Crystal strength parameters

S is the ionic spin and D, ID, and a are crystal field parameters describing the strength of the axial, the rhombohedral, and the cubic crystal field terms, respectively. The coordinate system of the cubic crystal field (ij, rj, g) may differ from that used to describe the axial and the rhombohedral crystal field interactions (x,y,z). 

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. 

Although it is not possible to directly compare the individual crystal-field parameters obtained for different hosts, it is possible to define an overall scalar crystal-field strength S which is independent of the specific crystal structure. The strength parameter S can be calculated according to (Chang et al., 1982) ... 

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.

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. 

From the above formulae it is evident that the splitting of an atomic term is a linear function of the crystal field strength parameter A. For larger values of A, however, the energies of certain states originating in different atomic terms tend to cross over. For example, the states T g(3F) and Tig(3P) of the electron configuration d2 approach each other at the higher A. In such a case the approximation of the weak crystal field loses its battle and the correct treatment is represented by the intermediate crystal field. 

Table 8. Effect of pressure on the crystal field parameters B q (cm ) for Eu + in several lanthanide oxyhalide systems. S (cm ) is an average crystal field strength parameter (see text). P denotes pressure in kbar and represents the maximum pressure achieved in each study. The linear shifts given in the table are good approximations of data given in graphical or tabular...

Figure 5-13. Evolution of the crystal field strength parameter Ny in the RE203 Em series. (Reproduced with permission from ref. 35. Copyright 2002 Elsevier Science B.V.)...

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