Random orientation/sample

Ever since Pasteur s work with enantiomers of sodium ammonium tartrate, the interaction of polarized light has provided a powerful, physical probe of molecular chirality [18]. What we may consider to be conventional circular dichroism (CD) arises from the different absorption of left- and right-circularly polarized light by target molecules of a specific handedness [19, 20]. However, absorption measurements made with randomly oriented samples provide a dichroism difference signal that is typically rather small. The chirally induced asymmetry or dichroism can be expressed as a Kuhn g-factor [21] defined as ... 

This forward-backward asymmetry of the photoelectron distribution, expected when a randomly oriented sample of molecular enantiomers is ionized by circularly polarized light, is central to our discussion. The photoelectron angular... 

The experimental dichroism is seen to have its greatest magnitude some 5 eV above threshold, where 0.10. This corresponds to an asymmetry factor in the forward-backward scattering of y 20%. Such a pronounced PECD asymmetry from a randomly oriented sample looks to comprehensively better the amazingly high 10% chiral asymmetry recorded with highly ordered nanocrystals of tyrosine enantiomer [25] or the spectacular 12.5% asymmetry reported from an oriented single crystal of a cobalt complex [28]. 

Finally, Frisk et al. have proposed a third method, the "depolarization" method, that does not need the assumption of a cylindrical Raman tensor [56]. A randomly oriented sample is again necessary but the depolarization ratio takes the general form... 

At first glance, it would appear that all orientation dependence should be lost in the spectrum of a randomly oriented sample and that location of the g- and hyperfine-matrix principal axes would be impossible. While it is true that there is no way of obtaining matrix axes relative to molecular axes from a powder pattern, it is frequently possible to find the orientation of a set of matrix axes relative to those of another matrix. 

Electron Spin Resonance Spectroscopy of Randomly Oriented Samples Hund s Rule Vindicated ... 

Note here that in some instances, even when the molecule has lower symmetry, the value of E can be so small as to be indistinguishable from zero, especially with a randomly oriented sample. In that case again, only four of the expected six lines may be observed. With this caution in mind, we can see that a non-zero E value may be interpreted confidently as indicative of a carrier with low symmetry, but the converse, an approximately zero value, could be due to true symmetry, or to an accidental equivalence of two axes. We return to this point in the discussion... 

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. 

This relationship is for randomly oriented samples (e.g., amorphous or polycrystalline). 

Figure 7.3 Normal direction (ND) pole figures for (a) random and (b) strongly textured sheet. Note the absence of features for the pole figure of the randomly oriented sample, while the strongly texture sample shows a concentrations of reflections along the ND as well as 90° away in the transverse (TD) and rolling (RD) as well. This alignment of the crystal orientation with the reference orientation is referred to as a cube texture.

Finally, in a single crystal experiment it is possible to extract all five independent elements of the traceless NQI tensor, usnaUy chosen to be the orientation of the EFG principal axis system, in addition to the two parameters accessible for randomly oriented samples (jj and vq). This, of course, requires that it is possible to make a single crystal incorporating the radioactive mother nucleus, and is therefore limited to cases where the preparation can be completed within roughly the lifetime of the mother nucleus, for example, see Ref 138. 

Paterson, E., Bunch, J.L. Duthie, D.M.L. (1986) Preparation of randomly orientated samples for X-ray diffractometry. Clay Mineralogy 21, 101-106. 

One-versus Two-Dimensional Detectors. For the most part, powder diffraction is the norm when dealing with lipid dispersions. Quantitative time-resolved powder diffraction measurements are possible with a one-dimensional detector only when randomly oriented samples are used and the powder character is preserved throughout the transition. Lipids have a propensity for preferentially orienting and for forming large crystallites in certain phases [18, 96]. In both instances, quantitation with a one-dimensional detector is likely to give rise to uninterpretable kinetics. In this regard... 

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