Divergence slit

Fig. 3. X-ray diffractogram of Class-F bituminous coal fly ash. Analytical conditions diffraction data were collected using a Philips X-ray powder diffractometer (45 kV/30-40 mA CuKa theta-compensating variable divergence slit diffracted-beam graphite monochromator scintillation detector) automated with an MDI/Radix Databox. The scan parameters were typically 0.02° step size for 1 s count times over a range of 5-60° 2-theta. All data were analysed and displayed using a data reduction and display code (JADE) from Materials Data Inc., livermore, CA.

Figure 6.1 Comparison of 26 — 6 scan profiles obtained by a monochromatized (pure Cu kal) parallel beam configuration (hybrid x-ray mirror) and a conventional parallel beam configuration achieved by divergence slit (ds) module measured at 001/100 (a), 002/200 (b), 003/300 (c), 004/400 (d) of 500nm-thick Pb(Zro.B4Tio.46)03 thin film. Dotted lines represent the second derivative of the profiles, indicating the peak positions. Note that the profiles are simulated fitted profiles for obtained spectrum using pseudo-Voight function (mixed Lorentz and Gauss function).

The simplest collimation can be achieved by placing a slit between the x-ray source and the sample, as shown in Figure 2.9, top left. The angular divergence of thus collimated beam is established by the dimensions of the source, the size, and the placement of the slit. This slit is usually called the divergence slit and in the majority of powder diffractometers, the placement of the divergence slit is fixed at a certain distance from the x-ray tube focus. 

Figure 2.9. The schematic showing collimation of the incident x-ray beam by using a single divergence slit (top, left) or coupled divergence slits (top, right). The schematic on the bottom left illustrates the size of the source (5) when the projection of the cathode ) is viewed at a take-off angle, v . Equation 2.5 is derived on the bottom, right.

Each pair of the neighboring plates works similar to a regular divergence slit. The major differences in the design of Sober slits, when compared to... 

Figure 2.10. The schematic showing how the x-ray beam is collimated by using both the divergence and Soller slits (top). The beam, collimated in-plane by the divergence slit, is further collimated axially by the Soller slits. The coordinates in the middle of the drawing indicate the corresponding directions. The bottom part of the figure illustrates the analogy of Eq. 2.6 with Eq. 2.5.

Figure 3.8. The schematic of the Bragg-Brentano focusing geometry using a flat sample when the self-focused diffracted beam is registered by the detector after reflection from the sample. F - focus of the x-ray source, DS - divergence slit, RS - receiving slit, D - detector, 0 -Bragg angle.

The slit box located between the x-ray source and the sample Figure 3.12, left) contains two divergence slits, which control the aperture and the divergence of the incident beam in the vertical plane. The two divergence slits are separated by a set of Soller slits, which limit the divergence of the incident beam in the horizontal plane. The sample holder here is an automatic four-specimen sample changer. 

Figure 3.14. The schematic of a powder diffractometer with the vertical goniometer axis, cylindrical sample in the transmission mode and a curved position sensitive detector (PSD). Solid arrows indicate the incident beam and broken arrows indicate the diffracted beams pathways. F - focal point of the x-ray source, M - monochromator, DS - divergence slit, T -incident beam trap.

Figure 3.24. The length of the projection of the incident beam, L, on the surface of the flat sample in Bragg-Brentano geometry. F - focal point of the x-ray source, DS - divergence slit, R - goniometer radius,

The varying incident beam aperture has minimal effect on the resolution of the instrument due to excellent focusing. As shown in Figure 3.35, right, the average full width at half maximum (FWHM) increases from -0.073 to -0.077° (i.e. only by -5%) when the divergence slit aperture increases from 0.05° to completely opened (i.e. by as much as -10,000%). The dependence of the FWHM on the slit opening saturates at wide apertures, whieh is consistent with the full illumination of the specimen when DS exceeds 1°. 

This is expected assuming the ideal homogeneity of both the incident beam and the sample packing density. The former is true for small divergence slit openings, and the latter is true for the used sample, which was prepared from the nearly spherical particles. 

Figure 3.38. The set of x-ray powder diffraction patterns collected from the LaNi4 gsSno.ij powder (see the inset in Figure 3.32) on a Rigaku TTRAX powder diffractometer using Mo Ka radiation. Goniometer radius R = 285 mm Divergence slit DS = 0.5° flat specimen diameter d = 20 mm. Diffracted beam apertures were 0.01,0.02,0.03, 0.04,0.05, 0.06, 0.07, 0.08, 0.1, 0.12° and completely opened ( 1°), respectively. An automatic variable scatter slit was used to reduce the background. The data were collected with a fixed step A20 = 0.01°, and the sample was continuously spun during the data collection.

Figure 3.40. Examples of proper (ScS) and improper (ScS ) selection of scatter slit aperture. DS - divergence slits, RS - receiving slits.

Figure 3.41. The schematic of goniometer optics during data collection employing variable divergence and scatter slits apertures, which enables one to maintain the irradiated area of the sample constant at any Bragg angle. DS - divergence slit, ScS - scatter slit, RS - receiving slit.

Intensity gain due to Lorentz-polarization factor (see Chapter 2, section 2.10.4) is partially offset by the requirement of reduced divergence slit opening (see sections 3.5,3 and 3.6.3), provided all other things remain constant, including the brightness of the incident beam. 

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