W. T. Carnall

Electronic Energy Levels in the Trivalent Lanthanide Aquo Ions. I. Pr3+, Nd3+, Pm3+, Sm3+, Dy3+, Ho3+, Er3+, and Tm3+

The free‐ion energy‐level schemes of the Pr3+, Nd3+, Pm3+, Sm3+, Dy3+, Ho3+, Er3+, and Tm3+ aquo ions have been determined from their absorption spectra in dilute acid solution at 25°. Energy‐level assignments were made by comparison with crystal spectra, and on the basis of correlations between calculated and observed band intensities. For most of the ions, it was possible to identify several transitions giving rise to bands at energies as high as 45 000–50 000 cm−1. Sufficient numbers of assignments were made to justify inclusion of the effects of configuration interaction in the calculation of the energy‐level parameters. Variation of the electrostatic, spin–orbit coupling, and configuration‐interaction parameters across the lanthanide series is examined.

Spectral Intensities of the Trivalent Lanthanides and Actinides in Solution. II. Pm3+, Sm3+, Eu3+, Gd3+, Tb3+, Dy3+, and Ho3+

We have correlated the experimentally determined band intensities in the solution absorption spectra of the trivalent lanthanides with a theoretical expression derived by Judd. The spectra were measured in a single medium, dilute acid solution, and, in most cases, in the range ≈6000–50 000 cm−1. In general, the correlation between calculated and observed intensities was very good, even at higher energies. The variation of the intensity parameters over the series is discussed as is the somewhat unexpected degree of correlation obtained in the ultraviolet region.

A systematic analysis of the spectra of the lanthanides doped into single crystal LaF3

The optical spectra of the lanthanides doped into single crystal LaF3 have been interpreted in terms of transitions within 4f N configurations. Energy matrices combining free‐ion terms with a crystal field for an approximate model which assumes C2v instead of the actual C2 site symmetry were diagonalized. Excellent correlations were obtained between experimental transition energies and the computed level structures. We also report the results of previously unpublished experimental spectroscopic investigations of Nd3+ and Sm3+:LaF3, as well as predicted energy levels for Pm3+:LaF3. The spectroscopic data for each ion were independently interpreted using an effective‐operator model, then the model parameters were intercompared. Systematic trends have been identified, and a comprehensive energy level diagram is presented.

Spectral Intensities of the Trivalent Lanthanides and Actinides in Solution. I. Pr3+, Nd3+, Er3+, Tm3+, and Yb3+

We have correlated the experimentally measured intensities of the solution absorption spectra of Pr3+, Nd3+, Er3+, Tm3+, and Yb3+ in three different solvents with a theoretical expression derived by Judd. The expression, P=Σ lim λTλσ(fNψJ‖∪(λ)‖fNψJ′′)2λ=2,4,6 is derived from a theory in which the ligand‐field interactions with the central 3+ ion cause a mixing of higher configurations of opposite parity into the fN configuration and gives rise to induced electric‐dipole transitions. A prerequisite for the intensity calculations is the computation of complete intermediate coupling eigenvectors for the energy levels investigated. Other possible mechanisms such as magnetic‐dipole and electric‐quadrupole transitions are considered. The oscillator strengths of important magnetic‐dipole transitions are tabulated.The results give the first experimental verification of the ability of the theory to account for large changes in certain bands of the same lanthanide observed in different solvents. Conclusions are dra...

Electronic Energy Levels of the Trivalent Lanthanide Aquo Ions. III. Tb3

The free‐ion energy level scheme of Gd3+ (aquo) to ∼52 000 cm−1 has been determined from the absorption spectrum of Gd3+ in dilute acid solution at 25°C. Several new absorption bands near 50 000 cm−1 have been ascribed to transitions from the ground state to components of the 6G multiplet. Energy level assignments were made on the basis of correlations between calculated and observed intensities. The resulting parameters were: E1 = 5761, E2 = 28.02, E3 = 582.0, ζ4f = 1450, α = 22.55, β = − 103.7, γ = 997.

A systematic analysis of the spectra of trivalent actinide chlorides in D3h site symmetry

The optical spectra of actinide ions in the compound AnCl₃ and doped into single crystal LaCl₃ were interpreted in terms of transitions within 5f{sup N} configurations. Energy-level calculations were carried out using an effective operator Hamiltonian, the parameters of which were determined by fitting experimental data. Atomic and crystal-field matrices were diagonalized simultaneously assuming an approximate D{sub 3h} site symmetry. The spectroscopic data were taken from the literature but in most cases supplemented by unpublished measurements in absorption and in fluorescence. Spectroscopic data for each ion were analyzed independently, then the model parameters were intercompared and in many cases adjusted such that in the final fitting process the principal interactions showed uniform trends in parameter values with increasing atomic number. Consistent with analyses of the spectra of lanthanide ions in both LaCl₃ and LaF₃, abrupt changes in magnitude of certain crystal-field parameters were found near the center of the 5f{sup N}-series. This resulted in two groups of parameter values, but with consistent trends for both halves of the series, and generally very good agreement between observed and computed energies. A new energy level chart based on computed crystal-field level energies for each trivalent actinide ion has been prepared. in addition, the parameters of the atomic part of each 5f{sup N} Hamiltonian were used to calculate the matrix elements of U{sup ({lambda})} for selected transitions. The values were tabulated to facilitate calculation of intensity-related parameters for 5f{sup N}-transitions using the Judd-Ofelt theory. 44 refs., 10 figs., 3 tabs.

Analysis of the crystal‐field spectra of the actinide tetrafluorides. I. UF4, NpF4, and PuF4

An interpretation of the low‐temperature absorption spectra of AnF4 (An=U, Np, Pu) is presented. Using an effective operator Hamiltonian with orthogonalized free‐ion operators and initializing crystal‐field parameter values based on a superposition model calculation for An4+ sites with C2 symmetry, good agreement between the model calculations and experimentally observed absorption band structure could be obtained. Correlations with published magnetic and heat capacity measurements are discussed.

Energy level analysis of Np3+:LaCl3 and Np3+:LaBr3

The polarized absorption and fluorescence spectra of 0.01–5% Np3+ doped into single‐crystal LaCl3 were measured at moderate and high resolution in the range to 50 000 cm−1 at 298, 77, and 4 K. The 150 crystal field components identified were fit by a parametrized model which has previously been shown to provide an excellent account of the energy level structures observed for lanthanides doped into LaCl3. This constitutes the first successful evaluation of the crystal field interaction for an actinide ion in LaCl3 in which J mixing effects were explicitly included. The crystal field parameters for Np3+:LaCl3, B20=163, B40=−632, B60=−1625, and B66=1028, all in cm−1, were determined to be approximately twice as large as those for the analogous lanthanide, Pm3+:LaCl3. From analysis of Zeeman patterns in the fluorescence spectra, the ground state was found to be doubly degenerate, having crystal quantum numbers ±2 and a parallel splitting factor 0.17 LU (Lorentz unit).

1S0 Level of Pr3+ in Crystal Matrices and Energy‐Level Parameters for the 4f2 Configuration of Pr3+ in LaF3

The absorption spectrum of Pr3+ in LaF3, LaCl3, CaF2, Pr(Y)Cl3·6H2O, and Pr2(SO4)3·8H2O was investigated. Evidence for the 1S0 level in Pr3+:LaF3 at 46 986 cm−1 is presented; this level was not observed directly in absorption in any of the other matrices studied. An analysis of the 13 observed levels in Pr3+:LaF3, based in part upon a re‐examination of the experimentally observed crystal‐field components of certain levels, gave the following electrostatic, spin–orbit, and configuration‐interaction parameters: E1 = 4559.0, E2 = 21.954, E3 = 467.75, ζ4f = 744.44, α = 15.294, β = − 669.02, γ = 1411.8, with an rms deviation= 33 cm−1.

Energy level analysis of Pm3+:LaCl3

A diagonalization of the matrices representing the combined atomic and crystal‐field interactions for the 4f4 configuration has provided the basis for interpreting the spectrum of Pm3+:LaCl3. Experimental data were drawn from the literature and were augmented by unpublished absorption and fluorescence results. A method of truncating the large matrices involved is discussed and shown to yield results in excellent agreement with complete calculations. Use of fluorescence branching ratio calculations based on the Judd–Ofelt intensity theory to monitor the interpretation of fluorescence spectra is discussed.