Vacancies electronic structures

Detailed investigation of the C vacancy electronic structure has been carried out by both band and cluster methods. Gubanov, Ivanovsky, Shveikin and Ellis (1984) used the Ti6C,2Tig cluster ( is the vacancy) including three first coordination spheres of the defect in order to model defect TiC. The calculations were carried out by the X DV method in the imbedded cluster approximation. In order to study the vacancy charge, the AO basis included effective vacancy Is and 2p functions. The calculations showed that the additional Is and 2p functions contribute little to the MOs of the valence band, and the effective charge of the vacancy in TiC is very low ( 0.24c). 

The presence of a defect in the lattice (impurity, surface, vacancy...) breaks the symmetry and induces perturbations of the electronic structure in its vicinity. Thus it is convenient to introduce the concept of local density of states (LDOS) at site i ... 

A very important criterion for electron structure is the percent d-character, which characterizes the number of unpaired electrons in the rf-orbitals of the individual metal atom. Because of the vacancies existing in these orbitals, metals will interact with electron-donating species forming electron pairs. It is this interaction that determines the special features of adsorption of these species and, as a consequence, the catalytic activity of a given metal. 

The key parameters of the electronic structure of these surfaces are summarized in Table 9.3. The calculated rf-band vacancy of Pt shows no appreciable increase. Instead, there is a shght charge transfer from Co to Pt, which may be attributable to the difference in electronegativity of Pt and Co, in apparent contradiction with the substantial increase in Pt band vacancy previously reported [Mukerjee et al., 1995]. What does change systematically across these surfaces is the J-band center (s ) of Pt, which, as Fig. 9.12 demonstrates, systematically affects the reactivity of the surfaces. This correlation is consistent with the previous successes [Greeley et al., 2002 Mavrikakis et al., 1998] of the band model in describing the reactivity of various bimetallic surfaces and the effect of strain. Compressive strain lowers s, which, in turn, leads to weaker adsorbate-surface interaction, whereas expansive strain has the opposite effect. 

Metals are immune to radiation damage by ionization. This is also a consequence of the free electron structure. Fast charged particles and ionizing rays can knock off electrons from the atoms they encounter. In metals, the positive vacancies so formed are immediately filled up by the electron gas, leaving no sign of damage apart from a small amount of heat. 

When normal sites in a crystal structure are replaced by impurity atoms, or vacancies, or interstitial atoms, the local electronic structure is disturbed and local electronic states are introduced. Now when a dislocation kink moves into such a site, its energy changes, not by a minute amount but by some significant amount. The resistance to further motion is best described as an increase in the local viscosity coefficient, remembering that plastic deformation is time dependent. A viscosity coefficient, q relates a rate d8/dt with a stress, x ... 

Fig. 1. Ligand-field model for the electronic structure of substitutional hydrogen in silicon in terms of the interactions between the vacancy orbitals and the atomic-hydrogen orbitals [Although the a state is shown as being not entirely passivated (still below the bottom of the conduction-band edge), it could in fact be in the conduction band, but with a host-like state pushed down slightly into the band gap.] (Reprinted with permission from the American Physical Society, DeLeo, G.G., Fowler, W.B., Watkins, G.D. (1984). Phys. Rev. B 29, 1819.)...

If an electron is removed from an inner energy level of one of the heavier elements (in practice, with an atomic number greater than sodium), a vacancy or hole is produced in the electronic structure. This is an unstable arrangement, and two competing processes act to rectify this ... 

Thermodynamic considerations imply that all crystals must contain a certain number of defects at nonzero temperatures (0 K). Defects are important because they are much more abundant at surfaces than in bulk, and in oxides they are usually responsible for many of the catalytic and chemical properties.15 Bulk defects may be classified either as point defects or as extended defects such as line defects and planar defects. Examples of point defects in crystals are Frenkel (vacancy plus interstitial of the same type) and Schottky (balancing pairs of vacancies) types of defects. On oxide surfaces, the point defects can be cation or anion vacancies or adatoms. Measurements of the electronic structure of a variety of oxide surfaces have shown that the predominant type of defect formed when samples are heated are oxygen vacancies.16 Hence, most of the surface models of... 

Considerable progress has been realized in characterizing the TMS materials. Much effort has been put into trying to understand the fundamental basis for their catalytic activity and selectivity. Numerous relationships that highlight the particular importance of the electronic structure, the crystallographic structure, and the sulfur vacancies have been reported in the literature. 

This equation can be applied to a wide class of problems including the electronic structure of vacancies, impurities, and of other localized perturbations of solids and atomic clusters. The methods considered here make it possible to construct G(x, x ) for any potential function v(x) defined throughout the coordinate space Of3. 

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