On predicting scan profiles: the nature of the `aberration function'

In an earlier treatment [Destro & Marsh (1987). Acta Cryst. A43, 711–718], an attempt was made to predict the shapes of high-angle θ–2θ scan profiles by convoluting a low-angle profile with the presumedly known spectral distribution function for the incident (crystal-monochromated Mo Kα) radiation but it was found necessary to introduce a third component, an 'aberration function', that varied with the Bragg angle θ. It is shown here that the primary purpose of the aberration function is to correct for defects in the spectral-distribution function. In particular, the effective intensity ratio between the Kα₂ and Kα₁ spectral lines can apparently deviate greatly (by more than 10%) from the theoretical value of 0.499, depending upon the alignment of the monochromator crystal, and an appreciable amount of white radiation may also be present. By a suitable modification of the spectral-distribution function, high-angle scan profiles can be predicted from accurate measurements of a low-angle profile; as a result, scan-truncation losses can, for the most part, be removed. However, modeling the spectral distribution function appropriate to a particular experiment remains a difficult empirical procedure.