Diffraction atom position effect

The techniques can be broadly classified into two groups those which directly identify the atomic species present and then provide structural information about the identified species from diffraction or scattering effects (EXAFS, SEXAFS, and XPD) and those which are purely diffraction-based and do not direcdy identify the atoms involved, but give long-range order information on atomic positions from... 

The diffraction lines due to the crystalline phases in the samples are modeled using the unit cell symmetry and size, in order to determine the Bragg peak positions 0q. Peak intensities (peak areas) are calculated according to the structure factors Fo (which depend on the unit cell composition, the atomic positions and the thermal factors). Peak shapes are described by some profile functions 0(2fi—2fio) (usually pseudo-Voigt and Pearson VII). Effects due to instrumental aberrations, uniform strain and preferred orientations and anisotropic broadening can be taken into account. 

The present chapter deals first with all the preliminary steps which must be taken to obtain suitable data for structure determination (whether by direct or indirect methods)—the measurement of the intensities of diffracted beams, and the application of the corrections necessary to isolate the factors due solely to the crystal structure from those associated with camera conditions. It then goes on to deal with the effect of atomic arrangement on the intensities of diffracted beams, the procedure in deducing the general arrangement, and finally the methods of determining actual atomic coordinates by trial. It follows from what has been said that, as soon as atomic positions have been found to a sufficient degree of approximation to settle the phases of the diffracted beams, then the direct method can be used this, in fact, is the normal procedure in the determination of costal structures. 

As the amount of Fe is increased, the (111) peak shifts to smaller d-spacings, reflecting a contraction of the lattice. The (111) peak positions in Fig. 11.5 show a continuous shift from pure Pt to pure Fe. The Pt-Fe XRD patterns are consistent with a single-phase, substitutional solid solution (disordered alloy) over the entire compositional range. In contrast, Fig. 11.6 clearly displays diffraction from inter-metallic compounds of lower symmetry. Post-deposition annealing has resulted in an ordering of the Pt and Fe atoms, the effect of which is the crystallization of an ordered metal alloy of lower symmetry than 100% Pt. In essence, the applied vacuum deposition method is ideally suited for the preparation of multi-component,... 

Extinction, which is the failure of the kinematic scattering theory (Ihki hki) is only a minor problem in X-ray diffraction. In neutron diffraction, extinction is serious and pervasive throughout the whole data, as shown by the examples in Thble 3.2. The best methods available for extinction correction require careful measurement of crystal dimensions. Although somewhat empirical, it has proved to be very effective [184, 185]. At least one, and sometimes six, additional extinction parameters, gis0 or gij, have to be added to the variable parameters. Uncertainty in the validity of these extinction parameters appears to have very little effect on atomic positional coordinates, but may influence the absolute values of the atomic temperature factors. This is important in charge density or electrostatic potential... 

Disorder may strongly influence the precision with which all atomic positions in that crystal can be measured, and it is often difficult to obtain a model that accounts adequately for the disorder. Consequently diffraction effects resulting from disorder may be compensated for b (erroneous) shifts in other parameters that involve ordered atoms. Bond distances may appear unusually long or short and bond angles may be atypical. These effects almost certainly result from inadequacies in the model. If the disorder occurs in only a small fraction of the content of the asymmetric unit, it is presumed that the conformation of the (well-ordered) remainder of the asymmetric unit (molecule) is driving the crystal packing rather than vice versa. Disorder is often observed in solvent of crystallization, since there may be space in the crystal structure for the solvent molecules to organize in one of several manners. ... 

Fig. 4-8 The effect of atom position on the phase difference between diffracted rays.

WILLIAMS pointed out that even in the case of neutron diffraction, hydrogen atom positions may not be well determined because of large thermal motion. In p-CH3C6H4NH3 (HF2), the apparent methyl C-H distances range from 0.92 A to 0.96 A these short values are artifacts caused by large-amplitude torsional motion of the methyl group. Furthermore, it is very difficult to correct reliably for such effects. 

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