Second-order crystal-field parameters

Russian workers have been active recently in this field. Thus [Eu(thenoyltrifluoro-acetate)3(phen)] has been shown to retain its structure in polystyrene or PVC 298 the second order crystal field parameters ° and have been obtained for a series of complexes [EuL phen)] where L was a series of eight /S-diketonates,299 and the temperature broadening has been investigated, for similar adducts and for EuL2(N03)(Ph3P0)2, of the Stark components of the 1F levels.300... 

The quantities eqlf and rjlat are related to the second-order crystal-field parameter B (n = 2) by... 

The magnetocrystalline anisotropy calculated for a variety of combinations of crystal field parameters is shown in Fig. 24. It is noted that the second order crystal field term and the exchange term are the most dominant parameters. 

In a seminal contribution, Bleaney demonstrated that when the crystal-field splitting of the ground multiplet is smaller or comparable to kT, a situation often met with lanthanide complexes, the anisotropic part of the axial paramagnetic susceptibility tensor originates from second-order effects and can be simply estimated by the product of magnetic constants Cj, characteristics of the electronic configuration of each lanthanide (i.e., Bleaney factor), multiplied by the second-rank crystal-field parameter Bq (Eq. (34), Bleaney, 1972). 

The determination of the sixth-order crystal-field parameters for Gd + is really problematic, because none of the levels which can be determined by spectroscopic measurements have sufficiently high values for the IT reduced matrix element. The crystal-field splitting is in a good approximation determined by the second- and fourth-rank parameters only. 

A new treatment for S = 7/2 systems has been undertaken by Rast and coworkers [78, 79]. They assume that in complexes with ligands like DTPA, the crystal field symmetry for Gd3+ produces a static ZFS, and construct a spin Hamiltonian that explicitly considers the random rotational motion of the molecular complex. They identify a magnitude for this static ZFS, called a2, and a correlation time for the rotational motion, called rr. They also construct a dynamic or transient ZFS with a simple correlation function of the form (BT)2 e t/TV. Analyzing the two Hamiltonians (Rast s and HL), it can be shown that at the level of second order, Rast s parameter a2 is exactly equivalent to the parameter A. The method has been applied to the analysis of the frequency dependence of the line width (ABpp) of GdDTPA. These results are compared to a HL treatment by Clarkson et al. in Table 2. 

Gallium ( Ga) (/=3/2). Gallium was for the first time incorporated into the crystal structure of a mesoporous MFI zeolite. The Ga contents correspond to molar ratios of Si/Ga = 43 and 38 for the conventional and mesoporous Ga-MFI, respectively. The Ga isotropic chemical shift and second-order quadrupolar effect parameter was reported for tetrahedral Ga incorporated in the MFI structure and absorbed water molecules had an important impact on the Ga electric field gradients and thereby on the quantitative evaluation of the Ga MAS NMR... 

The above rules for an extraction of the 5 crystal-field parameters directly from experimental data caimot be applied for most symmetries to J levels for which J >1, because of the presence of a large number of off-diagonal matrix elements. Every level is in this case a function of at least three parameters. It is more difficult to determine the parameters than the second- or fourth-rank parameters. One can first determine the parameter and subsequently the 5 parameters 0). In the end both and 5 are varied in order to remove discrepancies. An alternative approach is to restrict 5 /5g to the PCEM ratio, because in this way only one sixth-rank parameter will remain. 

Two of the most important nonlinear optical (NLO) processess, electro-optic switching and second harmonic generation, are second order effects. As such, they occur in materials consisting of noncentrosymmetrically arranged molecular subunits whose polarizability contains a second order dependence on electric fields. Excluding the special cases of noncentrosymmetric but nonpolar crystals, which would be nearly impossible to design from first principles, the rational fabrication of an optimal material would result from the simultaneous maximization of the molecular second order coefficients (first hyperpolarizabilities, p) and the polar order parameters of the assembly of subunits. (1)... 

Second, the octahedral crystal field splitting parameters, values of which are higher for smaller sites, are expected to decrease in the same order as eq. 

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