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

In fig 59 the mass attenuation coefficient as a

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In Fig. 5.9, the mass attenuation coefficient as a function of wavelength is given for three pure compounds: Fe 2 O 3 , TiO 2 , and SiO 2 . Note the rapid Compton RhK a 100 150 200 0.08 0.06 0.04 1 / m Fig. 5.8. Inverse of the mass attenuation coefficient at the wavelength of Rb K α , versus the intensity of Compton scattered Rh K α tube line, for a variety of oxide matrices. The linear relationship of (5.89) can clearly be seen
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5 Quantitative Analysis 365 500 400 300 200 100 0 0.0 0.1 0.2 0.3 m (cm 2 g –1 ) Wavelength (nm) Tio 2 Sio 2 Fe 2 O 3 Fig. 5.9. Mass attenuation coefficient as a function of wavelength for Fe 2 O 3 , TiO 2 and SiO 2 . Note the large differences between the curves for the different materials and the absorption edges increase with wavelength (approximately proportional to λ 3 ), as well as the K-absorption edges of Fe and Ti. The K-absorption edge for Si is at a wave- length not covered by the scale of Fig. 5.9. At any given wavelength, there is a considerable difference between the value of the mass attenuation coefficients for Fe 2 O 3 , TiO 2 , and SiO 2 (except for Fe 2 O 3 and SiO 2 on the long wavelength side of the Fe K-edge). However, when the mass attenuation coefficient at any wavelength is divided by the value at a given wavelength, this ratio is sim- ilar, irrespective of the compound. This is illustrated in Fig. 5.10 where the ratio of the mass attenuation coefficients is plotted for the same compounds. From Fig. 5.10 it appears that the ratio of the value of the mass attenuation coefficient at any given wavelength and its value at 0.07 nm is very similar for all three compounds considered. At about 0.17 nm (the wavelength of the Fe K-edge) the plot for Fe 2 O 3 diverges rapidly, while the values for TiO 2 and SiO 2 are still very similar, until the Ti K-edge (at 0.25 nm) is crossed. The method is thus limited to those cases where only trace elements have absorption edges in that wavelength range. Under these conditions, the ratio I i /I s is proportional to the concentration of the analyte. Combination of (5.89) and (5.90) yields I i C i µ s C i I s ( λ s ) . (5.91) In Fig. 5.11, the intensity of Rb K α is plotted against the chemical con- centration (circles); the crosses represent the ratio of the intensity of Rb K α and the scattered Rh K α . The spread around the line is much reduced in the latter case: the root mean square in the first case is about 14 ppm, while – with Compton corrected intensities – it is reduced to about 3 ppm. In practice, both coherently and incoherently scattered primary radiation, such as tube lines, as well as the scattered continuous radiation can be used. The contribution of Compton scatter to the total scatter at a given wavelength
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366 B.A.R. Vrebos 60 40 20 0 0 0.1 0.2 0.3 Wavelength (nm) TiO SiO Fe 2 O m ( l / m ( l =0.07nm)) Fig. 5.10. Ratio of the mass attenuation coefficient for Fe 2 O 3 , TiO 2 , and SiO 2 divided by the mass attenuation coefficient at 0.07 nm. Note the agreement between the curves in the region up to the absorption edge of Fe (0.174 nm) 0 0 20 40 60 500 Rb concentration (ppm) Intensity (kcps) 1000 Fig. 5.11. Intensity of Rb K α versus chemical concentration (
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