Valence band structure

Fig. 8. LDF valence band structure of [9,2] chiral nanotube. The Fermi level lies at midgap at -3.3 eV. Dimensionless wavenumber coordinate k ranges from 0 to t.

The valence band structure of very small metal crystallites is expected to differ from that of an infinite crystal for a number of reasons (a) with a ratio of surface to bulk atoms approaching unity (ca. 2 nm diameter), the potential seen by the nearly free valence electrons will be very different from the periodic potential of an infinite crystal (b) surface states, if they exist, would be expected to dominate the electronic density of states (DOS) (c) the electronic DOS of very small metal crystallites on a support surface will be affected by the metal-support interactions. It is essential to determine at what crystallite size (or number of atoms per crystallite) the electronic density of sates begins to depart from that of the infinite crystal, as the material state of the catalyst particle can affect changes in the surface thermodynamics which may control the catalysis and electro-catalysis of heterogeneous reactions as well as the physical properties of the catalyst particle [26]. 

Table 2. Summary of valence band structures of a-U metal as reported by different authors (AE is the experimental resolution)...

Table 3. Summary of valence band structures of UO2 (occupied and empty states) as observed and analysed by different methods... 

From Table 1 the scheme for the actinide metals shown in Fig. 4 is arrived at. The valence band structure is evidently more complicated in detail than that of the d-transi-tion metals because there are now four different angular momentum states to deal with. However, the d bands are now broad conduction bands. This is not surprising since the broadening of d-bands is a systematic trend from the 3rd to the 5th transition metal series and has now passed a stage further. The reason for this is that the wave functions of each new d-series must be orthogonal to those of the earlier series. The necessary additional orthogonality mode extends the wave functions spatially and broadens the bands. Precisely the same phenomenon occurs between the 4f and 5f series. Thus d-electrons play the role of the major conduction electrons in the actinides and the relative population of the sp conduction bands is reduced. The narrow f-bands are pinned to the Fermi level... 

When UV photons are used, the available energy provides only the possibility of studying the outer electron shells. Therefore UPS (Ultraviolet Photoelectron Spectroscopy) studies the valence band structures of materials. 

Primary surface information valence band structure, bonding. 

Alg, Zn i, 0 crystallizes in the wurtzite or in the rocksalt structure, depending on the Mg mole fraction x. The alloys remain direct-gap materials over the whole composition range. The wurtzite-structure part reflects a valence-band structure, which is similar to ZnO. For the rocksalt-structure part the... 

Figure 4.31 shows ultraviolet photoelectron spectra recorded during the same interface experiment shown in Fig. 4.26. A clear transition from the Cu(In,Ga)Se2 valence band structure with a valence band maximum at 0.8eV binding energy to the ZnO valence band structure with a valence band maximum at 3eV is observed with increasing ZnO deposition. The well-resolved valence band features are enabled by the in situ sample preparation. Also very sharp secondary electron cutoffs are obtained, which allow for an accurate determination of work functions. The work functions of Cu(In,Ga)Se2 and ZnO are determined as 5.4 and 4.25 eV, respectively. These result in ionization potentials of 6.15 and 7.15 eV for Cu(In,Ga)Se2 and ZnO.

Fig. 4.31. UPS valence bands recorded during deposition of undoped ZnO onto de-capped Cu(In,Ga)Se2 showing the valence band structure (right) and the secondary electron cutoff (left). The deposition times are indicated in seconds...

A useful approach to the wurtzite valence band structure is the quasi-cubic model of J.J. Hop field [3], In this framework, the relative energies of the valence band maxima are ... 

Mikheikin et al. (11) have formulated an alternative approach where terminal valencies are saturated by monovalent atoms whose quantum-chemical parameters (the shape of AO, electronegativity, etc.) are specially adjusted for the better reproduction of given characteristics of the electron structure of the solid (the stoichiometry of the charge distribution, the band gap, the valence band structure, some experimental properties of the surface groups, etc.). Such atoms were termed pseudo-atoms and the procedure itself was called the method of a cluster with terminal pseudo-atoms (CTP). The corresponding scheme of quantum-chemical calculations was realized within the frames of CNDO/BW (77), MINDO/3 (13), and CNDO/2 (30) as well as within the scope of the nonempirical approach (16). 

Experimental information on the valence levels comes essentially from photoemission XPS and UPS measure densities of states (DOSs) convoluted with absorption cross sections, and these DOS values can be compared with those computed from VEH valence-band structures [195]. This has now been done for several CPs and the agreement is good. It would be more instructive to compare the actual band structure to angle-resolved (ARUPS) measurements, but this has never been done. What comes nearest is an ARUPS study of a series of long alkanes taken as models for polyethylene, a nonconjugated polymer [196]. 

Ultra-violet photoemission spectroscopy (UPS) probes the density of states, and ion neutralization spectroscopy (INS) and surface Penning ionization (SPI) provide similar information with probes of ions and metastable atoms, respectively. Angle-resolved UPS can determine the valence band structure. X-ray Photoelectron Spectroscopy (XPS) provides information on chemical shifts of the atomic core levels, and this can also help in understanding chemical bonding at the surface. 

Information available from XPS data includes valence band structure and the detection of n orbitals. Procedures for obtaining these types of data arc not discussed further in this review because they are not commonly encountered in surfactant materials analysis. Reviews of these procedures have been published II4.I5). 

Figure I. Electronic structure of all-trans polyethylene (A) valence band structure (B) density of states histogram and its integration curve (C) experimental ( ) and theoretical (-----------------------) XPS spectra.

A third example of this effect is evidenced by a study of the valence band structures of the series of n-phenyl molecules converging to the polymer p-polyphenyl whose valence band spectrum can be seen in Figure 6 ( ). This experience confirms the results obtained for the alkanes and the polyacenes. 

Hydrocarbon Based Polymers. The substitution of one hydrogen atom in the -CH2-CH2- unit by some short carbon chains induces subtle modifications in the electronic structure (molecular orbitals) of the polymers. Though these modifications cannot be easily evidenced on the XPS carbon Is core level spectra, it appears that the XPS valence band structures are much more sensitive to these substitutions and that they become unique and readable fingerprints of the polymers (1, 22). We will not speak here of the Cls shake-up data that were revealed useful to distinguish between saturated and unsaturated bonds (this field with various applications was recently reviewed (23)). 

Angle-resolved ultraviolet photoemission spectroscopy ARUPS Electrons photoemitted from the valence and conduction bands of a surface are detected as a function of angle. This gives information on the dispersion of these bands (which is related to surface structure) and also structural information from the diffraction of the emitted electrons. Valence band structure... 

Fig. 5.34. Schematic valence-band structure of BjO, (band limits and shapes are not intended to be accurate) (after Joyner and Hercules, 1980 reproduced with the publisher s permission).

Sugiura, C., I. Suzuki, J. Kashiwakura, and Y. Gohshi (1976). Sulfur K x-ray emission bands and valence band structures of transition metal disulfides. J. Phys. Japan 40, 1720-24. 

The electronic state calculations of transition metal clusters have been carried out to study the basic electronic properties of these elements by the use of DV-Xa molecular orbital method. It is found that the covalent bonding between neighboring atoms, namely the short range chemical interaction is very important to determine the valence band structure of transition element. The spin polarization in the transition metal cluster has been investigated and the mechanism of the magnetic interaction between the atomic spins has been interpreted by means of the spin polarized molecular orbital description. For heavy elements like 5d transition metals, the relativistic effects are found to be very important even in the valence electronic state. 

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