Asymmetry, shift, diffraction peak

Figure 6.8. The observed and calculated powder diffraction patterns of LaNi4,85Sno,i5 after the polynomial background and asymmetry were refined together with lattice parameters, zero shift and peak shape parameters (U,V,Wand r o) ...

The use of Mo Ka radiation shifts all diffraction peaks to lower Bragg angles and therefore, asymmetry effects are more severe than in the previous example, where Cu Ka radiation was used. As a result, the order in which parameters were refined was changed to avoid potential least squares instability problems. When all parameters were refined in essentially the same approximation as in the previous example (see row 5 in Table 6.9), the resultant figures of merit were satisfactory, but a carefiil analysis of Figure 6.15 indicates that the selected peak shape function does not adequately describe the observed peak shapes at low Bragg angles. 

As can be seen from the figure the conics produced by the diffraction cone with the different Bragg angles fill the receiving slit plane differently, being responsible for the asymmetry, apparent shift, and width of the diffraction peak (see also the Section 6.6.1.4). 

To further improve the fit, the following parameters were consequently included into the least squares minimization strain peak broadening parameter Y, then peak asymmetry a, and sample displacement. At this point, a linear background was substituted by a fourth order shifted-Chebyshev polynomial and refined with all other profile parameters fixed. Finally, all relevant parameters were refined together. The convergence was achieved, and the final fit, which is illustrated in Figure 7.41, is quite satisfactory considering the poor resolution of the powder diffraction pattern. 

Instrumentation for studies of this nature are usually variations of the normal powder X-ray diffractometer. Except for faulting and strain in single crystals, which are better treated as defects, the very nature of the material limits studies to powders or aggregates. X-ray powder patterns of simple metals can be analyzed to yield information on particle size, deformation fault probability, mean-square strain, and twinning. The theory and techniques used to study diffraction line broadening, peak shifts, and line profile asymmetry have been derived and applied by Warren, " and Warren and Averbach. To assess faulting probability, certain drastic assumptions are necessary, reducing the detectability limit to approximately one faulted layer in 200. 

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