Powder-pattern line shape

Table 4. Powder pattern line shape simulation results of H quadrupole experiments for [3,3- H2]Ser-labeled B. mori and S.c. ricini silk fibroins...

Fig. 7.8 Solid-state C NMR "powder pattern" line shape for the case of C— H dipolar interaction and an ensemble of randomly oriented C- H units. The frequency axis is...

Fig. 7.9 Solid-state C[ H] NMR powder pattern line shape for C chemical shift anisotropy and an ensemble of randomly oriented — C=C (alkyne) units. Vertical bars show the resonance frequency at 0—0°, 10°,. .. to...

Figure 3 (A) Powder pattern line shape of an I nucleus coupled to a quadrupolar (S= 1) nucleus when fe/vos) = 1, J so = 0. The frequency axis is in units of the dipolar coupling constant D. (B) Frequencies (in units of D) of the three lines expected for an l,S pair S= 1) as a function of the ratio / os- The line positions marked with symbols have been obtained by full-matrix Hamiltonian calculations. The solid lines are the values given by Equation [6].

Figure 4 (A) Powder pattern line shape of an I nucleus coupled to a quadrupolar (S = 3/2) nucleus when = 1, = 0. The...

The analysis of XRPD patterns is an important tool studying the crystallographic structure and composition of powder compounds including the possibility to study deviation from ideal crystallinity, i.e. defects. Looking at an X-ray powder diffractogram the peak position reflects the crystallographic symmetry (unit cell size and shape) while the peak intensity is related to the unit cell composition (atomic positions). The shape of diffraction lines is related to defects , i.e. deviation from the ideal crystallinity finite crystallite size and strain lead to broadening of the XRPD lines so that the analysis of diffraction line shape may supply information about sample microstructure and defects distribution at the atomic level. 

This chapter considers the distribution of spin Hamiltonian parameters and their relation to conformational distribution of biomolecular structure. Distribution of a g-value or g-strain leads to an inhomogeneous broadening of the resonance line. Just like the g-value, also the linewidth, W, in general, turns out to be anisotropic, and this has important consequences for powder patterns, that is, for the shape of EPR spectra from randomly oriented molecules. A statistical theory of g-strain is developed, and it is subsequently found that a special case of this theory (the case of full correlation between strain parameters) turns out to properly describe broadening in bioEPR. The possible cause and nature of strain in paramagnetic proteins is discussed. 

The line shapes were calculated for the flipping motion with the two-site jump model described above, and the calculated spectra are shown in Fig. 11 for the higher temperature region. The experimental line shapes at 20 and 30° C are well reproduced showing the motional mode and rates obtained by T analysis are reasonable at least around these temperatures. Above 40°C the calculated line shapes are invariable and remain in the powder pattern undergoing a rapid flipping motion, while the experimental ones... 

The temperature dependent line shape of racemic PBG-yd2 is shown in Fig. 34 together with those of PBLG-yd2. The line shapes at room temperature appear to be the rigid state powder pattern, showing the absence of the large amplitude motion in the y position. The signal intensity of the... 

Figure 48 shows representative experimental 2H NMR spectra from the labeled retinal in bR in a dark-adapted PM sample. The line shape simulations that were generated in the data analysis are superimposed on the experimental spectra. The powder pattern [Figure 48(a)] serves as a general reference for the tilt series of spectra recorded at various sample inclinations [Figure 48(b)], because it defines the accessible frequency region over which the spectral intensity can occur. The oriented sample was measured at every 22.5° between 0° and 90°, of which three inclinations are represented in Figure 48(b) with a = 0°, 45° and 90°. 

Powder patterns of crystals with axial symmetry yield the value of qQ but do not, of course, give the direction of the axis of symmetry. Line shapes to be expected for the magnetic resonance in this situation have been calculated (95) and for / = %, the shape is illustrated in Fig. 11 for polycrystalline corundum (a-AbOs). 

A method known as Rietveld analysis has been developed for solving crystal structures from powder diffraction data. The Rietveld method involves an interpretation of not only the line position but also of the line intensities, and because there is so much overlap of the reflections in the powder patterns, the method developed by Rietveld involves analysing the overall line profiles. Rietveld formulated a method of assigning each peak a gaussian shape and then allowing the gaussians to overlap so that an overall... 

Representative broad line 2H NMR spectra obtained at -140, 30 and 60°C are presented in Fig. 5a, 5b and 5c, respectively. Differences in the signal to noise ratios of the spectra that appear in Fig. 5 may be attributed to the different number of transients that were observed during each experiment. Note that the surface bound acetone-d6 molecules, which would give rise to a very intense peak at the isotropic frequency, have been removed with gentle heating (60°C) prior to collecting the NMR spectra that are presented in Fig. 5. The shapes of the powder patterns are therefore dependent solely upon the motional state of the acetone-d6 molecules that are present within the microporous channels. 

In Fig. 5b, which was obtained at 30°C, the powder pattern displays a severely distorted, intermediate rate line shape. This line shape is characteristic of both fast methyl group rotation and 2 fold molecular re-orientation about the carbonyl bond at a rate comparable to the reciprocal of the quadrupolar coupling constant ( 105 Hz). At room temperature, therefore, the acetone-d6 molecules in the microporous channels of sepiolite are able to undergo restricted re-orientations. 

Fig. 4. Quadrupolar powder patterns (a) Spin NMR powder pattern showing that the central -)<- ) transition is broadened only by dipolar coupling, chemical shift anisotropy, and the second-order quadrupolar interactions, (b) Spin 1 NMR powder pattern for a nucleus in an axially symmetric electric field gradient (see text). The central doublet corresponds to 6 = 90° in Eq. (10). The other features of low intensity correspond to 6 = 0° and 6 = 180°. (c) Theoretical line shape of the ) - -) transition of a quadrupolar nuclear spin in a powder with fast magic-angle spinning for different values of the asymmetry parameter t (IS) ...

The narrow component corresponds to the amorphous fraction of the polymer and the axially symmetric powder pattern to the crystalline fraction of the polymer. Moreover, the amorphous as well as the crystalline line shapes extracted from samples of different crystallinity are essentially identical, which indicates that the structure and dynamics in the crystalline and amorphous fractions are independent of the degree of crystallinity. 

Neutron diffraction patterns of powder samples were taken on a neutron diffractometer (X = 1.085 A) mounted on the thermal column of a WR-SM nuclear reactor [3]. The DBW-3.2 program for the Rietveld neutron diffraction line shape analysis was used in calculations and structure refinement [4]. A DRON-3M X-ray diffractometer (CuK - radiation) was used to measure X-ray powder diffraction patterns. 

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