dc bias electric fields of < 7 kV/cm the contribution of a relaxor state dominates over that of a normal FE state. A proper formation of glassy or FE properties of the NERS is prearranged during zero-field cooling and field cooling the system through the freezing temperature T f ≈ 182 K, respectively.

Dielectric properties of partially disordered lanthanum-modified lead zirconate titanate relaxor ferroelectrics

Linear and third-order nonlinear dielectric susceptibilities and the dielectric polarization were measured in $6.5∕65∕35$ lanthanum lead zirconate titanate (PLZT) hot-pressed ceramics. On cooling linear dielectric data show a transition from an ergodic to a nonergodic relaxor phase, while, on heating, a ferroelectric to ergodic relaxor phase transition appears. The third-order dielectric response is reminiscent of an ergodic to nonergodic relaxor phase transition. Below the Vogel-Fulcher temperature, at which the longest relaxation time diverges, spontaneous polarization exists, which indicates the possibility that the sample breaks up at low temperatures into relaxor glasslike and ferroelectric order--dominated regions at nonzero transition temperatures. Additional measurements of the quasistatic field-cooled--field-heated dielectric susceptibilities revealed an electric-field--temperature phase diagram, which confirmed the coexistence of both phases. The dielectric susceptibility at various bias electrical fields, obtained from polarization data, revealed a field-induced transformation between the disordered state and ordered ferroelectric state. The results were analyzed in the framework of the spherical random-bond--random-field model.

Relaxor and incipient ferroelectric phases in 6.5/65/35 PLZT ceramics

The linear and third harmonic nonlinear dielectric constants were measured in 6.5/65/35 PLZT hot-pressed ceramics. Linear dielectric data obtained on ooling show the transition from an ergodic to a nonergodic relaxor phase while, on heating, a ferroelectric to ergodic relaxor phase transition appears. The third harmonic di-electric response is reminiscent of an ergodic to nonergodic relaxor phase transition. Existence of the spontaneous polarization below the Vogel–Fulcher temperature at which the longest relaxation time diverges, indicates the possibility that the sample breaks up at low temperatures into relaxor glass-like and ferroelectric order dominated regions.

Linear and nonlinear dielectric constant as function of bias electric field in relaxor materials

Abstract The quasistatic linear and nonlinear dielectric constants eS in 9/65/35 PLZT ceramics and PMN crystal were investigated by means of the charge accumulation technique and by monitoring the first, e1, and the third, e3, harmonic response. The zero field cooled and field cooled static susceptibilities show a crossover from a nonergodic relaxor to inhomogeneous ferroelectric behaviour. At electric fields above the critical value contribution from the saturated spontaneous polarization was observed. The temperature dependence of the total third order nonlinear response was determined in 9/65/35 PLZT ceramics.