Shubnikov groups

Shannon, C. E., 190,195,219,220,242 Shapley, L. S316 Skirokovski, V. P., 768 Shortley, O. H., 404 Shot noise process, 169 Shubnikov, A. V., 726 Shubnikov groups, 726 Shubnikov notation for magnetic point groups, 739 Siebert, W. M., 170 Signum function, 313 Similar matrices, 68 Simon, A408 Simplex method, 292 Simulation, 317... 

The matrices Mjg and phases can be deduced from the relations between the Fourier coefficients and atomic basis functions [Equation (54)]. The matrices Mp correspond, in the case of commensurate magnetic structures, to the rotational parts of the magnetic Shubnikov group acting on magnetic moments. 

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... 

Cracknell, A. P. (1968) Crystal field theory and the Shubnikov point groups. Adv. Phys. 17, 367-420. 

Shubnikov, A. V. and Belov, N. V. (1964) Colored Symmetry. Oxford Pergamon Press. Stokes, H. T. and Hatch, D.M. (1988) Isotropy Subgroups of the 230 Crystallographic Space Groups. Singapore World Scientific. 

Pierre Curie suggested a broad application of the term dissymmetry. He called a crystal dissymmetric in case of the absence of those elements of symmetry upon which depends the existence of one or another physical property in that crystal. In Pierre Curie s original words Dissymmetry creates the phenomenon ( C est la dissymetrie qui cree le phenomene ) [51], Namely, a phenomenon exists and is observable due to dissymmetry, i.e., due to the absence of some symmetry elements from the system. Finally, Shubnikov called dissymmetry the falling out of one or another element of symmetry from a given group [52], He argued that to speak of the absence of elements of symmetry makes sense only when these symmetry elements are present in some other structures. 

Figure 9-22. The crystal structure of the rock salt after Shubnikov and Koptsik [32], (a) A unit cell (b) Projection of the structure along the edges of the unit cell onto a horizontal plane (c) Projection of some symmetry elements of the Fm3m space group onto the same plane. The vertical screw axes 2 and 42 are marked by their respective symbols. Used with permission.

By expressing the twin laws through the Shubnikov s two-color group notation (in which the twin elements are dashed Curien and Le Corre 1958), the three twin laws are 6 2 2 6 m l, 3T2//w. The complete twin [i.e. twin by merohedry or reticular... 

Shubnikov and Koptsik [8-2] have analyzed the influence of the various space groups of bands and networks on people s perception of movement. A one-sided band decoration without a polar axis induces no feeling of movement. The vertical synunetry planes of the fence and wall in Figure 8-36 act as if preventing motion. On the other hand, the bands with polar axes in Figure 8-37 act as if inducing left-bound (top) and right-bound (middle) movement. 

Shubnikov (Magnetic) Group Point Group Spatial Group... 

In the Schdnflies notation we denote this magnetic group as G H). The corresponding notations in the Shubnikov system and in the international system are also used [58]. 

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