Scattering power

A modified fonn of equation (B 1.9.16) is usually used to express the scattering power of a system in tenns of the Rayleigh ratio defined as... 

In a sense, a superconductor is an insulator that has been doped (contains random defects in the metal oxide lattice). Some of the defects observed via neutron diffraction experiments include metal site substitutions or vacancies, and oxygen vacancies or interstituals (atomic locations between normal atom positions). Neutron diffraction experiments have been an indispensable tool for probing the presence of vacancies, substitutions, or interstituals because of the approximately equal scattering power of all atoms. 

Streuungswinkel, m. angle of scattering. Streu-vermbgen, n. scattering power, -wachs,... 

CuZn would be expected, because the scattering powers of the two atoms for slow electrons in the lattice are probably considerably different, even though the scattering powers for fast electrons and for x-rays are very nearly the same. 

The reliability factor B was 0276 after the first refinement and 0-211 after the fourth refinement. The parameters from the third and fourth refinements differed very little from one another. The final values are given in Table 1. As large systematic errors were introduced in the refinement process by the unavoidable use of very poor atomic form factors, the probable errors in the parameters as obtained in the refinement were considered to be of questionable significance. For this reason they are not given in the table. The average error was, however, estimated to be 0-001 for the positional parameters and 5% for the compositional parameters. The scattering power of the two atoms of type A was given by the least-squares refinement as only 0-8 times that of aluminum (the fraction... 

Fig. 1.—Radial distribution curves for (A) ethane, (B) propane, (C) isobutane and (D) neopentane. The positions of the heavy arrows indicate the interatomic distances determined by the comparison of the photographs with theoretical intensity curves their heights show the relative scattering power associated with each distance.

The scattering power of an electron distribution q for the effective interplaner distance D given by the equation... 

In this expression, G is the number of elements of the space group of the crystal, and / and n are the scattering power and number of the point random scatterers in... 

In addition to point-focus apparatus there are scattering devices with an extremely elongated cross-section of the primary beam. Historically this geometry has been developed as a compromise between ideal collimation and insufficient scattering power. Their practical importance is decreasing as more powerful point-collimated sources become available. Kratky camera (Alexander [7], p. 107-110) and Rigaku-Denki camera (BaltA Vonk [22], p. 83) are the most frequent representatives of slit-focus devices. 

I bis treatment simply assumes that the material is a homogeneous medium with a scattering power of unity. Thus relative changes are correctly described. In order to put the results back on an absolute scale It (s = 0) must be considered. 

The calibration process then involves measurement of the complete scattering curve of the secondary standard and the evaluation26 of k by determination of Porod s law with its asymptote Ap and the density fluctuation background Ipi, numerical extrapolation of the function s2 (/ (s) - Ipi) towards s = 07 and finally computation of the scattering power... 

The best-known projection in the field of scattering is the scattering power k it is a number, k is the total scattered intensity63... 

Mathematically spoken k is the zero-dimensional projection / 0 of the scattering intensity. After calibration to absolute units 7(s) turns into 7(s) /V - its scattering power is known as Porod s invariant... 

Figure 8.15. The invariant as a function of the composition of a two-phase material. Between 30 and 70 vol.-% the scattering power is almost constant. The regions 0-30 vol.-% and 70 -100 vol.-% exhibit almost linear relations... 

If we know that in our two-phase material the volume fraction of one fraction is between 30 and 70%, then the term v (1 - v) 0.23 is constant to a first approximation (cf. Fig. 8.15). If in this case during the experiment a considerable change of the invariant is observed, it is probably caused by a variation of the contrast67. If, on the other hand, the contrast is known to be constant and nanostructure is evolving from a homogeneous phase, the initial increase of the scattering power is proportional to the change of the materials composition. 

In many cases the consideration of only two phases is sufficient, because according to Eq. (8.53) the scattering power is a function of the square of the contrast between two phases. This means that the scattering from a small contrast between a second and a third phase is frequently negligible. For those cases in which three or more phases have to be considered, the corresponding equations have been reported by JAnosi [138,149]. 

If the scattering power of an anisotropic material shall be determined, it is convenient to first project the scattering pattern... 

Let us, first, discard the topological information and only determine the scattering power k. For this purpose we utilize Table 8.3 and find that the classical... 

For a multiphase structure this information is made from both some direction-dependent topological information, and the non-topological information that is collapsed in the scattering power. 

Scattering powers are conventionally represented in terms of the Rayleigh factor defined as... 

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