Judd-Ofelt theory/parameters

Fig, 24. Comparison of reported Judd-Ofelt theory parameters for aquated trivalent lanthanide ions (open symbols) and actinide ions (solid symbols, error limits shown, data points connected by broken line). Lanthanide data are taken from Carnall (1979), actinide data from Carnal and Crosswhite (1985b), based on fixing the value of 1 x 10" cm. ... 

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... 

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... 

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]. 

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]. 

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

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 n parameters for a given ion-host combination are derived from a least squares fit of calculated and observed intensities. The validity of the Judd-Ofelt treatment has been tested for most trivalent rare earths in both crystals and solutions and has been applied to rare earth molecular vapors. Peacock (1975) has presented a thorough review of the Judd-Ofelt theory and experimental results. 

One reason for the interest in computing absorption intensity correlations is that, once the parameters of the Judd-Ofelt theory are evaluated, they can be used to compute the radiative lifetime of any excited state of interest via the Einstein expression... 

The parametrization scheme by Judd and Ofelt for J-multiplet transition intensities in terms of Qx parameters (sect. 7.3) is completely general. It is only limited to the assumption of one-electron, one-photon interaction. The parametrization scheme is independent of the nature of the metal-ligand interactions. In this way, the Judd-Ofelt theory can also be used for the parametrization of vibronic interactions (see sect. 11). The... 

Over the years, the Judd-Ofelt theory has been proved to be quite successful for the intensity analysis of the trivalent lanthanide ions. A lot of pioneering work concerning the determination of experimental intensities of the f-f transitions over the lanthanide series and the systematic intensity parametrization has been done by Camall and coworkers (Carnall et al. 1965, 1968a, see also Camall 1979). They studied the spectra of the trivalent lanthanide ions in aqueous solution (diluted HCIO4). In order to extend the range of measurements to the near-infrared, spectra were also recorded in diluted DCIO4. The intensity of the transitions between J-multiplets in the spectrum can be rationalized in terms of only three parameters Qx- One can make predictions about the intensity of transitions which cannot be observed experimentally (e.g. infrared 4f-4f transitions in aqueous solution). The parameter sets are a useful tool to compare the f-f intensity properties of different lanthanide systems. They may be used to derive relationships between spectral and stractural properties for different kinds of lanthanide complexes. 

For Pr ", the Judd-Ofelt theory does not seem to work well (Goldner and Auzel 1996). Difficulties are experienced if one tries to fit both the F3, F4 <— H4 and the P2,i,o, l6 transition groups with the same set of Qx intensity parameters (Camall... 

It should be mentioned also that the hypersensitive transition F2 -f— H4 has to be included in the fit of Pr " systems, because otherwise a negative value for the U2 parameter is found (just as is sometimes observed by inclusion of the transition in the fit). An intensity parameter with a negative value has no physical significance. Extraction of a reliable 2 parameter is often a problem for Pr " ", since the p2 <— H4 transition is situated in the infrared spectral region and caimot be observed in an aqueous solution (it is masked by vibrational transitions). In order to find more reliable intensity parameters for Pr +, Quimby and Miniscalco (1994) introduced a modified Judd-Ofelt theory in which the luminescence branching ratios are included in the fit (see sect. 7.7). 

A possible breakdown of the Judd-Ofelt theory was suggested by Henrie and Henrie (1977) for the absorption spectrum between 18 400 cm and 22 600 cm for NdBre " in acetonitrile. In this region the observed intensities are much larger than the calculated ones. But in general, the Judd-Ofelt theory works very well for Nd ". The Judd-Ofelt theory is not very suitable for the ah initio calculation of intensity parameters. Especially the so-called hypersensitive transitions give problems (see sect. 8). Therefore, a number of refinements of the intensity theory have been published after the original papers of Judd and Ofelt. These models are discussed in detail in sections 6.2 and 8.2. 

The variation of the intensity parameter across the lanthanide series has been studied by Peacock (1973, 1975). If the intensity is produced by a static perturbation (Judd-Ofelt theory), a monotonous decrease of the Qx parameters from Pr to Tm is predicted. It is assumed that the lanthanide ions have been doped into the same host matrix or that an isostructural series of lanthanide complexes is considered. A change in S5mimetry would result in an abrupt change of the parameters. To a good approximation, a linear variation was found for the Q(, parameter of [RWio035] with the number of 4f electrons. The same behavior was found for Q4, but there was more scatter due to a larger uncertainty on the values of this parameter. The Q2 parameters appeared to vary randomly. 

For non-stoichiometric and amorphous systems (e.g. liquids, glasses, polymers,. ..), where the local structure cannot be determined by diffraction methods, the Judd-Ofelt theory can be combined with molecular-dynamics simulations for the calculation of intensity parameters (Edvardsson et al. 1992, 1996, Wolf et al. 1993, Klintenberg et al. 

The aim of this presentation is to answer the question about the physical mechanisms that contribute to the intensity parameters which are determined from (10.1) in a semiempirical way. The present discussion demonstrates the generality and universality of the Judd-Ofelt theory which, in fact, goes far beyond the initial limitations of its original derivation. ... 

With the development of the Judd-Ofelt Theory, Judd (1962) pointed out that of the three parameters, T, eq. (24.6), T2 most closely monitors changes in the environment, and that hypersensitivity was strongly correlated with those transitions having large matrix elements of J0rgensen and Judd (1964)... 

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