Crystal field splitting evaluation

As a last remark, it should be mentioned that also a few evaluations of the crystal-field parameters of Pr3"1" in LaCH in the scope of the angular overlap model have been made. Urland et al. (1985) andUrland (1989) used the angular overlap model to calculate the crystal-field splittings of LaCHiPr3"1" under pressure. In addition, Gregorian et al. (1989) derived the parameters of both models and found that both approaches were capable to successfully describe the high-pressure results. 

Evaluation of A Energy separations between resolved 3d orbital energy levels correspond to visible and near-infrared radiation. Measurements of absorption spectra of transition metal compounds and minerals are used to obtain A and to evaluate the CFSE of the ions. Crystal field splittings may also be estimated from plots of thermodynamic data for the first-series transition metal compounds. The magnitude of A depends on ... 

TABLE 3 Hole effective masses (mo) of wurtzite GaN and AIN. The superscripts L and stand for the perpendicular and parallel to the kz direction, respectively. m h denotes the density of states effective mass, which is evaluated according to m h = (nrjmn)13. HH, LH and CH denote heavy, light and crystal-field split-off hole masses, respectively. 

However, as we have already pointed out, the value of Sgg — t2g is quite insensitive to the electronic configuration (2). Therefore, in the present paper, we approximated all of these effective crystal-field splittings by the value of eg — t2g Calculated in the ground state. On the other hand, the Racah parameters represent the electron-electron repulsion interaction and can be calculated by the radial part of the pure 3d atomic orbitals of the impurity chromium ion (1). After evaluating the value of these parameters, the multiplet structure of ruby can be obtained by diagonalizing the Tanabe-Sugemo matrices. 

In the crystalline regions, the chain is a planar zig-zag with all trans placements at the C-C bonds. In the common crystal form, with an orthorhombic unit cell, there are two CH -CH groups per unit cell. Crystal field splitting, as at 733/721 and 1460/1475 cm , is directly an effect of the crystal, and not just the preferred conformation of a single chain. This offers a solution for the evaluation of the relative crystallinity of materials. 

For the pseudo-tetragonally elongated Ml octahedral site in the olivine structure, an alternative method for obtaining the CFSE of Fe2+ ions in this site is to evaluate the ligand field splitting parameters in the equatorial plane and along the axial direction using eqs (3.14) to (3.16). The crystal field spectral data for the fayalite Ml site (see fig. 5.11a) yield values for 10 Dq(m) and 10 Dq(eq) of 8,172 cm-1 and 9,327 cm-1, respectively. The mean 10 Dq value of 8,942 cm-1 and the CFSE of 4,133 cm-1 compare favourably with A0 = 8,830 cm-1 and CFSE = 4,250 cm-1 for Fe2+ in the fayalite Ml sites determined by the baricentric method (fig. 5.11a). 

The splitting of other atomic terms due to the crystal field potential of the given symmetry (group) can be evaluated in an analogous way [9]. The results for octahedral and tetrahedral fields are collected in Table 8.16. 

Detailed ENDOR measurements have been made by Chan and Hutchison (1972) on LaClj doped with samarium, oihanced in the two odd-neutron isotopes 147,149 (both 1 = j). The energies of the two low-lying doublet levels of J = f, split by the crystal field, as well as the splitting of the J = 1 manifold, have been determined by optical spectroscopy (Varsanyi and Dieke 1961, Magno and Dieke 1962). Also, the size of the 7-mixing (Axe and Dieke 1962) was evaluated from these measurements. The ENDOR experiments determine the net hyperfine interactions in the lowest doublet, together with the effective nuclear Zeeman interaction, the tensor... 

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