Double diffraction spots

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... 

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.

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.

As illustrated in Figure 2.10, the intersections between rings of reciprocal lattices and the surface of the Ewald sphere generate diffraction. Consequently, the oriented crystals in fiber generate a diffraction pattern as shown in the film plane of Figure 2.29. The diffraction spots on the equatorial plane represent the diffraction of [hkO] planes. A line of diffraction spots above or below the equatorial plane should represent the diffraction of (hkl) planes or (hkl) planes, respectively. The diffraction principles of oriented crystals discussed here apply to all type of samples through which X-rays can be transmitted, even though the main applications of WAXD are for crystalline polymers and proteins (special types of polymers). The most famous application to proteins is probably the determination of the DNA double helix structure. 

An intensifying screen should not be used if it is important to record fine detail in the Laue spots, as in some studies of crystal distortion, since the presence of the screen will cause the spots to become more diffuse than they would ordinarily be. Each particle of the screen which is struck by x-rays emits light in all directions and therefore blackens the film outside the region blackened by the diffracted beam itself, as suggested in Fig. 5-5. This effect is aggravated by the fact that most x-ray film is double-coated, the two layers of emulsion being separated by an appreciable thickness of film base. Even when an intensifying screen is not used, double-coated film causes the size of a diffraction spot formed by an obliquely incident beam to... 

New diffraction spots develop above 20% relative humidity necessitating a doubling of the unit-cell i dimension). It seems that water induces a variation of the unit-cell by modifying the relative orientation of the chains. 

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-... 

Fig. 8 TEM image of a single GO sheet on a lacey carbon support a double fold is visible in the top right corner, (b) Selected-area diffraction pattern of the centre of the region shown in (a), the diffraction spots are labelled with Miller-Bravais indices. (Reproduced with permission.)... 

Consider the experimental data from native starch. Fiber diffraction patterns indicate the helical symmetry and the pitch, so the main helical descriptors n and h can be worked out. One complication arises from the possibility of multistranded helices. The fiber axis repeat distance is 10.5 A and three-fold symmetry is indicated by diffraction spots on the meridian at the third and sixth layer lines. Those data could result from either a three-fold helix repeating in 10.5 A (n —3, p = 10.5 A), or from a double helix composed of two strands, with n 6 and p = 21.0 A, that are related by rotational symmetry. Modeling studies were important in working out the accepted double helical result. ... 

Whereas only hh0 can diffract with the beam along a fivefold axis of the icosatwin because of the tilt of the cubic crystals, any plane in the zone 110 of the decatwin can diffract because the seed orients the cubic crystals with this zone axis parallel to the fivefold axis of the twin. It is seen from Fig. 1 (b) that the meridional spots of decagonal FeAl are the same as for icosahedral MnAl6, representing orders of hh0, but that there are many more equatorial spots, eleven instead of three. Indices are assigned in Table II some spots involve double... 

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