New x-ray diffraction methods for the analysis of the structure and morphology of nanocrystalline powders

The Scherrer formula, the Williamson-Hall plot and the Warren-Averbach method are the most misused tools for the quantitative estimation of the “average size” of a nanocrystalline powder from an X-ray diffraction pattern. In fact, it will be shown that, even if mathematically correct, the result of the traditional analyses is not the one suggested or sought, i.e. the mean of the domain size distribution: a physical interpretation of quoted ‘average size’ or ‘microstrain’ values is not always straightforward or possible. Those traditional analysis techniques are based on rather simplified hypotheses and the microstructure information is extracted from partial or pre-processed data (i.e. peak width): the consistency between measurement and results cannot be verified and, in general, is not preserved. Modern alternatives for the analysis of powder diffraction data are here revised, demonstrating the possibility of extracting a physically sound microstructure description, with a level of detail that matches and in most cases surpass that of transmission electron microscopy. The Whole Powder Pattern Modelling (WPPM) and an alternative formalism for cases where faulting is dominant are analysed in detail and some examples of application are provided and commented.