AVS 60th International Symposium and Exhibition
    Atom Probe Tomography Focus Topic Tuesday Sessions
       Session AP+AS+SS-TuA

Paper AP+AS+SS-TuA1
Multivariate Analysis of Atom Probe Tomography Data: Methods to Simplify Factor Interpretation

Tuesday, October 29, 2013, 2:00 pm, Room 203 A

Session: Microstructural and Interface Analysis of Metals Subjected to Various Conditions
Presenter: M.R. Keenan, Consultant
Authors: M.R. Keenan, Consultant
V. Smentkowski, General Electric Global Research Center
Correspondent: Click to Email
Multivariate statistical analysis has been used successfully for several years to analyze spectral images acquired in three spatial dimensions. Examples include energy dispersive x-ray images obtained from serially sectioned samples, and depth profiles in ToF-SIMS. More recently, multivariate methods have begun to be applied to atom probe tomography (APT) data. The analysis of APT data, however, poses some unique challenges, and it is important for the APT community to understand the principles that underpin the multivariate approach in order to maximize its effectiveness. The basic assumption made during multivariate analysis is that the composition of a sample at a particular location can be described as a linear combination of a limited number of “pure components”, with each component having a characteristic spectral signature. The job of multivariate analysis, then, is to discover the number components, extract spectral information suitable for identifying them, and determine the spatial distributions of their abundances. The primary tool of multivariate analysis is the Singular Value Decomposition (SVD), or the closely related Principal Component Analysis (PCA). These techniques distill the chemically relevant information in high-dimensional raw data sets into a small number of factors or components. These components, however, are abstract and not easily interpreted. For instance, typical components may contain negative spectral features and abundances, which are not physically plausible. In order to find a more straightforward representation of the components, they can be post-processed to impose certain constraints or preferences on the factor model. In this talk, a chemically simple sample will be used to illustrate some of these multivariate concepts in geometric terms. In particular, factor rotation procedures, such as the Varimax rotation, will be shown suitable for obtaining factor models that are in some sense simple, either spectrally or spatially, and the natural duality of the spectral and spatial domains will be highlighted. Multivariate Curve Resolution (MCR) will also be considered. MCR imposes constraints, often non-negativity, on the model components. MCR is problematic, however, in the presence of high noise levels typical of APT data, and some approaches for improving the fidelity of MCR models will be presented. APT is capable of producing quantitative results. As will be shown, achieving them with multivariate analysis requires tailoring the methods to the specifics of APT and paying careful attention to the details.