Differential convergent beam electron diffraction: Experiment and theory

Abstract

The derivative of intensity with respect to scattering angle in an electron diffraction pattern is shown to be almost completely independent of whether the pattern has been energy filtered or not. This is attributed to the diffuse nature of inelastic scattering. A simple approach to quantitative convergent beam electron diffraction (QCBED), developed on this basis and tested on a corresponding pair of energy-filtered and unfiltered diffraction patterns from $\ensuremath{\alpha}{\text{-Al}}_{2}{\text{O}}_{3}$, produces a fit between experimental and theoretical differential CBED patterns that is well within experimental uncertainty. Structure factors measured from the unfiltered data are indistinguishable from those from the filtered data. Furthermore, those measurements made by angular-difference QCBED appear to be less influenced by parameter correlation and the inelastic components of CBED patterns than those made by conventional QCBED. The outcome is a new avenue for accurate charge density studies that does not depend on energy-filtering optics or acquisition of multiple patterns requiring translation of the specimen.