Characterization Of Anisotropic Materials Research Articles

An Expansion for Use in the Simulation and Analysis of NMR Data

Abstract The time-domain NMR signal that results from chemical shifts or first-order quadrupolar effects in materials with either a few well-defined sites or a distribution in orientation or coupling constants is given by an integral of exp[ikt(3 cos2θ − 1)] or exp[ikt(3 cos2θ − 1 + η sin2θ cos 2 φ)] times a weighting probability for orientation and/or coupling constants. Data analysis requires either execution of angular averages, as for a powder sample, or determination of the weighting function, as for an oriented sample. Development of expansions of the above exponential forms in spherical harmonics for use in such data analysis is initiated. This development is analogous to the Ray leigh expansion of exp (ikr cos θ) in spherical harmonics that is ubiquitous throughout scattering theory. Applications to analysis of a 2D NMR experiment, characterization of anisotropic materials, and determination of the distribution of coupling constants are discussed as examples of the reduction of computation time, by use of analytic, rather than the currently used numerical, execution of angular averages. It is also expected that the availability of algebraic forms provides a useful alternative perspective, complementary to numerical calculations, offering a potential for direct extraction of motional correlation functions from NMR data and estimation of orientation probabilities. A transformation needed for application of the expansion to magic-angle spinning of rigid-lattice samples is developed.

Wavelet representation of the three‐dimensional anisotropic elastodynamic Green’s function

A detailed knowledge of waveforms is required for nondestructive ultrasonic characterization of anisotropic materials. The waveforms can be calculated in terms of the elastodynamic Green’s function of solids. The traditional Fourier/Laplace transform methods are computationally inefficient for three‐dimensional anisotropic solids since they require four‐dimensional numerical integration in the wave vector and the frequency space. A representation of the Green’s function has been developed in terms of highly localized Huygens‐type wavelets in which the Green’s function is expressed in the space of slowness vectors rather than that of wave vectors and frequency. The wavelet representation requires only a one‐dimensional numerical integration of simple functions and thus saves computational (CPU) time by a factor of about 1000 compared to the Fourier transform method. A solution of the tensorial elastodynamic Cauchy problem and calculation of the retarded Green’s function will be described in terms of these wavelets. Results will be presented for pulse propagation in anisotropic solids.

Rheological characterization of anisotropic materials

Constitutive equations are considered to describe the behaviour of anisotropic materials produced by continuous reinforcement of a matrix with one or two families of relatively stiff fibres. In particular, the shear response of such materials is investigated, and it is shown how torsional tests on thin plate specimens can be used to directly determine the transverse and longitudinal shear moduli for elastic, viscoelastic and elastic-plastic behaviours.

The converging-surface-acoustic-wave technique: anaylsis and applications to nondestructive evaluation

Converging surface-acoustic waves (SAW) are generated by irradiating the inspected material with an annular-shaped pulsed laser beam. The converging-SAW pulse arrival is detected by a laser interferometer focused on the center of the annulus, where the converging effect produces a strong amplification of the ultrasonic pulse. This technique can be applied either to the detection of defects or to the characterization of the material by measuring the SAW velocity or attenuation. In this paper we present an analysis of the converging-wave propagation in order to explain some features of the detected signal, such as its shape and amplitude for different positions of the probing beam. A comparison with the signal intensities expected for a diverging as well as a collimated SAW is also presented. Applications of this technique to the characterization of anisotropic materials as well as to the detection of subsurface planar defects are presented and discussed.