Band formation

The position of the 4-derived t2g band in the mixed oxides shifts from 0.8 eV for Ru02 to 1.5 eV for Ir02 proportional to the composition of the oxide. As a consequence of common 4-band formation the delocalized electrons are shared between Ir and Ru sites. In chemical terms, Ir sites are oxidized and Ru sites are reduced and electrochemical oxidation potentials are shifted. Oxidation of Ru sites to the VIII valence state is now prohibited. Thus corrosion as well as 02 evolution on Ru sites is reduced which explains the Tafel slope and overpotential behaviour. Most probably Ru sites function as Ir activators [83]. 

The results of the above mentioned study on mixed oxides prepared by thermal decomposition [84] are not in contradiction to the results obtained on reactively sputtered electrodes. A premise for common d-band formation is the formation of a solid solution with homogeneous properties which is probably not obtained during thermal decomposition. Indeed the authors find a trend towards the behaviour of the sputtered electrodes when homogeneity is improved by changing the solvent for the starting compounds. 

The most detailed NMR study of impurity band formation in a semiconductor in the intermediate regime involved 31P and 29 Si 7). line width and shift measurements at 8 T from 100-500 K for Si samples doped with P at levels between 4 x 1018 cm 3 and 8 x 1019 cm 3 [189], and an alternate simplified interpretation of these results in terms of an extended Korringa relation [185]. While the results and interpretation are too involved to discuss here, the important conclusion was that the conventional picture of P-doped Si at 300 K consisting of fully-ionized donors and carriers confined to extended conduction band states is inadequate. Instead, a complex of impurity bands survives in some form to doping levels as high as 1019 cm 3. A related example of an impurity NMR study of impurity bands is discussed in Sect. 3.8 for Ga-doped ZnO. 

The basic mechanism of toughening is one of void formation and shear band formation (cavitation) when stress is applied. 

Fig. 2-12. Electron energy band formation of silicon crystals from atomic frontier orbitals number of silicon atoms in crystal r = distance between atoms rg = stable atom-atom distance in crystals, sp B8 = bonding band (valence band) of sp hybrid orbitals sp ABB = antibonding band (conduction band) of sp hybrid orbitals.

Fig. 8.1. Toughening mechanisms in rubber-modified polymers (1) shear band formation near rubber particles (2) fracture of rubber particles after cavitation (3) stretching, (4) debonding and (5) tearing of rubber particles (6) transparticle fracture (7) debonding of hard particles (8) crack deflection by hard particles (9) voided/cavitated rubber particles (10) crazing (II) plastic zone at craze tip (12) diffuse shear yielding (13) shear band/craze interaction. After Garg and Mai (1988a).

In the preceding sections, we have rapidly reviewed the concepts that are involved in the band formation of actinide metals. We would like to point out what more is involved in the band formation of actinide compounds. This is very obvious the anion valence band. In fact, the hybridization with anion states which we presented as the main correction to the simple Hill scheme is indeed the central question involved in detailed band structure calculations in actinide compounds. We pointed out in the previous paragraph the case of UGea we would like here, as an example, to compare somewhat UO2 and NaCl compounds of uranium. As confirmed by recent photoemission studies " , UO2 has well localized 5 f states whereas NaCl compounds have a narrow 5 f band pinned at the Fermi level. Nevertheless the U-U spacing is the same in UO2, UP and US. This difference may be understood in terms of charge transfer versus f-p hybridization. 

Coulomb correlation energy, U. The energy gain due to band formation is of the order of the bandwidth, W. Provided U can be calculated Table 1 can be used to examine the criterion UAV = 1 for Mott-localization ... 

For hydrogen, only the Is orbital is energetically accessible for band formation. For elements of lithium through fluorine, the 2s and, at somewhat higher energy, the three 2p orbitals are available, and, depending on the ways in which the atomic orbitals align with the crystal structure, these may form either a continuous s,p band or a pair of bands with the same... 

The absorption edge of (Ga,Mn)As is not sharp, as shown in fig. 20 (Kuroiwa et al. 1998 Szczytko et al. 1999b). This is probably due to impurity band formation caused by the high concentration of ionized Mn and compensating donors (Kuroiwa et al. 1998). Even below the fundamental absorption edge, the absorption coefficient is rather large due to free-carrier (Casey et al. 1975) and intra-Mn absorption. There is no report on the observation of exciton states or photoluminescence, which is probably due to non-radiative recombination, carrier screening, and the formation of an impurity band (Ando et al. 1999). 

There are many contributions to this field from other laboratories as well. The reader is referred to the cited literature for details on other results. To summarize the results, four conclusions can be drawn (i) there still exists uncertainty about the exact compositions of the complexes involved the formal oxidation states are not always known, but it is certain that nonintegral ones are essential for high conductivity (ii) the formation of linear stacks of parallel ions and close stacking create the necessary intermolecular exchange interactions which result in band formation and conductivity ... 

Figure 1. Simple chemical bonding model showing that unbound or partially bound atoms on a semiconductor surface contribute states within the band gap. The states of unbound atoms (a) are split upon partial bonding (b), then further split when the fully bound species (c) is formed. Evolution of the periodic lattice broadens the bonding states to form the valence band (vb) and the antibonding orbitals to form the conduction band (cb). In the process of band formation, the unbound and partially bound states (a and b) remain between vb and cb.

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