Narrow-band solids

Fig. 14 a, b. Hubbard sub-bands for the localized ("f or j.) and polar states in a narrow band solid... 

Localization versus itineracy and the degree of hybridization of 5 f states with orbitals of the actinide atom (especially 6 d) as well as with those of the ligand in compounds are central questions for the understanding of bonding in actinide solids. Photoelectron spectroscopy provides answers to these questions. In narrow band solids, like the actinides, the interpretation of results requires the use of band calculations in the itinerant picture, as well as models of final state emission in the atomie picture. 

Such details in photoemission spectroscopy may therefore give indirect, but very useful hints towards the solution of the localization vs. itineracy problem of narrow band solids. 

Photoelectron spectroscopy has long be considered as to be able to provide a photographic picture of the one-electron density of state of solids. In reality, the spectra of actinide solids (as of other narrow band solids) need very often more than this naive interpretation. In the case of 5 f response, final state effects are found to provide useful information even in the case of metals, as illustrated in this chapter. The general conclusion that the photoelectron spectroscopic response depends on many-electron excited final states as much as it depends on the initial states, when narrow bands are involved, must be emphasized. This points to the necessity both of better final state models and of band calculations giving reliable pictures of conduction bands. 

As shown in Table 1, hollow waveguides (HWGs) are the only fibers capable of transmitting radiation across the entire MIR band at comparatively low attenuation losses similar to usually more narrow-band solid-core IR fibers. 

Z. G. Soos, L. R. Ducasse, and R. M. Metzger, Partial ionicity, cohesion, and charge correlations in narrow-band solids, J. Chem. Phys. 77 3036-3045 (1982). 

O. Gunnarsson, Alkali-Doped Fullerides Narrow-Band Solids with Unusual Properties (World Scientific, Singapore, 2004)... 

Calculations for Ceo in the LDA approximation [62, 60] yield a narrow band (- 0.4 0.6 eV bandwidth) solid, with a HOMO-LUMO-derived direct band gap of - 1.5 eV at the X point of the fee Brillouin zone. The narrow energy bands and the molecular nature of the electronic structure of fullerenes are indicative of a highly correlated electron system. Since the HOMO and LUMO levels both have the same odd parity, electric dipole transitions between these levels are symmetry forbidden in the free Ceo moleeule. In the crystalline solid, transitions between the direct bandgap states at the T and X points in the cubic Brillouin zone arc also forbidden, but are allowed at the lower symmetry points in the Brillouin zone. The allowed electric dipole... 

This equation indicates that polarizability is proportional to the inverse square of the excitation energy. Therefore, atoms, molecules, and solids with small values of A are easily polarized. That is, they are chemically and mechanically soft. The gaps in their bonding energy spectra are small. Since they absorb light easily, they tend to be colored. If A lies in a narrow band as in a dye, the coloration is bright and saturated. If it lies in broad band as in adhesive polymers, it may be a muddy brown. 

Table 4.1. Various processes contributing to the spectral line broadening for local vibrations. Frequencies of collectivized local vibrations QK (solid arrows) are supposed to exceed phonon frequencies oiRq (dashed arrows) Ok > max oncq. For an extremely narrow band of local vibrations, diagrams A and B respectively refer to relaxation and dephasing processes, whereas diagrams C account for the case realizable only at the nonzero band width for local vibrations.

The rest of the chapter is structured in such a way as to give the reader the possibility to get convinced of this description. The description originates from the peculiar properties of the 5 f electron states. Therefore, in Part II, these states will be examined in free actinide atoms. In Part III, the meaning of the atomic information for solids will be discussed the puzzling problem of atomic-like localized states, which, however, spread enough to form narrow bands and allow a delocalized description. In this part, the conceptual tools to understand the puzzle are provided. 

Fig. 12a-c. Schematic representation of the effective potential Vejf and of different possibilities of localized and itinerant states for electrons of high 1 quantum number, a) The solid line d represents the periodic potential set-up by the cores R and R +i, which is a superimposition of central potential a dashed line). The dashed line b represents the centrifugal potential of kinetic origin 1(1 + l)/2 R in an atom, and c dashed line) the effective potential V f for an atom (compare Fig. 6) and full line) for a solid, b) Relative to two shapes of the effective potential Ve, two examples of localized state are given 1. resonant state 2. fully localized state. Notice that 1. is very near to Ep. h and t represent hopping and tunneling processes, c) A narrow band is formed (resonance band), pinning Ep 3. narrow band... 

Difficulties arise when the d- and f-electrons are in an intermediate state between i. and ii. This is the case for narrow bands (Fig. 12c). This intermediate state of affairs has been at the center of theoretical and experimental investigations for d-transition solids, especially metallic solids ... 

One important point is whether narrow bands would display permanent magnetic moments and undergo magnetic collective phenomena. This depends clearly upon their bandwidth and will lead again to the problem localization vs itineracy. In band calculations, new ways have to be looked for, since the set of hypotheses examined previously, which hold for non-magnetic solids, must be corrected for spin-polarization. 

These concepts are very importcint also for actinide solids. In particular, the Stoner model for collective magnetism in narrow bands, the frame in which d-transition metals and actinide metals magnetism has been discussed, will be reviewed briefly. 

When the cores are approached, the sub-bands split, acquiring a bandwidth, and decreasing the gap between them (Fig. 14 a). At a definite inter-core distance, the subbands cross and merge into the non-polarized narrow band. At this critical distance a, the narrow band has a metallic behaviour. At the system transits from insulator to metallic (Mott-Hubbard transition). Since some electrons may acquire the energies of the higher sub-band, in the solid there will be excessively filled cores containing two antiparallel spins and excessively depleted cores without any spins (polar states). 

In recent times, the bond indicators , which are the ground state properties of the solid related to its cohesion (metaUic radii, cohesive energy, bulk moduli), have been interpreted in the light of band calculations. The bond in metals and in compounds has been described by an easily understandable and convincing thermodynamic formalism, which we shall illustrate in this chapter. Essentially, narrow bands, as the 5 f electrons form, are considered to be resonant with the wider (spd) conduction band. The 5 f electronic population is seen as a fluid the partial (bonding) pressure of which assists in cohesion along with the partial pressure of another fluid constituted by the conduction electrons of (s and d) character. ... 

From the experimental viewpoint 1. the analysis of the variation of photoionization cross sections (affecting the intensities of photoelectron spectroscopy), gives an insight into the orbital composition of the bands of the solid 2. the combination of direct and inverse photoemission provides a powerful tool to assess the structure of occupied and of empty states, and, in the case of localized 5 f states, permits the determination of a fundamental quantity, the Coulomb correlation energy, governing the physical properties of narrow bands. 

The actinide solid state properties are to a large extent based on the properties of the 5f wave-functions. Central to the actinide solid state research has been the co-existence of evidence and of concepts pointing clearly to the recognition of light actinides as being elements in which a metallic bond is enhanced by the overlapping of 5 f wave-functions. The narrow band, itinerant character of the 5 fs is similar to the one d-shells have hence, the classification of these elements as 5 f-transition metals. 

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