On some multiplicative product of kth derivative of Dirac's delta in x0+|x| and x0−|x|

In this paper we give a sense to the products $${{\left| x \right|^{(n - 2)/2} }} \cdot \frac{{\delta ^{(k - 1)} (x_0 + \left| x \right|)}} {{\left| x \right|^{(n - 2)/2} }}$$ and $\delta ^{(k - 1)} (x_0 - \left| x \right|) \cdot \delta ^{(k - 1)} (x_0 + \left| x \right|)$ . The first of them is a generalization of the product $${{\left| x \right|^{(n - 2)/2} }} \cdot \frac{{\delta (x_0 + \left| x \right|)}} {{\left| x \right|^{(n - 2)/2} }}{\text{ }}$$ given in [1, p. 158].     

Hydrogen content in proton-conducting perovskites CaZr1 − x Sc x O3 − x /2 (x = 0.0–0.2)

The hydrogen content in CaZr_{1 ? x} Sc _x O_{3 ? x/2} (x = 0.00–0.20) and BaZr_0.9Y_0.1O_3-α (for comparison) was studied by powder nuclear microanalysis. The samples were saturated with heavy water (D₂O) vapors at 350 and 400°C in air. The chemical expansion of the CaZr_0.95Sc_0.05O_3-α and BaZr_0.95Y_0.05O_3-α samples at 700°C was measured at different water vapor pressures. A model was suggested to explain the lowered hydrogen content in oxides based on CaZrO₃.     

Atoms state and interatomic interactions in perovskite-like oxides: XXXII. Formation of paramagnetic clusters in the La1−0.33x Ca0.33x Fe x Al1−x O3 and La1−0.33x Sr0.33x Fe x Al1−x O3 solid solutions

Calcium- and strontium-containing lanthanum orthoferrites have been studied using magnetic dilution method. It has been shown that the iron-atom clusters with competing ferro- and antiferromagnetic exchange interactions can exist. By using Mossbauer spectroscopy, Fe(IV) atoms have been found in the La_1?0.33x Ca_0.33x Fe_xAl_1?x O₃ solid solutions and Fe(III) atoms in two different surroundings have been found in the La_1?0.33x Sr_0.33x Fe _x Al_1?x O₃ solid solutions. The compositions of paramagnetic clusters stable at the infinite dilution have been proposed basing of the magnetic susceptibility and Mossbauer spectroscopy data.     

Radiation damage in Si1−x Ge x heteroepitaxial devices

Results are presented of an extended study on the induced lattice defects and their effects on the degradation of Si_1−x Ge _x devices, subjected to a 20 MeV alpha-ray, 1 MeV electron, 1 MeV fast neutron, and 20 and 86 MeV proton irradiations. The degradation of the electrical device performance increase with increasing fluence, while it decreases with increasing germanium content. In the Si_1−x Ge _x epitaxial layers, electron capture levels associated with an interstitial-substitutional boron complex are induced. The radiation source dependence of performance degradation is attributed to the difference of mass and the probability of nuclear collision for the formation of lattice defects.     

Electrochemical studies of LiCr x Fe x Mn2?2x O4 in an aqueous electrolyte

In this paper, LiCr _x Fe _x Mn_2−2x O₄ (x = 0, 0.05, 0.1) electrode materials were prepared by sol–gel technique and characterized by X-ray diffraction (XRD) and transmission electron microscopy or high-resolution transmission electron microscopy techniques. XRD results reveal that the Cr–Fe-co-doped LiCr _x Fe _x Mn_2−2x O₄ materials are phase-pure spinels. The electrochemical properties of the LiMn₂O₄, LiCr_0.05Fe_0.05Mn_1.9O₄, and LiCr_0.1Fe_0.1Mn_1.8O₄ electrodes in 5 M LiNO₃ aqueous electrolyte were investigated using cyclic voltammetry, AC impedance, and galvanostatic charge/discharge methods. In the current range of 0.5–2 A g⁻¹, the specific capacity of the LiCr_0.05Fe_0.05Mn_1.9O₄ electrode is close to that of the LiMn₂O₄ electrode, but the specific capacity of the LiCr_0.1Fe_0.1Mn_1.8O₄ electrode is obviously lower than that of the LiMn₂O₄ electrode. When the electrodes are charge/discharge-cycled at the high current rate of 2 A g⁻¹, the LiCr_0.05Fe_0.05Mn_1.9O₄ electrode exhibits an initial specific capacity close to that of the LiMn₂O₄ electrode, but its cycling stability is obviously prior to that of the LiMn₂O₄ electrode.     

Solid potassium-conducting electrolytes in the K2 − 2x Ga2 − x V x O4 system

New potassium-conducting solid electrolytes based on potassium monogallate in the K_2?2x Ga_2?x V _x O₄ system are synthesized and studied. It is found that an introduction of V⁵⁺ ions leads to a considerable increase in the KGaO₂ conductivity due to the formation of vacancies in the potassium sublattice. The conductivity for optimal compositions is approximately 10^?3 S cm^?1 at 400°C and above 10^?2 S cm^?1 at 700°C. The results are compared with early obtained data for potassium monogallate dopped with four-charged cations.     

Synthesis and crystal structure of Mo6−x Nb x I11 (x = 1–1.5)

A solid solution Mo_{6 ? x} Nb _x I₁₁ (x = 1.1–1.5) containing cluster cores {Mo₅NbI₈} is obtained by the high-temperature reaction of molybdenum, niobium, and iodine (550°C, 70 h, quartz ampule). According to the X-ray diffraction data, heating at 800°C in a molybdenum container results in the decomposition of the solution to Mo₆I₁₂ and Nb₆I₁₁. According to the X-ray structure analysis data, the compounds are isostructural to the high-spin modification Nb₆I₁₁ (space group Pccn). The presence of Nb atoms in the structure changes the structural type from the layered (Mo₆I₁₂) to framework structure, noticeably increases the metalmetal distances (2.661–2.716 Å, 2.695 Å) Mo₆ octahedron with the retention of the distance from the metal (M) to the μ₃-“capped” I atoms, and strongly elongates the M₆-I-M₆ bridges almost to the value observed in Nb₆I₁₁.     

Electroconductance of single-crystal Li2 + x Fe 2 − 2x 2+ Fe x 3+ (MoO4)3 (x = 0.22)

Electrophysical properties of single-crystal Li_{2 + x} Fe _{2 ? 2x} ²⁺ Fe _x ³⁺ (MoO₄)₃ (x = 0.22) are studied at 25–400°C. It is found that the conduction is of electronic nature and the conductivity equals 5 × 10^-2 S/cm at 300°C. The activation energy for the electron transport is 0.23 eV. The conductance in molybdate Li_2.22Fe _1.56 ²⁺ Fe _0.22 ³⁺ (MoO₄)₃ is markedly anisotropic.     

Glycolate Ti1 − x Fe x (OCH2CH2O)2 − x/2 as a precursor for the preparation of quasi-one-dimensional (1D) solid solutions Ti1 − x Fe x O2 − 2x/2 (0 ≤ x ≤ 0.1)

Quasi-one-dimensional (1D) solid solutions Ti_{1 ? x} Fe _x (OCH₂CH₂O)_{2 ? x/2} (0 < x ≤ 0.1) with the structure of anatase were prepared by heating the glycolate Ti_{1 ? x} Fe _x (OCH₂CH₂O)_{2 ? x/2} in an atmosphere of air at a temperature of >450°C. The conditions of formation and the properties of the new glycolate Ti₃Fe₂(OCH₂CH₂O)₉ were described. It was found that the synthesized Ti_{1 ? x} Fe _x O_{2 ? 2x/2} solid solutions exhibit photocatalytic activity in the reaction of hydroquinone oxidation in an aqueous solution on irradiation with UV light. A correlation between the rate of oxidation of hydroquinone and the concentration of iron in the catalyst was established. A procedure for the preparation of titanium dioxide with the structure of anatase doped with iron and carbon (Ti_{1 ? x} Fe _x O_{(2 ? x/2) ? yCy)} and also composites on its basis, which contain an excess amount of carbon, was proposed.     

Electrochemical sensors based on platinized Ti1 − x Ru x O2

Electrocatalysts based on platinized titania modified with ruthenia (0–9 mol %) were studied. The synthesized materials were investigated as working electrodes in potentiometric sensors sensitive to hydrogen and carbon monoxide. All electrocatalysts showed reproducible behavior at pure gas concentrations from 400 to 4000 ppm. In CO-H₂ mixtures with comparable concentrations of both gases, the sensors were selective toward hydrogen at ≥0.05 mol % Ru, but not selective to hydrogen or CO at less than 0.05 mol % Ru in the substrate.     

Phase Transitions in the BaCe1–x Nd x O3–δ System (x = 0–0.15)

Phase transitions in BaCe_{1 – x} Nd _x O_3– (x = 0–0.15) are studied on ceramic samples by dilatometry (at 370–1100 K) and by measuring electroconductivity (at 750–1220 K). Ion transport numbers are measured by an EMF method at 850–1240 K. All measurements are done in dry air (₂ 40 Pa). By treating the obtained temperature dependences of linear expansion with a difference method (difference between first-degree polynomial approximating the dependence and experimental points), the position and the sort of the phase transitions are determined. High-temperature phase transitions are confirmed by measuring the electroconductivity and ion transport numbers. Second-order phase transitions in pure BaCeO₃ are discovered at 480 ± 10, 530 ± 10, 900 ± 10, 1030 ± 20, and 1170 ± 10 K and a first-order transition, at 665 ±10 K. Phase transitions at 900 and 1030 K are discovered for the first time ever.     

Longitudinal conductivity of thin films of La1 − x Sr x F3 − x solid solutions on glass ceramics

The longitudinal conductivity of La_{1 ? x} Sr _x F_{3 ? x} solid solution films (x = 0–0.24) with thicknesses of 40–260 nm grown on glass ceramics at temperatures from room temperature to 300°C and frequencies of 10^?1–10⁶ Hz was studied by impedance spectroscopy. The concentration dependence of film conductivity on the SrF₂ content had a maximum near x = 0.05. An equivalent circuit was constructed on the basis of the impedance plots to describe migration processes. The DC conductivity was evaluated for all samples under study. The activation energies were estimated from the temperature dependences of the DC conductivities of the films. The resulting dependences of electrophysical parameters were compared with those for bulk materials in terms of the relaxation conductivity model.     

Preparation and characterization of Ca1 − x Ce x MnO3 perovskite electrodes

The electrochemical properties of Ca_1 − x Ce _x MnO₃ perovskite-type oxide electrode have been investigated by cyclic voltammetry in Na₂SO₄ aqueous solutions with pH 14. The structural and morphological characterizations have also been investigated and the information used to interpret the electrochemical behavior. An estimation of the electrode’s capacitance and roughness factor has been obtained by means of cyclic voltammetry. The specific capacitance and consequently the roughness factor values are affected by the presence of Ce ions in the oxide. These findings are in agreement with the increase of the oxide-specific surface area by the introduction of Ce ion. The open-circuit potential and the voltammetric patterns are dependent on the presence of Ce ion in the electrodes and support that the surface electrochemistry of the perovskite oxide electrodes is governed by the Mn⁴⁺–Mn³⁺ redox couple.     

High-pressure synthesis and local structure of corundum-type In(2-2x)Zn(x)Sn(x)O(3) (x ≤ 0.7)

The corundum-type In(2-2x)Zn(x)Sn(x)O(3) solid solution (cor-ZITO, x ≤ 0.7) was synthesized at 1000 °C under a high pressure of 70 kbar. cor-ZITO is a high-pressure polymorph of the transparent conducting oxide bixbyite-In(2-2x)Zn(x)Sn(x)O(3) (x ≤ 0.4). Analysis of the extended X-ray absorption fine structure suggests that significant face-sharing of Zn and Sn octahedra occurs, as expected for the corundum structure type. In contrast to the ideal corundum structure, however, Zn and Sn are displaced and form oxygen bonds with lengths that are similar to those observed in high-pressure ZnSnO(3). Powder X-ray diffraction patterns of cor-ZITO showed the expected unit cell contraction with increased cosubstitution, but no evidence for ilmenite-type ordering of the substituted Zn and Sn. A qualitative second harmonic generation measurement, for the solid solution x = 0.6 and using 1064 nm radiation, showed that Zn and Sn adopt a polar LiNbO(3)-type arrangement.     

Lithium-cationic conductivity in the Li4 − 2x Cd x GeO4 system

The lithium-conducting solid electrolytes in the Li_{4 ? 2x} Cd _x GeO₄ (0 ≤ x ≤ 0.6) system are synthesized. Their crystal structure and temperature and concentration dependences of conductivity are studied. The specimens with the highest conductivity have a γ-Li₃PO₄-derivative structure. The solid solutions with x = 0.15–0.25 are stable at the room temperature, whereas the specimens with x ≥ 0.3 decompose yielding Li₂CdGeO₄ below 310 ± 10°C. Li_3.6Cd_0.2GeO₄ solid solution exhibits the highest conductivity (5.25 × 10^?2 S cm^?1 at 300°C). The factors, which affect the conductivity of synthesized solid electrolytes, are considered.     

Electrochemical preparation and magnetic properties of submicron Co x Pb1−x dendrites

Magnetic dendrites of Co _x Pb_1−x were fabricated through potentiostatic electrochemical deposition on Cu substrates in boric acid solution at room temperature. The as-deposited dendrites were determined by scanning electron microscopy (SEM), X-ray diffraction (XRD), transmission electron microscopy (TEM), electrodeposition (ED), and energy dispersive X-ray spectroscopy (EDS). SEM results indicate that the Co _x Pb_1−x dendrites are highly symmetrical in structures. The diameters of the branches are about 50 ~ 200 nm, and the backbones are continuous with lengths up to about 10 μm. XRD patterns show that the as-deposited dendrites are solid solutions. The annealing treatment can result in the recrystallization of these metastable alloys into two separate phases. TEM, ED, and EDS results also reveal that the backbones and the branches of the dendrites are composed of different amounts of cobalt. Magnetic measurements confirm that the as-deposited Co _x Pb_1−x dendrites have a softly ferromagnetic behavior, and a small coercive force (about 80 Oe). Also the saturation magnetizations of the Co _x Pb_1−x dendrites decrease rapidly with the temperature increasing.     

Characterization of superparamagnetic Mg x Zn1−x Fe2O4 powders

Structural and magnetic properties of Mg _x Zn_1−x Fe₂O₄ powders have been studied with respect to the application for thermal cancer therapy (magnetic hyperthermia). Mg _x Zn_1−x Fe₂O₄ (x=0.1–0.5) powders with particle sizes between 5 and 8 nm were produced by citrate method. The X-ray diffraction patterns of the samples correspond to a spinel phase. The lattice constant and the volume of the elementary cell increase when x changes from 0.1 to 0.5. The FTIR-spectra ascertain the spinel phase formation. The Mossbauer studies reveal the presence of extremely small particles, which undergo superparamagnetic relaxation at room temperature. The core-shell model has been applied to explain quadruple doublets. The quadruple splitting at “shells” is bigger than those at “cores” whereas the isomer shifts remain close. Magnetic studies confirm the presence of extremely small particles that behave as superparamagnetic ones.      

Formation of helium cluster ions HHe x + (x≦14) and H3He x + (x≦13) in a very low temperature drift tube

The formation of cluster ions when hydrogen molecular ions H ₂ ⁺ and H ₃ ⁺ are injected into a drift tube filled with helium gas at 4.4 K has been investigated. When H ₂ ⁺ ions are injected, cluster ions HHe _x ⁺ (x≦14) are produced. No production of H₂He _x ⁺ ions is observed. When H ₃ ⁺ ions are injected, cluster ions HHe _x ⁺ (x≦14) are produced as well as H₃He _x ⁺ (x≦13), and very small signals corresponding to H₂He _x ⁺ (3≦x≦10) are observed. Information on the stability of HHe _x ⁺ and H₃He _x ⁺ is derived from the drift field dependence of the cluster size distributions. The cluster sizex=13 is found to be a magic number for HHe _x ⁺ , and for H₃He _x ⁺ ,x=10 and 11.     

Multivariate analysis of melting points for homologous series C x H2x − 1NO (x = 3−6)

A multivariate analysis of the empirical structure data for isomeric homologues using principal-component analysis has been carried out, and the correlation with experimental melting points has been shown. Based on the data on the CSD structure, we discuss the impact of molecular H-aggregation.     

Synthesis and characterization of nano-structured Th1?x Ce x O2 mixed oxide

GEL combustion technique was applied to obtain oxides of thorium and cerium from their respective nitrate solutions using citric acid as the gelating agent. The dried samples were characterized by IR and TG studies. Intermediate and final products during TG studies have been isolated and characterized by XRD studies. All the TG runs during heating of thorium and cerium nitrate with citric acid dried Gels showed a two step process. The weight loss at each step and the X-ray data of the product at each step, helped in suggesting a possible mechanism. Kinetic study was carried out independently for each step. The reaction mechanism as observed during interactive procedure was found to be diffusion controlled. The kinetic parameters (activation energy and pre-exponential factor) for each step in all reactions have been calculated. Observations from XRD studies show that with increase in cerium concentration in the oxides, the lattice parameter values have shown a decreasing trend for all the five compositions studied. It was observed that in TG studies with increase in cerium concentration, the final temperature of the reactions have shown a decreasing trend. SEM studies of the powders reveal that synthesized oxides have a tendency to form agglomerate of varying size ranging from 50 to 100 μm in case of mixed oxides but the size of thorium oxide powder so synthesized have pore size 10–100 μm. SEM images shows that GEL combustion may result in agglomeration, if the temperature is not properly controlled to the desired value. SEM studies also reveal that each agglomerate contains approximately 10–100 individual particles. Surface area of the mixed oxide powders were determined using Gas adsorption technique. The surface area was found to be in the range of 3–17 m²/g in all cases. Specific surface area of thorium oxide was found to be lesser than cerium oxide but in case of mixed oxides surface area decreases with increase in cerium content. Majority of pores, indicating the particle size are in the range of 0.01–0.04 cm³/g.