Divergence-slit intensity corrections for Bragg–Brentano diffractometers with circular sample surfaces and known beam intensity distribution

Author(s) of this paper may load this reprint on their own web site provided that this cover page is retained. Republication of this article or its storage in electronic databases or the like is not permitted without prior permission in writing from the IUCr. Bragg±Brentano powder diffractometers equipped with ®xed-divergence slits show a loss of intensity at small 2 angles as a result of the over¯ow of the beam exceeding the sample surface. To correct this effect, geometrically derived algorithms are presented to calculate correction factors for circular sample surfaces. It is shown that the algorithms for rectangular samples can be applied to circular samples with suf®cient accuracy if the value for the length of the sample is replaced by a value intermediate between the diameter of the circular sample and the length of the corresponding rectangular sample. Inhomogeneous beam intensity distribution also has serious effects on the correction factors, especially for wide divergence-slit apertures. 1. Introduction To obtain correct intensities, the irradiated sample volume has to be constant for all diffraction angles, which is usually achieved by ®xed-divergence slits in Bragg±Brentano geometry. For decreasing diffraction angles, the irradiated surface of the sample increases until the cross section of the X-ray beam exceeds the sample area. Consequently, intensity is lost below a limiting angle and the over¯owing beam hits the sample support, which usually increases the background due to incoherent scattering from the sample holder. The effect can be avoided if the beam aperture, i.e. the divergence slit, is chosen to be small enough. However, if only a small amount of sample is available, small sample holders must be used and intensity will be lost at low diffraction angles. Taylor et al. (1986) introduced empirically derived correction factors to account for the intensity loss. Moore & Reynolds (1989) recommended accounting for the intensity loss by dividing the area of the beam cross section by the illuminated area of the sample, which is equivalent to dividing the length of the beam cross section by the length of the illuminated area. A more complex procedure for intensity corrections was developed by Matulis & Taylor (1993). Their algorithm also includes tube self-absorption, sample transparency, receiving-and diver