Transformation elemental concentration data

Figure 7.1. Elovich model (b), respectively. Soils were incubated under the saturation paste regime (modified after Han et al., 2002b. Reprinted from J Environ Sci Health, Part A, 137, Han F.X., Banin A., Kingery W.L., Li Z.P., Pathways and kinetics of transformation of cobalt among solid-phase components in arid-zone soils, p 192, Copyright (2003), with permission from Taylor Francis). Trace element concentrations in plants on California Donimo soil (pH 7.5) amended with metal sulfate-enriched sludge (Data from Mitchell et al., 1978).

The raw concentration data were subjected to several mathematical and statistical transformations. The ratio of the element of interest to Fe helps offset inherent variation in Fe across the data set A logio transform is a standard statistical conversion for elemental data. This transformation reduces the weighting effect from very small to very large concentrations in the data (48). More details on the calculations and reasoning behind these transforms can be found elsewhere (5). 

Data Representation. Transformations can be applied to the data so that they will more closely follow the normal distribution that is required for certain procedures or for removing (or lessening) unwanted influences. Certainly for data analysis in which major, minor, and trace elemental concentrations are used, some form of scaling is necessary to keep the variables with larger concentrations from having excessive weight in the calculation of many coefficients of similarity. 

The following are considerations of variable importance in the selection of an instrumental method. Is the instrument available in our laboratory If not, how much does it cost What kind of space and utilities does it require Can this instrument determine one element at a time or various elements simultaneously How is the sample to be presented to the instrument Will our particular type of sample require processing Can the instrument be operated by a technician Can the data be directly transformed into concentration or must it be processed or interpreted Useful information concerning reliability, frequency of adjustments, calibration and repairs can be obtained from users whose names are usually provided by the manufacturer. And finally an often forgotten consideration is there in town a factory representative qualified to service the instrument ... 

Fourier transform infrared (FTIR) spectroscopy of coal low-temperature ashes was applied to the determination of coal mineralogy and the prediction of ash properties during coal combustion. Analytical methods commonly applied to the mineralogy of coal are critically surveyed. Conventional least-squares analysis of spectra was used to determine coal mineralogy on the basis of forty-two reference mineral spectra. The method described showed several limitations. However, partial least-squares and principal component regression calibrations with the FTIR data permitted prediction of all eight ASTM ash fusion temperatures to within 50 to 78 F and four major elemental oxide concentrations to within 0.74 to 1.79 wt % of the ASTM ash (standard errors of prediction). Factor analysis based methods offer considerable potential in mineral-ogical and ash property applications. 

Results For the St. Louis data, the target transformation analysis results for the fine fraction without July Uth and 5th are given in table 6. The presence of a motor vehicle source, a sulfur source, a soil or flyash source, a titanium source, and a zinc source are indicated. The sulfur, titanium and zinc factors were determined from the simple initial test vectors for those elements. The concentration of sulfur was not related to any other elements and represents a secondary sulfate aerosol resulting from the conversion of primary sulfur oxide emissions. Titanium was found to be associated with sulfur, calcium, iron, and barium. Rheingrover ( jt) identified the source of titanium as a paint-pigment factory located to the south of station 112. The zinc factor, associated with the elements chlorine, potassium, iron and lead, is attributed to refuse incinerator emissions. This factor could also represent particles from zinc and/or lead smelters, though a high chlorine concentration is usually associated with particles from refuse incinerators ( ). The sulfur concentration in the refined sulfate factor is consistent with that of ammonium sulfate. The calculated lead concentration in the motor vehicle factor of ten percent and a lead to bromine ratio of about 0.28 are typical of values reported in the literature (25). The concentration of lead in... 

Pattern Recognition. An alternative treatment of the data is possible and has been discussed by some of us (70). This approach involves the application of pattern recognition, a subject which has received considerable attention in the recent literature. Essentially, the technique involves the transformation of the concentrations of the five target (fingerprint) elements into points in 5-dimensional space which is represented by "pattern vector", for example ... 

A straightforward Fourier transform of the EXAFS signal does not yield the true radial distribution function. First, the phase shift causes each coordination shell to peak at the incorrect distance. Second, due to the element specific back-scattering amplitude, the intensity may not be correct. Third, coordination numbers of distant shells will be too low mainly because of the term 1/r in the amplitude (10.10) and also because of the small inelastic mean free path of the photoelectron. The appropriate corrections can be made, however, when phase shift and amplitude functions are derived from reference samples or from theoretical calculations. Figure 11.17 illustrates the effect of phase and amplitude correction on the EXAFS of a Rh foil [38]. Note that unless the sample is that of a single element, N is a fractional coordination number, i.e. the product of the real coordination number and the concentration of the element involved. Also, the EXAFS information is an average over the entire sample. As a consequence, meaningful data on supported catalysts are only obtained when the particles have a monodisperse size distribution. 

Valence compounds, like elements, satisfy the Hume-Rothery rule, as can be seen by calculating the average coordination number for these compounds. At the same time, they retain the tetrahedral distribution of the atoms, i.e., the tetrahedral bonds. The structure of defect diamond-like phases has been studied in some detail but corresponding data for excess phases are not available. The problem of the change in the structure of excess phases with varying valence electron concentration is more complicated since it is neither immediately apparent nor known how a sphalerite-type structure is transformed into a defect antifluorite-type structure. 

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