Michael R. Keenan

Automated analysis of SEM X-ray spectral images: a powerful new microanalysis tool.

Spectral imaging in the scanning electron microscope (SEM) equipped with an energy-dispersive X-ray (EDX) analyzer has the potential to be a powerful tool for chemical phase identification, but the large data sets have, in the past, proved too large to efficiently analyze. In the present work, we describe the application of a new automated, unbiased, multivariate statistical analysis technique to very large X-ray spectral image data sets. The method, based in part on principal components analysis, returns physically accurate (all positive) component spectra and images in a few minutes on a standard personal computer. The efficacy of the technique for microanalysis is illustrated by the analysis of complex multi-phase materials, particulates, a diffusion couple, and a single-pixel-detection problem.

Tomographic Spectral Imaging with Multivariate Statistical Analysis: Comprehensive 3D Microanalysis.

A comprehensive three-dimensional (3D) microanalysis procedure using a combined scanning electron microscope (SEM)/focused ion beam (FIB) system equipped with an energy-dispersive X-ray spectrometer (EDS) has been developed. The FIB system was used first to prepare a site-specific region for X-ray microanalysis followed by the acquisition of an electron-beam generated X-ray spectral image. A small section of material was then removed by the FIB, followed by the acquisition of another X-ray spectral image. This serial sectioning procedure was repeated 10-12 times to sample a volume of material. The series of two-spatial-dimension spectral images were then concatenated into a single data set consisting of a series of volume elements or voxels each with an entire X-ray spectrum. This four-dimensional (three real space and one spectral dimension) spectral image was then comprehensively analyzed with Sandias automated X-ray spectral image analysis software. This technique was applied to a simple Cu-Ag eutectic and a more complicated localized corrosion study where the powerful site-specific comprehensive analysis capability of tomographic spectral imaging (TSI) combined with multivariate statistical analysis is demonstrated.

Application of multivariate statistical analysis to STEM X-ray spectral images: interfacial analysis in microelectronics.

Multivariate statistical analysis methods have been applied to scanning transmission electron microscopy (STEM) energy-dispersive X-ray spectral images. The particular application of the multivariate curve resolution (MCR) technique provides a high spectral contrast view of the raw spectral image. The power of this approach is demonstrated with a microelectronics failure analysis. Specifically, an unexpected component describing a chemical contaminant was found, as well as a component consistent with a foil thickness change associated with the focused ion beam specimen preparation process. The MCR solution is compared with a conventional analysis of the same spectral image data set.

Multi-Window Classical Least Squares Multivariate Calibration Methods for Quantitative ICP-AES Analyses

The advent of inductively coupled plasma atomic emission spectrometers (ICP-AES) equipped with charge-coupled device (CCD) detector arrays allows the application of multivariate calibration methods to the quantitative analysis of spectral data. We have applied classical least-squares (CLS) methods to the analysis of a variety of samples containing up to 12 elements plus an internal standard. The elements included in the calibration models were Ag, Al, As, Au, Cd, Cr, Cu, Fe, Ni, Pb, Pd, and Se. By performing the CLS analysis separately in each of 46 spectral windows and by pooling the CLS concentration results for each element in all windows in a statistically efficient manner, we have been able to significantly improve the accuracy and precision of the ICP-AES analyses relative to the univariate and single-window multivariate methods supplied with the spectrometer. This new multi-window CLS (MWCLS) approach simplifies the analyses by providing a single concentration determination for each element from all spectral windows. Thus, the analyst does not have to perform the tedious task of reviewing the results from each window in an attempt to decide the correct value among discrepant analyses in one or more windows for each element. Furthermore, it is not necessary to construct a spectral correction model for each window prior to calibration and analysis. When one or more interfering elements were present, the new MWCLS method was able to reduce prediction errors compared to the single-window multivariate and univariate predictions. The MWCLS detection limits in the presence of multiple interferences are 15 ng/g (i.e., 15 ppb) or better for each element. In addition, errors with the new method are only slightly inflated when only a single target element is included in the calibration (i.e., knowledge of all other elements is excluded during calibration). The MWCLS method is found to be vastly superior to partial least-squares (PLS) in this case of limited numbers of calibration samples.

New method for predicting lifetime of seals from compression-stress relaxation experiments

Interpretation of compression stress-relaxation (CSR) experiments for elastomers in air is complicated by (1) the presence of both physical and chemical relaxation and (2) anomalous diffusion-limited oxidation (DLO) effects. For a butyl material, we first use shear relaxation data to indicate that physical relaxation effects are negligible during typical high temperature CSR experiments. We then show that experiments on standard CSR samples (-15 mm diameter when compressed) lead to complex non-Arrhenius behavior. By combining reaction kinetics based on the historic basic autoxidation scheme with a diffusion equation appropriate to diskshaped samples, we derive a theoretical DLO model appropriate to CSR experiments. Using oxygen consumption and permeation rate measurements, the theory shows that important DLO effects are responsible for the observed non-Arrhenius behavior. To minimize DLO effects, we introduce a new CSR methodology based on the use of numerous small disk samples strained in parallel. Results from these parallel, minidisk experiments lead to Arrhenius behavior with an activation energy consistent with values commonly observed for elastomers, allowing more confident extrapolated predictions. In addition, excellent correlation is noted between the CSR force decay and the oxygen consumption rate, consistent with the expectation that oxidative scission processes dominate the CSR results. INTRODUCTION When polymers are placed under constant mechakical strain, the resulting stress will relax with time from a combination of physical and chemical processes [l-31. The physical processes involve such things as flow of chains and movement of entanglements. For elastomeric (crosslinked) materials in the absence of chemical effects, the physical effects are reversible in the sense that the material will eventually recover its original shape once the mechanical strain is removed. The chemical processes, on the other hand, are irreversible, involving mainly scission and crosslinking effects (breakage and formation, respectively, of covalent bonds). Various stress-relaxation methods, involving primarily tensile and compressive sample loading, have been used for many decades to study and model these effects [ 1-61. Our current objective is to derive better methods for estimating the lifetime of elastomeric seals in oxygen-containing environments (e.g., air). Since service lifetimes depend primarily on the decay in compressive force between the seal and its mating surface and since compression stress-relaxation (CSR) techniques [4-61 follow the force for compressively loaded samples, CSR is usually considered to be the most appropriate approach for lifetime predictions of seals and will therefore be used for that purpose in the current study. P t)lSTRIBUT#IN OF THIS DOCUMENT IS UNLIMKED a3 Q3 0 r€34 -=a0 W DISCLAIMER This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employe#, makes any warranty, exprey or implied, or assumes any legal liability or responsibility for the accuracy,.completenr?ss. or usefulness of any infomation, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference henin to any speafic commercial product, proccs~. or service by trade name, trademark, manufacturer, or otherwise dots not necessarily constitute or imply its endorsement, m m mendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not n d l y state or reflect those of the United States Government or any agency thereof.

Angle-Constrained Alternating Least Squares

When resolving mixture data sets using self-modeling mixture analysis techniques, there are generally a range of possible solutions. There are cases, however, in which a unique solution is possible. For example, variables may be present (e.g., m/z values in mass spectrometry) that are characteristic for each of the components (pure variables), in which case the pure variables are proportional to the actual concentrations of the components. Similarly, the presence of pure spectra in a data set leads to a unique solution. This paper will show that these solutions can be obtained by applying angle constraints in combination with non-negativity to the solution vectors (resolved spectra and resolved concentrations). As will be shown, the technique goes beyond resolving data sets with pure variables and pure spectra by enabling the analyst to selectively enhance contrast in either the spectral or concentration domain. Examples will be given of Fourier transform infrared (FT-IR) microscopy of a polymer laminate, secondary ion mass spectrometry (SIMS) images of a two-component mixture, and energy dispersive spectrometry (EDS) of alloys.

Advantages of clustering in the phase classification of hyperspectral materials images.

Despite the many demonstrated applications of factor analysis (FA) in analyzing hyperspectral materials images, FA does have inherent mathematical limitations, preventing it from solving certain materials characterization problems. A notable limitation of FA is its parsimony restriction, referring to the fact that in FA the number of components cannot exceed the chemical rank of a dataset. Clustering is a promising alternative to FA for the phase classification of hyperspectral materials images. In contrast with FA, the phases extracted by clustering do not have to be parsimonious. Clustering has an added advantage in its insensitivity to spectral collinearity that can result in phase mixing using FA. For representative energy dispersive X-ray spectroscopy materials images, namely a solder bump dataset and a braze interface dataset, clustering generates phase classification results that are superior to those obtained using representative FA-based methods. For the solder bump dataset, clustering identifies a Cu-Sn intermetallic phase that cannot be isolated using FA alone due to the parsimony restriction. For the braze interface sample that has collinearity among the phase spectra, the clustering results do not exhibit the physically unrealistic phase mixing obtained by multivariate curve resolution, a commonly utilized FA algorithm.

In situ X-ray diffraction analysis of (CFx)n batteries: signal extraction by multivariate analysis

(CFx)n cathode reaction during discharge has been investigated using in situ X-ray diffraction (XRD). Mathematical treatment of the in situ XRD data set was performed using multivariate curve resolution with alternating least squares (MCR–ALS), a technique of multivariate analysis. MCR–ALS analysis successfully separated the relatively weak XRD signal intensity due to the chemical reaction from the other inert cell component signals. The resulting dynamic reaction component revealed the loss of (CFx)n cathode signal together with the simultaneous appearance of LiF by-product intensity. Careful examination of the XRD data set revealed an additional dynamic component which may be associated with the formation of an intermediate compound during the discharge process.

Algorithms for constrained linear unmixing with application to the hyperspectral analysis of fluorophore mixtures

In this paper, we describe the use of linear unmixing algorithms to spatially and spectrally separate fluorescence emission signals from fluorophores having highly overlapping emission spectra. Hyperspectral image data for mixtures of Nile Blue and HIDC Iodide in a methanol/polymer matrix were obtained using the Information-efficient Spectral Imaging sensor (ISIS) operated in its Hadamard Transform mode. The data were analyzed with a combination of Principal Components Analysis (PCA), orthogonal rotation, and equality and non-negativity constrained least squares methods. The analysis provided estimates of the pure-component fluorescence emission spectra and the spatial distributions of the fluorophores. In addition, spatially varying interferences from the background and laser excitation were identified and separated. A major finding resulting from this work is that the pure-component spectral estimates are very insensitive to the initial estimates supplied to the alternating least squares procedures. In fact, random number starting points reliably gave solutions that were effectively equivalent to those obtained when measured pure-component spectra were used as the initial estimates. While our proximate application is evaluating the possibility of multivariate quantitation of DNA microarrays, the results of this study should be generally applicable to hyperspectral imagery typical of remote sensing spectrometers.

Atomic-scale phase composition through multivariate statistical analysis of atom probe tomography data.

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.