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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

REFERENCES

Barrett, C.S. & Massalski, T.B. (1980). Structure of Metals. Oxford, UK: Pergamon Press.Google Scholar
Davis, T.A. (2006). Direct Methods for Sparse Linear Systems. Philadelphia, PA: SIAM.CrossRefGoogle Scholar
Gault, B., Moody, M.P., De Geuser, F., La Fontaine, A., Stephenson, L.T., Haley, D. & Ringer, S.P. (2010). Spatial resolution in atom probe tomography. Microsc Microanal 16(1), 99–110.Google Scholar
Golub, G.H. & Van Loan, C.F. (1996). Matrix Computations. Baltimore, MD: The Johns Hopkins University Press.Google Scholar
Jollife, I.T. (2002). Principal Component Analysis. New York: Springer-Verlag.Google Scholar
Keenan, M.R. (2007). Multivariate analysis of spectral images composed of count data. In Techniques and Applications of Hyperspectral Image Analysis, Grahn, H.F. & Geladi, P. (Eds.), pp. 89–126. Chichester, UK: John Wiley & Sons, Ltd.CrossRefGoogle Scholar
Keenan, M.R. (2009). Exploiting spatial-domain simplicity in spectral image analysis. Surf Interface Anal 41, 79–87.Google Scholar
Keenan, M.R. & Kotula, P.G. (2004). Accounting for Poisson noise in the multivariate analysis of ToF-SIMS spectrum images. Surf Interface Anal 36(3), 203–212.CrossRefGoogle Scholar
Keenan, M.R., Smentkowski, V.S., Ulfig, R.M., Oltman, E., Larson, D.J. & Kelly, T.F. (2010). Multivariate statistical analysis of atom probe tomography data. Microsc Microanal 16(S2), 270–271.Google Scholar
Kelly, T.F. & Miller, M.K. (2007). Atom probe tomography. Rev Sci Instrum 78, 031101.Google Scholar
Kotula, P.G., Keenan, M.R. & Michael, J.R. (2003). Automated analysis of SEM X-ray spectral images: A powerful new microanalysis tool. Microsc Microanal 9(1), 1–17.Google Scholar
Kotula, P.G., Keenan, M.R. & Michael, J.R. (2006). Tomographic spectral imaging with multivariate statistical analysis: Comprehensive 3D microanalysis. Microsc Microanal 12, 36–48.CrossRefGoogle Scholar
Larsen, R.J. & Marx, M.L. (1986). An Introduction to Mathematical Statistics and Its Applications. Englewood Cliffs, NJ: Prentice-Hall.Google Scholar
Malinowski, E.R. (1987). Theory of the distribution of error eigenvalues resulting from principal component analysis with application to spectroscopic data. J Chemometrics 1, 33–40.CrossRefGoogle Scholar
Parish, C.M., Capdevila, C. & Miller, M.K. (2010). Applying multivariate statistical analysis to atom probe tomography. Microsc Microanal 16(S2), 1858–1859.CrossRefGoogle Scholar
Parish, C.M. & Miller, M.K. (2010). Multivariate statistical analysis of atom probe tomography data. Ultramicroscopy 110, 1362–1373.CrossRefGoogle Scholar
Rosman, K.J.R. & Taylor, P.D.P. (1998). Isotopic compositions of the elements 1997. Pure Appl Chem 70(1), 217–235.Google Scholar
Smentkowski, V.S., Ostrowski, S.G., Braunstein, E., Keenan, M.R., Ohlhausen, J.A. & Kotula, P.G. (2007). Multivariate statistical analysis of three-spatial-dimension TOF-SIMS raw data sets. Anal Chem 79(20), 7719–7726.Google Scholar
Smentkowski, V.S., Ostrowski, S.G. & Keenan, M.R. (2009). A comparison of multivariate statistical analysis protocols for ToF-SIMS spectral images. Surf Interface Anal 41, 88–96.Google Scholar
Wu, W., Massart, D.L. & de Jong, S. (1997). The kernel PCA algorithms for wide data. I. Theory and algorithms. Chemometrics Intell Lab Syst 36(2), 165–172.Google Scholar