New PDF release: Crystallography and Practical Crystal Measurement

By Tutton A.E.H.

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2 Symmetry Directions The orientation of a structure in space is fixed by the choice of the basis vectors a, band c. In contrast to the situation with the elements of molecular symmetry, it is necessary to specify how the symmetry elements of a crystal are orientated with respect to the axes of the unit cell. In order to do this as simply as possible, unit ceIl axes are always chosen (cf. chapter 2) so that the symmetry elements always lie either along an edge or along a diagonal of the cell. For this purpose, it is necessary to define for the seven crystal systems a set of up to three positions in the point group symbol along which the various symmetry elements are orientated.

4, and renamed the "Debye- Waller factar" B, whieh is signifieant in other fields of physies. f I = s i n tJ } f . In reality, it is normal that the amplitudes of vibrations are dependent on the direetion in spaee. For example, the O-atom in a earbonyl group will vibrate mueh less strongly along the C=Ü bond than normal to it. The deseription of sueh a direetion dependent quantity requires the use of a tensor, i. e. a quantity whieh is defined in magnitude and orientation with respeet to three mutually perpendieular veetors.

G. when two molecules oeeupy two inversion centers in the spaee group P2de. In inorganie solid -state materials, e. g. co ordination eompounds forming 3-dimensional networks, such as the perovskites ABX 3, the asymmetrie unit may be such a formula unit, a fraetion of it or an integral multiple of it. Sinee the asymmetrie unit is reprodueed by the symmetry elements, the unit eell must invariably contain an integral multiple of the asymmetrie unit. Number offormula units per unit eell, Z: It is useful at the beginning of a strueture determination, to know Z, the number of formula units in the eell, sinee when the spaee group is known, it is then possible to ealculate how big the asymmetrie unit is, i.

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Crystallography and Practical Crystal Measurement by Tutton A.E.H.

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