Metal energy bands

Figure Al.3.8. Schematic energy bands illustrating an insulator (large band gap), a semiconductor (small band gap), a metal (no gap) and a semimetal. In a semimetal, one band is almost filled and another band is almost empty.

Simple metals like alkalis, or ones with only s and p valence electrons, can often be described by a free electron gas model, whereas transition metals and rare earth metals which have d and f valence electrons camiot. Transition metal and rare earth metals do not have energy band structures which resemble free electron models. The fonned bonds from d and f states often have some strong covalent character. This character strongly modulates the free-electron-like bands. 

Massidda S, Continenza A, Posternak M and Baldereschi A 1997 Quasiparticle energy bands of transition-metal oxides within a model GW scheme Phys. Rev. B 55 13 494-502... 

Fig. 1. Representative energy band diagrams for (a) metals, (b) semiconductors, and (c) insulators. The dashed line represents the Fermi Level, and the shaded areas represent filled states of the bands. denotes the band gap of the material.

MetaUic behavior is observed for those soHds that have partially filled bands (Fig. lb), that is, for materials that have their Fermi level within a band. Since the energy bands are delocalized throughout the crystal, electrons in partially filled bands are free to move in the presence of an electric field, and large conductivity results. Conduction in metals shows a decrease in conductivity at higher temperatures, since scattering mechanisms (lattice phonons, etc) are frozen out at lower temperatures, but become more important as the temperature is raised. 

The ID electronic energy bands for carbon nanotubes [170, 171, 172, 173, 174] are related to bands calculated for the 2D graphene honeycomb sheet used to form the nanotube. These calculations show that about 1/3 of the nanotubes are metallic and 2/3 are semiconducting, depending on the nanotube diameter di and chiral angle 6. It can be shown that metallic conduction in a (n, m) carbon nanotube is achieved when... 

The existence of carbon nanotubes with diameters small compared to the de Broglie wavelength has been described by Iijima[l,2,3] and others[4,5]. The energy band structures for carbon nanotubes have been calculated by a number of authors and the results are summarized in this issue by M.S. Dresselhaus, G. Dres-selhaus, and R. Saito. In short, the tubules can be either metallic or semiconducting, depending on the tubule diameter and chirality[6,7,8]. The calculated density of states[8] shows singularities... 

Fig. 4. Some examples of calculated energy bands of a metallic CNT in magnetic fields perpendicular to the axis.

Fig. 5. Energy bands of a metallic CNT in the presence of a magnetic flux and allowed optical transitions for the x and y polarisations.

In the optical absorption, two different polarisations of light should be considered the electric field is along (parallel or y polarisation) and perpendicular (perpendicular or x) to the axis. Figure 5 shows the energy band of a metallic CNT for flux < )/< )o =0, 1/4 and 1/2 and the process of optical transitions for the parallel and perpendicular polarisations. Some examples of calculated absorption... 

Recent papers [4-6] of the NRL group have concentrated on a tight-binding methodology that simultaneously fits the energy bands and the total ener — of the fee and bcc structures as a function of volume, and correctly predicts the ground state for those metals that crystallize in the hep or even the Of-Mn structure. 

Switendick was the first to apply modem electronic band theory to metal hydrides [5]. He compared the measured density of electronic states with theoretical results derived from energy band calculations in binary and pseudo-binary systems. Recently, the band structures of intermetallic hydrides including LaNi5Ht and FeTiH v have been summarized in a review article by Gupta and Schlapbach [6], All exhibit certain common features upon the absorption of hydrogen and formation of a distinct hydride phase. They are ... 

It was pointed out in my 1949 paper (5) that resonance of electron-pair bonds among the bond positions gives energy bands similar to those obtained in the usual band theory by formation of Bloch functions of the atomic orbitals. There is no incompatibility between the two descriptions, which may be described as complementary. It is accordingly to be expected that the 0.72 metallic orbital per atom would make itself clearly visible in the band-theory calculations for the metals from Co to Ge, Rh to Sn, and Pt to Pb for example, the decrease in the number of bonding electrons from 4 for gray tin to 2.56 for white tin should result from these calculations. So far as I know, however, no such interpretation of the band-theory calculations has been reported. 

The energy band describing the bonding in lithium metal can be constructed by adding atoms one at a time. 

As described in Section 10-, the bonding in solid metals comes from electrons in highly delocalized valence orbitals. There are so many such orbitals that they form energy bands, giving the valence electrons high mobility. Consequently, each metal atom can be viewed as a cation embedded in a sea of mobile valence electrons. The properties of metals can be explained on the basis of this picture. Section 10- describes the most obvious of these properties, electrical conductivity. 

The first term is attractive (it increases the bonding energy) while the second is repulsive (decreases the bonding energy). Hence three parameters play a role in determining the bond strength between the metal d band and the atomic adsorbate ... 

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