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].     

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.     

Effect of electronic state of ions on the electrochemical properties of layered cathode materials LiNi1−2x Co x Mn x O2

The cathode materials of the composition LiNi_{1 − 2x} Co _x Mn _x O₂ (x = 0.1, 0.2. 0.33) synthesized from the Ni, Co, Mn mixed hydroxides and LiOH by using mechanical activation method are studied. It is shown that all synthesized compounds have layered structure described by the space group R-3m. With the decreasing of the nickel content the cell volume and the degree of structure disordering decrease. According to XPS data, the electronic main state of d-ions at the prepared samples’ surfaces corresponds to Ni²⁺, Co³⁺, and Mn⁴⁺. An increase in the nickel content leads to the increase of the Ni2p _3/2 and Co2p _3/2 binding energy, which points to the change in the Me-O bond covalence. According to magnetic susceptibility measurements data, the nickel ions in LiNi_0.6Co_0.2Mn_0.2O₂ exist in the two oxidation states: Ni²⁺ and Ni³⁺. It is shown that this sample has the highest specific discharge capacity (∼170 mAh/g). The positions of redox peaks in the differential capacitance curves depend on the sample composition: with the increasing of nickel content they are shifted toward lower voltages. Based on the paper presented in the IX International Conference “Basic Problems of Energy Conversion in Lithium Electrochemical Systems” (Ufa, 2006).     

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.     

Optical response of bimetallic Li x Na8−x (0≦x≦8) and of doped Na8Zn clusters

Total (elastic + inelastic) cross-sections for electron scattering from C, N, O atoms and their simple molecules are studied theoretically. Thee ^–-C, N, O atomic calculations are done in the complex optical potential approach. To study the electron scattering from O₂, N₂, CO, NO, CN, C₂ as well as CO₂, N₂O, NO₂ O₃ targets, we have adopted an additivity rule, wherein the molecular cross-section is an incoherent sum of the cross-sections of the constituent atoms. The cross-sections of C, N & O atoms are presented at incident energiesE _i =10–1000 eV, the molecular cross-sections are presented atE _i =100–1000 eV. The reliability of the additivity rule is discussed against the background of experimental data.     

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.     

Electrophysical properties of solid solutions of Zn2 − x (Zr a Sn b )1 − x Fe2x O4 compositions

The electrophysical properties of the multicomponent Zn₂ZrO₄ ? Zn₂SnO₄ ? ZnFe₂O₄ system are studied. The electrophysical parameters of solid solutions of Zn_{2 ? x} (Zr _a Sn _b )_{1 ? x} Fe_2x O₄ (x = 0–1.0, Δx = 0.1, a + b = 1) are determined. It is found that the formed solid solutions are semiconductors with electrophysical properties that change in a regular fashion with composition and are distinguished by high values of resistivity (107–1012 Ω cm).     

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.      

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.     

Thermal stability and features of the synthesis of mixed ceramic oxides La2−x Sr x CoO4

Thermal behavior of the mixed oxides La_2?x Sr _x CoO₄ (0.1 < x < 1.5) in the temperature range 1200–1700 K was studied. The use of the ceramic synthesis method makes it possible to obtain homogeneous samples at the calcination temperature of 1673 K. It was found by the high-temperature mass-spectrometry method that a charge can be depleted of cobalt oxide during the high-temperature synthesis.     

Thermal stability of cluster structure in Bi x Sn1− x molten alloys in vicinity of eutectic point

Structure of liquid Bi _x Sn_{1? x} molten alloys has been studies in the vicinity of eutectic point at temperatures of complete melting and above by 100?K. It is shown that the structure parameter concentration dependences reveal the deviation from linear function with extremum points at eutectic composition. Such features exist also at higher temperatures. The reason of untypical behaviour of structure parameters is supposed to be attributed to the existence of two kinds of clusters with Sn‐ and Bi‐like structures.     

Gas-sensing properties of Ta-doped MoO3−x

During a search for alternative materials to replace tin(IV) oxide in semiconducting oxide gas sensors it has been found that sensors comprising sub-stoichiometric molybdenum trioxide exhibit promising characteristics.     

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.     

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.     

Effect of hydration on conductivity of Ba4La x Ca2 − x Nb2O11 + 0.5x (x = 0.5, 1, 1.5, 2) phases

Substitution of Ca by La in initial cubic double perovskite Ba₄(Ca₂Nb₂)O₁₁[VO]₁ allowed obtaining phases with a similar structure with a lower content of structural oxygen vacancies, Ba₄(La _x Ca_{2 ? x} Nb₂)O_{11 + 0.5x} [VO]_{1 ? 0.5x} (x = 0.5, 1, 1.5, 2). The impedance technique was used to measure the temperature dependences of conductivity in the atmosphere of dry and humid air. Transport numbers determined using the EMF method in an oxygen-air and water steam concentration cells point to the predominantly hole nature of conductivity in the high-temperature region (T > 600°C) and to predominance of proton conductivity in the low-temperature region. Activation energies of hole and proton conductivity were calculated. Thermogravimetric measurements were carried out under heating from 25 to 1000°C with simultaneous mass-spectrometric determination of evolved H₂O and CO₂. The properties of the studied Ba₄(La _x Ca_{2 ? x} Nb₂)O_{11 + 0.5x} (x = 0.5, 1, 1.5, 2) phases were compared with the earlier studied Ba_{4 ? x} La _x (Ca₂Nb₂)O_{11 + 0.5x} phases with similar lanthanum content.     

Synthesis and optical properties of quasi-2D CdS x Se1 − x nanoparticles

Colloidal 2D CdS _x Se_{1 ? x} nanoparticles have been synthesized by a solution method in octadecene using oleic acid as a stabilizer. Growth of quasi-2D nanoparticles has been promoted by the presence of cadmium acetate in the reaction mixture. The resulting nanoparticles are platelets with lateral sizes 20–30 nm. The absorption and luminescence spectra of these nanoparticles show narrow bands of lh-e and hh-e exciton transitions corresponding to 2D systems. The spectral position of the lowest energy hh-e transition monotonically changes within 382–461 nm with a change in the composition of nanoparticles. The observed absorption bands are broader than those for the individual CdSe and CdS nanoparticles. The suggested method makes it possible to vary the exciton band position for quasi-2D nanoparticles by changing their composition.     

Nature of conductivity of Perovskites La1 ? x Sr x ScO3 ? α (x = 0.01–0.15) under oxidative and reducing conditions

Transport numbers of ions and protons are measured on ceramic samples of La_{1 ? x} Sr _x ScO_{3 ? ??} (x = 0.01?C0.15); partial conductivities (hole, proton, and oxygen-ion) are determined in the temperature range of 500?C900°C at pH₂O = 0.04?C2.35 kPa and pO₂ from air to 10^?15 Pa.     

Synthesis and characterization of a NASICON phase of variable composition Na1 − x Ni1 − x Sc1 + x (MoO4)3 (0 ≤ x ≤ 0.5)

Subsolidus phase ratios in the Na₂MoO₄-NiMoO₄-Sc₂(MoO₄)₃ system have been studied using X-ray diffraction, differential thermal analysis, and vibrational spectroscopy. A phase of variable composition Na_{1 ? x} Ni_{1 ? x} Sc_{1 + x} (MoO₄)₃ (0 ≤ x ≤ 0.5) having NASICON structure (space group \(R\bar 3c\) ) and a triple molybdate crystallizing in triclinic system (space group \(P\bar 1\) ) have been obtained. The high conductivity of Na_{1 ? x} Ni_{1 ? x} Sc_{1 + x} (MoO₄)₃ allows the phase of variable composition to be regarded as a promising sodiumion-conductive solid electrolyte.     

Structures and optical properties of Zn1?x Ni x O nanoparticles by coprecipitation method

Nanocrystals of undoped and nickel-doped zinc oxide (Zn_1?x Ni _x O, where x?=?0.00?C0.05) were synthesized by the coprecipitation method. Crystalline size, morphology, and optical absorption of prepared samples were determined by X-ray diffraction (XRD), transmission electron microscope (TEM), scanning electron microscope (SEM), and UV?Cvisible spectrometer. XRD and SEM studies revealed that Ni-doped ZnO crystallized in hexagonal wurtzite structure. Doping of ZnO with Ni²⁺ was intended to enhance the surface defects of ZnO. The incorporation of Ni²⁺ in place of Zn²⁺ provoked an increase in the size of nanocrystals as compared to undoped ZnO. Crystalline size of nanocrystals varied from 10 to 40?nm as the calcination temperature increased. Enhancement in the optical absorption of Ni-doped ZnO indicated that it can be used as an efficient photocatalyst under visible light irradiation. Optical absorption measurements indicated a red shift in the absorption band edge upon Ni doping. The band gap value of prepared undoped and Ni-doped ZnO nanoparticles decreased as annealing temperature was increased up to 800?°C.     

Study of ceramic pigments based on Er2Ce2?x Mo x O7

This contribution is focused on the synthesis, characterization and optical properties of new inorganic pigments which are environment friendly and can substitute some toxic metals in interesting colour compounds. Pyrochlores belong to the group of high-temperature pigments, and are a variety of actual and potential applications for several materials. Examples include catalysts, thermal barrier coatings, solid electrolytes, nuclear waste forms and host materials for luminescence centers. The pigments were prepared by the solid state reaction and also by method of suspension mixing of materials in the series with increasing content of molybdenum. The pigments were applied into organic matrix and ceramic glaze. The colour properties of these applications were investigated depending on content of Mo, method of preparation and temperature of calcination (1350?C1550?°C after step 50?°C). The optimum conditions for their synthesis were determined. The pigments were evaluated from standpoint of their structure, colour and particle sizes. Characterization of Er₂Ce_2?x Mo _x O₇ pigments (x?=?0.1, 0.3, 0.5 and 0.7) suggests that they have a potential to be alternative yellow or orange colourants for paints, plastics, ceramics and building materials.