shielded fro« the crystal field to a large extent by the filled 5s and 5p atomic shells. However, even though adjusting Bl and Bl generally leads to only a small variation in the relative energy level positions (eigenvalues), it does have a more marked effect on the transition strengths (eigenfunctions) Such extreme sensitivity of the eigenfunctions compared with the eigenvalues to changes in the adjustable parameters is a well known characteristic of systems of this type. Often, in an approximate treatment, Bl and Bl are neglected (see for example (4,51) thereby leading to reasonable energy levels but poor intensities.
In the present study it was felt important to retain all of the crystal field parameters although certain assumptions as to their interrelation were made based on a survey of existing published
experimental results. On a simplistic level it is expected that D q , B« and Bi will all increase in magnitude with decreasing impurity ion-anion(1igand) distance R. According to the point ion model both Dq and Bl are proportional to R~B while BI is proportional to R~7. Experimentally the dependance for B« is observed to be more like R"3 171. Another interesting fact to emerge from the published experimental results is that, for a particular ion, the ratio Bl/Bl remains relatively constant for a wide range of host crystals 17,81. Even for different rare earth ions the ratio varies only slightly. For the Ho3* ion (Sf11) in CaF* the ratio is found to be equal to -0.18 C83. The ratio becomes -0.19 for Tm3* (4f * *) in the same host 191. Extrapolating from this slight but general trend and anticipating that the extra d electron for the 4f1*5d configuration will improve the shielding slightly, a reasonable value for the Yb3* ion is
(B:/b:>.u. > -0.20 5.22
The equivalent value corresponding to a crystal field of octahedral symmetry is, according to equations 3.81, given by
<
b:/
b;>«» = -o.o75
5.23It is more difficult to justify connecting Dq and B« via a simple relationship of this type. The 5d electron is strongly influenced by the surrounding lattice ions whereas the deeper 4f electrons are well shielded and only weakly influenced. Nevertheless, by considering the dependence of
on host crystal for the Dy5* ion in a range of alkaline earth fluorides 110,111 and on assuming typical values for Dq from results obtained elsewhere 15], it is possible to derive a linear relationship of the form
Bi « -(a + blDql ) 5.24
where B« and Dq are in units of cm-1 and the absolute value of Dq is indicated. The best fit is provided when the parameters a and b take the values 150 cm-1 and 0.067 respectively.
When a divalent ion is considered in the same alkaline earth flouride system, it is found that the absolute value of B« is considerably smaller. For example, Dy2* in CaF* yields a value Bi » -257.2 cm-* [11] consistent with equation 5.24, whilst Ba ■ -180 cm-1 [9] or -189 cm'1 [12] for the lsoelectronic divalent ion Tm2* in the same host. Siailarly for CaFaiDy2* a value of Bi ■ -188 ca~* is obtained [7]. It is assumed that a functional dependence similar to equation 5.24 connects Bi and the magnitude of Dq for divalent ions. A direct scaling of the coefficients gives
(8:>eu. - -(100 ♦ 0.05 IDqI) 5.25
for the Yb2* ion in a cubic field. This relationship is used in the present study along with the corresponding form relating to octahedral symmetry given
by
( B * ) o c t 100 + O.OSIDql 5.26
In figure 5.14 the energy levels and their associated transition strengths are plotted against the crystal field strength Dq. The relations derived above (equations 5.22, 5.23, 5.25 and 5.26) have been used to obtain reasonable values for b; and B&. A comparison with figure 5.9 shows that, while the inclusion of B* and BX significantly alters the transition strength: the energy level positions differ only slightly.
5.4 The optical absorption spectrum of Yb2* in the alkali halides 5.4.1 Experimental results
The optical absorption spectra associated with Yb2* in KI, Nal,
KBr, NaBr, KC1, NaCl, KF and NaF obtained at both room temperature (RT) and liquid nitrogen temperature (LNT), and with Yb2 * in LiF obtained at
RT, are shown in figures 5.15 to 5.23 respectively. It is noted that the spectrum for NaCliYb2* agrees well with that reported by Tsuboi et al C131. All crystals, except for NaF and LiF, were annealed at approximately 100*C below their respective melting points in a dry nitrogen atmosphere until no further shifts were observed in their optical absorption band positions. This procedure was adopted in order to elialnate the effects of stress and strain within the crystal. The spectra shown for NaF and LiF were obtained immediately after quenching following the diffusion of Yb2*. Annealing of these particular crystals resulted in other more subtle effects which will be discussed later.
A number of common features characterise the absorption band structure for Yb2* in KI, Nat, KBr, NaBr, KC1, NaCl and KF. In all cases
absorption starts at around 25000 cm*1 (400 nm> with two distinct bands, designated Al and A2, of approxiaately constant separation and
T T T T
» » »___________l I I I
8 0 0 1 0 0 0 1 2 0 0 1 4 0 0 1 6 0 0 1 8 0 0
Dq (c m - 1 )