The axial (or vertical) divergence error associated with Seemann-Bohlin geometry is evaluated for arrangements containing one, two or no sets of Soller slits. It is found that the error resulting from measurements of high angle reflexions amounts, typically, to about 0.0002/~ in the lattice parameter and corrections for axial divergence are, therefore, necessary in precision diffractometry. It is also observed that little is gained in return for loss of intensity when Soller slits are used in the high angle region. In the lower angle regions, however, the effect of a set of Solier slits in the reflected beam is very marked. To provide a complete error analysis using a uniform system of presentation, all the other geometrical errors associated with the Seemann-Bohlin geometry, are evaluated or re-evaluated.
Differential response errors due to dispersion and the Lorentz factor have tan3θ dependence for the powder diffractometer and should thus become critical for Bragg angles greater than ~ 155°, 2θ. The magnitude of these errors is demonstrated by measuring centroids and peaks at Bragg angles up to 170°, 2θ using Seeman–Bohlin geometry. Lattice parameters calculated from a single high angle centroid fall up to 0.0008 Å below the values obtained by extrapolation using the data of many profiles. No significant deviation using peak positions was observed within the limits of experimental error. While these errors are considered to be significant for residual stress measurements they can be ignored for routine lattice parameter determinations.
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