On the breakdown of Friedel's Law for coherent microdiffraction from amorphous materials

Abstract

Electron microdiffraction from amorphous solids using nanometric probes in FEG-STEMs frequently shows breakdown of Friedel's Law, i.e. the diffraction pattern is no longer centrosymmetric. We have previously simulated the effect using simple models for uniform disordered materials. Here, we present an analytical demonstration for the case of a weak phase object with a finite probe of coherent illumination. This shows that the breakdown is due to lens aberrations and/or mixing, in reciprocal space, of the broadened straight-through beam with the diffracted beams. In our analysis these appear as cross-terms which are normally zero for an infinite incident plane wave. The sensitivity of this effect on parameters such as probe size and thickness are investigated with the aid of simulations for our model disordered system.