On the Reconstruction of NQR Nutation Spectra in Solids with Powder Geometry

Abstract

In single crystals the NQR nutation frequency depends on the relative orientation of the coil and the quadrupole axes. In powders the nutation lineshape is a superposition of spectra from the randomly oriented single crystals, so that powder patterns appear in such experiments if the recon­struction is performed by the Fourier transform method. In this paper an alternative reconstruction method of nutation spectra is suggested making use of the Hankel Transform. In this way the nutation spectra are simplified. Singularities arising with experiments for the determination of the asymmetry parameter η can easily be resolved. In the particular case of an axially symmetric quadrupolar tensor and a homogeneous radiofrequency field one can reduce the powder pattern to a single line without heterogeneous broadening with respect to orientation. Further improvement o f the nutation spectra can be achieved by taking advantage of the maximum entropy method, which strongly reduces apodisation and noise problems. Applications of the new data manipulation techniques to N Q R imaging methods published elsewhere and 2D zero-field N Q R spectroscopy are reported.

Solid State Proton Imaging Detected by Quadrupole Resonance

“…The reconstruction of the one-dimensional profile was performed by the maximumentropy method to remove the powder distribution of nutation frequencies that distort the image from the profile (11). As the same surface coil was used for signal detection, adequate B 1 field correction was applied in the spatial dimension to compensate for the spatial dependence of sensitivity.…”

Two-Dimensional Rotating-Frame NQR Imaging

“…complicated for NQR in powders than for NMR, and special data-evaluation procedures must be applied in this case After removing the powder distribution from the 2D nutation NQR spectrum, X (v 1 , v 2 ), the surfaces of constant H i (13,14). The reconstruction procedure must take into consideration both the orientational dependence of the nutation correspond to surfaces of constant nutation frequency v i Å gH i , and the total NQR intensity in each frequency interval frequency, which results in an inhomogenous broadening of the nutation lineshape, and the departure of the encoding is proportional to the number of nuclei in the sample lying between those surfaces.…”

“…The orientational distortion of the image, even for must be considered. In order to keep image reconstruction simple, the surfaces of constant field should ideally be planes an arbitrary value of h, can then be overcome by suitable reconstruction procedures (14). perpendicular to the gradient directions, and the RF encoding gradients, G x and G y , must be orthogonal everywhere over For the reconstruction of the planar images from Eq.…”

A Fast Method for the Spatial Encoding in Rotating-Frame NQR Imaging

“…In NQR, no such magThe deconvolution procedures, Fourier-transform based (6), netization vector exists; then there is no single pictorial deHankel transform (HT) (7), and maximum-entropy method (MEM) (7), have been described elsewhere.…”