The electronic density of states

One conclusion from the structure studies in Chapter 2 is that the bonding disorder of a-Si H is relatively small. The silicon atoms have the same tetrahedral local order as crystalline silicon, with a bond angle variation of about 10% and a much smaller bond length disorder. Fig. 

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Another usefiil quantity is defining the electronic structure of a solid is the electronic density of states. In general the density of states can be defined as... 

Flowever, when the metal can be detected directly (mainly Pt), it is possible to relate the form of the NMR spectmm to the dispersion of the metal and to calculate the electron density of states at the Fermi level. 

Scanning tunneling spectroscopy (STS) can, in principle, probe the electronic density of states of a singlewall nanotube, or the outermost cylinder of a multi-wall tubule, or of a bundle of tubules. With this technique, it is further possible to carry out both STS and scanning tunneling microscopy (STM) measurements at the same location on the same tubule and, therefore, to measure the tubule diameter concurrently with the STS spectrum. No reports have yet been made of a determination of the chiral angle of a tubule with the STM technique. Several groups have, thus far, attempted STS studies of individual tubules. 

Figure 5. Temperature development of the electronic density of states in fee FeaNi with the temperature dependent input taken from the Ginzburg-Landau theory (magnetic moments are given per atom).

To interpret the strong dependence of the conductivity from composition, we also evaluated the electronic density-of-states and analyzed its specific atomic contributions. For this discussion and for comparison we also calculated the electrical conductivities and the electronic densitity-of-states using a simplified density-functional (DFT)- based LCAO scheme [12]. 

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]. 

A detailed description of the local bond rearrangement has been derived [439], using the concept of the HDOS with a low-energy tail that corresponds to the H present at weak Si —Si bonds. The width of this tail is 2 i o, i-c., twice the width of the valence band tail in the electronic density of states, which in turn is about equal to the Urbach energy Eq [442,443]. The HDOS then is [439]... 

Very useful information concerning the surface of emersed electrodes, however, can be deduced from UPS spectra directly, like the electronic density of states at the Fermi level, the position of the valence band with respect to the Fermi level or possible band gap states. The valence band of UPD metals might help to explain the respective optical data (see Sections 3.2.1 and 3.2.5). 

Bakhshi, A. K., P. Otto, C.-M. Liegener, E. Rehm, and J. Ladik. 1990. Modeling of Real 20-Component Protein Chains Determination of the Electronic Density of States of... 

Typically the contributions of the two bands to the current are of rather unequal magnitude, and one of them dominates the current. Unless the electronic densities of states of the two bands differ greatly, the major part of the current will come from the band that is closer to the Fermi level of the redox system (see Fig. 7.6). The relative magnitudes of the current densities at vanishing overpotential can be estimated from the explicit expressions for the distribution functions Wled and Wox ... 

Spectra as in Fig. 3.17 can also be obtained as a function of polar and azimuthal angle, and with polarized UV light, enabling one to probe band structures in all directions [18]. In this chapter we limit ourselves to angle-integrated measurements of the electron density of states. 

Our discussion of electronic structure has been in terms of band filling only. Of course, there is a lot more to know about band structures. The density of states represents only a highly simplified representation of the actual electronic structure, which ignores the three-dimensional structure of electron states in the crystal lattice. Angle-dependent photoemission gives information on this property of the electrons. The interested reader is referred to standard books on solid state physics [9,10] and photoemission [16,17]. The interpretation of photoemission and X-ray absorption spectra of catalysis-oriented questions, however, is usually done in terms of the electron density of states only. 

Figure 16. Calculated evolution of the electronic density of states of propene with increasing density (pressure) (A) 0.86 g/cm (B) 1.45 g/cm (C) 2.08 g/cm. ...

One of the primary quantities used to describe the electronic state of a material is the electronic density of states (DOS) ... 

The charge transfer induced polarizability of a surface atom is closely related to the electronic density of states of the atom as can be seen by... 

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