Books
in black and white
Main menu
Home About us Share a book
Books
Biology Business Chemistry Computers Culture Economics Fiction Games Guide History Management Mathematical Medicine Mental Fitnes Physics Psychology Scince Sport Technics
Ads

Europium - Sinha S.P.

Sinha S.P. Europium - Springer-Verlag, 1967. - 88 p.
Download (direct link): europium1967.djvu
Previous << 1 .. 40 41 42 43 44 45 < 46 > 47 48 49 50 51 52 .. 69 >> Next

There is, however, one possibility, which is still unexplored, viz. to look forirhe f—f transitions of these divalent ions in the infrared region. Some information \49I\ on these transitions in Dy2+(/10), Ho2+(/11), Er2+(/12) and Tm2+(/13) is available from fluorescence spectral measurements.
The crystal spectra of the trivalent rare earth ions have been quite successfully interpreted. However, the data on f—f transitions are limited particularly to the lower energy portions and extension to the vacuum ultraviolet is strongly warranted due to the presence of strong continuous / -► d absorption, and possible absorption due to the host crystal. Moreover, the number of lines originating from various lowest configurations may be very large further complicating the issue. Table 41 shows the possible number of levels that may originate from the four lowest configurations of the trivalent rare earths.
Table 41. The possible number of levels for the four lowest configurations of the trivalent rare earths
Ma+ Configuration Total
4/» 4/»~15d 4/n-16s 4/n-16p
La 1 - - - 1
Ce 2 2 1 2 7
Pr 13 20 4 12 49
Nd 41 107 24 69 241
Pm 107 386 82 242 817
Sm 198 977 208 611 1994
Eu 295 1878 396 1168 3737
Gd 327 2725 576 1095 4723
Tb 295 3006 654 1928 5883
Dy 198 2725 576 1095 4594
Ho 107 1878 396 1168 3549
Er 41 977 208 611 1837
Tm 13 386 82 242 723
Yb 2 107 24 69 202
Lu 1 20 4 12 37
The extensive experimental analysis of the rare earth spectra in doped crystals has enabled us to deduce the Ft and £4/ parameters for M3+ ions. These are presented in Table 42. It is interesting here to examine these values closely. Inspection of the F* data reveals much irregularity throughout the series whereas £4/ shows a tendency to increase from Ce3+ to Yb3+. The author has tried to correlate the F2 and £4/ parameters with the polarizing power (e/r2) of the rare earth ions and obtained Fig. 21. The F2 parameter shows a linear increase up to Tb3+ followed by a decrease to Ho3+ and then another increase. However, the noteworthy aspect is the linear behaviour of Xa/ with e/r2 having a small but distinct gadolinium break near the Gd—Dy region.
Absorption Spectra of the Europium Ion and Its Complexes 113
Table 42. Comparison of F^ and t4/ parameters (in cm-1) of trivalent rare earths deduced from crystal spectra
M*+ F2 F, F* C*/ Reference*
Ce — - - 644 [482]
Pr 305.4 51.88 5.321 729.5 [49 3-498]
Nd 327.5 48.66 5.356 884.6 [499-501]
Pm 346 47.68 5.232 1050 [502-507]
Sm 370 51.08 5.591 1200 [508-511]
Eu 401 55.36 6.059 1320 [512 -513*]
Gd 406 56.05 6.135 1583 [514-517]
Tb 434 59.91 6.558 1705 [512, 518, 519]
Dy 420 57.98 6.346 1900 [508, 511, 520-524]
Ho 414.6 68.80 7.272 2163 [502, 524-528]
Er 433.2 67.13 7.356 2393.3 [524, 529-537]
Tm 450 68.07 7.437 2700 [514, 538-541]
Yb — — — 2924 [542-544]
a The references in bold type refer to the theoretical calculations and the following references are those of experimental works.
b For more theoretical and experimental work see reference [562—572].
e/r2 -►
Fig. 21. Variation of F2 (—o—o—o—) and t4/ (—#—•—#—) parameters with the polarizing power of the tripositive rare earth ions
Crystal Field Parameters
It has been found experimentally that the crystal field effect in rare earths is quite small and of the order of — 200 cm-1. Thus its magnitude
8 Sinha, Europium
114
Spectroscopic Properties of Europium
is smaller than spin-orbit coupling, whereas for the 3<J-transition series the 'spin-orbit coupling is smaller than the crystal field splitting.
The Hamiltonian for an ion in an electric field provided by the crystal environment may be expressed (eq. (53)) in terms of the Hamiltonian of the free ion (Jff) and the potential, Vc, acting as a perturbation on the /-electrons.
^ ^ ~f* Vc (53)
The unperturbed eigenfunctions have complete spherical symmetry and Vc can be expanded in terms of the crystal field parameters, A™, and the usual spherical harmonics Y™ (6, <p) to give
Vc = 2 VZ = 2 K rn Y” (0, <p) (54)
n,m n,ro
When the matrix elements are calculated for states built from /-electron configurations it is always found that the constants A™ (these quantities are related to the strength of crystal field) always occur with <rn> (the sharp brackets denote integration with respect to 4/ radial function). A% <rn> parameters play an important role in crystal field calculations and can be used as parameters in describing the crystal field. For the lowest L S J state they can easily be determined by using the operator equivalent technique of Elliott and Stevens [545—647] and with the help of existing tables of matrix elements. Wyboubne [548], however, feels that a better approach is to expand Vc in terms of the tensor operators, C™ , as
Vc = IK (C™). (55)
where the summation involving i is over all the electrons of the ions in consideration, and the quantity 2?” is related to A™ <rn > as
Bnm = \A™ <r"> (56)
Previous << 1 .. 40 41 42 43 44 45 < 46 > 47 48 49 50 51 52 .. 69 >> Next