Fermi energy, actinides

Figure 17 is a clear illustration of the Mott-Hubbard transition in the actinide series the 5f emission occurs, for a-Pu, at Ep, indicating a high 5f-density of states pinned at the Fermi-level, whereas the 5 f emission occurs at lower energy for americium metal. In this case, therefore, a theoretical concept deduced indirectly from the physical properties of the two metals, finds direct (one might even say photographic ) confirmation in the photoemission spectra. 

In the d-transition series the conduction bands at the Fermi level are predominantly narrow d-bands superimposed upon a broad s-p band structure. In the actinides narrow f-bands at the Fermi level are superimposed upon an spd band structure, the d-bands now being broad conduction band states. The energy bands of the rare earths and heavy actinides are so narrow that it is energetically favourable for Mott-localized states to form. The reason is that polar states are present in bands and this costs... 

Spectroscopy. The application of optical and photoelectron spectroscopy to elucidate electron energy states of pure actinide metals is still in the initial stages (46). Reflectivity measurements on Th samples (mechanically polished, electropolished, or as grown from the vapour phase) demonstrate the importance of sample and surface preparation (47), and explain reasons for discrepancies in published results (48, 49). Preliminary measurements of the optical reflectivity of Am films evaporated on different window materials (50) seem to indicate that the 5f levels are lying more than about 6 eV below the FERMI level, thus supporting the interpretation of the electrical resistivity results... 

The f-electrons of Am, though quite localized, are still very close to the Fermi level (like Ce) compared to most rare-earths, and the energy bandwidth is comparable to that for Ce. Therefore, we should still expect some complexities in bonding and valence-level interactions. The entropy position of Am in Fig. 4 is representative of a rather normal trivalent metal exhibiting an "actinide-contraction" beginning at Ac. 

A central feature in the chemistry of No is the dominance of the divalent oxidation state (26). In this respect, No is unique within the lanthanide and actinide series, since none of the other twenty-seven members possess a highly-stable divalent ion. The electronic configuration of the neutral atom obtained from relativistic Hartree-Fock calculations is 5f 7s 2 (j>). Clearly, the special stability of No + must arise from the difficulty in ionizing an f valence electron from the completed 5f shell. Thus, pairing of the last electron, to close the shell, results in the f electron levels taking a rather abrupt drop in energy below the Fermi surface. 

The study of Coulomb transitions is especially valuable in actinide metals and intermetallic compounds (McEwen et al. 1990, Osborn et al. 1990). Because of the greater radial extent of the 5f charge distribution, the actinide f electrons tend to hybridise more strongly with band electron states than their lanthanide counterparts. In a number of actinide metals, it is evident that the f electrons contribute to the cohesive energy through the formation of 5f bands, either by direct f-f overlap, as in a-uranium, or by hybridisation with conduction bands, as in URUj or URhj (Oguchi and Freeman 1986, Johansson et al. 1987). In these cases, relativistic band theory is successful in predicting lattice constants, photoemission and Fermi surfaces (Arko et al. 1985) provided the f states are included as itinerant. 

Arko, A.J., D.D. Koelling and J.E. Schirber, 1985, Energy band structure and Fermi surface of actinide materials, in Handbook on the Physics and Chemistry of the Actinides, Vol. 2, eds A.J. Freeman and G.H. Lander (North-Holland, Amsterdam) ch. 3, p. 175. 

In a recent publication, Cox et al. (1992) presents photoemission data for Am metal and AmHj. Both materials are expected to exhibit fully localized rare-earth-like spectra nevertheless, as shown in fig. 21, the 5f peak distribution is still dominant with its centroid about 3eV from the Fermi level. As with the rare earths, a reduced conduction-band intensity can be seen quite clearly. Positive chemical shifts for all the metal levels (4f, 5p, 4d and 3d) indicate electron transfer from the metal. As expected, the 6p3/2 binding energy for AmHj increases by about 0.6 eV, an amount similar to that found for Ce and Pr. Although the peak maximum for AmHj appears to shift to lower binding energies, the centroid is actually coincident with that for Am metal. In spite of these complications, cross-section effects and initial-final state considerations, the Am-I-H system is clearly the first unambiguously rare-earth-like actinide-hydride system. These observations are corroborated by resistivity measurements described in section 6.3.1. 

The chapter by Wachter (132), which is one of the most extensive and comprehensive ones in the entire Handbook series, reviews intermediate valence and heavy fermions in a wide variety of lanthanide and actinide compounds, ranging from metallic to insulating materials. The behaviors of these materials are discussed from the basic idea that a gap exists between two narrow f-like subbands, i.e. the hybridization gap model, which can account for the observed physical and electronic properties. As pointed out by Wachter, heavy fermions are intermediate valence materials by virtue of the fact that they have nonintegral f occupation values. The main difference between normal intermediate valence materials is that their Fermi energies are in the hybridization gap, while for the heavy fermion materials the Fermi energy is not in the gap. 

An overview of the electronic structure of the actinide metals is shown in fig. 17. The figure shows the bottom, centre and top of the 5f bands and the bottom of the s, p and d bands of the entire series, Fr-Lr, as a function of the Wigner-Seitz radius, as evaluated by Skriver and co-workers (Brooks et al. 1984). For the left of the series, Ra-Th, at the equilibrium radius, Sq, the bottom of the 7s band always lies below the Fermi energy, the bottom of the 6d band moves through the Fermi energy from above between Fr and Th, and the bottom of the 5f band is above the Fermi energy. Hence the 7s and 6d bands are the only occupied bands and Th is a 6d-band transition metal. However, the unoccupied 5f band is so close to the Fermi energy that it... 

Fig. 17. Energy bands for Fr and the actinides, evaluated as function of the atomic radius, S. The potential, K(S), at the sphere, the bottom, B, and the top, / , of the relevant bands, together with the Fermi energy, p, are plotted, Sg is the measured equilibrium atomic radius.

The calculated state densities at the Fermi energy have been collected and compared to experimentally observed specific heat coefficients in fig. 19. One should bear in mind that most of the calculations assume an fee structure, and therefore one cannot expect too detailed an agreement between theory and experiment. In the beginning of the series, i.e. for Fr-Th, the 5f contribution is small, and N Ep) for Th is typical for a transition metal. In Pa the 5f contribution starts to dominate the state density, which by Am has increased by an order of magnitude. The measured electronic specific heat coefficients show a similar trend up to, and including, Pu. However, in Am it is down by one order of magnitude with respect to the value for Pu, and is in fact close to the spd contribution to the state density. Hence, in this respect Am behaves like a rare earth metal. The interpretation of the above-mentioned observations is that the 5f electrons in Pa Pu are metallic, hence the high electronic specific heat, in the same sense that the 3d, 4d and 5d electrons in the ordinary transition series are metallic, and that this metallic 5f state turns into a localized one at Am, hence the relatively low electronic specific heat. Am and the later actinides form a second rare earth series. 

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