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

They also introduced a third element term to

Info icon This preview shows pages 364–366. Sign up to view the full content.

approximating a curve by linear fitting. They also introduced a “third element term” to compensate for the fact that the algorithm cannot be simply “a sum of binary correction terms.” The COLA model sought to replace the linear curve fitting with a hyper- bolic curve fitting, involving a correction algorithm of the type: 1 + { α ij, hyp + α ijk C k } C j where the subscript “hyp” is used to denote that the binary influence coeffi- cients are approximated by an hyperbola (compare Figs. 5.6 and 5.7). In 1981 Lachance [32] proposed the following expression for quantifying the correction term, namely: C i = R i 1 + j α 1 + α 2 C M 1 + α 3 (1 C M ) + α ijk C k C j (5.50) and the better quality of the hyperbolic fit to the binary influence coefficient values is shown in Fig. 5.7. The COLA model also takes into consideration the observation by Tertian that the influence coefficient α ij should be calculated at the C i concentration level. For the Claisse–Quintin model, this translates into the introduction of C M , where C M is equal to the sum of the matrix elements, i.e., C M = C j + C k + · · · + C n . 1 2.4 2.3 2.2 2.1 2 0 0.5 a FeCr a FeCr a 1 a 3 a 2 Fig. 5.7. Explanation of the three influence coefficients in the COLA algorithm
Image of page 364

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

344 J.P. Willis and G.R. Lachance This approach meant that, in the absorption context, { . . . } ijk values were for all practical purposes equal to 0, and in the cases where enhancement was present, the values as computed by C–Q were reduced by as much as a factor of 2 to 3. If the C–Q model is retained, this is equivalent to using the formulation [1 + { α ij + α ijj C M } C j ] instead of [1 + { α ij + α ijj C j } C j ] in the case of a linear approximation. Tao et al. [55] published “NBSGSC – A FORTRAN . . . ” program for perform- ing quantitative analysis of bulk specimens by X-ray fluorescence spectrome- try. This program corrects for absorption/enhancement phenomena using the comprehensive alpha coefficient algorithm proposed by Lachance (COLA). NBSGSC is a revision of the program ALPHA and CARECAL originally developed by R.M. Rousseau of the Geological Survey of Canada. The process can be described in the following steps: The value of the correction term, i.e., [ . . . ], is calculated using the classical Criss and Birks approach; The value of [ . . . ] is calculated using the six binary influence coefficients α 1 , α 2 , and α 3 in Table 5.4, where α 1 are the values when C i approaches the limit 1.0 and are calculated for C i = 0 . 999: 2.3456 and 0 . 1954 for α FeCr and α FeNi , respectively; α 2 is the difference between those values calculated for C i = 0 . 001 and the above values, i.e., 2 . 0837 2 . 3456 = 0 . 2619 and 0 . 4861 ( 0 . 1954) = 0 . 2906, respectively; α 3 is the value that defines the “degree of curvature” of the hyperbola (deviation from the straight line at C i = 0 . 5) and causes α ij,hyp to match the theoretical value at the mid point. α 3 is defined as α 3 = α 2 m ij, bin ,C i =0 . 5 α 1 2 .
Image of page 365
Image of page 366
This is the end of the preview. Sign up to access the rest of the document.
  • Spring '14
  • MichaelDudley

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern