F band

There are two main kinds of dye aggregates, characterized by their typical spectral properties J-aggregates and H-aggregates. The absorption band maximum (f-band) of the J-aggregates is shifted bathochromicaHy with respect to that of an isolated molecule (M-band) the absorption maximum of the H-aggregates is shifted hypsochromicaHy (H-band). The dyes can also form dimers with a shorter absorption wavelength (D-band). 

It has been possible, as already noted (footnote, p. 1240) to study the spectra of Ln ions stabilized in CaF2 crystals. It might be expected that these spectra would resemble those of the -)-3 ions of the next element in the series. However, because of the lower ionic charge of the Ln" ions their 4f orbitals have not been stabilized relative to the 5d to the same extent as those of the Ln " ions. Ln" spectra therefore consist of rather broad, orbitally allowed, 4f 5d bands overlaid with weaker and much sharper f f bands. 

Thus the rather easily obtained atomic sizes are the best indicator of what the f-electrons are doing. It has been noted that for all metallic compounds in the literature where an f-band is believed not to occur, that the lanthanide and actinide lattice parameters appear to be identical within experimental error (12). This actually raises the question as to why the lanthanide and actinide contractions (no f-bands) for the pure elements are different. Analogies to the compounds and to the identical sizes of the 4d- and 5d- electron metals would suggest otherwise. The useful point here is that since the 4f- and 5f-compounds have the same lattice parameters when f-bands are not present, it simplifies following the systematics and clearly demonstrates that actinides are worthy of that name. 

Locher im [Pg.21]

Capasso F., Band-Gap Engineering From Physics and Materials to New emiconductor Devices, Science, 1987 235 172-176. 

Fig. 1 Scheme of the OCT system. SLD—superluminescent diode FBS—fiber-optic beam splitter M—mirror L—lenses S—sample PD—photo-diode F—band-pass filter A— logarithmic amplifier AD—amplitude detector ADC—analog-to-digital converter PC— computer. 

In contrast to the red PL band, the green-blue PL band of PS commonly shows decay times in the nanosecond regime and is therefore termed the fast band or F-band. This PL band can be observed under several conditions ... 

From the full width at half maximum (FWHM), AE = 0.34 eV, of the F band, we can determine the FWHM in frequency units, Aoj ... 

The first successful first-principle theoretical studies of the electronic structure of solid surfaces were conducted by Appelbaum and Hamann on Na (1972) and A1 (1973). Within a few years, first-principles calculations for a number of important materials, from nearly free-electron metals to f-band metals and semiconductors, were published, as summarized in the first review article by Appelbaum and Hamann (1976). Extensive reviews of the first-principles calculations for metal surfaces (Inglesfeld, 1982) and semiconductors (Lieske, 1984) are published. A current interest is the reconstruction of surfaces. Because of the refinement of the calculation of total energy of surfaces, tiny differences of the energies of different reconstructions can be assessed accurately. As examples, there are the study of bonding and reconstruction of the W(OOl) surface by Singh and Krakauer (1988), and the study of the surface reconstruction of Ag(llO) by Fu and Ho (1989). 

For the light actinides from a) and b) qualitative consequences may be drawn. It follows, from f-f overlapping, that the atomic 5 f wave functions will broaden into 5 f bands when building the metal. Moreover, since the 5 f, 6 d and 7 s energy eigenvalues are very close (see Sect. A.II) the 5 f band will hybridize strongly with the 5 d and 7 s bands. 

The f-f overlapping in light actinides may cause broadening of the 5 f wave functions into 5 f bands. On the other hand, from Am on, this overlapping having decreased, this effect occurs much less. It follows that physical properties which depend from 5f orbitals may be better understood, in one case, in the band Umit, in the other case, in the atomic limit. 

Experimental Evidence of 5 f-Band Behaviour in Lighter Actinides... 

Spectroscopic properties Photoemission from the valence band of uranium and plutonium indicates a 5 f band at the Fermi leveT (see Chap. E). 

Fig. 16 a, b. Proposed band structure for uranium metal by FriedeP . a) a-phase b) y-phase. Bi, BJ and B2 indicate hybridized d-f bands the numbers inscribed are the number of electrons per atom in these hybridized bands. In b), the Bj narrow band is simulated with a square band, with bandwidth W and center C... 

Some years ago, it had become customary to speak of f-band superconductors. Behind these words, there was the assumption that narrow f-bands might give rise to f level, or f band, polarization ... 

It has now become apparent that f-band superconductors can be understood in a normal way, like d-band ones" we have just to think about density of states, bandwidth lattice unstabilities and electron correlations to interpret it. This was clearly summarized by Smith after the discovery of superconductivity of Pa and Am. Superconductivity of Am is made by the J = 0 ground state of its six 5 f electrons as was stressed by Johansson , this could also be the case for stabilized trivalent europium metal. The importance of lattice instabilities (like in A-15 high Tc superconductors) was put forward by Fournier who showed that the very large 6T/8p slope for U was mainly due to a very targe change in the electron-phonon coupling associated with the low temperature phase transition. 

Detailed studies - band structure calculations, de Haas-van Alphen effect and polarized neutron diffraction - have evidenced the strong hybridization of 5 f bands either with p anions bands (USi3, UGes, USns) or 4d bands (URhs, UIts). 

In the preceding sections, we have rapidly reviewed the concepts that are involved in the band formation of actinide metals. We would like to point out what more is involved in the band formation of actinide compounds. This is very obvious the anion valence band. In fact, the hybridization with anion states which we presented as the main correction to the simple Hill scheme is indeed the central question involved in detailed band structure calculations in actinide compounds. We pointed out in the previous paragraph the case of UGea we would like here, as an example, to compare somewhat UO2 and NaCl compounds of uranium. As confirmed by recent photoemission studies " , UO2 has well localized 5 f states whereas NaCl compounds have a narrow 5 f band pinned at the Fermi level. Nevertheless the U-U spacing is the same in UO2, UP and US. This difference may be understood in terms of charge transfer versus f-p hybridization. 

The contributions Ef to the bonding energy E), of the itinerant 5f electrons can be evaluated in a simple way following the lines of Friedel s model Essentially the density of state peak Nf(E) of the 5 f band is substituted by a square function (see Fig. 16 in Chap. A) ... 

Band calculations show that 6 d-5 f hybridization reduces considerably the occurence of ferromagnetism (Stoner criterion) in the 5 f band. 

As a remark, it should be noted that a single electron ground state from a filled band (which would be the case of americium within a band description because the 5 f band is spin-orbit splitted into a filled 5/2 sub-band and an empty 7/2 sub-band) is equivalent to a localized state and thus a spin-polarized band description leads to the same conclusion as a simple Mott description. 

In the case of narrow bands - and this will be the case of hybridized 5 f bands when 5 f electrons are itinerant - an approximate treatment has to be done. Kubo and Obata have studied the case of transition metals in the tight binding approximation. The narrow band susceptibility is the sum of 4 terms... 

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