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.     

Kinetics of nucleation of thermodynamically ordered ferroelectric phases in PbMg<Subscript>1/3</Subscript>Nb<Subscript>2/3</Subscript>O<Subscript>3</Subscript>–<Emphasis Type="Italic">x</Emphasis>PbTiO<Subscript>3</Subscript> crystals with different compositions

The kinetics of electric field-induced nucleation of ordered ferroelectric phases from a mixed glassy relaxor state has been studied in a number of single-crystal (1–x)PbMg_1/3Nb_2/3O₃–xPbTiO₃ (PMN–xPT) solid solutions (x = 29, 33, 35%) lying in a morphotropic phase region. It is shown that the formation of these phases and fast establishment of a macroscopic polarization are preceded by some delay time, depending on the electric field strength and temperature. It is found that the monoclinic phase is thermodynamically stable at room temperature in all the compounds in the time (~3000 s) and electric field (~1 kV/cm) ranges under study, whereas the monoclinic phase of the compound with x = 35% transforms, at temperatures near the temperature of the morphotropic phase transition after insignificant time interval of ~100 s, to another stable ferroelectric tetragonal phase.     

Heat capacity study of double perovskite-like compounds BaTi<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript>Zr<Subscript>x</Subscript>O<Subscript>3</Subscript>

The temperature dependence of the heat capacity of two compositions in the solid solution system BaTi_1?xZr_xO₃ (x = 0.25, 0.35) was measured using adiabatic calorimetry. In the T-x phase diagram, these compounds occupy positions near the crossover from conventional ferroelectric behavior to the relaxor state. Both compounds reveal diffuse heat capacity anomalies: two anomalies in the temperature ranges 250–350 and 150–200 K at x = 0.35 and one anomaly within the range ～150–320 K at x = 0.25. The results obtained are discussed together with structural and dielectric measurements.     

Electrophysical properties of six-component ZTS-based ferrosoft ceramic

The properties of six-component ZTS-based ferrosoft ceramic are studied. The ceramic is found to exhibit properties of a ferroelectric relaxor. The R3c → R3m rhombohedral phase transition is observed in the ferroelectric phase of this composite. Polarization of samples with a constant electric field upon cooling through the Curie point enlarges the temperature range of the R3m phase’s existence, compared to roomtemperature polarization.     

Specific features of dielectric anomalies in Pb<Subscript>1 − <Emphasis Type="Italic">x</Emphasis></Subscript>Ge<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>Te(Ga) near a ferroelectric phase transition

The dielectric properties of Pb_{1 ? x} Ge _x Te(Ga) (x = 0.02, 0.03, 0.05) were studied in the temperature range 77–150 K at frequencies of 10⁴–10⁶ Hz. It is revealed that the ferroelectric phase transition temperature T _c and the permittivity ? of Pb_{1 ? x} Ge _x Te(Ga) increase substantially with the Ge content. The temperature dependence of the permittivity of Pb_{1 ? x} Ge _x Te shows two peaks; the main peak is at the ferroelectric phase transition temperature T _c , and an additional peak is at T ₁ > T _c .     

Thermooptical and Dielectric Studies of a Calcium-Induced Ferroelectric Phase in a SrTiO<Subscript>3</Subscript> Incipient Ferroelectric

We have examined temperature changes of the light refraction, birefringence, dielectric permittivity, and dielectric hysteresis loops in Sr_{1 – x}Ca_xTiO₃ single crystals with x = 0.014 (SCT-1.4). The dielectric properties of Sr_{1 – x}Ca_xTiO₃ with x = 0.007 (SCT-0.7) have been studied. We have performed ab initio calculations of equilibrium structures and total energies for three low-temperature phases of SrTiO₃ and CaTiO₃, based on which we have determined an expected symmetry of the ground state of their solid solution and spontaneous polarization directions in a calcium-induced ferroelectric phase in Sr_{1 – x}Ca_xTiO₃. In SCT-1.4, we have separated a spontaneous contribution to the light refraction, which arises due to the spontaneous electrooptical effect caused by the spontaneous polarization and its fluctuations. From the spontaneous contribution to the light refraction, based on a previously developed our phenological approach, we have quantitatively determined for the first time the values and temperature dependences of root-mean-square fluctuations of the order parameter—the polarization P_sh = 〈P _fl ² 〉^1/2(short-range, local polar order) in the ferroelectric phase. From optical and dielectric measurements in SCT-1.4, the average value of spontaneous polarization P_s (the contribution from the long-range order) has been determined. We have estimated the values of P_sh and P_s, which characterize the short- and long-range orders in the ferroelectric phase of SCT-0.7. Separate determination of the values and temperature dependences of P_s and P_sh (which considerably exceeds the value of P_s in the ordered phase) has allowed us to reveal on a quantitative level new particular features of the formation of the induced polar phase in Sr_{1 – x}Ca_xTiO₃.     

A free convective boundary layer in a conducting fluid in the presence of a transverse magnetic field

The properties of free convection in a conducting fluid in laminar regime near a hot solid vertical w all in the presence of a transverse magnetic field are theoretically analyzed. The existence of two regimes of heat transfer from the wall to the fluid are established. In the first regime, at small heights x?x* where the magnetic field effect can be disregarded, heat transfer is described by the well-known results for a free convective boundary layer in a nonconducting fluid with the Nusselt number Nu_x∝x^3/4. In the second regime, at x? x* where the magnetic field plays a crucial role, the dependence of heat transfer on the height and field strength is \(Nu_x \propto {{\sqrt x } \mathord{\left/ {\vphantom {{\sqrt x } B}} \right. \kern-\nulldelimiterspace} B}\). The location of the boundary between these regimes strongly depends on the magnetic field, x*∝ B^?4.     

Heat capacity of the Pb<Subscript>5</Subscript>(Ge<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript>Si<Subscript>x</Subscript>)<Subscript>3</Subscript>O<Subscript>11</Subscript> ferroelectric system

The temperature dependences of the molar heat capacity at constant pressure, C_p, of Pb₅(Ge_1?xSi_x)₃O₁₁ crystals with x=0, 0.39, and 0.45 in the range 5–300 K, as well as of their permittivity, dielectric losses, and the pyroelectric effect, have been measured. Experimental data on the temperature behavior of the heat capacity are presented in the form of a sum of two Debye and one Einstein terms, C_p(T)=0.405C_D1(Θ_D1=160 K, T)+0.53C_D2(Θ_D2=750 K, T)+0.046C_E(Θ_E=47 K, T). Besides a peak in the region of the ferroelectric Curie point T_c=450 K for crystals with x=0, the temperature dependences of the heat capacity did not reveal any other pronounced anomalies.     

A study of the effect of gradual substitution NH<Subscript>4</Subscript> → Cs on phase transitions in NH<Subscript>4</Subscript>LiSO<Subscript>4</Subscript> crystals

Solid solutions in the Cs_x(NH₄)_1?xLiSO₄ (0≤x≤0.35) system are grown and investigated. The birefringence (n_a?n_b) and the heat capacity are measured in the temperature range 100–530 K. The (x-T) phase diagram is constructed. It is demonstrated that the substitution of cesium for ammonium in the NH₄LiSO₄ crystal affects the transition temperatures in such a way that the region of the ferroelectric phase increases and the ferroelastic phase disappears at x>0.22. The character of the high-temperature transition remains unchanged (2β=0.24±0.01 for all compositions), but the birefringence anomaly and enthalpy decrease. As the concentration x increases, the low-temperature transition becomes more similar to a first-order transition: the birefringence jump δn and the temperature hysteresis ΔT increase.     

Switching of spontaneous electric polarization in the DyMnO<Subscript>3</Subscript> multiferroic

For the DyMnO₃ multiferroic with a modulated magnetic structure, switching of its spontaneous electric polarization (P ‖ c axis) near the ferroelectric transition (T < T _FE ～ 20 K) is revealed by measuring the dielectric hysteresis loops. It is found that the coercive field strongly increases as the temperature decreases (up to 2.6 kV/mm at 17.6 K). The values obtained for the spontaneous polarization are found to agree well with the data obtained from pyroelectric measurements. In addition, anomalies are observed in the temperature dependences of the spontaneous polarization P _c , dielectric constant ? _c , and magnetic susceptibility x _b at T ～ 6 K; these anomalies are attributed to the antiferromagnetic ordering of the Dy³⁺ ions.     

Ferroelectric phase transitions in ionic conductors based on bismuth vadanate

Ceramic solid solutions (Bi_{1 ? x} La _x )₄V₂O_{11 ? z} (I), Bi₄(V_{1 ? x} Fe _x )₂O_{11 ? y} (II), and (Bi_{1 ? x} La _x )₄(V_0.96Fe_0.04)₂O_{11 ? y} (III) (x = 0–0.3, step Δx = 0.02) are prepared using solid-phase synthesis. The concentration and temperature ranges of stabilization of different polymorphic modifications, including the ranges of concentrations x corresponding to the stabilization of the ferroelectric phase, are established. It is revealed that an increase in the concentration x in the region of existence of the pseudoorthorhombic phase α of the solid solutions studied leads to a decrease in the transition temperature, smearing of the transition, and an increase in the width of the thermal hysteresis of the ferroelectric phase transition. The effect of compressing of the domain walls by oxygen vacancies was revealed in the samples from the region of existence of the ferroelectric α phase, and the effect of dielectric relaxation was detected in the samples from the region of existence of the orthorhombic phase β.     

Dielectric and optical properties of Pb(Mg<Subscript>1/3</Subscript>Nb<Subscript>2/3</Subscript>)<Subscript>0.8</Subscript>Ti<Subscript>0.2</Subscript>O<Subscript>3</Subscript> (PMNT-0.2) ferroelectric relaxor single crystals

The dielectric and optical (optical transmission, small-angle light scattering, birefringence) properties of PMNT-0.2 single crystals and their variation induced by a dc electric field have been studied. The birefringence was found to increase anomalously at the transition from the rhombohedral ferroelectric to the inhomogeneous relaxor phase (the spontaneous ferroelectric transition temperature T_sp). Below T_sp, the dielectric and optical properties were observed to exhibit anomalies originating from reorientation and growth of domains in size. Unlike ferroelectric relaxors of the type of PbB′_1/3B′_2/3O₃ and PbB′_1/2B′_1/2O₃, in PMNT-0.2 neither induction of the ferroelectric phase by an electric field nor thermally stimulated destruction of the ferroelectric state occurs through the percolation mechanism (i.e., they are not accompanied by anomalously narrow maxima in small-angle light scattering). This is attributed to the inhomogeneous structure of the relaxor phase, as a result of which the phase transition does not take place simultaneously in various regions of the crystal.     

Neutron-diffraction study of the crystal structure of BaTiO<Subscript>3</Subscript> ferroelectric doped with iron

The crystal structure of iron-doped barium titanate BaTi_1–x Fe _x O₃ is studied by neutron diffraction in the range of 0 ≤ x ≤ 0.12. At low concentrations of iron, x < 0.01, and at room temperature, these compounds have a polar structure with tetragonal symmetry with space group P4mm. The temperature of the transition of the tetragonal ferroelectric phase into the cubic paraelectric phase with space group Pm \(\bar 3\) m for an iron concentration of x = 0.01 is 390 K (for pure BaTiO₃, it is 410 K). At an iron concentration of x = 0.07, the crystal structure of the studied compounds varies, and it is described by the centrosymmetric hexagonal space group P6₃/mmc. The structural parameters of various phases of compound BaTi_1–x Fe _x O₃ are determined from the experimental data.     

Effect of cation substitution on the lattice dynamics and ferroelectric instability of cubic BaTiO<Subscript>3</Subscript> and BaZrO<Subscript>3</Subscript> doped with Bi and La ions

The spectra of lattice vibration frequencies of solid solutions Ba_{1 ? x} Bi_2x/3? _x/3Ti(Zr)O₃ and Ba_{1 ? x} La _x Ti(Zr)_{1 ? x/4}? _x/4O₃ are calculated in terms of a generalized Gordon-Kim model with inclusion of the dipole and quadrupole polarizabilities. Over the entire concentration range, the calculated phonon spectra contain a ferroelectric soft mode. The effect of various interactions on the ferroelectric instability of these solid solutions is studied. It is shown that the character of ferroelectric instability is largely determined by the mechanism of charge compensation.     

Kinetic Properties of the Mn<Subscript>1 – <Emphasis Type="Italic">x</Emphasis></Subscript>Gd<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>Se Solid Solutions

The results of kinetic study of the Mn_{1 – x}Gd_xSe chalcogenide solid solutions with different substitute concentrations (0 ≤ x ≤ 0.15) in the temperature range of 80–400 K are reported. The difference between the Hall constant and thermopower signs has been found. The electron-type conductivity determined from the Hall constant and hysteresis of the I–V characteristics have been explained by the existence of nanoareas with local electric polarizations. The sharp extrema observed in the temperature dependence of thermopower are explained by splitting of a narrow 4f subband by the crystal field.     

Structure,Ferroelectric, and Magnetoelectric Properties of Bulk PZT–NiFe<Subscript>1.9</Subscript>Co<Subscript>0.02</Subscript>О<Subscript>4 – δ</Subscript> Composites

The phase composition, microstructure, and dielectric, ferroelectric, magnetic, and magnetoelectric properties of bulk ceramic (1 – x)PZT–xNiFe_1.9Co_0.02О_{4 – δ} composites with 3–0 connectivity have been studied. Using X-ray diffraction and electron microscopy, it has been established that the ferrimagnetic (spinel- like) and ferroelectric (tetragonal perovskite-like) phases separately exist in the composites of all compositions. The simultaneous existence of ferroelectric and ferrimagnetic properties in the composites is confirmed by measuring their P(E) and σ(B) hysteresis loops and studying the temperature dependences of dielectric and magnetic properties. The synthesized composites have high magnetoelectric characteristics: their voltage coefficient at x = 0.4 is 215 mV/A at a frequency of 1 kHz and 130 V/A at an electromechanical resonance frequency of 380 kHz.     

Dependence of the heat capacity of La<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript>Ag<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>MnO<Subscript>3</Subscript> manganites on the Ag content

The heat capacity of La_1?x Ag _x MnO₃ manganites with x = 0.1, 0.15, and 0.2 is measured in the temperature range 77–350 K. An analogy between the effect of doping and the effect of a magnetic field on the temperature dependence of heat capacity of the La_1?x Ag _x MnO₃ system is revealed. As lanthanum is replaced by silver, the volume fraction of the ferromagnetic phase increases, while, in the paramagnetic state, the Jahn-Teller distortions are eliminated. The results of the aforementioned measurements suggest that the phase transition near the Curie point is caused by the competition between the Coulomb and exchange electrostatic interactions. The comparison of the concentration dependences of T _C for La_1?x Sr _x MnO₃ and La_1?x Ag _x MnO₃ points to good potentialities of the latter system from the viewpoint of applications.     

1/<Emphasis Type="Italic">E</Emphasis><Superscript>2</Superscript> Law: Solution of the Unsolved Problem in the Physics of Ferroelectrics

An unusual frequency dependence of a coercive field observed in polycrystalline ferroelectric films of Pb(Zr_{1 ? x}Ti_x)O₃ solid solutions in a wide frequency range has been explained within the model of surface sources emitting thin ferroelectric domains with reversed polarization. This model makes it possible to interpret experimental data as the manifestation of the coercivity paradox in polycrystalline films and predicts the existence of the limiting frequency for switching of domains in agreement with the experiment. The proposed mechanism of polarization switching explains the observed temperature dependence of the activation field E_a ∝ T^?1/2. Furthermore, it predicts an increase in the activation energy for the nucleation of domains with an increase in the size of the source, indicating that the coercive field increases with the degradation of small     

Phase Diagram of a Generalized ABC Model on the Interval

We study the equilibrium phase diagram of a generalized ABC model on an interval of the one-dimensional lattice: each site i=1,…,N is occupied by a particle of type α=A,B,C, with the average density of each particle species N _α /N=r _α fixed. These particles interact via a mean field nonreflection-symmetric pair interaction. The interaction need not be invariant under cyclic permutation of the particle species as in the standard ABC model studied earlier. We prove in some cases and conjecture in others that the scaled infinite system N→∞, i/N→x∈[0,1] has a unique density profile ρ _α (x) except for some special values of the r _α for which the system undergoes a second order phase transition from a uniform to a nonuniform periodic profile at a critical temperature \(T_{c}=3\sqrt{r_{A} r_{B} r_{C}}/2\pi\).     

Dielectric properties of lead zirconate titanate films synthesized through oxidation of metal layers

Films of the composition Pb(Zr _x Ti_1?x )O₃ are prepared by magnetron sputtering of metal layers onto titanium substrates with subsequent heat treatment in an oxygen atmosphere. The electrical properties of the samples prepared are investigated using impedance spectroscopy in the frequency range from 10² to 5 × 10⁵ Hz at temperatures of 300–750 K. The temperature dependences of the permittivity and the dielectric loss tangent at different frequencies exhibit a behavior typical of ferroelectrics and indicate the occurrence of a ferroelectric phase transition at temperatures close to T = 663 K. Analysis of the imaginary part of the electric modulus has revealed two possible relaxation mechanisms. The activation energy for dc electrical conduction in the paraelectric phase is determined.