Interpretation of angular symmetries in electron nanodiffraction patterns from thin amorphous specimens

The interpretation of angular symmetries in electron nanodiffraction patterns from thin amorphous specimens is examined. It is found that in general there are odd symmetries in experimental electron nanodiffraction patterns. Using simulation, it is demonstrated that this effect can be attributed to dynamical scattering, rather than other divergences from the ideal experimental conditions such as probe-forming lens aberrations and camera noise. The departure of opposing diffracted intensities from Friedel's law in the phase grating formalism is calculated using a general structure factor for disordered materials. On the basis of this, a simple correction procedure is suggested to recover the kinematical angular symmetries, and thus readily interpretable information that reflects the symmetries of the original projected object. This correction is numerically tested using both the phase object and multislice calculations, and is demonstrated to fully recover all the kinematical diffracted symmetries from a simulated atomic model of a metallic glass.