Scattering power, definition

The weighting factors m , are useful in the study of copolymers, and especially so when the copolymer is studied by scattering measurements in which the effective scattering power differs strongly for the various components of the macromolecule. Here, however, we shall assume that these differences are not important, and will adopt the simpler definition of s2 that arises when all of the m, are identical ... 

The method of isomorphous replacement is the primary method used to determine the relative phases of protein crystal structures. The phenomenon of isomorphism was first described by Mitscherlich in 1819. and is described in Chapter 2. Isomorphous crystals have, by definition, almost identical structures, but with one or more atoms replaced by chemically similar ones (with different X-ray scattering power). The method by which relative phases are determined for a pair of isomorphous crystals depends on a knowledge of the intensity differences between the data sets for the two isomorphous crystals and the location of the varied atom, a quantity that is available from an analysis of the Patterson map or difference map. 

The general procedure in the analysis of molecular structure is then as follows. We assume a definite molecular model (a tetrahedron for the tetrachlorides, a hexagon or pentagon for cyclic compounds), and thence deduce the ratios of the different interatomic distances and the number of times each of them occurs in the molecule (periods). If, as in the case of tetrachlorides where the scattering power of the central atom may be neglected (e.g. CCI4), only one period exists, the distribution of intensity in the diffraction pattern may be expected to follow that of the simple function sinx/x (fig. 1). The first maximum occurs... 

Here the structure factor signifies the vectorial sum of the waves scattered by the single atoms which show amplitude f and phase y. Every atom contributes a scattered wave to the whole diffraction effect, the amplitude of which is proportional to the so-called form factor. The phase is thus defined by the position of the atom in the elementary cell, whilst the form factor is a characteristic constant for every sort of atom which represents a measure of its scattering power. Hence no special differences exist in the positions of the diffracted beams, which in both X-ray and electron diffraction cases satisfy the geometric relations between lattice constant and X-ray or material wavelengths, according to the Bragg equation. However, there are definitely differences in their intensities. 

The X-rays are scattered mainly by the extra-nuclear electrons and the important characteristic of the molecule is its distribution of electron density. The scattering power of an atom therefore depends upon its atomic number Z but, since it occupies a definite region of space, the electron density falls off in a particular manner. 

Projections are integral operators which map functions onto subspaces of their definition domain. They shall be denoted by a pair of curly parentheses. The best known projection in the field of scattering theory maps the scattering intensity I ( ) onto a zero-dimensional subspace, which is the number Q, known as "invariant or scattering power ... 

Figure 17-46 shows such a performance curve for the collection of coal fly ash by a pilot-plant venturi scrubber (Raben "Use of Scrubbers for Control of Emissions from Power Boilers, United States-U.S.S.R. Symposium on Control of Fine-Particulate Emissions from Industrial Sources, San Francisco, 1974). The scatter in the data reflects not merely experimental errors but actual variations in the particle-size characteristics of the dust. Because the characteristics of an industrial dust vary with time, the scrubber performance curve necessarily must represent an average material, and the scatter in the data is frequently greater than is shown in Fig. 17-46. For best definition, the curve should cover as wide a range of contacting power as possible. Obtaining the data thus requires pilot-plant equipment with the flexibility to operate over a wide range of conditions. Because scrubber performance is not greatly affected by the size of the unit, it is feasible to conduct the tests with a unit handling no more than 170 m3/h (100 ftVmin) of gas.

The International Union of Pure and Applied Chemistry recommends that the definition should now be based on the ratio of the radiant power of incident radiation (Pq) to the radiant power of transmitted radiation (P). Thus, A = log(Po/P) = log T. In solution, Pq would refer to the radiant power of light transmitted through the reference sample. T is referred to as the transmittance. If natural logarithms are used, the quantity, symbolized by P, is referred to as the Napierian absorbance. Thus, B = ln(Po/P). The definition assumes that light reflection and light scattering are negligible. If not, the appropriate term for log(Po/P) is attenuance. See Beer-Lambert Law Absorption Coefficient Absorption Spectroscopy... 

Figure IB displays relative catalytic activity (RA) - in terms of pseudo first-order rate constants, corrected for coke content, related to the fresh, sulfided catalyst vs carbon content. The individual HDS, HVD and CNH activities all decrease with increasing carbon content, the order of deactivation being HYD < HDS < CNH. (The results for relative HDN activities followed closely those of CNH, and are not shown). Relative activities fall off less sharply as coke content increases. Because of the limited set and scatter of the data, a definitive deactivation correlation could not be obtained. Best fit curves to the data were constructed from a power-deactivation equation in C (1), and are shown by the solid curves in Fig. IB.

Apart from this extensive increase in power of the theoretical treatment, the fast cathode rays possess the practical advantage of easy manipulation, so that now, after but few years of development, certain methods of investigating structure by means of electron waves can be carried out with almost as great precision as has hitherto been possible in the analogous experiments with X-rays. In some respects, notably as regards times of exposure, some of the characteristic features of electron scattering give it a definite superiority. 

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