Determination of crystal structures from powder diffraction data by direct methods: Extraction of integrated intensities from partially overlapping Bragg reflections

The development of direct methods for solving crystal structures from powder diffraction data constitutes a very active research field. The basic requirement for the success of direct methods is that enough integrated intensities can be extracted from the powder pattern. One of the most efficient extraction methods is the two-stage Le Bail method in which the integrated intensities and the profile parameters are refined separately. In this paper, a new recursive formula for the estimation of the integrated intensities of partially overlapping peaks, using the same philosophy as the Le Bail method, is derived. It is extremely robust, allowing to introduce zero valued initial estimates of the integrated intensities. The practical application of the procedure is discussed on the basis of two representative test examples.