Crystallographic position Special

The number of different orientations of the EFG tensor due to the symmetry operations of the Laue group is lower if the nuclei occupy special crystallographic sites (special point positions). Information about such special sites of nuclei can be found from NQR single-crystal Zeeman spectroscopy. This is... 

Finally it should be emphasized, that Luzzati et al. have pointed out [69], that the topological properties of the micellar phases are profoundly different from those of the bicontinuous phases. Introducing the term chaotic zones for the regions of highest disorder it could be shown, that these zones occupy special crystallographic positions, which belong either to symmetry elements or to the IPMS. 

Table 17.1 Crystallographic data of the hexagonal and cubic closest-packings of spheres. +F means +(j,0), +(j,0, j), +(0, j, j) (face centering). Values given as 0 or fractional numbers are fixed by space-group symmetry (special positions)...

Besides the crystallographic and chemical symbols and nomenclature previously introduced, a few special symbols have been used in this chapter. Generally, for nearly all the metals (Me), a summary is given of their reactivity with the other elements. This is outlined in the text and in figures representing the Periodic Table. In some cases, more than one table is provided for each element. The different binary systems Me-X are identified by the position in the Table of the element X, and their characteristics are briefly described by one of the following symbols inserted in the corresponding box ... 

Figure 3. Schematic representation of the microcrystal considered in the computations/ the asymmetric unit (4 DeS residues, 5 Na ions and 16 water molecules, evidenced by heavy lines) is reproduced according to the crystallographic symmetry note the two ions and the water molecule in special position (on the diagonal 2-axis at -c/8). Hydrogen atoms in the polymer and lone-pairs are omitted in the drawing.

Compounds 39, 42 and 44 exist as discrete monomeric molecules. The Zn—C bond distances are close to the values of simple diafkylzinc compounds obtained from gas-phase electron diffraction studies and are also close to the values predicted by DFT computational studies . Because the zinc atoms in 39, 42 and 44 are located at special positions in the crystallographic unit ceU (at 0.25, 0.25, 0.5 in 39, and at 0, 0, 0 in both 42 and 44) the C—Zn—C bond angles are by definition 180° as a consequence of space-group symmetry. Compound 43 forms dimers in the solid state via hydrogen bridges between... 

Molecular Symmetry and Crystal Symmetry, In some cases, and with care, a knowledge of the space group together with the number of molecules in the unit cell can indicate forthwith something about the symmetry of the molecule. This can happen when the molecule is required to reside on one of the special positions and hence on a symmetry element (or several). It is then said to have crystallographically required (or imposed ) symmetry. Actually, such statements are unjustified, although the literature abounds with them. We shall see why presently. 

II has a two-dimensional structure with an asymmetric unit of 16.75 non-hydrogen atoms (Figure 5a). The Pb2+ cations are in three crystallographically distinct positions with Pb(l) and Pb(3) landing with 0.5 occupancies in 4fand 4h special positions, respectively, and Pb(2) with a full occupancy. One CHDC anion, one-quarter of the oxalate anion (with C at 4h), one hydroxyl anion (with the O at 4/), one independent oxo dianion (at 4/), and one-quarter of a lattice water molecule (at 2a) are also in the asymmetric unit. Three of the four anions are shown in Figure lc—e. The CHDC anion in the anti, e,e conformation with a torsional angle of 176.74(2)° has (2223) connectivity and binds to six Pb2+ cations [three Pb(2) and three Pb(3)]. The oxalate anion has (2222) connectivity and binds to six Pb2+ cations [two Pb-... 

Parameters have been obtained from supplementary data via the Cambridge Crystallographic Data Center when not listed in published work. Parameters quoted are for molecules on general positions of 12 molecules in the unit cell, 8 are on general and 4 on special positions. 

Clearly, when molecules occupy special positions in the crystal structure, the number of variable degrees of freedom may be reduced from (6-hi). For example, when a molecular inversion centre is coincident with a crystallographic inversion centre, the molecule has no translational degrees of freedom, and each member of the population is defined by (3+ ) variables T= 0, q>, y>, r, r2,..., r (where n is the number of variable torsion angles in half the molecule). 

Both general and special positions are also called Wyckoff positions, in honor of the American crystallographer Ralph Walter Graystone Wyckoff (1897-1994). Wyckoff s 1922 book. The Analytical Expression of the Results of the Theory of Space Groups, contained tables with the general and special positional coordinates permitted by the symmetry elements. This book was the foremnner of International Tables for X-ray Crystallography, which first appeared in 1935. 

What is the difference between a crystallographic general position and special position ... 

In a crystal structure in which a molecule occupies a crystallographic special position, some chemically equivalent atoms can become crystallographically equivalent. 

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