Size distribution of single-crystal nanoparticles by Monte Carlo fitting of wide-angle X-ray scattering peak shape

According to Bertaut's theorem [Acta Cryst. (1950), 3, 14-18], the size distribution of a powder sample constituted by perfect single-crystal particles can be easily determined from the peak shape analysis. The comparison between particle size distributions determined by a Monte Carlo fitting algorithm and those determined by direct observation using transmission electron microscopy shows that, as expected, the X-ray diffraction determination cannot be confidently used for particles with maximum dimensions above about 60 nm.