Refinement using x-ray diffraction data

Initial parameters for Rietveld refinement were assumed as follows background, peak shape, unit cell dimensions and zero shift as determined from Le Bail s full pattern decomposition (see section 6.10), and the model of the crystal structure from the ab initio solution in the space group I4mm 

Refinement of all free variables except the coordinates and displacement parameters of individual atoms, begiiming with the scale factor (rows one through three in Table 7.9), results in low residuals, basically confirming the model of the crystal structure. When the coordinate parameters of atoms in the unit cell were included in the refinement (row four. Table 7.9), all residuals improve, especially Rb, which is lowered from 6.45 to 3.12%. Similar to the previous example, the quality of the experimental data is quite high, therefore, we easily refine individual isotropic and then individual anisotropic displacement parameters of all atoms. 

Finally, as may be established by a trial-and-error approach, a small extinction correction further improves the agreement between the observed 

Displacement parameters of atoms are also expected to be different as the temperature of the powder diffraction experiment varies. Furthermore, it is also feasible that atomic positions may change due to generally anisotropic thermal expansion of crystal lattices. These considerations are in addition to the most obvious cause (different lattice parameters) preventing combined refinement using powder diffraction data collected at different temperatures. In general, material may also be polymorphic but this is not the case here, as was established in Chapter 6, sections 6.10 and 6.11. 

Initial (profile from Le Bail, model from Table 6.24, overall 5 = 0.5 A ) 1468 1557 1526 3x10  

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A serious complication arises, however, in the application of the least squares approach to structure refinement using X-ray diffraction data. (One seems to appear in almost every aspect of X-ray crystallography, doesn t it ) Here we are trying to minimize the difference between the observed and calculated structure amplitudes Fobs and Fcaic that is, Fobs — Fcalc j or more properly, the sum of their squares taken over the entire data set. 

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