The Electronic Properties and Density of States

It is immediately apparent from Fig. 20-1 that along the one symmetry line in the Brillouin Zone shown, there are two or three bands crossing the Fermi energy for each metal and therefore quite a complex set of Fermi surfaces. These have been thoroughly studied, using the techniques discussed in connection with simple metals. It would, however, be quite inappropriate here to attempt any complete discussion of this problem, Instead, the Fermi surface of a single system, chromium, will be discussed. It is perhaps the most interesting case, and it illustrates the principal effects that enter considerations of the other systems. We shall then turn to the density of states, which dominates many of the electronic properties. 

The Fermi surface of chromium has been studied by Rath and Callaway (1973), who used an LCAO approach, They obtained bands looking very much like those shown for chromium in Figs. 20-1 and 20-3, and also obtained some cross-sections of the Fermi surfaces. In Fig. 20-5 we give the sections for a (001) plane through the center of the Brillouin Zone containing the [100] line. We may 

A (001) section of the body-ccnlercd cubic Brillouin Zone showing the Fermi surface cross-sections for chromium, as determined by Rath and Callaway (1973). The energy bands from F at the center to H at the right are shown for comparison they are taken from Fig. 20-1. The surfaces separated by q produce antiferromagnetic order. [After Rath and Callaway, 1973.] 

A schematic construction of Fermi surface sections in a plane slightly displaced from the plane of F ig. 20-5. 

A treatment of transport properties in terms of this surface is no more complicated in principle than that in the polyvalent metals, but there is not the simple free-clectron extended-zone scheme that made that case tractable. Friedel oscillations arise from the discontinuity in state occupation at each of these surfaces, just as they did from the Fermi sphere. When in fact there arc rather flat surfaces, as on the octahedra in Fig. 20-6, these oscillations become quite strong and directional. A related effect can occur when two rather flat surfaces are parallel, as in the electron and hole octahedra, in which the system spontaneously develops an oscillatory spin density with a wave number determined by the difference in wave number between the two surfaces, the vector q indicated in Fig. 20-5. This generally accepted explanation of the antiferromagnetism of chromium, based upon nesting of the Fermi surfaces, was first proposed by Lomer (1962). 

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Empirically, one finds that the fine structure around the absorption edge depends on the local structure around the absorbing atom. So, it should be possible to obtain the local structure from an XAS spectrum. The difference between EXAFS and XANES lies in the different kind of information that can be retrieved from them. The EXAFS signal is sensitive to structural parameters such as bond distances and coordination numbers (the number of neighbors at a certain bond distance), while the XANES is more sensitive to electronic properties such as oxidation states, symmetry of the local coordination, and density of states. 

For comparison, we applied also a simplified LCAO-DFT method to get the conductivity by means of the Kubo-Greenwood formula. This method is a hybrid between ab initio and empirical methods and is described in detail in Ref. [12]. It allows a faster computation of the electronic properties and the consideration of larger supercells than the Car-Parrinello method. Within this scheme it is also possible to split the total DOS into fractions referring to the sodium and tin atoms, respectively, i.e. to get the partial densities-of-states. 

Due to size confinement on electronic interactions and density of phonon states, nano-structured materials exhibit distinct optical, magnetic and thermal properties in comparison with their bulk counterparts. Currently, there is growing interest for understanding how the confinement and other nanoscale mechanisms of electronic interactions in nanophosphors affect luminescence efficiency and photodynamics for such applications as three-dimensional displays, high-performance fight emitting devices, and highly sensitive bioassays. 

The electronic structure and spectroscopy of metallo-bis(dithiolenes) are considerably more complicated than that of the metallo-mono(dithiolenes) discussed in Section II.C because there are now two dithiolene donors, which result in twice as many sulfur-based MOs that contribute to the overall metal-ligand bonding scheme. The result is an increase in the density of states in the valence region, with a concomitant increase in the number of Sdithioiene — M CT excitations. Nevertheless, numerous spectroscopic studies and bonding calculations have been undertaken in order to explain the unique electronic properties of these molecules. The fact that two dithiolene ligands are now coordinated to... 

The electronic properties of binary and ternary intermetallic Zintl phases crystallizing in the NaTl type of structure are investigated and reported. The crystal and defect structure, the electronic band structure and density of states, the bonding mechanisms and the charge transfer are discussed. Comparison is made between the electronic states in the B2 and the B32 types of structure. Furthermore, based upon theoretical studies of the electronic valence states the optical properties (imaginary part of the dielectric constant and reflectivity) and the magnetic properties (susceptibility and Knight shift) are considered. 

For the 90K superconductor yBa2Cu307 j, discovered by Chu et al. (2>, we presented (15-16) detailed high resolution results on the electronic band structure and density of states derived properties as obtained from the same highly precise state-of-the-art local density approach. These results demonstrated the close relation of the band structure to the structural arrangements of the constituent atoms and have helped to provide an integrated chemical and physical picture of the Interactions. 

An accurate determination of the electronic band structure and density of states is essential to obtain a precise representation of structure of these carbides and understand their bonding mechanisms and the relation between bonding characteristics and properties. The band structure is usually well characterized and experimental observations are feirly extensive for the simpler carbides such as the carbides of Groups IV (Ti, Zr, HQ and the monocarbides of Group V (V, Nb, Ta). However, the band structure for other compositions and non-stoichiometric compounds is not as thoroughly investigated and is not as well determined. ... 

The other major difference between fluid metals and semiconductors concerns the phase behavior and the electronic character in various regions of the temperature-density plane. The low-temperature liquid-vapor equilibrium of semiconducting liquids involves two nonmetallic phases whereas the vapors of metallic elements are, by definition, in equilibrium with a liquid metal phase. The metallic state develops in fluid semiconductors when the temperature and pressure are high enough to disrupt the structural order responsible for semiconducting electronic structure. If this occurs near the critical region, there exists the possibility of rapid MNM transitions and strong interplay between the electronic properties and critical density fluctuations. In this respect, fluid metals and semiconductors behave similarly under extreme conditions whereas they are markedly different near their respective triple points. 

Historically, solid state theory has been dominated by physicists. One consequence of this is that the conventional methods which resulted have tended to emphasize physical rather than chemical properties, such as band structures, electron effective masses, and densities of states, rather than bond orders, geometries, and electron distributions. Another consequence of the way these methods developed is that the... 

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