  The increasing scientific and technological interest in nanoparticles has
raised the need for fast, efficient and precise characterization techniques.
Powder diffraction is a very efficient experimental method, as it is
straightforward and non-destructive. However, its use for extracting
information regarding very small particles brings some common crystallographic
approximations to and beyond their limits of validity. Powder pattern
diffraction calculation methods are critically discussed, with special focus on
spherical particles with log-normal distribution, with the target of
determining size distribution parameters. A 20-nm CeO$_{2}$ sample is analyzed
as example.
