Nanoparticle size distribution estimation by a full-pattern powder diffraction analysis

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 nondestructive. 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 distributions, with the target of determining size distribution parameters. A 20-nm CeO₂ sample is analyzed as an example.