408 Microsc. Microanal. 27 (Suppl 1), 2021
doi:10.1017/S1431927621001987 © Microscopy Society of America 2021
A Machine Learning Approach to Cluster Characterization for Atom Probe
Tomography
Roland Bennett
1
, Andrew Proudian
2
and Jeramy Zimmerman
3
1
Colorado School of Mines, GOLDEN, Colorado, United States,
2
Colorado School of Mines, Physics,
Golden, Colorado, United States,
3
Colorado School of Mines, Physics, GOLDEN, Colorado, United
States
The clustering properties of solute species drive performance in materials ranging from metal alloys to
organic light emitting diodes [1][2][3]. In atom probe tomography (APT) people have typically used
cluster detection algorithms, such as the maximum separation algorithm (MSA), to detect and then
characterize individual clusters. MSA, in particular, has the drawbacks of requiring user input parameters
and not being sensitive to low density clustering [4][5]. While other cluster detection techniques have
been developed, they often share similar limitations requiring high contrast between clusters and
background [6][7][8]. In this work, we advance a machine learning model implemented using rapt [9],
which we have developed in the statistical computing language R. Our model is based on spatial statistics
summary functions that characterize global clustering properties and behavior in APT data sets, providing
an alternative characterization approach to cluster detection analysis. In previous work, we utilized a
Bayesian regularized neural network (BRNN) machine learning model, trained on features derived from
Ripley’s K function to measure four metrics that characterize clusters: the cluster dopant density (ρ1), the
background dopant density (ρ1), the mean cluster radius (r), and the radius blur ( δr) (i.e. the standard
deviation of the cluster radius divided by the mean cluster radius) [5]. Here, we improve upon our
previous work by incorporating features derived from the first-order summary functions G, G-cross, and
F into our models, resulting in more accurate cluster analysis.
These first order summary functions enable ρ1 and ρ2 to be predictions with very low error: in simulated
training and testing data sets, 90% of predictions for both were within 3.5% of the actual value, as shown
for ρ1 in Figure 1 (an improvement from 18% for ρ1 in our previous work). While the percent error
of ρ2 was not measured in our previous work, the value of absolute error of the 90
th
error percentile was
reduced by 94%. These first order summary functions enable decoupling of r from δr, enabling the
prediction of the average cluster radius itself, with 90% of predictions falling within 15% of the actual
value (in comparison to 18% for predictions based solely on the K-function). The predicted value vs true
value for ρ1 is shown in Figure 2.
The simulated data sets used in this work (clustered point patterns of random clustering metrics, 10,000
for training and 2,500 for testing) were created on a single 28-core high-performance computing node and
required only 90 minutes to generate and 15 minutes to train and create predictions, meaning it is also
feasible on common desktop computers. A larger model using ten times as much data was also examined,
but only minor improvements were seen, therefore not justifying the greater computational costs.
In this talk, we discuss development and results of this algorithm, its applications to experimental data,
and the implications of global clustering behavior. We have made example analyses available on our
website, enabling other users of the APT community to easily adopt this method of cluster analysis.
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