Abstract
Upon doping an inorganic crystal with lanthanide ions, excited states that alter the local electronic structure of the lanthanide moiety are introduced. The de-excitation of these local excited states underlies the fascinating luminescent properties of these materials. In this Chapter, the numerous states belonging to the (atomic-like) 4\(f^{N}\) and 4\(f^{N-1}\)5\(d\) configurations of the dopants are discussed for various lanthanide-activated materials. In addition, states of so-called impurity trapped exciton (ITE) character, where the dopant is partially oxidized, are described. The complete oxidation or reduction of the dopants in charge-transfer states requires the involvement of two optical centers and is reserved for Chap. 7. Special attention is paid to the quantum chemical and computational recipes and choices that enable one to obtain accurate information on these states from first principles.
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Notes
- 1.
These calculations are performed in the \(D_{2h}\) point symmetry group due to the limitations of the program, which is bound to use abelian groups [15]. The use of a lower symmetry than the real atomic symmetry originates 100–200 cm\(^{-1}\) maximum broken degeneracies in the spin-orbit-free first step. These broken degeneracies are corrected in the spin-orbit-coupling second step by proper averaging. E.g. the energy of a \(^3P\) term used in the second step is the average of the three broken degeneracy energies of the \(^3T_{1g}\) components obtained in the first step.
- 2.
The reason for this is the same behind the ionization potential series: The fourth ionization potential of a lanthanide element Ln (i.e. the ionization potential of Ln\(^{3+}\)) is smaller than the third ionization potential (i.e. the ionization potential of Ln\(^{2+}\)) due to the increase in positive charge. This is also applicable to a 4\(f\) \(\rightarrow \)5\(d\) excitation because it is a first step towards ionization, an incomplete ionization, where the inner 4\(f\) electron has to cross the more external \(5s^25p^6\) shell ending up in an even more external 5\(d\) orbital shell. As a matter of fact, only a 5\(d\) ionization remains for a full ionization, and this is small and almost independent of the lanthanide [41]. Hence, 4\(f\) \(\rightarrow \)5\(d\) excitations and 4\(f\) ionization potentials follow the same trends.
- 3.
Any reference in the following discussion to the 5\(de_g\) shell in difluorides, where Eu\(^{2+}\) occupies an 8-fold coordinated cubic \(O_h\) site, must be changed to 5\(dt_{2g}\) in sulfides, where Eu\(^{2+}\) occupies a 6-fold coordinated octahedral \(O_h\) site, meaning the lowest of the ligand-field split 5\(d\) shells. Equivalently, 5\(dt_{2g}\) in difluorides corresponds to 5\(de_g\) in sulfides, meaning the highest of the 5\(d\) shells.
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Barandiarán, Z., Joos, J., Seijo, L. (2022). Impurity States. In: Luminescent Materials. Springer Series in Materials Science, vol 322. Springer, Cham. https://doi.org/10.1007/978-3-030-94984-6_6
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