Intensity azimuthal

The quantitative assessment of the degree of crystallite orientation by x-ray examination is not free of ambiguity. From a comparative analysis [23] in which results obtained from the consideration of (105) and from three different variations of equatorial reflection were compared, the conclusion was that the first procedure can lead to underrated results, i.e., to the underestimation of the orientation. However, it can be assumed that this does not result from an incorrect procedure, but from ignoring the fact that the adjacent (105) reflex can overlap. The absence of the plate effect of the orientation is characteristic of the orientation of crystallites in PET fibers. The evidence of this absence is the nearly identical azimuthal intensity distributions of the diffracted radiation in the reflexes originating from different families of lattice planes. The lack of the plate effect of orientation in the case of PET fiber stretching has to do with the rod mechanism of the crystallite orientation. 

The aramids also exhibit very unusual properties laterally. Indeed under crossed polars, complete cross sections show an azimuthal intensity distribution which is... 

The microdomain orientation as a function of the electric field strength was monitored by a series of scanning force microscopy (SFM) images taken in the center between the electrodes. The entire electrode length of 6 mm was screened in steps of a few tens of microns. From the azimuthal intensity distribution of the 2D Fourier transformations of the SFM images, the orientational order parameter P2 was calculated according to ... 

The angle (p quantifies the in-plane direction, with cp = 0° corresponding to the direction along the stripe-like electrodes. For an alignment of the lamellae along the field direction (maximum azimuthal intensity distribution of the 2D Fourier transform intensity at (p = 90°), P) ranges from 0 to -0.5 with P2 = -0.5 corresponding to the fully oriented case. 

Fig. 61. Cluster pattern observed during the electrodissolution of a Fe ring electrode in the active/passive transition region under potentiostatic conditions. The RE was located in the plane of the WE. (a) and (b) Snapshots taken during two successive oscillations of the total current, (c) Spatiotemporal plot of the azimuthal intensity. (Reproduced with permission from B. J. Green and J. L. Hudson, Phys. Rev. E 63 (2001) 026214, (2001) by the American Physical Society).

In this way, separate meridional intensity profiles were generated for each dimer, corrected for polarization, and plotted in the range of 0comparison with calculated intensity distributions. Similarly, azimuthal intensity distributions passing through the equatorial reflections (measured as a function of azimuthal angle from the meridian) were used to determine the Hermans order parameters (8). 

There are only two papers describing the physical properties of discotic LCEs [35, 36]. X-ray diffraction showed that a narrower azimuthal intensity distribution can be obtained when a second crosslinking step is done under an external load reflecting a macroscopic alignment parallel to the direction of the external stress [35]. X-ray diffraction experiments on monodomains (LSCE) show the occurrence of sharp maxima in the azimuthal distribution. Thermal expansion has also been studied for polydomain LCEs and for LSCEs in [36]. It is found that well inside the discotic phase, that is sufficiently far below the discotic-isotrop-ic transiton, the length parallel to the stress axis of both, poly- and monodomain samples, increases approximately linearly with increasing temperature as expected from the isobaric expansion of the network. 

The degree of orientation in drawn samples was determined from Laue diffraction patterns obtained with a Phillips PW1030 flat plate camera using unfiltered Cu-Ka radiation in transmission. The azimuthal intensity profiles from the diffraction patterns were obtained by measuring light transmission through the developed flat... 

Fig, 21 Two-dimensional SAXS pattern of (a) iPP crystallized at 140 °C after shear-alignment in the melt (b) step-sheared (rate of 30 s" and strain of 1500%) and crystallized at 140 °C. The corresponding azimuthal intensity dustribution of the smectic and crystalline peaks are shown in (c) and (d), respectively. The arrow indicates the flow direction (after Li and de Jeu [6])... 

From the azimuthal intensity distribution of the strongest meridional reflection (20 = 43 for CuK radiation) we have calculated the orientation parameters and P, which are averages of the Legendre polynomials given by... 

Figire 46 (a) Calculated intensity distribution corresponding to tbe (102)/ (1-1-2) reflections visualized as intersection of the Polanyi (gray) and Ewald sphere (violet). Only a part of the Ewald sphere is shown in the figure for the sake of clarity, (b) Intersection between the Polanyi and Ewald spheres projected on the plane of a fiat 2D detector showing the azimuthal intensity distribution for the calculated (102)/(1-1-2) doublet reflection. 

Figure 28a displays a typical three-dimensional plot of the neutron intensity scattered by a nematic lyotropic solution in the (qv,qvv)-plane. The data were obtained on the SDS/Dec calamitic phase at 50 s (concentration c = 29.5 wt. % and R = [Dec]/[SDS] = 0.33). As shown in the iso-intensity contour plot (Fig. 28b), the patterns are characterized by two crescent-like peaks aside from the velocity axis. The maximum scattering corresponds to the first order of the structure factor, from which the distance between the center-of-mass of the micelles can be estimated (here 6 nm for a radius of nm). The modulation of the azimuthal intensity is also of interest since it reflects the distribution of micellar orientations. The spectra were analyzed in terms of angular distribution of the scattered intensity. The scattering was integrated over an elementary surface dgvdgvv = where corresponds typically to the half width at half... 

The order parameter S of the nematic phase under shear (Eq. 5). The analytical technique to transform the azimuthal intensity into an orientational distribution has been quoted in several papers [109,276,278]. 

At deformations lower than 300-400 %, the SAXS patterns tend to assume an elliptical geometry characterized by a concentration of intensity above and below the equatorial region (Fig. 11.9b, c, b, c ). The corresponding azimuthal intensity profiles show broad maxima centred on the meridian (j = 0° and 180°) for the... 

In this expression, ( ) represents an average weighted by the azimuthal intensity distribudon For example the average cos is given as ... 

Voids Size and distribution Height (length) when voids are elongated Misoiientation Characteristics of the decay in central diffuse scattering Width of the diffuse scattering along the meridian extrapolated from a series of meridional shces Azimuthal intensity distribution of diffuse streak... 

In samples with cylindrical symmetry, is obtained from the XRD patterns from the azimuthal intensity distributions /(a) of suitably chosen reflections, where a is the angle between a crystal axis and the deformation direction (external reference). For example, a meridional reflection can be used to calculate the orientation of the chain axis with respect to the draw direction. A degree of orientation,/, of a crystal axis with respect to the fiber axis is calculated from the intensity distribution by first calculating the mean cos

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Fig. 21.6 Wide angle light blue) and small angle dark blue) X-ray scattering patterns and the azimuthal intensities at the correlation lengths of the magnetic NPs red curve), smectic layers green curve) and mesogens blue curve) of the LCE in (a) the OFF state and (b) the ON state. The red arrow is the X-ray beam direction, (c) Schematic representation of the magnetic susceptibility components in the OFF and ON states (adapted with permission from Haberl et al. 2013a)...

Heffels, C. M. G., Heitzmann, D., Hirleman, E. D., Scarlett, B., The Use of Azimuthal Intensity Variation in Diffraction Patterns for Particle Shape Characterization, Part. Part. Syst. Charact, 1994, 11, 194-199. 

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