Theoretical Simulation Of F-d Transitions Of Lanthanide And Actinide Ions Doped In Crystals

This thesis presents a theoretical simulation of the f-d transitions of lanthanide and actinide ions doped in crystals,which contains four parts:A)Theoretical study of the f-d transition spectra of Er³⁺and Tm³⁺ions doped into the cubic elpasolite Cs₂NaYF₆;B)Review of the simple model for the f-d transition spectra of lanthanide and actinide ions in crystals,and its supplementary applications to two spectra;C) The effective Hamiltonian theory for f-d transition spectra of lanthanide and actinide ions in octahedral crystal field based on the correction due to the spin-orbit interaction of 5d(or 6d)electron(recent advances of the simple model);D)Application of the point group bases to the f^N-f^N-1d transitions of lanthanide and actinide ions doped in crystals.In part A,a detailed interpretation and analysis of the 4f-5d transition spectra of Tm³⁺ions in Cs₂NaYF₆ is presented,where energy-level and intensity calculation and spectral simulation are performed by using the extended f-shell programs of Prof.M.F. Reid.The electronic states of the 4f¹¹5d¹ configuration are calculated to span from 58318 cm^-1to 86900 cm^-1.At least 5 structured bands observed in the excitation spectrum and their intensities are fairly well simulated by this calculation.Strict O_h point group selection rules are operative for the transitions observed in the optical spectra.Measurements from the intensities of vibronic bands in the f-d excitation spectrum are not always suitable for the assignment of the energy of the first spin-allowed transition,since the lower 4f¹¹5d¹ states are of mixed SLJ parentage in which only certain components with the proper quantum numbers(not only S,but also LJ)which satisfy the select rulesâ–³S=0;â–³L=0,±1;â–³J=0,±lcontribute to the studied f-d transitions.The d-f emission spectrum is well-explained by this calculation and most of the intensity is located in one band:4f¹¹5d¹(high spin)→4f¹²H₆.In addition, the f-d excitation spectrum of Er³⁺ions in Cs₂NaYF₆ is also simulated and interpreted by the calculation results using the extended f-shell programs.Some similar analyses and conclusions for the electronic states of the 4f¹⁰5d¹ configuration are also given.In part B,the development and extension of the simple model for the f-d transitions of lanthanide and actinide ions in crystals is reviewed.The model can give the positions of zero-phonon lines for various f-d transition bands based on the values of 2-3 parameters,and calculate relative transition line strengths based on the quantum numbers of the initial and final states of the transitions.Its successful application to f-d transition spectra of rare-earth ions(4f³-4f¹¹)in crystals is sumraarized.As a supplementary study,this model is further applied to the remaining configurations f¹¹d and f¹²d,where the parameterized energy matrix elements are obtained and tabulated.As an example,the excitation spectrum of Tm³⁺doped in crystal CaF₂ is well explained.In part C,the simple model for f-d transitions is extended to the case where the lanthanide(or actinide)ion substitutes the center ion in the octahedral six-fold coordination compounds,where,for the low-energy tE component of the 5d(or 6d) orbitals,the spin-orbit interaction of the d-electron cannot be neglected due to it induces energy splitting.In this so-called "effective Hamiltonian theory",by introducing a effective orbital angular momentum l=1 for the t₂ orbitals,the expressions of the energy levels for the f^V-1d configuration and the relative line strengths for the f^N←→f^N-1d transition are rederived in detail based on the Racah-Wigner algebra.The result is firstly applied to the interpretation of the low-temperature 4f-5d absorption spectrum of Cs₂NaYCl₆:Tb³⁺.Applications to the more complicated 4f-5d excitation spectra of Er³⁺and Tm³⁺ions in Cs₂NaYF₆ are also explicitly presented.The calculation results and interpretations using this extended theory agree well with those using the extended f-shell programs.In the last part,the Butler's point-group coupling coefficients are applied to modeling of f^N←→f^N-1d transitions of lanthanide and actinide ions in crystals.There are several possible coupling schemes for the states of the f^N-1d configuration,which are related to the simple model for f-d transitions.Formulae for matrix elements of the Hamiltonian for the f^N-1d configuration and the relative line strengths for f^N←→f^N-1d transitions are derived by using the Butler's point-group irreducible tensor coupling techniques.As an example,the f-d absorption spectrum of the crystal Yb²⁺:SrCl₂ are calculated using these coupling coefficients based on the "RACAH" software developed by Butler and co-workers.The advantages and disadvantages of various coupling schemes are demonstrated.Moreover,the formula of the relative line strengths for the f-d transition in part C is further simplified by utilizing the Butler's point-group bases and irreducible tensor coupling techniques.With this expression,a lot of sums of magnetic quantum numbers in the original form are avoided and the evaluation of the relative line strengths simply depends on the angular momentum quantum numbers of the initial and final states of the transitions.