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The model which has been adopted in the analysis presented thus far assumes localised charge distributions and purely electrostatic forces. In particular, the excited state configuration of the impurity ion in a crystal field was treated as being highly localised spatially. The limitations of the point-ion approach are well known and have been

discussed by Jorgensen [16,171. A more realistic approach should consider the excited 5d electron orbital as extending to a certain degree over the surrounding anions rather than being totally localised on the impurity ion. One particular consequence of overlap is a transfer of charge from the anion to the impurity ion, with the impurity ion behaving as if it possessed an effective ionic charge below its oxidation number. This effect is referred to as central-field covalency. A second effect, known as symmetry-restricted covalency, relates to the formation of molecular orbitals from the anion and impurity-ion orbitals. Electron delocalisation into the molecular orbitals results in a lowering of the charge density close to the impurity ion. The outcome of these overlap effects is an expansion of the outer orbitals for which the mean extension appears to increase as the electronegativity of the anion decreases (polarismbility

increases). Behaviour involving orbital expansion is usually refered to as the nephelauxetic (fro» the Greek tor "cloud expanding") effect C181.

A consequence of an effective orbital expansion is a reduction in the Magnitude of the radial integrals below their free ion values which, in turn, leads to a reduction in the associated SIater-Condon, or equivalent Racah, and spin-orbit parameters. The extent to which the nephelauxetic effect is significant is rather more difficult to establish. Jorgensen has derived an eepirical series reflecting the ability of a number of different anions (ligands) to produce a reduction in the Racah parameters B <* F* - 5F«) and C (■ 35F«) for a particular transition metal ion. This nephelauxetic series takes the form 0a" > I- > Br" > Cl" >> F ~ for the commonest anions.

The ordering reflects the polarisabi1ity of the anion to which the degree

of covalence night well be related. The nephelauxetic ratio 6 ■ B'/B,

where B' is the reduced value of the Racah parameter B, is often used to quantify the observed reduction. Examples of such usage are common in the literature C193 with B often taking a value between 0.6 and 0.9.

Treatments of this nature are much less common for the rare earth ions. Alig C203 has studied Ta3* in SrCl2 and found it necessary to use a reduced value for the electrostatic interaction (S * 0.6). Similar, though such weaker, effects have been observed for some trivalent rare earth ions in a series of crystals of the type LaCls. Hong and Richnan 1211,

Hong et al C223 and McLaughlin and Conway C233 have studied Pr3* in a number of such hosts and have discovered a snail change in the Slater integrals. They all attribute the effect to a small change in the

covalence of the bonds, that is an increase in orbital overlap. Hong and Richean C243 have also detereined that Nd3* behaves in an identical, if less narked, manner in the sane hosts.

In all of the above cases the optical transitions studied are weak, being of the parity disallowed type 4fn — 4f". Only the direct SIater-Condon paraaeters are Involved together with one type of spin-orbit parameter. The

changes observed are of the order of 1 to 2 percent which is to be expected for the inner, well shielded, 4f shell. In the present work, which concerns the divalent rare earth ions, the problem encountered is more complex.

Allowed transitions to the outer, less localised, 5d orbital are involved. Consequently the overlap effects are expected to be more important. In addition, there are now not only the direct SIater-Condon parameters to

consider, but also the exchange and two types of spin-orbit parameter. In

total there are eight adjustable parameters, F*, F«, 6,, 63, 6„, and

Dq. The effect of a reduction of each of these parameters separately on the energy level structure will first be investigated. The intention is to establish the relative importance of each of the parameters as a precursor to the formulation of a suitable scheme for approximation.

In figures 5.25 to 5.29 the crystal field parameter Dq has been held fixed at 1000 cm~‘ and each of the five SIater-Condon parameters have in turn been reduced by up to SOX. In general the SO parameters depend less on the radial integrals than do the electrostatic parameters 171. This is

particularly true of the parameter t* since the 4f wavefunction is less sensitive to the surrounding anions than the unshielded 5d wavefunction. Figure 5.30 shows the effect of reductions in the spin-orbit parameters by up to 10X.

The energy level structure is found to be most sensitive to reductions

in Fa and 6,. The other parameters, with the possible exception of F«, have

a comparltively negligible effect on the energy level positions. Therefore the most important features of the crystal field spectrum will be quite sucessfully reproduced by altering only these two parameters. Based on the premise that similar classes of parameter (direct, indirect or spin-orbit) produce energy level variations in the same direction, it was decided to link these similar types in a specific way. In the following analysis the ratios F«/Fa, 63/81, 60/61 and t«/|* have been held fixed at their free ion values. As a result of the approximations described above, an analysis based on eight

En erg y (x 1 0 ^ c m " 1 ) P ercentage reduction in F2

Fig.5 . 2 5 The e f f e c t of reductions in the par ameter F2

on the energy level structure. The numbers