International
Tables for
Crystallography
Volume C
Mathematical, physical and chemical tables
Edited by E. Prince

© International Union of Crystallography 2006
International Tables for Crystallography (2006). Vol. C. ch. 2.3, p. 48

Section 2.3.1.1.5. Focal line and receiving-slit widths

W. Parrisha‡ and J. I. Langfordb

a IBM Almaden Research Center, San Jose, CA, USA, and bSchool of Physics & Astronomy, University of Birmingham, Birmingham B15 2TT, England

2.3.1.1.5. Focal line and receiving-slit widths

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The projected source width [F_w] and receiving-slit width RSw each add a symmetrical broadening to the profiles that is constant for all angles. Both the profile width and the intensity increase with increasing take-off angle (Section 2.3.5[link]). However, the contribution of [F_w] is small when the line focus is used, Fig. 2.3.1.9(a)[link] . The receiving slit can easily be changed and it is one of the most important elements in controlling the profile width, intensity, and peak-to-background ratio, as is shown in Figs. 2.3.1.9(a) and (c)[link]. Because of the contributions of other broadening factors, αRS can be about twice αF (line focus) without significant loss of resolution.

[Figure 2.3.1.9]

Figure 2.3.1.9| top | pdf |

(a) Effect of source size on profile shape, Cu Kα, αES 1°, αRS 0.05°, Si(111). [\matrix{{\rm No.} &{\rm Projected \, size \,(mm)} &{\rm FWHM} \, (^\circ 2\theta) \cr 1 &1.6 \times 1.0\, ({\rm spot}) &0.31 \cr 2 &0.32 \times 10 \, ({\rm line}) &0.11 \cr 3& 0.16 \times 10 \, ({\rm line}) &0.13 \cr 4 &0.32 \times 12 \,({\rm line}) &0.17 \cr}] Effect of receiving-slit aperture αRS on profiles of quartz (b) (100) and (c) (121); peak intensities normalized, Cu Kα, αES 1°.

The projected width of the X-ray tube focus [F_w] is given in equation (2.3.1.2[link]). The aperture is [\alpha_F= 2 \arctan (F_w/2R).\eqno (2.3.1.8)]For a line focus with actual width [F^{\prime}_{w}] = 1 mm, ψ = 5°, and R = 185 mm, αF = 0.011°. The receiving-slit aperture is [\alpha _{\rm RS}= 2 \arctan ({\rm RS}_w/2R). \eqno (2.3.1.9)]For RSw = 0.2 mm and R = 185 mm. αRS is 0.062°. The FWHM of the profiles is always greater than the receiving-slit aperture because of the other broadening factors.








































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