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A method allowing the calculation of the diffraction line profiles of a powder, whose crystallites are convex polyhedrons, is described. The decomposition of the crystallite volume into elementary prisms distinguishes three cases. The analytical expression of the results allows their derivation in the case of a linear size distribution. With instrumental broadening causes taken into account, an application of this method is given in restoring the whole X-ray diffraction pattern of samples of finely divided powders of boehmite, AlOOH.
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