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Symmetry point

The most important materials among nonlinear dielectrics are ferroelectrics which can exhibit a spontaneous polarization PI in the absence of an external electric field and which can spHt into spontaneously polarized regions known as domains (5). It is evident that in the ferroelectric the domain states differ in orientation of spontaneous electric polarization, which are in equiUbrium thermodynamically, and that the ferroelectric character is estabUshed when one domain state can be transformed to another by a suitably directed external electric field (6). It is the reorientabiUty of the domain state polarizations that distinguishes ferroelectrics as a subgroup of materials from the 10-polar-point symmetry group of pyroelectric crystals (7—9). [Pg.202]

Hmktsjonmetrisch, a. of or pertaining to point symmetry, point-symmetrical, punktuell, a. (Optica) point-focal. [Pg.350]

Magnetic crystals determination of magnetic point symmetry, 744... [Pg.777]

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... [Pg.777]

Stable Mn(HI) compounds, Mn(R2r fc)3, have been known for a long time (42, 46). The structure of Mn(Et2C tc)3 is elucidated (47). The inner geometry of the Mn(CS2)3 core does not conform to the usual D3 point symmetry of transition metal complexes of this type, but shows a strong distortion attributed to the Jahn-Teller effect. The electronic spectrum (48, 49) and the magnetic properties of this type of complexes are well studied (50). [Pg.95]

Table 4 Symmetry operations used (o describe the point symmetry of a rigid"... [Pg.100]

The orange, air-stable, homoleptic tetrakis( 71-phosphabenzene)nickel (1046) is tetrahedral (point symmetry 54) and can be obtained from phosphabenzene and [Ni(cod)2].2 25 It features a short Ni—P bond length of 2.1274(5) A with considerable N i P 7r-backbonding and a i/(Ni—P) stretch at 168 cm-1. In solution, partial dissociation of one phosphabenzene ligand is observed. 2-Diphenylphosphino-3-methylphosphinine forms with [Ni(cod)2] in the presence of the CO the dinuclear complex (1047) with a W-frame structure.2526... [Pg.506]

Several studies have addressed the cubic NLO properties of salts of heteropolymolybdate/ tungstate cluster anions.360,557-561 The tetraanion in a-H4SiW12O40,4HMPA,2H2O (HMPA= hexamethylphosphoramide) has a Keggin structure which has idealized Td point symmetry... [Pg.666]

Table 1.2 Non-vanishing crystal field terms (Stevens formalism) for common lanthanide point symmetries. Table 1.2 Non-vanishing crystal field terms (Stevens formalism) for common lanthanide point symmetries.
In much the same way as Stevens operators, the summation in Equation 1.15 is limited to well-defined values for f-electrons, the restriction k <7 holds, while q is limited to those values consistent with the point symmetry of the site. Finally, the even part k = 0, 2,4,6) is responsible for the CF splitting, while the odd part k = 1,3, 5,7) is responsible for the intensity of induced electric dipole transitions in optical spectroscopy [5b, 26]. [Pg.13]

It is evident that the approach described so far to derive the electronic structure of lanthanide ions, based on perturbation theory, requires a large number of parameters to be determined. While state-of-the-art ab initio calculation procedures, based on complete active space self consistent field (CASSCF) approach, are reaching an extremely high degree of accuracy [34-37], the CF approach remains widely used, especially in spectroscopic studies. However, for low point symmetry, such as those commonly observed in molecular complexes, the number of CF... [Pg.15]

Taking into account that Bq parameters represent the coefficient of an operator related to the spherical harmonic ykq then the ranges of k and q are limited to a maximum of 27 parameters (26 independent) Bq with k = 2,4,6 and q = 0,1,. .., k. The B°k values are real and the rest are complex. Due to the invariance of the CF Hamiltonian under the operations of the symmetry groups, the number of parameters is also limited by the point symmetry of the lanthanide site. Notice that for some groups, the number of parameters will depend on the choice of axes. In Table 2.1, the effect of site symmetry is illustrated for some common ion site symmetries. [Pg.30]

N Is the number of molecules per unit volume (packing density factor), fv Is a Lorentz local field correction at frequency v(fv= [(nv)2 + 2]/3, v = u) or 2u). Although generally admitted, this type of local field correction Is an approximation vdilch certainly deserves further Investigation. IJK (resp Ijk) are axis denominations of the crystalline (resp. molecular) reference frames, n(g) Is the number of equivalent positions In the unit cell for the crystal point symmetry group g bjjj, crystalline nonlinearity per molecule, has been recently Introduced 0.4) to get general expressions, lndependant of the actual number of molecules within the unit cell (possibly a (sub) multiple of n(g)). [Pg.83]

Crystal lattices can be depicted not only by the lattice translation defined in Eq. (7.2), but also by the performance of various point symmetry operations. A symmetry operation is defined as an operation that moves the system into a new configuration that is equivalent to and indistinguishable from the original one. A symmetry element is a point, line, or plane with respect to which a symmetry operation is performed. The complete ensemble of symmetry operations that define the spatial properties of a molecule or its crystal are referred to as its group. In addition to the fundamental symmetry operations associated with molecular species that define the point group of the molecule, there are additional symmetry operations necessary to define the space group of its crystal. These will only be briefly outlined here, but additional information on molecular symmetry [10] and solid-state symmetry [11] is available. [Pg.189]

The relationship of the wheel-rim-type structure of 62 to the metal can be demonstrated by a 30° rotation of the two centered Alg rings followed by a shift of the six rings towards each other (cf. Figure 2.3-13) [92], The other possibility of the formation of an Al14 polyhedron with point symmetry by displacement of the two naked central atoms in the direction of a polyhedral entity has been shown to be energetically unfavorable by quantum chemical calculations i.e., the observed metalloid structure (Figure 2.3-13) is favored over the anticipated polyhedral structure as described by Wade-Mingos [5, 96] (see Chapter 1.1.2). [Pg.146]

In concluding this section in which some properties of modulated structures and of quasicrystals have been considered, we underline that the characteristics of these two types of structures do not coincide. Incommensurately modulated structures show main and satellite diffractions, an average structure and crystallographic point symmetry. The quasicrystals have no average structure, non-crystallographic point symmetry, and give one kind of diffraction only. [Pg.200]

We shall illustrate the principle here using four examples of centrosymmetric crystals (/ ,S)-serine (45,78), W-acetylvaline, glycine (47), and glyclygly-cine (79). All four crystal structures appear in monoclinic symmetry (point symmetry Urn). [Pg.42]

S)-Serine forms tabular crystals with point symmetry 2hn (Figure 22a) the crystals affected by either (/ )- or (S)-thr exhibit reduced morphological symmetry 2 (the mirror plane is lost) and are enantiomorphous (Figure 22b, c). When (R,S)-thr is used as the additive, the morphological symmetry 2/m is left unchanged because the effects induced by each additive separately combine. The crystals turn into rhombs, with a clear increase in the areas of the 011 side faces relative to those of the pure crystals (Figure 22d) (45, 78). [Pg.42]

Noncentrosymmetric achiral crystals of monoclinic point symmetry m and of orthorhombic point symmetry mm2 are also appropriate for determination of the absolute configuration of chiral resolved additives. For the point group m, only the left or right halves of Schemes 13a are relevant. In such an arrangement,... [Pg.55]

The monoclinic point symmetry 2 comprises a twofold axis and applies to the commonly observed monoclinic chiral space groups P2X and C2. [Pg.81]

The monoclinic point symmetry 2lm is the combination of a twofold axis and a mirror plane perpendicular to it. This combination automatically generates a center of inversion T at their intersection. This point symmetry applies to all centrosymmetric monoclinic crystals of such space groups as P2xla, P2Ja, and C2/c. [Pg.81]

Orthorhombic symmetry mm2 comprises two mirror planes perpendicular to each other, which automatically generates a twofold axis along the line of intersection. This point symmetry applies to all noncentrosymmetric orthorhombic crystals that have mirror or glide planes such as those of space groups Pna2t and Pca2,. [Pg.81]


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