Coherent X-ray scattering

A Tartari, E Casnati, C Bonifazzi and C Baraldi (1997) Molecular differential cross sections for x-ray coherent scattering in fat and polymethyl methacrylate. Phys. Med. Biol. 42, 2551-2560. 

The contrast for scattering by dispersion of pores (phase 1) in a medium (phase 2) is (Ap)2 = (Pg - Ps)2> where pg and ps are the x-ray coherent scattering length densities for the pores and solid, respectively. The scattered intensity I(q) is proportional to the contrast. 

The intensity of x rays coherently scattered by a molecule is proportional to F 2 where... 

When X-rays illuminate a crystalline material, the atoms in the crystal act as scattering centers. Because of the periodic nature of crystals, the scatterers can be considered to be associated with periodically spaced parallel planes a distance d apart. For certain angles of incidence to these planes the X-rays are scattered coherently and in phase. The coherent scattering is known as X-ray diffraction and the geometric condition required for diffraction, the Bragg equation, is given by... 

When the layer thickness increases, so does the volume of the layer scattering X-rays coherently. Therefore, for many cases, the narrowing of the RC with increasing layer thickness is just an effect of X-ray diffraction. 

Figure 2.59. The electron (left) and nuclear (right) density distributions in the xOz plane of the unit cell of CeRhGcs calculated from x-ray and neutron powder diffraction data, respectively Figure 2.58). The contour of the unit cell is shown schematically as the rectangle under each Fourier map. The peaks correspond to various atoms located in this plane and are so marked on the figure. The volumes of the peaks are proportional to the scattering ability of atoms for x-rays the scattering power decreases in the series Ce(58 e) Rh(45 e) Ge(32 e) for neutrons, the coherent scattering lengths decrease in the reverse order Ge(8.19 fm)...

FIGURE 6.28 Effects in a sample irradiated with x-rays. The characteristic (fluorescence) emission is the desired analytical effect that needs to be separated from the other secondary emissions. The primary x-ray beam scatters coherently (without loss in energy) and incoherently (losing energy) and is recorded to a small amount in the detector. The characteristic fluorescence beam not only undergoes absorption by other metals in the sample but may also be excited by secondary or tertiary fluorescence from other elements. 

The x-ray crystallite (as opposed to the actual oxide particle, ivhich may be composed of a great many crystallites in an ordered or disordered pattern) is defined as the smallest subdivision of the solid which scatters x-rays coherently. The crystallite size can, in principle, be determined from the width of the x-ray diffraction peak, the width being greater the smaller the average crystallite size [41]. 

X-ray diffraction consists of the measurement of the coherent scattering of x-rays (phenomenon 4 above). X-ray diffraction is used to determine the identity of crystalline phases in a multiphase powder sample and the atomic and molecular stmctures of single crystals. It can also be used to determine stmctural details of polymers, fibers, thin films, and amorphous soflds and to study stress, texture, and particle size. 

Interference of Waves. The coherent scattering property of x-rays is used in x-ray diffraction appHcations. Two waves traveling in the same direction with identical wavelengths, X, and equal ampHtudes (the intensity of a wave is equal to the square of its ampHtude) can interfere with each other so that the resultant wave can have anywhere from zero ampHtude to two times the ampHtude of one of the initial waves. This principle is illustrated in Figure 1. The resultant ampHtude is a function of the phase difference between the two initial waves. 

THE USE OF INTENSITY OF COHERENT AND NON-COHERENT SCATTERED RADIATION OF THE X-RAY TUBE FOR THE COMPENSATION OF MATRIX EFFECTS AT THE ANALYSIS OF SOLUTIONS BY X-RAY FLUORESCENCE... 

During an NFS experiment with a sample that contains more than one kind of scatterer (i.e., HS and LS isomer), the superposition of forward scattered waves could occur coherently or incoherently. Longitudinal scattering is always coherent, because there is no path-length difference for nuclei located along the X-ray beam. 

Projectors often arise in attempts to describe experiments within the structure of Quantum Mechanics. For example, in the case of the coherent scattering of X-rays by crystals the ideal measured intensities are given by the square of the structure factors... 

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