Group symbols for

In the orthorhombic system, for ten space groups (Nos. 16, 19, 22, etc.), each setting gives the same space group symbol for two space groups, (Nos. 61, 73) two symbols, for the others three or six. 

Figure 4.5 The five Platonic solids (a) regular tetrahedron (b) regular octahedron (c) regular cube (d) regular icosahedron (e) regular dodecahedron. The point group symbol for each solid is given below each diagram...

The two most complex Platonic solids, the icosahedron and dodecahedron, (Figure 4.5 d, e), both have 5 (five-fold inversion) axes. In these a vertex is rotated by 12°, (360/5)°, and then translated by the height of the solid. In the case of a dodecahedron a 5 axis passes through each vertex, while in the case of a regular icosahedron, a 5 axis passes through the centre of each face. The point group symbol for both of these solids is 2/m 3 5, sometimes written as 5 3 2/m. 

The least symmetrical of the Bravais lattices is the triclinic primitive (aP) lattice. This is derived from the oblique primitive (mp) plane lattice by simply stacking other mp-likc layers in the third direction, ensuring that the displacement of the second layer is not vertically above the first layer. Because the environment of each lattice point is identical with every other lattice point, a lattice point must lie at an inversion centre. This is the only symmetry element present, and the point group symbol for this lattice is I. 

The disposition of the symmetry elements is shown in Figure 5.2a. The diagrams reveal all of the symmetry elements present, including extra ones generated by the principal symmetry elements described in the space group symbol. For example, the position of the tetrad axis at the unit cell corner also generates another at the cell centre... 

Write out the full Hermann-Mauguin space group symbols for the short symbols ... 

Boundary classifications Soils possessing characteristics of two groups are designated by combinations of group symbols. For example, GW-GC, well-graded gravel-sand mixture with clay binder ... 

List of space-group symbols for various settings - Liste der Raumgruppensymbole... 

To arrive at the standard space group symbols, consult Index of Three-dimensional Space-group Symbols for Various Settings in International Tables for X-ray Crystallography, vol. I, 3rd edn., pp. 543-553. 

Consider now a molecular pair formed over a center of symmetty, symbolized here by the capital letter I, and apply the same translation procedure to the molecular pair (Fig. 5.2). It is now intuitively obvious that the origin of the cell system must be chosen in the one very unique point in the whole structure, the center of symmetty. It turns out that with this choice not only does the visual picture of the suiicture becomes clearer and simpler, but also all the mathematical manipulations pertaining to crystal structure analysis become much easier. The space-group symbols for the pure translation of a single object or of a centrosymmetric pair are PI and PI respectively, where the letter P stands for primitive cell and the symbol 1 is the traditional crystallographic symbol for the inversion operator. The contents of the unit cell is the portion of crystalline matter that is repeated in space by pure translation. 

The Wiswesser Line Notation (WLN) was introduced in 1946, in order to organize and to systematically describe the cornucopia of compounds in a more concise manner. A line notation represents a chemical structure by an alphanumeric sequence, which significantly simplifies the processing by the computer [9-11], (n many cases the WLN uses the standard symbols for the chemical elements. Additionally, functional groups, ring systems, positions of ring substituents, and posi-... 

A. Term Symbols for Non-Degenerate Point Group Symmetries... 

The claims for discovery and the naming of Element 104 are still in question. The Berkeley group proposes for the new element the name rutherfordium (symbol Rf), in honor of Ernest R. Rutherford, a New Zealand physicist. Meanwhile, the International Union of Pure and Applied Physics has proposed using the neutral temporary name, unnilquadium. 

R (Section 4 1) Symbol for an alkyl group Racemic mixture (Section 7 4) Mixture containing equal quantities of enantiomers... 

Alkyl group (Section 2.13) Structural unit related to an alkane by replacing one of the hydrogens by a potential point of attachment to some other atom or group. The general symbol for an alkyl group is R —. 

The five processes are not really independent. This is well illustrated in Fig. 2. The symbols I, II, III, IV, V under each group of isomers give the number of Berry steps needed to reach them from 12, considered as the starting isomer. However, if one performs one P2 step, it is easy to convince oneself that one reaches also the six isomers of group 11 For this reason the symbols I, III,... etc., refer also to the index of the process needed to reach the corresponding groups in one step. The only difference is that multiple steps allow for a wider variety of paths, because one can come back to the starting point. 

Figure 4.12 (left). The hardness data is grouped by stamp, (right). By subtracting the weight-dependent portion of the hardness, the residuals are seen to cluster much more closely, particularly for those stamps marked with arrows. Because of the limited hardness resolution (0.1 kg), the symbols for two or more data points can overlap. The vertical bar indicates sfj. 

To state the existence of individual, finite atom groups, 2, can be set in front of the symbol. For their further specification, the following less popular symbols may be used ... 

Figures 3.8 and 3.9 list point group symbols and illustrate them by geometric figures. In addition to the short Hermann-Mauguin symbols the Schoenflies symbols are also listed. Full Hermann-Mauguin symbols for some point groups are ...

Every space group listed in the family tree corresponds to a structure. Since the space group symbol itself states only symmetry, and gives no information about the atomic positions, additional information concerning these is necessary for every member of the family tree (Wyckoff symbol, site symmetry, atomic coordinates). The value of information of a tree is rather restricted without these data. In simple cases the data can be included in the family tree in more complicated cases an additional table is convenient. The following examples show how specifications can be made for the site occupations. Because they are more informative, it is advisable to label the space groups with their full Hermann-Mauguin symbols. 

Note that dj2 is the short notation for d7l2 2 2, as it appears in the cubic point groups (Appendix VII). Similarly, fti, fxtj and are the abbreviated symbols for... 

We would be remiss if we did not indicate that some authors have defined yet another Thiele-type modulus ( ) for this problem as <. = 0s/3 and they have developed their analysis according to this parameter. In using plots of f] versus S9 one must be careful to determine which of the two alternative definitions has been adopted for s. Otherwise his value for rj may be considerably in error. A variety of other symbols for dimensionless groups akin to the Thiele modulus have been employed by different authors. 

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