Comparison of APT Cluster Analysis Methods 373


Table 3. Summary of Observations. MSM


Perfect data


Imperfect detection efficiency


Perfect detection but degraded lateral resolution


Imperfect detection efficiency and degraded lateral resolution


All clusters identified Solute content of dilute smallest clusters overestimated


All clusters identified Solute content of dilute smallest clusters overestimated


All, or nearly all, clusters identified Lateral scatter increases apparent cluster size Solute content of concentrated clusters underestimated


Significant fraction of smallest clusters not identified Increasingly difficult to determine cluster sizes accurately


The observed compositions of dilute clusters are reasonable but the compositions of the more concentrated clusters are underestimated


MSM, maximum separation method; IPM, Isoposition method.


imperfect detection efficiency and degradation of lateral resolution are simulated. However, even under these condi- tions, both methods worked extremely well for clusters with radii ≳1nm. Accurate characterization of the smallest clusters (0.5nm radius) proved more challenging. The MSM method failed to separate a significant number of these clusters from random solute fluctuations. The IPM proved to be more effective at identifying the presence of these clusters, but it was not possible to distinguish between the concentrated (100% solute) clusters and the dilute (containing 50% solute). Several reasons can explain these observations. First, in


Analysis becomes more challenging when both the


terms of statistics, the smallest clusters contain so few solute atoms that their definition is strongly influenced by surface effects. So, strong difference in composition can result from the interface definition. Including an erosion procedure, can strongly modify the results in this case. Second, as it is shown in Figure 9, the lateral scatter (without considering any trajectory aberration due to difference in field evaporation) can result in the introduction of a significant level of matrix atoms in the cluster core. So, a concentrated small solute cluster


appears to be significantly diluted due to the lateral scatter. Thus, both MSM and IPM will detect a high level of Fe in the smallest clusters. In real APT data, local magnification will result in an


increase in the density of atoms in the clusters. Counter- intuitively, this can actually aid identification of solute clus- ters with the MSM as it is predicated on finding regions in which the solute atoms are more closely spaced. On the contrary, local magnification has no influence on the cluster detection using IPM. This is not surprising as the IPM is based on concentration threshold and not on distance between atoms. As explained previously, the algorithm applied to reproduce local magnification results in a change in the local atom density, but not in local concentration as trajectory overlaps were not simulated. The limitations reported here in the methods of analysis of


APTdata in terms of correct detection (or not) of clusters below a certain size, over- or underestimation of size and concentra- tion of solutes, etc. should be used also to provide atomistic modelers with indications, and possibly protocols, about how to analyze the results of simulations for a fair comparison.


IPM All clusters identified and correctly characterized


All clusters identified Solute content of dilute smallest clusters overestimated


All clusters identified Good estimates of cluster sizes and solute content excepted for pure small (0.5nm) clusters (overestimation of Fe content)


A small fraction of smallest clusters not identified. More scatter observed on cluster sizes, but the mean cluster sizes are approximately correct


The observed compositions of dilute clusters are reasonable but the compositions of the more concentrated clusters are underestimated


Not possible to distinguish dilute and concentrated smallest clusters in terms of composition


Figure 9. Effect of lateral scatter on the definition of a solute cluster.


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