Diffraction group

Consider a single-crystal its crystal structure belongs to one of the 32 point groups and prepare a thin foil for electron microscopy with the shape of a perfect parallel slab. Depending on the way this slab is cut from the single-crystal, 31 different types of specimen can be obtained if symmetry elements are taken into account. These 31 types of specimen will give 31 different types of diffraction pattern named diffraction groups. 

In an opposite way, if we are able to identify the diffraction group from experimental diffraction patterns, then, we can obtain the point group. This is the basis of the point group determination. To reach this aim, two experimental methods are available a method proposed by Buxton et al. [3] and a multi-beam method proposed by Tanaka et. al. [4]. 

Table I. Identification of the diffraction group from the WP, BF, DF and +/g symmetries. Table from references [3] and [4],...

The connection between the diffraction group and the point group is obtained from Table II. High symmetry diffraction groups are very useful. One or a few Zone-Axis Patterns are required to identify the point group. 

Table II. Identification of the space group from the diffraction groups. Table from reference [3].

Hagen, K., Hedberg, K. The Norwegian Electron Diffraction Group, Annual Report 1977... 

Measurement of multiple Bragg diffraction. Some sets of phases may be derived from experimental measurements of i/ -scan profiles of reflections exhibiting the effects of multiple Bragg diffraction. Groups of relative phases have absolute values that can be detected by this method which is currently in the developmental stage, and is only applicable to those sets of Bragg reflections that display the effect. 

As follows from Table 2.12, there are only two possible diffraction groups for the monoclinic C-centered lattice. The second diffraction group, Clcl, differs from the first one, C1-1, by the presence of /(O/reflections only with even 1. As is easy to see from Table 2.11, none of the Bragg peaks hQl with / = 2 + 1 is observed, or in other words, the allowed reflections condition is / = 2n for hOl (these are shown in bold). Other conditions are... 

The last step should be repeated for all colunms under the general header Reflection conditions . When finished, the list should be narrowed to a single line, i.e. the corresponding diffraction group should be found for the known S5mimetry of the unit cell shape. 

These diffraction groups have the same reflection conditions as the following hexagonal groups P—, P62-, P—c, and P-c-. Therefore, they are indistinguishable from systematic absences using powder data. 

The presence of distinct systematic absences and an unambiguous determination of the diffraction group makes a particular indexing solution especially probable. Exceptionally encouraging are centered lattices and, for example, such space groups as P2)/c, Pbca, I4i/amd,... 

As early as the late 1960s the Orsay electron diffraction group in France successfully used a supersonic nozzle for production of large clusters of rare gas atoms, carbon dioxide and water [56-61]. Bartell and his coworkers at the University of Michigan [62-65] continued this important research in the early 1980s. First, formation of benzene clusters was studied... 

Data collected in Table 3 illustrates these options showing how it is practically done in different electron-diffraction groups [134-165]. 

The relation between the diffraction groups and the crystal point groups can be seen in Table 3. 

Table 3. Relation between diffraction groups and crystal point groups (from Buxton et al [17])...

The author is grateful to all the members of the electron-diffraction group in Oslo for helpful discussions. Cand. real. R. Stolevik should be thanked especially for his valuable suggestions during the work on the accuracy section, and Professor O. Bastiansen for his critical reading of the manuscript. Many helpful comments from Professor K. Kuchitsu are also gratefully acknowledged. 

Gas-phase electrrai diffraction as a technique for the determination of molecular structures was first developed by H. Mark and R. Wierl in 1930, but the usefulness of the method was demonstrated by studies of only a handful of molecules before the project was abandoned 3 years later [57]. After a visit to Mark s laboratory, L. Pauling and his graduate student L. Brockway built up an extremely productive electron diffraction group at California Institute of Technology, fri 1936 they were able to publish a review article with structural information on nearly 150 different molecules determined with error limits ranging from 1 to 3 pm. 

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