Objective tools for characterizing materials at the atomic level are often difficult to develop because of the size or structure of the data. Atom probe tomography (APT) is a measurement tool that maps the location and type of atoms in materials in three-dimensions (3D), producing data sets with potentially billions of observations. In this work, we present a set of spatial statistics methods developed to test the null hypotheses of no global spatial association; no local spatial association; and no local spatial cross-correlation and apply these for the first time to APT data. The empirical and modeled covariogram and Moran's I can be used to study the global structure of a spatially referenced atomic element. The local indicator of spatial association (LISA) identifies volumes where high levels of values (hot spots) or low levels of values (cold spots) of elemental clustering exist. The local indicator of spatial cross-correlation (LISC) reports where simultaneously high levels or low levels of two atomic elements occur. For each test statistic at each location, an associated p -value is produced that can be used to weigh the evidence in favor of spatial clustering. The size of APT data sets presents some challenges, so the effect of weight functions and neighborhood selection on the computation and significance of the test statistics are discussed, and the issue of multiple statistical testing is also considered. These methods are illustrated using an APT data set with atomic percentages reported in voxels binned to 1 nm3.
|Original language||English (US)|
|Journal||Statistical Analysis and Data Mining: The ASA Data Science Journal|
|State||Published - Jun 8 2020|
Bibliographical noteKAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): OSR-2015-CRG4-2582
Acknowledgements: The authors wish to thank an Associate Editor and threeanonymous reviewers whose valuable comments havegreatly improved this manuscript. Y. Y. and A. S. H. weresupported by the King Abdullah University of Science andTechnology (KAUST) Office of Sponsored Research (OSR)under Award No: OSR-2015-CRG4-2582
This publication acknowledges KAUST support, but has no KAUST affiliated authors.