Ionic scattering factor

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. 

Two points, however, should be taken into account. First, natural crystals can show significant variability that depends upon the growth conditions and locality (e.g., solid solutions and incorporation of impurities). It is necessary to measure the bulk crystal structure of such samples before it is possible to determine the surface structure using the CTR approach for such samples. Second, the CTR intensities can depend on the type of form factors (e.g., neutral or ionic form factors) used in the bulk structure analysis. At minimum, the calculated bulk Bragg reflectivities must reproduce the observed values precisely internal consistency requires that we use the same atomic form factors that were used in the determination of the bulk crystal structure. Similarly, the bulk vibrational amplitudes derived from the original bulk crystal structure analysis must be used. In many cases, vibrational amplitudes are anisotropic and are therefore described by a tensor. The appropriate projection of the vibrations for each scattering condition, Q, needs to be included in the expression for Fuc-... 

Such anion-anion overlap causes a broadening of the Compton profile, and it has been shown that quite good agreement between experiment and a free ion model may be obtained for other rock-salt compounds if the effect is included, although it is always smaller than in LiH. Thus for LiF and LiCl< > the anion-anion overlap is calculated to have a 10% effect on the Compton profile at low momentum values but only a 1 % effect on x-ray scattering factors. As expected, MgO shows larger overlap effects than the halides. In other, more covalent compounds, for example BeO< > and A1N< >, the expected large departures from ionic model behavior have been observed but have yet to lead to improved wavefunctions for the solids. 

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 ... 

Several authors [1, 2] have shown that a direct experimental determination of the spatial distribution of the electron density and potential is possible not only by the x-ray diffraction methods, which are widely used, but also by the electron diffraction methods. Also, when investigating certain problems, for example, in the study of ionic compounds, electron diffraction methods of analysis are more promising in view of the profound effect of atomic ionization on the curves of the atomic scattering factor. 

It is notable that the structure factors, proportional to the scattered intensity, for gels could be very different between gels composed of non-ionic neutral polymers and of ionized polymers. In the case of the non-ionic gels, the structure factor is characterized by the screening length of the polymer chains, which is the so-called correlation length, On the other hand, an additional screening... 

PAMAM dendrimer in methanol[19], and larger also than the 60 A maximum physical radius of a completely stretched structure, but has been employed consistently. In terms of the model, some of the scatter in Figure 4 can be explained by considering that the radius of gyration of this polyelectrolyte is likely to depend on the ionic strength, pH, and even the concentration of borate diesters (internal cycles) none of these factors were systematically controlled in this study. 

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