Two-beam condition

Electron diffraction performed with a parallel incident beam, i.e. Selected-Area Electron Diffraction is used to obtain good electron micrographs. The two-beam condition allows the observation of defects. SAED is also used in High-Resolution Electron Microscopy (HREM) to set a crystal to a zone axis so that the atomic columns are vertical in the microscope. SAED is very useful for the identification of phases and the... 

Figure 9. Phase difference for the transmitted beam in the undisturbed crystal comparing the phase under kinematical conditions and for (lower curve) 0002 or (upper curve) 11-20 two-beam conditions as a function of the thickness.

The kinematic approximation breaks down at a certain crystal thickness when the diffracted intensity approaches that of the incident beam. A usefiil criterion for kinematic approximation is r < fg/4, where fg is the extinction distance of the strongest reflection in the diffraction pattern. The extinction distance is orientation dependent. In case only one set of lattice planes is strongly diffracting (the two-beam condition), the extinction distance is given by = h lmeX Vg. 

The reason we see a dislocation is that it bends a crystal plane near its core region. Indicate a case where we may not be able to see the dislocation in diffraction contrast under a two-beam condition (a two-beam condition refers to a crystal orientation in which the intensity of one diffraction spot is much higher than those of the other diffraction spots). Indicate the answer either graphically or using the relation of vectors g (the normal of planes which generate the diffraction beam) and b (Burgers vector of dislocation). 

Several different types of diffraction condition are used to characterise radiation damage. These are achieved by tilting the specimen with reference to the Kikuchi pattern. These include dynamical two-beam , bright-field kinematical and weak-beam conditions - see Jenkins and Kirk for a full description. Under dynamical two-beam conditions, small dislocation loops located close to foil surfaces exhibit black-white contrast (Fig. 9.3), and their symmetry can be used to determine the Burgers vectors and habit-planes. 

Several techniques can be used to determine the point group [169]. The method developed by Buxton et al. [170] is based on the use of zone axis patterns and of dark-field diffraction patterns obtained under exact two-beam conditions. By... 

Using a Kikuchi pattern, one can tilt TEM specimen to a two-beam condition to get diffraction contrast imaging, or a zone axis to obtain diffraction patterns and HREM images. Figure 5.3 shows a schematic diagram of a Kikuchi map for... 

Fig. 5.3 schematic diagram of a KiKuchi map for a face-centered cubic crystal. The arrows are used to mark where the two-beam conditions are taken... 

In 1960, Hirsch, Howie, and Whelan developed the theory for diffraction contrast imaging [3]. In the case of two beam condition, the diffracted beam intensity Id for a perfect crystal is written as ... 

Experimentally, diffraction contrast imaging is done by first tilting the crystal to a two-beam condition and obtaining a selected-area electron diffraction pattern. A BE image can be obtained by placing the objective aperture to the transmitted beam. To obtain a DE image, one can place the objective aperture to the diffracted beam and form a DE image. In order not to move the objective aperture and switch between BE and DE modes, one needs to use a centered dark-field (CDE) method. 

The best way to determine density of stacking faults in a sample grown on the nonpolar (1120) plane is to observe these defects in plan-view configuration. In this orientation, BSFs are seen as thin lines parallel to the c plane of GaN when two-beam conditions with g = 1100 are appKed (Figure 10.6a). 

Figure 10.24c represents a bright-field image of a wing area obtained with the same two-beam condition as Figure 10.24b. A drastic decrease in the density of BSFs in the wing areas in comparison to the seed areas can be noticed. Arrows on Figure 10.24c mark two BSFs. The average density of BSFs measured over a number of wings is 1.2 x 10 cm h...

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