The terrace-ledge-kink model

The surface of real crystals are not perfect. At high temperatures thermal disorder will lead to a non-zero concentration of defects. At low temperatures, defects created at high temperatures may be frosen at the surface, defects in the bulk may extend to the surface. Also the orientation of the surface with respect to the crystal lattice may be oriented so that an atomically flat arrangement of the atoms is impossible. 

The simplest model of a surface with defects is the terrace-ledge-kink model. In this model only 4 types of defects are assumed present in the surface  

Adatoms are a limiting case of a terrace made up of a single atom. 

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On an atomic scale, metal surfaces are usually described in terms of the terrace-ledge-kink model shown in Fig. 20.36Z>. Essentially, it is suggested that clean metal surfaces consist of low-energy low-index terraces separated by ledges of monatomic height which occasionally contain monatomic kinks. 

Fig. 20.36 (a) Crains of different orientation intersecting a free surface and (b) the terrace-ledge-kink model of a free metal surface... 

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... 

The terrace-ledge-kink (TLK) model (Kossel, 1927 Stranski, 1928) is commonly used to describe equilibrium solid surfaces. This model was proposed by the German physicist Walther Kossel (1888-1956), who had contributed to the theory of ionic bonding earlier in the century, and by the Bulgarian physical chemist Iwan Nichola Stranski (1897-1979). It categorizes ideal surfaces or... 

Figure 1.5 Atomic-scale illustration of the terrace-ledge-kink (TLK) model. The top partial layer of spheres represent a terrace, and the bottom layer, the underlying surface atoms.

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. 

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. 

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). 

A single crystal surface exhibits terraces (T) with low Miller index crystal faces and high surface density. They are separated by ledges (L) which may have kinks (K). A terrace between two ledges is a step. Defects on terraces consist of vacancies or adsorbed atoms. Thus the smooth surface may indeed be rough on an atomic scale. This model is called as TLK model (Fig. 2.6). The systematic... 

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