Crystal field parameters estimation

The problem of estimating crystal field parameters can be solved by considering the CFT/LFT as a special case of the effective Hamiltonian theory for one group of electrons of the whole A -electronic system in the presence of other groups of electrons. The standard CFT ignores all electrons outside the d-shell and takes into account only the symmetry of the external field and the electron-electron interaction inside the d-shell. The sequential deduction of the effective Hamiltonian for the d-shell, carried out in the work [133] is based on representation of the wave function of TMC as an antisymmetrized product of group functions of d-electrons and other (valence) electrons of a complex. This allows to express the CFT s (LFT s or AOM s) parameters through characteristics of electronic structure of the environment of the metal ion. Further we shall characterize the effective Hamiltonian of crystal field (EHCF) method and its numerical results. 

Within the estimated uncertainties, table 7 shows that a common set of intrinsic parameters for k = 6 can be found which describes all samples studied there. One remarkable difference is observed only in the case of B (Rq ) for LaOCl Pr3+. However, this difference was caused simply by the use of different data sets in the determination of the crystal-field parameters. 

A major difference between the 5d and 4f orbitals is that the 5d crystal-field strength remains relatively constant across the lanthanide series. This means that it is usually possible to get a good estimate of the 5d crystal-field parameters from the Ce3+ spectrum, though fine-tuning will be necessary. Sometimes it is possible to determine 5d crystal field parameters directly from the 4f 15d spectra, as was done by Laroche et al. (2000) for LiYF Pr3"1". However, values of the 5d crystal field parameters may most easily be determined from examination of the Ce3+ spectra, values which can then be applied to ions across the lanthanide series. 

The reflectance spectrum of Ni2Si04 spinel contains intense bands with absorption maxima of 9,150 cm-1, 14,780 cm-1 and 22,550 cm-1 at atmospheric pressure (Yagi and Mao, 1977). These led to initial estimates of the crystal field parameters for Ni2+ in silicate spinel of A0 = 9.,150 cm-1 and CFSE = 10,980 cm-1. However, there is also a prominent shoulder in the reflectance spectra around 8,000 cm-1 attributable to trigonal distortion of the octahedral site in the spinel structure (Bums, 1985a). This led to revised estimates for Ni2+ in Ni2Si04 spinel of... 

Before discussing the dominant Fe2+/M2 site crystal field spectra of pyroxenes, it is necessary to identify the locations of absorption bands originating from Fe2+ ions in the less distorted Ml sites. Crystal field spectra of stoichiometric hedenbergite, CaFeSi206, consist of two broad bands centred at 10,200 cm-1 and 8,475 cm-1 (Rossman, 1980 Straub et al., 1991), from which the crystal field parameters are estimated to be... 

Chlorites have been studied spectroscopically mainly on account of Fe2+- Fe3+ IVCT bands near 14,300 cm-1 that contribute to their optical spectra (e.g., White and Keester, 1966 Faye, 1968b Smith and Strens, 1976 Smith, 1977). Two other bands centred near 11,500 cm-1 and 9,500 cm-1 provide estimates for the crystal field parameters of Fe2+ ions in chlorite of A0 = 11,200 cm-1 and CFSE = 4,300 cm-1. Crystal spectra of Cr3+-bearing chlorite, kammererite, yield absorption bands at 18,450 cm-1 and 25,000 cm-1, giving A0 = 18,450 cm-1 and a CFSE of 22,140 cm-1 for octahedrally coordinated Cr3+ ions surrounded by OH- ions in the brucite sheets. The spectra of other Cr3+-bearing clay silicates have been described (Calas et al., 1984), including clinochlore and stichtite. 

Chapter 5 summarizes the crystal field spectra of transition metal ions in common rock-forming minerals and important structure-types that may occur in the Earth s interior. Peak positions and crystal field parameters for the cations in several mineral groups are tabulated. The spectra of ferromagnesian silicates are described in detail and correlated with the symmetries and distortions of the Fe2+ coordination environments in the crystal structures. Estimates are made of the CFSE s provided by each coordination site accommodating the Fe2+ ions. Crystal field splitting parameters and stabilization energies for each of the transition metal ions, which are derived from visible to near-infrared spectra of oxides and silicates, are also tabulated. The CFSE data are used in later chapters to explain the crystal chemistry, thermodynamic properties and geochemical distributions of the first-series transition elements. 

Finally, the highest valence state reported for plutonium in a non-oxygen-containing compound is exemplified in PuFe whose optical spectrum has been shown to be extremely complex (39). Estimated free-ion. Table V, and ligand-field parameters used in the present analysis are consistent with those reported earlier (44), but differ considerably from the free-ion parameters developed by Boring and Hecht (45) whose values for F and F would appear to us to be distorted. The crystal-field parameters characteristic of NpFe, Table VII, should represent a good basis for estimating the similar interaction in PuFe Our results are summarized in Fig. 10. 

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). 

Rhodium and Iridium.—Ford16 has discussed the deficiencies of the ligand-field model for d9 systems14 when applied to RhUI photochemistry. In particular he criticizes (i) the neglect of possible variations in the efficiency of radiationless processes in estimating the relative quantum yields for the reactions of the photo-excited states and (ii) the use of crystal-field parameters derived from the ground-state configuration. 

From the 7/ = 0 critical temperature, the T = 0 critical field, and the spin-canting angle a at the critical field, Bjerrum-Moller et al. (1977) derived estimates for the nearest- and next-nearest neighbor exchange constants, = —3 x 10" meV and Jnnn = 1.3 X 10 meV, and the cubic crystal-field parameter B4 = 4 x 10 meV. 

Magnetocrystalline energies, (Vc)ioo (V Jni and < Vc)ioo-(V"c)no. can be derived from magnetization measurements in the ferromagnetic state, and from these the crystal-field parameters can also be estimated. 

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