Double diffraction

There are only three equatorial spots. Each of the three can be accounted for by double diffraction (of 330, 5 50, and 880, with the factor for R of 1.9021 —2sin72°). By vector addition it is seen that the other spots can be accounted for by multiple diffraction of hh 0. 

Figure 31 BiPbSr2YCusOfi Several types of satellites are observed in different areas of the same crystals ([001]) (a) satellites set up along a direction roughly parallel to [120] (q-6.25) (b) bidimens-ional system of satellites resulting from the existence of misori-ented areas and double diffraction phenomena, the angle between both systems is close to 100 (c) satellites along [110] with q 3.65 (d) previous satellites have disappeared but streaks remain along (II0 (e) multisplitting of the spots and first satellites they are indications of distortions and microtwins.

Figure 33 Tin tSr CaCugO (001J E D. pattern. numerous extra spots are observed whkh van be interpreted as the result of the mnoraentation of two lamellae and double diffraction phenomena.

Occasionally, reflections that are forbidden by the structure factor are observed in a diffraction pattern. These forbidden reflections are due to double diffraction, which occurs when a strong diffracted beam in the crystal acts as an incident beam for further diffraction by the crystal. These extra spots can be found by translating the diffraction pattern, without rotation, so that the 000 spot coincides successively with all the strong diffraction spots of the pattern. All new spots introduced by this procedure are geometrically possible double-diffraction spots. If A AT / and h2k2h are the indices of any two allowed primary diffraction spots, then all spots... 

In the case of plan view images the information due to the particle and the support overlap in the space. From the point of view of the interaction of the electron beam with the sample, the most relevant aspect in this case is the occurrence of a double diffraction process. The electron beams, which aregenerated in a first diffraction process in the particles, are further diffiacted by the support crystallites. Doubly... 

Figures 4.30(c) and 4.31(c) show HREM images representative of the catalysts reduced at 1173 K and further oxidised in pure O2 at 1173 K. The structure of both catalysts is clearly different from that observed after re-oxidation at 773 K. Notice that in this case both materials seem to be formed by small, crystalline, metal particles dispersed over the ceria surface. Fringe analysis confirms that these crystallites consist of metallic rhodium and platinum, respectively. Thus, the DDPs of the larger particles observed in the image of the Pt catalyst show 0.8 nm Moire-type fringes aligned with the (111 )-Ce02 reflections. These spots arise from double diffraction in the (lll)-Pt and (Ill)-Ce02 planes under a parallel orientation relationship. Therefore this result, in addition to confirm the presence of metallic Pt particles in the sample oxidised at 1173 K, suggest that these particles are epitaxially grown on the support. A detailed inspection also reveals that the exposed surfaces of these particles are clean, i.e. free from support overlayers.

Fig. 9.S. High-resolution transmission electron micrograph of a gold nanorod showing the double diffraction pattern, indicating twinning, taken from [45]. Scale bar = 5 nm. Reproduced by permission ofThe Royal Society of Chemist. ...

The dihedral angles about the glycosidic bonds in a-chitin were the same as those in p-chitin, " but in a-chitin there are two chitin chains in the unit cell. To account for an X-ray reflection which should not have been diffracted by crystals of the derived space group, it was proposed that the hydroxymethyl group was disordered. Subsequently, however, it was shown that this reflection was a double diffraction artefact. The detailed structure of a-chitin is therefore uncertain. 

Figure 8.1 Diffraction pattern obtained from a GaN/SiC plan-view sample showing no lattice rotation between the GaN epitaxial layer and the SiC substrate. Reflections from GaN and SiC are marked by horizontal arrows and vertical arrows, respectively. All other reflections arise from double diffraction. The (0110) reflection is forbidden in 6H-SiC. The GaN layer was grown by H. Morkof and his group at the Virginia Commonwealth University by MOCVD on (0001) SiC at 900°C. Most of the GaN grown layer and SiC substrate were polished and ion milled away until a thin (<50 nm thick) bi-layer remains for the transmission electron microscope observations...

Tilting experiments with the c -axis as tilt-axis have allowed determination of the reflection conditions in the [001] zone diffraction pattern. In Fig. 7.10 streaks at positions A -I-1, h- - and h- -, A -I-1 are systematically absent. Indexed with respect to the superstructure mesh one obtains streaks AO/ with A odd and Okl with k odd are absent. Reflection conditions in the plane thus become AO with A even and OA with k even. Note that double diffraction fills in the forbidden reflections in the [001] zone diffraction pattern. Knowledge of... 

On the other hand, Singh et al. (1976, 1977) have studied SmSe thin films by electron microscopy and electrical resistance. They found a new compound with a hexagonal cell, which was obtained after annealing at 470 K. This lattice, as deduced from electron diffraction patterns, seems quite curious. Indeed, the authors interpret the presence of two rings as (00.1) and (00.3) by a double diffraction effect. But the rings relative to (00.2) or (00.4) are not observed, and this destroys their hypothesis. Moreover, the more intense ring of the pattern corresponds to the (222) diffraction of C-SmzOs. 

J.D. Gates, A. Atrens, I.O. Smith, Microsttucture of as-quenched 3.5 NiCrMoV rotor steel. Part II. Double diffraction, Z. Werkstoftech 18 (1987) 179-185. 

Optical Analog of Electron Double Diffraction to Produce Moire Patterns... 

To produce an optical analog of the electron double diffraction pattern one can draw two line lattices, as shown in Figs. A.17.1 and A.17.2. Next, Fig. A.17.3 shows the... 

Space group determination is based on the observation of the Gjonnes - Moodie lines [173] in certain forbidden diffraction disks. Reflections that are kinematically forbidden may appear as a result of double diffraction under multibeam dynamic diffraction conditions. If such forbidden spots are produced along pairs of different symmetry-related diffraction paths that are equally excited, the interfering beams may be exactly in antiphase for certain angles of incidence if the structure factors have opposite signs. Since the convergent beam disks are formed by beams with con-... 

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