Effect of static deflection on natural frequency of non-linear spring mass system by direct linearization method

An exact expression for the frequency of a non-linear cubic spring mass system is obtained considering the effect of static deflection. An alternative expression for the approximate frequency is also obtained by the direct linearization procedure; it is shown that this is very accurate as compared with the exact method. This approximate frequency equation is used to explain a “dual behaviour” of the frequency amplitude curves.

Response spectrum of non-linear spring mass system subjected to transient disturbances

The transient response spectrum of a cubic spring mass system subjected to a step function input is obtained. An approximate method is adopted where non-linear restoring force characteristic is replaced by two linear segments, so that the mean square error between them is a minimum. The effect of viscous damping on the peak response is also discussed for various values of the damping constant and the non-linearity restoring force parameter.

Elastic constants of triclinic copper sulphate pentahydrate crystals

Using an iterative technique to obtain the exact solutions of the cubic Christoffel equation, the 21 elastic constants of copper sulphate pentahydrate have been determined at 25°C by the ultrasonic pulse echo method. The elastic constants, referred to the IRE recommended system of axes, are c11=5·65, c12=2·65, c13=3·21, c14=−0·33, c15=−0·08, c16=−0·39, c22=4·33, c23=3·47, c24=−0·07, c25=−0·21, c26=0·02, c33=5·69, c34=−0·44, c35=−0·21, c36=−0·16, c44=1·73, c45=0·09, c46=0·03, c55=1·22, c56=−0·26 and c66=1·00 in units of 1010 N m−2.

The change of complete symmetry of the crystals during the phase transitions in ferroelectrics and ferromagnetics

The extension of the superposition principle of the symmetries (P. Curie principle of symmetry) for the case of complete symmetry is given. The enumeration of all crystallographical groups of complete symmetry is presented, the number of elements having complete symmetry for each class of the crystals being indicated. The change of complete symmetry of the crystals under the phase transitions is obtained by superimposing the elements of complete symmetry of polar or axial vectors on the one hand, and the elements of complete symmetry of the crystals on the other. The tables of complete symmetry changes for the cubic, rhombic, monoclinic and triclinic crystals during the ferroelectric and ferromagnetic phase transitions are given.

Effect of fuel on the formation structure, transport and magnetic properties of LaMnO3+nanopowders

Single-step low-temperature solution combustion (LCS) synthesis was adopted for the preparation of LaMnO3+ (LM) nanopowders. The powders were well characterized by powder X-ray diffraction (PXRD), scanning electron microscopy (SEM), energy dispersive spectroscopy (EDS),surface area and Fourier transform infrared spectroscopy (FTIR). The PXRD of as-formed LM showed a cubic phase but, upon calcination (900degrees C, 6 h), it transformed into a rhombohedral phase. The effect of fuel on the formation of LM was examined, and its structure and magnetoresistance properties were investigated. Magnetoresistance (MR) measurements on LM were carried out at 0, 1, 4 and 7 T between 300 and 10 K. LM (fuel-to-oxidizer ratio; = 1) showed an MR of 17% at 1 T, whereas, for 4 and 7 T, it exhibited an MR of 45 and 55%, respectively, near the TM-I. Metallic resistivity data below TM-I showed that the double exchange interaction played a major role in this compound. It was interesting to observe that the sample calcined at 1200 degrees C for 3 h exhibited insulator behavior.

Atomically resolved scanning tunneling microscopy on perovskite manganite single crystals

Atomically resolved scanning tunneling microscopy was conducted on cleaved single crystals of the cubic perovskite Pr0.68Pb0.32MnO3.Several different surface configurations could be resolved including a frequent square arrangement with atomic distances in excellent agreement to the bulk lattice constant of the cubic structure. We also observed stripe formation and a surface reconstruction. The latter is likely related to a polar rare earth-oxygen terminated surface. (C) 2010 American Institute of Physics.

Optical properties of magnetic crystals

From symmetry considerations and using generalized Onsager relations, it is shown that 66 of the 90 magnetic classes, consisting of 29 single colour and 37 double colour ones, can exhibit what may be called the strain gyrotropic rotation. Similarly, 69 of the 90 magnetic classes, consisting of 21 single colour and 48 double colour ones, can exhibit what may be called the strain gyrotropic birefringence. A crystal in the class m3 or m3 m is interesting as it can exhibit strain gyrotropic rotation despite its being cubic and incapable of exhibiting gyrotropic rotation in the unstressed state. Similarly, a crystal in the class m3 m, is interesting as it can exhibit strain gyrotropic birefringence despite its being cubic and incapable of exhibiting gyrotropic birefringence in the unstressed state.

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.

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.

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.