Singular face

Figure 2.8 The structure of a singular face of a crystal with a simple cubic lattice at lower temperar tures.

At room temperatures singular faces of metal crystals show a relatively low degree of roughening and exhibit only single adatoms and monatomic vacancies, as well as kink sites on steps, if present. 

If the potential of an atomically smooth (non-stepped) singular face is changed, e.g., to a value more negative than the reversible potential, the enhanced deposition rate dep,free will increase the adatom concentration above its equilibrium value Co,ads until the opposite reaction of dissolution idiss,ads reestablishes the balance. The adatom concentration Cads(r/) increases and becomes a function of overpotential as given by eq. (2.29). 

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. 

A crystal is surrounded at equilibrii n by flat, atomically smooth, low-index faces or, in Frank s classification, by singular faces. These faces in equilibrium forms are defined by the Gibbs definition of the equilibrium form requiring a minimum of the surface free energy of the crystal at constant volume (see Section 5.1). 

At elevated temperatures, due to thermal fluctuations, singular faces acquire a surface roughness manifested by the formation of adatoms and surface vacancies, di- or polyatomic surface clusters, and vacancies and steps with kinks as shown in Figure 1. The surface roughness becomes appreciable only above a critical roughening temperature T,. The theoretical value of Tr for a simple cubic crystal lattice, T, = where i(fx denotes the... 

Figure 1. The structure of a crystalline singular face and paths of atom incorporation. 1, Adatom 2, adatom cluster 3, vacancy 4, vacancy cluster 5, half-crystal (kink) atom DT, direct transfer to a kink position TR, transfer to an adatom SD, surface diffusion and incorporation jcq step half-distance.

A perfect crystal bound by singular faces exhibits no sites for growth. A 2D nucleation process is required for the deposition of every new layer, as first noted by Gibbs and developed later by Volmer and Weber, Brandes, and Kaischew. This is because one atom deposited on the crystal face has a smaller bond energy to the crystal than a kink atom and it stays only temporarily on the surface as an adatom. A very important factor is the tendency of these surface atoms to cluster together thereby increasing their stability. Clusters of that kind are potential nuclei of a new lattice net. 

Many authors have agreed that the dissolution reaction mainly starts from the kinks sites. Among the various surface defects that characterize the structure of the singular faces [adatoms, vacancies, adatom and cluster vacancies, half-ciystal atoms (kinks), steps], the kink position has a salient... 

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