Calculation of the X-ray powder reflection profiles of very small needle-like crystals. I. Principles of the method

The aim of this paper is to develop a calculation method which allows the theoretical profiles of X-ray powder reflections to be obtained in the case of very small needle-like crystallites. This method takes into account not only the shape transform of the crystallite but also the variation of the structure factor. The study is limited to the case where the cross section of the needles contains two of the principal crystallographic axes and the third axis is along the crystallite direction of elongation. An example of the application of this method is given for a microcrystallized fibrous silicate known as sepiolite.