Stepped surface

Mobility of this second kind is illustrated in Fig. XVIII-14, which shows NO molecules diffusing around on terraces with intervals of being trapped at steps. Surface diffusion can be seen in field emission microscopy (FEM) and can be measured by observing the growth rate of patches or fluctuations in emission from a small area [136,138] (see Section V111-2C), field ion microscopy [138], Auger and work function measurements, and laser-induced desorption... 

Most fiindamental surface science investigations employ single-crystal samples cut along a low-index plane. The single-crystal surface is prepared to be nearly atomically flat. The surface may also be modified in vacuum. For example, it may be exposed to a gas that adsorbs (sticks) to the surface, or a film can be grown onto a sample by evaporation of material. In addition to single-crystal surfaces, many researchers have investigated vicinal, i.e. stepped, surfaces as well as the surfaces of polycrystalline and disordered materials. 

Figure Bl.19.24. Friction loop and topography on a heterogeneous stepped surface. Terraces (2) and (3) are composed of different materials. In regions (1) and (4), the cantilever sticks to the sample surface because of static friction The sliding friction is tj on part (2) and on part 3. In a torsional force image, the contrast difference is caused by the relative sliding friction, Morphological effects may be...

A kinked surface, like fee (10,8,7), can also be approximately expressed in this fomi the step plane (h k / ) is a stepped surface itself, and thus has higher Miller indices than tlie terrace plane. However, the step notation does not exactly tell us the relative location of adjacent steps, and it is not entirely clear how the terrace width M should be counted. A more complete microfacet notation is available to describe kinked surfaces generally [5]. 

Nishihara C and Nozoye H 1995 influence of underpotentiai deposition of copper with submonolayer coverage on hydrogen adsorption at the stepped surfaces Pt(955), Pt(322) and Pt(544) in sulfuric acid solution J. Electroanal. Chem. 396 139-42... 

FIG. 11-62 Vibratory-conveyor adaptations as indirect heat-transfer equipment, a) Heavy-duty jacketed for bqiiid coolant or high-pressure steam, (h) Jacketed for coolant spraying, (c) Light-duty jacketed construction, (d) Jacketed for air or steam in tiered arrangement, (e) Jacketed for air or steam with Mix-R-Step surface, Coutiesy of Jeffrey Mfg. Co.)... 

For more information on kinematic treatment of diffraction from stepped surfaces, see M. G. Lagally, D. E. Savage, and M. C. Tringides. In Reflection High-Energy Electron Difraction and Rflection Electron Ima ng of Surfaces. NATO ASI Series B, Plenum, New York, 1988, Volume 188. 

FIG. 3 Model stepped surface used in computer simulation studies. 

Another special case of weak heterogeneity is found in the systems with stepped surfaces [97,142-145], shown schematically in Fig. 3. Assuming that each terrace has the lattice structure of the exposed crystal plane, the potential field experienced by the adsorbate atom changes periodically across the terrace but exhibits nonuniformities close to the terrace edges [146,147]. Thus, we have here another example of geometrically induced energetical heterogeneity. Adsorption on stepped surfaces has been studied experimentally [95,97,148] as well as with the help of both Monte Carlo [92-94,98,99,149-152] and molecular dynamics [153,154] computer simulation methods. 

Additional applications of the transfer matrix method to adsorption and desorption kinetics deal with other molecules on low index metal surfaces [40-46], multilayers [47-49], multi-site stepped surfaces [50], and co-adsorbates [51-55]. A similar approach has been used to study electrochemical systems. 

The simplest case to be analyzed is the process in which the rate of one of the adsorption or desorption steps is so slow that it becomes itself rate determining in overall transformation. The composition of the reaction mixture in the course of the reaction is then not determined by kinetic, but by thermodynamic factors, i.e. by equilibria of the fast steps, surface chemical reactions, and the other adsorption and desorption processes. Concentration dependencies of several types of consecutive and parallel (branched) catalytic reactions 52, 53) were calculated, corresponding to schemes (Ila) and (lib), assuming that they are controlled by the rate of adsorption of either of the reactants A and X, desorption of any of the products B, C, and Y, or by simultaneous desorption of compounds B and C. 

Figure 16. Plot of the potential of zero charge, Eamo, vs. the electron work function of several low-index and stepped surfaces of Au. E a0 and measured on the same...

More recently, Silva et a/.447,448 have found that the temperature coefficients of dEa /dT for a number of stepped Au surfaces do not fit into the above correlation, being much smaller than expected. These authors have used this observation to support their view of the hydrophilicity sequence the low 9 (rs0/97 on stepped surfaces occurs because steps randomize the orientation of water dipoles. Besides being against common concepts of reactivity in surface science and catalysis, this interpretation implies that stepped surfaces are less hydrophilic than flat surfaces. According to the plot in Fig. 25, an opposite explanation can be offered the small BEod0/dT of stepped surfaces is due to the strong chemisorption energy of water molecules on these surfaces. 

It is worth noting that for both systems the observed AUWr value corresponding to the onset of the formation of the ordered Na adlattice is practically the same, which strongly supports the idea that this AUwr value is characteristic of the chemical potential of this structure. The fact that a small but not negligible Na coverage (0ga < 0.015) preceeds the formation of the ordered Na structure on the surface of polycrystalline Pt samples (Fig. 5.54) may indicate preferential Na adsorption on stepped surfaces before Na adsorption on Pt(lll) starts taking place. 

In this figure, the activation energies of N2 dissociation are compared for the different reaction centers the (111) surface structure ofan fee crystal and a stepped surface. Activation energies with respect to the energy of the gas-phase molecule are related to the adsorption energies of the N atoms. As often found for bond activating surface reactions, a value of a close to 1 is obtained. It implies that the electronic interactions between the surface and the reactant in the transition state and product state are similar. The bond strength of the chemical bond... 

Figure 1.5 Plot of computed reaction barriers for dissociation at Eaa. for N2 dissociation as a function of nitrogen atom adsorption energy on surface terrace and stepped surface [2]. The upper curve is for surface terrace of (111) type of fee crystals, and the lower curve presents data on the stepped surfaces.

This is characteristic for the activation of molecular tt bonds. The same principle was found to apply for stepped surfaces. It is also characteristic of other reactions with surface fragments that have strong repulsive interactions when they share binding with the same surface atom, for example, NH and O, which typically prefer bonding in high-coordination sites. 

Note that the dissociation proceeds with a much lower barrier on the stepped surface. As the structure diagrams show, at all stages in the dissociation the species are more strongly bound on the stepped surface, for reasons discussed in connection with Eq. (87). However, the transition state is most affected, because two N atoms are bound to four metal atoms in the transition state on a perfect surface, whereas that on the stepped surface consists of five metal atoms. As noted above, geometries in which atoms bind to different metal atoms are always more stable than when the two adsorbate atoms share one metal atom. Hence, dissociation is favored over step sites, and if a surface contains such defects they may easily dominate the kinetics. 

All these questions can be answered if we consider the transition states for the dissociation reactions, which are all very similar. The transition state structure for a given substrate geometry is essentially independent of the type of molecule and substrate. Thus the close packed surfaces as well as the stepped surfaces considered in Fig. 6.42 each form a group. Dissociation is furthermore characterized by a late transition state, in which the two atoms have already separated to a large extent and... 

Similar studies have been carried out with Pt(l 11) and stepped surfaces with (111) terraces [Angelucci et al., 2007a, b]. The voltammetric profiles of these surfaces agree qualitatively with those depicted in Fig. 6.9. For the stepped surfaces, the potentials Ex and 2 depend linearly on the step density for terraces wider than 5 atoms. This hnear dependence is a consequence of the dependence of the oxidation rate on the step density, as was observed in the chronoamperometric CO stripping experiments. In H2SO4... 

Shin J, Tomquist WJ, Korzeniewski C, Hoaglund CS. 1996. Elementary steps in the oxidation and dissociative chemisorption of ethanol on smooth and stepped surface planes of platinum electrodes. Surf Sci 364 122. 

It has been often stressed that low eoordinated atoms (defeets, steps, and kink sites) play an important role in surfaee ehemistry. The existenee of dangling bonds makes steps and kinks espeeially reaetive, favoring the adsorption of intermediate species on these sites. Moreover, smdies of single-crystal surfaces with a eomplex geometry have been demonstrated very valuable to link the gap between fundamental studies of the basal planes [Pt( 111), Pt( 100), and Pt(l 10)] and applied studies of nanoparticle eatalysts and polycrystalline materials. In this context, it is relevant to mention results obtained with adatom-modified Pt stepped surfaces, prior to discussing the effect of adatom modification on electrocatalysis. 

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