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

N i 1 c i 1 the procedure is terminated if either of

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n i =1 C i = 1. The procedure is terminated, if either of the following conditions is met: C ( k +1) i C ( k ) i < ε, (7.36) n i =1 ( I i, meas I i, calc ) 2 σ 2 i, meas < δ, (7.37) where ε and δ are given as input values for limitation of the iteration steps, and σ j is the standard deviation of the measured X-ray intensities of the j th
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Methodological Developments and Applications 631 1 10 100 1000 10000 100000 0 4 6 8 10 Energy (keV) Intensity (counts) Measurement Simulation C O N Mg Si C 2 Fig. 7.122. Measured and simulated EPMA spectra of a 20- µ m diameter soda-lime glass standard sphere (SPI #2716) with a 100-nm carbon layer element. According to our experience, the convergence speed of the numer- ical approximation depends strongly on the number of simulated electrons and the number of elements considered in the sample. The average num- ber of steps is between 5 and 10 for accuracy values 0 . 005 < ε < 0 . 01 and 1 . 5 < δ < 2 . 0. The zero-approximation of the elemental concentrations C 0 i for EPMA can be assumed as the normalized measured intensity of element i , because practically all elements are observed (except H, He, Li, and Be): C i, 0 = I i, meas n j =1 I j, meas . (7.38) In micro-XRF, however, the irradiated mass, the shape, and the matrix of the particles are not known and it is very difficult to determine these parameters experimentally. Therefore it is necessary to make some a priori assumptions on the basis of independent bulk measurements. The shape of the particles can be assumed to be spherical. The diameter or mass of the particle-sphere can be estimated by using optical microscopy or from the intensity of the scatter peaks, respectively. It can be assumed that each element with a detectable X-ray line is present in its most common oxide form in the particle, such as SiO 2 , SO 3 , K 2 O, CaO, TiO 2 , and Fe 2 O 3 . All other elements can be assumed to be present in atomic form. The sum of the elemental and oxide concen- trations can be assumed to be 100% in the case of coal fly ash and sediment particles.
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632 S. Kurunczi et al The initial concentration of analyte i , C i, 0 with detectable X-ray line was calculated as: C i, 0 = I i, meas / S i n j = m +1 I j, meas /S j × 1 m j =1 C j , (7.39) where S i is the sensitivity for element i , n is the total number of elements in the sample, and the first m elements constitute the dark matrix (which can be derived from stoichiometry or known from other, bulk measurements). If EPMA results are available for exactly the same particle or the same particle type (including light elements such as C, N, and O), the dark matrix compo- sition considered for micro-XRF can be calculated from the major elemental composition obtained from EPMA. Using the Monte Carlo based quantification method, the minor element content of individual microparticles can be determined using laboratory scale micro-XRF setups based on a standard diffraction X-ray tube and capillary optics. If the trace element content of the particles is demanded, micro-SRXRF measurements are necessary, using the matrix composition determined for
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  • Spring '14
  • MichaelDudley

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