Crystal intrinsic parameters

Bk(R) intrinsic crystal-field parameters HOMO Highest Occupied Molecular Orbital... 

Non-metallic rare-earth compounds studied under high pressure. In almost all cases the energy level shifts as a function of pressure have been determined. The second column gives details concerning the measurements and evaluations made. In particular the following abbreviations are used L Luminescence-, A Absorption-, E Excitation-, S Site-selective spectroscopy, O Other methods, EPC Electron-Phonon Coupling, Int Intensities, LT Lifetime, CFP Crystal-Field Parameters, FIP Free-Ion Parameters, IP Intrinsic Parameters, ET Energy Transfer... 

The quantities B (Rq) and are treated as adjustable parameters and Rq is a reference distance that can be chosen arbitrarily. In principle, the number of ligand shells considered for the calculation of intrinsic parameters is not limited, however, it is usually assumed that only the nearest neighbors of the rare-earth ion contribute significantly to the crystal-field potential. Thus, especially long-range interactions like electrostatic interactions are not accounted for explicitly. Because these interactions are most important for k = 2 parameters, in many cases only the k = 4, 6 intrinsic parameters have been considered. 

Intrinsic crystal-field parameters 4,6(Ro) fin cnl 1) and power law exponents r4 6 for chloride ligands for Pr3+... 

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. 

According to the superposition model the intrinsic parameters found for SrFCl Sm2+ were simply transferred to either CaFCl Sm2+ or BaFCl Sm2+. Then, combining the intrinsic parameters with crystal-field parameters gained from optical high pressure studies on CaFCl Sm2+... 

The intrinsic parameters discussed in the previous section open a practicable possibility to analyze the fundamental interactions occurring between the f-electrons and the ligands. In an ab initio calculation for the system Pr3+-Cl , Newman and Ng (1986) took into account five different mechanisms contributing to the intrinsic crystal-field parameters at various Pr3+-Cl distances. These were point charges, charge penetration, exchange, p and, v overlap, and p and covalency. 

Following the approach suggested by Newman and Ng (1986), an improved ab initio calculation of the intrinsic crystal-field parameters for the systems Pr3+-Cl (Shen and Holzapfel, 1994) and Nd3+-Cl (Shen, 1994) has been presented. The comparison of these results with experimental intrinsic parameters derived for LaCl3 Pr3+ and LaCl3 Nd3+ (Troster et al., 1993) is shown in fig. 9. Similar to the observations made by Gregorian et al. (1989), it is obvious that the ambient pressure values of the theoretical calculations are too small, yet the distance dependence is reasonably reproduced. 

Although the high-pressure method itself is rather simple to use, high-pressure physics is still a somewhat exotic tool for investigating rare-earth compounds. This seems rather surprising if the unique possibilities for example for the determination of intrinsic crystal-field parameters are considered. In many cases, theories explicitly predict certain distance dependences, which can be verified straightforward by the application of pressure, which continuously alters the interatomic distances. 

The superposition model has also been applied to experimental crystal field parameters obtained for lanthanides [31] substituted into host lattices of oxides, zircons, anhydrous trihalides, oxysulphides, alkaline earth fluorides and some other cubic crystals. The intrinsic parameters obtained from the analysis are given in Table 8.23. The solution spectrum of Er3+ aquo ion is given in Fig. 8.29. 

Crystal field parameters and, in a ligand field hypothesis, intrinsic parameters relative to europium-oxygen bonding are determined. 

The first assumption is that the total crystal field can be built from the separate contributions of each ligand around the rare-earth. The phenomenological parameters B are expressed in terms of intrinsic parameters A (Rj) depending only on the Rj distance of the ligand j from the lanthanide ion (11). 

Curves 7, for Pt and for Ir, show a different intrinsic activity but have the same shape. Barbier and Marecot (267) have suggested that since Pt and Ir have almost identical crystal structural parameters, the similarity in the curves 7 must mean that the structure sensitivity arises from geometric factors. The monotonic nature and the direction of the variation support this explanation also. 

Figures 8 and 9 also show an attempt to model the distance dependence of the intrinsic crystal field parameters B4 and Bg using an ab initio approach. The approach is based on relating the intrinsic parameters to the one-electron 4f orbital energies through [207]...

Fig. 8. Experimental (open symbols) and calculated closed symbols) values of the intrinsic crystal field parameters and of the Sm +-Cl pair in Sm + SrFCl as a function of Sm +-Cl bond length. The experimental bond length was varied with pressure and determined from high pressure X-ray diffraction data. The calculated curve was obtained from an ab initio calculation based on Eq. (33) [210]...

A number of crystal-field data sets have been analysed by the superposition model, for rare-earth substituted garnets by Newman and Stedman (1969), for CaF2, SrF2 and LaCh by Newman (1971, 1978), for LaAlOs, La203 and La202S by Linares and Louat (1975), for vanadates, arsenates and phosphates by Linares et al. (1977), etc. Some examples (intrinsic parameters and power law when determined) are listed in table 3. 

The method was applied to the system Pi LaCl3. The authors identified new contributions to rank-6 crystal field one-electron cfp originating from the correlated mechanisms Bl k, k2). They stated that neither covalency nor ligand polarization could significantly contribute to the reduction of Slater parameters in crystals and identified probable influential excitations namely 4f —> nf. The quality of the final match between experimental and calculated intrinsic parameters is moderate 180/607, 38.8/30.3 and 15.8/9.12cm for A, and A, respectively, in Pr LaCl3. The paper is rather a theoretical reference to be consulted as to which process contributes most to the cjp and which one is therefore worth calculating. 

Intrinsic crystal-field parameters B4,g(Ro) (w cm ) and power law exponents f4 5 for chloride ligands for Pr +,... 

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