Systematic intensity errors caused by spectral truncation : origin and remedy

The wavelength dispersion of graphite(002)-monochromated X-ray beams has been determined for a Cu, a Mo and an Rh tube. The observed values for Δλ/λ were 0.03, 0.14 and 0.16, respectively. The severe reduction in monochromaticity as a function of wavelength is determined by the absorption coefficient μ of the monochromator. μ(monochromator) varies with λ3. For an Si monochromator with its much larger absorption coefficient, Δλ/λ values of 0.03 were found, regardless of the X-ray tube. This value matches a beam divergence defined by the size of the focus and of the crystal. This holds as long as the monochromator acts as a mirror, i.e. μ(monochromator) is large. In addition to monochromaticity, homogeneity of the X-ray beam is also an important factor. For this aspect the mosaicity of the monochromator is vital. In cases like Si, in which mosaicity is practically absent, the reflected X-ray beam shows an intensity distribution equal to the mass projection of the filament on the anode. Smearing by mosaicity generates a homogeneous beam. This makes a graphite monochromator attractive in spite of its poor performance as a monochromator for λ < 1 A. This choice means that scan-angle-induced spectral truncation errors are here to stay. These systematic intensity errors can be taken into account after measurement by a software correction based on the real beam spectrum and the applied measuring mode. A spectral modeling routine is proposed, which is applied on the graphite-monochromated Mo Kα beam. Both elements in that spectrum, i.e. characteristic α1 and α2 emission lines and the Bremsstrahlung, were analyzed using the 6_\prime3_\prime18 reflection of Al2O3 (s = 1.2 A−1). The spectral information obtained was used to calculate the truncation errors for intensities measured in an ω/2θ scan mode. The results underline the correctness of previous work on the structure of NiSO4·6H2O [Rousseau, Maes & Lenstra (2000). Acta Cryst. A56, 300–307].