Site Symmetry for the

The various possible site symmetries for the different point groups have been tabulated in several places 3, 19—21). The necessary correlation tables between point and site groups, which are used in discussions of the examples in this text are assembled in the Appendix. 

The IR spectrum of Ba3[BN2]2 shows low site symmetry for the BN23 groups.68 Vibrational data for Eu3[BN2]2, however, were interpreted in terms of discrete BN23- units of D jh symmetry.69 IR data were reported for a 1,3,2-oxazaborolidine dimer derived from (V)-a,a-diphenylprolinol.70 The IR and Raman spectra of the new adduct P8012.2BH3 included vPB at 565 cm-1 (IR), 574 cm-1 (Raman), as well as characteristic vBH bands.71 High-pressure Raman spectroscopy was used to follow pressure-induced phase transitions for B12As2.72... 

If it is assumed that the TDDs are oriented preferentially along a <110> axis, with a C2V site symmetry, the piezospectroscopic results can be explained satisfactorily on the basis of the stress-induced line shifts and polarizations calculated by Kaplyanskii [73], which are discussed in the next section. This led to propose the C2V site symmetry for the TDDs in silicon [137]. In expression (8.15), the non-zero components of the piezospectroscopic tensor for C2v centres, labelled as orthorhombic (or rhombic) I, are Axx (A2), Ayy (A2), Azz Wi) and Axy = Ayx (A3). These orthorhombic I centres have a C2 symmetry axis in the <100> direction and the 1 s —> 2po transitions have their transition dipole moment oriented along this axis for a Is state constructed from a pair of valleys along this axis, while the Is —> 2p transitions have their transition dipole moment oriented in a plane perpendicular to this axis. In a cubic crystal, a C2V centre has a sixfold orientational degeneracy represented by the six diagonals of a cube (see Fig. 8.16a). 

The pressure dependence of the Raman-active vibron modes (Figs. 11(a) and 11(b)) was studied on unloading at 300 K in new phases. 1-N2 exhibits typical behavior for such molecular crystals branching of vibrational modes and increasing of separation between them with pressure due to increasing intermolecular interactions. All of the vibrational modes originate from the same center, which is close to the frequency of the V2 disk-like molecules in E-N2. Thus, the structure of the i phase is characterized by the presence of just one type of site symmetry for the molecules and the large number of vibrational modes arises from a unit... 

The tables of site symmetry for the 230 space groups shown below were reproduced with permission from the book of J. R. Ferraro and J. S. Ziomek (Ref. 9 of Chapter 1). The number in front of the point group notation represents the number of distinct sets of sites, and those in parentheses indicates the number of equivalent sites for each distinct set. Since the number of sites for C, (p = 1, 2, 3,. ..) and is infinite, no coefficients are given in front of these point group notations. 

The bond site symmetry for the B atom is C. The non-vanishing elements will be associated with symmetry species A (x and z) and A" (y). The polar tensor of atom B has the form... 

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