Measured Dispersion Curves Research Articles

Contactless characterization of antisymmetric edge wave dispersion along truncated wedge using electromagnetic acoustic transducer

Accurate laboratory measurements are compared with approximate theoretical calculations on the dispersion of antisymmetric flexural edge waves propagating along the apex of a truncated 6061 aluminum wedge with an apex angle Θ=26.7°. The wedge waves are detected with a specially designed electromagnetic acoustic transducer in the frequency range 30–500 kHz. Phase velocity dispersion plots are obtained from gated sinusoidal signals and wavelength measurements averaged over 10–20 wavelengths. The general characteristics of the experimental phase velocity dispersion data closely matched the approximate theoretical parabolic model by McKenna etal. [IEEE Trans. Sonics Ultrason. SU-21(3), 178–186 (1974)] derived for small apex angle. The measured dispersion curve was duplicated using a truncated wedge tip width 57 μm in the parabolic approximation calculations while the actual measured tip width was 62 μm Antisymmetric flexural wedge waves obtained from a sharp apex (3 μm) are practically nondispersive as expected in the same frequency range. Previously reported laser ultrasonic dispersion measurements obtained by Jia etal. [Appl. Phys. Lett. 61, 2970–2972 (1992) and IEEE Ultrason. Symp. Proc. 1993, paper B4] revealed unexplained measured dispersion behavior of antisymmetric wedge flexural waves based on a phase analysis method. Contactless electromagnetic acoustic direction of antisymmetric wedge waves provided dispersion results in agreement with theoretical calculations. [Work supported by ONR.]

Dispersion curve analysis of laser-generated Lamb waves

Experiments have been conducted with a Q-switched ruby laser to study thermoelastic generation of Lamb waves in plates. The objective of this study was to resolve experimentally the various modes that propagate in a thick plate after absorption of a short laser pulse at its upper surface. The methodology consists of acquiring several laser-generated waveforms at various points on the plate. These waveforms are processed with a two-dimensional fast Fourier transform, in space and time, to obtain the dispersion curves of the plate, in wave-number and frequency. The technique can be used to determine which modes propagate in the structure as well as their relative amplitudes. This method, which is commonly used in structural acoustics, has not previously received much attention in laser ultrasonics even though it is particularly well adapted for measuring dispersion curves, because optical methods alleviate the problem of irreproducible coupling that exists with conventional piezoelectric ultrasonic transducers.

On the lattice dynamics of alkali metals

The phonon frequencies of alkali metals calculated on the basis of a valence force field model (used by Mishra and Singh) are compared with those previously deduced on the basis of the present author's CGW model, to examine the claim that the former model produces a crossover in lithium along the [ζ 0 0] direction. It is shown that this model which is neither selfconsistent nor in confirmity with the symmetry requirements of the lattice, is incapable of producing a crossover in any alkali metal. The distortions introduced by the deficiencies of this model into the elastic constants and phonon frequencies of alkali metals, the dubious claims regarding the electron-ion interactions and the reproduction of the observed crossover in lithium as well as the apparent between the calculated and measured dispersion curves, are discussed.

THEORETICAL STUDY OF LATTICE DYNAMICAL PROPERTIES IN FERROELECTRIC LiTaO3

We present the phonon-dispersion curves, the one-phonon density of states, the lattice specific heat cv(T) and the Debye temperature Θ(T) of the ferroelectric LiTaO 3, based on full lattice dynamical model whose parametèrs are fitted to the optical data and neutron measured dispersion curves. A model theory is developed to describe the transition from Debye to non-Debye behaviors observed in the low temperature part of the cv/T3 curve. The cv/T3 function, when is properly scaled, can be fitted by a general function derived from the model. It can be characterized by the temperature T max at which it has maximum, its maximum value (cv/T3)T=T max and its value at zero temperature (cv/T3)T=0. These results are considered useful in searching possibly anomalous phonon behavior from the specific heat cv(T).

Interface-phonon dispersion and confined-optical-mode selection rules of GaAs/AlAs superlattices studied by micro-Raman spectroscopy.

Using micro-Raman spectroscopy, we study backscattering from (010) and (11\ifmmode\bar\else\textasciimacron\fi{}0) surfaces of [001]-grown superlattices and establish experimental selection rules. By changing the momentum transfer ${\mathit{q}}_{\mathrm{\ensuremath{\parallel}}}$ parallel to the superlattice layers over a wide range (0\ensuremath{\le}${\mathit{q}}_{\mathrm{\ensuremath{\parallel}}}$\ensuremath{\le}9\ifmmode\times\else\texttimes\fi{}${10}^{5}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$), we studied the dispersion of the interface phonons. The measured dispersion curves are compared to calculations based on the dielectric-continuum model.

QUANTITATIVE NONDESTRUCTIVE EVALUATION USING GUIDED WAVES

Abstract This paper deals with two applications of guided waves in quantitative nondestructive evaluation (QNDE): the detection of cracks in beams and the determination of elastic material constants of filament-wound cylindrical composite shells. As an alternative to the use of bulk waves, the reflection characteristics of guided waves having a wavelength much larger than the size of a defect are used to assess defects in structural elements as beams or plates. Bending waves incident at a lateral notch in an isotropic beam of circular cross-section are considered both experimentally and theoretically. When shear effects are taken into account both in the modelling of the crack and the propagation of the elastic waves, then theory and experiment are in good agreement up to a ratio of beam radius to wavelength of 0.25. Filament-wound circular cylindrical shells were examined by measuring dispersion curves for the first two axisymmetric modes of propagation and torsional waves using a combination of resonanc...

Surface dynamics of ordered Cu 3Au(001) studied by elastic and inelastic helium atom scattering

Inelastic helium atom scattering has been used to measure the surface phonon dispersion curves for the (001) face of the ordered phase of Cu 3Au along the 〈100〉 (i.e., γ − M ′) direction. We report the spectroscopic observation of two surface phonon modes on this fcc alloy, and present a detailed description of the scattering instrument that was used for making these measurements. The lower-energy surface phonon mode, the Rayleigh wave, has an energy of 7.1 ± 0.5 meV at M̄'. The higher-lying feature is an optical mode with an energy of 12.5 ± 1.0 meV, which shows little dispersion across the surface Brillouin zone. This phonon mode might be interpreted as a folded Rayleigh mode. The experimentally measured dispersion curves do not agree with those generated by a lattice dynamical slab calculation which uses a pair potential force-field that successfully models the bulk vibrations of the ordered alloy. The best fit to our experimental data indicates that the force constant between the first and second layer Cu atoms needs to be stiffened by ∼ 20% with respect to the corresponding bulk value.

Alternative stable rotors in an excitable medium

A given excitable medium (continuous, uniform, isotropic, simply connected, two- or three-dimensional) may support alternative types of vortex-like solution radiating from a ‘rotor’. These have distinct periods, wavelengths, behaviors near interfaces, and, in rotationally symmetric vortex rings, different contraction or expansion rates and drift rates. Initial conditions select among the discrete alternatives. Rotors of different types may coexist within one medium, until the interface between their domains encroaches upon the rotor of longer period. Examples are given using the FitzHugh-Nagumo model. They are interpreted in terms of the measured dispersion curve for one-dimensional propagation and a hypothetical ‘curvature relation’ with one undetermined parameter.

Evaluation of friction-welded aluminum-steel bonds using dispersive guided modes of a layered substrate

In nondestructive evaluation the inspection of bond quality is a very important problem. In this paper we suggest an experimental method based on dispersion curve measurements for evaluating the quality of the bond between a layer and a substrate bonded by the inertia-friction welding process. The experimental results are in good agreement with theoretical calculations which show that the behavior of the lowest velocity modes is very sensitive to the interface conditions and to the quality of the bond.

Excitation-induced modification of polariton dispersion curves in molecular media within different approaches

Giant polarition dispersions by Frenkel excitons are derived and compared within three approaches: the boson representation, the effective Hamiltonian formalism and that based on the exact commutation relations for non-boson exciton operators. The latter approach resulted in a situation which could serve as a possible method of determining the effective dynamical exciton-exciton coupling constant by measuring dispersion curves of the polariton energy lower-branches under different levels of excitation.

Evaluation of In Situ Effective Shear Modulus from Dispersion Measurements

A procedure is described for evaluating shear modulus depth profiles of uniformly deposited soil strata. The method combines steady-state vibration techniques for subsoil exploration and results from the analytical treatment of surface wave propagation problems in an elastic half-space with depth-depending stiffness. The model proposed covers a wide range of real soil deposits. The shear modulus variation with depth is obtained from the measured dispersion curve by assigning the surface wave velocity to the soil conditions at a depth of 0.3 times the wavelength.

Eigenvalues and eigenvectors in CuCl at 4.2 K

A simple 11-parameter rigid-ion model (RIM) is used to describe the low temperature phonon dispersion curves of CuCl measured by the neutron scattering technique. By using an optimized set of force constant parameters, this model is shown to reproduce the measured dispersion curves. Using this set of force constants the eigendisplacements due to both atoms are calculated along the lines of high symmetry directions. In the absence of any information on the eigendisplacements, the present prediction are compared with those calculated on the basis of 14-parameter shell model (SM) by us.

Interference of Raman and parametric processes in small angle scattering

Angular spectra of light scattering by polaritons are discussed. The angular line shape in the case of interference between Raman and parametric processes is considered. It is shown that the angular line shape can be used for calculation of complex dielectric function ϵ and complex quadratic susceptibility χ at a given polariton frequency. The proposed method is used for measuring dispersion curves of Re χ, Im χ and Im ϵ for lithium-natrium formate crystal at frequencies 3000–3700 cm -1.

Adsorption distance of S on Ni(001): An electron-energy-loss-spectroscopy cross-section analysis of the Ni(001)-c(2 x 2)S system.

The inelastic-electron-scattering cross sections of surface and antinode adsorbate-induced bulk phonons are calculated for the Ni(001)-c(2\ifmmode\times\else\texttimes\fi{}2)S system. The calculated cross sections are sensitive to variations in the incident electron energy, phonon ${\mathrm{q}}_{?}$, and the spacing between S and Ni layers. By comparing calculated cross sections with measured electron-energy-loss spectra at different electron energies and phonon ${\mathrm{q}}_{?}$ vectors, we determined the S-Ni spacing unambiguously at 1.35 A\r{}. An ad hoc non-central-force model was introduced to explain the measured dispersion curves.

Effects of Covalency on the Phonon Dispersion Relations in the NaCl-Type Alkali Halide Crystals. III.

A lattice dynamical model for the NaCl-type crystals are constructed which is a composite of the covalency model and the deformation dipole model. Using this model, the covalency parameter n c , the number of electrons occupying the outer most s orbitals of an alkali metal atom, is determined from the measured dispersion curves of 13 NaCl-type alkali halides by the least-squares analyses subject to the constraint that the model parameters reproduce the dielectric and elastic constants. The obtained n c values are contrary to the expectation of the traditional idea ( n c =0): about 0.08 for the fluorides, 0.10 the chlorides, and 0.15 the bromides and iodides.

Magnetic excitations in the quasi one-dimensional antiferromagnetic singlet groundstate system CsFeBr 3

The measured dispersion curves of the magnetic excitations in CsFeBr 3 are very unusual. The observed intensities are interpreted by a heuristic model including antiferro- as well as ferromagnetic fluctuations. The main dispersion curve with strong intensity is obtained due to “in-plane” fluctuations. A “mirrored” curve which is not predicted by theory is observed with weak intensity due to “out-of-plane” fluctuations.

Magnetic excitations in the quasi one-dimensional antiferromagnetic singlet groundstate system CsFeBr3

We have measured the magnetic excitations in CsFeBr3 along the chain direction (z-axis) and perpendicular to it by inelastic neutron scattering. The measured dispersion curves can be reproduced by the formula $$\omega ^2 (q) = A^2 - 8A[J\cos (\pi q_c ) + J'\gamma (2\pi q_ \bot )]R(T)$$ which is very different from dispersion relations for usual 1 D antiferromagnets, because of the singlet groundstate of this system. The large value of the anisotropy energyA/k=29.8±0.5 K, which is independent of temperature, causes the singlet groundstate. The intra-and inter-chain exchange parameters areJ/k=−3.2±0.15K andJ'/k=−0.32±0.02 K determined atT=1.4 K. At 1.4 K the renormalisation factor is taken to beR(T)=1. AtT=30 K the value forR(T) was found to be 0.5±0.1 keepingJ andJ' unchanged. The excitations at (1/3 1/31) show soft mode behaviour but no phase transition. The observed intensities are interpreted by a heuristic model for the eigenvectors in the excited state including antiferro-as well as ferromagnetic configurations of the fluctuations.

A study of generalized Lamb waves in solid-state bonded aluminum-steel samples

Wave propagation in the aluminum layer on a steel substrate and the steel layer on an aluminum substrate has been studied. These material combinations correspond to the special case where the transverse velocities are close to each other while the densities and longitudinal velocities are not. Experimental measurements were carried out using two different methods: (i) single transducer broadband, and (ii) double transducer narrow band. Experimentally obtained dispersion curves for the phase velocities were compared to existing theoretical calculations. A method to evaluate the quality of solid-state bond based on the measured dispersion curve is also suggested. [Work supported by D.O.E.]

Digital signal processing techniques for plasma dispersion curve measurements

Five different digital signal processing techniques for estimating the dispersion properties of plasma or fluid instabilities are discussed. The implementation of each method on a minicomputer is described, and a comparison of their relative merits made by employing data obtained from a steady-state linear quadrupole plasma containment device.

Effects of Covalency on the Phonon Dispersion Relations in the NaCl Type Alkali Halide Crystals.II

A lattice dynamical model for the NaCl-type crystals are constructed which is a composite of the covalency model and the deformation dipole model. Using this model, the covalency parameter n c , the number of electrons occupying the outer most s orbitals of an alkali metal atom, is determined from the measured dispersion curves of 13 NaCl-type alkali halides by the least-squares analyses subject to the constraint that the model parameters reproduce the dielectric and elastic constants. The obtained n c values are contrary to the expectation of the traditional idea ( n c =0): about 0.08 for the fluorides, 0.10 the chlorides, and 0.15 the bromides and iodides.