[B._Beckhoff,_et_al.]_Handbook_of_Practical_X-Ray_(b-ok.org).pdf

The measured line intensities from unknown and

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the measured line intensities from unknown and standards are affected in the same manner and by the same factor by these errors, this factor may cancel by building appropriate ratios. This is, however, not a matter of course and a careful analysis of the problem is strongly advised, because many errors depend in a complex way on concentrations and the qualitative composition.
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326 M. Mantler Count-rate ratios. In almost all practical applications, count-rate ratios are used rather than absolute counts. Such ratios are built with the count rates from the same element in another specimen, which can be a standard of any composition, or a pure element. The main advantage is that thereby a number of unknown or less accurately known factors cancel, namely all factors included in G i of (5.11), as well as any scaling constant in the absolute photon flux of the primary radiation (which is rarely ever known in practice), and the detection efficiency, which is omitted in (5.11). Note that the factors g J and g K in the secondary and tertiary excitation terms in (5.17) and (5.18) do not cancel. In this chapter, all count-rate ratios are relative to pure elements unless otherwise indicated: R i = N i N ( i ) . (5.19) (Non-) Necessity of measuring pure element counts. It is not necessary to actually measure pure elements in order to obtain count-rate ratios relative to pure elements. This is an important point because several elements cannot be produced or analyzed by reasonable means, in pure form. Assume that the counts from a specimen, N i,S , and a standard, N i,St , have been measured. Then the count-rate ratio of the standard, R i,St , relative to a pure element can be computed by FP methods, and the count-rate ratio of the specimen, R i,S , relative to a pure element obtained from (see also Sect. 5.3.1 and (5.31)): R i,S = N measured i,S N extrapolated ( i ) = N measured i,S N measured i,St · R computed i,St . (5.20) Requirement and selection of additional standards. While one standard is re- quired in order to build relative intensities, additional standards can improve the accuracy of the analysis. Standards with a similar composition as the unknown are called local standards . A single local standard pins the cali- bration curve to the point defined by this standard and its measured count rates. When several standards are used, an average calibration factor can be computed. This is achieved by computing pure element count rates for each analyte line and standard, and averaging these values. The observed standard deviation of these data should match the expected uncertainty of the certi- fied chemical composition, eventual preparatory inconsistencies, and the error introduced by counting statistics. Sets of standards that give larger errors should not be used. Instead of local standards, standards with widely varying composition may be employed with advantage. These are global standards . The same as given earlier applies with respect to averaging and consistency. A weighting factor may be introduced for each standard, which matches the differing statisti- cal reliability of low and high element counts. Note that reanalyzing sets of
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  • Spring '14
  • MichaelDudley

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