Multivariate Statistical Analysis of a Multimodal Diffraction and X-ray Spectral Series Data Set

Abstract

Multivariate statistical analysis (MSA) methods comprise a number of powerful techniques for reducing high-dimension data to a more manageable and interpretable lower dimension solution [1][2]. Moving beyond spectroscopic data large image and diffraction series can now be acquired [2,3]. Previously the analysis with MSA of a 183 Gb diffraction series was described [2] and in this work we will describe a deeper look in to the same data set combined with simultaneously acquired X-ray spectral data at each real-space point.Position-resolved diffraction data were acquired on a FEI Company Titan G2 80-200 operated at 200kV and equipped with three-condenser lenses and a probe spherical-aberration corrector. Diffraction patterns were acquired on a PNDetector direct electron camera [2,4]. Figure 1 shows the results of a 256 by 256 real-space pixel convergent-beam diffraction data acquired from the Arltunga meteorite where each pattern consisted of 264 by 264 reciprocal-space pixels with 20 replicate patterns at each point for a data set of 183 Gb. The data were analyzed with Sandia's Automated eXpert Spectral Image Analysis (AXSIA) MSA software [3] such that the unfolded reciprocal-space pixels were the pixels and the realspace pixels were the channels. The specific analysis performed had the result of making the real-space (pixel) domain simple [5].The resulting scree plot of the log-eigenvalues versus sorted eigenvalue index (Fig. 1A) showed a clear break-point at 8 factors and the solution showed both crystallographic phase and orientation information (Figs. 1Band C) but the orientation differences are washed out for the most part. The same data were reanalyzed with a rank-45 corresponding to the second break point in Fig. 1A. The X-ray spectral image data were also analyzed with AXSIA resulting in two factors, Fe and Ni, with the quantified Ni component shown in Fig. 2B. A cover overlay of the uppermost Kamacite (low Ni phase, bcc) factors (Fig. 2C) and at corresponding 6 factors ( Fig. 2D) describe just the uppermost Kamacite region. The angular tilt resolved between the cyan and magenta factors is 0.03º. MSA has efficiently reduced over 65,000 dimensions to 45 while still retaining such sensitivity to small orientation changes. In this case there's enough redundancy in the data to make MSA a worthwhile approach to reducing the dimensionality which ultimately would allow us to understand the chemistry, phases and orientations within the sample more quickly and with greater sensitivity [6].