Phase transition in CdHfO<Subscript>3</Subscript>

The phase transition from an orthorhombic phase (space group Pnma) to a rhombohedral phase (space group R3m) of the CdHfO₃ hafnate is investigated using methods of structural analysis. It is shown that crystal lattices of both phases contain polar structural units (octahedra, cubooctahedra). On this basis, it is assumed that the orthorhombic and rhombohedral phases of the CdHfO₃ compound are the antiferroelectric and ferroelectric phases, respectively.     

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.     

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.     

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.     

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.     

Thermophysical studies of the phase transitions in (NH<Subscript>4</Subscript>)<Subscript>3</Subscript>NbOF<Subscript>6</Subscript> crystals

The thermophysical properties of oxyfluoride (NH₄)₃NbOF₆ were studied in detail over wide ranges of temperatures and pressures. At atmospheric pressure, a sequence of four structural phase transitions was established with the following changes in entropy: ΔS ₁ = Rln 2.7, δS ₂ = Rln38.3, ΔS ₃ = 0.08R, and ΔS ₄ = 0.17R. An external hydrostatic pressure was found to narrow the region of existence of the initial cubic phase. A triple point was detected in the p-T diagram; at a pressure above 0.07 GPa, the transition between the tetragonal and monoclinic phases occurs through a distorted high-pressure phase.     

Structural transformations of K<Subscript>3</Subscript>H(SO<Subscript>4</Subscript>)<Subscript>2</Subscript> crystals with variations in temperature

Single crystals of the K₃H(SO₄)₂ compound are investigated using X-ray diffraction on Xcalibur S and Bruker diffractometers. The structure of the low-temperature monoclinic phase is refined (space group C2/c, z = 4, a = 14.698(1) Å, b = 5.683(1) Å, c = 9.783(1) Å, β = 103.01(1)°, T = 293 K, Bruker diffractometer), the structural phase transition is revealed, and the structure of the high-temperature trigonal phase is determined (space group R \(\bar 3\) m, z = 3, a = 5.73(1) Å,c = 21.51(1) Å,T = 458 K, Xcalibur diffractometer).     

Superposition of M<Subscript>5</Subscript>X<Subscript>5</Subscript> superstructures and X-ray diffraction in TiO<Subscript>1.0</Subscript> titanium monoxide

The interpretation of diffraction spectra of ordered high-temperature phases of solid solutions and strongly nonstoichiometric compounds is discussed. It has been shown that variations of the intensities of superstructure reflections, which cannot be explained within simple ordering models, can be due to the superposition of superstructures with different symmetries in the matrix of the basis crystal structure. Using an example of atom–vacancy ordering in TiO_1.0 titanium monoxide, a model of the order–order transition state formed by the superposition of low-temperature monoclinic (space group A2/m (C2/m)) and high-temperature cubic (space group Pm3?m) M₅X₅ superstructures has been proposed. It has been shown that the transition state is thermodynamically equilibrium and should be implemented instead of the M₅X₅ cubic superstructure. The transition state model can be considered as an M_(5–i)X_(5–i) superstructure (i = 1, 14/18, 11/18) with the monoclinic symmetry (space group P1m1).     

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.     

Phase transitions in polarized samples of multicomponent solid solutions based on lead zirconate titanate

The physical properties of multicomponent solid solutions that are based on lead zirconate titanate and belong to the rhombohedral part of the phase diagram are investigated. The conditions for the existence of the R3c, R3m, and P4mm phases in polarized samples are determined. The region of existence of the relaxor phase is revealed.     

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.     

Comparative study of the spectral and structural properties of EuAl<Subscript>3</Subscript>(BO<Subscript>3</Subscript>)<Subscript>4</Subscript> single crystals with different morphologies

Europium alumoborate EuAl₃(BO₃)₄ microcrystals have been synthesized by the flux method at a temperature of 1050°C. The obtained crystals have different morphologies: both plane-faced and skeletal microcrystals have been observed. Infrared spectroscopy, cathodeluminescence, and transmission electron microscopy investigations of individual microcrystals showed that the spectral and structural characteristics of these morphological forms coincide. The obtained crystals are characterized by the rhombohedral symmetry (sp. gr. R32) with the inclusions of C2/c monoclinic phase domains.     

Stabilization of Ferromagnetism in BiFeO<Subscript>3</Subscript>:Ho at Hydrostatic Pressure

The isothermal magnetization of the Bi_{1 – x}Ho _x FeO₃ (x = 0?0.2) multiferroic has been studied at a hydrostatic pressure up to 9 GPa in the range of room temperatures. A new anomaly at P_C ≈ 3.81 GPa related to intermediate phases between the structural transition R3c → Pnma has been found against the background of the pressure-induced antiferromagnetic ordering in BiFeO₃ (BFO) at P ≈ 2.59 GPa. It is established that the ferromagnetic behavior under pressure depends on the Ho impurity concentration: P_C decreases at 0.05 ≤ x ≤ 0.1 because of the decrease in R3c bond lengths in the structure, and the stabilization of ferromagnetism is implemented at 0.1 ≤ x ≤ 0.2 probably because of the coexistence of the R3c and Pnma phases. The results of studies indicate that, in Bi_{1 – x}Ho _x FeO₃ with x = 0.2, the transition pressure P_C = 3.7 GPa exceeds the values for BFO doped with other 4f elements (Eu, Y, Sm) in the region R3c → Pnma of the transition.     

Optical investigations of structural phase transformations in PbMg<Subscript>1/3</Subscript>Nb<Subscript>2/3</Subscript>O<Subscript>3</Subscript>-<Emphasis Type="Italic">x</Emphasis>PbTiO<Subscript>3</Subscript> single crystals located at the morphotropic phase boundary

A study has been made of the effect of a dc electric field (0 < E < 4 kV/cm) on the optical transmittance of single-crystal compounds PbMg_1/3Nb_2/3O₃-xPbTiO₃ (PMN-xPT) located at the boundaries of the morphotropic region (x = 32.0 and 36.5%) and directly at the center of the morphotropic region (x = 35%). It is shown that, at temperatures close to the morphotropic phase transition point, the electric field induces two phase transitions in PMN-32PT and PMN-35PT crystals and only one phase transition in PMN-36.5PT. The tetragonal (T) phase induced in all three compounds remains stable after the electric field is removed only in crystals with x = 35.0 and 36.5%, whereas the T phase is metastable and transforms into the monoclinic M _c phase after the field is switched off in the PMN-32PT crystals lying at the boundary of the morphotropic region on the rhombohedral side. It is found that the electric-field-induced intermediate phase M _c in PMN-35PT is inhomogeneous and that M _c transforms into the tetragonal phase in a continuous transition. It is suggested that only the presence of a third orthorhombic phase can account for the continuous character of the transition between the M _c and T phases in PMN-35PT crystals. The results obtained are interpreted in terms of the Devonshire theory for strongly anharmonic crystals. The E-T phase diagrams are constructed for all the crystals.     

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.     

Preparation,Structure, and Dielectric and Magnetic Properties of SrFe<Subscript>2/3</Subscript>W<Subscript>1/3</Subscript>O<Subscript>3</Subscript> Ceramics

Polycrystalline samples of SrFe_2/3W_1/3O₃ (SFWO) ceramic were obtained by solid-phase reactions with subsequent sintering using conventional ceramic technology. X-ray diffraction analysis showed that at room temperature, the SFWO ceramic is single-phase and has a perovskite-type structure with tetragonal symmetry and parameters a = 3.941(9) Å, c = 3.955(6) Å, and c/a = 1.0035. In studying the magnetic properties and the Mössbauer effect in SFWO ceramics, it is found that the material is a ferrimagnet, and the iron ions are only in the valence state of Fe³⁺. It is suggested that in the temperature range of T = 150–210°C, a smeared phase transition from a cubic (paraelectric) phase to a tetragonal (ferroelectric) phase takes place in SFWO with decreasing temperature.     

Chiral and deconfinement phase transitions in QED<Subscript>3</Subscript> with finite gauge boson mass

Based on the experimental observation that there is a coexisting region between the antiferromagnetic (AF) and d-wave superconducting (dSC) phases, the influences of gauge boson mass m _a on chiral symmetry restoration and deconfinement phase transitions in QED₃ are investigated simultaneously within a unified framework, i.e., Dyson–Schwinger equations. The results show that the chiral symmetry restoration phase transition in the presence of the gauge boson mass m _a is a typical second-order phase transition; the chiral symmetry restoration and deconfinement phase transitions are coincident; the critical number of fermion flavors N ^c _f decreases as the gauge boson mass m _a increases, which implies that there exists a boundary that separates the N ^c _f –m _a plane into chiral symmetry breaking/confinement region for (N ^c _f , m _a ) below the boundary and chiral symmetry restoration/deconfinement region for (N ^c _f , m _a ) above it.     

Phase transitions in the oxyfluoride (NH<Subscript>4</Subscript>)<Subscript>3</Subscript>NbOF<Subscript>6</Subscript>

(NH₄)₃NbOF₆ single crystals were grown, polarization-optical studies were performed, and birefringence was measured over the temperature range 90–500 K. A sequence of first-order structural phase transitions was found at temperatures T _1↓ = 259.7 K and T _2↓ = 257.7 K with temperature hysteresis δT ₁ = 0.9 K and δT ₂ = 1.9 K. The transitions are accompanied by twinning and the following change in the crystal symmetry: cubic ? tetragonal ? monoclinic. Optical second harmonic generation is found to occur at room temperature, which indicates that the cubic phase is not centrosymmetric. It is assumed that the phase transitions are ferroelastic and ferroelectric in nature.     

Phase transitions of SC(NH<Subscript>2</Subscript>)<Subscript>2</Subscript> ferroelectrics in Al<Subscript>2</Subscript>O<Subscript>3</Subscript>-based nanoporous matrices

Temperature dependences of the linear permittivity ε' and the third harmonic amplitude γ_3ω of composites prepared by introducing ferroelectrics SC(NH₂)₂ into matrices of porous aluminum oxide Al₂O₃ with pore sizes 60 and 100 nm are determined. It is found that temperature T _c of the ferroelectric phase transition and the temperature T _i of the phase transition from incommensurable phase to the paraphrase increase significantly. The transition shifts increase as pore diameters decrease.     

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.