Schonflies

Magnetic ordering, 746 Magnetic point groups, 738, 739 international notation, 739 properties of, 740 Schonflies notation, 739 Shubnikov notation, 739 Magnetic point symmetry, determination of, 744... 

Scattering processes, 586 Schiff, L. J., 437,444 Schiffer, M.% 363 SchUchting, H., 24 Schmidt orthogonalization, 65 Schonflies notation for magnetic point groups, 739... 

Arthur Moritz SchOnflies, German mathematician (1853-1928). The SchOnflies symbols are employed io spectroscopic applications, while in crystallography the international, or Hennann-Maugiur) notation is used. 

The SchOnflies notation for this operation is i, although the circumflex is... 

Schonflies notation is widely used to describe molecules or assemblages of atoms (polyhedron) such as the local environment of an atom. Thus, it is widely used to describe the symmetry of structural sites. It is a more compact notation but less complete than the Hermann-Mauguin notation. It consists generally of one capital letter, followed by one subscript number and one final letter. 

In the top row are these entries In the upper left comer is the Schonflies symbol for the group. Then, along the top row of the main body of the table, are listed the elements of the group, gathered into classes the notation is the kind explained in Section 3.13. 

Second, there are five rotoinversion operations, symbolized 1, 2, 3, 4, and 6. We need to examine these more closely to see how they relate to the Schonflies symbols 5, m, and / (where it is well to recall that m = Sx and / s S2). 

Let us now look more closely at these 32 point groups, for each of which Table 11.3 gives both the familiar Schonflies symbol and the crystallographic one. For many of the simpler cases we have already discussed the basis for the crystallographic symbol, but it is worthwhile to do this for a few more. 

Number Schonflies Symbol Crystallographic Costal Symbol System ... 

Table 2.5. Abbreviated International symbols and Schonflies notation.

Schonflies symbol Full International symbol Abbreviated symbol... 

In each column, the symbol for the point group is given in International notation on the left and in Schonflies notation on the right. When n = 2, the International symbol for D2h is mmm. When n is odd, the International symbol for C v is nm, and when n is even it is nmm. Note that n = n/2. In addition to these groups, which are either a proper point group P, or formed from P, there are the three cyclic groups 1 or Ci = E, 1 or Q = EI, and morCs = E a. ... 

Table 2.9. The thirty-two crystallographic point groups in both International and Schonflies notation.

List a sufficient number of symmetry elements in the molecules sketched in Figure 2.21 to enable you to identify the point group to which each belongs. Give the point group symbol in both Schonflies and International notation. 

Underlines in the International notation for G show which operators are complementary ones. Alternatively, these may be identified from the classes of G H by multiplying each operator by 0 G is the ordinary crystallographic point group from which G was constructed by eq. (14.1.2) H is given first in International notation and then in Schonflies notation, in square brackets. Subscript a denotes the unit vector along [1 1 0]. 

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