Comparison of APT Cluster Analysis Methods 367 There are several known limitations of APT, including
concerns that the reconstruction algorithms used are too simplistic. For instance, for the analysis of RPV steels, one major concern is that trajectory aberrations, due to differ- ence of the evaporation field between the solute clusters and the surrounding matrix, could bias their measured chemical composition and structure. Other concerns, include (i) the fact that APT cannot directly detect the presence of vacancies, (ii) the spatial resolution is imperfect, (iii) the detection efficiency is imperfect, and (iv) the very small analyzed volume may not be fully representative of a mate- rial as complex as a steel (Miller et al., 1996; Miller, 2000; Gault et al., 2012). Demonstrating that cluster detection algorithms accu-
rately characterize the multitude of microstructural features observed in RPV steels is also challenging. The very small size of these solute clusters and their apparently dilute nature makes their identification, inside three-dimensional (3D) data sets containing tens or hundreds of millions of atoms, very challenging. The very small size of the features means that a relatively high fraction of the associated atoms are interface atoms, and thus their measured sizes, number density, and compositions can also strongly depend on the algorithms used to detect them. Currently, there is no agreement on what constitutes the most “appropriate” ana- lysis methodology (Marquis & Hyde, 2010). Furthermore, all methods require the use of user-defined parameters and their selection is not trivial. Methods based on the maximum separation method (MSM) (Hyde & English, 2001; Heinrich et al., 2003; Kolli & Seidman, 2007; Morley et al., 2009; Styman et al., 2013) are most widely used, but there are many variants and options at each stage of the process, including defining the chemical identities of core atoms, selecting an appropriate maximum separation distance, identifying which noncore atoms also belong to each cluster and whe- ther to apply an erosion step to minimize interface effects. Other methods, based on concentration threshold criteria, have also been developed and used (Lefebvre et al., 2016) by several groups. As for MSMs, the definition of the chemical identities and the selection of appropriate parameters is an important step to get quantitative and reliable results. In this work, simulations have been used to create
representative APT data sets with known microstructures. The microstructural data have been degraded to simulate the
limitations of APT and the resulting data have been analyzed blind using two analysis methodologies. The results have been compared with each other and the strengths and weaknesses of the methods assessed. This builds on previous work by Hyde et al. (2011) by using multiple analyses methods, and adding the effect of local magnification.
METHODOLOGY
Simulated Microstructures In all, six simulated microstructures, each 60×60×60nm3, of a simple ferritic alloy were created (bcc lattice with a lattice parameter of 0.28 nm). The simulated microstructures were populated with clusters with a number density of between 5 and 10× 1023m−3. Three different cluster sizes were cho- sen (approximate radii of ~0.5, 1.0, and 1.5nm) with each cluster having a solute content of either ~50 or 100%. Thus each simulatedmicrostructure contained multiple clusters of different sizes and compositions (~18 of each radius and composition combination). A bulk alloy concentration of ~1% was chosen. The simulated microstructures also took into account experimental artifacts. In three data files, the imperfect detection efficiency of the CAMECA LEAP 3000 or 4000HR was simulated by randomly removing 60% of the atoms. In four of the simulations, uncertainties in the atom positions were modeled by adding a Gaussian scatter to the coordinates (2σ = 0.5 or 1 nm for the X and Y coordinates, and 2σ = 0.1nmfor the Z coordinates). The resulting matrix of simulated microstructures is summarized in Table 1. In addition, three of the simulations were further degraded by modeling the compression of atoms in reconstructed APT data associated with the local magnification effect (only simulation 6 was analyzed here, yielding a total of seven datasets for analysis). The compression algorithm used is detailed in the next section. The combinations were designed to enable the influence of experimental artifacts on the detectability and characterization of clusters to be assessed. A further nine simulated microstructures were
generated for an alloy with a bulk solute concentration of 4% and then a further 12 simulated microstructures were created to model core shell cluster structures. The analysis of these additional simulations will be the subject of a future paper.
Table 1. Simulated Microstructures and Simulations of Experimental Artifacts. Cluster
Simulation no.
1 2 3 4 5 6
Radius (nm) 0.5, 1.0, 1.5
0.5, 1.0, 1.5 0.5, 1.0, 1.5 0.5, 1.0, 1.5 0.5, 1.0, 1.5 0.5, 1.0, 1.5
Cluster Solute Concentrations (%)
~50 and 100 ~50 and 100 ~50 and 100 ~50 and 100 ~50 and 100 ~50 and 100
Bulk Solute Concentration (%)
1 1 1 1 1 1
Detection Efficiency
100 40
100 40
100 40
Lateral Scatter (Width of Gaussian Applied to X and Y Coordinates) (nm)
NAa NA 0.5
0.5a 1.0
1.0a aThese simulated microstructures were further degraded to simulate the increased density of atoms associated with local magnification effects.
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