Atomic scattering factor table

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 functions Hartree-Fock valence shells of the atoms are tabulated in scattering factor tables (International Tables for X-ray Crystallography 1974,... 

The structures of the zeolite frameworks have been determined by X-ray and neutron diffraction techniques. Some of the naturally occurring minerals were characterized in the 1930s, and the synthetic zeolites have been investigated from 1956 onward. Unfortunately, it is extremely difficult for diffraction techniques to determine a structure unequivocally because A1 and Si are next to each other in the Periodic Table and thus have very similar atomic scattering factors (Chapter 2). It is possible to determine the overall shape of the framework with accurate atomic positions but not to locate the Si and A1 atoms precisely. 

It is easy to distinguish Ba + ions from Na+ for several reasons. Firstly, their atomic scattering factors are quite different, 54 e for Ba2+ vs 10 e for Na+. Secondly, their ionic radii are quite different, Ba2+ = 1.34 X and Na = 0.97 X (5). Also, the approach distances between these ions and zeolite oxide ions in dehydrated Na 2 A (16) and hydrated Bag-A are known (see Table III). Finally, the requirement that 12 cationic charges be placed per unit cell does not allow the major positions to refine to acceptable occupancies with an alternative assignment of ionic identities. 

The difference Fourier synthesis, phased by the P, Cl, N, C and O atoms, revealed the hydrogen atoms with their expected locations. Thus, the final refinement could be performed on the entire set of atoms including hydrogens with fixed isotropic thermal parameter factor, BH = 4 A2. Final R and S values are 0.022 and 0.948, respectively. The last difference Fourier map showed no values to be greater than 0.3 eA 3 (Table 15). Atomic scattering factors were corrected for anomalous dispersion from Cromer and WaberS8). 

Viervoll, H., and Ogrim, O. An extended table of atomic scattering factors. Acta Crysi. 2, 277-279 (1949). 

International Tables for X-ray Crystallography, Vol. III. Physical and Chemical Tables. (Eds., MacGillavry, C. H., and Rieck, G. D.) Atomic scattering factors, pp. 201-245. Kynoch Press Birmingham, New York (1962). 

Vol. III. Physical and Chemical Tables (1962). Includes data on characteristic wavelengths, absorption coefficients, atomic scattering factors, Compton scattering, etc. Also treatments of intensity measurements, texture determination, particle size broadening, small angle scattering, and radiation hazards. 

Vol. IV. Revised and Supplementary Tables (1974). Contains revised data on characteristic wavelengths, absorption coefficients, and atomic scattering factors. Also some new material useful in structure determination. 

Reduction of the temperature of the crystal decreases the thermal motion of the atoms, which can be expressed in terms of the temperature factor (B). A reduction in B enhances the atomic scattering factors (Fig. 3.1.2) and thus the corresponding structure factors and measured intensities (Table 3.1.1), particularly at higher Bragg angles. 

Systematic absences arise from symmetry considerations and always have F(hkl) equal to zero. They are quite different from structural absences, which arise because the scattering factors of the atoms combine so as to give a value of F(hkl) = zero for other reasons. For example, the (100) diffraction spots in NaCl and KC1 are systematically absent, as the crystals adopt the halite structure, which is derived from an all-face centred (F) lattice, (see Table 6.4). On the other hand, the (111) reflection is present in NaCl, but is (virtually) absent in KC1 for structural reasons - the atomic scattering factor for K+ is virtually equal to that of Cl-, as the number of electrons on both ions is 18. 

Single-crystal x-ray studies of the contact-ion pair complexes shown in Table II have been completed. The data were measured with a Picker automated diffractometer, and the structures were solved by direct methods. Hydrogen atom positions were included in all the structures but usually not refined. Refinements of the structures were made using a full-matrix, least-squares technique with neutral-atom scattering factors. 

Unlike the normal atomic scattering factor, f0, the values of/ and/" do not decrease with scattering angle because the radius of the inner absorbing electron shell is much less than the wavelength of the radiation used (table 9.1). This actually aids the signal to noise of the anomalous effects at high resolution (equation (2.22)). 

It is evident from Table 1 that the Hall coefficient R and the electrical conductivity or, measured at 1.7 K, were the highest for samples 1-3. These samples were characterized also by the largest values of the characteristic temperatures. An analysis of the atomic scattering factors fiig of samples 5 and 6 indicated that they were 0.44% smaller than the factors / g for samples 1-3. This indicated that samples 5 and 6 were not stoichiometric but deficient in mercury. The lattice period was the same for all the samples and equal to 6.4590 0.0005 A. The constancy of the lattice period could be explained by the superposition of two effects. The formation of vacancies at the expense of the component with the larger atomic radius reduced the lattice period but the weakening of the atomic binding forces compensated this reduction. This was confirmed by a decrease in the characteristic temperatures of samples 5 and 6. 

The following table lists the cation radii in LiF, NaCl, and KCl, the distances of the p (r) minima from the centers of the cations, and the ionic radii rg which we deduced from the radial electron density distributions obtained by approximating the atomic scattering factors with smooth curves ... 

For specific applications, the tunability of synchrotron radiation sources allows the X-ray wavelength to be changed readily, and this can be exploited to enhance the contrast between close elements in the periodic table. These studies are termed anomalous (resonant) scattering experiments. The atomic scattering factor for X-rays is defined as... 

Atomic scattering factors for the elements A periodic table/form-based data resource. 

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... 

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