Absent reflections

It is seen for this structure that (100) is a reflection plane, (010) a glide plane with translation a/2, and (001) a glide plane with translation a/2 + bj2. The space group is accordingly Y h—Pman. The absent reflections required by V h are (hOl), h odd, and (M0), h- -k odd. Hassel and Luzanski report no reflections of the second class. However, they list (102) in Table V as s.s.schw. This reflection, if real, eliminates this space group and the suggested structure I believe, however, in view of the reasonableness of the structure and the simple and direct way in which it has been derived, as well as of the fact that although thirty reflections of the type (hOl), h even, were observed, only one apparently... 

Intensity distribution in relation to space-group symmetry. We have seen that information on space-group symmetry is given by a consideration of the types of absent reflections, and by a recognition of the symmetries shown by the diffraction pattern as a whole. Yet another approach based on the diffraction pattern as a whole (before we proceed to the intensities of individual reflections) is a consideration of the distribution of intensities. First of all, it should be remembered that for any unit cell containing a given set of atoms, the average value of F2 is a constant, whatever the symmetry it is equal to the sum of the... 

The statistical methods are valuable because they detect symmetry elements which are not revealed by a consideration of absent reflections, or by Laue symmetry5. In principle, it is possible to distinguish between all the crystal classes (point-groups) by statistical methods in fact, as Rogers (1950) has shown, it is possible by X-ray diffraction methods alone (using absent reflections as well as statistical methods) to distinguish between nearly all the space-groups (see p. 269). 

Although systematic absences are almost always more easily recognized in electron diffraction, occasionally dynamic diffraction effects lead to a weak diffraction for a supposedly absent reflection. Repeated observations on crystals of various thicknesses, allow a decision in such doubtful cases. 

Diffraction symmetry, 6/tnmm. Systematically absent reflections 00/ when / 6 . Space-group P6i22-D, (or its enantiomorph P6j22). 

The structure was solved by heavy-atom methods at the U.C. Berkeley CHEXRaY facility using full-matrix least-squares refinement procedures detailed elsewhere. Systematically absent reflections were eliminated from the data set, and those remaining were corrected for absorption by means of the calculated absorption coefficient. A three-dimensional Patterson synthesis gave peaks that were consistent with Xe atoms in Wyckoff position 4c and Ge atoms in 4a in space group Pnmb (see Pnma, No. 62). Three cycles of... 

Full circles denote observed reflections, open circles absent reflections that would be observed if all orientations about the fiber axis were present (fiber type orientation). While the 100 reflection is observed in poly(i.-methionine), it is weaker than would be expected if the orientation were fiber type, and it appears that the (100) planes develop preferentially parallel to the surface and (110) planes perpendicular (5). The diagram for poly(y-methyl-ia-glutamate) is constructed from earlier data (12) with a very similar unit cell a = 11.8 A, c = 27.0 A, compared with a = 11.46 A, c = 26.8 A for poly(i.-methionine). The cell size and the positions of the reflections are consistent with the presence of an a-helix containing 18 residues in five turns. The hatched areas denote the position of layer line streaks. The meridional 00,18 reflections at about 1.5 A are not shown. 

To single out the correct space group among those showing the same Laue symmetry the systematically absent reflections have to be studied. Since the structure factor ... 

The eombination of the information on the Laue group with the analysis of the systematieally absent reflections allows the determination of the so-called Extinction symbol fES). In the International Tables for Crystallography the list of extinetion symbols is given per erystal system. There are 14 ES for the... 

To give a practical example, Figure 7.3 shows a small 26 interval of the experimental pattern of a P2]/n crystal structure. The three vertical bars, generated in the Laue group P2lm, correspond to the positions of the reflections (20-1), (210) and (201). The reflection (20-1) corresponds to a systematically absent reflection, but its intensity is ambiguous because it is overlapped with (210). 

Values of the structure factors were not calculated for the accidentally absent reflections. 

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... 

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