X-rays production

Another consideration in the determination of the optimum Eq is the depth of X-ray production in bulk samples, especially if one component strongly absorbs the radiation emitted by another. This is often the case when there is a low-Z element in a high-2 matrix, e.g., C in Fe. Here X rays from carbon generated deep within the sample will be highly absorbed by the Fe and will not exit the sample to be detected. The usual result will be an erroneously low value for the carbon concentration. In these situations the best choice for Eq will be closer to Eq with U rather than a much higher value with U = 2.5. 

The standardless approach attempts to apply first principles descriptions of X-ray production to the calculation of interelement relative sensitivities. Several of the key parameters necessary for first principles calculations are poorly known, and the accuracy of the standardless method often suffers when different X-ray families must be used in measuring several elemental constituents in a specimen. 

A tabulation of the ECPSSR cross sections for proton and helium-ion ionization of Kand L levels in atoms can be used for calculations related to PIXE measurements. Some representative X-ray production cross sections, which are the product of the ionization cross sections and the fluorescence yields, are displayed in Figure 1. Although these A shell cross sections have been found to agree with available experimental values within 10%, which is adequate for standardless PKE, the accuracy of the i-shell cross sections is limited mainly by the uncertainties in the various Zrshell fluorescence yields. Knowledge of these yields is necessary to conven X-ray ionization cross sections to production cross sections. Of course, these same uncertainties apply to the EMPA, EDS, and XRF techniques. The Af-shell situation is even more complicated. 

Figura 1 Calculated K X-ray production cross sections for protons using the tabulated ECPSSR Ionization cross sections of Cohen end Harrigan, and the fluorescence yields calculated es In Johansson et al. (1 barn h IIT cm l.

In FIXE the X-ray spectrum represents the integral of X-ray production along the path length of the decelerating ion, as mediated by X-ray absorption in the mate-... 

The detection of impurities or surface layers (e.g., oxides) on thick specimens is a special situation. Although the X-ray production and absorption assumptions used for thin specimens apply, the X-ray spectra are complicated by the background and characteristic X rays generated in the thick specimen. Consequently, the absolute detection limits are not as good as those given above for thin specimens. However, the detection limits compare very favorably with other surface analysis techniques, and the results can be quantified easily. To date there has not been any systematic study of the detection limits for elements on surfaces however, representative studies have shown that detectable surface concentrations for carbon and... 

The total power, or integrated intensity,4 of the x-ray beam, in watts, is the product of the (empirical) efficiency11 of x-ray production and cathode-ray power iV or... 

Usually, high intensity is desirable in a continuous spectrum to be used for x-ray excitation. The efficiency of x-ray production,... 

Fig. 9-2, a and b. X-ray production as a function of voltage wave form. The shaded curves give the relative x-ray production as calculated from Eq. 4-7. 

X-ray production by electron excitation, 5-9, 27, 28, 98-102, 176-179 X-ray radiance, definition, 6 X-ray radiant energy, definition, 6 X-ray radiant flux or power, definition, 6... 

The height of a given X-ray peak is a measure of the amount of the corresponding element in the sample. The X-ray production cross-sections are known with good accuracy, the beam current can be measured by, for example, a Faraday cup (Figure 4.1) and the parameters of the experimental set-up are easily determined so that the sample composition can be determined in absolute terms. 

Computer software codes are available to deconvolute PIXE spectra and to calculate peak areas with accuracy, so that absolute amounts of elements present in the specimen may be derived. With a beam of 5 mm diameter incident on a thin organic specimen on a thin backing foil, trace elements can be detected at picogram levels. The x-ray production cross-sections, absorption coefficients and the various... 

The spatial resolution in quantitative analysis is defined by how large a particle must be to obtain the required analytical accuracy, and this depends upon the spatial distribution of X-ray production in the analysed region. The volume under the incident electron beam which emits characteristic X-rays for analysis is known as the interaction volume. The shape of the interaction volume depends on the energy of the incident electrons and the atomic number of the specimen, it is roughly spherical, as shown in Figure 5.7, with the lateral spread of the electron beam increasing with the depth of penetration. 

In EPMA, X-rays are produced over a range of depths from the surface before their energy falls below Ec. In order to derive the effective absorption factor, an integration must be carried out which requires a knowledge of the shape of the depth distribution of X-ray production. 

A numerical matrix correction technique is used to linearise fluorescent X-ray intensities from plant material in order to permit quantitation of the measurable trace elements. Percentage accuracies achieved on a standard sample were 13% for sulfur and phosphorus and better than 10% for heavier elements. The calculation employs all of the elemental X-ray intensities from the sample, relative X-ray production probabilities of the elements determined from thin film standards, elemental X-ray attenuation coefficients, and the areal density of the sample cm2. The mathematical treatment accounts for the matrix absorption effects of pure cellulose and deviations in the matrix effect caused by the measured elements. Ten elements are typically calculated simultaneously phosphorus, sulfur, chlorine, potassium, calcium, manganese, iron, copper, zinc and bromine. Detection limits obtained using a rhodium X-ray tube and an energy-dispersive X-ray fluorescence spectrometer are in the low ppm range for the elements manganese to strontium. 

Figure 1. Schematic representation of secondary x-ray production for (a) bulk sample and (b) thin-film sample.

Qualitative Analysis. A simple determination of the elements present in a small region of sample and an indication of their relative proportions (e.g. major or minor element) can be rapidly obtained using EDS detectors monitoring X-ray production from a thin-film of sample. If there is some prior knowledge of the likely... 

Elemental Precision. For the determination of element concentrations in a multi-component phase, it is assumed that, for suitably thin samples absorption and fluoresence of X-rays are negligible. Thus, the relative intensities of characteristic X-ray peaks can be related to the concentration ratio of elements by a factor, k [4]. This k-factor accounts for the relative efficiencies of X-ray production and detection during the analysis. This relationship can be expressed by the equation... 

For multi-component phases commonly encountered in mineralogy, it may not be possible to construct precise experimental k-factor curves for all elements due to uncommon element abundances in silicates or to a lack of suitable standards. For example, Ni or Cr can occur in silicates in low concentrations, but sufficient to be detected using an AEM. In such instances, calculated k-factors can be determined based upon theoretical cross-sections for X-ray production [34] and are generally suitable for higher-Z elements (Z>Ti) to within 10% relative error [37]. Alternatively, the relationship shown in equation 5 can be used to advantage in the calculation of uncommon k-factors, though with a concommitant reduction in accuracy due to accumulation of errors in determination of the individual k values. 

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