Study Of Rare-Earth Luminescent Materials Using First Principle And Parametric Model

The calculation of crystal-field parameters and spin-orbit coupling parameters of f electron and d electron of lanthanide ions was systematically studied in this paper. In the introduction section we described the background of rare earth ions as luminescent materials, the research and analysis methods of energy levels and spectra of rare earth ions including phenomenological model, empirical formula on f-d transition spectra proposed by Dorenbos and simplified model by Duan Chang-kui. There were many limitations when the models were applied to analysis the energy levels and spectra of rare earths ions. Such as, exact experimental data were needed when using the phenomenological model and a large number of parameters were too difficult to fit in case of the f-d spectra containing a lot of phonon spectra. Dorenbos'model was widely used by experimental physicists on predicting f-d transition and transitions of charge transfer state of lanthanide ions in crystals rare earths, but it was still uncertain of its reliability. Simplified model was usually used for the single 5d crystal-field level of ions. Since the 5d crystal-field splitting usually formed the main parts of the f-d transition spectra, the simplified model was not able to predict the main f-d transition spectra of lanthanide ions in crystals.As the most important method in the study of rare earth ions at present, phenomenological model was introduced in Chapter 1. It was widely used in explaining and predicting spectra of rare earth ion as luminescence materials. We started from the center-field approximation, explained the energy levels of lanthanide ions in crystals by introducing the interactions in f^N configuration and f^N-1d configuration, such as Coulomb interaction, spin-orbit interaction, crystal field and configuration interaction.In Chapter 2, we described the method of calculating the parameters of the phenomenological model in combination of density functional theory. The approach combined the advantages of high accuracy of phenomenological model and no experimental data needed in the density functional theory. We applied this approach to the calculation of rare earth ions as the first time.In Chapters 3 and 4, crystal-field parameters and spin-orbit coupling parameter were calculated for various lanthanides ions in different crystals by the method basing the module space model. In chapter 3, the crystal-field parameters and spin-orbit coupling parameters of Ce³⁺ in various groups, including S₄ in LiYF₄, O_h group in CaF₂ and Cs₂NaYCl₆, C_4v in KY₃F₁₀ and D₂ in YAG. We systematically analyzed the results on crystal-field parameters in various symmetry groups. The numbers of crystal-field parameters were related to the groups and symmetry. Our results were consistent with the prediction by group theory in the number of parameters and symbols of crystal-field parameters. In addition, we also compared our calculated parameters with those reported in the literature. The accuracy of our parameters was in a reasonable range and our parameters were close to those by fitting.In Chapter 4, we calculated crystal-field parameters and spin-orbit coupling parameter of Ce³⁺, Pr³⁺, Nd³⁺, Eu³⁺ in YPO₄ crystal and Ce³⁺, Tb³⁺ in BaBPO₅ crystal. Our calculations showed that the parameters calculated by module space method of lanthanides were consistent with the expected trend, that was, the crystal-field parameters decreased while spin-orbit coupling parameters increased with the nuclear charge. Furthermore, we used atomic parameters in literatures and the calculated parameters to reconstruct the Hamiltonian of lanthanide ions and calculated the eigen value energy levels and eigen states. By calculating the transition matrix elements, we simulated the absorption spectra of lanthanide ions, and compared with the excitation spectra. Using this method, we found that our calculation was quite consistent with the experimental spectra. We also found that the strengths of spin allowed and spin forbidden transitions were close to those in experiment.In Chapter 5, we calculated excited state absorption spectrum of Yb²⁺ in SrCl₂. By comparing the calculated spectrum with the experimental spectrum, we might speculate the changes of bond lengths of rare earth ions when they transitioned from 4f^N configuration to 4f^N-15d configuration.In Chapter 6, we calculated f-d transition spectra of Er³⁺ in different crystals such as CaF₂, LiYF₄ and Cs₂NaYCl₆. We studied dependency of f-d transition spectra of Er³⁺ on the parameters of the f-d Coulomb interaction and spin-orbit parameters of 5d electron.