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Atomic-Scale Phase Composition through Multivariate Statistical Analysis of Atom Probe Tomography Data

Published online by Cambridge University Press:  23 May 2011

Michael R. Keenan ,
Vincent S. Smentkowski ,
Robert M. Ulfig ,
Edward Oltman ,
David J. Larson  and
Thomas F. Kelly
Michael R. Keenan*
Affiliation:
8346 Roney Road, Wolcott, NY 14590, USA
Vincent S. Smentkowski
Affiliation:
General Electric Global Research Center, Niskayuna, NY 12309, USA
Robert M. Ulfig
Affiliation:
CAMECA Instruments, Inc., 5500 Nobel Drive, Madison, WI 53711, USA
Edward Oltman
Affiliation:
CAMECA Instruments, Inc., 5500 Nobel Drive, Madison, WI 53711, USA
David J. Larson
Affiliation:
CAMECA Instruments, Inc., 5500 Nobel Drive, Madison, WI 53711, USA
Thomas F. Kelly
Affiliation:
CAMECA Instruments, Inc., 5500 Nobel Drive, Madison, WI 53711, USA
*
Corresponding author. E-mail: [email protected]
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Abstract

We demonstrate for the first time that multivariate statistical analysis techniques can be applied to atom probe tomography data to estimate the chemical composition of a sample at the full spatial resolution of the atom probe in three dimensions. Whereas the raw atom probe data provide the specific identity of an atom at a precise location, the multivariate results can be interpreted in terms of the probabilities that an atom representing a particular chemical phase is situated there. When aggregated to the size scale of a single atom (∼0.2 nm), atom probe spectral-image datasets are huge and extremely sparse. In fact, the average spectrum will have somewhat less than one total count per spectrum due to imperfect detection efficiency. These conditions, under which the variance in the data is completely dominated by counting noise, test the limits of multivariate analysis, and an extensive discussion of how to extract the chemical information is presented. Efficient numerical approaches to performing principal component analysis (PCA) on these datasets, which may number hundreds of millions of individual spectra, are put forward, and it is shown that PCA can be computed in a few seconds on a typical laptop computer.

Keywords

atom probe tomography (APT)multivariate statistical analysis (MVSA)PCA
Type
Materials Applications
Information
Microscopy and Microanalysis , Volume 17 , Issue 3 , June 2011 , pp. 418 - 430
Copyright
Copyright © Microscopy Society of America 2011

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References

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