Atomic displacements, induced

Asymmetric diarylmethanes, hydrogenolytic behaviors, 29 229-270, 247-252 catalytic hydrogenolysis, 29 243-258 kinetics and scheme, 29 252-258 M0O3-AI2O3 catalyst, 29 259-269 relative reactivity, 29 255-257 schematic model, 29 254 Asymmetric hydrogenations, 42 490-491 Asymmetric synthesis, 25 82, 83 examples of, 25 82 Asymmetry factor, 42 123-124 Atom-by-species matrix, 32 302-303, 318-319 Atomic absorption, 27 317 Atomic catalytic activities of sites, 34 183 Atomic displacements, induced by adsorption, 21 212, 213 Atomic rate or reaction definition, 36 72-73 structure sensitivity and, 36 86-87 Atomic species, see also specific elements adsorbed... 

Figure 4.45 Adsorbate-induced reconstructions of Ni(lOO) by atomic displacements induced by oxygen in the phase Ni(100)-c(2x2)-0 (top panels) and by carbon in the phase Ni(100)-p4g(2x2)-C. Panels (a) and (c) provide a perspective view, while panels (b) and (d) give side and top views, respectively.

A wide variety of process-induced defects in Si are passivated by reaction with atomic hydrogen. Examples of process steps in which electrically active defects may be introduced include reactive ion etching (RIE), sputter etching, laser annealing, ion implantation, thermal quenching and any form of irradiation with photons or particles wih energies above the threshold value for atomic displacement. In this section we will discuss the interaction of atomic hydrogen with the various defects introduced by these procedures. 

T(S) is the Debye-WaUer factor introduced in (2). The atomic form factors are typically calculated from the spherically averaged electrcai density of an atom in isolation [24], and therefore they do not contain any information on the polarization induced by the chemical bonding or by the interaction with electric field generated by other atoms or molecules in the crystal. This approximation is usually employed for routine crystal stmcture solutions and refinements, where the only variables of a least square refinement are the positions of the atoms and the parameters describing the atomic displacements. For more accurate studies, intended to determine with precisicai the electron density distribution, this procedure is not sufficient and the atomic form factors must be modeled more accurately, including angular and radial flexibihty (Sect. 4.2). 

Fig. 18. Elementary unit cell and atomic displacements that induce disproportionation of an ABO3 cubic perovs-kite into high-spin (S ) and low-spin (fl) or low-valence (B ) and high-valence (B) cations to give rhombohedral R 3 m symmetry...

Figure II 2 9a-s. The valence electron iso-density lines in the plane of B atoms (a-b plane) for equilibrium (a) and distorted structures (b-e). The electron density is localized at B atom positions for equilibrium structure (a). The B atoms displacements ( Af = 0.005) induce the alternating interatomic charge density delocalization, different for the particular types of the distortion (b-d). Nuclear microcirculation enables then effective charge transfer over the lattice in an external electric potential. The Fig (e) corresponds to the case of the distortion (d) over the larger lattice segment...

Interatomic Force Constants (IFCs) are the proportionality coefficients between the displacements of atoms from their equilibrium positions and the forces they induce on other atoms (or themselves). Their knowledge allows to build vibrational eigenfrequencies and eigenvectors of solids. This paper describes IFCs for different solids (SiC>2-quartz, SiC>2-stishovite, BaTiC>3, Si) obtained within the Local-Density Approximation to Density-Functional Theory. An efficient variation-perturbation approach has been used to extract the linear response of wavefunctions and density to atomic displacements. In mixed ionic-covalent solids, like SiC>2 or BaTiC>3, the careful treatment of the long-range IFCs is mandatory for a correct description of the eigenfrequencies. 

The most widely known case of phonon-induced charge transfer may be that in ferroelectric oxides, such as BaTi03. In the classic picture of ferroelectricity polarization is produced by positive and negative ions displaced in opposite directions. The polarization is given by uZ, where u is the atomic displacement and Z is the ionic charge. In reality, however, the actual polarization is much larger because of charge transfer ... 

A variety of defect formation mechanisms (lattice disorder) are known. Classical cases include the - Schottky and -> Frenkel mechanisms. For the Schottky defects, an anion vacancy and a cation vacancy are formed in an ionic crystal due to replacing two atoms at the surface. The Frenkel defect involves one atom displaced from its lattice site into an interstitial position, which is normally empty. The Schottky and Frenkel defects are both stoichiometric, i.e., can be formed without a change in the crystal composition. The structural disorder, characteristic of -> superionics (fast -> ion conductors), relates to crystals where the stoichiometric number of mobile ions is significantly lower than the number of positions available for these ions. Examples of structurally disordered solids are -> f-alumina, -> NASICON, and d-phase of - bismuth oxide. The antistructural disorder, typical for - intermetallic and essentially covalent phases, appears due to mixing of atoms between their regular sites. In many cases important for practice, the defects are formed to compensate charge of dopant ions due to the crystal electroneutrality rule (doping-induced disorder) (see also -> electroneutrality condition). 

The sequence of elementary steps shown in Fig. 13.2 suggests that one can formulate the problem of carbon poisoning in terms of the selectivity associated with the formation of C-0 vs. C-C bonds on Ni. In order to prevent carbon-induced deactivation, a catalyst should be able to selectively oxidize C atoms (and CH fragments) rather than form C-C bonds. This elementary step mechanism was the basis for the DFT calculations that focused on the identification of catalysts (mainly Ni-containing alloys), which preferentially oxidize C atoms rather than form C-C bonds [15, 16]. In these DFT calculations, the potential energy surfaces for the formation of C-C and C-0 bonds were calculated for different Ni alloys. The alloy model system used in these calculations contained mainly Ni, with some Ni atoms displaced by another atom in the surface layer. While we have examined a number of different alloys, we will focus our discussion on the alloy material (Sn/Ni). We note that this alloy material has also been studied by others previously [35, 38, 41, 49, 50]. 

A final point about radiation-induced reactions with covalent bonds at the surface is that a purely electronic event, the ionization of a bond in a surface group or molecule, may lead to an atomic displacement. If a bond is broken by the ionization, the thermal motion of the fragments involved can result in their diffusion to new locations without the necessity for appreciable momentum interchange with the causative radiation. Thus even photolysis of surface molecules might lead to atomic displacements, an eventuality not possible in straightforward radiation damage with such low-momentum radiation as ultraviolet. 

The connection of an induced catal3d ic activity with a trapped electron or hole can be approached through production methods which emphasize electron rather than atom displacement and by annealing experiments which may distinguish between different types of electronic defect. The electronic state of the defect can frequently be followed by ESR. Even if a particular defect is tied to a catalytic activity by annealing experiments, the interaction may be a remote rather than a local one. 

Proper identification of the order parameter of a particular system often needs detailed physical insight, and sometimes is complicated because different degrees of freedom are coupled. For example, there are many reports in the literature that an order-disorder transition of adsorbates on loose-packed substrates causes an adsorbate-induced reconstruction of the substrate surface. In such a situation, the order parameter of the adsorbate order-disorder transition is the primary order parameter whereas the lattice distortion of the substrate surface is a secondary order parameter . However, for pure surface reconstruction transitions (i.e. structural phase transitions of the surface of crystals where no adsorbates are involved) all considered degrees of freedom are atomic displacements relative to positions of higher symmetry. The proper distinction between primary and secondary order parameters is then much more subtle. 

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