Diffracted beam aperture

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.

Unlike the goniometer radius and radiation wavelength, both the diffracted beam aperture and the step size (or sampling step), are easily controlled by the experimentalist. Their effects on the resolution of the powder diffraction pattern were examined in section 3.6, which should be consulted for proper selection of beam apertures. 

In bright-field microscopy, a small objective aperture is used to block all diffracted beams and to pass only the transmitted (undiffracted) electron beam. In the... 

By deriving or computing the Maxwell equation in the frame of a cylindrical geometry, it is possible to determine the modal structure for any refractive index shape. In this paragraph we are going to give a more intuitive model to determine the number of modes to be propagated. The refractive index profile allows to determine w and the numerical aperture NA = sin (3), as dehned in equation 2. The near held (hber output) and far field (diffracted beam) are related by a Fourier transform relationship Far field = TF(Near field). 

One problem of the measurement of weak absorption in the far IR is that short absorption paths must be used. At wavelengths comparable to the beam apertures diffraction effects lead to beam divergence [252]. (The combination of high gas pressures and short absorption paths may not be useful if many-body induction effects must be avoided, and an accurate measurement of a under conditions of weak absorption, I/Iq 1, is difficult [368].)... 

Table I shows the calculated diffracted beam amplitudes for the (000), (002), (004) and (006) beams for both topologies, for a crystal 60 A thick. The principal difference between the intensities for the two structures lies in the intensity of the (004) beam relative to (006). [Note that in both cases the intensity of the central (000) beam is approximately the same and hence the intensities are approximately normalised with respect to each other thus allowing direct comparison]. In the case of the Imma structure the (004) beam is weak with respect to the (006) and hence the (006) must be included to resolve the satellite channels clearly. At a limited resolution of 3.5 A the (006) beam lies outside the objective aperture and hence the satellite channels are only very faint in the image. However, for the Cmcm model the relative intensities are reversed with the (004) beam stronger than the (006) and hence even if the (006) beam is excluded from the aperture the satellite channels will be clearly resolved.

Figure 1.13. Diffraction pattern (la) and image (lb) of a defective grid. If the aperture in the back focal plane is so small that none of the mmn diffracted beams can pass (2a), then the grid is not resolved but the defect is seen in the image (2b).

It will be recalled from Chapter 2 that a dark field (DF) image is obtained by allowing a diffracted beam to pass through the aperture in the back focal plane of the objective lens. The DF image is determined by 7g and... 

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