Electrons, delocalized, conduction band

The isomorphous diiodides of Ce, Pr and Gd stand apart from all the other, salt-like, dihalides. These three, like LaH, are notable for their metallic lustre and very high conductivities and are best formulated as (Ln ,2I",e", the electron being in a delocalized conduction band. Besides the dihalides, other reduced species have been obtained such as LnsCln (Ln = Sm, Gd, Ho). They have fluorite-related structures (p. 118) in which the anionic sublattice is partially rearranged to accommodate additional anions. 

In some oxides containing transition metals in very low oxidation states, metal d electrons enter delocalized conduction bands and the materials have metallic properties an example is NbO. 

Answer 13 It is probably a scandium(iii) compound Sc " (H )2(e ). The free electrons are in a delocalized conduction band and thus enable it to conduct electricity. 

Electrochemical capacitors, also called supercapacitors, are very attractive electricity sources because of their high power, very long durability, and intermediate energy between the classical dielectric capacitors and batteries. The performance of a typical electrochemical capacitor is based on the accumulation of charges in the electrical double layer without faradaic reactions (no electron transfer The electrons involved in double layer charging are the delocalized conduction-band electrons of the electrode material. As shown in Fig. 23.9, an electrochemical capacitor contains one positive electrode with electron deficiency and the second one with electron excess (negative). The capacitance C of one electrode due to a pure electrostatic attraction of ions is proportional to the surface area S of the electrode-electrolyte interface, according to the formula (23.3) ... 

This can be used as a measure of the density of electrons accumulated in the film [47-50]. Although there is some debate about whether the states giving rise to the absorbance are delocalized conduction band states or intraband trap states, the evidence favors the latter [19, 51]. 

It is well known that the rigid-rod polymer materials have good dielectric properties. However, it is interesting that because the extended 7r-conjugated structure provides extensive electron delocalization, the band gap calculated for PBZT in a coplanar conformation is 1.73 eV, which is close to that of polyacetylene (195,196). Therefore, although PBZT has low conductivity (about 10 S/cm)... 

For the investigation of doped semiconductors, temperature is an important factor [110]. At room temperature, most of the donors are ionized and contribute their electrons to delocalized conduction band states. At very low temperatures, the electrons are either localized at the donor sites or form an impurity band (high donor concentrations). The frequency of the LO-plasmon coupled mode is given by [31,110-112]... 

Monochalcogenides, LnZ (Z = S, Se, Te), have been prepared for all the lanthanides except Pm, mostly by direct combination.They are almost black and, like the monoxides, have the NaCl structure. However, with the exceptions of SmZ, EuZ, YbZ, TmSe and TmTe, they have metallic conductivity and evidently consist of Ln -t- Z ions with 1 electron from each cation delocalized in a conduction band. EuZ and YbZ, by contrast, are semiconductors or insulators with genuinely divalent cations, but SmZ seem to be intermediate and may involve the equilibrium ... 

Assuming perfect stoichiometric structures, the stabilization of the boron frameworks of MB2, MB4, MBg, MBj2 and elemental B requires the addition of two electrons from each metal atom. Whatever the Bj2 unit, icosahedron or cubooctahe-dron, 26 electrons are required for internal bonding and 12 for external bonding. Since the 12 B possesses only 36 electrons, the metal must supply two electrons to each Bi2 group. The results for YB,2 are consistent with this model measurements indicate that one electron per Y is delocalized in the conduction band. ... 

Solid mixed ionic-electronic conductors (MIECs) exhibit both ionic and electronic (electron-hole) conductivity. Naturally, in any material there are in principle nonzero electronic and ionic conductivities (a i, a,). It is customary to limit the use of the term MIEC to those materials in which a, and 0, 1 do not differ by more than two orders of magnitude. It is also customary to use the term MIEC if a, and Ogi are not too low (o, a i 10 S/cm). Obviously, there are no strict rules. There are processes where the minority carriers play an important role despite the fact that 0,70 1 exceeds those limits and a, aj,i< 10 S/cm. In MIECs, ion transport normally occurs via interstitial sites or by hopping into a vacant site or a more complex combination based on interstitial and vacant sites, and electronic (electron/hole) conductivity occurs via delocalized states in the conduction/valence band or via localized states by a thermally assisted hopping mechanism. With respect to their properties, MIECs have found wide applications in solid oxide fuel cells, batteries, smart windows, selective membranes, sensors, catalysis, and so on. 

In this Section we want to present one of the fingerprints of noble-metal cluster formation, that is the development of a well-defined absorption band in the visible or near UV spectrum which is called the surface plasma resonance (SPR) absorption. SPR is typical of s-type metals like noble and alkali metals and it is due to a collective excitation of the delocalized conduction electrons confined within the cluster volume [15]. The theory developed by G. Mie in 1908 [22], for spherical non-interacting nanoparticles of radius R embedded in a non-absorbing medium with dielectric constant s i (i.e. with a refractive index n = Sm ) gives the extinction cross-section a(o),R) in the dipolar approximation as ... 

Moreover, it was shown that the presence of Hal Hal interactions between the partially oxidized molecules also contribute to the electronic delocalization. Indeed, the presence of non-zero atomic coefficients on the halogen atoms in the HOMO of EDT-TTF-Br2 or EDT-TTF-I2 [66], together with the short Hal Hal contacts, leads to a sizeable increase of the band dispersion and stabilizes a rare (V structure through the side-by-side arrangement of the inversion-centred dyads connected by Hal- Hal interactions. Both 13 salts are semiconductors with room temperature conductivities around... 

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