Judd-Ofelt theory

From the Judd-Ofelt theory, some general rules have been derived for ED transitions between 4f" states of (RE) + ions in crystals ... 

In the scope of the Judd-Ofelt theory three parameters .22, 24, and 2 are commonly used to describe the transitions between J multiplets. For this case, the contributions from individual crystal field split levels of a given multiplet are simply summed up. To account for individual transitions, effective transition operators can be used to derive a parametrization... 

According to Judd-Ofelt theory, one can evaluate the radiative lifetime of any excited state of interest via Einstein spontaneous emission coefficients. The rate of relaxation, A, from an initial state fJ) to final state if J ) through radiative processes is given by (Condon and... 

Moreover, the radiative lifetime is not a constant for a given ion and a given electronic level. Indeed, there is a dependence on the refractive index, as clearly shown by eq. (14), so that transposition of a literature value to a specific compound cannot be made directly, which explains the wide range of rrad values reported for an individual Lnm ion. As an example, reported radiative lifetimes for Er111 range from 3 to 12 ms, even for relatively similar compounds (see table 19 below) Another hypothesis inherent to Judd-Ofelt theory is that 4f functions do not contain contributions from 5d orbitals, which is not quite the case for Pr111 and Tbm for instance. Selected data reported in the literature are listed in table 5. 

In order to compare the T-, parameters of Judd-Ofelt theory for different lanthanides, Camell et al. [99] have removed the dependence of Tk on the ground state multiplicity (27 + 1) and defined a new set of parameters, T given by... 

The Judd-Ofelt theory propounded in 1962 has been of immense value in the quantitative interpretation of the intensities of absorption spectral bands and continues to be the cornerstone of the field of absorption spectra of rare earth ions [56,57]. 

The absorption spectrum of the aquo ion has been analyzed, the intensities of the bands can be explained by the Judd-Ofelt theory. The energy levels of Pm3+ ion are given in Table 8.15. 

Crystal field theory, intensities of 4f-4f transitions, Judd-Ofelt theory of electric-dipole transitions, covalency model of hypersensitivity, dynamic coupling mechanism, solution spectra, spectral data for complexes, solvent effects, fluorescence and photochemistry of lanthanide complexes are dealt with in spectroscopy of lanthanide complexes. 

Extensive research including the study of radiative and non-radiative properties of rare-earth ions has been carried out. Especially, the Judd-Ofelt theory has been applied to most rare-earth — fluoride-glass combinations. Typical Judd-Ofelt parameters are reported in Table 3 for ZBLAN glass [31-34], An exhaustive list of such parameters for glasses and crystals can be found in Ref. [35]. 

Special care must be taken when applying the Judd-Ofelt theory to Eu3+ ions. At room temperature, absorption occurs not only from the 7F0 ground state, but also from the thermalized 7Fj level located a 300 cm-1 above. Thus, the respective population of both levels must be considered to properly apply the theory [37,38], Very good agreement between experiment (4 ms) and calculation (4.2 ms) was obtained for the 5D0 lifetime of Eu3+ in a fluorophosphate glass [38],... 

Several solutions were proposed to improve the standard Judd-Ofelt theory in the case of Pr3+. Thus, Medeiros Neto et al. [39] have described a modified Judd-Ofelt theory based on a 4-phenomenological-parameter fitting procedure. This modified theory leads to a significant improvement of the quality of the fit and a consequent acceptable agreement between experimental and calculated lifetimes for the D2 level. Other techniques derived from the Judd-Ofelt approach incorporate the measured fluorescence branching ratios [40] or take into account a relative deviation between experimental and calculated oscillator strengths [41]. 

A detailed description of the Judd-Ofelt theory may be found for instance in papers by Reisfeld (1) and Peacock (18). 

Theoretical determination of MCD parameters by the Judd-Ofelt theory... 

Within the frame of Judd-Ofelt theory, the intensity matrix element of an induced electric dipole transition is given by Gorller-Walrand and Binnemans (1998) and Judd (1962) ... 

The Judd-Ofelt theory explains how the observation of strictly parity forbidden transitions results from non-centro-symmetric interactions that lead to a mixing of states of opposite parity. One of the most obvious mechanisms is simply the coupling of states of opposite parity by the odd terms of the crystal field expansion. The transition, giving a... 

Vandevyver, C.D.B., Chauvin, A.-S., Comby, S., Bunzli, J.-C.G., 2007. Chem. Commun. 1716. Van Holde, K.E., 1985. Physical Biochemistry, 2nd ed Prentice HaU, Englewood Cliffs, NJ. Vogtle, F., 1991. Supramolecular Chemistry. John Wiley Sons, Chichester (Chapter 2). Walsh, B.M., 2006. Judd-Ofelt theory Principles and practices. In Di Bartolo, B. (Ed.), Advances in Spectroscopy for Lasers and Sensing Part 1. Springer-Verlag, Berlin, pp. 403-433. 

In this paper, the transparent 3at.%Nd Lu20j ceramics are fabricated by pressureless sintering under flowing H2 atmosphere at 1880 C for 8 h without any additives. The spectra properties and parameters are calculated in detail by Judd-Ofelt theory. Based on the spectral characterization results of transparent sample, the relevant spectral parameters such as Oabs, 2, O4, 6, r d and the fluorescence branching ratio p for Nd in LU2O3 lattice are calculated. 

The Judd-Ofelt theory was applied to study the spectral properties of 3at.%Nd Lu20j ceramic in this work. For Nd ions, the magnetic dipole (md) transitions are much weaker than the electric dipole (ed) transitions and they can be neglected in the J-O calculations. The experimental line strength for electric dipole (ed) transitions Sediexp) can be obtained from the absorption spectrum according to the following equation (2)... 

In the Judd-Ofelt theory, the line strength can be written as (Axe, 1963)... 

The optical spectrum of LaFsiPr has been analyzed along with neutron scattering results in PrFs using a C2 crystal-field Hamiltonian (Hennig et al., 1974). A priori line-to-line intensity calculations have been performed for all the rare earths in LaFj by means of the Judd-Ofelt theory (Leavitt and Morrison,... 

---