Kinks in steps

An important modification of this model was performed by Wakai.33 The main assumptions are that the solution and precipitation reactions take place at line defects as kinks in steps formed at the grain boundaries (Fig. 16.4), and the spacing between kinks is small enough for the step to be considered as an ideal source or sink of solute particles. Thus, the solution and precipitation of crystalline materials at these steps produces their movement, and consequently strain and strain rate will have an expression analogous to Orowan s equation for dislocation movement ... 

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 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... 

The surface processes may comprise adsorption, surface migration (across terraces or along steps), dehydration of ions, and integration in the growth sites which are assumed to be kinks in surface steps. Any of these processes may be rate controlling, either alone or several together (10-11). 

Assume that the two sites are separated by N steps in the x-direction. (The formula can be straightforwardly generalized to arbitrary locations of the two trap sites.) The number of extra kinks in the path of length N > N is K, which is the number of pairs of non-essential steps. The formula given then follows from the combinatorials of N total steps which may be taken in any order, and which consist of six classes of objects, N + k, forward steps (in the -I- x direction), k, backward steps ( — x), ky sideways steps ( 4- y), ky sideways steps back ( — y), and k ( + z), and kj ( — z), where we must also have that k, H- ky 4- k = K. Asymptotically for large N > N the number of paths grows as 6 /N ... 

Figure 3.16. Some simple defects found on a low-index crystal face 1, the perfect flat face, a terrace 2, an emerging screw dislocation 3, the intersection of an edge dislocation with the terrace 4, an impurity adsorbed atom 5, a monatomic step in the surface, a ledge 6, a vacancy in the ledge 7, a kink, a step in the ledge 8 an adatom of the same type as the bulk atoms 9, a vacancy in the terrace 10, an adatom on the terrace. (From Ref. 12, with permission from Oxford University Press.)...

Figure 7 Application of the dimer method to a two-dimensional test problem. Three different starting points are generated in the reactant region by taking extrema along a high temperature dynamical trajectory. From each one of these, the dimer isjirst translated only in the direction of the lowest mode, but once the dimer is out of the convex region a full optimization of the effective force is carried oat at each step (thus the kink in two of the paths). Each one of the three starting p>oints leads to a different saddle point in this case.

Crystallizing particles arriving at the surface will diffuse onto the surface (surface diffusion). As this occurs, some may return to the ambient phase, while some will be caught at kinks or steps (see Section 3.6) on the surface and will be incorporated into the crystal. When these particles are incorporated into the crystal, the solvent component will be dissociated. This process is called desolvation. In solution growth, this process will determine the growth rate. At certain points in these processes, it is necessary to overcome the energy barriers required to climb the respective steps (Fig. 3.5). 

The slice through a bulk crystal can differ from both the 111 plane and the 100 plane by small angles. This produces a kink in the face of the step. By an extension of the analysis that leads to step characterization, these kinks can also be characterized. For example, a plane with Miller indices 10,8,7 has 111 terraces seven atoms wide, 110 steps one atom high, and kinks of 100 orientation every two atoms. Because of the greater thermodynamic stability of the planes of low Miller index, these surfaces of ordered roughness are stable and can be prepared and studied. Since it is sensitive to periodicity over a domain about 20 nm in diameter, LEED sees the pattern associated with terraces of various widths and may be used to characterize these surfaces. Satisfactory LEED patterns do not require absolute uniformity of terrace width but may be obtained with experimental surfaces that display a distribution of widths. 

ACTIVE CENTER. Atoms which, by their position on a surface, such as at the apex of a peak, at a step on the surface or a kink in a step, or on the edge or corner of a crystal, share with neighboring atoms an abnormally small portion of their electrostatic field, and therefore have a large residual field available for catalytic activity or for adsorption. 

On cutting a crystal surface in the middle of the stereographic triangle, a surface structure that exhibits a large density of kinks in the steps will be produced. One of these high-kink-density surfaces is shown schematically in Fig. 3c. 

The chemisorption of over 25 hydrocarbons has been studied by LEED on four different stepped-crystal faces of platinum (5), the Pt(S)-[9(l 11) x (100)], Pt(S)-[6(l 11) x (100)], Pt(S)-[7(lll) x (310)], and Pt(S)-[4(l 11 x (100)] structures. These surface structures are shown in Fig. 7. The chemisorption of hydrocarbons produces carbonaceous deposits with characteristics that depend on the substrate structure, the type of hydrocarbon chemisorbed, the rate of adsorption, and the surface temperature. Thus, in contrast with the chemisorption behavior on low Miller index surfaces, breaking of C-H and C-C bonds can readily take place at stepped surfaces of platinum even at 300 K and at low adsorbate pressures (10 9-10-6 Torr). Hydrocarbons on the [9(100) x (100)] and [6(111) x (100)] crystal faces form mostly ordered, partially dehydrogenated carbonaceous deposits, while disordered carbonaceous layers are formed on the [7(111) x (310)] surface, which has a high concentration of kinks in the steps. The distinctly different chemisorption characteristics of these stepped-platinum surfaces can be explained by... 

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