Spedding reasoned that this was due to the peculiar atomic structure of the rare-earth metals in the mineral. The first rare earth metals were discovered at the end of the eighteenth century.
H. Spedding's awards
Heiser, Isopystic determination of the activity coefficients of some aqueous rare earth electrolyte solutions at 25°C. Rard, Isopystic determination of the activity coefficients of some aqueous rare earth electrolyte solutions at 25°C.
Chapter 73
The beginnings: yttrium and cerium
He was one of the first champions in Sweden of the new antiphlogistic chemistry based on oxygen. Berzelius was elected a member of the Swedish Academy of Sciences in 1808 and became its secretary in 1820.
Mosander's activities: the first division
The sulphate of cerium oxidul is the least soluble, that of lanthanum oxide somewhat more and that of the third metal oxide the most easily. The former is carefully distinguished, the latter consists of the sulphate of didymium oxide.
Rearrangement and further divisions: 1843-1886
In 1904, this element was also separated from gadolinium by the last great figure in the history of the discovery of the rare earth elements, Urbain. He was the author of the first monograph on photometry: Koloriraetrie und quantitative Spektralanalyse (Hamburg/Leipzig, 1891).
Setting things in order and interpretation
In 1882 he became an assistant at the Czech branch of Charles University in Prague and became professor of inorganic chemistry in 1897. After the unification of Italy in 1871, he became a professor at the University of Rome and at the same time a senator for the new kingdom. DISCOVERY AND SEPARATION OF THE RARE EARTHS 77 George de Hevesy was born in Budapest in 1885.
Dmitri Ivanovich Mendeleev was born in 1834 in the Siberian town of Tobolsk where his father was the director of the secondary school. At the outbreak of the First World War he was in Australia, but immediately returned to England and volunteered for the army.
Introduction
The tone of the article is one of educated speculation, as the reconciliation of apparently conflicting experimental data is worked out. The two examples of modern work cited above give us an idea of the general direction that theory and experiments have taken since the 1930s. In another area, the perturbation theory had to be extended to allow deviations from the central-field approach, i.e. the approach that each electron of the lanthanide moves in a spherically symmetric potential that is shared by all the other charged particles in the system study.
The SCCF parameters mentioned above are an example of the many ways that neighbor configurations make themselves felt. It goes without saying that many of the later developments in theory would have been impossible without the speed and efficiency of the modern computer.
- Theory
Deviations from the Land~ interval rule in the hyperfine structures indicated that interaction terms of the type A I. It was more difficult to make progress with the spectra of the lanthanide ions in crystals. Bizarre as these arguments seem to us today, it is important to realize that the nature of optical transitions was unknown in the 1930s.
The analyzes of the two-electron configurations 4fSd and 4f 2 carried out by Condon and Shortley (1931) achieved great importance in being the only lanthanide spectrum described in detail in their subsequent monograph (Condon and Shortley 1935). Nothing so striking as this occurred at that time in the interpretation of the spectra of rare-earth ions in crystals.
Consolidation and compression
For us, the best example of the latter is fNs, which can be easily handled with alternative techniques. It took some time for the full force of the WE phrase to be appreciated. Racah (1942a) used the WE theorem to evaluate the matrix elements of Pk(COS~O12) for a term L in the 1112 configuration.
In 1942, the stage was set for the development of the modern quantum spin theory. The roots of the 3 × 3 Coulomb interaction matrix give the energies of 4 D and two 2D terms.
The non-invariance groups of Racah 1. Interim experimental developments
They undoubtedly served to emphasize the need for a better understanding of shell structure f. There are as many terms in the set as require the set of Kronecker products. It is here that the detailed properties of the representations of G 2 and SO(7) play a role.
The linear combination of Pk (COS O~j) corresponding to a particular W U entails the isoscalar factors (WU k k) as well as the renormalization factors for Ykq. It would be too great a digression to describe the enormously rich structure of Racah's (1949) tables.
Crystal spectra
One of the most active theoretical groups in the early 1950s was the Ufford group at the University of Pennsylvania. A generalized hypergeometric function appears instead of the Racach coefficient W(ll 12 Ii 12; Lk) (mentioned in Section 3.4). It turns out that the group notations for SO(7) and G2 are (110) and (11), respectively, and the annihilation of the second matrix element in Eqs.
No major modifications to the Van Vleck calculation of the electric dipole intensity were suggested by Broer et al. That is, the relative energies of the configurations as a whole are included in the calculation.
Racah's 1964 lectures at the Colli~ge de France
- Single-electron excitations
Viewed slightly differently, the parameters F k are associated with the two-electron parts of the operators (v(k)) 2, while L 2 is proportional to (V(1)) 2. It is now standard procedure to add the parameters take T ~ when fitting the conditions of the configurations 4f N (see Goldschmidt 1978). Differences in differences (in cm ~) between the energies of low-lying levels of types A and B in the second and third spectrums of the lanthanides.
At the time of Racah's lectures, the position of the lowest level of the A P r I I type was unknown. He was quite aware of the fact that both 4f25d 2 and 4fZ5d6s must start quite close to the floor.
Ligand effects
- Crystal-field invariants
- Anisotropic ligands
- Correlation crystal fields
ATOMIC THEORY AND OPTICAL SPECTROSCOPY 135 5p orbitals of Pr 3 + in the outer orbitals of the C I - ligands. The numerical values of the Akq crystal field parameters depend on the choice of coordinate axes. The solution to the paradox lies in the actual transition that was chosen to be studied.
In addition to terms of the type (94) coming from the electrostatic model, they took into account contributions from the dynamic coupling mechanism (or equivalently the mechanism based on an inhomogeneous dielectric). There is some improvement in the fit to the solution data, and the values of the dt are reasonably stable (although unnervingly large in a few cases).
Free-ion work since 1965
- Isotope shifts
These results provided direct evidence of the expansion of the 4f wave function in the crystal. A tabulation of the latter for the ground configurations of R I - X I I is included in the H a n d b o o k of Atomic Data published by Fraga et al. He used the SU(3) model of Elliott (1958) to associate the p-electron with the three-dimensional irreducible representation ]-1] of SU(3), while the combination d + s was associated with the six-dimensional representation [ 2] of the same group.
The relation of L a p o r t e - P l a t t degeneracies to delta function interactions has been explored (Judd and Lister 1984). Cheng and Childs (1985) used a multi-configuration D i r a c - F o c k (MCDF) program developed by Desclaux (1975) (but applied only to states of single 4f N configurations) to calculate hyperfine structures (as well as Land6 9 values) for ground multiples of most neutral lanthanides.
Non-linear spectroscopy
- Two-photon absorption
Any closure procedure that combines the two vectors D to form an equivalent operator of the type V "~ must thus lead us to (EE)(2) • V(2). Although rough agreement was obtained for the line polarizations, , significant differences were observed intensity deviations. Electronic Raman spectra of the type 7F 0 ~ 7Fj were observed by Koningstein (1966) for europium yttrium gallium garnet and Koningstein and Mortensen (1967) for E u : Y V O.
1985) found that the calculated strength of the antisymmetric tensor turned out to be much larger than their experiments suggested. After all, we know from the total closure argument that a suitable weighting of excitations f , , d and f--, g can be found that eliminates V ~ ~ altogether.
Satellite lines
- Hole-burning spectroscopy
1980) detected the hyperfine splittings for the levels 5D o and 7F0 of E u 3 + in EuPsO14 by the so-called hole burning technique. Through this experimental procedure, the populations of the hyperfine levels are redistributed, and the 'holes' and 'anti-holes' are detected by scanning the transition VF o - 5D o with an attenuated laser beam and changes in the fluorescence 5D o - monitor. -* 7Fj. Subsequent experiments on Eu 3 +:YA103 determined the fission induced in the nuclear doublets ]I, _+ Mr ) by an external magnetic field (Shelby and Macfarlane 1981).
The symmetry of the D2d Eu 3 + site in EuVO4 prevents any 0 ~ 0 type transitions, so each line must be due to a specific defect or dislocation site in the crystal. The fact that a different set of axes has been set for each line makes it difficult to analyze the effect of the external magnetic field H on the nuclear moment p.
Mathematical implications
Similar methods can be used to account for some of the properties of e2 mentioned in paragraph 11, note (a), above. The development of the theory of spin-up and spin-down spaces did not put an end to the search for a new group structure in the f-scale. A detailed description of the quasi-particle method for atomic shells has been given by Condon and Odabasi (1980) in their update of the classic text by Condon and Shortley (1935).
The possibility of using a chain of the type given by (131) to classify the states of a many-fermion system was known to Moshinsky (1968) and many others (not to mention Weyl himself, in all probability). Extensions of the unit group approach to a N spin configurations have also been carried out (see e.g. Kent et al. 1985).
Concluding remarks
Despite the work of the Windsor group, as well as the work of Harter and Patterson, the unit calculus cannot yet be said to be competitive with Racah's methods. The two-electron operators needed to describe residual crystal-field effects have not yet been determined, and a complete Lie group classification of the four-electron electrostatic operators for the f-shell remains to be performed. However, the shortcomings of the H a r t r e e - F o c k method seem at present to be most in need of attention.
Much of the debate has turned on heavy atoms, which have very few electrons; however, a paper by Dietz (1985) on the g-Hartree method paved the way for multi-electron atoms. Cross-white, 1977, Energy-level structure and transition probabilities of the trivalent lanthanides in LaF3 (Report of the Department of Physics, Johns Hopkins University, Baltimore, MD).
