The effect of finite detector slit height on peak positions and shapes in powder diffraction

The finite height of the detector slit of a powder diffractometer has three observable effects: (1) the peak is shifted by an amount that is proportional to −cot 2θ; (2) the peak is broadened by an amount proportional to cot²2θ; (3) an asymmetry is introduced into the peak shape that depends on cot³2θ. If the underlying instrumental resolution function has a Gaussian shape, the slit height effects can be approximated, over a rather broad range of shapes for the vertical resolution function, by an Edgeworth series making use of one adjustable parameter. This peak shape function is compared with experimental observations and with other shape functions that have been proposed. A well characterized peak shape is at least as important as resolution when the data are to be used for structure refinement by the Rietveld technique, and diffractometers should be designed so as to keep the slit height within the range that leads to shapes that can be described mathematically. Diffractometers with multiple detectors can usefully have different vertical divergences for detectors that cover different angular ranges.