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- W3100800631 abstract "One of the fascinations of crystallography is the beautiful external appearance of crystals (Fig. 2.1), and the corresponding beauty of the atomic arrangements within them. At an early stage of studying a crystal, a crystallographer needs to analyse its underlying symmetry. This must be done because the crystallographic results must satisfy this symmetry and are constrained by it. It is needed to decide on the appropriate strategy for observation of X-ray scattering by the crystal. It is also essential to know the precise symmetry when interpreting the scattering data to obtain the crystal structure. The analysis of many crystal structures has been delayed because of mistakes in the symmetry assignment, and some have been incorrectly analysed. This chapter sets out to give an overview of crystal symmetry. It does not provide an exhaustive presentation. In particular, we shall concentrate on the symmetrical arrangements of chiral objects, in which mirror symmetry is forbidden. Much more detail about crystal symmetry can be found in many textbooks of crystallography, and a complete reference guide is provided in International Tables for Crystallography, Volume A (see Further Reading at the end of this chapter). An object is symmetrical if, after some operation has been carried out, the result is indistinguishable from the original object. Consider, for example, an equilateral triangle. If the triangle is rotated 120° about its centre, the resulting triangle is, in all respects, identical to the original triangle. This means that a second 120° rotation, producing a total rotation of 240°, also makes no change to the object. A third 120° rotation makes, of course, a 360° rotation, bringing the triangle back to its original orientation. So these rotations are called 3-fold rotation operations, and the equilateral triangle is said to possess 3-fold symmetry. The meaning of 3-fold symmetry is that the object may be rotated repeatedly by 360°/3 120° about its symmetry axis without changing it. Similarly 2-fold symmetry refers to rotation by 360°/2 180° and 6-fold symmetry refers to rotation by 60°. A left hand has no symmetry. Reflect it in a mirror and what you see looks like a right hand." @default.
- W3100800631 created "2020-11-23" @default.
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- W3100800631 date "2002-04-11" @default.
- W3100800631 modified "2023-09-25" @default.
- W3100800631 title "Crystals and symmetry" @default.
- W3100800631 doi "https://doi.org/10.1093/oso/9780198510512.003.0006" @default.
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