Thickness sample correction

In contrast to all these attractive properties there are some disadvantages. The absorption effects of the primary radiation and the fluorescence radiation created in the analyte result in a shallow layer a few tenths of a millimeter deep that provides information on its composition. This requires a perfectly homogeneous sample, which often occurs naturally but must sometimes be produced by acid dissolution into liquids or by grinding and the preparation of pressed pellets. In both instances the feature of non-destructiveness is lost. Thin films or small amounts of microcrystalline material on any substrate are the ideal analyte where also the quantification process is simple because there is Hnearity between fluorescence intensity and concentration. In thick samples corrections for absorption and enhancement effects are necessary. 

If we choose a much larger than 1 (thin samples d<0.5L) or h pL (thick samples d>>L), the final steady-state exhalation deviates very little from the free exhalation rate and we do not need to know the reshaping time or use Equation 2 for corrections. An air grab sample taken at any time (and corrected for radioactive decay if necessary) after closure, will yield the free exhalation rate to a good approximation, provided that the can is perfectly radon-tight. 

This method is commonly nsed on spectral data to correct for multiplicative variations between spectra. In spectroscopy, snch variations often originate from nnintended or uncontrolled differences in sample path length (or effective path length, in the case of reflectance spectroscopy), caused by variations in sample physical properties (particle size, thickness), sample preparation, sample presentation, and perhaps even variations in spectrometer optics. Snch variations can be particularly problematic because they are confounded with mnltiplicative effects from changes in component concentrations, which often constitute the signal in qnantitative applications. It is important to note that multiplicative variations cannot be removed by derivatives, mean-centering or variable-wise scaling. 

A thick sample will absorb so many neutrons that the radiation field will be perturbed and the measurement will not give the correct flux. 

A thick sample will cause a depression of the flux in its interior. In such a case, correction factors will have to be applied to all the equations of this section that contain the flux . 

The third dimension in the analysis (depth) is significant because the synchrotron X-rays penetrate deeply in most materials. This has several ramifications. First, buried volumes, such as fluid inclusions, can be analyzed. Second, one needs to know the sample thickness to correct for absorption effects (see quantification discussion below). Third, it is important to minimize the mounting substrate because this material is a source of scattered radiation that contributes to the spectral background. Fourth, the sampling depth depends on the energy of the fluorescence X-ray and therefore is element dependent. This fact can be used to advantage by selecting a sample thickness to achieve optimum sensitivity for the suite of elements of interest. 

In aerosol samples 12 elements (K, Ca, Ti, V, Mn, Fe, Cu, Zn, Br, Rb, Sr and Pb) have been determined in concentration range 10-700 ng/m (Bandhu et al., 1996). In fly ash where the concentrations are higher the elements Al, Si, K, Ca, Ti, Mn, Fe, Ni, Cu, Zn, As, Rb, Sr, Y, Pb and Th are determined with precision below 10% in an concentration interval 15 mg/kg (Th) - 13% (Si). The accuracy evaluated by analysis of NIST-SRM 1633a is very good for all elements but As (Van Dyck et al., 1986). The good analytical parameters have been achieved after introduction of a secondary fluorescence correction for medium thickness samples. The same approach has lead to the successful determination of 20 elements in soils (IAEA Soil 5) with excellent accuracy and precision, and of 12 elements in plant matrices (NIST-SRM 1571). 

Since the majority of materials analyzed using XRF are prepared as solid samples (of infinite thickness), matrix correction procedures must be applied to fluorescence measurements. Several approaches are described in this section, their use depending on both the application and the range of elements to be determined. 

A useful alternative method for calibration in the thick sample case is to perform thick target correction on thin-sample sensitivity factor K Z) by the help of a calculated function I Z) to be obtained by rewriting O Eq. (33.2) to give... 

Another important matrix effect is the enhancement of X-ray emission through secondary X-ray fluorescence in thick samples. This effect can lead to a significant overestimation of concentration data for some combinations of elements, in which energy differences between the primary X radiation and absorption edge of the lighter component is small. Some numerical and analytical procedures offer more or less appropriate corrections for this effect. 

The absorption correction term (3, for intermediate thick sample, is given by... 

Eq. (12) was derived under the assumption that tAe l/v absorber did not harden the neutron spectrum. A thin sample of high transmission (transmission T = i/Iq) would approximate the above condition, but then the accuracy of the cross section would be poor due to any small error in the count rates Iq and I, which differ by a small amount. Therefore, a thicker sample has to be used to increase the accuracy. But the thick sample hardens the neutron beam spectrum that passes through it, and so Eq. (12) no longer holds. A correction for hardening now has to be applied to relate correctly the experimentally obtained cross section with the cross section... 

The right part of equation [4], E = e c d, represents Lambert-Beer s law. E is called the extinction, c is the substance concentration, and d is the thickness of the sample. The E values span from 0 (this is the case when all light is transmitted and no absorption takes place, i.e., 1 = Iq) to inhnity, °o (this is the case of maximal extinction when no incident light is transmitted, i.e., 1 = 0). Realistic E values that can be correctly measured by normal spectrometers range between 0 and 2. Instead of using the E expression for extinction, A for absorbance is often used. E and A are dimensionless values, i.e., numbers without units. Nevertheless, OD, the symbol for optical density, is often added to E and A in order to clarify their meanings. 

The above brief analysis underlines that the porous structure of the carbon substrate and the presence of an ionomer impose limitations on the application of porous and thin-layer RDEs to studies of the size effect. Unless measurements are carried out at very low currents, corrections for mass transport and ohmic limitations within the CL [Gloaguen et ah, 1998 Antoine et ah, 1998] must be performed, otherwise evaluation of kinetic parameters may be erroneous. This is relevant for the ORR, and even more so for the much faster HOR, especially if the measurements are performed at high overpotentials and with relatively thick CLs. Impurities, which are often present in technical carbons, must also be considered, given the high purity requirements in electrocatalytic measurements in aqueous electrolytes at room temperature and for samples with small surface area. 

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