Metals band theory

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... 

An accurate value for the cohesive energy of a metal will require knowledge of the number and distribution of the energy levels in the band as well as of other factors that have not been described, and will vary from metal to metal. Band theory, described in Section 2.3.8, is needed to take this further and to account for the differences between one metal and another. 

Much of the work done on metal clusters has been focused on the transition from cluster properties to bulk properties as the clusters become larger, e.g. the transition from quantum chemistry to band theory [127]. 

Terakura K, Qguchi T, Williams A R and Kubler J 1984 Band theory of insulating transition-metal monoxides Band-structure calculations Phys. Rev. B 30 4734... 

The beginnings of the enormous field of solid-state physics were concisely set out in a fascinating series of recollections by some of the pioneers at a Royal Society Symposium (Mott 1980), with the participation of a number of professional historians of science, and in much greater detail in a large, impressive book by a number of historians (Hoddeson et al. 1992), dealing in depth with such histories as the roots of solid-state physics in the years before quantum mechanics, the quantum theory of metals and band theory, point defects and colour centres, magnetism, mechanical behaviour of solids, semiconductor physics and critical statistical theory. 

The other place to read an authoritative histoi7 of the development of the quantum-mechanical theory of metals and the associated evolution of the band theory of solids is in Chapters 2 and 3 of the book. Out of the Crystal Maze, which is a kind of official history of solid-state physics (Hoddeson et al. 1992). 

We have carried out impurity calculations for a zinc atom embedded in a copper matrix. We first perform self consistent band theory calculations on pure Cu and Zn on fee lattices with the lattice constant of pure Cu, 6.76 Bohr radii. This yields Fermi energies, self consistent potentials, scattering matrices, and wave functions for both metals. The Green s function for a system with a Zn atom embedded in a Cu matrix... 

In Chapter 9, we considered a simple picture of metallic bonding, the electron-sea model The molecular orbital approach leads to a refinement of this model known as band theory. Here, a crystal of a metal is considered to be one huge molecule. Valence electrons of the metal are fed into delocalized molecular orbitals, formed in the usual way from atomic... 

The high electrical conductivity of metals as well as the high electron (and hole) mobility of inorganic covalently bound semiconductors have both been clarified by the band theory [I9, which slates that the discrele energy levels of individual atoms widen in the solid stale into alternatively allowed and forbidden bands. The... 

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. 

All these properties of metals are consistent with a bonding description that places the valence electrons in delocalized orbitals. This section describes the band theory of solids, an extension of the delocalized orbital ideas... 

A pure transition metal is best described by the band theory of solids, as introduced in Chapter 10. In this model, the valence s and d electrons form extended bands of orbitals that are delocalized over the entire network of metal atoms. These valence electrons are easily removed, so most elements In the d block react readily to form compounds oxides such as Fc2 O3, sulfides such as ZnS, and mineral salts such as zircon, ZrSi O4. ... 

The reciprocal lattice is useful in defining some of the electronic properties of solids. That is, when we have a semi-conductor (or even a conductor like a metal), we find that the electrons are confined in a band, defined by the reciprocal lattice. This has important effects upon the conductivity of any solid and is known as the "band theory" of solids. It turns out that the reciprocal lattice is also the site of the Brillouin zones, i.e.- the "allowed" electron energy bands in the solid. How this originates is explciined as follows. 

Gold forms a continuous series of solid solutions with palladium, and there is no evidence for the existence of a miscibility gap. Also, the catalytic properties of the component metals are very different, and for these reasons the Pd-Au alloys have been popular in studies of the electronic factor in catalysis. The well-known paper by Couper and Eley (127) remains the most clearly defined example of a correlation between catalytic activity and the filling of d-band vacancies. The apparent activation energy for the ortho-parahydrogen conversion over Pd-Au wires wras constant on Pd and the Pd-rich alloys, but increased abruptly at 60% Au, at which composition d-band vacancies were considered to be just filled. Subsequently, Eley, with various collaborators, has studied a number of other reactions over the same alloy wires, e.g., formic acid decomposition 128), CO oxidation 129), and N20 decomposition ISO). These results, and the extent to which they support the d-band theory, have been reviewed by Eley (1). We shall confine our attention here to the chemisorption of oxygen and the decomposition of formic acid, winch have been studied on Pd-Au alloy films. 

---