Line broadening phenomena

NMR spectra of solids with the quality of high resolution can be achieved when the above mentioned line broadening phenomena are removed or at least considerably reduced. Only in these cases spectra can be obtained which enable, for example, crystallographically nonequivalent sites of a zeoiitic material framework to be resolved as individual resonance lines. High resolution NMR spectra of solids can be received by use of one or more experimental techniques described in the following ... 

The causes of line-broadening phenomena in carbons can therefore be summarized as follows ... 

On the other hand, the concept of the graphitic crystallite and its assitmed existence within all carbons have stimulated crystallographers to fine-tune their analyses and interpretations of line-broadening phenomena. The Japanese Society for the Promotion of Science (JSPS, 1963) standardized procedures for the calculation of crystallite sizes (Shiraishi, 2003). 

The cross-correlation effects between the DD and CSA interactions also influence the transverse relaxation and lead to the phenomenon known as differential line broadening in a doublet [40], cf Figure Bl.13.8. There is a recent experiment, designed for protein studies, that I wish to mention at tire end of this section. It has been proposed by Pervushin etal [4T], is called TROSY (transverse relaxation optimized spectroscopy) and... 

X-ray line broadening provides a quick but not always reliable estimate of the particle size. As Cohen [9] points out, the size thus determined is merely a ratio of two moments in the particle size distribution, equal to /. Both averages are weighted by the volume of the particles, and not by number or by surface area, as would be more meaningful for a surface phenomenon such as catalysis. Also, internal strain and instrumental factors contribute to broadening. 

In the case of solutions, concentration fluctuations only contribute to the central elastic part of the scattering spectrum. However, the Brownian movement of solute molecules creates weak frequency displacements that broaden the central peak. This phenomenon is called Rayleigh line broadening or quasielastic scattering [26-28]. This section deals with elastic scattering only. 

The powder pattern of H-BOR-E is intermediate between the patterns of H-BOR-C and H-BOR-D (see Figure 1). In particulat, the intensities of the reflections with h+k+l=2n+l (according to the unit cell characteristic of H-BOR-C) are lower in the pattern of H-BOR-E with respect to the pattern of H-BOR-C and are accompanied by some line broadening (see for example 133 at 20 24.5° in the patterns of Figure 1). The intensities of the remaining reflections are practically invariant. Moreover a partial coalescence of hkl and khl reflections is observed in the pattern of H-BOR-E. These effects occur to varying extent in the patterns of different samples of H-BOR-E. The trend observed in the pattern of H-BOR-D is similar to that observed in the pattern of H-BOR-E, but the extent of the phenomenon is more pronunced for the latter. 

An expression for the line broadening resulting from rapid radiationless transitions has been derived by introducing a number of simplifying assumptions into the physical description of the phenomenon. 

Due to the finite propagation time T of the wavepackets, the Fourier transformation causes artifacts known as the Gibbs phenomenon [122]. In order to reduce this effect, the autocorrelation function is first multiplied by a damping function cos jtt/IT) [81,123]. Furthermore, to simulate the experimental line broadening, the autocorrelation functions will be damped by an additional multiplication with a Gaussian function exp — t/xd)% where zj is the damping parameter. This multiplication is equivalent to a convolution of the spectrum with a Gaussian with a full width at half maximum (FWHM) of /xd- The convolution thus simulates... 

When the line broadening becomes a serious obstacle, one can take advantage of a phenomenon that results in narrower lines. Specifically, substitution of1H atoms with the 2H isotope coupled with 2H NMR spectroscopy results in spectral lines that are up to 40 times narrower than those of corresponding ll NMR, due to slower nuclear relaxation of the 2H nuclei in paramagnetic compounds. 

The above studies on H-NMR spectra of these stemona alkaloids allowed discovery of a phenomenon and called " a line broadening effect of H-NMR signal". Addition of a trace quantity of DCL resulted in extensive broadening of the signals due to protons spatially close to the nitrogen lone pair later it was found that by adding an appropriate amount... 

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