Surface reconstruction approach

Fig. 2. (a)-(f) principle steps of the proposed multi-resolution surface reconstruction approach, (a) input point cloud of the Stanford bunny data set, consisting of 35,947 points,... 

In this review article we have tried to show that an analytical approach to the thermodynamics and the kinetics of adsorbates is not restricted to simple systems but can deal with rather complicated situations in a systematic approach, such as multi-site and multi-component systems with or without precursor-mediated adsorption and surface reconstruction, including multi-layers/subsurface species. This approach automatically ensures that such fundamental principles as detailed balance are implemented properly. 

The abilities of this approach will then be illustrated with two examples (i) the potential-induced lifting of the Au(lOO) surface reconstruction and (ii) the electrochemical oxidation of Pt(l 11). 

We have also discussed two applications of the extended ab initio atomistic thermodynamics approach. The first example is the potential-induced lifting of Au(lOO) surface reconstmction, where we have focused on the electronic effects arising from the potential-dependent surface excess charge. We have found that these are already sufficient to cause lifting of the Au(lOO) surface reconstruction, but contributions from specific electrolyte ion adsorption might also play a role. With the second example, the electro-oxidation of a platinum electrode, we have discussed a system where specific adsorption on the surface changes the surface structure and composition as the electrode potential is varied. 

One important aspect not discussed above is the change in atomic structure at a surface. Contrary to the schematic picture of the Si(lll) surface shown in Fig. 14.6, a solid surface is usually not just the end of a perfect crystal. Surfaces reconstruct in response to the changes in the electronic distribution caused by the surface itself. Again, all these changes occur selfconsistently, and in principle, if the total energy for various configurations of atomic structures at a surface could be evaluated, the shifts in the positions of the atoms and the electronic structures of the surface could be determined theoretically. This approach will be discussed in the next section, but the first calculations for reconstructed surfaces were done using experimental determinations of the atomic positions. 

Another, more direct approach to overcome the problem of surface reconstruction, is the variation of the mesogenic unit of the surface active molecule. Instead of using flexible n-alkyl moieties with high conformational freedom, SAMs formed from molecules featuring a rigid mesogen in which conformational disorder has been eliminated as completely as possible should be suitable for the preparation... 

Furthermore, surface reconstruction may be viewed, for the variation of certain properties, simply as a response to depression , or to a strain of dilatation, in the surface layer. This approach has been applied with success to account for the surface phonon, and for the global destabilization (blue shift) of the surface exciton. In contrast, the modification of the surface excitonic structure is not amenable to such a simple image of the reconstruction. 

The kinetics of chemical reactions on surfaces is described using a microscopic approach based on a master equation. This approach is essential to correctly include the effects of surface reconstruction and island formation on the overall rate of surface reactions. The solution of the master equation using Monte Carlo methods is discussed. The methods are applied to the oxidation of CO on a platinum single crystal surface. This system shows oscillatory behavior and spatio-temporal pattern formation in various forms. 

In the following, we will discuss DMC simulations on the CO oxidation on the Pt(lOO) surface, that were done in our laboratories. The simulations show oscillations in the CO2 production rate as well as several types of spatio-temporal pattern formation. In essence, it is an extension of the ZGB model with desorption and diffusion of A, finite reaction rates and surface reconstruction. We will discuss it to illustrate the complexity of the models with which DMC simulations can be done nowadays. For clarity, we will stick to the A and B2 notation employed in the previous section. Species A corresponds to CO and B2 corresponds to 02- Furthermore, we will speak in terms of reaction rates instead of relative reaction probabilities. This terminology is entirely justified in the DMC approach that we used. 

Despite the complexity of the silicon systems, theoretical approaches allow to understand a large variety of adsorption processes. The complexity conies from the surface reconstruction which imposes very large unit cells (Si(lll) 7x7) and which also corresponds to very large amplitudes for the variations of the geometric parameters... 

In this work, we applied the DPTB method to some fundamental aspects of adhesion on oxide surfaces and validated the approach by comparison with rigorous DPT calculations. In Section 2.2, DPTB results for surface reconstructions on ideal a-Si02 were investigated to serve as a benchmark for surface structures. In Section 2.3, we presented calculations concerning the structures of organic components of the adhesive and introduced a new computational scheme based on QM/MM coupling for surface-adhesive interactions. 

If is much smaller than [ksp], the number of kink site positions decrease, because the renewal of the kink site positions by accumulation of metal ions is so slow that more and more kink site positions disappear because of the natural surface reconstruction. If is much larger than [ksp], however, the number of kink positions will increase because new surface structures can develop. Thus one can say for stationary conditions that N,should approach the value = 1. The density of kink site positions [fop] finally therefore approach the value... 

This problem is solved by using Lagrange multipliers under a constrained minimization approach [10], With the cloud of points and the resulting approximated plane it is possible to evaluate maximum and minimum deviations and standard deviation of the measured points. Reverse engineering software and specific treatment programs are able to analyze quality of the approximation. Catia V5 surface reconstruction modules and Inspect + software of Steinbichler have been used for this work. 

Surface (3D) Reconstruction Surface reconstruction from point clouds is fundamental in many applications. Using the raw point clouds or volumetric data acquired from an unknown surface, an approximation of the surface can be constructed and used to compare it with CAD models or for smface-based automated programming. Reconstruction methods can be classified into two types the computational geometry approach focuses on the piecewise-linear interpolation of unorganised points and defines the surface as a carefiilly chosen sub-set of the Delaunay triangulation in a Cartesian coordinate system, and the computer graphics... 

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