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

In 1995 another step was taken by lachance and

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In 1995 another step was taken by Lachance and Claisse [34] in expanding the generalization of influence coefficients in order to address the analytical context mainly used in practice, namely, { polychromatic incident sources, ma- trix effects, multielement, explicitly from theory } , by taking advantage of the contribution of Broll and Tertian [10] who proposed a valid expression for the long sought “weighting factor,” which was none other than the monochro- matic component of Criss and Birks [12] equation numbered “7.” This led to defining influence coefficients as:
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338 J.P. Willis and G.R. Lachance m ij = A ij E ij I i A + I i E , (5.40) where I i A is the theoretical intensity excited by absorption of the primary radiation and I i E is the theoretical intensity resulting from enhancement by matrix elements, and the terms A ij and E ij are based on the summation of related monochromatic components. The definitions are given here. The process of defining influence coefficients for the comprehensive con- text, i.e. Polychromatic incident excitation source; Matrix effect(s), absorption and enhancement; Multielement systems; Defined explicitly as a function of FPs; can be visualized as consisting of four steps: 1. Define monochromatic absorption and enhancement influence coefficients α ijλ = µ j µ i µ i e ijλ = e j ( e j + e j ) (5.41) in which e j relates to incident λ, ψ , µ s , and µ j , e j relates to emitted λ i , ψ , µ s , and µ j , where the superscripts and refer to incident and emergent radiation, respectively, and where e j = 0 . 5( p λ j µ j µ ) µ p λj is the probability that a λ j photon will be emitted, which in turn is the product of three probabilities; µ j is the mass absorption coefficient of the analyte element for the wavelength of the enhancing matrix element line; µ is the mass absorption coefficient of the enhancing element for the incident monochromatic wavelength; µ is the mass absorption coefficient of the analyte element for the incident monochromatic wavelength. For example, in the case of the K α line, p λ j = r K 1 r K ω K p f K α , where ( r K 1) /r K is the probability that the absorbed incident photon ejects a K shell electron rather than an L or M shell electron, and r K is the
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5 Quantitative Analysis 339 K edge absorption jump ratio; ω K (the fluorescent yield) is the probability that the electronic transition leads to the emission of a characteristic pho- ton rather than ejecting an Auger-electron; p f K α is the probability that a K α photon is emitted rather than a K β , and e j = 1 µ s ln 1 + µ s µ j e j = 1 µ s ln 1 + µ s µ j . 2. Define A ijλ and E ijλ A ijλ = I i A λ a ijλ E ijλ = I i A λ e ijλ . (5.42) 3. Define A ij and E ij A ij = λ Edge λ min A ijλ λ E ij = λ Edge λ min E ijλ λ. (5.43) 4. Define a ij and e ij a ij = A ij I i A + I i E e ij = E ij I i A + I i E . (5.44) In summary, therefore, a ijλ A ijλ A ij, poly a ij, poly (absorption) e ijλ E ijλ E ij, poly e ij, poly (enhancement) .
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  • Spring '14
  • MichaelDudley

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