Centroid shifts due to axial divergence and other geometrical factors in Seemann-Bohlin diffractometry

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 reflections amounts, typically, to about 0.0002 Å 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 Soller 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.