Seitz operator

The space group G of a crystal is the set of all symmetry operators that leave the appearance of the crystal pattern unchanged from what it was before the operation. The most general kind of space-group operator (called a Seitz operator) consists of a point operator R (that is, a proper or improper rotation that leaves at least one point invariant) followed by a translation v. For historical reasons the Seitz operator is usually written R v. However, we shall write it as (R ) to simplify the notation for sets of space-group operators. When a space-group operator acts on a position vector r, the vector is transformed into... 

When a Seitz operator acts on configuration space all functions defined in that space are transformed, and the rule for carrying out this transformation is the same as that for rotation... 

A symmetry operation can have both rotational and translational components, and is described in the Seitz notation as R s. The terms R and s are the rotational and translational parts of the 3d symmetry element, respectively, such that... 

BCC real-space lattices are completely determined by the condition that each inner vector, k, go over into another by all the symmetry operations. This is not the case for the tmncated octahedron. The surface of the Wigner-Seitz cell is only fixed at the truncating planes, not the octahedral planes. Nonetheless, the volume enclosed by the truncated octahedron is taken to be the first BZ for the FCC real-space lattice (Bouckaert et ak, 1936). The special high-symmetry points are shown in Table 4.5. 

Partial order has for its own a rich mathematical theory and there is a manifold of relations to combinatorics, graph theory and algebra. Even relations to experimental designs and variance analysis can be established. However, mathematicians like to find more structure for their objects to be studied. In that sense posets are poor, because there is only one binary operator, i.e., the <-relation. Comparing with the daily life example where we have addition and multiplication as binary operators the mathematical multitude in posets is somewhat restricted. Should this deficiency bother the applications This question can be answered with "yes" if the chapters of Kerber and of Seitz are examined. 

Bauch K-H, Seitz W, Forster S and Keil U (with co-operation from Anke M, Giirtler H, Hesse V, Hiltscher A, Knappe G, Korber R, Meng W, Deckart H, Thomas G and Ulrich FE) (1991) Die interdisziplinare Jodprophylaxe der ehemaligen DDR nach der deutschen Wiedetvereinigung und der Stellenwert des jodierten Paket-Speisesalzes fiir die Verbesserung der alimentdren Jodversorgung. Bin Ruck- und Ausblick. Z Ges Inn Med 46 615-620. 

The site groups G, for all q e Q are called maximal isotropy subgroups in [40]. The set Q in the Wigner-Seitz unit cell is determined in the same way as the set K in the BriUouin zone. However, the action of symmetry operations in the direct and reciprocal spaces is different. 

Here the densities nR iR) are defined inside the Wigner-Seitz cell at R, shown by hexagons in Fig. 1. The partial components riRiirR) are expressed in terms of the EMTO s and the EMTO path operator. ... 

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