Terrace-step-kink model

Up to this point, only the structure of surfaces in terms of the terrace step kink model has been considered. FEED... 

Now a roughening of such a vicinal surface means that kinks may occur on the steps and these steps may shift relative to the neighboring ones. There is now ample evidence that roughening transitions of surfaces such as Cu(l 13) do occur (e.g., Liang el al., 1987 Salanon et al, 1988 Lapujoulade et al., 1990) and that these observations can be understood in terms of terrace-step-kink models (Selke and Szpilka, 1986) and related continuum models, where an effective step-step interaction is taken into account (Villain et al.. 1985). 

Fluctuations of an isolated step are also suppressed by the microscopic energy cost to form kinks. On coarse-graining, this translates into an effective stiffness or line tension that tends to keep the step straight. Standard microscopic 2D models of step arrays incorporating both of these physical effects include the free-fermion model and the Terrace-Step-Kink (TSK) model. Both models have proved very useful, though their microscopic nature makes detailed calculations difficult. 

Fig. 1. Model of a surface showing various typical features such as terraces, steps, kinks, vacancies, and adatoms [93Bonl].

For an effective discussion, it is necessary to introduce the Terrace-Step-Kink (TSK) model, which was proposed independently by Kossel [51] and Stranski [52] duringthe late 1920s. As might be expected from the name itself, this model simply regards the surface as a set of three physically distinctive entities such as terrace, step, and kink, as shown schematically in Figure 11.9a. The beauty of this model is that, despite its... 

As the crystal surface exposed to the atmosphere is usually not ideal, specific sites exist with even much lower co-ordination numbers. This is shown schematically in Fig. 3.5, which gives a model comprising so-called step, kink and terrace sites (Morrison, 1982). This analysis suggests that even pure metal surfaces contain a wide variety of active sites, which indeed has been confirmed by surface science studies. Nevertheless, catalytic surfaces often behave rather homogeneously. Later it will be discussed why this is the case. In short, the most active sites deactivate easiest and the poorest active sites do not contribute much to the catalytic activity, leaving the average activity sites to play the major role. 

Studies to correlate the reactivity and the surface structure and composition of platinum surfaces indicate that the active platinum crystal surface must be heterogeneous. The heterogeneity involves the presence of various atomic sites that are distinguishable by their number of nearest neighbors (atoms in terraces, steps, and kinks), and also variation in surface chemical composition. A model that depicts the active platinum surface is shown schematically in Fig. 28. Part of the surface is covered with a partially de-... 

As a consequence, real surfaces will not exhibit such evenly sized terrace or evenly spaced kinks as suggested by Fig. 8.12. The terrace-ledge-kink (TLK) model [332] can provide a more realistic description of vicinal surfaces. The distribution of the terrace widths is calculated taking into account the entropic repulsion between ledges. The confinement of a ledge between two neighboring steps (that cannot be crossed) leads to a reduction of the number... 

Based on the TLK (terrace, ledge and kink) model, growth on a perfect vicinal and singular surface proceed by a sequence of steps involving adsorption from vapor to form a surface adatom. This adatom diffuses to a kink site of the surface and incorporate into the crystal at the kink site. In order to determine the growth rate, the rate of formation of stable cluster must be determined. This is the rate at which cluster of radius r grow by the addition of one incremental atom from the adlayer. The rate is given by. 

For the fee system for each of the three families of planes 111, 100, and 110 there is only one type of site where an atom could be added in the nearest-neighbor position they are called singular faces (Fig. 9). Atomically flat surfaces nearly parallel to a singular face are called vicinal faces. The vicinal faces can be described by the composition of terraces of singular faces and by monoatomic steps (Fig. 11). The monoatomic steps are either densely packed in atoms or kinked. This model is called the TLK model (terrace, ledge, kink) and it can be easily extended to all faces on the three main zones of the unit triangle. 

Model of metal surface with step, kink, and terrace sites after Stranski and Kossel. (From Stranski, I.N., Z. Physik. Chem., 136, 259, 1928 Kossel, W., Nachr. Ges. Wiss. GSttingen. Math. Physik. K.L, 135,1927.)... 

To demonstrate the versatility of the coverage-dependent thermodynamic models described in this chapter, as well as to gain insight into the interrelated effects of coverage and structure in O adsorption on Pt, we describe in this chapter results for O adsorption at the Pt(321) surface. The (321) facet exposes steps, kinks, and close-packed terraces with five unique surface atoms, shown in Figure 2.3 and numbered 15 beginning at the kink atom and moving back across the terrace. 

The existence of active sites on surfaces has long been postulated, but confidence in the geometric models of kink and step sites has only been attained in recent years by work on high index surfaces. However, even a lattice structure that is unreconstructed will show a number of random defects, such as vacancies and isolated adatoms, purely as a result of statistical considerations. What has been revealed by the modern techniques described in chapter 2 is the extraordinary mobility of surfaces, particularly at the liquid-solid interface. If the metal atoms can be stabilised by coordination, very remarkable atom mobilities across the terraces are found, with reconstruction on Au(100), for example, taking only minutes to complete at room temperature in chloride-containing electrolytes. It is now clear that the... 

A block model of defects on a single-crystal surface is depicted in Figure 2.4.17 The surface itself in reality is a two-dimensional defect of the bulk material. In addition, one-dimensional defects in the form of steps which have zero-dimensional defects in the form of kink sites. Terraces, which are also shown in the figure, have a variety of surface sites and may also exhibit vacancies, adatoms, and point defects. Surface boundaries may be formed as a result of surface reconstruction of several equivalent orientations on terraces. 

Fig. 6. A model of a platinum surface on which 5/6 of the atoms are on terraces (the 111 and 1/6 of the atoms are at step and kink sites. Reproduced with permission from Ref.1 ...

Ideal Surfaces, A model of an ideal atomically smooth (100) surface of a face-centered cubic (fee) lattice is shown in Figure 3.13. If the surface differs only slightly in orientation from one that is atomically smooth, it will consist of flat portions called terraces and atomic steps or ledges. Such a surface is called vicinal. The steps on a vicinal surface can be completely straight (Fig. 3.13a) or they may have kinks (Fig. 3.13b). 

Figure 8.3a displays a simplified block model of a metal oxide surface showing one-dimensional defects in the form of steps. These steps in turn give rise to point defects in the form of kink sites. Terraces can also possess a variety of different surface sites such as adatoms, vacancies, and substitutional and interstitial point defects. Figure 8.3b shows that the... 

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