Unit cells, crystallographic types

U.S. Post Office abbreviations for United States and Canada, 103—104 Uniform resource locator (URL) acceptable line breaks, 212-213 in Internet reference citations, 211—213 WWW address format, 98 See also World Wide Web sites Unit cells, crystallographic types, 262 Unit modifiers... 

Fig. 8.2 S implified structures of CaC2 l-lll (from (a) to (c)), displayed as derivatives of the NaCI type structure, neglecting the relation of their true crystallographic unit cells.

The hydrogen-bonded arrangement in p-(HOMe2Si)2C6H4 is much more complicated than the other simple disilanols described earlier. There are three crystallographically independent types of molecules in the unit cell. Two are joined by hydrogen bonds to form chains, while... 

The cyclotetrasiloxane l,l,5,5-tetraphenyl-3,3,7,7-tetrahydroxycy-clotetrasiloxane forms a stable complex with two pyridine molecules trans to each other across the siloxane ring (316). The adduct may be prepared by the addition of an excess of pyridine to the free silanol the isomeric silanol [Ph(OH)SiO]4 does not form an adduct with pyridine (317). As well as hydrogen-bonding to the pyridine molecules, each of the two crystallographically independent molecules in the unit cell hydrogen-bonds to others of the same type to form two independent infinite chains (Fig. 24). Branching to form sheets by joining the chains, as in [But(0H)2Si]20, is partially blocked by the interactions with the... 

Accurate bond distances were expected, if only because each type of P-N bond is repeated, for example 12 times in molecules of T(j symmetry - or even 24 or 48 times when two (P4(NMe)5) or four (P4(NMe)804) crystallographically independent molecules are present in the unit cell - thus providing 12, 24 or 48 independent measurements of the same molecular quantity, from which an accurate average would ordinarily be expected. 

In fibres of some polymers, made under certain conditions, the crystalline regions are found to be tilted with respect to the fibre axis in a well-defined crystallographic direction. This is a very valuable feature, because the diffraction patterns of specimens in which this type of orientation occurs are of precisely the same form as tilted crystal diffraction patterns of single crystals rotated round a direction inclined to a principal axis. The unit cell cannot be obtained directly, for 90° oscillation tilted crystal photographs are required for direct interpretation, but unit cells obtained by trial can be checked by the displacements of diffraction spots from the layer lines this is a severe check, and consistent displacements would leave no doubt of the correctness of a unit cell. This procedure played an effective part in the determination of the unit cell of polyethylene terephthalate (Daubeny, Bunn, and Brown, 1954). 

This list is reproduced exactly as it appears in the International Tables. It tells us all the different kinds of locations that exist within one unit cell. In each instance we are given the multiplicity of the type of point, namely, how many of them there are that are equivalent and obtainable from each other by application of symmetry operations. There is also an italic letter, called the Wyckoff letter. This is simply an arbitrary code letter that some crystallographers sometimes find useful these letters need not concern us further. Next there is the symbol for the point symmetry that prevails at the site. Finally, there is a list of the fractional coordinates for each point in the set. 

Distance least squares (DLS), a method developed by Meier and Vill-iger (1) for generating model structures (DLS models) of prescribed symmetry and optimum interatomic distances, can supply atomic coordinates which closely approach the values obtained by extensive structure refinement. DLS makes use of the available information on interatomic distances, bond angles, and other geometric features. It is primarily based on the fact that the number of crystallographically non-equivalent interatomic distances exceeds the number of coordinates in framework-type structures. A general DLS program is available (8) which allows any combination of prescribed parameters (interatomic distances, ratios of distances, unit cell constants etc). In addition, subsidiary conditions (as discussed in Refs. 1 and 8) can also be prescribed. 

Another vital type of ligand is a heavy-metal atom or ion. Crystals of protein/ heavy-metal complexes, often called heavy-atom derivatives, are usually needed in order to solve the phase problem mentioned in Chapter 2 (Section VI.F). I will show in Chapter 6 that, for the purpose of obtaining phases, it is crucial that heavy-atom derivatives possess the same unit-cell dimensions and symmetry, and the same protein conformation, as crystals of the pure protein, which in discussions of derivatives are called native crystals. So in most structure projects, the crystallographer must produce both native and derivative crystals under the same or very similar circumstances. 

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