Geometric aspects of lattice contrast visibility in nanocrystalline materials using HAADF STEM

In conventional high-resolution transmission electron microscopy (HRTEM) imaging on nanopolycrystalline materials , the surprising abundance of lattice fringe contrast has been readily explained by the geometric relationship between the Ewald sphere and the streaking of reciprocal lattice spots from small crystals. However, in high-angle annular dark field (HAADF) imaging in scanning transmission electron microscopy (STEM) the same interference considerations do not apply. We present a new method to quantify the probability of seeing lattice contrast from a set of random crystals by estimating as a function of instrumental resolution, the range of angular misorientations from each crystallographic pole, which can give rise to lattice contrast. The maximum angular deviation for common HAADF imaging conditions has been experimentally determined by tilting perfect silicon off pole. The visibility of single and multiple sets of fringes has been successfully predicted for a range of microscope resolutions and for two materials of different unit cell sizes. As many as 70% of randomly oriented nanocrystals can be expected to show fringes in an aberration-corrected STEM.