A weighted mean square method of linearization in non-linear oscillations

The paper deals with a linearization technique in non-linear oscillations for systems which are governed by second-order non-linear ordinary differential equations. The method is based on approximation of the non-linear function by a linear function such that the error is least in the weighted mean square sense. The method has been applied to cubic, sine, hyperbolic sine, and odd polynomial types of non-linearities and the results obtained are more accurate than those given by existing linearization methods.

Raman spectrum of strontium titanate

The Raman spectrum of strontium titanate has been recorded using λ 4358 of mercury as exciter. The observed spectrum consists of 7 Raman lines, one of which is of low frequency, as expected from the recent theory of Cochran. 6 of these Raman lines have been interpreted as the first order spectrum arising from a small deviation of the cubic strontium titanate from its idealized symmetry. It has been shown that one normal mode of SrTiO3 neglected by J.T. Last, will be really active in infrared absorption in the region of 440 cm-1 and that it has to be taken into account in the interpretation of the infrared spectra of titanates. The four vibrational modes of the unit cell of SrTiO3 correspond to frequencies of 90, 335, 441 and 620 cm-1 observed in Raman effect. The large width of the Raman lines and the additional lines at 256 cm-1 and 726 cm-1 have been attributed to a splitting of the longitudinal and transverse optical modes. With the observed frequencies it has been found possible to account for in a satisfactory manner the specific heat of SrTiO3 in the range 54·84° K to 1800° K.

Elastic behaviour of matter under very high pressures - Uniform compression

In order to study the elastic behaviour of matter when subjected to very large pressures, such as occur for example in the interior of the earth, and to provide an explanation for phenomena like earthquakes, it is essential to be able to calculate the values of the elastic constants of a substance under a state of large initial stress in terms of the elastic constants of a natural or stress-free state. An attempt has been made in this paper to derive expressions for these quantities for a substance of cubic symmetry on the basis of non-linear theory of elasticity and including up to cubic powers of the strain components in the strain energy function. A simple method of deriving them directly from the energy function itself has been indicated for any general case and the same has been applied to the case of hydrostatic compression. The notion of an effective elastic energy-the energy require to effect an infinitesimal deformation over a state of finite strain-has been introduced, the coefficients in this expression being the effective elastic constants. A separation of this effective energy function into normal co-ordinates has been given for the particular case of cubic symmetry and it has been pointed out, that when any of such coefficients in this normal form becomes negative, elastic instability will set in, with associated release of energy.

Dielectric properties of some MM′O4 and MTiM′O6 (M=Cr, Fe, Ga; M′=Nb, Ta, Sb) rutile-type oxides

We describe an investigation of the structure and dielectric properties of MM'O-4 and MTiM'O-6 rutile-type oxides for M = Cr, Fe, Ga and M' = Nb. Ta and Sb. All the oxides adopt a disordered rutile structure (P4(2)/mnm) at ambient temperature. A partial ordered trirutile-type structure is confirmed for FeTaO4 from the low temperature (17 K) neutron diffraction studies While both the MM'O-4 oxides (CrTaO4 and FeTaO4) investigated show a normal dielectric property MTiM'O-6 oxides for M = Fe, Cr and M' = Nb/Ta/Sb display a distinct relaxor/relaxor-like response. Significantly the corresponding gallium analogs, GaTiNbO6 and GaTiTaO6, do not show a relaxor response at T<500K (C) 2010 Elsevier Inc All rights reserved

Solution-Combustion Synthesized Nanocrystalline Li4Ti5O12 As High-Rate Performance Li-Ion Battery Anode

Nanocrystalline Li4Ti5O12 (LTO) crystallizing in cubic spinel-phase has been synthesized by single-step-solution-combustion method in less than one minute. LTO particles thus synthesized are flaky and highly porous in nature with a surface area of 12 m(2)/g. Transmission electron micrographs indicate the primary particles to be agglomerated crystallites of varying size between 20 and 50 nm with a 3-dimensional interconnected porous network. During their galvanostatic charge-discharge at varying rates, LTO electrodes yield a capacity value close to the theoretical value of 175 mA h/g at C/2 rate. The electrodes also exhibit promising capacity retention with little capacity loss over 100 cycles at varying discharge rates together with attractive discharge-rate capabilities yielding capacity values of 140 mA h/g and 70 mA h/g at 10 and 100 C discharge rates, respectively. The ameliorated electrode-performance is ascribed to nano and highly porous morphology of the electrodes that provide short diffusion-paths for Li in conjunction with electrolyte percolation through the electrode pores ensuring a high flux of Li.

An approximate analysis of non-linear non-conservative systems subjected to step function excitation

This paper deals with the approximate analysis of the step response of non-linear nonconservative systems by the application of ultraspherical polynomials. From the differential equations for amplitude and phase, set up by the method of variation of parameters, the approximate solutions are obtained by a generalized averaging technique based on ultraspherical polynomial expansions. The Krylov-Bogoliubov results are given by a particular set of these polynomials. The method has been applied to study the step response of a cubic spring mass system in presence of viscous, material, quadratic, and mixed types of damping. The approximate results are compared with the digital and analogue computer solutions and a close agreement has been found between the analytical and the exact results.

Response of nonlinear systems to narrow-band excitation

The hardening cubic spring oscillator is studied under narrow-band gaussian excitation. Equivalent linearization leads to multiple steady states. The realizability of the solution is discussed through stochastic stability analysis. Theoretical results are supported by numerical simulation.

Ferroelectricity in Bi26-xMxO40-delta (M = Al and Ga) with the gamma-Bi2O3 structure

We report on the dielectric proper-ties of bismuth aluminate and gallate with Bi:AI(Ga) ratio of 1: 1 and 12:1 prepared at high temperature and ambient pressure. These compounds crystallize in a noncentrosymmetric body-centered cubic structure (space group 123) with a similar to 10.18 angstrom rather than in the perovskite structure.This cubic phase is related to the gamma-Bi2O3 structure which has the actual chemical formula Bi-24(3+) (Bi3+Bi5+)O40-delta. In the aluminates and gallates studied by us, the Al and Ga ions are distributed over the 24f and 2a sites. These compounds exibit ferroclectric hysteresis at room temperature with a weak polarization. (c) 2006 Elsevier Ltd. All rights reserved.

Activities in liquid Ga-Te alloys at 1120 k

The activity of gallium in liquid Ga-Te alloys has been measured at 1120 K using a solid state galvanic cell incorporating yttria-stabilized thoria as the solid electrolyte. The cell can be schematically represented as (−) W,Re,Ga(1)+Ga2O3(s)|(Y2O3) ThO2|Ga-Te(1) + Ga2O3(s), Re, W (+) The activity of tellurium was derived by Gibbs-Duhem integration. The activity of gallium shows negative deviation from Raoult's law for XGa < 0.6 and positive deviation from ideality for XGa > 0.6. The activity of gallium was constant in the composition range 0.73 < XGa < 0.89, indicating liquid state immiscibility in this region. The Gibbs energy of mixing and the concentration-concentration structure factor at long wavelength limit show a minimum at XGa ≈ 0.4, suggesting strong interactions in the liquid phase with formation of ‘Ga2Te3‘-type complexes

Formation of crystalline diamond from amorphous diamond-like carbon films by pulsed laser irradiation

The formation of crystalline diamond films from amorphous diamond-like carbon films by pulsed laser irradiation with a 300 μs non-Q-switched Nd:YAG laser has been established by a combined study of transmission electron microscopy, x-ray photoelectron spectroscopy, and electrical resistivity. The films have been prepared by glow discharge decomposition of a mixture of propane, n-butane, and hydrogen in a rf plasma operating at a frequency of 13.56 MHz. Prior to laser irradiation, the films have been found to be amorphous by transmission electron microscope studies. After irradiation, the electron diffraction patterns clearly point out the formation of cubic diamond structure with a lattice spacing of 3.555 Å. However, the close similarity between diamond and graphite electron diffraction patterns could sometimes be misleading regarding the formation of a diamond structure, and hence, x-ray photoelectron spectroscopic studies have been carried out to confirm the results. A chemical shift in the C 1s core level binding energies towards higher values, viz., from 286.5 to 287.8 eV after laser irradiation, and a high electrical resistivity >1013 Ω cm are consistent with the growth of diamond structure. This novel "low-temperature, low-pressure" synthesis of diamond films offers enormous potential in terms of device compatibility with other solid-state devices.

Crystallization Studies of ZrO2-SiO2 Composite Gels

Composite ZrO2-SiO2 powders were prepared using a gel route. Morphological and crystallographic features of ZrO2 particles formed during the heat treatment, and the particle sizes of the composites have been investigated. The following polymorphic changes have been observed during the heat treatment: amorphous -> metastable-cubic/tetragonal ZrO2 -> tetragonal ZrO2 -> monoclinic ZrO2. SiO2 crystallizes above 1273 K. The martensitic transformation of ZrO2 (t -> m) was observant in situ, when exposed to a high-energy electron beam. These results are important in the production of ZrO2-toughened ceramics of controlled microstructure.

Ba3ZnTa2-xNbxO9 and Ba3MgT2-xNbxO9: synthesis, structural and dielectric studies

Oxides of the families Ba3ZnTa2-xNbxO9 and Ba3MgTa2-xNbxO9 were obtained by the solid state reaction route at 1573 K and were found to crystallize in the disordered (cubic) perovskite structure. In Ba3ZnTa2-xNbXO9 and Ba3MgTa2-xNbxO9 the entire range (0 less than or equal to x less than or equal to 1) of solid solutions could be synthesized. The dielectric constant decreases with increase in frequency for all compositions in the range 40 Hz to 100 kHz (epsilon (r) varies from 16 to 22). The dielectric loss (D) shows a broad maximum for both Ba3ZnTa2-xNbxO9 and Ba3MgTa2-xNbxO9. The maxima is centered around 2 kHz in the former and near 10 kHz in the latter. (C) 2001 Elsevier Science Ltd. All sights reserved.

Characterization of barium titanate fine powders formed from hydrothermal crystallization

A detailed evaluation of size, shape and microstrains of BaTiO3 crystallites produced by hydrothermal crystallization at 90 – 180 °C and 0.1 – 1.2 MPa, from amorphous TiO2· xH2O (3 < × < 8) gel and aqueous Ba(OH)2 is presented, using X-ray line-broadening and TEM studies. Whereas the concentration of Ba(OH)2 and the acceptor impurities affect the crystallite shape, the stoichimetry with respect to Ba/Ti, donor as well as acceptor impurities, and the temperature of crystallization influence the microstrains. It is shown that strains in the crystallites are related to the point defects in the lattice. Compensation of the residually present hydroxyl ions in the oxygen sublattice by cation vacancies results in strains leading to metastable presence of the cubic phase at room temperature. Studies on the diffuse phase transition behaviour of these submicron powders show that the stable tetragonal phase is produced only on annealing at high temperatures where the mobility of cations vacancies are larger. Heat-treatment reduces anisotropy and strain in undoped samples, whereas annealing is less effective in doped materials. Comparison of the crystillite size by TEM showed better agreement with the Warren—Averbach method.

A comparative study of superconducting LaBa2Cu3O7−δ and La3−xBa3+xCu6O14+δ

Based on X-ray diffraction and electron microscopy it is shown that oxides of the general formula La Ba2Cu3O7−δ become tetragonal when δ deviates slightly from 0. This tetragonal structure is similar to that of La3−xBa3+xCu6O14+δ, with a cubic perovskite subcell and triple periodicity. Electron micrographs of these tetragonal oxides show 90° microdomains. Orthorhombic LaBa2Cu3O7−δ with high Tc (not, vert, similar77 K) is found only when δ reverse similar, equals 0; this sample is subject to formation of twins. Fluorine substitution seems to favor superconductivity.

Synthesis, characterization and photoluminescence properties of Gd2O3:Eu3+ nanophosphors prepared by solution combustion method

Gd2O3:Eu3+ (0.5-8.0 mol%) nanophosphors have been prepared by low temperature solution combustion method using metal nitrates as oxidizers and oxalyl dihydrazide (ODH) as a fuel. The phosphors are well characterized by powder X-ray diffraction (PXRD), scanning electron microscopy (SEM), Fourier transform infrared spectroscopy (FT-IR) and photoluminescence (PL) techniques. PXRD patterns of as-formed and calcined (800 degrees C, 3 h) Gd2O3 powders exhibit monoclinic phase with mean crystallite sizes ranging from 20 to 50 nm. Eu3+ doping changes the structure from monoclinic to mixed phase of monoclinic and cubic. SEM micrographs shows the products are foamy, agglomerated and fluffy in nature due to the large amount of gases liberated during combustion reaction. Upon 254 nm excitation the photoluminescence of the Gd2O3:Eu3+ particles show red emission at 611 nm corresponding to D-5(0)-> F-7(2) transition. It is observed that PL intensity increases with calcination temperature. This might be attributed to better crystallization and eliminates the defects, which serve as centers of non-radiative relaxation for nanomaterials. It is observed that the optical energy gap (E-g) is widened with increase Eu3+ content. (C) 2010 Elsevier B.V. All rights reserved.