By René E.Van Grieken, Andrzej A. Markowicz, 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 history within the x-ray spectrum.
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Extra info for Handbook of X-Ray Spectrometry Revised and Expanded
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.
The total coherent (Rayleigh) scattering cross section per atom sR can be calculated from Copyright © 2002 Marcel Dekker, Inc. , 1975). Recently, Szalo´ki (1996) proposed a useful combination of analytical functions to calculate F(x, Z): 8 0 x x1 f11 ðx; ZÞ ¼ a expðÀb1 xÞ þ ðZ À aÞ expðÀcxÞ; > > > f ðx; ZÞ ¼ f ðx ; ZÞ expðÀb ðx À xÞ; < x 1 x x2 12 11 1 2 1 ð74Þ F1 ðx; ZÞ ¼ f13 ðx; ZÞ ¼ f12 ðx2 ; ZÞ exp½Àb3 ðx2 À xÞ; x 2 x x3 > h ib4 > > : f14 ðx; ZÞ ¼ f13 ðx3 ; ZÞ x ; x 3 x x4 x3 where 1 7 8 < f21 ðx; ZÞ ¼ a expðÀb1 xÞ þ ðZ À aÞ expðÀcxÞ; 0 x x1 x 1 x x2 F2 ðx; ZÞ ¼ f22 ðx; ZÞ ¼ f21 ðx1 ; ZÞ exp½Àb2 ðx1 À xÞ; : f23 ðx; ZÞ ¼ f22 ðx2 ; ZÞ exp½Àb3 ðx2 À xÞ; x 2 x x3 Z ð75Þ where 8 Z 100 The parameters for the calculation of F(x, Z ), including the critical values of x1, x2, and x3, are given by Szalo´ki (1996) for all elements (Z ¼ 1–100) and the momentum transfer x from 0 to 15 A˚71.
INTENSITY OF CHARACTERISTIC X-RAYS This section provides some of the necessary background information for subsequent chapters dealing with quantitative x-ray analysis. Derivation of any relationship between excitation source intensity and measured characteristic x-rays is sometimes complex and is presented in detail in many relevant books, such as those by Jenkins et al. (1981) and Tertian and Claisse (1982) on XRF analysis and by Goldstein et al. (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.
Handbook of X-Ray Spectrometry Revised and Expanded by René E.Van Grieken, Andrzej A. Markowicz, Rene Van Grieken, A. Markowicz