Evaluation of particle statistics in powder diffractometry by a spinner-scan method

The uncertainty in measured diffraction intensities caused by particle statistics, which originates from the limited number of crystallites satisfying the diffraction condition, has been evaluated by a step-scan measurement about the rotation angle of a specimen-spinning attachment of a laboratory powder X-ray diffractometer. The residual statistical variance of the spinner-scan intensity data, after subtraction of periodic drift and variance caused by counting statistics, was assigned to the variance caused by particle statistics. Particle statistics for a standard Si powder (NIST SRM640c) and three size fractions (nominally 3–7, 8–12 and 18–22 µm in Stokes diameter) of quartz powder separated by a sedimentation method have been analysed by scanning electron microscopy (SEM) and the spinner-scan method using a powder X-ray diffractometer. It has been confirmed that the observed ratio of the squared diffraction-peak intensity to the variance caused by particle statistics is proportional to the multiplicity of reflections predicted by the crystal structure. The spinner-scan intensity data for the standard Si powder (NIST SRM640c), the effective particle diameter of which was estimated at 5.6 µm by SEM image analysis, was used as the standard for crystallite-size evaluation of quartz powder based on analysis of spinner-scan data. The effective crystallite diameters of the three quartz powder samples have been estimated at 6.5 (2), 11.7 (2) and 22.8 (2) µm by the analysis of the spinner-scan data, while the effective particle diameters evaluated by SEM image analysis are 7.1, 12 and 25 µm, respectively. Other possible applications of the analysis of particle statistics based on the spinner-scan method are also discussed.