Crystal-field parameters under pressure

The optical studies performed on most samples of table 1 were aimed at different aspects of the f-electron properties. A considerable amount of the work was concerned with the energy level shifts under pressure. From these shifts, variations of free-ion parameters, crystal-field parameters or crystal-field strengths with pressure have been deduced. Other studies concentrated on changes in lifetimes or intensities, the efficiency of energy transfer between rare earths or rare earths and other impurities or on electron-phonon coupling effects under pressure. The various aspects investigated under high pressure will be presented within the next sections. 

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... 

Fig. 6. Variation of the crystal-field parameters of LaCl3 Pr3+ under pressure. Solid lines correspond to the conventional one-electron crystal field, utilizing only the 4f2 wavefunctions as the basis set. S denotes the mean deviation as defined in the text. Dashed lines represent the results derived from the inclusion of the 4f15d1 configuration interactions.

Fig. 7. Variation of the crystal-field parameters and the crystal-field strength of / OCl Pr3+ (R = La, Pr, Gd) under pressure. The dashed fines show a superposition model calculation of die crystal-field strength.

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. 

Usually, it is assumed that pressure effects under the hydrostatic limit are isotropic, which causes a proportional decrease of all distances in the lattice without a change in the local symmetry of the Ln ion. As the result, a standard assumption is that angular factors C (0, (j>) in the crystal-field Hamiltonian are pressure independent and that the only pressure-sensitive parameters are the Slater integrals, spin-orbit coupling, and radial crystal-field parameters (R)- Then, in most cases, pressure causes small linear shifts of the sharp-lines luminescence related to f-f transitions in the Ln " and Ln ions. 

In sect. 4.4.1 the pressure-induced variations of the crystal-field parameters of LaClsiPr " " were shown in fig. 6. In this case the anomalous multiplet I>2 could also be measured under pressure (Troster et al., 1993), which opened a possibility to study the configuration interactions as a function of pressure. Including the 4f 5d configuration in the energy level fits and leaving only the energy distance to the 4f configuration as an adjustable parameter, the mean deviation 5 decreased from around 8 cm to less than 4 cm at ambient pressure (Troster and Holzapfel, 2002). 

However, the number of liquid crystals that have been studied under pressure is very limited. In most cases neither the equation of state nor the pressure dependence of the order parameter is known. Only the mean-field theory of Maier and Saupe was extended to explain the dielectric properties of liquid crystalline phases. However, a recent approach by Photinos et al. analyzed the nematic reentrance and phase stability based on the variational cluster method. The lack of a full theoretical description as well as insufficient experimental data should stimulate further high-pressure investigations in this field. 

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