Forbidden diffractions

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-... 

Misorientation can be an issue during the time of collection of ED patterns as sometimes this can exceed 60 min in accumulation mode, and d5mamical diffraction contribution is observed (we may anticipate its presence due to the appearence of forbidden kinematically reflections in the pattern like +- 002). However, is important to note that misorientation effects become less critical and intensity of such forbidden reflections is lowered after applying precession mode to the ED pattern. Similar results have also been observed by M.Gemmi with Si samples. 

The contribution of harmonics is not normally large at first- and second-generation synchrotron sources, as the F i i value falls rapidly with increasing diffraction vector. A major exception is where weak quasi-forbidden reflections... 

X-ray diffraction of 114 analcite at 25 °C revealed two weak reflections at d = 3.80 (at 23.4° 20) and 3.24 A (at 27.5 26) indexed as (320) and (411), respectively. These forbidden, weak reflections disappear from the pattern on heating the zeolite above 200° C. Their disappearance correlated closely with the pronounced second-order break in the dehydration curve at 200° C and suggests a randomization of the partially ordered distribution of 16Na+ ions over the 24Na+ sites (Vs, 0, x/4) in the unit cell. At the decomposition temperature, 916° C, the apparent cell edge is 13.69 A. 

Figure 15. X-ray fiber diffraction pattern obtained from an oriented film of the sodium salt of Klebsiella K8. It is evident that there is a slight perturbation from perfect four-fold symmetry giving rise to some weaker forbidden meridional...

Figure 5. An example of disordered stacking faults. The diffraction lines denoted by ( ) are forbidden by the offretite framework, allowed for erionite, and also allowed for ZSM-34 due to stacking faults between offretite layers.

Assuming a fixed band structure (the rigid band model), a decrease in the density of states is predicted for an increase in the electron/atom ratio for a Fermi surface that contacts the zone boundary. It will be recalled that electrons are diffracted at a zone boundary into the next zone. This means that A vectors cannot terminate on a zone boundary because the associated energy value is forbidden, that is, the first BZ is a polyhedron whose faces satisfy the Laue condition for diffraction in reciprocal space. Actually, when a k vector terminates very near a BZ boundary the Fermi surface topology is perturbed by NFE effects. For k values just below a face on a zone boundary, the electron energy is lowered so that the Fermi sphere necks outwards towards the face. This happens in monovalent FCC copper, where the Fermi surface necks towards the L-point on the first BZ boundary (Fig. 4.3f ). For k values just above the zone boundary, the electron energy is increased and the Fermi surface necks down towards the face. 

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... 

The diffraction line will be forbidden by the structure. Selection rules (of type h + k + I = 2w), which can be used to calculate the forbidden lines, apply to each of the various possible lattices. An unknown structure can thus be categorised into one of these types of lattice, even in the absence of chemical data. 

Such an effect is understandable in view of the distinction between erionite and offretite structures published by Bennett and Card (2, 9). The designated lines are forbidden for the offretite structure. Card has examined our synthetic erionite product by electron diffraction and found disordered intergrowth with widely varying proportions of erionite and offretite structures (8). 

Recent evidence favors Dg symmetry and a pentagonal bipyramidal structure for the heptafluoride. Claassen et al. (2) review the earlier debate about structure of lower symmetry. They provide convincing evidence of D symmetry from the first observation of Raman spectra of the vapor state and re-examination of the infrared spectra. Their data—including five fundamentals in Raman (two polarized), five fundamentals in infrared, no coincidences between Raman and infrared, and one fundamental inactive—are consistent only with symmetry. This is confirmed by Falconer et al. (4) who interpret their electric-deflection experiments as indicating a symmetry-forbidden dipole moment. Extended Huckel-molecular-orbital calculations (5) also predict Dg symmetry. The adopted structural parameters are from our approximate analysis of the electron-diffraction data of Thompson and Bartell (6). The authors gave a radial distribution curve and suggested only a gross (unrefined) structure because of the probable presence of... 

Figure 1 shows full diffraction profiles measured at 300 and 11 K. All of the peaks at 300 K can be indexed as fee, with ao 14.17 0.01 A, as previously reported. Note that no hOO peaks are present in this profile, despite the fact that hOO is allowed for h even. At 11 K, 00 has decreased to 14.04 0.01 A and many new peaks have appeared. The new peaks can all be indexed as simple-cubic (sc) reflections with mixed odd and even indices (i.e., forbidden fee reflections). The crystal has therefore undergone a transition to a simple-cubic structure, but since the cube edge has not changed appreciably the basis must still consist of four molecules per unit cell, which were equivalent in the fee structure but which somehow become inequivalent at low temperature. 

FIGURE 6 (a) Graphical construction for multiple diffraction on a square planar reciprocal lattice net.14 (b) Dependence, on rotation angle around die diffraction vector, of multiple reflection contribution to the apparent reflection intensity of 222, a forbidden reflection, in germanium.9 (c) Multiple reflection effects for several unrelated reflections, in rotation around the diffraction vector, showing peaks and dips. 1... 

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