Step atoms

What gives rise to streaks in a RHEED pattern from a real surface For integral-order beams, die explanation is atomic steps. Atomic steps will be present on nearly all crystalline surfaces. At the very least a step density sufficient to account for any misorientation of the sample from perfeedy flat must be included. Diffraction is sensitive to atomic steps. They will show up in the RHEED pattern as streaking or as splitdng of the diffracted beam at certain diffraction conditions that depend on the path difference of a wave scattered from atomic planes displaced by an atomic step height. If the path difference is an odd muldple of A./2, the waves scattered... 

First, analyze the one-step mechanism CO -I- NO2 CO2 4-NO This process is analogous to the reaction of NO and O3 discussed in Section 15-1. In a simple one-step atom transfer, the reaction is first order in each of the starting materials and second order overall ... 

Consider the general case of arbitrary sticking coefficients and two steps. Atoms may diffuse from a step (labelled 1) to itself, and to a step (labelled 2) at distance d from step 1. Pi is the probability that an atom which is on the lower terrace (with respect to step 1) and at distance a from step 1 is absorbed by step 1 at distance I from it starting position. Pj is the probability that the same atom is absorbed by step 2. We start with an atom which has detached from the step labelled 1, and hence is at one atomic spacing from the step edge. In this case, we solve. 

Figure 4.9. Projected densities of states onto the d states of the surface atoms for different Pt surfaces with decreasing atom density The hexagonally reconstructed (100) surface, the close-packed (111) surface, the step atoms on a (211) surface and the kink atoms on a (11 8 5) surface. Adapted from Ref. [19].

Fig. 3. LEED patterns and schematic representations of the surface configurations of platinum single-crystal surfaces, (a) Pt(Ill) containing less than 1012 defects/cm2, (b) Pt(557) face containing 2.5 x 1014 step atoms/cm2 with an average spacing between steps of 6 atoms, and (c) Pt(679) containing 2.3 x 10 4 step atoms/cm2 and 7 x 1014 kink atoms/cm2 with an average spacing between steps of 7 atoms and between kinks of 3 atoms.

Thus, at each time step, atoms under the most strain move fastest and farthest. To satisfactorily solve Newton s equations requires extremely short time steps, typically only 1 femtosecond (10 15sec). If the time increment is too long, atoms can come too close in each step, and the energy of interaction from the FF gets so high that the system becomes unstable and erratic in subsequent steps (80). 

If the R-group in the alkyne is a strongly electron-withdrawing moiety such as a carbonyl function, regioselectivity may be reversed, leading to the problem of E/Z-selectivity (Scheme 2). Irrespective of the type of alkyne, the one-step atom-economical process would need to be catalyzed because a simple thermal process does not provide the products. 

Figure 2. The most common type of imperfection site on a (111) crystal plane is steps. This illustration shows the perspective of regularly placed steps on the (111) surface. Every ninth row is a step (the step atoms are shaded) and this may be indexed as 9(111) X (111). The coordination number of step atoms is seven.

S mean binding energy of Meads on S step binding energy of Meads at a step atom-substrate binding energy lateral interaction parameter angular frequency, lateral interaction parameter deposition frequency of atoms to a site x dissolution frequency of atoms from a site x phonon frequency area of an adsorption site... 

On alloys, a key question in this respect is the composition of such sites, i.e., whether segregation differs between such special sites and flat terraces. Whereas well-defined STM studies of small clusters are extremely difficult, we could obtain chemical contrast at steps in a few cases. Fig. 12 shows two PtRh alloy surfaces with steps. Whereas the step of the (100) surface consists of almost exclusively Pt [60], the step on the (111) surface has almost the same composition as the remaining surface [39]. As step atoms on both, the (100) and the (111) surface, have 7 nearest neighbours, the difference in segregation to the two steps is unexpected and has not found any explanation so far. 

Figure 19. Initial rate of adsorbed CO formation at 0.05 V vs. RHE at various series of Pt single crystal electrodes in 0.1-M HCIO4 plotted against the kink and step atom density. Reprinted from Ref. 114, Copyright (2000) with permission from Elsevier.

Figure 32 presents spectra from Cu single crystal electrodes /7(111)-(111) series." It is remarkable that the infrared absorption intensity of adsorbed CO grows at the wavenumber 2057 to 2075 with the decrease of n value, or the increase of the step atom density. Figure 33 gives spectra from 77(111)-(IOO) series. The spectra from /7(lll)-(100) series also give an identical feature with Z7(l 11 )-(111) series. The absorption intensity at 2073 to 2077 increases with the step atom density. No infrared band is detected from (111) terraces including (111) surface, whereas voltammetric measurements evidently show that HER is heavily suppressed at the (111)... 

A novel acyclic SOjH-functional Brdnsted acidic halogen-free TSIL that bears a butane sulfonic acid group in an acyclic tri-methyl-ammonium cation has been synthesized (Fig. 12.65) [40] and used as the catalyst for one-pot three-component Mannich reaction (Fig. 12.66). The procedure was made up of two-step atom economic reaction. The zwitterionic-type precursor (trimethylammonium butane sulfonate) was prepared through a one-step direct sulfonation reaction of trimeth-ylamine and 1,4-butanesulfone. The zwitterion acidification was accomplished by... 

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