Isotropic scattering

The ratio / for a surface composed of particulate matter which scatters isotropically varies with from 1 when = 1 to 0.8 when = 0.07 (see Fig. 5-14). 

A remedy obviously should be available using polarization tricks. In conventional Raman spectroscopy, the isotropic and anisotropic components are deduced from linear combinations of the polarized and depolarized spectra, while a nonresonant part is not clearly recognized (41). In frequency-domain CARS it is known how to suppress the nonresonant contribution and solely measure resonant scattering (isotropic plus anisotropic part) (42). In time-domain CARS, polarization interference can do an even better job with three magic cases (derived in Refs. 35,39). These authors derived explicit expressions for the coupling factors F in Equations (2)-(4) ... 

Noble (op. cit.) has extended the present matrix methodology to the case where the gaseous absorbing-emitting medium also scatters isotropically. 

Although the formalism for X-ray and neutron diffraction is essentially the same, it is appropriate to treat them separately because of the nature of the basic interaction. For the case of neutron diffraction, neutrons are scattered isotropically by all the nuclei of the system. The degree to which this takes place is determined by the coherent neutron scattering length b, which varies from isotope to isotope (Table I). Because the scattering is isotropic, the results of a given experiment can readily be presented in terms of a total radial distribution function. 

The calculation ol the multiple scalterine is easy when one assumes that the liquid scatters isotropically, but must be performed by computer simulation when one assumes an ancle dependent scattering of the liquid. In the eases where the absorption of the X-rays by the sample is low. the multiple scattering can be neglected. Aftci normalization of the experimental data to an abso lute scale, the atom incoherent and multiple scattering is subtracted. The result is a distinct term (equation 10.18) which can be Fourier transformed according to equation (10.20). 

To make the formulas more transparent we omit (where possible) the arguments of functions. We consider an atmosphere that is optically semiinfinite, homogeneous, and plane-parallel in which the radiation is scattered isotropically and monochromatically. Radiative transfer in such an atmosphere is described by... 

Higashi et al. (1963) proposed a hopping model, in which they assumed that when a molecule adsorbed in a site jumps to one of the neighboring sites whether they are vacant or not, and if the site is occupied the molecule will not be bound to this site but rather collides with the former occupied molecule and scatters isotropically. Then the molecule continues to jump until it finds a vacant site. As 6 increases the number of hopping necessary for finding a vacant site increases. The expectation value n(0) is the summation of... 

HDPE/PA12/YP UDP MFC composition (wt%) Isotropic scattering Oriented scattering Isotropic scattering Oriented scattering ... 

The SAXS scattering contrast derives from electron density variations over length scales where the contributions of the individual atoms are indistinguishable and one only observes the spatially averaged electron density differences. Therefore it is intrinsically a low resolution technique. In this text we will assume that we are dealing with samples that scatter isotropically, which is the case when the scattering entities in the sample are randomly oriented. 

Neutrons are scattered isotropically from individual nuclei, whereas, for LS and SAXS, the scattering originates in the electron cloud, so the atomic form factors are in principle (2-dependent. However, the variation is small in practice (<1% for Q < 0.1 A ) and is usually neglected for SAXS and LS [36]. The Thompson-scattering amplitude of a classical electron is rj = 0.282 x 10 cm [65], so the X-ray scattering length of an atom, /, is proportional to the atomic number (/ = rjZ) and increases with the number of electrons per atom. For neutrons, values of b vary from isotope to isotope (see below). If the nucleus has nonzero spin, it can interact with the neutron spin, and the total cross section (atot) splits into coherent and incoherent components as explained below. 

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