Rough surfaces atomically

Several features of ISS quantitative analysis should be noted. First of all, the relative sensitivities for the elements increase monotonically with mass. Essentially none of the other surface spectroscopies exhibit this simplicity. Because of this simple relationship, it is possible to mathematically manipulate the entire ISS spectrum such that the signal intensity is a direct quantitative representation of the surface. This is illustrated in Figure 5, which shows a depth profile of clean electrical connector pins. Atomic concentration can be read roughly as atomic percent direcdy from the approximate scale at the left. 

Therefore, for a rough surface, although it is smooth macro-scopically, the friction coefficient is greatly affected by its surface morphology. For a smooth surface on atomic scale, 0 can be neglected and the friction coefficient is only related to the twist angle of the cantilever. 

We now describe a relatively simple MD model of a low-index crystal surface, which was conceived for the purpose of studying the rate of mass transport (8). The effect of temperature on surface transport involves several competing processes. A rough surface structure complicates the trajectories somewhat, and the diffusion of clusters of atoms must be considered. In order to simplify the model as much as possible, but retain the essential dynamics of the mobile atoms, we will consider a model in which the atoms move on a "substrate" represented by an analytic potential energy function that is adjusted to match that of a surface of a (100) face-centered cubic crystal composed of atoms interacting with a Lennard-Jones... 

Attempts to determine how the activity of the catalyst (or the selectivity which is, in a rough approximation, the ratio of reaction rates) depends upon the metal particle size have been undertaken for many decades. In 1962, one of the most important figures in catalysis research, M. Boudart, proposed a definition for structure sensitivity [4,5]. A heterogeneously catalyzed reaction is considered to be structure sensitive if its rate, referred to the number of active sites and, thus, expressed as turnover-frequency (TOF), depends on the particle size of the active component or a specific crystallographic orientation of the exposed catalyst surface. Boudart later expanded this model proposing that structure sensitivity is related to the number of (metal surface) atoms to which a crucial reaction intermediate is bound [6]. 

A few additional points have also been raised by specific surface-science work concerning the catalytic reduction of NO. For instance, it has been widely recognized that the reaction is sensitive to the structure of the catalytic surface. It was determined that rough surfaces such as (110), or even (100), planes enhance NO dissociation over flatter (111) surfaces, and also favor N2 desorption instead of N20 production. On the other hand, NO dissociation leads to poisoning by the resulting atomic species, hence the faster reaction rates seen with medium-size vs. larger particles on model rhodium supported catalyst (the opposite appears to be true on palladium). Also, at least in the case of palladium, the formation of an isocyanate (-NCO) intermediate was identified... 

The relative importance of the two mechanisms - the non-local electromagnetic (EM) theory and the local charge transfer (CT) theory - remains a source of considerable discussion. It is generally considered that large-scale rough surfaces, e.g. gratings, islands, metallic spheres etc., favour the EM theory. In contrast, the CT mechanism requires chemisorption of the adsorbate at special atomic scale (e.g. adatom) sites on the metal surface, resulting in a metal/adsorbate CT complex. In addition, considerably enhanced Raman spectra have been obtained from surfaces prepared in such a way as to deliberately exclude one or the other mechanism. 

The comparison of continuum and atomistic models by Luan and Robbins demonstrates that the atomic details of this contact can have a significant influence on the calculated friction. However, those calculations did not explore atomically rough surfaces, which are most likely found in real engineering contacts. The effect of roughness has been investigated recently by Qi et al. in a study of the friction at the interface between two Ni(100) surfaces.85 Two models were considered in that work. In the first model, both surfaces were atomically flat i.e., the rms roughness was 0.0 A. In the... 

Figure 21 Friction coefficient for differently oriented Ni(100)/Ni(100) interfaces. Rough surfaces have a 0.8 A rms variation in roughness added to the atomically smooth surfaces. Reproduced with permission from Ref. 85.

Hydrogen, which covers the internal surface of PS, can also be used to estimate its structural dimensions. IR measurements indicated a stoichiometry of roughly SiH for electrochemically prepared micro PS [Be2]. If dihydride groups are assumed to cover the internal surface, every second atom must be a surface atom. This is the case for a cube of about 1000 atoms that has a diameter of approximately 2 nm. A stoichiometry of SiH04 obtained by thermodesorption measurements points to a crystallite diameter in the order of 4nm [Pe2]. The chemical composition for a hydride coverage surface and for a 0.5 nm thick native oxide layer are given in Table 6.1. 

The concentration of the surface states is in the range from 1 x 10 to 1 x 10 cm-, which is 1/10 to 1 /lOOOOO of the concentration of surface atoms ( 1 x 10 cm- ). UsuaUy, the surface state concentration is greater on the rough siuface than on the smooth surface. 

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