Measurement of atomic modulation direction using the azimuthal variation of first order Laue zone electron diffraction

TL;DR

This paper demonstrates that azimuthal variation in the first order Laue zone electron diffraction can reliably measure atomic modulation directions with high precision using 4DSTEM, aiding 3D atomic structure characterization.

Contribution

It introduces a method to determine atomic modulation direction from FOLZ azimuthal variation using 4DSTEM, improving measurement accuracy and reliability.

Findings

Measurement precision of about 1 degree.

Measurement accuracy of about 3 degrees.

Potential for detailed 3D atomic structure analysis.

Abstract

We show that diffraction intensity into the First Order Laue Zone (FOLZ) of a crystal can have a strong azimuthal dependence, where this FOLZ ring appears solely because of unidirectional atom position modulation. Such a modulation was already known to cause the appearance of elliptical columns in atom resolution images, but we show that measurement of the angle via 4-dimensional Scanning Transmission Electron Microscopy (4DSTEM) is far more reliable and allows the measurement of the modulation direction with a precision of about 1{\deg} and an accuracy of about 3{\deg}. This method could be very powerful in characterising atomic structures in 3 dimensions by 4DSTEM, especially in cases where the structure deviates from that found in bulk crystals.