Rare energy transitions, diagram

Fig. 20.2. Schematic energy band diagram for rare earth monochalcogenides (Methfessel et al., 1966). On the left the atomic 5d states associated with the rare earth ion is shown. In the crystal these broaden to form the conduction band, the lowest having the Tj, symmetry. On the right the multiple splitting of the 4f states and its mixing with the crystal field split 5d states are shown. On the extreme right the absorption line shapes that result from 4f to 5d transitions are shown (from Holtzberg and Torrance, 1972).

Figure 10.4 Shows an energy-distance diagram for several configurations of a molecule with a surface. Not all of these paths will oceur for any given process of adsorption with a surface. In this example the molecule may make transitions from one of the various curves to another as reactions with the surface occur. The lowest-energy transitions are marked with open circles. For an example of a situation where chemisorption is very rare, consider how this figure would appear without the center of the three curves. In that case, transfer from the physisorbed to the chemisorbed case would add much more energy to the adsorbate than would be necessary to induce desorption.

Yttrium aluminum borate, YAlj (603)4 (abbreviated to YAB), is a nonlinear crystal that is very attractive for laser applications when doped with rare earth ions (Jaque et al, 2003). Figure 7.9 shows the low-temperature emission spectrum of Sm + ions in this crystal. The use of the Dieke diagram (see Figure 6.1) allows to assign this spectrum to the " Gs/2 Hg/2 transitions. The polarization character of these emission bands, which can be clearly appreciated in Figure 7.9, is related to the D3 local symmetry of the Y + lattice ions, in which the Sm + ions are incorporated. The purpose of this example is to use group theory in order to determine the Stark energy-level structure responsible for this spectrum. 

The ZSA phase diagram and its variants provide a satisfactory description of the overall electronic structure of stoichiometric and ordered transition-metal compounds. Within the above description, the electronic properties of transition-metal oxides are primarily determined by the values of A, and t. There have been several electron spectroscopic (photoemission) investigations in order to estimate the interaction strengths. Valence-band as well as core-level spectra have been analysed for a large number of transition-metal and rare-earth compounds. Calculations of the spectra have been performed at different levels of complexity, but generally within an Anderson impurity Hamiltonian. In the case of metallic systems, the situation is complicated by the presence of a continuum of low-energy electron-hole excitations across the Fermi level. These play an important role in the case of the rare earths and their intermetallics. This effect is particularly important for the valence-band spectra. 

Location of the localized states related to divalent and trivalent rare-earth ions relative to the valence and conduction bands of the host lattice is one of the most important factors that control the luminescence properties of rare-earth ions in solids. The location of the ground states of Ln ions with respect to the valence band can be estimated from the energies of the charge-transfer transitions (CTT), which are responsible for the broad bands in the excitation spectra of Ln ions. CTT is considered to be a transition of an electron fi om figands to the Ln ion. In the energetic diagram, it corresponds to the transition fi om the top of the valence band to the Ln " " level. The location of Ln " " can be estimated if the energy of the ionization transition (IT) is known. The IT is the opposite process to the CTT and corresponds to the transition of an electron from the Ln ion to the conduction band. 

In this part of the chapter we have looked at the energy diagram and associated optical transitions of a number of rare-earth ions. These diagrams and transitions are nowadays well known. The influence of the crystal lattice on the situation and intensity of absorption and emission bands or lines can also be well understood. In the next part we consider the efficiency of the luminescence. 

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