Anisotropic peak broadening

P.W. Stephens. Phenomenological model of anisotropic peak broadening in powder diffraction, J. Appl. Cryst. 32,281 (1999). 

In Table 12.7 we see that r4 for the group 4/m differs by one term from r4 for the group 4lmmm. The extra-term in 4/m splits those reflections that are nonequivalent but coincident in the absence of the macrostress. The same is valid for the trigonal group 3. The anisotropic peak broadenings caused by microstress are also different for coincident but non-equivalent peaks." ... 

Additionally, anisotropic chemical shift effects will also be present in the spectrum due to the nonexistence of molecular tumbling. This means that, since in solids the atoms and molecules are not moving, they do not change the orientation. Since the ability of the applied field to generate electron currents depends on the orientation of the nuclei relative to the applied field, the chemical shift depends on orientation, and since in solids this effect is not averaged out, it will contribute to the peak broadening. The chemical shift anisotropy also varies with the angle, 9,... 

Cemy, R.,etal., Anisotropic diffraction peak broadening and dislocation substructnre in hydrogen-cycled LaNi5 and snbstitntional derivatives. Journal of Applied Crystallography, 2000, 33(4) p. 997-1005. 

If the diffraction data are of above-average quality, the full-profile method can easily allow quantification of crystalline phases well below the 1 wt% accuracy level. Advanced nonroutine application of the full-profile technique involve modelling of anisotropic Bragg peak broadening for the quantification of defective or disordered crystal phases. The... 

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. 

A possible modification of this expression is presented elsewhere (82). The value of t, can be related to a diffusion coefficient (e.g., tj = l2/6D, where / is the jump distance), thereby making the Ar expressions qualitatively similar for continuous and jump diffusion. A point of major contrast, however, is the inclusion of anisotropic effects in the jump diffusion model (85). That is, jumps perpendicular to the y-ray direction do not broaden the y-ray resonance. This diffusive anisotropy will be reflected in the Mossbauer effect in a manner analogous to that for the anisotropic recoil-free fraction, i.e., for single-crystal systems and for randomly oriented samples through the angular dependence of the nuclear transition probabilities (78). In this case, the various components of the Mossbauer spectrum are broadened to different extents, while for an anisotropic recoil-free fraction the relative intensities of these peaks were affected. 

A second difficulty is the anisotropic size and strain broadening of the diffraction peaks, which is considerable as well, but highly correlated with the broadening due to stacking disorder. A de-convolution is not possible without determining the anisotropic size distribution, e.g., with electron microscopy, which is difficult to perform due to technical temperature and pressure constraints making it impossible to observe a stable sample of ice Ic. 

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