Quantitative compositional mapping

Figure 6 (a) Quantitative compositional map of the distribution of zinc at the grain... 

D.S. Bright, D.E. Newbury and R.B. Marinenko, Concentration-Concentration Histograms Scatter Diagrams Applied to Quantitative Compositional Maps, in Microbeam Analysis, (D.E. Newbury, Ed), San Francisco Press Inc., 1988. 

Fig. 9. The transmission images shown in Figure 8 are normalized to optical density (OD) images by inversion of Lamberh-Beer s Law. These OD images are now linear in the absorption coefficients a and thickness t. A set of OD images can subsequently be processed via a singular value decomposition (SVD) procedure to yield quantitative composition maps in terms of the thickness t. (Data acquired with the Stony Brook STXM.) Courtesy of D. A. Winesett, NCSU.

Fig. 16. Quantitative compositional maps derived via an SVD procedure of a nominally 143-nm thick 50/50 (w/w) PS/PMMA blend annealed for 1 week (A) PS mass thickness, (B) PMMA mass thickness, and (C) total thickness maps, ie, PS plus PMMA maps. All images are individually scaled for good contrast, with Black = 0 and White = maximum massthickness. The maximum total thickness of the films increases from the initial 143 nm to 460 nm in Figure 16C due to surface roughening. (Data acquired with the Stony Brook STXM at the National Synchrotron Light Source.) Adapted from Ref 100.

Technical processes that employ ionizing radiation are widely applied in the polymer field, and include the production of crosslinked wire insulation and of heat-shrink food wrappings and tubings for electrical connections, the vulcanization of rubber tires and rubber lattices, and the curing of coatings and inks. Moreover, various X-ray methods can also be appUed for the characterization and analysis of polymers, especially of the polymer surfaces. Both, X-ray imaging and X-ray microscopy allow the derivation of quantitative composition maps of polymer surfaces. Notable in this context are also near-edge X-ray absorption fine structure spectroscopy (NEXAFS), extended X-ray absorption fine structure spectroscopy (EXAFS) and X-ray photoelectron spectroscopy (XPS). 

Electron Probe Microanalysis, EPMA, as performed in an electron microprobe combines EDS and WDX to give quantitative compositional analysis in the reflection mode from solid surfaces together with the morphological imaging of SEM. The spatial resolution is restricted by the interaction volume below the surface, varying from about 0.2 pm to 5 pm. Flat samples are needed for the best quantitative accuracy. Compositional mapping over a 100 x 100 micron area can be done in 15 minutes for major components Z> 11), several hours for minor components, and about 10 hours for trace elements. 

Figure 5.25. (A) Quantitative Cu map of an Al-4wt% Cu film at 230 kX, 128 x 128 pixels, probe size 2.7nm, probe current 1.9 nA, dwell time 120 msec per pixel, frame time 0.75 hr. Composition range is shown on the intensity scale (Reproduced with permission by Carpenter et al. 1999). (B) Line profile extracted from the edge-on boundary marked in Figure 5.25a, averaged over 20 pixels ( 55 nm) parallel to the boundary, showing an analytical resolution of 8nm FWTM. Error bars represent 95% confidence, and solid curve is a Gaussian distribution fitted to the data (Reproduced with permission by Carpenter...

Compositional Mapping by Chemical Force Microscopy. As introduced in the section imder Adhesive Forces, CFM is an SFM-based technique, which allows one to determine and map the distribution of chemically distinct functional groups at surfaces. Owing to the small contact area between sample and the (fimctional-ized) tip, this mapping can be performed, depending on the modulus, down to the suh-50-nm level for typical polymers (66). The chemical contrast is achieved by exploiting the spatial or temporal variations of the relevant forces in quantitative measurements of the pull-off and/or friction forces between the tip and selected areas on the surface of interest (compare Fig. 6). 

In addition, the GPC trace, an example of which is shown in Fig. 42, reflects the composition signature of a given product and reflects the spectrum of molecular chains that are present. Analysis of the area, height, and location of each peak provides valuable quantitative information that is used as input to a CUSUM analysis. Numeric input data from the GPC is mapped into high, normal, and low, based on variance from established normal operating experience. Both the sensor and GPC interpretations are accomplished by individual numeric-symbolic interpreters using limit checking for each individual measurement. 

Moreover, the two procedures display different and complementary properties so that each of them is the method of choice to obtain specific information on the 2D separations. The SMO procedure is an unique tool to quantitatively estimate the degree of peak overlapping present in a map as well as to predict the influence of different experimental conditions on peak overlapping. The strength of the 2D autocovariance function method lies in its ability to simply single out ordered retention pattern hidden in the complex separation, which can be related to information on the chemical composition of the complex mixture. 

The SOM is mainly used as a qualitative tool, to identify groups rather than to provide some numerical estimate of similarity. Nevertheless, these methods also show promise as quantitative tools. Recent unpublished work by Leung and Cartwright4 on the fluorescence of dyes has shown that the SOM can be used as a sensitive way to determine quantitatively the composition of mixtures containing several fluorescent species. When a sample of unknown composition is fed into the trained map, the node to which the sample points indicates the concentration of each species by the value of each of the different weights (Figure 3.31). 

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