Site symmetry effects

The observed fiioulder in P3 of ClFg at 877 cm was explained to be due to C1 and C1 isotope shift, which is calculated to equal 12.S cm, compared to the observed split of 13 cm 3S,37) Qn the other hand, the observed splitting in P4 of BrFgAsFg does not seem to be due to Br, Br isotopes, since the observed value is larger than 2 cm, which is the calculated one. It is therefore assumed to result from crystal field or site symmetry effects ). 

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. 

For nuclei that have perfect cubic site symmetry (e.g., those in an ideal rock salt, diamond, or ZB lattice) the EFG is zero by symmetry. However, defects, either charged or uncharged, can lead to non-zero EFG values in nominally cubic lattices. The gradient resulting from a defect having a point charge (e.g., a substitutional defect not isovalent with the host lattice) is not simply the quantity calculated from simple electrostatics, however. It is effectively amplified by factors up to 100 or more by the Sternheimer antishielding factor [25],... 

The IR spectra of orthovanadates with trivalent cations are also well known as seen in Table 3 59, 60). In the IR spectra of the orthovanadates from Ce to Gd only one band less is observed as predicted and in no case is the vn band observed to split. On the contrary, for LaV04 more bands appear than are predicted from site symmetry rules due to strong correlation field effects. For the same reasons the Raman spectrum of this compound is difficult to interpret 60). 

The heavy alkali molybdates and -tungstates are known to exist in an orthorhombic modification as well, having the space group D h, Z =4) (55). The IR and Raman data 84), reproduced in Table 9, show clearly that vi and vz appear in the spectra for all these substances and that vz and vi are spht into three bands in the Raman effect. These comply for the most part with the simple site symmetry treatment where the anion has Cs S5nnmetry. 

More quantitatively, the effect of the thermal motion follows from the anharmonic thermal motion formalisms discussed in chapter 2. In the bcc structure, the relevant nonzero anharmonic term in the one-particle potential is the anisotropic, cubic site-symmetry allowed, part of uJuku um in expression (2.39). The modified potential for the cubic sites is given by (Willis 1969, Willis and Pryor 1975)... 

Investigate the effect of spin-orbit coupling on the crystal-field levels of a Ce3+ ion substituting for Ca2 + in CaF2 with a nearest-neighbor O2 ion (see Problem 7.2). Is any further splitting of these levels to be expected if the site symmetry at Ce3+ is lowered to Cs by a further crystal-field perturbation that is weaker than //s.i. ... 

One of plausible candidates for the entropy source is a dynamic structural disorder in the HS phase, which should be settled down in the LS phase. The crystallographic data for [Mn(taa)] [11] provide a clue, i.e., the presence of C3 axis in the HS molecule. An Mn(III) ion in the 5E state is a well-known Jahn-Teller ion [19]. Since the C3 site-symmetry cannot lift the orbital degeneracy of the 5E term (Fig. 1(b)), it is likely that the Mn ion is subjected to the E e Jahn-Teller effect, which gives rise to three energetically equivalent deformation structures. The apparent C3 symmetry should be observed in a time-averaged structure over three deformed structures. 

When S > 1/2 and the metal site symmetry is lower than Oh or Td, there is a term in the spin Hamiltonian, in addition to the Zeeman term (gfill), that will split the (2S + 1 )MS spin degeneracy even in the absence of a magnetic field.32 This is shown in Equation 1.8, where D in the first term describes the effect of an axial distortion of the ligand field (z / x y) and E in the second term accounts for the presence of a rhombic ligand field y). 

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