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.     

Ab initio calculations of Born charges in ferroelectrics with a perovskite structure

A method has been proposed for calculating Born effective charges in compounds with a cubic perovskite structure. The method is based on the first-principles calculation of individual contributions from the short-range interaction and the intercell dipole-dipole interaction to the Born tensor Z _ii (s) for crystalline dielectrics. It has been shown that the contribution from the short-range interaction Z _ii ^sr (s) to the Born tensor components can be derived from ab initio calculations performed for polyatomic clusters. The results of the calculations of the short-range interactions Z _ii ^sr (s) for the cubic phases of the BaTiO₃, SrTiO₃, CaTiO₃, PbTiO₃, BaZrO₃, PbZrO₃, KNbO₃, and KTaO₃ compounds with the use of the electronic structure calculations within the Hartree-Fock approximation and the density functional theory are presented. For the BaTiO₃, SrTiO₃, CaTiO₃, PbTiO₃, KNbO₃, and KTaO₃ compounds, the components of the complete Born tensor have been also calculated. The obtained values of Z _ii (s) are in good agreement with the results of the calculations in terms of the linear response theory and the Berry phase approach.     

Mechanical and Dynamic Stability of Complete and Nonstoichiometric 3<Emphasis Type="Italic">C</Emphasis>-Si<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>C<Subscript><Emphasis Type="Italic">y</Emphasis></Subscript> from Ab Initio Calculations

The energies of formation of vacancies in the carbon and silicon sublattices, the independent elastic constants, the all-round compression, shear and Young’s moduli, and the anisotropy coefficients are determined for the complete and nonstoichiometric cubic phases of 3C-Si_xC_y (x, y = 1.0–0.75) by ab initio methods of the band theory. In the formalism of the density functional perturbation theory (DFPT), the phonon dispersion dependences are obtained for these phases (the comparison with the experiment is given for the complete phase). It is shown that the mechanical characteristics of the phases become strongly anisotropic upon the transition from 3C-SiC_0.875 to 3C-SiC_0.75. It is established from the analysis of the phonon dispersion curves that the 3C-SiC_0.875 and 3C-SiC_0.75 phases, in contrast to the complete 3C-SiC phase, are dynamically unstable at T = 0 K.     

Magnetic phase diagram of the Bi<Subscript>1-<Emphasis Type="Italic">x</Emphasis></Subscript>Ca<Subscript>x</Subscript>MnO<Subscript>3</Subscript> manganites

The magnetic and elastic properties of the Bi_1-xCa_xMnO₃ manganites are studied. The phase transformations revealed are ferromagnet-spin glass (x≥0.15) and spin glass-charge-ordered antiferromagnet (x≥0.25). The ferromagnetic state is characterized by ordering of the Mn³⁺d _x ²-y orbitals. It is suggested that thespin glass state originates from local static Jahn-Teller distortions. The antiferromagnetic charge-ordered and the spin-glass disordered phases coexist in samples with 0.25<x<0.32, which may be due to the charge order-disorder phase transformation being martensitic in character. The magnetic phase diagram is constructed.     

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.     

Resonant Raman scattering in superconducting Ba<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript>K<Subscript>x</Subscript>BiO<Subscript>3</Subscript>

The effect of the photon energy of the exciting laser radiation on the Raman spectra of Ba_1?xK_xBiO₃ with x=0.25, 0.40, and 0.50 is studied. An increase in the laser wavelength from 488 to 750 nm scarcely affects the amplitudes and frequencies of the spectral lines in the Raman spectra of the nonsuperconducting compound with x=0.25. For the optimally doped (x=0.40) and overdoped (x=0.50) superconducting compounds, a substantial increase in the line intensity and a considerable shift of the characteristic frequencies are observed. This result suggests that, in the whole range of superconducting compositions 0.37≤x≤0.50, the local symmetry of the Ba_1?xK_xBiO₃ crystal lattice differs from the perfect cubic symmetry, which should take place according to the literature data. The fact that resonance phenomena are observed when the laser photon energy is shifted toward the optical gap testifies to the presence of local electron pairs in the whole range of superconducting compositions 0.37≤x≤0.50 and is evidence in favor of the superconductivity mechanism proposed for Ba_1?xK_xBiO₃ on the basis of the X-ray absorption studies in our previous paper.     

Geometric resonance in the optical properties of microinhomogeneous PdMn<Subscript>x</Subscript>Fe<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript> alloys

The optical properties of PdMn_xFe_1?x ternary alloys in the homogeneous ferromagnetic (F₁, for x ～ 0) and antiferromagnetic (A, for x ～ 1) states, as well as in the microinhomogeneous state (at x=0.7), are discussed. In the x=0.7 alloy, the presence of nuclei of the low-resistivity, PdFe-type F₁ phase in the high-resistivity, PdMn-type A matrix was shown to produce a narrow maximum on the optical-conductivity σ(ω) curve at E ～ 0.1 eV, which is due to a geometric resonance associated with light scattering from phase inhomogeneities of the sample. The behavior of σ(ω) in the interband transition region is dominated by parameters of the electronic spectrum of both the A and F₁ phases.     

Mössbauer studies of multiferroics BiFe<Subscript>1 – <Emphasis Type="Italic">x</Emphasis></Subscript>Cr<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>O<Subscript>3</Subscript> (<Emphasis Type="Italic">x</Emphasis> = 0–0.20)

The Mössbauer studies on ⁵⁷Fe nuclei in multiferroics BiFe_{1 – x} Cr _x O₃ (x = 0.05, 0.10, and 0.20) have been performed at room temperature. The multiferroics BiFe_{1 – x} Cr _x O₃ (x = 0.05, 0.10, and 0.20) with the rhombohedral R3c structure have been prepared by solid-state synthesis under high pressures. The effect of substitution of Cr cations for Fe cations on the spatial spin-modulated structure, and also hyperfine electrical and magnetic interactions of ⁵⁷Fe nuclei has been studied. The substituted ferrites demonstrate an anharmonic modulated spin structure of cycloid type, in which iron atoms with different cation environments take part. The anharmonism parameter of the cycloid linearly increases from m = 0.10 at x = 0 to m = 0.78 ± 0.02 at x = 0.20. The constants of magnetic uniaxial anisotropy K _u are estimated at room temperature: K _u ≈ 0.36 × 10⁶ erg/cm³ at x = 0 and K _u ≈ 4.22 × 10⁶ erg/cm³ at x = 0.20.     

Composition-induced transition of spin-modulated structure into a uniform antiferromagnetic state in a Bi<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript>La<Subscript>x</Subscript>FeO<Subscript>3</Subscript> system studied using <Superscript>57</Superscript>Fe NMR

By analyzing the NMR line shape, the transformation of a spatially spin-modulated magnetic structure in BiFeO₃ into an ordinary spatially uniform structure of the LaFeO₃ orthoferrite in Bi_1?xLa_xFeO₃ solid solutions is studied. The measurements are made using a spin-echo technique at temperatures of 77 and 4.2 K on ceramics with compositions x=0, 0.1, 0.2, 0.61, 0.9, and 1.0 enriched by the ⁵⁷Fe isotope. It is shown that the spin-modulated structure disappears near the concentration x=0.2, which corresponds, according to the published data, to the phase transition with a change in the unit-cell symmetry R3c → C222. A formula is obtained describing the NMR absorption line shape for the spin-modulated structure with account of local line-width. Theoretical spectra adequately describe the evolution of the experimental spectrum in the concentration range 0≤x≤0.2. Highly nonuniform local magnetic fields in the intermediate compositions make it impossible to detect NMR signals in a sample with x=0.61. A uniform magnetic structure characterized by a single narrow line arises in the range of existence of a phase with the symmetry Pnma typical of the pure orthoferrite LaFeO₃.     

On the nature of differences in the Ni charge states in barium and strontium titanates

XAFS studies of nickel-doped solid solution Ba_1–xSr_xTiO₃ show that the Ni charge state changes from 4 in SrTiO₃ to ~2.5 in BaTiO₃ as x is varied. First-principles electronic structure calculations show that nickel creates an impurity band in the forbidden gap of BaTiO₃ and SrTiO₃. Calculations of the formation energy of the oxygen vacancies explain the difference between the Ni charge states in these compounds by the different formation energies of these vacancies.     

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.     

Synthesis,structure, and properties of BIFENBVOX

Solid solutions Bi₄V_2-x Fe _x/2Nb _x/2O_11-δ (х?=?0.05–1.0) and Bi₄V_2-х-y Fe _x Nb _y O_11–δ (with fixed x or y?=?0.2 and variable х or y?=?0.2–0.5 with step 0.1) were synthesized by the standard ceramic technology in the temperature range 773–1113 K and by mechanochemical activation method using Bi₂O₃, V₂O₅ Fe₂O₃, and Nb₂O₅ oxides as initial compounds. The formation of solid solutions was studied. Ranges of stability and temperature values of phase transitions for different polymorphous modifications were defined using dylatometric and thermo gravimetric studies. The morphology and the local chemical composition of the ceramic samples were studied. Samples with concentration of dopants x?>?0.3 contain two phases; both major and impurity phases are solid solutions of the BIFENBVOX type although the dopants atoms distribution between them is random. The thermal expansion coefficients (TEC) were measured. The electrical conductivity of ceramic samples was investigated in a wide range of temperatures. The highest conductivity values among the studied solid solutions are observed for the sample with a small amount of dopants x?=?0.25.     

Electronic energy structure and x-ray spectra of wide-gap AlN and BN crystals and B<Subscript>x</Subscript>Al<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript>N solid solutions

The electronic energy structure of 2H and 3C AlN and BN crystals and B_xAl_1?xN solid solutions is calculated on the basis of the local coherent potential method using the cluster version of the MT approximation and the theory of multiple scattering. The features of the electronic structure of 2H-AlN crystals are compared with x-ray K and L absorption and emission spectra of aluminum and nitrogen. An interpretation of these features is given. The concentration dependences of the width of the upper subband of the valence band and the band gap in B_xAl_1?xN solid solutions (x = 0.25, 0.5, 0.75) are investigated. Charge transfer from aluminum to nitrogen atoms is shown to occur and increase with boron doping in both crystallographic modifications.     

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.     

X-ray spectra and electronic band structure of nitrogen in Al<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>Ga<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript>N solid solid solutions

The electronic energy structure of the valence band and the x-ray absorption near edge structure (XANES) region of nitrogen in Al _x Ga_1?x N solid solutions and binary crystals of gallium nitride GaN and aluminum nitride AlN are calculated using the local coherent potential method and the cluster version of the muffin-tin approximation within the framework of the multiple scattering theory. It is demonstrated that the calculated electron densities of states correlate with the nitrogen K x-ray emission and nitrogen K x-ray absorption spectra. The electronic energy structure of the top of the valence band and the XANES region in Al _x Ga_1?x N solid solutions are compared with those in the binary crystals of the GaN and AlN nitrides, and an interpretation of their specific features is proposed. An analogy is drawn between the evolution of the electronic energy structure of the valence band and the XANES region in the alloys under investigation and the evolution of the electronic band structure in the Al _x B_1?x N and B _x Ga_1?x N alloys. General trends in the transformation of the structure and variations in properties of these alloys are discussed.     

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).     

Structure and dielectric properties of solid solutions Bi7Ti4 + x W x Ta1–2x O21 (x = 0–0.5)

A number of solid solutions Bi₇Ti_{4 + x} W _x Ta_1–2x O₂₁ (x = 0–0.5) have been synthesized from oxides by solid-phase reaction. The crystal structure, the electrophysical characteristics, and the microstructure of the prepared ceramic samples have been studied. According to X-ray powder diffraction, all the compounds are single-phase with the structure of mixed-layer Aurivillius phases (m = 2.5) with the orthorhombic crystal lattice (space group I2cm, Z = 2). Temperature dependences of the relative permittivity ε(T) of the compound have been measured, from which it has been found that the Curie temperature T _C of perovskite-like oxides Bi₇Ti_{4 + x} W _x Ta_1–2x O₂₁ (x = 0–0.5) decreases linearly as substitution parameter x decreases. The activation energies of charge carriers have been found in different temperature ranges.     

Local features of the crystal structure of superconducting iron chalcogenides Fe(TeSe)<Subscript>1 – δ</Subscript>

The local crystal structure of superconducting powders of iron chalcogenides FeTe_xSe_1–x (x = 0.1, 0.22, 0.49, 0.8, 0.9) prepared by dry synthesis (without mineralizer) has been studied by EXAFS spectroscopy above the K Se and K Fe absorption edges in the temperature range of 80–300 K. The dependences of Se–Fe, Fe–Te, and Fe–Fe interatomic bond lengths and degrees of their local disordering (Debye–Waller factors) on the tellurium content and temperature have been obtained. Einstein temperatures characterizing the stiffness of each bond have been determined. The correlation of the Se–Fe bond stiffness with the dependence of the critical temperature of the superconducting transition T_c on the composition of the samples under study have been established, which indicates the specific role of the Se–Fe bond in the superconducting state formation in iron chalcogenides FeTe_xSe_1–x.     

Structure,microstructure, and dielectric responses of (1–<Emphasis Type="Italic">х</Emphasis>)BiFeO<Subscript>3</Subscript>–<Emphasis Type="Italic">x</Emphasis>BaTiO<Subscript>3</Subscript> solid solutions

The structure, microstructure, and dielectric responses of (1–х)BiFeO₃–xBaTiO₃ (0.0 < x ≤ 0.5) solid solutions prepared as ceramics are studied. Patterns in their dielectric parameters and the formation of their crystal and grain structures are investigated in a wide range of temperatures and frequencies.     

Peculiarities of the magnetic,galvanomagnetic, elastic,and magnetoelastic properties of Sm<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript>Sr<Subscript>x</Subscript>MnO<Subscript>3</Subscript> manganites

Manganites of the Sm1?xSr_xMnO₃ system (x=0.33, 0.4, and 0.45) possess giant negative values of the magnetoresistance Δρ/ρ and the volume magnetostriction ω near the Curie temperature T_C. In the compound with x=0.33, the isotherms of Δρ/ρ, ω, and magnetization σ exhibit smooth variation and do not reach saturation up to maximum magnetic field strengths (120 kOe) studied (according to the neutron diffraction data, this substance comprises a ferromagnetic (FM) matrix with distributed clusters of a layered antiferromagnetic (AFM) structure of the A type). In the compounds with x=0.4 and 0.45 containing, besides the FM matrix and A-type AFM phase, a charge-ordered AFM phase of the CE type (thermally stable to higher temperatures as compared to the A-type AFM and the FM phases), the same isotherms measured at T ≥ T_C show a jumplike increase in the interval of field strengths between H_c1 and H_c2 and then reach saturation. In the interval H_c1 > H > H_c2, the σ, ω, and Δρ/ρ values exhibit a metastable behavior. At temperatures above T_C, the anisotropic magnetostriction changes sign, which is indicative of rearrangements in the crystal structure. The giant values of ω and Δρ/ρ observed at T ≥ T_C for all compounds, together with excess (relative to the linear) thermal expansion and a maximum on the ρ(T) curve, are explained by the phenomenon of electron phase separation caused by a strong s-d exchange. The giant values of magnetoresistance and volume magnetostriction (with ω reaching ～10^?3) are attributed to an increase in the volume of the FM phase induced by the applied magnetic field. In the compound with x=0.33, this increase proceeds smoothly as the FM phase grows through the FM layers in the A-type AFM phase. In the compounds with x=0.4 and 0.45, the FM phase volume increases at the expense of the charge-ordered CE-type AFM structure (in which spins of the neighboring manganese ions possess an AFM order). The jumps observed on the σ(H) curves, whereby the magnetization σ reaches ～70% of the value at T=1.5 K, are indicative of a threshold character of the charge-ordered phase transition to the FM state. Thus, the giant values of ω and Δρ/ρ are inherent in the FM state, appearing as a result of the magnetic-field-induced transition of the charge-ordered phase to the FM state, rather than being caused by melting of this phase.