Isotropic scatterers, anisotropic systems

By these cross sections, an anisotropic scattering in elastic as welt as in exciting or dissociating collisions is taken into account in Eqs. (12). To obtain a simpler structure of system (12), it is usually assumed that excitation and dissociation take place with isotropic scattering of the colliding electron. As a consequence, all generalized total cross sections become zero and the... 

Equation (8.59) defines the ID interference function of a layer stack material. G (s) is one-dimensional, because p has been chosen in such a way that it extinguishes the decay of the Porod law. Its application is restricted to a layer system, because misorientation has been extinguished by Lorentz correction. If the intensity were isotropic but the scattering entities were no layer stacks, one would first project the isotropic intensity on a line and then proceed with a Porod analysis based on p = 2. For the computation of multidimensional anisotropic interference functions one would choose p = 2 in any case, and misorientation would be kept in the state as it is found. If one did not intend to keep the state of misorientation, one would first desmear the anisotropic scattering data from the orientation distribution of the scattering entities (Sect. 9.7). 

The usual methods for characterization of anisotropic patterns involve the calculations of the scattering patterns and their further analysis [167,168] in the Fourier space. Thus, for an isotropic system, the scattering intensity, S(k) is symmetric, its maxima of the same amplitude are arranged at the circle k = k ... 

Scattering media to which this matrix applies include randomly oriented anisotropic spheres of substances such as calcite or crystalline quartz (uniaxial) or olivine (biaxial). Also included are isotropic cylinders and ellipsoids of substances such as glass and cubic crystals. An example of an exactly soluble system to which (13.21) applies is scattering by randomly oriented isotropic spheroids (Asano and Sato, 1980). Elements of (13.21) off the block diagonal vanish. Some degree of alignment is implied, therefore, if these matrix elements... 

This formula is valid for isotropic molecules with the scsdar polarizability o. For a system of anisotropic molecules, the scattered light intensity comprises two summands, an isotropic one auid am auiisotropic ones (Vuks, 1977),... 

Some thermotropic polymer systems switch at a certain temperature reversibly between a highly transparent and a light scattering state. Such an optical effect can be caused either by a phase transition between an isotropic and an anisotropic (liquid crystalline) state or by a phase separation process. Two different classes of thermotropic polymer materials have been extensively studied in recent years polymer blends and polymer gels. 

Neutron scattering investigations have been extended from isotropic polymers to oriented systems. Sadler and Odell measured the scattering from two samples of polyethylene, one of which had been extruded and the other pressure-crystallized onto previously extruded fibres. The pressure-crystallized sample was isotropic unlike the extruded sample, which was found to be highly anisotropic. The authors derived a lower limit for the length of the extruded polymer molecule of 3 x 10 A from the width of the meridional streak, although no data analysis was given. 

Nagai K. Theory of light scattering by an isotropic system composed of anisotropic units with application to the Porod-Kratky chain. Polym J 1972 3 67-83. 

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