On the Intrinsic Limits of the Convolution Method to Obtain the Crystallite Size Distribution from Nanopowders Diffraction

The present work briefly reviews the convolution of crystallite shape functions and discusses its experimental limitations. The diffraction from a theoretical spherical shape powder is used to exemplify the limits of the convolution procedure. Mean lattice distortions were not considered since the discussed limitations are inherent to the convolution method using Fourier transforms. The diffraction pattern and the convolution were calculated using appropriate macros for the Topas program. It is shown that very small crystallites require a large 2θ convolution span and the smallest subdivision for the distribution will depend on this convolution span. To show the importance of the convolution limits and its application, the nanocrystalline CeO2 round-robin diffraction pattern was evaluated. The chord frequency distribution by XRD showed conformity with the chord distribution calculated from a grain size histogram obtained by transmission electron microscopy for this sample.