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

Range of wavelengths and it is not commonly measured

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range of wavelengths and it is not commonly measured; it is thus an excellent diluent in many cases. This method aims at reducing the effect caused by the variation in spec- imen composition. In theory, it could also eliminate the variation of matrix effect completely by adding very large quantities of diluent, but at the same time, the sensitivity is reduced significantly. A compromise must thus be sought between reduction of matrix variability and loss of sensitivity. 5.4.4 Scattered Radiation – Compton Scatter Compton scatter or incoherent scatter involves interaction of a photon with a single free (i.e., weakly bound) electron, in which part of the photon energy is transferred to the electron. The wavelength of the scattered photon is thus longer (has less energy) than that of the incident photon. It can be shown that the Compton shift ∆ λ is given by λ = λ s λ 0 = h m e c (1 cos ψ ) = 0 . 00243 (1 cos ψ ) , (5.88) where h is Planck’s constant, m e is the rest mass of the electron, and c is the velocity of light in vacuum. The angle ψ is the angle between the direction of the photon after scattering and its original direction. When ∆ λ is calculated in nm, the constants evaluate to 0.00243 nm. The intensity of the Compton scattered radiation from a tube line can be used to obtain an estimate of the absorption coefficient of the specimen at the
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364 B.A.R. Vrebos wavelength λ s of the scattered photons. Furthermore, it can be shown that the intensity of the scattered radiation is inversely proportional to the mass attenuation coefficient µ s of the specimen: I s ( λ s ) 1 µ s ( λ s ) , (5.89) where λ s is the wavelength of the scattered radiation and µ s ( λ s ) is the mass attenuation coefficient of the specimen for wavelength λ s . This relationship is illustrated in Fig. 5.8 for a number of standard specimens. The agreement is striking. This property can be used to the analysts’ advantage when deal- ing with analyses of elements whose characteristic radiation is mainly subject to absorption effects. In such cases, the variation in the magnitude of the matrix effect between specimens is mainly due to changes in the absorption properties. If enhancement can be neglected and the intensity of the fluores- cent radiation, I i , is inversely proportional to the mass attenuation coefficient (monochromatic excitation is assumed): I i C i µ s . (5.90) Knowledge of the value of µ s for each specimen thus enables quantitative analysis. The intensity of the X-rays scattered by the specimen can be used to determine the value of the mass attenuation coefficient at one wavelength. Mass attenuation coefficients at two different wavelengths are virtually propor- tional, independent of matrix composition, provided there are no significant absorption edges between these two wavelengths [23].
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