WIAS Preprint No. 2938, (2022)

Symmetries in TEM imaging of crystals with strain


  • Koprucki, Thomas
    ORCID: 0000-0001-6235-9412
  • Maltsi, Anieza
    ORCID: 0000-0003-2417-8770
  • Mielke, Alexander
    ORCID: 0000-0002-4583-3888

2020 Mathematics Subject Classification

  • 74J20 35L25 78A45


  • TEM imaging, symmetries, reciprocal theorem, Darwin--Howie--Whelan equation, deformed crystals, m-beam column approximation




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.

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