By G W Series

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91Þ where mi ðE0 Þ and mi ðEk Þ are the total mass attenuation coeﬃcients for the ith element at the energy of incident radiation ðE0 Þ and characteristic radiation of the element k ðEk Þ, respectively, mk ðE0 Þ is the total mass attenuation coeﬃcient for the element k at the energy E0, and mðEk Þ is the total mass attenuation coeﬃcient for the whole specimen at the energy Ek . 1. Thin-SampleTechnique If the total mass per unit area of a given sample m ¼ rT is small, Eq. (90) simpliﬁes to Iithin ðEi Þ ¼ G eðEi Þai ðE0 ÞI0 ðE0 Þm sin C1 ð92Þ The relative error resulting from applying Eq.

45)] ignores changes in the atomic wave function resulting from changes in the molecular, chemical, or crystalline environment of an atom. Above 10 keV, errors from this approximation are expected to be less than a few percent (except in the regions just above absorption edges), but at very low energies (10–100 eV), errors of a factor of 2 can occur (Deslattes, 1969). For situations more complicated than the narrow-beam geometry, the attenuation is still basically exponential, but it is modiﬁed by two additional factors.

Certain x-ray lines or bands appear or disappear with chemical combinations. In the case of the K series, the most noticeable chemical eﬀects on x-ray emission are seen in spectra from low-Z elements (4 Z 17). The L series shows as large or even larger changes with chemical combination of the elements than K series. The valence eﬀects in L spectra have been observed for elements of the ﬁrst transition series and others nearby in the periodic table. Because the ﬁne features of x-ray emission spectra may be applied to determine how each element is chemically combined in the sample (speciation), the valence eﬀects found numerous applications in such ﬁelds as physics of solids and surface or near-surface characterization.