The Half-Crystal Position

It was mentioned on page 306 (see Fig. 5.24) that, even at room temperature, a crystal plane contains steps and kinks (half-crystal positions). Kinks occur quite often—about one in ten atoms on a step is in the half-crystal position. Ad-atoms are also present in a certain concentration on the surface of the crystal as they are uncharged species, their equilibrium concentration is independent of the electrode potential. The half-crystal position is of basic importance for the kinetics of metal deposition on an identical metal substrate. Two mechanisms can be present in the incorporation of atoms in steps, and thus for step propagation ... 

The anodic dissolution of metals on surfaces without defects occurs in the half-crystal positions. Similarly to nucleation, the dissolution of metals involves the formation of empty nuclei (atomic vacancies). Screw dislocations have the same significance. Dissolution often leads to the formation of continuous crystal faces with lower Miller indices on the metal. This process, termed facetting, forms the basis of metallographic etching. 

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. 

Since the heat of evaporation of cesium atoms from the second atom layer is 17,500 cal., according to Taylor and Langmuir (54), and since evaporation occurs from the half crystal position c we find... 

Step-Edge Ion-Transfer Mechanism. The step-edge site ion transfer, or direct transfer mechanism, is illustrated in Figure 6.14. It shows that in this mechanism ion transfer from the solution (OHP) takes place on a kink site of a step edge or on any other site on the step edge. In both cases the result of the ion transfer is a M adion in the metal crystal lattice. In the first case, a direct transfer to the kink site, the M adion is in the half-crystal position, where it is bonded to the crystal lattice... 

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)... 

Among the different surface atom positions illustrated on Fig. 2.8, the kink site position, or the half crystal position, as introduced independently by Kossel [2.12] and Stranski [2.13], has a special significance for the definition of the equilibrium conditions (vapor pressure, equilibrium concentration, equilibrium electrode potential, etc.) of the infinitely large (bulk) crystal. 

The first kinetic relationships describing the inhibitory effect of halide ions at low anodic overvoltage followed by the sudden increase of current at the potential of unpolarizability were given by Heusler and Cartledge. The mechanism consists of two charge-transfer reactions occurring in parallel at the half-crystal position " " that is, at the kinks that are not covered by adsorbed anions, the main dissolution reaction occurs ... 

Table 1.2 Number of neighbours of the atom in the half-crystal position...

Therefore, if the crystal is considered infinitely large, - oo and W/rt -> 3 which is the value of the separation work (p a,o from the half-crystal position. Indeed, the atom in this position of the simple cubic lattice possesses three first neighbors, as seen also from Figure 1.19b. The separation work becomes + 6( or q>ui,u = 3 /i +... 

The separation work /2.oOfthe atoms from the half-crystal position is a bulk energy characteristic of the infinitely large crystal and determines its equilibrium with the ambient phase. Under equilibrium conditions, the probabilities of attachment (P+1/2) and detachment P. n) of atoms to and from the half-crystal position are both equal to H. In the same time the inequality P+, < P./ holds good for the probabilities of attachment (P+0 and detachment (P.,) of an atom from the tth site of the crystal surface if that atom is bonded less strongly than the atom in the half-crystal position, i.e. if... 

Concerning the separation work

half-crystal position, it is given by ... 

In the same fashion for the frequencies of attachment, W+ /i, and detachment, W. /2, of single particles to and from the half-crystal position it results ... 

In this ejq)ression the quantities pm and pi stand for the electrochemical potentials of the atoms in the half-crystal position and in the /th site of the crystal surface, respectively. Clearly, the difference pi - pm equals the... 

Equations (1.122) and (1.123) allow us to draw the following important conclusions. Since Ap. > 0 it appears that the inequality W.m V) +1/2(7) is fulfilled for any value of the cathodic overpotential 7 > 0. Therefore the bulk crystal will grow through a cathodic ions discharge on the kink sites. The inequality W. rj) < IT+,(7) is fulfilled for the rth sites of the crystal surface for which (p a and pi< pm- For these sites the attachment probability is higher than the detachment one at any cathodic overpotential 7, too. The situation is different for the sites of the crystal surface where the atoms are less strongly bound than at the half-crystal position, i.e. (pi <

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The meaning of equation (1.139 ) derived by Stranski [1.12, 1.13] in 1936 can be revealed in the following way. IfiVaAc atoms are separated from the half-crystal position (Figure 1.19b) the work done is equal to Ifr... 

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