Automated Atom-By-Atom 3D FIM Reconstruction 265
Figure 8. a: The last six atoms to evaporate from a [2,2,2] layer. The green circle marks the location of the sixth’s atom on this plane that is about to evaporate. b: Remaining atoms and their displacement after the evaporation of the atom marked by the green circle. The arrows mark the displacement direction, all displaced toward the evaporated atom’s original location. Colors represent the different atoms, marked with the same colors in (c). The numbers suggest the extent of the measured displacements relative to the nearest neighbors (NN) distance. c: The positions of all six atoms as tracked from the moment that they remained only six, and until after the evaporation of the first atom. The first atom to evaporate is marked in green, and corresponds to the position of the green circle in (a). The displacement of the rest of the atoms toward the former position of the green atom can be seen.
Implementation of the algorithm for the reconstruction
of alloys can become challenging as no direct unambiguous chemical information is provided by the FIM experiment. In cases where clear intensity regimes can be identified to sepa- rate the different elements in the sample, it is possible to define separate sets of analysis parameters for the optimal reconstruction of all atoms. Automatic detection of out of sequence evaporation events can also be employed to identify different elements. Furthermore, once the data are in the form of a 3Dpoint cloud, other post reconstruction analyses can be applied, such as NN statistics and atomic density measure- ments. Density measurements can potentially be used to detect precipitates that do not present significant contrast difference to the matrix; discriminate between the carbides in Figure 7, for example, and adjacent brightly imaged alloying elements in the matrix; and detect depleted features such as those incorporated at grain boundaries. In cases where no differences in intensity, size, or density exist between the ele- ments, or in cases where imaging conditions are significantly different such that atoms are evaporated without being imaged at all (and cannot be resolved by using a mixture of imaging gases), chemical distinction by the algorithm and reconstruction of all atoms will not be possible.
MEASUREMENT OF SUBANGSTROM DISPLACEMENTS
As field conditions change from image to image, lateral dis- placements in recorded atomic coordinates are observed. These displacements are mentioned above with regards to the reconstruction process, as they necessitate a tracking algorithm to identify the same atom across different images. By tracking the recorded positions of atoms across all images in which they appear, it is possible to quantify the series of very subtle displacements of each atom within the images. Measurements of atomic movements in FIM have previously
been utilized to great effect to track the successive positions of atoms during surface diffusion before evaporation (Wang & Ehrlich, 1989; Kellogg, 1991; Kellogg et al., 1991; Vurpillot et al., 2009). However, the displacements measured in this study represent subtler effects. A prominent example to such displacements is seen in
Figure 8. The last remaining six atoms on one of the [2,2,2] planes are shown in a with their peak intensities tracked across a series FIM images (Fig. 8c), from the point where
only those six atoms remained on the surface and until the first one of these is evaporated (Fig. 8b). The position from which this single atom was observed to evaporate is marked by the green circle in Figures 8a and 8b, whereas its imaged position is tracked across the series of images and is pre- sented in green in Figure 8c. Upon evaporation of this atom, the remaining atoms are imaged in coordinates that are displaced toward its former position, with relative displace- ment magnitude correlating to their proximity to the evaporated atom. The displacements sizes in Figure 8b are expressed in units relative to the average NN’s distance measured across all images before evaporation, with the largest displacements estimated at 0.05nm (estimated by calibration to the theoretical NN’s distance on the [2,2,2] plane). As the imaged positions of the atoms are constantly changing, even before evaporation, the average displacement of the five remaining atoms was calculated before the eva- poration of the green atom across the same range of images. It was found to be 1.8% of the NN’s distance, and is con- sidered as the error estimation for the post-evaporation displacements shown in Figure 8b. The precise origin of these displacements remains
un-resolved at this time. One possible explanation is that these are in fact displacements in “imaged” coordinates originating from artifacts due to how the imaging gas atoms arrange themselves on the surface. Imaging gas atoms adsorbed on atomic sites on the surface will have induced dipole moments, repelling one another, that could cause the adsorbed gas atoms
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