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

Lower detection eﬃciency and requiring x ray source

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Lower detection eﬃciency and requiring X-ray source of higher power In this section, the components, the varieties of equipments and some appli- cations of WDXRF are brieﬂy described. 4.4.1 Dispersion Materials for WDXRF The WDXRF spectrometer utilizes Bragg diffraction with crystals to disperse X-rays. Bragg’s equation is written as (4.62). = 2 d sin θ. (4.62) Here, n is the reﬂection order, λ is the wavelength of incident X-rays, d is the lattice spacing of the crystal and θ is the incident angle. Equation (4.62) shows λ must be smaller than 2 d . Practically, the scanning range of the goniometer (usually 2 θ < 150 ) limits λ < 2 d sin 75 . Angular dispersion of a spectrometer is obtained by differentiating (4.62). d λ = 2 d cos θ n . (4.63) Equation (4.63) illustrates that higher reﬂection angle θ and/or higher diffraction order n gives better wavelength resolution. The relationship between angular resolution and relative wavelength res- olution is derived from (4.62) and (4.63) as (4.64). d λ λ = d θ tan θ . (4.64) Equation (4.64) illustrates that higher reﬂection angle θ , in other words, using smaller 2 d value crystal gives higher wavelength resolution. Crystals There are several crystals commonly used in WDXRF spectrometers (Table 4.4). These are chosen by the 2 d value (spectral range) and resolu- tion or reﬂectivity. For the finite thermal expansion coeﬃcient, spectrometers are usually equipped with temperature-stabilizing systems to fix the 2 d value of the crystal. Synthetic Multilayers For analyses of lighter elements, i.e., detecting longer wavelength X-rays, we need a dispersion material with a larger 2 d value as mentioned above. For example, N - ’s wavelength is 3.16 nm. This cannot be diffracted even with

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Table 4.4. Common crystals for WDXRF Lightest Linear thermal Typical energy Chemical Miller measurable expansion coeﬃcient resolution in a Crystal formula indices 2 d (nm) element β (10 6 deg 1 .) spectrometer Remarks Lithium Fluoride LiF (220) 0.2810 24 Cr 34 [107] 14 eV @Mn-K α High resolution Lithium Fluoride LiF (200) 0.4028 19 K 34 [107] 25 eV @Mn-K α General use Sodium Nitride NaCl (200) 0.5640 16 S 40.4 [107] 5.5 eV @S-K α For sulfur High resolution Deliquescent Germanium Ge (111) 0.65327 15 P 6.1 [108] 5 eV @P-K α Eliminates second order reﬂection Graphite C (0002) 0.6705 15 P 28.2 [109] 8.5 eV @P-K α Higher reﬂectivity and poorer resolution than Germanium Indium Antimonide InSb (111) 0.74806 14 Si 4.7 [108] 4.5 eV @Si-K α For silicon PET (Penthaerythritol) C(CH 2 OH) 4 (002) 0.876 13 Al 131 [109] 4 eV @Al-K α Higher reﬂectivity but larger β than EDDT Deteriorative EDDT (Ethylene diamine dextrotartrate) C 6 H 14 N 2 O 6 (020) 0.8808 13 Al 20 [110] 4 eV @Al-K α Deliquescent ADP (Ammonium dihydrogen phosphate) NH 4 H 2 PO 4 (101) 1.0648 12 Mg 17 [107] 4 eV @Mg-K α For magnesium Deliquescent TlAP (Thallium acid phthalate) CO 2 HC 6 H 4 CO 2 Tl (001) 2.57626 8 O 32.7 [110] 15 eV @Na-K α Deliquescent
X-Ray Detectors and XRF Detection Channels 287 TlAP (2 d :2.576 nm), though Langmuir–Blodgett films such as lead stearate (2 d :10.04 nm) have been utilized for ultralight elements, with very low reﬂec- tivity.

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