Absolute strain and relative displacement over HR-(S)TEM images

Strain and relative displacement of sub-structures of complex crystals


July 7, 2023

Researchers from CEMES proposed two methods of reciprocal space treatment of HR-(S)TEM images, named AbStrain and Relative displacement. AbStrain allows for quantification and mapping of interplanar distances and angles, displacement fields and strain tensor components with reference to a user-defined Bravais lattice. Relative displacement provides atomic displacements between sub-structures, when a crystal is made up of two or more types of atoms.

For the reciprocal space treatment of HR-TEM and HR-STEM images like Geometric Phase Analysis (GPA), we overcame the limitation of using similar reference crystal structure in the same field of view, by directly treating the zone of interest corrected from the different types of image distortions specific to HR-TEM and HR-STEM imaging modes. We proposed to reconstruct the displacement fields and strain tensor components of the imaged structure with reference to a user-defined Bravais lattice by developing the method, named AbStrain, with two approaches. The first one provides the components of an absolute strain tensor and rigid body rotation by using the maps of measured reciprocal vectors and that of the Bravais lattice. Displacement field is then calculated by their integration. Alternatively, the second approach allows for the reconstruction of an absolute displacement field with reference to a Bravais lattice, from which strain and rotation are obtained by partial derivation. Interplanar distances and angles are reconstructed within both approaches from the absolute strain tensor and rigid body rotation maps.

We presented also the method, called Relative displacement, which allows for extracting images of sub-structures, when a crystal is made up of two or more types of atoms, and measuring atomic displacements with reference to each other, without the need to account for image distortions and be familiar with the crystal’s structural characteristics. Such an approach is interesting to apply for complex semiconductors and functional oxides where polarization related displacement exists.

The two methods proposed here extend the range of possible crystalline materials that can be analyzed by the treatment of their HR-(S)TEM images. Examples include, but are not limited to, nanoparticles embedded within different types of matrices, free-standing nanowires, high-angle grain boundaries, multiple stacks of heterostructures of complex oxides and semiconductors and anti-phase domains.

Left: decomposition of cross-sectional HR-STEM-HAADF image of BaTiO3(BTO)-on-SrTiO3 (STO) structure into images of sub-structures of Ba + Sr atoms and Ti atoms. Background: map of out-of-plane strain of Ba+Sr sub-structure with reference to BTO Bravais lattice obtained by AbStrain. Arrows: relative displacement between the sub-structure of Ti atoms and the sub-structure of barycenters of Sr or Ba atoms obtained by Relative displacement


Quantitative mapping of strain and displacement fields over HR-TEM and HR-STEM images of crystals with reference to a virtual lattice
Cherkashin, A. Louiset, A. Chmielewski, D.J. Kim, C. Dubourdieu, S. Schamm-Chardon
Ultramicroscopy 253 (2023) 113778

Nikolay Cherkashin | nikolay.cherkashin[at]cemes.fr


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