Site scattering factor

The atomic scattering factor applicable to such alloys or solid solutions is an average value, referred to as the site scattering factor, /site. In general, if two atoms, A and B, with atomic scattering factors fA and fB fully occupy a single site in a structure, the site scattering factor is... 

Despite the similarity of the electron densities of Si and A1 atoms, their scattering factor curves / are still different enough to allow a refinement of the Si-Al distribution of a T-site according to ... 

The modeling of a polymerization process is usually understood as formulation of a set of mathematical equations or computer code which are able to produce information on the composition of a reacting mixture. The input parameters are reaction paths and reactivities of functional groups (or sites) at monomeric substrates. The information to be modeled may be the averages of molecular weight, mean square radius of gyration, particle scattering factor, moduli of elasticity, etc. Certain features of polymerizations can also be predicted by the models. 

Site populations of less abundant cations estimated from X-ray diffraction measurements have limited accuracies particularly when iron is present, since diffraction phenomena involve the cooperative scattering effects of many atoms in the unit cell. It is very difficult, and sometimes impossible in X-ray structure refinements, to distinguish between cations of different valences, such as Fe2+ and Fe3+, Mn2+ and Mn3+ or Ti3+ and Ti4+, and between neighbouring elements in the periodic table with similar scattering factors, such as iron... 

It is obvious that atoms in the 2(c) site have much larger atomic displacement parameters than identical atoms in the 3(g) site. This situation is quite unusual for a simple intermetallic compound and likely indicates that our assumption about a statistical distribution of Ni and Sn in both crystallographic sites was incorrect. The enhanced isotropic atomic displacement parameter in the 2(c) site points to a lower scattering ability, while the reduced atomic displacement parameter in the 3(g) site points to a higher scattering factor when compared to the current distribution of atoms. Indeed, we may speculate that only 3(g) sites contain Sn atoms, which have greater scattering ability than Ni atoms. Another possibility is that the 2(c)... 

Refinement of the crystal structure is, therefore, a powerful chemical analysis technique. Unlike conventional chemical analysis, which only yields the bulk composition of the sample, powder diffraction analysis facilitates accurate determination of the occupancies of different crystallographic sites by various chemical elements, or in other words, establishes precise chemical composition of the crystal at the atomic resolution. It should be noted that the results may be considered reliable only when the difference in the scattering ability of atoms in question is significant, in addition to a very high quality of experimental data. This is indeed the case here because scattering factors of Sn and Ni are related as-1.8 1. 

Refining site population factors this is similar to the previous approach but is a more appropriate way of testing for the scattering power of an atom because the multiplication of the atomic number of the element, currently present on a certain site, by its fractional occupation factor results in the approximate number of electrons in the element that should occupy the given site. 

The original refinement for the two A1 sites used interpolated scattering factors for A1+1-5, which we model as an equal mix of A1 and Al3+. 

X-ray diffraction does not separate atoms that are Periodic Table neighbours well, as the scattering factors of these species are so similar. Thus, problems such as the distribution of Fe2+ and Fe3+ over the available sites in a crystal structure may be unresolved by conventional structure determination methods. The bond valence model is an empirical concept that correlates the strength of a chemical bond between two atoms and the length of the bond. Because crystal structure determinations yield accurate interatomic distances, precise values of the bond strength, called the experimental bond valence, can be derived. 

Because the X-ray scattering factors of Mg and A1 are similar, it is not easy to assign the cations in the mineral spinel, MgAl204 to either octahedral or tetrahedral sites (see Section 7.8 for more information). The bond lengths around the tetrahedral and octahedral positions are given in the table. Use the bond valence method to determine whether the spinel is normal or inverse. The values of r0 are r0 (Mg2+) = 0.1693 m, r0 (Al3+)= 0.1651 nm, B = 0.037 nm, from... 

The values for Cromer-Mann coefficients used in the calculation of atomic scattering factors were taken from http //www-structure.llnl.gov. This site has excellent on-line tutorials that allow calculation of scattering factors, structure... 

Ponzetto, C. et al., A multifunctional docking site mediates signaling and transformation by the hepatocyte growth factor/scatter factor receptor family. Cell, 77,261,1994. 

In this equation. / , is the scattering factor of the atom m associated with the lattice site at the locator r and which is displaced from its mean position by a small amount u ,. Expressed in Eq. 1 is the fact that the scattered intensity may be written as the sum of component intensities. The zero th-order term is independent of the displacements. The first-order term is dependent on the first moment of displacements, the second-order term on the second moments, etc. If we carry out a reduction of Eq. 1 by separating terms into those corresponding to the average lattice and those corresponding to the deviations from the average, this separation into scattering components is preserved. We can then express the total intensity as follows ... 

Although the intensity distribution in Fig. 2a looks complex, it can be described purely in terms of substitutional disorder, in which there are two different possible molecular orientations A and B in each site and can be understood in terms of a small set of intermolecular occupancy correlations. In addition, and most importantly, the overall form of the scattering is modulated by the difference of the molecular scattering factors, Fa — Fb. Because there are two different molecular sites (cell corners and cell centers), with different average orientations, some terms arise from pairs of molecules on a single sublattice (e.g., the cell corners), while others arise from pairs comprising a molecule on one sublattice (cell corner), with a molecule on the other sublattice (cell center). 

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