The nanodiffraction problem

The results of a systematic rigorous study on the accuracy of lattice parameters computed from X‐ray diffraction patterns of ideally perfect nanocrystalline powder and thin‐film samples are presented. It is shown that, if the dimensions of such samples are below 20 nm, the lattice parameters obtained from diffraction analysis will deviate from their true values. The relative deviation depends on the relevant size parameter through an inverse power law and, for particular reflections, depends on the angular peak positions. This size‐dependent error, Δa/a, is larger than the precision of typical X‐ray diffraction measurements for ∼20 nm‐thick diffracting domains, and it can be several orders of magnitude larger for particles smaller than 5 nm. A systematic rigorous self‐consistent modeling study of diffraction experiments from nancrystalline powders and thin films was performed. The results show that for such samples the lattice parameters determined from single‐peak or full‐pattern analysis have size‐dependent errors which are not due to artifacts of peak‐fit and refinement routines.