By Rene Van Grieken, A. Markowicz
Updates basics and purposes of all modes of x-ray spectrometry. Promotes the exact dimension of samples whereas decreasing the scattered historical past within the x-ray spectrum.
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Extra info for Handbook of X-Ray Spectrometry
1981) and Heinrich (1981) on EPXMA. A. Photon Excitation When continuous (polychromatic) radiation is used to excite the characteristic x-rays of element i in a completely homogeneous sample of thickness T (cm) and when enhancement eﬀects are neglected, the intensity of the ﬂuorescent radiation Ii (Ei) is described by Ii ðEi Þ dO1 dO2 ¼ dO1 dO2 eðEi Þ 4p sin C1 E Zmax 1 À exp½ÀrTðmðE0 Þ csc C1 þ mðEi Þ csc C2 Þ Â ai ðE0 Þ I0 ðE0 Þ dE0 mðE0 Þ csc C1 þ mðEi Þ csc C2 ð88Þ Ec;i with ai ðE0 Þ ¼ Wi t0i ðE0 Þoi pi 1 1À ji ð89Þ where dO1 and dO2 are the diﬀerential solid angles for the incident (primary) and emerging (characteristic) radiation, respectively; eðEi Þ is the intrinsic detector eﬃciency for recording a photon of energy Ei ; Ec;i and Emax are the critical absorption energy of element i and the maximum energy in the excitation spectrum; r is the density of the specimen (in g=cm3); C1 and C2 are the eﬀective incidence and takeoﬀ angles, respectively; mðE0 Þ and mðEi Þ are the total mass attenuation coeﬃcients (in cm2=g) for the whole specimen [Eq.
The anomalous dispersion causes the quantity d=l2 , Eq. (80), to vary slightly with the wavelength. The variations become important only in the neighborhood of the absorption edges of the constituents of the crystal. Dividing the quantity d=l2 into one normal part ½ðd=l2 Þn and one anomalous part ½ðd=l2 Þa , the theory of anomalous dispersion leads to an expression of Bragg’s law that can be written as (Sandstro¨m, 1957) ! 4d2 d 4d2 d yn nl ¼ 2d 1 À 2 À sin ð83Þ 2 2 2 n n 2 l n l a Combined with Bragg’s law in its uncorrected form, Eq.
88), the intensity of characteristic x-rays is modiﬁed by the eﬀects of primary [mðE0 Þ] and secondary [mðEi Þ] absorption in the specimen; this is a major source of the so-called matrix eﬀects in XRF analysis. If the excitation source is monochromatic (emits only one energy), Eq. (88) simpliﬁes to eðEi Þai ðE0 ÞI0 ðE0 Þ sin C1 1 À exp½ÀrTðmðE0 Þ csc C1 þ mðEi Þ csc C2 Þ Â mðE0 Þ csc C1 þ mðEi Þ csc C2 Ii ðEi Þ ¼ G ð90Þ The enhancement eﬀect, consisting of an extra excitation of the element of interest by the characteristic radiation of some matrix elements, modiﬁes the equations for the intensity Ii ðEi Þ.