Scattering matter

The atomic scattering factor for electrons is somewhat more complicated. It is again a Fourier transfonn of a density of scattering matter, but, because the electron is a charged particle, it interacts with the nucleus as well as with the electron cloud. Thus p(r) in equation (B1.8.2h) is replaced by (p(r), the electrostatic potential of an electron situated at radius r from the nucleus. Under a range of conditions the electron scattering factor, y (0, can be represented in temis... 

W L Bragg [7] observed that if a crystal was composed of copies of identical unit cells, it could then be divided in many ways into slabs with parallel, plane faces whose distributions of scattering matter were identical and that if the pathlengths travelled by waves reflected from successive, parallel planes differed by integral multiples of the... 

We have seen that the intensities of diffraction are proportional to the Fourier transfomi of the Patterson fimction, a self-convolution of the scattering matter and that, for a crystal, the Patterson fimction is periodic in tln-ee dimensions. Because the intensity is a positive, real number, the Patterson fimction is not dependent on phase and it can be computed directly from the data. The squared stmcture amplitude is... 

In the diffraction pattern from a crystalline solid, the positions of the diffraction maxima depend on the periodicity of the stmcmre (i.e. the dimensions of the unit cell), whereas the relative intensities of the diffraction maxima depend on the distribution of scattering matter (i.e. the atoms or molecules) within the unit cell. In the case of XRD, the scattering matter is the electron density within the unit cell. Each diffraction maximum is characterized by a unique set of integers h, k and I (Miller indices) and is defined by a scattering vector H in three-dimensional... 

For sample A, the electron density appearing on SI sites (6) at x = y = z = 0.045 was attributed without any ambiguity to palladium ions because of the short SI -0(3) distance (2.0 A) and the large amount of scattering matter corresponding to about 10 Pd2+. Sites SI and SI1 were assigned to palladium and sodium ions, respectively, although some Na+ may be mixed with Pd2+ in the former. 

In an ordinary optical or electron microscope, radiation is scattered by the object that one wishes to see at higher magnification. This radiation is recombined by the lens system, resulting in an image of the scattering matter, appropriately magnified. In such a microscope the... 

The process is now repeated for every vector u that can be drawn within the unit cell of the crystal until the value of P(u) for every point (u, v, w) in Patterson space has been calculated and entered. The collection of all points (u, v, w) with their associated value P(u, v, w) is the Patterson map of the crystallographic unit cell. The Patterson map yields, at least directly, no information regarding the absolute positions of scattering matter in the unit cell, atoms, but it does provide a map of all interatomic vectors in the crystal. The... 

The extent of space is so great, however, that the weight of the sparsely scattered matter between the stars is about equal to the weight of a hundred billion suns. 

Here AF = Fi Fr, where we have removed scattering matter of scattering amplitude Fr and inserted scattering matter of amplitude Fi at the position rj. Moving a single atom or electron A from position rj to rj + Ar gives... 

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