Evolution of domain processes during the transition from classical ferroelectric to relaxor ferroelectric

Dependences of the relative permittivity on the external bias electric field of ceramics of the yPZN-mPMN-nPNN-xPT (x = 0.25?C0.40) system have been studied. The evolution of domain processes during the concentration transition from classical ferroelectric to relaxor ferroelectric has been shown. Tentative conclusions on the mechanisms of electric field-induced transitions from the relaxor state to the ??normal?? ferroelectric state have been drawn.     

Electric-field-induced phase transition in the relaxor ceramics based on PMN-PT

The mechanisms of formation of a plateau in dependences of the reversible permittivity on the external electric field strength in a ceramic sample of the yPZN-mPMN-nPNN — xPT (x = 0, 3; y = 0.0982; m = 0.4541; n = 0.1477) system have been analyzed using X-ray diffraction and atomic force microscopy. It has been shown that, in electric fields corresponding to the permittivity anomaly, there occurs an induced phase transition from the heterophase (tetragonal + pseudocubic) state to the single-phase (tetragonal) state. This leads to significant strains of the tetragonal unit cell (up to 0.1%) and the termination of 90° domain switching. The proposed qualitative model of the formation of the observed dielectric anomaly is based on two processes occurring with an increase in the electric field strength: the growth of polar regions of the tetragonal phase and their switching.     

E-T phase diagrams of a solid solution of the multicomponent PbZn1/3Nb2/3O3-PbMg1/3Nb2/3O3-PbNi1/3Nb2/3O3-PbTiO3 system near the morphotropic phase boundary

The specific features of the dielectric and pyroelectric responses of a solid solution in the barium-doped multicomponent yPbZn_1/3Nb_2/3O₃-mPbMg_1/3Nb_2/3O₃-nPbNi_1/3Nb_2/3O₃-xPbTiO₃ system of the composition y = 0.0982, m = 0.4541, n = 0.1477, and x = 0.3 near the morphotropic phase boundary have been investigated. It has been assumed that the maxima revealed in the dependences of the reversible permittivity on the electric field strength with both the forward and backward changes in the field (E ₌) are associated with the induced phase transition. Based on the experimental results, the E-T phase diagrams are constructed in the temperature range from ?100 to 150°C for different temperature-field regimes: (i) variation in the electric field E ₌ at a fixed temperature of the sample and (ii) variation in the temperature of the sample at a constant value of E ₌. It has been found that there is a singular point in the E-T phase diagram and that, in the vicinity of this point, the dielectric and pyroelectric responses of the studied ceramics exhibit specific features.     

Phase Diagrams of Solid Solutions of Relaxor Ferroelectrics from the Dielectric Spectroscopy Data

The dielectric spectra of Pb(_1–z)Ba _z (Mg_1/3Nb_2/3) _m (Zn_1/3Nb_2/3) _y (Ni_1/3Nb_2/3) _n TixO₃ (x = 0.25–0.4, y = 0.1130–0.0842, m = 0.4844–0.1298, n = 0.1266–0.4726, z = 0–0.15) ceramics with substitution in both A and B crystallographic positions of the perovskite structure are studied. The system demonstrates a transition from the relaxor state to the normal ferroelectric state in both cases: when the concentration of lead titanate grows and the concentration of barium is reduced. On the basis of experimental results, the x–T and z–T phase diagrams are plotted. Despite different crystal chemical reasons of the relaxor state emergence in the investigated solid solutions, their diagrams demonstrate an evident similarity. We have revealed the disappearance of the temperature hysteresis at the transition to the relaxor state in both cases, which has allowed us to make an assumption of the existence of tricritical points on the corresponding diagrams.     

Large piezoelectric strain observed in sol–gel derived BZT–BCT ceramics

High performance lead (Pb)-free piezoelectric ceramics with excellent piezoelectric properties is in great demand for sensor and actuator applications. Barium zirconate titanate–barium calcium titanate [xBZT–(1 − x)BCT] (x = 0.5) is one such lead free system, which exhibits high piezoelectric properties similar to lead zirconate titanate (PZT). In this study we report the synthesis and characterization of this lead free [xBZT–(1 − x)BCT] (x = 0.5) via wet chemical sol–gel method. Calcination of the BZT–BCT precursor only at 1000 °C (against 1300 °C reported in the literature) for 4 h resulted in formation of single phase nanoparticles (<50 nm) as confirmed by X-ray diffraction (XRD) and transmission electron microscopy (TEM) studies. Highly dense and homogenous microstructure with 95% of the theoretical density was obtained by solid-state sintering of the green pellets at 1550 °C. Remanent polarization (Pr) of 11.55 μC/cm² and relative permittivity of 20,020 at the Curie temperature of 95 °C were obtained. Electrically poled BZT–BCT ceramics samples exhibited high piezoelectric charge coefficients, d₃₃ ∼ 530 pC/N, d₃₃* ∼ 942 pm/V, large electromechanical coupling coefficient k_p ∼ 0.45 and a large strain of 0.15%, which are comparable to those of lead based piezoelectric ceramics. The excellent piezoelectric properties of this sol–gel derived BZT–BCT system has been analyzed and correlated to its structure in this report.     

Dielectric, ferroelectric and pyroelectric properties of Pb[(Ni1/3Sb2/3)xTiyZrz]O3 ceramics

In the present study, various Pb[(Ni_1/3Sb_2/3)_xTi_yZr_z]O₃ where x+y+z=1, x=0.08 and y=0.44-0.49, ceramics in the morphotropic phase boundary (MPB) range were studied by dielectric and pyroelectric methods. The results of the investigations revealed an MPB composition range of y≅0.46. The study of the dielectric properties of these compounds as a function of temperature suggests that with increase in y the permittivity maximum increases and transition temperature shifts towards higher temperature. Well-saturated polarization versus electric field (P-E) hysteresis loops were obtained and values of P_r were calculated. The samples revealed good pyroelectric properties for y=0.44 and y=0.45 at room temperature with large figures of merit F_v=0.019 m²/C and F_D=1.34×10^-5Pa^1/2.     

Dielectric properties Ca-substituted barium strontium titanate ferroelectric ceramics

The dielectric and ferroelectric properties of Ba_1−xSr_xTiO₃ (BST) (x=0.10,0.20,0.30,0.40 and 0.60) ceramics and Ba_1−2xSr_xCa_xTiO₃ (BSCT) (x=0.10,0.20,0.30) ceramics have been investigated. The low temperature phase transitions of BST ceramics vanish after Ca²⁺ substitution while the high temperature transition is diffused and relaxed, which becomes more obvious with increasing x. Ca²⁺ substitution obviously decreases the dielectric constant maximum, K_m, of BST ceramics and changes the temperature of dielectric constant maximum, T_m, of BST ceramics. The shift of T_m in BST is attributed mainly to the Sr²⁺ and Ba²⁺ concentration. BST ceramics exhibit almost normal ferroelectric characteristics, while a typical relaxor behavior was observed in BSCT ceramics. The relaxor behavior observations may be understood by a random electric field induced domain state.     

A novel high-k ‘Y5V’ barium titanate ceramics co-doped with lanthanum and cerium

Structural, dielectric, and ferroelectric properties of a novel high-k ‘Y5V’ (Ba_1−xLa_x)(Ti_1−x/4−yCe_y)O₃ ceramics (where x=0.03 and y=0.05, denoted by BL3TC5) with the highest ‘Y5V’ dielectric response (ε′>10 000) among rare-earth-doped BaTiO₃ ceramics to date are investigated in detail using SEM, TEM, XRD, DSC, EPR, Raman spectroscopy (RS), temperature and frequency, electric field dependences of dielectric permittivity (ε′), and temperature and electric field dependences of ferroelectric hysteresis loops. The BL3TC5 diffusion of ferroelectric phase transition occurs around dielectric peak temperatures (T_m) near a room temperature characteristic of dielectric thermal relaxation. Powder XRD data and defect complex model were given. “Relaxor” behavior associated with an order/disorder model and formation of a solid solution were discussed. The EPR results provided the evidence of Ti vacancies as compensating for lattice defects. High-k relaxor nature of BL3TC5 is characterized by an average cubic structure with long-range lattice disordering and local polar ordering; a slow change of the ε′ (T) and P_r(T) curves around T_m; no phase transition observed by DSC; and a broad, red-shifted A₁ (TO₂) Raman phonon mode at 251 cm⁻¹ accompanying the disappearance of the “silent” mode at 305 cm⁻¹ and a clear anti-resonance effect at 126 cm⁻¹ at room temperature.     

Thermoelectric properties of n-Bi2Te3 − x − y Se x S y solid solutions under high pressure

The thermoelectric properties of n-Bi₂Te_{3 ? x ? y} Se _x S _y solid solutions with atomic substitutions in the tellurium sublattice (x = 0.27, 0.3, y = 0, and x = y = 0.09) have been studied under a pressure to 8 GPa. It has been found that the Seebeck coefficient and the resistance decrease with increasing P, and power factor χ increases in all compositions and becomes maximal at pressures of 2–4 GPa. It has been shown that the power factor χ, which is proportional to the product of the effective mass of the density of states m/m m/m ₀ and the charge carrier mobility μ₀ in the form (m/m ₀)^3/2μ₀, increases with increasing pressure mainly due to the increase in the mobility and also depends on the solid solution composition. In the composition with substitution Te → Se + S (x = y = 0.09), the peculiarity of the dependence of m/m ₀ on P in the pressure range corresponding to maximal values of the power factor can be explained by the existence of an electronic topological transition. The increase in the power factor under pressure in n-type Bi₂Te_{3 ? x ? y} Se _x S _y solid solutions combined with similar data for p-type Bi_{2 ? x} Sb _x Te₃ solid solutions obtained earlier, including the estimations of possible changes in the thermal conductivity with increasing pressure, give grounds to design thermoelements with improved value of the thermoelectric figure-of-merit, which can be 50–70% at pressures of 2–4 GPa.     

The effect of CuO and NiO doping on dielectric and ferroelectric properties of Na0.5Bi0.5TiO3 lead-free ceramics

In the present work, lead-free piezoelectric ceramics (Na_0.5Bi_0.5)TiO₃ –xCuO–yNiO (for x = 0.0, 0.02, 0.04 and 0.06) have been prepared by a conventional solid-state reaction method. An investigation of CuO and NiO doping in bismuth sodium titanate (BNT) and a study of the structure, morphology, and dielectric and ferroelectric properties of the NBT–CuNi system have been conducted. Phase and microstructural analysis of the (Na_0.5Bi_0.5)TiO₃ (NBT) based ceramics has been carried out using X-ray diffraction and scanning electron microscopy (SEM) techniques. Field emission scanning electron microscopy (FE-SEM) images showed that inhibition of grain growth takes place with increasing Cu and Ni concentration. The results indicate that the co-doping of NiO and CuO is effective in improving the dielectric and ferroelectric properties of NBT ceramics. Temperature-dependent dielectric studies have also been carried out at room temperature to 400 °C at different frequencies. The NBT ceramics co-doped with x = 0.06 and y = 0.06 exhibited an excellent dielectric constant ?_r = 1514. The study suggests that there is enormous scope of application of such materials in the future for actuators, ultrasonic transducers and high-frequency piezoelectric devices.     

The Vogel-Fulcher law as a criterion for identifying a mixed ferroelectric-glass phase in potassium tantalate doped with lithium

The dynamic dielectric response and the nonlinear dielectric susceptibility of K_1?xLi_xTaO₃ (x=0.010, 0.016, 0.030) compounds are measured in a dc electric field in the temperature range 4≤T≤150 K. It is found that the permittivity ?′ of K_1?xLi_xTaO₃ samples with two lower concentrations of lithium impurities decreases in an electric field E. For samples with a lithium concentration x=0.030, the permittivity ?′ decreases in electric fields E>1 kV/cm and increases in fields E<0.5 kV/cm. The observed dependences of the maximum of the permittivity on the temperature and the frequency of the measuring field obey the Arrhenius law for samples with lower concentrations of lithium impurities (x=0.010, 0.016) and the Vogel-Fulcher law for samples with a higher lithium concentration (x=0.030). The results of the theoretical treatment performed in the framework of the random-field theory are consistent with the experimental data. It is established that the Arrhenius law is valid for dipole glass phases, whereas the Vogel-Fulcher law holds true for a mixed ferroelectric-glass phase in which the short-range and long-range polar orders coexist. The inference is made that the results of measurements of the dielectric response can be used to identify a mixed ferroelectric-glass phase in any disordered ferroelectric material.     

Effect of an electric field on the I–V curves of DyBa2Cu3−x Oy/1 wt % Pt HTSC ceramics

This paper reports on an experimental study of the effect of a magnetic field, B≤70 G, and an electric field, E=120 MV/m, on the critical current I _c and I–V curves of DyBa₂Cu_3?x O_y HTSC ceramics (x=0 and 0.2), both undoped and doped with 1 wt % Pt. It has been established that, in stoichiometric ceramics (x=0) at 77 K, I _c drops sharply (by more than an order of magnitude) already at very low B<1 G. In copper-deficient ceramics (x=0.2), I _c decreases with increasing B slowly, with Pt-doped samples exhibiting [on the dropping I _c (B) dependence] a peak effect, i.e., an increase rather than decrease of I _c at B≈10 G. As for the effect of an electric field on I _c and the I–V curves (the E effect), it is not observed in ceramics of a stoichiometric composition. DyBa₂Cu_2.8O _y samples acted upon by an electric field reveal a substantial increase in I _c and a decrease in the resistance R for I>I _c . In the case of DyBa₂Cu_2.8O_y/Pt, the electric field practically does not affect I _c but R decreases for I>I _c . In a sample placed in a magnetic field, the magnitude of the E effect is observed to correlate with the I _c (B) dependence. In particular, in Pt-doped samples, the E effect decreases with increasing magnetic field B not gradually but with a maximum appearing at B ≈10 G, i.e., in the region of the peak effect in the I _c (B) dependence. The data obtained suggest the conclusion that the electric-field effect in ceramics exhibiting weak links of the superconductor-insulator-superconductor (SIS) type correlates with magnetic vortex pinning.     

The ground state of two-dimensional electrons in a nonuniform magnetic field

An exact solution to the Schrödinger equation for the ground state of two-dimensional Pauli electrons in a nonuniform transverse magnetic field H is presented for two cases. In the first case, the field H depends on a single variable, H = H(y), while in the second case, the field is axially symmetric, H = H(ρ), ρ²=x ²+y ². The electron density distributions n = n(y) and n = n(ρ) that correspond to a completely filled lower level are found. For quasiuniform fields of fixed sign, the functions n(y) and n(ρ) are locally related to the magnetic field: n(y) = H(y)/?₀ and n(ρ) = H(ρ)/?₀, where ?₀ = hc/|e| is a magnetic flux quantum. Magnetic fields are considered that are periodic, singular, and bounded in the plane xy. Finite electron objects in a nonuniform magnetic field are analyzed.     

Development of perovskite and phase transition in lead cobalt niobate modified lead zirconate titanate system

Ferroelectric lead zirconate titanate–lead cobalt niobate ceramics with the formula (1 − x)Pb(Zr_1/2Ti_1/2)O₃–xPb(Co_1/3Nb_2/3)O₃ where x = 0.0–0.5 were fabricated using a high temperature solid-state reaction method. The formation process, the structure and homogeneity of the obtained powders have been investigated by X-ray diffraction method as well as the simultaneous thermal analysis of both differential thermal analysis (DTA) and thermogravimetry analysis (TGA). It was observed that for the binary system (1 − x)Pb(Zr_1/2Ti_1/2)O₃–xPb(Co_1/3Nb_2/3)O₃, the change in the calcination temperature is approximately linear with respect to the PCoN content in the range x = 0.0–0.5. In addition, X-ray diffraction indicated a phase transformation from a tetragonal to a pseudo-cubic phase when the fraction of PCoN was increased. The dielectric permittivity is remarkably increased by increasing PCoN concentration. The maximum value of remnant polarization P_r (25.3 μC/cm²) was obtained for the 0.5PZT–0.5PCoN ceramic.     

Galvanomagnetic and thermoelectric properties of multicomponent n-type solid solutions based on Bi and Sb chalcogenides

The galvanomagnetic and thermoelectric properties of n-Bi_2-x Sb_xTe_3-y-z Se_yS_z multicomponent solid solutions with atomic substitutions (Sb → Bi; Se, S → Te) are studied. The principal components of the effective mass tensor (m ₁, m ₂, m ₃) for the isotropic mechanism of charge carrier scattering are determined within a many-valley model of the energy spectrum for compositions 0.08 ≤ x ≤ 0.4 and 0.06 ≤ y = z ≤ 0.15. The effect of a variation in the parameters of the constant-energy surface on the thermoelectric efficiency is analyzed for different compositions and carrier concentrations in solid solutions.     

Investigation of the ferroelectric–relaxor crossover in Ce-doped BaTiO3 ceramics by impedance spectroscopy and Raman study

BaCe _x Ti_{1? x} O₃ (x?=?0.06, 0.10, and 0.20) solid solutions were prepared via conventional the solid-state reaction and sintered at 1500°C for 4?h, resulting in dense single phase ceramics with homogeneous microstructures. The electric field dependence of permittivity of the BaCe _x Ti_{1? x} O₃ ceramics was investigated in detail, together with the ferroelectric–paraelectric phase transition features. A transformation from normal to relaxor ferroelectrics was observed by increasing the Ce concentration. For low-Ce content, a substitution of Ce on both A and B site positions was proposed from the dielectric study and confirmed by Raman analysis.     

Fatigue of lead titanate and lead zirconate titanate thin films

The fatigue of lead titanate and lead zirconate titanate ferroelectric thin films, i.e., a change in the polarization as a function of the number of switching cycles in an external electric field, is investigated experimentally. The threshold numbers of switching cycles are determined to be 10¹⁰–10¹¹ for the lead titanate films and 10⁹–10¹⁰ for the lead zirconate titanate films. It is shown that a change in the temperature does not substantially affect the threshold number of switching cycles at which the switched polarization decreases drastically. However, an increase in the external field strength leads to a noticeable decrease in the threshold number of switching cycles. The process of fatigue is accompanied by an increase in the coercive field and the internal bias field. It is established that, as the number of switching cycles increases, the internal bias field changes more significantly as compared to the coercive field. The absence of a change in the phase composition in repeatedly switched samples indicates that the fatigue processes have a nonchemical nature. The anomaly observed in the frequency dependence of the permittivity in the frequency range 10⁶–10⁷ Hz due to the domain structure disappears after multiple switching cycles. This suggests that the observed fatigue phenomenon has a domain nature.     

Enhanced ferroelectric and piezoelectric properties in La-modified PZT ceramics

The effect of lanthanum (La) doping on ferroelectric and piezoelectric properties of lead zirconate titanate (PZT) sample has been investigated. Pb_1?x La _x Zr_0.52Ti_0.48O₃ ceramics with x = 0.00, 0.02, 0.04, 0.06 and 0.10 were prepared by the sol–gel technique. Raman and Fourier transforms infrared spectroscopy have been employed to understand the structural modification due to ionic size mismatch. Raman spectra show the existence of both rhombohedral and tetragonal crystal symmetries. It also shows the dielectric relaxation with increase in La concentration in the sample. The increase in lattice strain due to La doping increases the remnant polarization and coercive field. The linear piezoelectric coefficient increases with the increase in La concentration. It reveals that La-substituted PZT is a better candidate for piezoelectric sensor applications as compared to that of PZT.     

Microstructure and electrical properties of Bi0.5Na0.5TiO3–Bi0.5K0.5TiO3–LiNbO3 lead-free piezoelectric ceramics

Lead-free piezoelectric ceramics of (1?x?y)Bi_0.5Na_0.5TiO₃–xBi_0.5K_0.5TiO₃–yLiNbO₃ (BNT–BKT–LN-x/y) have been fabricated by a conventional solid-state reaction method, and their microstructure and electrical properties have been investigated. The results of X-ray diffraction (XRD) measurement show that K⁺, Li⁺ and Nb⁵⁺ diffuse into the Bi_0.5Na_0.5TiO₃ lattices to form a solid solution with a pure perovskite structure. The BKT and LN addition has no remarkable effect on the crystal structure. However, a significant change in grain size took place. Simultaneously, with increasing amount of LN, the temperature for a ferroelectric–antiferroelectric phase transition is clearly reduced. The temperature dependence of dielectric properties suggests that the ceramics have diffuse-type phase transition characteristics. The piezoelectric constant d₃₃ and the electromechanical coupling factor k_p of the ceramics attain maximum values of 195 pC/N and 0.336 at x=0.18 and y=0.01.     

Dielectric properties and phase transitions of (Pb0.87La0.02Ba0.1)(Zr0.6Sn0.4−xTix)O3 ceramics with compositions near AFE/RFE phase boundary

The electrical properties and phase transition behavior of (Pb_0.87La_0.02Ba_0.1)(Zr_0.6Sn_0.4−xTi_x)O₃ solid solutions (PLBZST, 0.04≤x0.2) were investigated by the X-ray diffraction, permittivity, pyroelectric current, and P-E electric hysterisis loops. As the composition x increased from 0.04 to 0.2, the antiferroelectric ceramics (x≤0.07, AFE) with tetragonal phase changed to the ferroelectric relaxors (RFE, 0.09≤x). AFE ceramics showed a peculiar diffuse phase transition and dielectric relaxation at the low temperature (down to −100 °C) due to a frustration between AFE and FE state. With an increase in composition x, electrically field-induced AFE-FE switching field (E_AFE-FE) and AFE-paraelectric (PE) phase transition temperature (T_c) are depressed in the temperature (T)-Ti composition (x) phase diagram, a FE-AFE-PE triple phase point (T_tr) with the lowest transition temperature occurred at x=0.09. The pyroelectric currents under an application of various external electric field (E) were measured to identify a T-E phase diagram of the PLBZST compound.