Terrace kinetics

The secondary and ternary islands will keep growing in approximately concentric fashion, thereby producing a conical structure above the original nucleation centers. This process of kinetic roughening supported by the Schwoebel effect makes a rather bumpy surface structure. Looking finally at a vicinal surface, this will grow rather smoothly when the width of the terraces is smaller than the typical distance between nucleation centers 4i (see below), and becomes bumpy in the opposite case [12,93]. 

In order to assess the role of the platinum surface structure and of CO surface mobility on the oxidation kinetics of adsorbed CO, we carried out chronoamperometry experiments on a series of stepped platinum electrodes of [n(l 11) x (110)] orientation [Lebedeva et al., 2002c]. If the (110) steps act as active sites for CO oxidation because they adsorb OH at a lower potential than the (111) terrace sites, one would expect that for sufficiently wide terraces and sufficiently slow CO diffusion, the chronoamperometric transient would display a CottreU-hke tailing for longer times owing to slow diffusion of CO from the terrace to the active step site. The mathematical treatment supporting this conclusion was given in Koper et al. [2002]. 

An influence of particle size on the kinetics of COads electro-oxidation has been shown by Maillard and co-workers with FTIR spectroscopy. It has been suggested that the reaction starts on the terraces of large (> 3 nm) particles, and then propagates to the particle edges. Electro-oxidation of COads on small (<2nm) particles commences at more positive potentials, when COads on large particles is oxidized. 

Numerous quantum mechanic calculations have been carried out to better understand the bonding of nitrogen oxide on transition metal surfaces. For instance, the group of Sautet et al have reported a comparative density-functional theory (DFT) study of the chemisorption and dissociation of NO molecules on the close-packed (111), the more open (100), and the stepped (511) surfaces of palladium and rhodium to estimate both energetics and kinetics of the reaction pathways [75], The structure sensitivity of the adsorption was found to correlate well with catalytic activity, as estimated from the calculated dissociation rate constants at 300 K. The latter were found to agree with numerous experimental observations, with (111) facets rather inactive towards NO dissociation and stepped surfaces far more active, and to follow the sequence Rh(100) > terraces in Rh(511) > steps in Rh(511) > steps in Pd(511) > Rh(lll) > Pd(100) > terraces in Pd (511) > Pd (111). The effect of the steps on activity was found to be clearly favorable on the Pd(511) surface but unfavorable on the Rh(511) surface, perhaps explaining the difference in activity between the two metals. The influence of... 

Fig. 2. Kinetics scheme for NO/Pt(l 11) including terrace diffusion (1), trap-to-terrace jumps (II), and thermal desorption T/D. (Adapted from Ref 16.)...

Over broad temperature regimes, terrace diffusion is the dominant kinetic mechanism. In this process, an atom detaches onto the lower terrace with probability pi, and onto the upper terrace with probability pu. It then diffuses on the terrace and reattaches to the step edge(see Fig. Ic). We define the sticking coefficient on approach to the step edge from the lower terrace to be a, while the sticking coefficient on approach to the step edge from the upper terrace is ajj (here we use continuum sticking coefficients, and relate them to lattice parameters in Appendix B). In Appendix C we calculate P(J) for terrace diffusion (see Eq. (106) for Pi(/) with d <=<>), from which we find. 

The interpretation of this data on metals in terms of microscopic mechanisms of surface atom transport is not totally understood. The original papers[ 11] proposed that during surface transport the controlling process was adatom terrace diffusion between steps with the adatom concentration being that in local equilibrium with the atomic steps. This may indeed be the case, but in light of other experiments on adatom diffusion[13] and exchange processes at steps[14] the possibility of step attachment/detachment limited kinetics caimot be raled out. 

Next, the step-mobilityof Si(OOl) is estimated at lower temperatures, T 500°C, from the experiments of Webb et al. [25] on the relaxation kinetics of non-equilibrium step-spacings. In this experiment, the average terrace size was large, and therefore, due to the stress anisotropy of the 2 x 1 surface reconstruction, a long range interaction of the form... 

The implication of this behavior suggests that there will be a quantitative difference in the kind of step fluctuation dynamics observed for each kinetic law system. For i-kinetics, we expect steps to fluctuate by variations in the flux of adatoms hitting the step from a uniform, quickly moving sea of equilibrated adatoms on the adjoining terrace. In this case, the time to create a step fluctuation of amplitude y (perpendicular to both the surface normal and the average step direction) will be given by... 

For A/-kinetics, on the other hand, adatoms diffuse rapidly along steps, and we can expect a tendency to wash out the variation of the terrace adatom flux onto the step. Thus, at the very least, we can say that step fluctuations in this system should form more slowly than for /-kinetics, i.e.. 

Figures. Snapshots of a surface obeying/-kinetics illustrating the pinch-off mechanism. T= 0.56 Tb, = 64a. toVo= 1.75x10 (no pinch-off), /,Vo= 2.62x10 (firstpinch-off),t2v0= 3.78x105 (steady-statepinch-off), tsVo = 5.24x10 (terrace dissolution virtually complete).

So far, we tacitly assumed that the upper and lower terraces next to the step are below their roughening transition temperature. By fixing the boundary heights of the terraces, away from the step, at, say, level 0 for the lower and level 1 (in units of the lattice spacing) for the upper terrace, one can study the time evolution of the step width w, defined, for instance, as the second moment of the gradient of the step profile also above roughening. Then one obtains s =1/4 for terrace diffusion and 1/2 for evaporation kinetics, as predicted by the continuum description of Mullins and confirmed by our Monte Carlo simulations. 

Figure 2. Monte Carlo configuration of a pair of steps below the roughening transition temperature of the standard SOS model, at t = 5000 MCS. using evaporation kinetics. The initial width /,o of the center terrace is six lattice spacings.

Below roughening, pronounced lattice effects show up in the simulations, as in the case of wires. The meandering of the top(bottom) steps and the islanding on the top(bottom) terrace leads to slow and fast time scales in the decay of the amplitude. The profile shapes near the top(bottom) broaden at integer values of the amplitude and acquire a nearly sinusoidal form in between. Again, these features are not captured by the continuum theory. For evaporation kinetics, continuum theory suggests that the decay of the profile amplitude z scales like z t,L) = where g =... 

If thermal fluctuations were taken into account, the regular patterns selected by this kinetic mechanism would be expected to be less sharp. In particular, when wjwa, is not so small, the effects of mass conservation are spread out over many terraces and several terraces in front of the step bunch become larger than These would be particularly advantageous sites where thennal nucleation could occur, even before the induced width of the terrace as predicted by the deterministic models would exceed Wc. Thus nucleation sites and times are less precisely determined in this case, and we... 

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