Step interaction

N. C. Bartelt, T. L. Einstein, E. D. Williams. The influence of step-step interactions on step wandering. Surf Sci Lett 240 L591, 1990. 

Since oxidation of methanol is an electrocatalytic reaction with different adsorption steps, interactions of the adsorbed species with the metallic surface are important. Using platinum single-crystal electrodes, it has been proven that the electrooxidation of methanol is a surface-sensitive reaction. The initial activity of the Pt(llO) plane is much higher than that of the other low-index planes, but the poisoning phenomenon is so rapid that it causes a fast decrease in the current densities. The... 

MORPHOLOGIES OF PERIODIC SURFACE PROFILES AND SMALL PARTICLES A SOURCE OF STEP AND STEP INTERACTION ENERGIES... 

The constant a is proportional to the step formation energy, f and b and c account for step-step interactions. Entropic, dipole and elastic interactions between steps give rise to the pfterm [24,25] whereas the p term may be due to electronic effects [26], The experimental data of fig. 1 can be fitted by y(0) = jo cosq f(p) over the whole range of orientations when all terms of eq. (1) are allowed [27]. More about this point in section 6. In principle, it is a matter of great interest to test the validity of eq. (1) and to determine the step as well as step interaction energies. 

Dp and D are surface diffusion coefficients parallel and normal to steps, respectively, and e is the step interaction energy. Obviously, two simple cases arise for /= 0 and / = Jt/2, i.e. for the profile modulation parallel and perpendicular to the intrinsic steps. Since the step energ>" is in general larger than the step interaction energy [24,28] and the diffusion parallel to steps faster than normal to steps [29,30], the decay rate of such profiles is expected to be much faster when the modulation is parallel to the steps. The dependence of B, D and E on... 

Eqs. (3), (5) and (6) depend on the particular form of eq.( 1). If the main step interaction term in eq.(l) is proportional to rather than p, the expressions for E( /) would be different, particularly for the Mf = izH case. Whereas the variation of B(ji/2) with miscut a isstrong(atan a/cos a) for p dependence, it is weak a 1 /cos a) for p dependence. Thus a measurement of B(n/2) for several miscut surfaces, although tedious, would be a means to distinguish between those dependences. The anisotropy factor, eq.(6), would also exhibit a weaker variation with miscut for p dependence. 

The investigation of the exact ECS of small particles adsorbed on a flat (monociystalhne) substrate appears to be an excellent way to determine the relative orientation dependence of y(0) and from there the relative step and step interaction energies, provided the ECS exhibits all orientations, such that the conversion to y(0) is unique [1-4]. In that sense ECS studies are an important supplement to studies of transient morphological shapes which normally yield the product of mobility x energy. 

To extract a value of the step-mobility h from the grating relaxation experiments [12], we must evaluate the strength of the step-step interaction y. Computational work suggests that ydue to elastic interactions between Si(OOl) steps is 0.2 eV run [29], while, we estimate that the entropic interaction is 10 times larger. (We use a step stiffness P calculated from the geometric mean of P for Sa and Sb steps given in Ref [30] P, 0.03 eV mn-. ) Therefore, entropic repulsion should dominate, and... 

The experimental evidence for this scenario, mentioned at the outset of this section, is less compelling since it is harder to control this sort of dosage-sensitive STM experiment than a Monte Carlo simulation. (Specifically, it problematic to convert from CO dosage to the evolution time from initial instability the analysis would be better if the surface could be instantaneously de-oxidized.) From an earlier examination of the terrace-width distribution for Ag(110)2Y—>[001], Ozcomert et al. (1993) concluded that to a good approximation the step-step interactions were purely entropic repulsions (by finding a good fit to a free-fermion form (Jobs et al, 1991)). (But see also Pai et al (1994) for remarkable behavior under different conditions.) From the relationship (Bartelt el a/., 1992)... 

Figure 4. Early time adatom concentration profile for 7 =0.56r A = 32a (a) concentration, C vs. position, (b) schematic illustrating lower step interaction energy upon creation of adatoms on the top terrace (i) and higher step interaction energy upon creation of adatoms on the bottom terrace (ii).

A series or bunch of m initially straight and parallel steps, between heights 0 and m, may be expected to relax with the same asymptotics as a pair of steps. Modifications may occur, already for a pair of steps, when step-step interactions are present in addition to the entropic step repulsion. Here, we merely refer to recent reviews on experiments and theoretical analyses " on the much studied phenomenon of step bunching for vicinal surfaces, which is accompanied by interesting phase transistions. 

Most cases are well understood by now. Additional work seems to be needed for clarifying the flattening of gratings below roughening in the case of surface diffusion.- It is also desirable to elucidate the effect of (long-range) step-step interactions, induced, for example, by elastic forces, on step fluctuations. 

The expression for v would be different if the step-step interaction is dominated by elasticity or other effects. 

In this model, reconstruction modifies the effective step interactions and thus the dynamics. Both the presence of a reconstructed terrace behind a given step and repulsive entropic or elastic interactions from the step behind make positive contributions... 

Direct step-step interaction terms in the step energy ( direct interactions are entropic repulsion, strain terms, electronic structure effects etc.) do influence the step fluctuations, and they also drive the spreading of step trains, wires and bumps. Nevertheless, it is instructive to first ignore these direcf step-step repulsion, as is done in... 

A much more elaborate reaction scheme is postulated by Haszeldine and Nyman46 on the basis of three qualitative experiments to explain the liquid phase photolysis of hexachloroacetone. The rate of photolysis is extremely slow in the liquid phase, and the only products identified were trichloroacetyl chloride and octachloropropane. These are considered to arise by the following sequence of reactions in which the products of two competing primary steps interact. 

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