Dual structures and transition regions in <Emphasis Type="Italic">x</Emphasis>PbTiO<Subscript>3</Subscript>-(1−<Emphasis Type="Italic">x</Emphasis>)Pb(Zn<Subscript>1/3</Subscript>Nb<Subscript>2/3</Subscript>)O<Subscript>3</Subscript> crystals

Model concepts of dual structures are developed as applied to crystals of xPbTiO₃-(1?x)Pb(Zn_1/3Nb_2/3)O₃ solid solutions in the range 0 ≤ x ≤ 0.08. The conditions of the formation of dual structures upon partial and complete relaxation of internal mechanical stresses are considered. A new model of transition regions is proposed for analyzing several variants of changing the unit cell parameters that satisfy the condition of complete stress relaxation inside the transition regions in crystals at concentrations x = 0.045 and 0.08. The influence of the intermediate phase P4mm and stability of its 90° domain structure on the formation of dual structures at x ≥ 0.045 is discussed.     

Phase transitions and optical properties in 〈001〉 (1−<Emphasis Type="Italic">x</Emphasis>)PbZn<Subscript>1/3</Subscript>Nb<Subscript>2/3</Subscript>O<Subscript>3</Subscript>−<Emphasis Type="Italic">x</Emphasis>PbTiO<Subscript>3</Subscript> single crystals

The effect of a constant electric field (0 < E < 5 kV/cm) on the optical properties of PbZn_1/3Nb_2/3O₃?xPbTiO₃ (PZN-xPT) crystals with x = 7 and 9% has been analyzed. It has been shown that, at temperatures close to the temperature of the transition from the rhombohedral [R(X)] phase to the tetragonal (T) phase, two induced phase transitions are observed in the electric field, which are associated with the appearance of new intermediate phases M_a and M_c [R(X)-M_a-M_c-T]. Correlation between these two transitions and the PbTiO₃ content x has been found. The E-T phase diagrams have been obtained. The M_c phase in PZN-9PT crystals is found to remain the ground state after the removal of the electric field, whereas the M_c phase in PZN-7PT crystals is metastable and is transformed into the M_a phase after the removal of the electric field.     

Calorimetry of (1 − <Emphasis Type="Italic">x</Emphasis>)BaTiO<Subscript>3</Subscript>-<Emphasis Type="Italic">x</Emphasis>Ba(Mg<Subscript>1/3</Subscript>Nb<Subscript>2/3</Subscript>)O<Subscript>3</Subscript> solid solutions

Phase transitions in ceramic samples of (1 ? x)BaTiO₃-xBa(Mg_1/3Nb_2/3)O₃ solid solutions were studied by differential scanning calorimetry for x = 0, 0.01, 0.02, and 0.03 in the temperature ranges 255–290 K and 310–410 K. The experimental data obtained were used to derive the thermodynamic parameters of the phase transitions occurring at T _c ≈ 400?300 K and T ₁ ≈ 290?300 K and construct the concentration phase diagram.     

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.     

Intermediate phases in [111]- and [001]-oriented PbMg<Subscript>1/3</Subscript>Nb<Subscript>2/3</Subscript>O<Subscript>3</Subscript>–29PbTiO<Subscript>3</Subscript> single crystals

Phase transformations in [111]- and [001]-oriented PbMg_1/3Nb_2/3O₃–29PbTiO₃ single crystals have been studied using dielectric and optical measurements before and after applying an electric field. It is shown that the subsequence of phase transitions rhombohedral (R)—tetragonal (T)—cubic (C) phases is observed in nonpolarized samples of both orientations as temperature increases. In the [111]-oriented crystal, an additional intermediate monoclinic phase (it is possible, M _a ) is induced after preliminary polarization at room temperature and the R–M _a –T–C phase transitions are observed on heating. In the [001]-oriented crystal, after its polarization, the monoclinic phase forms instead of the rhombohedral phase even at room temperature and the M _a –T–C transitions occur on heating. The results are discussed from the point of view of the existence polar nanoregions with different local symmetries in a glasslike matrix.     

Ion ordering and ferroelectricity in Pb(<Emphasis Type="Italic">B</Emphasis>′<Subscript>0.5</Subscript><Emphasis Type="Italic">B</Emphasis>″<Subscript>0.5</Subscript>)O<Subscript>3</Subscript> perovskites

The Pb(B′_0.5 B″_0.5)O₃ ferroelectric with a perovskite structure and the antiferroelectric of the same composition are usually considered to be the same compound regardless of whether the B′ and B″ ions in the octahedral positions are ordered even though they differ substantially in behavior. It is established that ion ordering can also occur in PZT-type solid solutions of the composition Pb(B′_x B″_{1 ? x} )O₃ with x ≈ 0.5. The mechanism of the influence of ion ordering on the behavior of crystals of both complex perovskites and PZT-type ceramics is discussed.     

Critical evolution of the local order parameters related to the nanopolar domains in Pb(Mg<Subscript>1/3</Subscript>Nb<Subscript>2/3</Subscript>)O<Subscript>3</Subscript> ceramics

In the present paper, Pb(Mg_1/3Nb_2/3)O₃ (PMN) ceramics prepared by the columbite method were investigated. The dielectric study indicates typical relaxor properties, with a frequency dispersion in the range of 200–350 K. The relaxor-to-paraelectric phase transition was evidenced by the continuous decrease of the local order parameter derived from the permittivity-temperature data. As a result of the critical behavior, the main Raman modes show anomalies at: (i) ∼150 K; (ii) ∼220 K (i.e. close to the critical temperature reported for the field-induced ferroelectric state in PMN single crystal); (iii) ∼260 K (i.e. the temperature of the permittivity maximum); (iv) ∼350 K (the temperature for initiation of the cluster freezing process T ^*); (v) ∼620 K (Burns temperature). The frequency split of the doublet at ∼605 and ∼500 cm⁻¹ presents a critical behavior related to the local symmetry lowering and to the structure ordering due to a phase transformation which takes place below T ^*. The tunability in the paraelectric state was interpreted in terms of reorientation of the non-interacting nanopolar clusters in a double-well potential. The temperature dependence of the nanopolar domain size also shows anomalies in the range of T ^*. The size and dynamics of the polar nanodomains is essential in determining the functional properties of the Pb(Mg_1/3Nb_2/3)O₃ relaxor.     

Thermal expansion of (Sr<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript>La<Subscript>x</Subscript>)<Subscript>3</Subscript>Ru<Subscript>2</Subscript>O<Subscript>7</Subscript> single crystals at low temperatures

For single-crystal samples of the (Sr_1?xLa_x)₃Ru₂O₇ ruthenates, the temperature dependence of the thermal expansion coefficient α(T)) is measured in the range 4.2–80 K. The effect of magnetic fields H ≤ 3.5 T on thermal expansion is analyzed. It is found that the (Sr_1?xLa_x)₃Ru₂O₇ ruthenates exhibit an anomalous (negative) thermal expansion coefficient in the temperature range T ≤ 18 K. The position and width of the anomaly revealed in the temperature dependence of the thermal expansion coefficient α(T)) depend substantially on the magnetic field. The origin of the thermal expansion anomaly in ruthenates, the correlation of this anomaly with the stability of the crystal lattice, and the common nature of the anomalies in the thermal properties of ruthenates and high-temperature superconductors are discussed.     

Structural phase transition in (1−<Emphasis Type="Italic">x</Emphasis>)SrTiO<Subscript>3</Subscript>+<Emphasis Type="Italic">x</Emphasis>SrMg<Subscript>1/3</Subscript>Nb<Subscript>2/3</Subscript>O<Subscript>3</Subscript> solid solutions

The temperature dependences of the shear modulus and internal friction in ceramic samples of (1?x)SrTiO₃+xSrMg_1/3Nb_2/3O₃ solid solutions were studied by the torsional vibration method in the range 80–300 K. It was established that the temperature T _a of the O _h ¹ -D _4h ¹⁸ structural phase transition in these solid solutions increases with increasing x, although the lattice constant also increases. A discussion is presented of the contributions to the T _a (x) dependence due to a change in the volume and changes caused by the presence of a second solid-solution component (the impurity contribution). It is also shown that the defect-induced relaxation revealed earlier in a study of the dielectric properties of these materials manifests itself in internal friction peaks.     

Normal state conduction in Gd(Ba<Subscript>2–x</Subscript>Pr<Subscript>x</Subscript>)Cu<Subscript>3</Subscript>O<Subscript><Emphasis Type="Bold">7+δ</Emphasis></Subscript>

The normal state resistivity of single phase polycrystalline Gd(Ba_2–xPr_x)Cu₃O₇₊ samples with 0.0x0.50 have been investigated. There is a distinct metal-insulator transition at and a superconductor-insulator transition at with the increase of x. The two-dimensional variable range hopping is dominant in the normal state resistivity of the samples. The localization length, hopping range, and hopping energy of carriers show that Pr doping strongly localizes the carriers in normal state, and finally causes the suppression of superconductivity.     

High-temperature study of SrFe<Subscript>1 − <Emphasis Type="Italic">x</Emphasis></Subscript>Mo<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>O<Subscript>3−<Emphasis Type="Italic">z</Emphasis></Subscript> perovskites

The structure of high-temperature SrFe_{1 − x} Mo _x O_{3 − z} (0 ≤ x ≤ 0.5) phases was studied. Such studies are necessary to understand the mechanism of oxygen transport in membrane materials used for high-temperature oxygen separation.     

Thermal properties of K<Subscript>3</Subscript>Li<Subscript>2−<Emphasis Type="Italic">x</Emphasis></Subscript>Nb<Subscript>5+<Emphasis Type="Italic">x</Emphasis></Subscript>O<Subscript>15±δ</Subscript> crystals

The unit-cell parameters of the nonlinear crystal K₃Li_2?xNb_5+xO_15±δ were measured with x-ray diffraction in the temperature region 80–300 K. The room-temperature parameters of the crystal of this composition are a=12.599±0.001 and c=4.018±0.001 Å. The temperature dependences of the thermal expansion coefficients (TECs) along the [100] and [001] crystallographic directions were determined. A small TEC anisotropy was established. The specific heat of this crystal was measured using adiabatic calorimetry in the temperature interval 80–300 K. The experimental data on the specific heat were used to calculate the changes in the thermodynamic functions.     

Thin <Emphasis Type="Italic">W</Emphasis>′ and <Emphasis Type="Italic">W</Emphasis> domain walls in ferroelastic Pb<Subscript>3</Subscript>(PO<Subscript>4</Subscript>)<Subscript>2</Subscript>

A model of ferroelastic domain walls consisting of matching interlayers of crystal lattices is proposed. The dependences of the parameters of the interlayers and of the parameters of the equations for W′ and W domain walls on the crystal lattice parameters of the ferroelastic phase in Pb₃(PO₄)₂ are determined. The problem concerning the number of possible orientational states and their interaction in a polydomain crystal is considered.     

Synthesis,structural and dielectric properties of SrBi<Subscript>2 – <Emphasis Type="Italic">x</Emphasis></Subscript>Sm<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>Nb<Subscript>2</Subscript>O<Subscript>9</Subscript>

The SrBi_{2 – x} Sm _x Nb₂O₉ (x = 0, 0.4, 0.5) structure were synthesized by a conventional solid-state method. The X-ray diffraction shows an orthorhombic at room temperature. Dielectric constant, loss tangent and Ac conductivity of Sm-doped SrBi₂Nb₂O₉ were carried out, as well. A higher concentration of samarium (x = 0.4 and 0.5) doping leads to a significant reduction in dielectric constant and in Curie temperature. Rather relaxor type of behaviour took place.     

Optical activity of γ<Subscript>1</Subscript>-(Ga<Subscript>x</Subscript>In<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript>)<Subscript>2</Subscript>Se<Subscript>3</Subscript> crystals

The optical activity of uniaxial γ₁-(Ga_xIn_1?x )₂Se₃ crystals (x=0.1, 0.2, 0.3, 0.4) is studied at T=295 and 77 K in the spectral range 0.5–0.8 πm. It is found that the cationic substitution In → Ga leads to a nonlinear increase in the specific rotation of the plane of polarization ρ and the component g ₃₃ of the gyration tensor. It is shown that the gyrotropy of the crystals studied is determined by high-energy transitions whose energy exceeds the energy of the edge transitions and that the gyrotropy observed has a molecular origin.     

The 2009 world average of <Emphasis Type="Italic">α</Emphasis><Subscript><Emphasis Type="Bold">s</Emphasis></Subscript>

Measurements of α _s, the coupling strength of the Strong Interaction between quarks and gluons, are summarised and an updated value of the world average of a_s(M_Z⁰)\alpha_{\mathrm{s}}(M_{\mathrm{Z}^{0}}) is derived. Special emphasis is laid on the most recent determinations of α _s. These are obtained from τ-decays, from global fits of electroweak precision data and from measurements of the proton structure function F₂, which are based on perturbative QCD calculations up to O(a_s⁴)\mathcal{O}(\alpha_{\mathrm{s}}^{4}); from hadronic event shapes and jet production in e⁺e⁻ annihilation, based on O(a_s³)\mathcal{O}(\alpha_{\mathrm{s}}^{3}) QCD; from jet production in deep inelastic scattering and from ϒ decays, based on O(a_s²)\mathcal{O}(\alpha_{\mathrm{s}}^{2}) QCD; and from heavy quarkonia based on unquenched QCD lattice calculations. A pragmatic method is chosen to obtain the world average and an estimate of its overall uncertainty, resulting in

Electron paramagnetic resonance in mixed crystals (BaF<Subscript>2</Subscript>)<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript>(LaF<Subscript>3</Subscript>)<Subscript>x</Subscript> activated by Ce<Superscript>3+</Superscript> ions

The electron paramagnetic resonance (EPR) spectra of mixed crystals (BaF₂)_{1?x? y}(LaF₃)_x(CeF₃)_y (y = 0.001 = 0.1%, x = 0–0.02) are investigated in a magnetic field H‖C₄ at a frequency of 9.5 GHz. The angular dependence of the EPR spectrum is measured for the sample with x = 0.02. The lines attributed to Ce³⁺ impurity centers with tetragonal symmetry and g factors (g_‖ = 0.75, g_⊥ = 2.4) close to those measured for the KY₃F₁₀: Ce³⁺ compound are separated in the complex EPR spectrum. The assumption is made that the aforementioned impurity centers are cubooctahedral clusters of the La₆F₃₇ type in which one of the La³⁺ ions is replaced by the Ce³⁺ ion.     

Dielectric response of SrTiO<Subscript>3</Subscript>–SrMg<Subscript>1/3</Subscript>Nb<Subscript>2/3</Subscript>O<Subscript>3</Subscript> solid solutions in the terahertz–infrared range

The reflection and transmission spectra of ceramic samples of SrTiO₃–SrMg_1/3Nb_2/3O₃ solid solutions have been measured in the frequency range of 5–5000 cm^–1 and in the temperature range of 5–370 K. Based on these spectra, the spectra of the real ε'(ν) and imaginary ε''(ν) parts of the complex permittivity ε*(ν) have been simulated by the method of dispersion analysis. It has been found that the temperature evolution of the dielectric constant is entirely determined by the behavior of the soft mode.     

Magnetocaloric effect in La(Fe<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>Si<Subscript>1 − <Emphasis Type="Italic">x</Emphasis></Subscript>)<Subscript>13</Subscript> ferromagnets

The isothermal changes in the magnetic entropy and the lattice entropy and the adiabatic temperature change in La(Fe_0.88Si_0.12)₁₃ and La(Fe_0.86Si_0.14)₁₃ ferromagnets in a magnetic field are calculated. The calculations are performed with a generalized magnetostriction model of a ferromagnet; the calculation results are compared to experimental data. It is shown that the change in the lattice entropy decreases the magnetocaloric effect and makes it possible to explain the experimental data obtained for La(Fe _x Si_{1 − x} )₁₃ (x = 0.86, 0.88) ferromagnets. The temperature dependences of the bulk compression moduli of these ferromagnets are calculated, and these dependences indicate a strong lattice softening in the vicinity of the magnetic phase transition in them. The thermal expansion coefficient and some magnetic properties of the ferromagnet with x = 0.86 are measured to determine the numerical values of the parameters entering into calculation formulas.     

Crystal and magnetic structure of single-crystal La<Subscript>1-x</Subscript><Emphasis Type="Bold">Sr</Emphasis><Subscript>x</Subscript><Emphasis Type="Bold">MnO</Emphasis><Subscript>3</Subscript><Emphasis Type="Bold">(x ≈ 1/8)</Emphasis>

A neutron powder diffraction (NPD) study on the crystal and magnetic structure of a crushed La_1-xSr_xMnO₃ (x ≈ 1/8) single crystal has been performed. The sample belongs to orthorhombic (Pnma, O) above the Jahn-Teller (JT) transition temperature (T_JT) and monoclinic (P12₁/c1, M^′) in the JT regime. We have also refined the NPD data below the charge/orbital ordering (CO/OO) temperature (T_CO/OO) with a monoclinic (P12₁/c1, M^′′) model because the experimental resolution was insufficient to clearly identify a triclinic structure. The refined lattice parameters show an obvious breathing-mode distortion between T_CO/OO and T_JT, accompanied by a large deviation of the monoclinic angle β from 90°, signifying a very strong cooperative JT distortion. A ferromagnetic (FM) moment of 3.43(5)μ _B/Mn besides an A-type antiferromagnetic (A-AFM) moment of 0.54(2) μ _B/Mn is directed mainly along the b axis in P12₁/c1 symmetry at 5 K. With increasing temperature, the A-AFM domains transform into FM ones above ~100 K and the FM spin orientation turns from the b to the c axis in crystallographic b-c plane below T_c = 187(1) K. The magnetization measurements show typical anomalies around T_CO/OO and T_JT. The measured saturation moment of 3.9(1)μ _B/Mn at 70 kOe and 5 K is well consistent with the sum 3.97(5)μ _B/Mn of the refined FM and A-AFM moments at 5 K, implying the A-AFM spins are aligned in field direction at 70 kOe. The applied magnetic field can affect the paramagnetic insulating (PMI) state in the range of magnetic polarons. Based on the size of JT distortion and the bond-valence sums (BVS’s), the CO/OO phenomenon is being discussed.