Scattering elements

I k/X. For a system with a large number of scattering elements, the suimnation in equation (B1.9.28) may be replaced by an integral... 

For a continuous system with assorted scattering elements, the sum can be replaced by integration and be expn... 

The intensity of SS /. from an element in the solid angle AD is proportional to the initial beam intensity 7q, the concentration of the scattering element N., the neutralization probability P-, the differential scattering cross section da(0)/dD, the shadowing coefficient. (a, 5j ) and the blocking coefficient(a,5 ) for the th component on the surface ... 

We wish to obtain an image of the scattering elements in three dimensions (the electron density). To do this, we perform a 3-D Fourier synthesis (summation). Fourier series are used because they can be applied to a regular periodic function crystals are regular periodic distributions of atoms. The Fourier synthesis is given in O Eq. 22.2 ... 

The resulting increase in data quality is illustrated in Fig. 5, which shows a comparison of ADX and EDX data from the same sample of InSb. The quality achieved was such that more sophisticated techniques could be applied, such as the use of anomalous scattering to distinguish similarly-scattering elements, like In (Z = 49) and Sb (Z = 51) [164, 165]. And the combination of the high-resolu-tion 2D data and the GUI software made it possible to distinguish mixed phases simply from the difference in appearance of the diffraction rings [164, 245]. 

The next question we must consider is how this result may be applied to a particle that consists of N, not just two, scattering centers. If the composition of the particle is such that the scattering from one part of the particle has no effect (other than interference) on the scattering from another part, then the particle may be subdivided into N scattering elements, and Equation (58) can be applied to all possible pairs. If we define rtJ as the distance between the /th andy th members of the set of N scattering elements, then this argument leads to the result (given without proof)... 

Before turning to the applications of the Debye approximation, we should elaborate more fully on a point that was glossed over. This is the assumption —made at the outset, but explicated in going from Equation (58) to Equation (59) —that the scattering behavior of each scattering element is independent of what happens elsewhere in the particle. The approximation that the phase difference between scattered waves depends only on their location in the particle and is independent of any material property of the particle is valid as long as... 

It is these fluctuations that cause the inhomogeneities in the fluid and the reradiated waves. The total amplitude of the electric field at a distance R from the scattering volume is given by the summation of the contributions of the infinitesimal scattering elements and can be expressed as... 

For copolymers, each scattering element j scatters with an amplitude of Act,. We now assume that Aeq is proportional to the molecular weight of the individual monomeric units Moj and proportional to the corresponding refractive index increment Vj = (dn/dc)j. Instead of Eq. (B,9), the scattering intensity is now given by60,61)... 

When the Mixt is dissolved, because of the weakness of the corruptible elements which compose it, the ethereal part abandons it, and returns to its native country. Then derangement, disorder and confusion take place in the parts of the corpse, because of the absence of that which preserved order in it. Death, corruption, take possession of it, until this matter receives anew celestial influences, which reuniting the scattered Elements, will render them suitable for a new generation. 

The electric field generated by scattering elements within the differential slab is simply Es. = J Eq , and the total intensity from the entire sample is... 

The amplitude factor will vary on a timescale comparable to the transit time of a scattering element as it convects through the scattering volume. If this volume is characterized by a length scale, L, that timescale is... 

Here U is the mean velocity within the scattering volume and not the velocity of a specific scattering element. One finally obtains the following result ... 

The simplest way in which to use a lanthanide ion is as an electron dense material. The best known use in the study of crystals is that of Ln(III) as a scattering element replacement for Ca(II) or Mg(II). Examples are the structures of concanavallin A and t-RNA. The replacement is not always strictly isomorphous and care is required in interpretation. Some proteins bind Ln(III) although they function without metal ions, e.g. lysozyme, and use has been made of the cations in X-ray studies of this enzyme. The early compari-... 

Depolarized scattering occurs because of various forms of particle anisotropy. Distinct classes of depolarizing scatterers include nonspherical particles with uniform isotropic (scalar) polarizabilities (sometimes called form anisotropy), inhomogeneous particles with nonuniform distributions of isotropic polarizability, and particles with anisotropic (tensor) polarizabilities. For each of these classes, the intensity of depolarized light scattered by a particle will change as the particle translates, rotates, or manifests internal rearrangement of its scattering elements. DDLS can provide information on the dynamics of each of these processes. 

Hollow u.nd solid sphere ( radially oriented scattering elements with cy 1 i nd ienl sym inetry )... 

The above approach is very general in the sense that the correlation function Y(x ) contains both intra- and interfibrillar correlations. To discuss the scattering pattern of crazes in more detail, another approach is instructive. The existence of a well defined scattering element (craze fibril) suggests distinguishing intra-from interfibrillar correlations and writing the scattering intensity in the form ... 

What these four examples have taught us is perhaps a method for reassembling the scattered elements of our dissociated universe, and of reconstituting it. They teach us how to make good use of our Myths. 

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