Measurement of structure factors by parallel and convergent beam electron nanodiffraction

A quantitative understanding of transmission electron microscopic (TEM) images usually involves simulations as a central part. In the TEM community, the Bloch wave approach is frequently applied to simulate diffracted beam amplitudes in crystalline specimen. For example, the CELFA [1] technique compares the composition-dependent contrast in experimental (200) lattice fringe images with Bloch wave simulations to derive the local chemical composition x in InxGa1-xAs alloys. However, prior knowledge on the scattering properties of a crystal enters the Bloch wave method by means of structure factors (SF). Commonly, SF are calculated from isolated atom scattering data [2], so that the effect of a redistribution of electrons due to chemical bonding is neglected. Recent theoretical approaches overcome this problem by defining modified atomic scattering amplitudes (MASA [3]) which are calculated by density functional theory (DFT) methods. In this work, we introduce a new technique to measure SF from TEM spot diffraction patterns acquired under parallel illumination. Starting with the SF for isolated atoms, Bloch wave refinement routines have been developed to minimize the R-value defined by