Metallic band

Figure 6.22. Adsorption of an atom on a d metal. The valence electron of the adsorbate, initially at 12 eV above the bottom of the metal band, interacts both weakly with a broad sp band and strongly with a narrow d band located between 9 and 12 eV. Note the significant splitting of the adsorbate density of states into bonding and antibonding orbitals of Ha( ) due to the interaction with the d band.

In outer sphere electron transfer, the reactant is not adsorbed therefore, the interaction with the metal is not as strong as with the catal5d ic reactions discussed below. Hence, the details of the metal band structure are not important, and the couphng A(s) can be taken as constant. This is the so-called wide band approximation, because it corresponds to the interaction with a wide, structureless band on the metal. In this approximation, the function A(s) vanishes, and the reactant s density of states takes the form of a Lorentzian. The simation is illustrated in Fig. 2.3. 

Before considering our model for electrocatalysis, it is instructive to investigate the interaction of a single reactant orbital with a model metal containing a wide. sp-band and a narrow d-hsnA. For this purpose, it is convenient to use the model of a semi-elliptic band [Newns, 1969], for which several important quantities can be calculated explicitly. A single such metal band has the form... 

Figure 2.12 Chemisorption functions for the model metal band structure.

TABLE 7.1 Electrical Conductivity and Mobility of Charge Carriers in Metals, Band-like Semiconductors, and Hopping Semiconductors... 

Metal Band-like Semiconductor Hopping Semiconductor... 

A comparison of the relevant equations for metals, band theory semiconductors, and hopping semiconductors is given in Table 7.1. These equations can be used in a diagnostic fashion to separate one material type from another. In practice, it is not quite so easy to distinguish between the different conductivity mechanisms. 

Properties of hydrogen Properties of metals Band theory Properties of nonmetals Properties of transition metals Coordination compounds Crystal-held theory Complex ions... 

Copper is a face-centered cubic (fee) metal. Band structure calculations show the valence bands to be copper d bands and hybrid bands of sd, pd, and sp character. The hybridization is essential for the conductivity of copper, as some of the bands cross the Fermi surface and are thus only partially occupied (K. Schwarz, private communication). 

A metallic band structure is realized when the CT solids have a partial CT state and molecules form uniform segregated columns or layers. Figure 1 shows electrical conductivity data for 1 1 low-dimensional TTF TCNQ system, as a function of redox potentials [82]. The two lines a and b are related to the equation expressing the relationship between 7d, Ea, and the Madelung energy M 5) (5 = degree of CT) between partially charged component molecules (eq. 2) [83], where and Ea are... 

This transition has been emphasized by Mott for the case of localized impurity states in a semiconductor, forming a metallic band at some concentration of impurities (i.e. at some average distance between the impurities). It is referred to very often as the Mott (or Mott-Hubbard) transition. 

The reason why it is a useful concept in actinide solid state physics (as in d-transition metals) is that it describes the effect of overlapping in forming a band therefore, in d or f unfilled bands, a critical value of the inter-atomic distance should determine whether the electron states will be acting as localized (insulator s) states, or as an unfilled (metallic) band. If we refer to the concept of f-f-overlapping, it is thinkable that across a series such as the actinides the f-f-overlapping might come to a critical value distinguishing between band and localized behaviour. 

A projectile used in 120-mm HE, Comp B, M356 (T15A1) Separated Round has a base similar to that shown in Fig 1-2 (minus tracer) and two gilding metal bands instead of one. 

The behaviour of the transition-metal bands as the atoms are brought together to form the solid may be evaluated within the Wigner-Seitz sphere approximation by imposing bonding, = 0, or antibonding, R, = 0,... 

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