Discrete reflections

A further complication arises with this material in that the diffraction pattern is not a true fibre pattern. The molecular chain axis in the crystallites is tilted with respect to the fibre axis (2,3) and this causes reflections to be displaced above and below the mean layer line position. Thus it is possible that some reflectionswhich would overlap in a true fibre pattern to such an extent that their intensities could not be determined separately, might be resolved with the present material. When this happens for a reflection of observable intensity, then it will be measured as a discrete reflection and the resolution of the final structure will be higher than if the material had true fibre symmetry. However, Stambaugh et al (4)... 

Aristode s views about numbers likewise reflect some fairly quotidian facts about human practices, though, his account of numbers, as will become apparent shordy, is in some tension with other aspects of his metaphysics.3 His linking of numbers with discreteness reflects the... 

The polarization of the exciton spectra of ZnO does not follow the classical model. All the three exciton series are strongly polarized and can be observed only with E L c (A, B) and E c (C). This has led to contradictory position schemes of the two highest valence bands (Tg, Ty) and values of Aso, Acr. There are also certain discrepancies in the results of different papers on the nature of the lines of complex discrete reflectivity and absorption spectra of ZnO at 4.2 K, as well as on the bands and excitons parameters. " ... 

Figure 10 shows the dry diffraction pattern of the CTAHF. The sample was air dried at ambient temperature with no applied stress. Discrete reflections appear along the equatorial line underneath the general ring pattern. The appearance of discrete reflections Is expected, as the removal of water from the matrix would allow the polymer chains to collapse Into more ordered regions. Most notably, there appears to be better orientation of crystallites with the fiber axis In comparison to the original sample. 

In analogy to the Fourier transformation of the continuous intensity pattern leading to the autocorrelation function y(x) (see Eq. 6 and 7), the intensities of the discrete reflections from stacked samples can be used to construct a Fourer series according to... 

Fig. 23. Different stages of a realignment experiment on an 8CB liquid crystal oriented in a 6-T magnetic field. The unperturbed sample showed a diffraction peak in the lower right-hand corner. Once the sample is rotated inside the field the reflection moves to the top left-hand corner. The sample is forced to reorient to the original position by the magnetic field. The different time frames here show this reorientation effect. Interesting to notice is that when the sample is rotated back to about 50°, the x-ray reflection splits up in two discrete reflections. For this there is no explanation found yet. The time-frame rate was 0.25 s/frame. Unpublished data, courtesy of J. Seddon, B.A. Timimi, and W. Bras.

In addition to the discrete reflections from the crystallites, the diffraction pattern of a polymer shows diffuse scattering attributed to amorphous regions. Such polymers are said to be semicrystalline, with the crystalline fraction being controlled by molecular regularity. By comparing the relative amounts of crystalline and amorphous scattering of X-rays the crystallinity has been found to vary from more than 90 per cent for linear polyethylene to about 30 per cent for oriented polyethylene terephthalate. 

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