264 Michal Dagan et al.


Figure 7. Atom-by-atom reconstruction of carbides in a M50 bearing steel. a: All atoms above a threshold of 40% maximal intensity are identified. b: Reconstructed coordinates in image pixels. Red atoms are atoms imaged above an intensity threshold set at 95%—comprise mostly the carbides in the sample. Yellow atoms are low-intensity atoms, cor- responding to matrix atoms. c: High-intensity and high-density pixels from the reconstruction of 1000 FIM images, calibrated to real space coordinates.


sets that do not possess all of these definitions of high-quality data. By applying some straight forward adjustments to the algorithm, larger areas of the field of view can be analyzed, as well as a variety of cases exhibiting different imaging con- trasts and evaporation characteristics. For example, the approach can be adapted such that a specific microstructure in the data is reconstructed “atom-by-atom” with this method, as demonstrated in Figure 7 for secondary carbides in a M50 bearing steel. In this case, the entire FIM field of view has been incorporated into the analysis, and scanned for atomic coordinates. As the matrix exhibits lower contrast in comparison with the carbides, the threshold for atom identification was chosen so as to include most of the matrix atoms. As the carbides are imaged much brighter than the selected threshold, the “blinking” effects described above are less of an issue for the carbide reconstruction, and any “break” in imaging longer than an experimentally deter- mined number of images is defined to indicate an evapora- tion event (three images in this case). As the reconstruction now extends over the entire field


requires high-quality data defined by a high level of control in the evaporation process, atomic resolution and a “layer- by-layer” evaporation. It is thus equally applicable to other poles exhibiting such behavior. Poles that do not exhibit atomic resolution, such as the central [1,1,0] pole of the analyzed tungsten sample, can be analyzed in the same way, however, they will not provide a final reconstruction that consists of 100% of the atoms in the analyzed volume, as this information is not resolved by the FIM experiment. The algorithm can also be implemented on FIM data


of view, the integrated intensity plots cannot be employed across this entire area in a meaningful way. Hence, the depth coordinate for each atom in this case is assigned according to the time at which it is first detected. Alternatively, it could be defined by its evaporation time, similar to the way in which the depth coordinate is assigned in an APT reconstruction. By choosing the relative detection time to define the depth coordinate, retention of these carbides on the surface, which is known to bias their reconstruction in APT data (Marceau et al., 2013), is accounted for. Estimation of the tip radius can


be used to calibrate x and y pixel coordinates to real space coordinates, and integrated intensity plots measured from around prominent crystallographic poles of the matrix are used to approximate the depths evaporated locally. Instead of assuming a constant depth increment between successive images across the whole data set, the use of intensity plots enables nonuniform evaporation rates to be accounted for in this data set too. The depth increment between successive images is set as constant only across images from the same intensity interval, and depth calibration is done relative to the evaporation time of the current plane, rather than the whole data set. Figure 7b displays the reconstructed atoms from 500 FIM images (the carbides in red are distinguished from the matrix in yellow). Figure 7c shows the carbides extracted by intensity and density filters, from the recon- struction of 1000 such FIM images, calibrated to real space coordinates. The curvature of the tip and projection effects are not taken into account in the current reconstruction, and should be incorporated into the final stage of the algorithm in the future, for cases where large portions of the tip are analyzed (Vurpillot et al., 2007), as opposed to smaller ana- lyses around single crystallographic poles. The example in Figure 7 demonstrates the application of


the algorithm to a system comprising of a more complex microstructure than the tungsten example, larger recon- structed features, and alloying elements that exhibit different imaging contrast. The resultant 3D reconstruction of the carbides is not as accurate as in the case of the [2,2,2] tung- sten pole, as the depth coordinate is assigned by detection time and not a discrete crystallographic plane number. However, the approach still enables an atomistic 3D analysis of the carbides, and the underlying matrix allows direct calibration of the carbides size and relative depth in com- parison with atom probe data. Reconstruction of the matrix will yield less accurate results than the carbides in this case, as the threshold for detection of atoms and evaporation events was optimized for the analysis of the carbides. Improved imaging conditions to better capture both carbides and matrix could be achieved by using a mixture of imaging gases (Akré et al., 2009).


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