Characterization of grain structure in nanocrystalline gadolinium by high-resolution transmission electron microscopy

A method is presented for recognition of nanograins in high-resolution transmission electron microscope (HRTEM) images of nanocrystalline materials. We suggest a numerical procedure, which is similar to the experimental dynamic hollow cone dark-field method in transmission electron microscopy and the annular dark-field method in scanning transmission electron microscopy. The numerical routine is based on moving a small mask along a circular path in the Fourier spectrum of a HRTEM image and performing at each angular step an inverse Fourier transform. The procedure extracts the amplitude from the Fourier reconstructions and generates a sum picture that is a real space map of the local amplitude. From this map, it is possible to determine both the size and shape of the nanograins that satisfy the selected Bragg conditions. The possibilities of the method are demonstrated by determining the grain size distribution in gadolinium with ultrafine nanocrystalline grains generated by spark plasma sintering.