Synthesizing and fitting linear position-sensitive detector step-scanned line profiles

An X-ray powder diffractometer has been modified by the addition of a narrow-bandpass germanium pre-monochromator and a linear position-sensitive detector (LPSD) with its centre set at the normal θ–2θ focusing condition. Diffraction data are recorded using a step-scan procedure in which the patterns recorded at each step are summed to form the final pattern over a wide angular range. In this way, diffraction patterns covering 120 2θ can be recorded 100 times more rapidly than with conventional receiving-slit diffractometers for the same level of counting statistics. In this paper, an analysis has been carried out of the contribution of the instrumental parameters to the shapes of the X-ray diffraction lines obtained with either a stationary or a step-scanned LPSD. This is done by calculating theoretical profiles for defocusing, parallax error, thermal-noise broadening and LPSD pixel size and convoluting them with the Cu Kα emission spectrum and aberration profiles associated with a standard focusing powder diffractometer. Theoretical profiles for fitting to experimental step-scan data are synthesized by summing convoluted profiles across the detector window. The validity of this procedure is tested by fitting to experimental step-scan data from well characterized reference specimens of MgO and Y₃Al₅O₁₂ (YAG). The extra broadening associated with the inclusion of a LPSD is refined in terms of the depth of the detector, the angular window of the LPSD and the angle of divergence of the incident beam. Good fits have been obtained to the reference profiles and the physical parameters of the diffractometer determined in this way agree well with directly measured values.