Individual parameters, free and constrained variables

At this point, we may begin to refine atomic displacement parameters of the individual atoms. This is done by substituting individual B s (which were kept at 0) by the refined overall atomic displacement parameter. The overall B after this substitution should be set to 0. The distribution of atoms in the model of the crystal structure of LaNi4,85Sno.i5 is such that two of the sites, 2(c) and 3(g), see Table 7.2, are occupied by different types of atoms simultaneously. Generally, atomic displacement parameters of different atoms occupying the same crystallographic site should be constrained at identical values.  

In LHPM-Rietica and almost every other commonly available software product, any dependent parameter, Pdependem, may be constrained to any free 

This is a reasonable simplification especially because it is nearly impossible to differentiate properly between the vibrational motions of different atoms located in the identical environment. Furthermore, individual displacement parameters of atoms occupying the same crystallographic sites have a tendency to strong correlation, thus causing severe instabilities of non-linear least squares. If a site has variable coordinate parameters, the latter should be constrained equal for all atoms occupying the site due to the same reasons. 

The resulting refinement further reduces the residuals (see row five in Table 7.3) and yields the following distribution of the individual atomic displacement parameters  

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) 

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