Axial anisotropy

Axial Anisotropy Axial direction Radial direction nane anisotropy ... 

MAS Si speetnim of a sample of sodium disilieate (Na Si O,) erystallized from a glass is shown as an example. Whilst the statie speetnim elearly indieates an axial ehemieal shift powder pattern, it gives no evidenee of more than one silieon site. The MAS speetnim elearly shows four resolved lines from the different polymorphs present in die material whose widths are 100 times less than the ehemieal shift anisotropy. 

Figure 3 Characteristic solid state NMR line shapes, dominated by the chemical shift anisotropy. The spatial distribution of the chemical shift is assumed to be spherically symmetric (a), axially symmetric (b), and completely asymmetric (c). The top trace shows theoretical line shapes, while the bottom trace shows rear spectra influenced by broadening effects due to dipole-dipole couplings.

It has been shown that the anisotropy depends on the orientation of the diagonals of indentation relative to the axial direction 14). At least two well defined hardness values for draw ratios A. > 8 emerge. One value (maximum) can be derived from the indentation diagonal parallel to the fibre axis. The second one (minimum) is deduced from the diagonal perpendicular to it. The former value is, in fact, not a physical measure of hardness but responds to an instant elastic recovery of the fibrous network in the draw direction. The latter value defines the plastic component of the oriented material. 

This simple relaxation theory becomes invalid, however, if motional anisotropy, or internal motions, or both, are involved. Then, the rotational correlation-time in Eq. 30 is an effective correlation-time, containing contributions from reorientation about the principal axes of the rotational-diffusion tensor. In order to separate these contributions, a physical model to describe the manner by which a molecule tumbles is required. Complete expressions for intramolecular, dipolar relaxation-rates for the three classes of spherical, axially symmetric, and asymmetric top molecules have been evaluated by Werbelow and Grant, in order to incorporate into the relaxation theory the appropriate rotational-diffusion model developed by Woess-ner. Methyl internal motion has been treated in a few instances, by using the equations of Woessner and coworkers to describe internal rotation superimposed on the overall, molecular tumbling. Nevertheless, if motional anisotropy is present, it is wiser not to attempt a quantitative determination of interproton distances from measured, proton relaxation-rates, although semiquantitative conclusions are probably justified by neglecting motional anisotropy, as will be seen in the following Section. 

It is also worth noting that nine times out of ten, equatorial protons absorb at somewhat lower field than the corresponding axial protons. This can be reversed in certain cases where the specific anisotropies of the substituents predominate over the anisotropies of the rings themselves but this is relatively rare. The difference is typically 0.5-1.0ppm, but may be more. 

Much of the width arises from incomplete averaging of anisotropies in the g-and hyperfine matrices (Chapter 3). For radicals with axial symmetry the parameters of eqn (2.8) depend on Ag = - g , AA, = AiM - A and tr,... 

A detailed treatment of the temperature dependence and anisotropy of the magnetic moments of all the dx configurations in pseudo-axial (CooV) symmetry has though now been given by Warren (101), in which variation of the orbital reduction factor, k, and distortions from effective Cv symmetry were also considered. This has lately been followed by a similar treatment due to Cerny (102) of the d d2, d8, and d9 configurations but, although some sophistications were included the results are essentially equivalent to those of the author, and furthermore only the undistorted situation, with k = 1, was considered. Consequently the author s own treatment (101) is here briefly summarised, the theoretical approach being that most appropriate for the sandwich complexes of the 3 d series, to which the bulk of the available experimental material relates. 

In principle it should be possible to determine the anisotropy of the paramagnetic susceptibility for some systems of pseudo-axial symmetry, but apart from the citation (74) of a private communication regarding the ferricenium cation, no experimental data are available for metal sandwich complexes. Such measurements should however be possible for at least some metallocenes and mixed sandwich complexes since these are found to crystallise in either a monoclinic (Fe(Cp)2 (6)) or orthorhombic (Ru(Cp)2, (Cp)V(Ch),... 

FIGURE 5.3 Axial anisotropy in an S = 1/2 system. A simplified representation is drawn of the porphyrin prosthetic group in low-spin ferricytochrome c in a magnet (Hagen 2006). (Reproduced by permission of The Royal Society of Chemistry.)... 

The previous discussion refers mainly to diagonal anisotropy terms. 6° 0°, which only contain powers of Jz and are often dominant. Deviations from pure axial symmetry lead to non-zero off-diagonal terms with m 0. These terms mix... 

This study [13] calculated the Schottky heat capacity for a hypothetical spin of s = 10, with an axial anisotropy, — D, of —0.5K. Across three different fields, Figure 9.9 shows that the larger the field, the smaller the contribution of this heat capacity. More relevant here is that the derived —ASM values showed the maximum —ASM shifts and decreases with increasing anisotropy from D = —0.5 to —1.5K and — 3.0K, as shown in Figure 9.9, for AH = 0 — 7T up to 200 K. 

It should be noted that these types of spectra are expected only for quadrupolar nuclei of semiconductors in non-cubic axially-symmetric forms such as the WZ structure cubic forms such as ZB or rocksalt structures ideally lack any anisotropy, and the ST peaks overlap the CT peak. However, defects in such cubic structures can produce EFGs that have random orientations, and the resulting ST are spread out over a wide range. 

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