Measurement of Atomic Modulation Direction Using the Azimuthal Variation of First-Order Laue Zone Electron Diffraction.

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 four-dimensional scanning transmission electron microscopy (4DSTEM) is far more reliable and allows the measurement of the modulation direction with a precision of about 1° and an accuracy of about 3°. This method could be very powerful in characterizing atomic structures in three dimensions by 4DSTEM, especially in cases where the structure is found only in nanoscale regions or crystals.