Convergence angle

FINAL LENS FINAL APERTURE CONVERGENCE ANGLE... 

Figure 5.38. Illustrating the incident electron beam convergence angle (a), the scattering angle (6) and the spectrometer acceptance angle (/l) in electron energy loss spectroscopy. (After Joy, 1981.)...

For high order reflections with a large g, the rapid increase in the excitation error away from the Bragg condition results a rapid decrease in diffraction intensity. Under the kinematical condition, the maximum intensity occurs at the Bragg condition, which appears as a straight line within a small convergence angle. 

Figure 2.6. An example of a contrast transfer function (CTF). The calculated CTF of a 200CX HRTEM at Scherzer defocus and Cs = 1.2 mm. The first zero is arrowed (corresponding to 0.23 nm resolution) and the resolution in angstrdms is shown on the horizontal axis. A-D are envelope functions plotted as a function of convergence angle (0) of the beam and beam energy spread (A V). Parallel illumination is necessary for high resolution (after Boyes et al 1980).

There is another diffraction mode, called convergent beam electron diffraction (CBED), in which the incident electron beam is focused to a fine spot on the specimen. If the convergence angle is appropriately chosen, the diffraction pattern consists of an array of nonoverlapping disks. For thin specimens ( SO nm) the CBED disks are featureless, but... 

Apertures which, by imposing a small convergence angle on the beam, are used to reduce the aberrations of the lenses and, if necessary, reduce the intensity of the probe current. 

Figure 4.4 Relationship between the probe diameter, convergence angle and working distance.

The working distance and aperture size, illustrated in Figure 4.4, are the operation variables that strongly affect depth of field. We often need to make full use of the most important feature of an SEM the three-dimensional appearance of topographic images. Recall that the depth of field is related to the resolution (R) and the convergence angle of objective aperture (or) as (Equation 1.7). 

The resolution of an SEM image on a display screen is limited by the pixel size of the screen. The product of the resolution and the SEM magnification (M) should be equal to the pixel size. Suppose that the pixel size is 100 /xm, the resolution of a SEM image on the display screen can be expressed as 100 M l /mi. The convergence angle of an SEM probe ( /) is much less than 1 rad. Thus, the depth of field in SEM can be expressed as follows. 

Table 4.1 lists the depth of field as a function of the convergence angle and magnification. af is controlled by the final aperture radius and the working distance between the aperture and specimen surface (Figure 4.4). Equation 4.11 can be rewritten to express the depth of field as a function of the aperture radius (Rfap) and the working distance (Dw) as follows. 

For FEG transmission electron microscopes, it is possible to demagnify the electron beam to a subnanometer electron probe. The diameter of the electron probe determines the sample area contributing to the (nano-) diffraction pattern. Electron nanodiffraction (END) makes possible the recording of a diffraction pattern from areas smaller than Inm. Therefore, END is the appropriate technique to study the structure of nanoparticles, as for instance nanotubes and quantum dots. Although a nanoprobe is a convergent beam, the convergence angle is usually smaller than in CBED. As will be shown, END is fundamental for STEM. 

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