Kink positions

The half-crystal position is the same as the position called a kink site, and is shown in Fig. 7.134. This term is due to Kossel (1927) and Stranski (1928). The half-crystal position occurs in the way shown in Fig. 7.134. The energy of binding of an atom in the kink position is just half of the total energy of an atom in the bulk of the ciystal. 

Fig. 7.134. The half-crystal (or kink) position. The figure shows the binding energy of an atom in a kink position and how the name half-crystal position has been derived. A represents the missing part of the bulk crystal above the surface plane, fithe missing half of the surface plane, and Cthe missing half of the atomic row along the step in front of the kink atom. Together they add the halfcrystal to a bulk crystal. (Reprinted from E. Budevski, G. Staikov, and W. J. Lorenz, Electrochemical Phase Formation and Growth, 18, copyright 1996, John Wiley Sons. Reproduced by permission of John Wiley Sons, Ltd.)...

Since the hydrogenolysis of cyclohexane and cyclohexane derivatives is less probable than the thermodynamically favored dehydrogenation to form aromatic compounds, most studies address hydrogenolysis only in connection with aromati-zation as an unwanted side reaction. An interesting observation by Somorjai showed, however, that hydrogenolysis of cyclohexane to form n-hexane becomes competitive with aromatization on Pt single crystals with increasing kink density.302 On a Pt surface where approximately 30% of the atoms in the steps are in kink positions, benzene and n-hexane are formed in 1 1 ratio. 

Half-crystal position (kink position) — The term was introduced into the theory of crystal growth simultaneously and independently by W. Kossel [i] and - St ran-ski [ii,iii], who were the first to realize the necessity of a close consideration of the elementary acts of attachment and detachment of single particles (atoms, ions, or molecules) to and from a crystal surface. 

An atom in the half-crystal position (also called kink position) (Fig. 1), is bonded (i) with a semi-infinite crystal block, (ii) with a semi-infinite crystal lattice plane, and (iii) with a semi-infinite crystal row. Attaching or detaching one atom to and from the half-crystal position a new half-crystal position is created and this is what makes this position a repeatable step in the successive building or disintegration of the bulk crystals. 

Half-crystal position (kink position) — Figure. The Kossel s cubic crystal (a) and the atom in the half-crystal position (b)... 

Kink position - half-crystal position Klemensiewicz, Zygmunt Aleksander... 

The salient feature of the kink position is the fact that if an atom is removed fi om such a position, the next atom, in the row of the step edge atoms, will find itself in the same position. The removal of a kink atom fi om the step edge does not change the structure of the surface and is, hence, a repeatable step. A sufficiently large crystal can be disintegrated (evaporated or dissolved) by consecutive removal steps (detachment... 

The second remarkable feature of an atom in a kink position is that it is bonded to the crystal with exactly one half of the bonds of one bulk atom. This is schematically illustrated in Fig. 2.9 for a crystal with a simple cubic lattice. The parts A, B, and C represent exactly the missing half of the infinitely large crystal. After adding A, B, and C, the half ciystal position is changed to a bulk position. For a crystal with a hep or fee (bulk) lattice, a kink atom or an atom in a half crystal position has 6 first neighbors, that is, half of the coordination number of a bulk atom. 

The third veiy important feature of a kink atom is the fact that it represents the final stage of the transfer of an atom from the ambient phase to the crystal. Only after integration of an atom in a kink position can the atom be considered as belonging to the bulk crystal. Therefore, a kink site can be considered as the site of growth or dissolution of the crystal. 

According to Volmer [2.14] the chemical potential,, of kink atoms is related to the separation work of an atom from a kink position, ink. by the equation... 

With a typical value of the sublimation enthalpy of metals, Asubff = 150 kj mol the detachment enthalpy (work of separation) per atom in a kink position is calculated to be ink = 250 X 10 J and the binding energy of two next neighbor atoms to be y/i = 41.7 X 10 J per atom. With that value of y/ every 75th atom on a step would be in a kink position at room temperatures. 

The adatom concentration at equilibrium, o,ads [atoms cm ], is determined by the Gibbs energy AGdispi [J mol ] of the displacement reaction of atoms from kink positions to free" adsorption sites on the surface, where it can form an adatom [2.1] ... 

This causes a diffusion flux, I>sd(cads - fo,ads) /, of adatoms towards the step edge, where the adatoms are rapidly incorporated into kink positions. Therefore, the adatom concentration at the step edge is kept at the equilibrium value Co,ads- At room temperatures, where the average kink distance, i k (cf. eq. (2.5)), is low and smaller than the mean displacement of adatoms, diffusion along the steps can be neglected and the diffusion process can be treated as linear. The incorporation of atoms in the step results in a step propagation with a rate Vsd [cm s ] determined by the flux Dsd Acads/Asd [mol cm s ] and the area 0 hU) occupied by one mole. 

A high-indexed surface zone with a high density of steps or growth sites (kink positions) would follow the same growth law as liquid metals, i.e., the Butler-Volmer relation. Vicinal faces, characterized by low-index surface zones separated by uniformly distributed monatomic steps show an intermediate behavior. 

The constant k contains the ratio of the vibrational frequencies of cluster atoms in position X and in the kink position, and can be assumed to be of the order of unity [4.13]. It has to be remembered, however, that if entropy terms are neglected (cf. Section 2.1), particularly when dissociation enthalpies are used for the calculation of AGcrit, the value of the pre-exponential term in the nucleation rate-overvoltage relation becomes largely uncertain. 

Figure 2 The (a) mass- and (b) surface-averaged distribution of atoms on the (111) and (100) crystal faces and on the edges and corner sites of a cubo-octahedral cluster model. (From Ref. 4.) Mass-averaged and surface-averaged distributions are based on calculations using cubo-octahedron cluster model and represent number of different crystallographic planes divided by the (a) mass or (b) the surface area of the cluster (at the corresponding particle size). Hence (e- -c) in (a) represents edge and kink positions and (100) (111) the normal cubic crystal planes.

For both catalysts, the IR spectra (Fig. 3) exhibit bands in the range of linear/subcarbonyl (2100-2000 cm" ) and bridged carbonyl species (2000-1700 cm" ) [7,8,17-20]. Their broadness reflects the surface heterogeneity of the Ni particles. In both cases, the range of linear carbonyls is dominated by a component at 2067 cm", which may be assigned to subcarbonyl nickel species Ni(CO)n (n = 2,3) formed on low coordinated Ni atoms (comer, step or kink position) [19,20]. 

The first in situ atomic-scale visualization of this growth mechanism was recently demonstrated for the incorporation of chloride ions at kink positions of the c(2 X 2) chloride adlayer on Cu(lOO) in 0.01 M HCl [144]. 

Sublimation enthalpies, energies of atoms in ideal kink positions and bond energies between the two nearest atoms, main group and transition metals ... 

The Gibbs energy of an atom in the kink position (chemical potential) can be derived from the sublimation enthalpy (Vohner ) a discussion is also found in the book of Budevski, Staikov and Lorenz. ... 

No strict distinction between free energy and enthalpy is made. Values for enthalpies of atoms in kink positions for main group and transition metals are listed in Table 2.3. 

Using an appropriate lattice model, one can calculate the bond energy between two atoms. For instance, in a closed packed hexagonal or cubic lattice with 12 nearest neighbors and 6 nearest neighbors in the kink position, one can approximately write... 

The ad-atoms are an intermediate in the mechanism of metal deposition. On one hand, they are in exchange with the metal ions in the electrolyte and, on the other, with atoms in step and kink positions. The density of step atoms and kink sites on a step is also called the step roughness. 

In the model the main three surface processes are shown, which are (1) the charge transfer process, (2) surface diffusion, and (3) the transfer from the ad-atom position into a step or kink position. Not shown are the diffusion processes in the electrolyte. Each step can be rate determining, such as the charge transfer between electrolyte and metal surface (Chapter 6), surface diffusion (Chapter 4), or the transfer into a step or kink position, the final crystallization process. 

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