Determining Atomic Site-Specific Strain

High-Precision STEM for Imaging and Quantifying Local Strain

  • Fig. 1: (a) Selected images from a HAADF STEM image series of an alumina-supported Pt NP viewed along [110]. (b) The high-precision image produced from the series shown in (a). The support interface is at the bottom of the NP. The blue and red boxes mark the{111} and {311} twin boundaries respectively (adapted from [12]).
  • Fig. 2: (a) Atomic column displacement map showing the direction and magnitude of lattice deformations in the NP shown in figure 1. (b-c) Projected strain maps for the labeled crystallographic planes that are marked by arrows. Red and blue signify compressive and expansive strain, respectively. Bright yellow and light blue signify large values off the color scale. (d-f) Magnified views of the black rectangles in figures a-c (adapted from [12]).
This article presents a method for quantitatively measuring strain in crystalline materials with atomic-scale resolution directly from high-precision scanning transmission electron microscopy images. The method is applied to platinum nanocatalysts to reveal atomic site-specific strain patterns that are predicted to influence catalytic activity. This technique opens up possibilities for imaging and in-depth studies of strain-related phenomena in a wide range of crystalline material systems.
Since the advent of aberration correction, scanning transmission electron microscopy (STEM) has been providing atomic-scale views into the structure and composition of materials that were previously unattainable. Once atoms are clearly resolved, the question becomes how precisely their location can be measured. Currently, for many STEM applications, the information that can be extracted from the data is no longer limited by the resolution of the instrument, but by image precision that is degraded by environmental and experimental factors. These factors include instabilities in the microscope, sample stage, and environment that create distortions within STEM images and reduce the quality and quantifiability of the data. Emerging data science techniques offer the possibility to overcome some of these limitations, enabling higher quality data that is richer in materials information.
Supported metallic nanoparticles (NPs) are critical materials for catalytic applications [1,2]. Presently, NP size, composition and support material are parameters routinely used to tune the catalytic efficiency, but the effect of strain is not completely understood, partly due to the difficulty of measuring local NP strain. Atomic resolution S/TEM can reveal local strain in NPs [3-5], but high precision is also required for a more detailed view of atomic site-specific strain variations.
High-Precision STEM imaging
Here, the strain within a platinum (Pt) NP is measured using a combination of high-precision STEM imaging and strain analysis techniques. The alumina-supported Pt NPs were synthesized by incipient-wetness impregnation [6] and dispersed on ultra-thin carbon films.

The NPs were imaged in side view to resolve the support interface. STEM imaging was performed using a probe-corrected FEI Titan 80-300 instrument at 300 kV. The high angle annular dark field (HAADF) detector was used because the atomic number contrast is well suited for imaging small metallic NPs.

To enhance the precision in locating the Pt NP atom columns in STEM images, we used a post-acquisition non-rigid registration (NRR) and averaging technique that has been shown to enable sub-pm precision [7,8]. As shown in figure 1a, this technique involves acquiring a series of tens to hundreds of consecutive HAADF images of the same NP using short pixel dwell times (2-3 µs) to sample fast instabilities. The beam current was reduced to ~3 pA to mitigate beam-induced sample damage. The pixelwise NRR algorithm corrects the image distortions within each frame that are created by instrumental and environmental instabilities. The distortion-free image series was averaged to enhance the image precision. Figure 1b shows the resulting high-precision side-view image of a Pt NP on an alumina support. This technique has been demonstrated to improve the image precision for single crystals and nanocatalysts, the quality of 3D atomic structure information, and atomic-scale composition information [8-11].
In order to assess image precision and measure strain, the atom column positions were determined by fitting a two-dimensional Gaussian function [8] to each atom column. In each NP grain, a precision area was defined that was at least four atomic layers away from any grain boundary, interface or surface. These precision areas were used as reference areas and assumed to be free of strain. The image precision, defined as the standard deviation of the atomic column separations within the precision area, was measured to be 1-2 pm for the data in figure 1b.
Extracting Atomic Site-Specific Strain Information
In order to visualize the lattice deformations, two methods were used [12]:
1. Projected Displacement Maps
Projected displacement maps (fig. 2a,d) show the displacement of atom columns from their unstrained position [8]. They are calculated by first generating an ideal periodic lattice for each grain that represents the unstrained atom positions. The ideal lattice is created from the average lattice parameters in the precision area, registered to the precision area fit positions, and extended over the whole grain. For shared sites at twin boundaries, multiple displacements are calculated from each grain’s ideal lattice. The displacement of each atomic column fit position from the corresponding ideal lattice position is measured and indicated by a colored arrow in the displacement direction. Projected displacement maps are an intuitive way of visualizing the global NP lattice deformation behavior, but they tend to not reveal the small-scale local lattice deformations because the displacements accumulate away from the precision area.
2. Projected Strain Maps
Projected strain maps (fig. 2b,c,e,f) are a more accurate and quantitative way to assess local lattice deformations between nearest neighbors. They are calculated by comparing each individual nearest-neighbor distance to reference values in different crystallographic directions. Here, strain is defined as the deviation from the average atomic column spacing within the precision area divided by the average spacing. On this data, the technique enables a strain precision of <0.7%. The local strain is indicated as a colored region in the strain maps between each of the two neighboring atomic columns, and separate strain maps are created for each crystallographic direction.
Nanoparticle Strain Behavior
These strain analysis tools reveal pm-scale crystallographic deformations (fig. 2). The displacement maps (fig. 2a,d) reveal large global lattice deformations at a {311} twin boundary and at specific surface and interface sites. The strain maps (fig. 2b,c,e,f) reveal moderate expansive and compressive strain of atoms at the free surfaces. These strains vary in magnitude depending on whether the site is at an edge, corner, or facet. The {111} twin boundaries show ~1% lattice expansion perpendicular but not parallel to the boundaries, while the {311} twin boundary induces much larger strains. The interface shows strong and localized strain that could originate from lattice mismatch and interface roughness. See reference [12] for visualization of strain in other Pt NPs. Finally, we used a theoretical density functional theory based scaling relation kinetic Monte Carlo method [13] to predict how the experimentally observed strain patterns affect the attainable catalytic activity [12].
We developed a high-precision STEM imaging method and strain analysis technique that allow for quantitative atomic site-specific strain measurements with <0.7% strain precision. We have applied this to reveal the complex intrinsic and extrinsic strain behavior in supported Pt nanocatalysts that are present at twin boundaries, surface sites, and the support interface. Combining precise and site-specific strain measurements with kinetic simulations opens up new possibilities for understanding and controlling the relationships between strain and catalytic properties.
The authors acknowledge funding from the Chalmers Competence Centre for Catalysis, the Knut and Alice Wallenberg Foundation, the Swedish Research Council, the Chalmers Excellence Initiative Nano, and the European Network for Electron Microscopy (ESTEEM2). This work was performed in part at the Chalmers Material Analysis Laboratory.

Andrew B. Yankovich1#, Torben Nilsson Pingel1,2#, Mikkel Jørgensen1,2, Henrik Grönbeck1,2, Eva Olsson1,2

1 Department of Physics, Chalmers University of Technology, Gothenburg, Sweden
2 Competence Centre for Catalysis, Chalmers University of Technology, Gothenburg, Sweden
# shared contribution


Dr. Andrew B. Yankovich

Department of Physics
Chalmers University of Technology
Gothenburg, Sweden

Prof. Eva Olsson
Department of Physics
Chalmers University of Technology
Gothenburg, Sweden

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