Symmetries in transmission electron microscopy imaging of crystals with strain

Abstract

Transmission electron microscopy (TEM) images of strained crystals often exhibit symmetries, the source of which is not always clear. To understand these symmetries, we distinguish between symmetries that occur from the imaging process itself and symmetries of the inclusion that might affect the image. For the imaging process, we prove mathematically that the intensities are invariant under specific transformations. A combination of these invariances with specific properties of the strain profile can then explain symmetries observed in TEM images. We demonstrate our approach to the study of symmetries in TEM images using selected examples in the field of semiconductor nanostructures such as quantum wells and quantum dots.

Plasma Cleaning of Cationic Surfactants from Pd Nanoparticle Surfaces: Implications for Hydrogen Sorption

“…Specifically, the darker regions might stem from high diffraction angles which can be inferred from induced strain or defects on the surface, as reported, for example, for lattice dislocations and stacking faults. 62,63 This effect is particularly apparent after the H 2 plasma treatment step (Figure 6a, dashed-line highlighted region) and in line with earlier reports of plasma treatments structurally altering Pd surfaces at the atomic level. 64,65 Furthermore, atomic force microscopy (AFM) topographical scans of representative nanoparticles corroborate the surface structuring as a significant increase of surface roughness from 0.1 ± 0.0 nm on a pristine Pd nanoparticle to 0.8 ± 0.0 nm after H 2 plasma treatment (Figure 7.…”

Three dimensional classification of dislocations from single projections

“…Nevertheless, a fundamental ambiguity of electron scattering for centro-symmetric scattering geometries exists 19 : displacements fields with inhomogeneities, which exhibit a mirror symmetry with respect to the specimen midplane in beam direction will result in the same diffraction pattern.…”