Incident beam aperture

In the transmission geometry the requirements are different. When a flat transmission sample is used, the aperture of the incident beam is defined by the largest Bragg angle of interest, since at 0 = 0 the sample is perpendicular to the incident beam (and not parallel, as in the Bragg Brentano geometry). Equation 3.1 then becomes as follows (where the notation are the same as in Eq. 3.1) 

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. 

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Figure 3.29. Poorly ground powder, suitable incident beam aperture. Experimental data are shown using small circles the calculated diffraction pattern is shown using solid lines. The difference fobs - fcaic is shown at the bottom of the plot and the calculated positions of Bragg peaks are marked using vertical bars. The data were collected without spinning the sample.

Figure 3.31. Poorly ground powder and an improper incident beam aperture. The data were collected without spinning the sample. Notations are identical to Figure 3.29.

Figure 3.34. The set of x-ray powder diffraction patterns collected from the nearly spherical LaNi4 gsSno.is powder (see Figure 3.32, inset) on a Rigaku TTRAX rotating anode powder diffractometer using Mo Ka radiation. Goniometer radius R = 285 mm receiving slit RS = 0.03° flat specimen diameter d = 20 mm. Incident beam apertures were 0.05, 0.17, 0.25, 0.38, 0.5, 0.75, 1, 1.5, 2° and completely opened ( 5°), 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.

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°. 

In a confocal microscope, invented in the mid-1950s, a focused spot of light scans the specimen. The fluorescence emitted by the specimen is separated from the incident beam by a dichroic mirror and is focused by the objective lens through a pinhole aperture to a photomultiplier. Fluorescence from out-of-focus planes above and below the specimen strikes the wall of the aperture and cannot pass through the pinhole (Figure 11.3). 

For a long time, Selected-Area Electron Diffraction (SAED) performed with a parallel incident beam and a selected-area aperture was the only experimental method available. During the three last decades, new diffraction techniques based on a convergent electron incident beam (CBED Convergent-Beam Electron Diffraction, LACBED Large-Angle... 

Nevertheless, this technique has a main disadvantage the minimum size of the diffracted area, which is selected by means of the selected-area aperture, is about 500 nm. It becomes difficult to prevent some thickness variations and/or some orientation variations in the diffracted area. The SAED patterns are, in fact, average patterns and the diffracted intensities can be strongly affected. For that reason, it is recommended to use Microdiffraction or CBED because the diffracted area is directly defined by the incident beam and can reach a few nanometers with recent microscopes. 

Figure 7a. EEL spectrum of a chromite spinel under different incident beam orientations showing enhancement for the octahedral (a) and tetrahedral (b) sites. The position of the detection aperture to achieve enhanced localization for the low energy O-K edges is shown in the insert...

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