Structural and magnetic phase transformations in the BiFeO<Subscript>3</Subscript>-CaFe<Subscript>0.5</Subscript>Nb<Subscript>0.5</Subscript>O<Subscript>3</Subscript> system

The crystal structure and magnetic properties of the Bi_{1 ? x} Ca _x Fe_{1 ? x/2}Nb _x/2O₃ system were studied. It is shown that, at x ≤ 0.15, the unit-cell symmetry of solid solutions is rhombohedral (space group R3c). Solid solutions with x ≥ 0.3 have an orthorhombic unit cell (space group Pbnm). The rhombohedral compositions are antiferromagnetic, while the orthorhombic compositions exhibit a small spontaneous magnetization due to Dzyaloshinski?-Moriya interaction. In CaFe_0.5Nb_0.5O₃, the Fe³⁺ and Nb⁵⁺ ions are partially ordered and the unit cell is monoclinic (space group P2₁/n). In the concentration range 0.15 < x < 0.30, a two-phase state (R3c + Pbnm) is revealed.     

The Nernst-Ettingshausen coefficient in the normal phase of doped HTSCs of the YBa<Subscript>2</Subscript>Cu<Subscript>3</Subscript>O<Subscript>y</Subscript> system

The temperature dependence of the Nernst-Ettingshausen coefficient Q(T) in the normal phase of doped HTSCs of the yttrium system was studied. The main features characterizing the behavior of this coefficient were revealed, and the character and mechanism of the effect that various nonisovalent substituents exert on the Q(T) dependence were analyzed. It is shown that the narrow-band model permits one not only to describe all the specific features observed in the Q(T) curves but also to perform a simultaneous quantitative analysis of the temperature dependences of four kinetic coefficients (the electrical resistivity and the Seebeck, Hall, and Nernst-Ettingshausen coefficients) with the use of a common set of model parameters characterizing the band structure and carrier system in the normal phase of an HTSC. This approach was employed to determine the carrier mobilities and the asymmetry of the dispersion curve in the systems studied (YBa₂Cu₃O_y, y = 6.37–6.91; YBa₂Cu_3?xCo_xO_y, x = 0–0.3; Y_1?xCa_xBa₂Cu₃O_y, x = 0–0.25; Y_1?xCa_xBa_2?xLa_xCu₃O_y, x = 0–0.5) and to analyze the effect of the substitutions involved on the variation of these parameters.     

Weak ferromagnetism in BiFeO<Subscript>3</Subscript>-based multiferroics

The magnetic properties of the Bi_{1 ? x} Ln _x FeO₃ (Ln is a rare-earth ion), Bi_{1 ? x} A _x FeO_{3 ? x/2} (A is an alkali earth ion), and BiFe_{1 ? x} Ti _x O_{3 + δ} solid solutions in magnetic fields up to 14 T have been studied. The concentration ranges of the existence of the ferroelectric phase described by the space group R3c have been determined. It is shown that the substitution of the rare-earth ions for the Bi³⁺ ions leads to a sharp decrease in the critical fields inducing the metamagnetic transition from a modulated antiferromagnetic state to a weakly ferromagnetic one; however, the modulated structure in the concentration range of the R3c phase is mainly retained. The substitution of the alkali earth ions (x ～ 0.1) for the bismuth ions leads to the total destruction of the modulated structure and to the implementation of the weakly ferromagnetic state within the R3c phase. A homogeneous weakly ferromagnetic state has been revealed when the Ti⁴⁺ ions (x = 0.1) are substituted for the Fe³⁺ ions in the ferroelectric R3c phase.     

Symmetry and lattice parameters of SrTiO<Subscript>3</Subscript>-PbTiO<Subscript>3</Subscript> solid solutions

The lattice parameters of ceramic samples of (1 ? x)SrTiO₃-xPbTiO₃ solid solutions are measured at room temperature. It is found that the samples have cubic symmetry in the concentration range x = 0?0.3 and tetragonal symmetry for x > 0.3. The lattice parameter a is virtually independent of temperature for x < 0.8 and slightly decreases in the range x = 0.8?1.0, while the lattice parameter c increases with increasing x. The reduced cubic parameter varies nonlinearly and deviates from Vegard’s linear law as the concentration x increases.     

High-temperature complex impedance and modulus spectroscopic studies of doped Na<Subscript>0.5</Subscript>Bi<Subscript>0.5</Subscript>TiO<Subscript>3</Subscript>-BaTiO<Subscript>3</Subscript> ferroelectric ceramics

Lead-free Na_0.5Bi_0.5TiO₃ (NBT) and (1 ? x)Na_0.5Bi_0.5TiO₃ + xBaTiO₃ with x = 0.1 and 0.2 (where x = 0.1 and 0.2 are named as NBT1 and NBT2, respectively), (1 ? y)Na_0.5Bi_0.5TiO₃ + yBa_0.925Nd_0.05TiO₃ with y = 0.1 and 0.2 (where y = 0.1 and 0.2 are named as NBT3 and NBT4, respectively)-based relaxor ferroelectric ceramics were prepared using the sol-gel method. The crystal structure was investigated by X-ray diffraction (XRD) at room temperature (RT). The XRD patterns confirmed the presence of the rhombohedral phase in all the samples. The electrical properties of the present NBT-based samples were investigated by complex impedance and the modulus spectroscopy technique in the temperature range of RT–600 °C. The AC conductivity was found to increase with the substitution of Ba²⁺ ions to the NBT sample whereas it significantly decreased with the addition of Nd³⁺ ions. The more anion vacancies in Ba-added samples and the lower anion vacancies in Nd-added samples were found to be responsible for higher and lower conductivities, respectively.     

Microstructure and superconducting properties of the DyBaCuO ceramic doped with Na<Subscript>2</Subscript>CO<Subscript>3</Subscript>, NaCl,and KClO<Subscript>3</Subscript>

This paper reports on a study of the effect of doping with Na₂CO₃, NaCl, and KClO₃ salts on the microstructure and superconducting characteristics of ceramics with nominal compositions Dy_{1 ? x} M _x Ba₂Cu_{3 ? y} O_{7 ? δ} and DyBa₂Cu_{3 ? y} O_{7 ? δ} : M _x for M = Na, K; x = 0.2, 0.3, and y = 0, 0.2. The microstructure was characterized by transmission electron microscopy with local energy-dispersive x-ray in situ analysis (probe size ～1 nm). An analysis shows that none of the doping elements (Na, K, or Cl) enters into 123 grains in sizable amounts and that, as a result, the critical temperature of the superconducting transition remains practically constant in the range 90.0–93.5 K. Potassium and chlorine segregate at grain boundaries. It is shown that grain-boundary segregation of chlorine leads to a substantial increase in the superconducting critical current (by a factor 3–5 at 70 K) as compared to the undoped sample. The possible mechanisms accounting for the effect of Cl on intergrain critical current are discussed.     

Optical studies of phase transitions in the (NH<Subscript>4</Subscript>)<Subscript>3</Subscript>Ti(O<Subscript>2</Subscript>)F<Subscript>5</Subscript> crystal

Polarization-optical study of twinning and measurements of the Raman spectra and birefringence in oxyfluoride (NH₄)₃Ti(O₂)F₅ were carried out over the temperature range 90–350 K. Phase transitions were detected at temperatures T ₀₁ = 266 K (second-order transition) and T ₀₂ = 225 K (first order). It is assumed that the crystal symmetry is changed as follows: Fm3m ? I4/mmm ? I4/m. Anomalies of the spectral parameters are established in the frequency range of internal vibrations of ammonium ions and Ti(O₂)F₅ complexes. An analysis of the results shows that the transition at T ₀₁ is likely due to small shifts of the tetrahedral groups from their position on the triad axis and that the transition at T ₀₂ is due to fluorine-oxygen ordering of Ti(O₂)F₅ complexes.     

Effect of KNbO<Subscript>3</Subscript> modification on structural,electrical and magnetic properties of BiFeO<Subscript>3</Subscript>

The polycrystalline samples of (Bi_1?x K _x ) (Fe_1?x Nb _x ) O₃ (BKFN) for x = 0.0, 0.1, 0.2 and 0.3 were synthesized by a solid-state reaction method. The X-ray diffraction patterns of BKFN exhibit that the addition of KNbO₃ in BiFeO₃ gradually changes its structure from rhombohedral to pseudocubic. The analysis of scanning electron micrograph clearly showed that the sintered samples have well-defined and uniformly distributed grains. Addition of KNbO₃ to BiFeO₃ enhances the dielectric, ferroelectric and ferromagnetic properties of BiFeO₃. Detailed studies of impedance and related parameters of BKFN using the complex impedance spectroscopic technique exhibit the significant contributions of grain and grain boundaries in the resistive and transport properties of the materials. Some oxygen vacancies created in the ceramic samples during high-temperature processing play an important role in the conduction mechanism. The leakage current or tangent loss of BiFeO₃ is greatly reduced on addition of KNbO₃ to the parent compound BiFeO₃. Preliminary studies of ferroelectric and magnetic characteristics of the samples reveal the existence of ferroelectric, and weak ferromagnetic ordered ceramics.     

Effect of heterovalent substitution of rare-earth elements on the magnetic and transport properties of YBa<Subscript>2</Subscript>Cu<Subscript>3</Subscript>O<Subscript>7</Subscript>

The Y_{(1 ? x} Ce _x Ba₂Cu₃O₇ system with low cerium concentrations has been synthesized. The cerium solubility limit measured using x-ray powder diffraction analysis is about 2.4 at. %. The temperature dependences of the magnetization M(T) are measured for samples cooled in a magnetic field (FC) and in a zero field (ZFC). The difference between the magnetizations M _ZFC-M _FC at 77.4 K, which is proportional to the pinning potential, passes through a maximum at x = 0.0156. This concentration corresponds to the average distance (equal to eight lattice constants) between the impurity ions in the plane of the rare-earth elements, which is comparable to the diameter of Abrikosov vortices in YBa₂Cu₃O₇.     

Comparative study of solid-state reaction and sol-gel process for synthesis of Zr-doped Li<Subscript>0.5</Subscript>La<Subscript>0.5</Subscript>TiO<Subscript>3</Subscript> solid electrolytes

We investigated the synergistic influences of synthesis methods (solid-state reaction vs. sol-gel process) and Zr⁴⁺ doping on the structure and ionic conductivity of perovskite-structured Li_0.5La_0.5TiO₃ (LLTO) solid electrolytes. The lithium-ion conductivity of Li_0.5La_0.5Ti_1???x Zr _x O₃ ceramic specimens was evaluated as a function of x value and compared carefully between those two synthesis methods. Regarding the conductivity, sol-gel process is better for the synthesis of LLTO than solid-state reaction. As a result, the highest grain conductivity is obtained in the sol-gel-derived pure LLTO sample with x?=?0, reaching 1.10?×?10^?3 S?·?cm^?1. Partial substitution of Zr⁴⁺ enlarges the LLTO’s grain aggregate size and increases the total superficial area of aggregates. Consequently, Zr⁴⁺ substitution not only affects the grain (bulk) conductivity, but more importantly, also improves the grain boundary conductivity and the total conductivity. The highest total conductivity is 5.84?×?10^?5 S?·?cm^?1 with x?=?0.04 by sol-gel process.     

Spontaneous ferroelectricity in strained low-temperature monoclinic Fe<Subscript>3</Subscript>O<Subscript>4</Subscript>: A first-principles study

As a single-phase multiferroic material, Fe₃O₄ exhibits spontaneous ferroelectric polarization below 38 K. However, the nature of the ferroelectricity in Fe₃O₄ and effect of external disturbances such as strain on it remains ambiguous. Here, the spontaneous ferroelectric polarization of low-temperature monoclinic Fe₃O₄ was investigated by first-principles calculations. The pseudo-centrosymmetric FeB42–FeB43 pair has a different valence state. The noncentrosymmetric charge distribution results in ferroelectric polarization. The initial ferroelectric polarization direction is in the -x and -z directions. The ferroelectricity along the y axis is limited owing to the symmetry of the Cc space group. Both the ionic displacement and charge separation at the FeB42–FeB43 pair are affected by strain, which further influences the spontaneous ferroelectric polarization of monoclinic Fe₃O₄. The ferroelectric polarization along the z axis exhibits an increase of 45.3% as the strain changes from 6% to -6%.     

Crystal-structure and magnetic phase transformations in solid solutions of BiFeO<Subscript>3</Subscript>-AFe<Subscript>0.5</Subscript>Nb<Subscript>0.5</Subscript>O<Subscript>3</Subscript> (A = Ca,Sr, Ba,Pb)

Solid solutions of Bi_{1 ? x} A _x (Fe_{1 ? x/2}Nb _x/2)O₃, where A = Ca, Ba, and Pb, are obtained and their crystal structure and magnetic properties are investigated. It is shown that for A = Ca and x ≈ 0.15, the symmetry of the unit cell changes from rhombohedral (space group R3c) to orthorhombic (Pbnm). The transformation leads to the emergence of spontaneous magnetization due to the Dzyaloshinskii-Moriya interaction. Solid solutions with A = Pb remain rhombohedral up to a concentration of x = 0.3. Spontaneous magnetization sharply increases in the compound with x ≈ 1 at low temperatures and is due to the formation of the spin-glass component.     

Optical and dielectric studies of phase transitions in single crystals of NaNbO<Subscript>3</Subscript>-Gd<Subscript>1/3</Subscript>NbO<Subscript>3</Subscript> solid solutions

The temperature dependences of the permittivity ? and the false-color image patterns obtained by the rotating polarizer method for single crystals of (1 ? x)NaNbO_3?x Gd_1/3NbO₃ (x = 0.003, 0.090) solid solutions with different degrees of diffuseness of the phase transition are investigated. A multifractal analysis of the false-color images has revealed anomalies in the temperature dependences of the parameter ?_∞ of the multifractal spectrum. For a sample with a sharp phase transition (x ≈ 0.003), the temperature of this anomaly is in good agreement with the temperature of the jumps in the permittivity ?(T) and birefringence. For an NNG crystal with x ≈ 0.09, which exhibits a diffuse maximum of ?(T), the temperatures of the anomalies of ?_∞(T) differ in the central and peripheral regions, which correlates with the distribution of Gd over the crystal.     

Raman scattering spectroscopy of inclusions of carbon in Al<Subscript>2</Subscript>O<Subscript>3</Subscript> films and its solid solutions with HfO<Subscript>2</Subscript>

We apply Raman scattering spectroscopy to study the nature of carbon inclusions in Al₂O₃ and (HfO₂) _x (Al₂O₃)_{1 ? x} films deposited using volatile complex compounds. Raman spectra of the films under investigation contain D and G vibrational modes, which indicate that carbon clusters of the sp ² configuration tend to form in the films. We estimate the size of clusters from the integrated intensity ratio I _D /I _G and find it to be in the range of 14–20 Å. The content of hydrogen in carbon clusters is calculated from the height of the photoluminescence pedestal and is found to vary from 14 to 30 at % depending on the regime of the film’s synthesis.     

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.     

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     

Oxygen isotope effect in chromium-doped Pr<Subscript>0.5</Subscript>Ca<Subscript>0.5</Subscript>MnO<Subscript>3</Subscript> manganites

The effect of oxygen isotope substitution on the properties of Pr_0.5Ca_0.5Mn_{1 ? x} Cr _x O₃ manganites (x = 0, 0.02, 0.05) have been studied. The introduction of chromium favors (i) the decomposition of a charge-ordered state and (ii) the appearance of a ferromagnetic metallic phase in Pr_0.5Ca_0.5Mn_{1 ? x} Cr _x ^16–18O₃. The isotope substitution ¹⁶O → ¹⁸O leads to a decrease in the content of the ferromagnetic phase, an increase in the charge-ordering transition temperature (T _CO), and a decrease in the ferromagnetic transition temperature (T _FM). The isotope mass exponent is evaluated.     

Acoustic emission and thermal expansion of Pb(Mg<Subscript>1/3</Subscript>Nb<Subscript>2/3</Subscript>)O<Subscript>3</Subscript> and Pb(Mg<Subscript>1/3</Subscript>Nb<Subscript>2/3</Subscript>)O<Subscript>3</Subscript>-PbTiO<Subscript>3</Subscript> crystals

The temperature dependence of the elongation per unit length for Pb(Mg_1/3Nb_2/3)O₃ crystals unannealed after growth and mechanical treatment is investigated in the course of thermocycling. It is revealed that this dependence deviates from linear behavior at temperatures below 350°C. The observed deviation is characteristic of relaxors, is very small in the first cycle, increases with increasing number n of thermocycles, and reaches saturation at n≥3. In the first cycle, a narrow maximum of the acoustic emission activity is observed in the vicinity of 350°C. In the course of thermocycling, the intensity of this maximum decreases and becomes zero at n>3. For (1?x)Pb(Mg_1/3Nb_2/3)O₃-xPbTiO₃ crystals, the dependence of the temperature of this acoustic emission maximum on x exhibits a minimum. It is assumed that the phenomena observed are associated with the phase strain hardening due to local phase transitions occurring in compositionally ordered and polar nanoregions.     

Lattice dynamics of BiFeO<Subscript>3</Subscript> under hydrostatic pressure

The vibrational frequencies of the BiFeO₃ crystal lattice in the cubic phase (Pm3m) and the rhombohedral paraelectric phase (R3c) are calculated in terms of the ab initio model of an ionic crystal with the inclusion of the dipole and quadrupole polarizabilities. In the ferroelectric phase with the symmetry R3c, the calculated spontaneous polarization of 136 μC cm^?2 agrees well with the experimental data. The dependences of the unit cell volume, the elastic modulus, and the vibrational frequencies on the pressure are calculated. It is found that the frequency of an unstable ferroelectric mode in both the cubic (Pm3m) and rhombohedral (R3c) phases are almost independent of the applied pressure, in contrast to classical ferroelectrics with a perovskite structure, where the ferroelectric instability is very sensitive to a variation in the pressure.     

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.