Metals electron band structures

The bulk of UPS literature has appeared since 1970, and it has concentrated in two areas (1) interpreting spectra of organic vapors and (2) studing transition metal electronic band structure changes caused by sorption of simple gases on the metal surfaces. Interpreting uv photoelectron spectra is very difficult and until a data base of spectral measurements is accumulated, it will be used infrequently in surface chemical studies. 

Seebeck used antimony and copper wires and found the current to be affected by the measuring instrument (ammeter). But, he also found that the voltage generated (EMF) was directly proportional to the difference in temperature of the two junctions. Peltier, in 1834, then demonstrated that if a current was induced in the circuit of 7.1.3., it generated heat at the junctions. In other words, the SEEBECK EFFECT was found to be reversible. Further work led to the development of the thermocouple, which today remains the primary method for measurement of temperature. Nowadays, we know that the SEEBECK EFFECT arises because of a difference in the electronic band structure of the two metals at the junction. This is illustrated as follows ... 

The structure of MnP is a distorted variant of the NiAs type the metal atoms also have close contacts with each other in zigzag lines parallel to the a-b plane, which amounts to a total of four close metal atoms (Fig. 17.5). Simultaneously, the P atoms have moved up to a zigzag line this can be interpreted as a (P-) chain in the same manner as in Zintl phases. In NiP the distortion is different, allowing for the presence of P2 pairs (P ). These distortions are to be taken as Peierls distortions. Calculations of the electronic band structures can be summarized in short 9-10 valence electrons per metal atom favor the NiAs structure, 11-14 the MnP structure, and more than 14 the NiP structure (phosphorus contributes 5 valence electrons per metal atom) this is valid for phosphides. Arsenides and especially antimonides prefer the NiAs structure also for the larger electron counts. 

CNTs can exhibit singular electronic band structures and can show metallic and semiconducting behavior. As a general rule, n.m tubes with n-m being an integer multiple of 3 are metallic, while the remaining tubes are semiconducting. 

Band Theory of Metals, Three approaches predict the electronic band structure of metals. The first approach (Kronig-Penney), the periodic potential method, starts with free electrons and then considers nearly bound electrons. The second (Ziman) takes into account Bragg reflection as a strong disturbance in the propagation of electrons. The third approach (Feynman) starts with completely bound electrons to atoms and then considers a linear combination of atomic orbitals (LCAOs). 

We distinguish three kinds of nitrides, i.e. ionic nitrides (e g. Th3N2), covalent nitrides (e.g. BN) and intermediate forms (e g. VN). These intermediate forms are extremely inert, very hard and they have high melting points. VN has a Mohs hardness of 9-10 and a melting point of 2570 °C. Furthermore, the intermediate form conducts electricity since the electronic band structure of the metal is maintained when N atoms are placed in the cavities of the crystal lattice... 

It is also interesting to consider charge-transfer models developed primarily for metal surfaces. There are clear parallels to the metal oxide case in that there is an interaction between discrete molecular orbitals on one side, and electronic bands on the other side of the interface. The Newns-Anderson model [118] qualitatively accounts for the interactions between adsorbed atoms and metal surfaces. The model is based on resonance of adatom levels with a substrate band. In particular, the model considers an energy shift in the adatom level, as well as a broadening of that level. The width of the level is taken as a measure of the interaction strength with the substrate bands [118]. Also femtosecond electron dynamics have been studied at electrode interfaces, see e.g. [119]. It needs to be established, however, to what extent metal surface models are valid also for organic adsorbates on metal oxides in view of the differences between the metal an the metal oxide band structures. The significance of the band gap, as well as of surface states in it, must in any case be considered [102]. 

Thin-lilm photoelectrodes are needed in photoelectrocatalytic systems to apply a bias potential, either for the photoelectrode characterization or to facilitate the photocatalytic reactions. However, to be able to present a more comprehensive view on the performance of different materials, our subsequent discussions will focus on particulate semiconductor photocatalysts since the latter have been much more extensively investigated. Their electronic band structure (i.e., both the bandgap energy and the positions of CB and VB) is the key factor to determine whether or not a semiconductor material is suitable for a specific photocatalytic reaction, as will be demonstrated by reviewing a number of selected metal oxides and cou-pled/composite materials based on various semiconductors. 

Properties of the electrode material (in particular metals) itself (e.g., electronic band structure or features related to surface crystallography) can be studied in the... 

Another demonstration of the validity of these calculations is provided by BEDT-TTF-based salts. The calculated Fermi surface of these materials exhibit closed orbits characteristic of two-dimensional electronic interactions and this has been confirmed experimentally. For example, in the case of (BEDT-TTF)2I3, the calculated surface of these orbits (Fig. 21) [61] agrees well with the one measured by magnetic experiments [161]. However, the overall good agreement between calculation and experiment must not hide the fact that some qualitative discrepancies may arise in some cases. For example, (TMTTF)2X salts exhibit a resistivity minimum at a temperature at which no structural transition has yet been observed. The resistivity minimum is not explained by the one-electron band structure, and to account for this progressive electron localization, it is necessary to include in the calculations the effect of the electronic correlations [162]. Another difficulty has been met in the case of the semiconducting materials a -(BEDT-TTF)2X, for which the calculated band structure exhibits the characteristic features of a metal [93,97,100] and it is not yet understood... 

Earlier chapters in this volume have dealt with the molecular properties and crystal structures of organic metals. The large planar molecules under consideration here are usually stacked face to face in chains sometimes the molecular planes are perpendicular to the stacking axis, as in the case of the Bechgaard salts, or they may be tilted by as much as 30°, as in TTF-TCNQ. Because the overlap of the partially occupied tt orbitals is much better along the stacking axis, their electronic band structures are often quasi-one-dimensional. 

As will be shown in the following sections the results of the one-electron band structure calculations allow to describe several important properties of the tetracyanoplatinates, like the dominance of the Pt 5 dz2 and Pt 6 p2 orbitals for the red-shift of the main optical transitions with decreasing metal-metal distance82 6, the admixture of Pt(6pz, CNji ) character into the valence band82,89, or several stabilization effects upon partial oxidation84. On the other hand, a series of experimentally found features is out of the scope of the one-electron band model. In the following some of these properties are specified ... 

Some transition metal nitrides,10 MN, of Ti, Zr, and Hf have cubic (Nad type) structures. Others which are often not exactly stoichiometric (being N deficient), are chemically very inert and extremely hard with high melting points. The electronic band structure of the metal persists, the appearance is metallic and the compounds are electrically conducting. As an example, VN has mp 2570°C and hardness 9-10. 

Figure 7.7a shows the extended-zone electronic band structure for a one-dimensional crystal - an atom chain with a real-space unit cell parameter a and reciprocal lattice vector Tr/n - containing a half-filled (metallic) band. In this diagram, both values of the wave vector, +k, are shown. The wave vector is the reciprocal unit cell dimension. The Fermi surface is a pair of points in the first BZ (Fig. 7.7c). When areas on the Fermi surface can be made to coincide by mere translation of a wave vector, q, the Fermi surface is said to be nested. The instability of the material towards the Peierls distortion is due to this nesting. In one dimension, nesting is complete and a one-dimensional metal is converted to an insulator because of a Peierls distortion. This is shown in Figure 7.7b, where the real-space unit cell parameter of the distorted lattice is 2a and a band gap opens at values of the wave vector equal to half the original values, 7r/2a.

Gallium arsenide s native oxide is found to be a mixture of nonstoichiometric galhum and arsenic oxides and elemental arsenic. Thus, the electronic band structure is found to be severely disrupted, causing a breakdown in normal semiconductor behavior on the GaAs surface. As a consequence, the GaAs MISFET (metal insulator semiconductor field-effect transistor) equivalent to the technologically important Si-based MOSFET (metal-oxide semiconductor field-effect transistor) is, therefore, presently unavailable. 

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