Scattering azimuthally dependent

Figure 15 Morphological map of linear polyethylene fractions. Plot of molecular weight against crystallization temperature. The types of supermolecular structures are represented by symbols. Patterns a, b and c represent spherulitic structures with deteriorating order from a to c. Patterns g and d represent rods or sheet-like structures whose breadth is comparable to their length g or display a different aspect ratio d. Pattern h represents randomly oriented lamellae. Neither h nor g patterns have azimuthal dependence of the scattering. Reproduced with permission from Ref. [223]. Copyright 1981 American Chemical Society. (See Ref. [223] for full details.) Note the pattern a is actually located as o in the figure this was an error on the original.

Scattering by single, or collections of oriented, nonspherical particles may, unlike scattering by spheres, be azimuthally dependent. 

Since the parallel components of the dynamic dipole are active in RAIRS, it is possible to use the azimuthal dependence to obtain the orientation of the adsorbate at the surface. A similar technique has been applied to adsorbates on metals in HREELS measurements made off specular in order to observe parallel modes through impact or resonant scattering processes. This was first demonstrated for the Rh(CO)2 molecule on anisotropic TiO2(110) surface [72]. The results of this study also allow a test of the three layer model theory (Fig.5,6) as applied to S-polarised radiation. Fig. 11 shows the FT-RAIRS spectrum for 1/3 monolayer of Rh(CO)2 on Ti02(l 10) measured with P and S polarised radiation. 

In many cases, however, azimuthally dependent patterns are obtained as, for example in annealed polytetrafluoroethylene film. Such scattering may be treated in terms of the previously described non-random orientation correlation theories. An alternate approximate approach is that proposed by Keijzers et in which a scattering pattern... 

For a spherically symmetrical potential there is no azimuthal dependence of the scattered intensity per unit solid angle. Thus, one can work with the differential (polar) cross-section dcr/d9, which represents the fractional contribution to q-R from any polar angle 9, by integrations over the azimuthal angle... 

Again, for a spherically symmetrical potential with no azimuthal dependence of the scattered intensity, one can write... 

Figure 7 Incident electron energy dependence of the X v = 0, 1, 2, 3 vibrational and the a Ag (v = 0) electronic loss scattered intensities from a 10-layer film of O2 condensed on Pt(lll). was set at 10° with 6 at 45° and the azimuth at 10°. Also shown is the energy dependence of the inelastic background intensity located just before the v = 1 loss peak onset at Aif = 0.16 eV along with that contributing to each energy-loss profile (dashed lines). (From Ref. 118.)...

If the incident light is obliquely polarized at an angle of 45° to the scattering plane, the scattered light will, in general, be elliptically polarized, although the azimuth of the vibration ellipse need not be 45°. The amount of rotation of the azimuth, as well as the ellipticity, depends not only on the particle characteristics but also on the direction in which the light is scattered. 

Here I0 is the intensity of the x-ray beam, r0 = e2/mc2 is the classical electron radius (2.82 x 10 15 m)., P(9,) is the polarization of the x-rays it depends on the angle between the polarization and the scattering vector. For horizontally polarized x-rays, it takes the form P(0, < >) = 1 - sin220 sin2t)>, where 20 is the scattering angle and < > the azimuthal angle with respect to the vertical direction. The formfactor ) is the Fourier transform of the atomic electron density ... 

For the elastic scattering of a beam of unpolarized projectiles by an unpolarized target, the cross section has axial symmetry about the incident beam direction and therefore no dependence upon the azimuthal angle 4>, so that the differential elastic cross section is related to its integral counterpart by... 

For anisotropic samples, the space correlation function will depend on the orientation imposed to the vector and P(q) will vary both with the scattering angle 6 and azimuthal angle define scattering form factors along the reference axes as ... 

In a scattering experiment a beam of electrons of momentum k hits a target. We consider the target to be represented by a potential V(r). Electrons are observed by a detector placed at polar and azimuthal angles 9,(f) measured from the direction of the incident beam, which is the z direction in a system of spherical polar coordinates (fig. 4.2). For a central potential the problem is axially symmetric. Relevant quantities do not depend on (f). The detector subtends a solid angle... 

The variation with the electron wave vector k is associated with an intensity variation in the experimentally observed polar and azimuth angles. (In order to include vibrational attenuation of interference effects, each scattered wave has to be multiplied by the temperature dependant Debye-Waller factor.)... 

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