Anisotropic sample broadening

An improved modelling of the average structure of ice Ic includes linear combination of stacking-probability driven structure models and anisotropic size broadening. It allows for a quantitative modelling of neutron diffraction data of different ice Ic samples. It will serve as well for the description of ice Ih samples with stacking faults. 

Even for a single radical tire spectral resolution can be enlianced for disordered solid samples if the inliomogeneous linewidth is dominated by iimesolved hyperfme interactions. Whereas the hyperfme line broadening is not field dependent, tire anisotropic g-matrix contribution scales linearly with the external field. Thus, if the magnetic field is large enough, i.e. when the condition... 

The diffraction lines due to the crystalline phases in the samples are modeled using the unit cell symmetry and size, in order to determine the Bragg peak positions 0q. Peak intensities (peak areas) are calculated according to the structure factors Fo (which depend on the unit cell composition, the atomic positions and the thermal factors). Peak shapes are described by some profile functions 0(2fi—2fio) (usually pseudo-Voigt and Pearson VII). Effects due to instrumental aberrations, uniform strain and preferred orientations and anisotropic broadening can be taken into account. 

Molecules in the solid state are in fixed orientations with respect to the magnetic field. This produces chemical shift anisotropic powder patterns for each carbon atom since all orientations are possible (Fig. 2). It was shown as early as 1958 that rapid sample rotation of solids narrowed dipolar-broadened signals [18]. Several years later, it was recognized that spinning could remove broadening caused by CSA yet retain the isotropic chemical shift [19]. 

The nucleus is quadrupolar (spin 7/2, natural abundance 99.76%), and thus, the spectra can be affected by both the first- and second-order quadru-pole interaction, though the second-order broadening is generally not the largest source of line broadening in these materials. In general, three major anisotropic interactions influence the line shapes seen in the NMR spectra of solid samples (i) the qua-... 

Fig. 3. Magic angle spinning and its effect on anisotropic interactions. The dashed vector, denoting one particular dipolar interaction, or some other measure of molecular orientation, is shown on the right in terms of the geometry of sample spinning. By rotating the sample rapidly about an appropriate axis, the anisotropy or broadening experienced by the nucleus can be reduced to zero.

A possible modification of this expression is presented elsewhere (82). The value of t, can be related to a diffusion coefficient (e.g., tj = l2/6D, where / is the jump distance), thereby making the Ar expressions qualitatively similar for continuous and jump diffusion. A point of major contrast, however, is the inclusion of anisotropic effects in the jump diffusion model (85). That is, jumps perpendicular to the y-ray direction do not broaden the y-ray resonance. This diffusive anisotropy will be reflected in the Mossbauer effect in a manner analogous to that for the anisotropic recoil-free fraction, i.e., for single-crystal systems and for randomly oriented samples through the angular dependence of the nuclear transition probabilities (78). In this case, the various components of the Mossbauer spectrum are broadened to different extents, while for an anisotropic recoil-free fraction the relative intensities of these peaks were affected. 

Figure 14.1 ID spectra of a typical rubber, styrene-butadiene-rubber (SBR). a) Static spectrum acquired at a Larmor frequency of 500 MHz. The dipolar coupling is motionally averaged and different lines can be distinguished although they are still broadened by the residual dipolar couplings, b) MAS spectrum of the same sample at a MAS spinning frequency of 15 kHz. The line-broadening due to anisotropic spin interactions, e.g., residual dipolar couplings, is removed...

Theoretically, ESR lines should be infinitely narrow, experimentally, they are broadened by various mechanisms, both intrinsic (determined by sample properties and the physics of the resonance experiment) and extrinsic (dependent on spectrometer operating conditions) Line shapes of ESR signals of peroxy radicals in lignin are often asymmetric because of the solid-state or power spectrum effects of the vanous anisotropic interactions... 

In organic metals, the nature of the molecular tt orbitals that form the conduction bands leads to a dipolar hyperfine interaction that may be nonnegligible when compared with the contact contribution discussed above [23]. The various terms in the dipolar interaction modify K and Tx 1 in different ways. The dipolar component [3] can be written as a sum of terms, some of which produce anisotropic Knight shifts (or line broadening in powder samples) and contribute to the spin-lattice relaxation rate. 

---