Symmetry in crystal structures

Application of space group symmetry in crystal structure determination... 

Piezoelectricity is a physical effect exhibited by crystals that are electrically neutral, but that do not have a center of reflective symmetry in crystal structure. The essential property of a point of reflective symmetry is that for each atomic position in the crystal lattice there is a matching atomic position at a point that is directly opposite the first with respect to the point of symmetry this second position is at a same distance from the point of symmetry as the first. For example, the face-centered cubic structure has a point of reflective symmetry at the geometrical center of the unit cell whereas the cubic zinc blende structure does not have a center of symmetry. 

Considerations of complementarity in molecular packing culminated in the works of Kitaigorodskii. His most important contribution was the prediction that three-dimensional space groups of lower symmetry should be much more frequent than those of higher symmetry among crystal structures. This was a prediction at a time when few crystal structures had been determined experimentally. 

Such a set of interhelical parameters relates directly to the symmetry operations which are found in crystal structures. 

The most characteristic feature of any crystal is its symmetry. It not only serves to describe important aspects of a structure, but is also related to essential properties of a solid. For example, quartz crystals could not exhibit the piezoelectric effect if quartz did not have the appropriate symmetry this effect is the basis for the application of quartz in watches and electronic devices. BCnowIcdge of the crystal symmetry is also of fundamental importance in crystal structure analysis. 

Figure 4 Relationship of donor and acceptor stacks in crystal structure of (HMTSF)(TCNQ) showing shared planes of symmetry between donor and acceptor stacks...

Pseudosymmetry creates some of the most difficult problems in crystal structure work. The pseudo-symmetric crystal may be a true single crystal with small deviations from a higher symmetry (case 1) or (case 2) a twin producing a symmetrized structure (3) with a simulated higher symmetry. In both cases, the true structure of low symmetry [H-structure (3, 11)] may give the same reflections with only slight intensity variations (a), or additional reflections (b) exist which are weak, so... 

The English physicist William Barlow began as a London business man later he became interested in crystal structures and devoted his life to that study. In 1894, he published his findings of the 230 space groups. It is amazing that from consideration of symmetry three scientists in different countries arrived at the 230 space groups of crystals at about this time. Barlow then worked with ideas of close packing. He pictured the atoms in a crystal as spheres, which, under the influence... 

The JT origin of structural phase transitions in crystals with JT centers was realized at very early stages of the study of the JT effect. It is obvious that the interaction of JT local distortions in crystals, as mentioned above, under certain conditions, at temperatures T0 in equation (1) may lead to their ordering resulting in crystal structures of lower symmetry (cooperative JT effect for review see Ref. [8]). 

Mossbauer spectrum, the positions and separations of which depend on the oxidation state, electronic configuration, magnetic ordering, coordination number and symmetry of the iron atoms in a mineral structure. Computed peak areas enable Fe3+/Fe2+ ratios and site populations of Fe2+ ions in crystal structures to be readily determined for several minerals without interference from coexisting Mn, Cr and other transition elements. 

In the normal alkanes (Table 31) one finds the alternation of the increase of melting point also well known in the fatty acids. This is a consequence of the difference in crystal structure of even and odd molecules resulting from a difference in symmetry (centre or plane through the middle). 

The conversion of antiprismatic conformation into a dodecahedron arrangement involves a small spatial rearrangement and hence it is not easy to decide which idealized geometry to choose in crystal structures for which the shape of the polyhedron is not certainly fixed by elements of symmetry. 

Hydration water molecules indicate substrate-binding sites. In crystal structures of native proteins, the active sites are usually hydrated if they are not in direct contact with symmetry-related protein molecules. Since the substrates or inhibitors are recognized by the protein and bound to its active site by hydrogen bonds and/or by insertion of hydrophobic residues into hydrophobic pockets, it is not surprising to find, in the native protein, water associated in positions which are the... 

Symmetry operation A symmetry operation or a series of symmetry operations converts an object into an exact replica of itself. In crystal structures, the possible symmetry operations are axes of rotation and rotatory inversion, screw axes, and glide planes, as well as lattice translations. Proper operations, which convert an object into a replica of itself, are translation and rotation. Improper operations, which convert an object into the mirror image of its replica, are reflection and inversion. 

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