Weak crystal fields

The crystal field model may also provide a calciflation scheme for the transition probabilities between levels perturbed by the crystal field. It is so called weak crystal field approximation. In this case the crystal field has little effect on the total Hamiltonian and it is regarded as a perturbation of the energy levels of the free ion. Judd and Ofelt, who showed that the odd terms in the crystal field expansion might connect the 4/ configuration with the 5d and 5g configurations, made such calculations. The result of the calculation for the oscillator strength, due to a forced electric dipole transition between the two states makes it possible to calculate the intensities of the lines due to forced electric dipole transitions. 

Our results are rather similar to those of Wojtowicz (1991). Two narrow lines at 689 and 706 nm with long and slightly different decay times together with broad bands at 750 and 790 nm with short decay times characterized time resolved spectra of kyanite at 300 K (Fig. 4.46). Those data clearly indicate that we have emissions coming from the Cr in three different sites site A with a strong crystal field - doublet i -lines at 689 and 706 nm, site B with a weak crystal field - quartet broad band at 750 nm accompanied by only one doublet i -line at 704 nm which may be detected only at low temperatures, and site C with a weak crystal field - quartet broad band at 790 nm. 

Garnet activated by trivalent Cr is a promising system for tunable laser appUcations and those systems have been well studied. Cr + replaces Ap" in octahedral sites with a weak crystal field. The transition involved in laser action is T2- A2, a vibrationally broadened band. At room temperature it has a maximum in the 715-825 nm range with a decay time in the 100-250 ps range depending on AE between the E and T2 levels. When the AE is maximal, narrow fines also appear from the E level. At low temperatures, when thermal activation of the T2 level is difficult, J -lines luminescence becomes dominant with the main fine at 687 nm (Monteil at al. 1988). We studied pyrope artificially activated by Cr and also found the two emission types described above (Fig. 5.26). 

Laser-induced time-resolved liuninescence spectra of natural garnet demonstrate broad red bands with a relatively short decay time which may be ascribed to Cr + emission in a weak crystal field (Fig. 4.56a). 

The electronic spectrum (36) of the pol5uner is dominated by a very broad ultraviolet band, with shoulders at 280 and 470 m/t, which tails into the visible region and is responsible for the deep brown color of the polymer. Very weak crystal field excitations are found at 640 and 880 m. From the latter transition one can estimate that for high-spin Fe +, Dq = 1100 cm i. This value is typical of Fe3+ in octahedral coordination with oxygen ligands, but the X-ray evidence (see below) indicates that the coordination is tetrahedral, so that Dq seems anomalously high. However, the coordination symmetry is actually lower than tetrahedral, since both hydroxide and oxide ligands are involved. 

Strong and Weak Crystal Fields. The preceding discussion assumed that 2 (e2/rjk) > Vc> ls This is the situation for many of the ions in the... 

For a weak crystal field the ESR results on d5 ions have been fitted to the spin Hamiltonian... 

Spin Hamiltonian Parameters for d5 Ions in Weak Crystal Fields °... 

Free- ion terms Weak crystal field Intermediate crystal field Strong- field terms Strong-field configurations... 

Example 8.2-1 Examine the effect of spin-orbit coupling on the states that result from an intermediate field of O symmetry on the Russell-Saunders term 4F. Correlate these states with those produced by the effect of a weak crystal field of the same symmetry on the components produced by spin-orbit coupling on the 4F multiplet. 

A partial character table of the point group D3h is given in Table 8.4. Find the missing characters of the vector and spinor representations of the double group D3h. Determine whether El transitions E-/ E3/2 and E./2 —> E5/2 are allowed in a weak crystal field of D3h symmetry. State the polarization of allowed transitions. 

Table 28 Type of magnetism in d complexes (weak crystal field, high-spin complexes)...

Fig. 123 Energy levels of nearly-octahedral d4 (nearly-tetrahedral d6) systems on symmetry lowering (not to scale). Weak crystal field strength, 10Dq/B < 20...

The assignment of multiplicities can now be settled. For a d ion in an octahedral environment there are no states in the weak crystal field and thus solution (3) for the t, configuration is ruled out since it includes such a state. Also the highest of the states in the... 

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