Factor scattering

Scattering Factor The scattering function P 6) depends on polymer dimension, wavelength of the light, and the refractive index of the solvent. The following function has been derived for random coil polymer (Doty and Edsall, 1951)  

To detennine the scattering factors of Na and Cl from the structure factors of NaCl. 

Intensity measurements of the various X-ray reflections from powdered sodium chloride lead to values of its structure factor F (Havighurst, Phys. Rev. 1926, 28, 869) given in table 1, where 0 denotes the Bragg angle and A the wave-length. These measurements were made with Mo Ka radiation having A = 0.710 A. Since however F is a function of sin 6/A values of this rather than sin 0 are tabulated. 

Reflections with h, k, I aH odd (marked in the table by an asterisk) are from alternating planes of Na and of Cl. For these reflections 

F = fa —/sa where / denotes a scattering factor. All other reflections are from planes containing alternating Na and Cl atoms. For these reflections F = /a + /xa. 

WeplotFagainst (sin 0)/A and draw the tw o cur es. We then plot the means to obtain/a and the half-differences to obtain /x . 

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Figure Bl.8.1. The atomic scattering factor from a spherically synnnetric atom. The volume element is a ring subtending angle a with width da at radius r and thickness dr.

Because the neutron has a magnetic moment, it has a similar interaction with the clouds of impaired d or f electrons in magnetic ions and this interaction is important in studies of magnetic materials. The magnetic analogue of the atomic scattering factor is also tabulated in the International Tables [3]. Neutrons also have direct interactions with atomic nuclei, whose mass is concentrated in a volume whose radius is of the order of... 

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... 

Equation (Bl.8.6) assumes that all unit cells really are identical and that the atoms are fixed hi their equilibrium positions. In real crystals at finite temperatures, however, atoms oscillate about their mean positions and also may be displaced from their average positions because of, for example, chemical inlioniogeneity. The effect of this is, to a first approximation, to modify the atomic scattering factor by a convolution of p(r) with a trivariate Gaussian density function, resulting in the multiplication ofy ([Pg.1366]

Potassium chloride actually has the same stnicture as sodium chloride, but, because the atomic scattering factors of potassium and chlorine are almost equal, the reflections with the indices all odd are extremely weak, and could easily have been missed in the early experiments. The zincblende fonn of zinc sulphide, by contrast, has the same pattern of all odd and all even indices, but the pattern of intensities is different. This pattern is consistent with a model that again has zinc atoms at the comers and tlie face centres, but the sulphur positions are displaced by a quarter of tlie body diagonal from the zinc positions. 

A teclmique that employs principles similar to those of isomorphous replacement is multiple-wavelength anomalous diffraction (MAD) [27]. The expression for the atomic scattering factor in equation (B1.8.2h) is strictly accurate only if the x-ray wavelength is well away from any characteristic absorption edge of the element, in which case the atomic scattering factor is real and Filiki) = Fthkl V- Since the diffracted... 

In this approximation, the wave fiinction is identical to the incident wave (first tenn) plus an outgoing spherical wave multiplied by a complex scattering factor... 

In the conventional theory of elastic image fomiation, it is now assumed that the elastic atomic amplitude scattering factor is proportional to the elastic atomic phase scattering factor, i.e. 

X-ray diffraction has been used for the study both of simple molten salts and of binary mixtures thereof, as well as for liquid crystalline materials. The scattering process is similar to that described above for neutron diffraction, with the exception that the scattering of the photons arises from the electron density and not the nuclei. The X-ray scattering factor therefore increases with atomic number and the scattering pattern is dominated by the heavy atoms in the sample. Unlike in neutron diffraction, hydrogen (for example) scatters very wealdy and its position cannot be determined with any great accuracy. 

The Calculation and Interpretation of X-ray Term Values, and the Calculation of Atomic Scattering Factors... 

Atomic scattering factors were then found by... 

Two helices are packed antiparallel in the orthorhombic unit cell. Association of the helices occurs through a series of periodic carboxylate potassium water - carboxylate interactions. An axial projection of the unit-cell contents (Fig. 23b) shows that the helices and guest molecules are closely packed. This is the first crystal structure of a polysaccharide in which all the guest molecules in the unit cell, consistent with the measured fiber density, have been experimentally located from difference electron-density maps. The final / -value is 0.26 for 54 reflections, of which 43 are observed, and it is based on normal scattering factors.15... 

A factor known as scatter factor has been characterized which causes the break up and stimulates motility of epithelial cell clumps (Stoker et al., 1987). This factor is identical to hepatocyte growth factor and increases the rate of locomotion of several other cell types. Motility factors elaborated from tumor cells are considered to play an important role in metastasis (see later). Guidance of cells by the physical topography of the substratum is another factor that profoundly affects the behavior of cells. 

Stoker, M., Gherardi, E., Perryman, M., Gray, J. (1987). Scatter factor is a fibroblast-derived modulator of epithelial cell motility. Nature, 327,239-242. 

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