# Europium - Sinha S.P.

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The coefficient £ has the following values for n = 2, 4, 6

Bnm Bi B*2 B\ *2 3!

2 y 42 8 -2V10 55 —2^35 81/70 35 55 16 2 J/105 10395 —8^ 105 ^14 16J/231 105 21 231

Elliott and Stevens [546] found A™ to vary roughly with the change in the ionic radius whereas <rn> changed rather more quickly. They proposed

F” a (Z—55)~nl4 (57)

However, the validity of the above relationship has been questioned by

Absorption Spectra of the Europium Ion and Its Complexes 115

Judd [549], Powell and Orbach [550], and Hufner [551]. Freeman and Watson [552] have examined the Hartree-Fock <rn > values and found these to be in good agreement with Elliott and Stevens parametri-zation formula, although the analysis of trichloride and ethylsulphate data shows that the assumption of a smooth variation of A™ with Z is not valid (see also ref. 551). They have also found [553] considerable deviations from the crystal field level scheme predicted by Ve alone, which are due to shielding and distortion of the charge of the rare earth ions. These effects strongly warrant the use of standard crystal field parameters for fitting the observed spectra.

It will be realized that the values of n and m of A™ will depend on the metal site symmetry and n will only have even values for states of the same parity. In a frequently overlooked paper Eisenstein [554] tabulated the symmetry classifications of the metal ion and ligand orbitals for most of the point group site symmetries of interest. These classifications are often very useful in constructing a molecular orbital energy diagram. Predictions regarding the number and classification of the excited electronic states can then easily be made with the help of such diagrams. We will, however, resist the temptation to reproduce those tables here, in order to conserve space, as they are easily available.

The symmetry types frequently occuring in rare earth salts are D3h and C3v. The rare earth trichlorides (MCI3), the tribromides (MBrs) from La to Gd and the ethylsulphates, M^HsSO^ * 9H2O, exhibit1 Dsn symmetry. The Cav symmetry is found for rare earth bromates, M(Br0s)3 * 9H2O, and rare earth double nitrates with magnesium or zinc, M Mgs(N03)2*24H20 or M Zna(N03)2 * 24H2O. Lower symmetry such as Cgv, has also been found in crystal and in solutions of rare earth salts.

Assuming a static crystalline field the potential, Vc, of the Hamiltonian for the pure fn configuration for different symmetries may be written as follows

for D3h Ve = A 2 (3^2 _ f2) (35z4 — 30r2z2 + 3r4)

-f- Al S (231z6 — 315r2z2 + 105r4z4 — 5r«) (58)

+ A\ S (x? — 15a^2 + 15x*y* — y«) for Csv

Vc = Al S (3z2—r2) + Al S (35z4-30r2z2 + 3»*) + A\ S Z

+ AS S (231z6—315r2z2 + 1057^—5r®) + Al S (llz3—32r2)

(a?—3xyt) + Al 2 (it8 — 15ar*3/2 + 15*2^ _ y*) (59)

1 The true point group symmetry is C^n but the effective potential can

be approximated to that of The difference between these two symmetries

is that terms such as A\ S [a (x + iy)3 + b (x — iy)3] enter into the

expression of the potential Ve in a complete calculation.

8*

116

Spectroscopic Properties of Europium

The usual contribution of the crystal field potential to the Hamiltonian is much smaller than the Fu’s and £4/. It should be recognized that all parameters, A” <rn>, F* and £4/ cannot be treated as free variables. The parameters Ft and £4/ are first adjusted to fit the free ion levels and then the crystal field parameters are considered to get a best fit with the crystal levels. The available crystal field parameters of the rare earth ions in LaCl3 and ethylsulphate hosts are compared in Table 43.

Table 43. Comparison of the Am <rw> parameters (in cm-1) of the trivalent rare earth ions in LaCh(LC) and ethylsulphate (ES) hosts

M3+ A% <r2> A\ <чл> A% <r*> A% <re>

Pr (LC) [493] 47.26 - 40.58 - 39.62 405.5

(ES) [555] 15.31 — 88.32 - 48.76 548.48

Nd(LC) [499] 97.59 - 38.67 - 44.44 443.0

(ES) [501] 58.4 - 68.2 - 42.7 595.0

Sm(LC) [511] 80.85 - 22.75 - 44.39 425.7

(ES) [509t551] 78 - 53 — —

Eu(LC) [513] 89 - 38 - 51 495

(ES) [570] 80 - 63.1 — 38.6 510

Tb(LC) [518] 92 - 40 - 30 290

(ES) [551] 110 - 75 - 34 465

Dy(LC) [511] 91.30 - 38.97 - 23.17 257.8

(ES) [551] 124 - 79 - 31 492

Ho(ES) [551] 125 - 79 - 30 391

Er (LC) [529] 93.89 - - 37.28 - 26.56 265.23

Tm(ES) [540] 129.8 - 71.0 - 28.6 432.8

The Splitting of J Levels in a Crystal Field

Hellwege [556—560] in a series of articles considered the general problem of crystal field potential and term splittings for each of 5 cubic and 27 non-cubic symmetries due to electric and magnetic dipole, electric quadrupole and Kramers’ degeneracy. These theoretical papers of high merit are perhaps too involved for less theoretically minded chemists but fortunately Runciman [561] has classifield the 32 symmetry classes into four groups and pointed out that J will split into the same number of components for each member of a particular group. The members of the four groups are as follows and the number of levels arising from a state of given J are tabulated in Table 44. The maximum 2J 1 levels are

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