Particle statistics and whole-pattern methods in quantitative X-ray powder diffraction analysis

Modern powder diffraction employing computer-controlled diffractometers now allows quantitative analytical methods to use the whole diffraction trace rather than only individual peaks. Two such methods are in common use: the Rietveld method, which refines the crystal structures of the component phases as part of the matching calculation, and the pattern-fitting method, which uses reference patterns from a database. Potential accuracies of these methods seems to be around 1 % absolute. The most severe limitation on the potential accuracy of these methods is particle statistics, which has been reviewed in considerable detail.