Hostname: page-component-78c5997874-8bhkd Total loading time: 0 Render date: 2024-11-04T19:34:45.274Z Has data issue: false hasContentIssue false
  • English
  • Français

Refining Spatial Distribution Maps for Atom Probe Tomography via Data Dimensionality Reduction Methods

Published online by Cambridge University Press:  09 October 2012

Santosh K. Suram  and
Krishna Rajan
Santosh K. Suram
Affiliation:
Department of Materials Science and Engineering, Iowa State University, Ames, IA 50011, USA
Krishna Rajan*
Affiliation:
Department of Materials Science and Engineering, Iowa State University, Ames, IA 50011, USA
*
*Corresponding author. Email: [email protected]
Get access

Abstract

A mathematical framework based on singular value decomposition is used to analyze the covariance among interatomic frequency distributions in spatial distribution maps (SDMs). Using this approach, singular vectors that capture the covariance within the SDM data are obtained. The structurally relevant singular vectors (SRSVs) are identified. Using the SRSVs, we extract information from z-SDMs that not only captures the offset between the atomic planes but also captures the covariance in the atomic structure among the neighborhood atomic planes. These refined z-SDMs classify the Δ(Δz) slices in the SDMs into structurally relevant information, noise, and aberrations. The SRSVs are used to construct refined xy-SDMs that provide enhanced structural information for three-dimensional atom probe tomography.

Keywords

atom probe tomography (APT)crystal structuresingular value decomposition (SVD)spatial distribution maps (SDM)singular vectorsrefined z-SDM and refined xy-SDM
Type
Techniques and Equipment Development
Information
Microscopy and Microanalysis , Volume 18 , Issue 5 , October 2012 , pp. 941 - 952
Copyright
Copyright © Microscopy Society of America 2012

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Bas, P., Bostel, A., Deconihout, B. & Blavette, D. (1995). A general protocol for the reconstruction of 3D atom-probe data. Appl Surf Sci 87–88, 298–304.Google Scholar
Boll, T., Al-Kassab, T., Yuan, Y. & Liu, Z.G. (2007). Investigation of the site occupation of atoms in pure and doped TiAl/Ti3Al intermetallic. Ultramicroscopy 107(9), 796–801.Google Scholar
Camus, P.P., Larson, D.J. & Kelly, T.F. (1995). A method for reconstructing and locating atoms on the crystal lattice in three-dimensional atom probe data. Appl Surf Sci 87–88, 305–310.CrossRefGoogle Scholar
Cerezo, A., Abraham, M., Lane, H., Larson, D.J., Thuvander, M., Seto, K., Warren, P.J. & Smith, G.D.W. (1999). Three dimensional atomic scale analysis of interfaces. Electron Microscopy and Analysis 1999. Instrum Phys Conf Ser 161, 29–34.Google Scholar
Duponchel, L., Elmi-Rayaleh, W., Ruckebusch, C. & Huvenne, J.P. (2003). Multivariate curve resolution methods in imaging spectroscopy: Influence of extraction methods and instrumental perturbations. J Chem Inf Comput Sci 43(6), 2057–2067.Google Scholar
Gault, B., Haley, D., de Geuser, F., Moody, M., Marquis, E., Larson, D. & Geiser, B. (2010). Advances in the reconstruction of atom probe tomography data. Ultramicroscopy 111(6), 448–457.Google Scholar
Geiser, B., Larson, D., Oltman, E., Gerstl, S., Reinhard, D., Kelly, T. & Prosa, T. (2009). Wide-field-of-view atom probe reconstruction. Microsc Microanal 15(S2), 292–293.Google Scholar
Geiser, B.P., Kelly, T.F., Larson, D.J., Schneir, J. & Roberts, J.P. (2007). Spatial distribution maps for atom probe tomography. Microsc Microanal 13(6), 437–447.CrossRefGoogle ScholarPubMed
Golub, G.H. & Loan, C.F.V. (1996). Matrix Computations. Baltimore, MD: The Johns Hopkins University Press.Google Scholar
Kelly, T.F., Gribb, T.T., Olson, J.D., Martens, R.L., Shepard, J.D., Wiener, S.A., Kunicki, T.C., Ulfig, R.M., Lenz, D.R., Strennen, E.M., Oltman, E., Bunton, J.H. & Strait, D.R. (2004). First data from a commercial local electrode atom probe (LEAP). Microsc Microanal 10(3), 373–383.CrossRefGoogle ScholarPubMed
Miller, M.K. (1987). The effects of local magnification and trajectory aberrations in atom probe analysis. J Phys Colloq 48(C-6), 565–570.Google Scholar
Miller, M.K. (2000). Atom Probe Tomography: Analysis at the Atomic Level. New York: Kluwer Academic/Plenum Publishers.CrossRefGoogle Scholar
Miller, M.K. & Hetherington, M.G. (1991). Local magnification effects in the atom probe. Surf Sci 246(1-3), 442–449.Google Scholar
Miranda, A.A., Le Borgne, Y.A. & Bontempi, G. (2008). New routes from minimal approximation error to principal components. Neural Process Lett 27(3), 197–207.Google Scholar
Moody, M.P., Gault, B., Stephenson, L.T., Haley, D. & Ringer, S.P. (2009). Qualification of the tomographic reconstruction in atom probe by advanced spatial distribution map techniques. Ultramicroscopy 109(7), 815–824.Google Scholar
Philippe, T., Gruber, M., Vurpillot, F. & Blavette, D. (2010). Clustering and local magnification effects in atom probe tomography: A statistical approach. Microsc Microanal 16(5), 643–648.Google Scholar
Suram, S.K. & Rajan, K. (2009). Informatics for quantitative analysis of atom probe tomography images. MRS Proceedings 1231, 1231-NN03-14 Google Scholar
Tsong, T. & Kellogg, G. (1975). Direct observation of the directional walk of single adatoms and the adatom polarizability. Phys Rev B-Condens Matter Mater Phys 12(4), 1343–1353.Google Scholar
Vurpillot, F., Bostel, A. & Blavette, D. (1999). The shape of field emitters and the ion trajectories in three-dimensional atom probes. J Microsc-Oxford 196, 332–336.CrossRefGoogle ScholarPubMed
Vurpillot, F., Bostel, A. & Blavette, D. (2000). Trajectory overlaps and local magnification in three-dimensional atom probe. Appl Phys Lett 76(21), 3127–3129.Google Scholar
Vurpillot, F., Da Costa, G., Menand, A. & Blavette, D. (2001). Structural analyses in three-dimensional atom probe: A Fourier transform approach. J Microsc-Oxford 203(3), 295–302.Google Scholar
Vurpillot, F., Renaud, L. & Blavette, D. (2003). A new step towards the lattice reconstruction in 3DAP. Ultramicroscopy 95(1-4), 223–229.Google Scholar
Waugh, A., Boyes, E. & Southon, M. (1976). Investigations of field evaporation with a field-desorption microscope. Surf Sci 61(1), 109–142.Google Scholar