Azimuthal reflections

Frederick B G, Power J R, Cole R J, Perry C C, Chen Q, Flaq S, Bertrams T, Richardson N V and Weightman P 1998 Adsorbate azimuthal orientation from reflectance anisotropy spectroscopy P/rys. Rev. Lett. 80 4490-3... 

Several sections of the diffraction space of a chiral SWCNT (40, 5) are reproduced in Fig. 11. In Fig. 11(a) the normal incidence pattern is shown note the 2mm symmetry. The sections = constant exhibit bright circles having radii corresponding to the maxima of the Bessel functions in Eq.(7). The absence of azimuthal dependence of the intensity is consistent with the point group symmetry of diffraction space, which reflects the symmetry of direct space i.e. the infinite chiral tube as well as the corresponding diffraction space exhibit a rotation axis of infinite multiplicity parallel to the tube axis. 

Azimuth dependence is clearly present for achiral tubes such as for instance the (10, 10) tube of Fig. 12, where it reflects the 20-fold rotation symmetry of this tube in direct space. 

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. 

Fig. 4.1 Reflection high-energy electron diffraction (RHEED) patterns corresponding to the best epitaxial conditions of CdSe deposited on a (111) InP face (thickness 85 nm). (a) Observation under the (112) azimuth (b) observation under the (110) azimuth. (With kind permission from Springer Science-l-Business Media [6])...

Motivation and Principle. Broadened reflections are characteristic for soft matter. The reason for such broadening is predominantly both the short range of order among the particles in the structural entities, and imperfect orientation of the entities themselves. A powerful method for the separation of these two contributions is Ruland s streak method [30-34], Short range of order makes that the reflection is considerably extended in the radial direction of reciprocal space - often it develops the shape of a streak. This makes it practically possible to measure reflection breadths separately on several11 nested shells in reciprocal space. As a function of shell diameter one of the contributions is constant, whereas the other is changing12. If the measurement is performed on spheres (azimuthal), the orientation component is constant. 

Fig. 1 Solid-state NMR structure analysis relies on the 19F-labelled peptides being uniformly embedded in a macroscopically oriented membrane sample, (a) The angle (0) of the 19F-labelled group (e.g. a CF3-moiety) on the peptide backbone (shown here as a cylinder) relative to the static magnetic field is directly reflected in the NMR parameter measured (e.g. DD, see Fig. 2c). (b) The value of the experimental NMR parameter varies along the peptide sequence with a periodicity that is characteristic for distinct peptide conformations, (c) From such wave plot the alignment of the peptide with respect to the lipid bilayer normal (n) can then be evaluated in terms of its tilt angle (x) and azimuthal rotation (p). Whole-body wobbling can be described by an order parameter, S rtlo. (d) The combined data from several individual 19F-labelled peptide analogues thus yields a 3D structural model of the peptide and how it is oriented in the lipid bilayer...

Spontaneous reflection symmetry breaking in achiral LCs is also well known, driven by specific boundary conditions. A very simple example of this type of chiral domain formation is illustrated in Figure 8.11. Suppose we start with two uniaxial solid substrates, which provide strong azimuthal anchoring ... 

Figure 3. Azimuthal distortion of an arc-shaped reflection (hzardite IT).

A simplified picture of the transducer, lens surface, and reflecting object is shown in Fig. 7.4. The waves radiated by the transducer are refracted by the lens so as to form a spherical wavefront centred on the focal point of the lens. Each point on this wavefront can be described by its angular coordinates from the focus let these be 6 for the zenithal angle (i.e. the angle to the lens axis, again taken to be normal to the specimen surface) and for the azimuthal angle. Thus the spherical wave emerging from the lens can be described by... 

Fig. 2. Reflection high energy electron diffraction (RHEED) patterns taken from [110] azimuth, (a) Low-temperature grown GaAs at 250°C. (b) (Ga,Mn)As at 250°C. (c) I70°C, and (d) 320°C (Shen ei al. 1997a).

Figure 9 Aerosol attenuation factor I) (A)= 1- F er (A)/ Fckjr (A) at 325 nm for nonabsorbing (triangles) and absorbing (diamonds) aerosols as a function of the TOMS Lambert-equivallent reflectivity (R-0.05)/0.9 (the true surface reflectivity Rj= 0.05). Solar zenith angle is 50°, satellite zenith angle 32° and azimuth 90°...

Generally it is found that PPT fibres are highly oriented and that those variants with the lowest values of orientation angle exhibit the highest tensile modulus. Indeed the average crystallite orientations derived from azimuthal peak widths at half maximum intensities of the 200 reflections in Kevlar 49 and Kevlar 29 are found to be nine and eleven degrees respectively. 

---