INDEX space group

All tenus in the sum vanish if / is odd, so (00/) reflections will be observed only if / is even. Similar restrictions apply to classes of reflections with two indices equal to zero for other types of screw axis and to classes with one index equal to zero for glide planes. These systematic absences, which are tabulated m the International Tables for Crystallography vol A, may be used to identify the space group, or at least limit die... 

All of the observed reflections could be indexed on the basis of a cubic unit cell with Oo = 11.82 A the estimated probable error is 0.01 A. The only systematic absences were hhl with l odd this is characteristic of the space group 0 -PmP>n, which also was reported by von Stackelberg from his single-crystal work on sulfur dioxide hydrate. For 46 H20 and 6 Cl2 in the unit cell the calculated density is 1.26 densities reported by various observers range from 1.23 to 1.29. 

The structure of PuB,qq is not yet clear. A satisfactory indexing can be made for a primitive cubic cell with a = 23.42 A, but with 10 reflections not characteristic of space group Fm3c . ... 

The orbitals <]) j(k r) are Bloch functions labeled by a wave vector k in the first Brillouin zone (BZ), a band index p, and a subscript i indicating the spinor component. The combination of k and p. can be thought of as a label of an irreducible representation of the space group of the crystal. Thequantity n (k)is the occupation function which measures... 

A suitable way to represent group-subgroup relations is by means of family trees which show the relations from space groups to their maximal subgroups by arrows pointing downwards. In the middle of each arrow the kind of the relation and the index of the symmetry reduction are labeled, for example ... 

The group-subgroup relation of the symmetry reduction from diamond to zinc blende is shown in Fig. 18.3. Some comments concerning the terminology have been included. In both structures the atoms have identical coordinates and site symmetries. The unit cell of diamond contains eight C atoms in symmetry-equivalent positions (Wyckoff position 8a). With the symmetry reduction the atomic positions split to two independent positions (4a and 4c) which are occupied in zinc blende by zinc and sulfur atoms. The space groups are translationengleiche the dimensions of the unit cells correspond to each other. The index of the symmetry reduction is 2 exactly half of all symmetry operations is lost. This includes the inversion centers which in diamond are present in the centers of the C-C bonds. 

In the same paper (Yamamoto 1996) an authoritative description is given of several interrelated topics such as super-space group determination, structure determination, indexing of diffraction patterns of quasicrystals, polygonal tiling, icosahedral tiling, structure factor calculation, description of quasicrystal structures, cluster models of quasicrystals. 

The main purpose of extracting the diffraction information from any kind of diffraction pattern is to continue with stmcture solution using the extracted quantitative data. This data includes the calculated unit cell parameters obtained during the indexing procedure, s mimetry determination such as a space group or a set of possible space groups and integrated intensities for indexed reflections. 

ELVES has been developed as an expert system, by James Holton and Tom Alber, to go from data collection frames to structure without human intervention and will obviate the need for intermediate space-group determination described above. Very recently, 12 different European sites have been collaborating to develop a software package known as DNA (automateD collectioN of datA) for the automatic collection and indexing of macromolecular diffraction data. Further information is available at the web site www.dna.ac.uk. 

It was possible to index all of the observed reflections by using a reduced, one-chain, monoclinic unit-cell, with a = 0.446 nm, b (fiber axis) = 1.034 nm, c = 0.725 nm, and )8 = 98.6°. The space group is P21 with one chain per unit cell. Thus, the chains have parallel polarity. There are two intrachain hydrogen-bonds of the type OH-3— 0-5 and OH-2—0-6, and an OH-6—0-3, interchain hvdrogen-bond. 

The X-ray patterns of the samples obtained for PTES/TEOS = 1 4 with these two synthesis procedures are presented in Figure 1. For preparation A, the pattern is similar to that reported for the cubic SBA-1 phase and assigned to the Pm3n space group [19]. All the peaks can be indexed, and lead to an average cell parameter of 83.8 A. Preparation B gives the usual pattern due to a two-dimensional (p6m) hexagonal phase, with a cell parameter of 39.5 A. 

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