Diffraction symmetry

Symmetry determinations allow the identification of very important crystallographic features like the crystal system, the Bravais lattice and the point and space groups. Although it is usually performed from X-ray and neutron diffraction, symmetry determinations can also be obtained from electron diffraction. 

Crystal system Diffraction symmetry Space groups ... 

Diffraction symmetry in relation to point-group symmetry. So far, in our consideration of the intensities of X-ray reflections in the process of discovering the general arrangement in a crystal, we hare dealt only with reflections of zero intensity, and we have seen that when certain types of reflections have zero intensity the presence... 

Since the diffraction symmetry is shown so strikingly in Laue photographs, it is often called the Laue symmetry . The information on diffraction symmetry is of course all contained in moving-crystal photographs taken by monochromatic X-rays, provided that reflections with similar indices are separated, as they are in tilted crystal photographs... 

Effect of screw axes and glide planes on X-ray diffraction patterns 251 Diffraction symmetry in relation to point-group symmetry 258... 

INTERRELATING LATTICE SYMMETRY, CRYSTAL SYMMETRY, AND DIFFRACTION SYMMETRY... 

The term diffraction symmetry, which is often called Laue symmetry because it can be most conspicuous in a type of X-ray photograph called a Laue photograph, is applied to those point groups that are recognizably different in the diffraction pattern. 

In all other crystal systems we encounter the same general situation, namely, that a few space groups (69, in fact) can be uniquely identified from a knowledge of diffraction symmetry and systematic absences, while the rest form mostly pairs, or small groups that are indistinguishable in this way. Table 11.9 lists for the triclinic, monoclinic, and orthorhombic crystal systems the uniquely determined space groups and the sets with identical systematic absences. 

Knowledge of the diffraction symmetry of a crystal is useful for its classification. If the Laue group is observed to be 4/mmm, the crystal system is tetragonal, the crystal class must be chosen from 422,4mm, 42m, and 4/mmm, and the space group is one of those associated with these four crystallographic point groups. 

The previously determined unit-cell and space-group data were confirmed from precession photographs, the 6/wtnwt diffraction symmetry being further confirmed by careful intensity measurements with scintillation counters of several sets of symmetry-equivalent reflections. 

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

F191a R. M. Fleming et al, Diffraction Symmetry in Crystalline, Close-Packed Ceo, in Clusters and Cluster-Assembled Materials, edited by R. S. Averback, D. L. Nelson and J. Bern-holc. Mat. Res. Soc. Symp. Proc. 206, 691-695 (Materials Research Society, Pittsburgh, 1991). 

Often one has several options for choosing the net, or reciprocal lattice axes. The rule is that an axial system is always chosen that preserves the highest symmetry of the diffraction pattern. That is, the axes are chosen to be consistent with the real unit cell of highest symmetry. Sometimes, before the diffraction symmetry is fully clear, incorrect axes may be chosen. The axial system, or reciprocal lattice net, can, however, always be reassigned and the hkl indexes of the reflections reindexed at a later time. The choice of axes determines the crystal class. 

Fig.1.3-12a-d Some 2-D quasiperiodic tilings the corresponding four basis vectors ai,. .., 04 are shown. Linear combinations of r = M,a, reach all lattice points, (a) Penrose tiling with local symmetry 5mm and diffraction symmetry... 

To date, aU known 2-D quasiperiodic materials exhibit noncrystallographic diffraction symmetries of 8/mmm, 10/mmm, or 12/mram. The structures of these materials are called octagonal, decagonal, and do-decagonal structures, respectively. Quasiperiodicity is present only in planes stacked along a perpendicular periodic direction. To index the lattice points in a plane, four basis vectors a, 2. 4 are needed a fifth one,... 

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