Crystal kink

The process of growth of crystalline particles involves several steps, such as diffusion of solute molecules from the bulk of the solution to the crystal surface, adsorption on the crystal surface, diffusion over the surface, attachment to a step, diffusion along a step, and integration into a crystal kink site. The rates of these different processes depend on the type of material and on the operating conditions. The final overall molar flux of solute molecules, which has previously been indicated with /(U, , U, ), will of course be... 

The appearance of the molecules of a solid surface and how it differs from the appearance of the bulk molecules in the case of crystals, kinks and dislocations... 

Slip bands and kink bands were first studied in compression of oriented nylon 6,6 and 6,10 by Zaukelies, and subsequently in tensile specimens of oriented high density polyethylene (HOPE) by Kurakawa and Ban and Keller and Rider Zaukelies interpreted the angle between kink bands in oriented nylon and the compression axis in terms of Orowan s theory of crystal kinking, postulating dislocation mechanisms for the process. Keller and Rider ° and Kurakawa and Ban were impressed by the appearance of deformation bands in high density polyethylene in directions close to the IDD. In this polymer system 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.

Fig. 8.5 Types of surface site on a perfect crystal. Kink sites are denoted by (1), edge sites by (2) and adatoms by (3).

The catalysts with the simplest compositions are pure metals, and the metals that have the simplest and most uniform surface stmctures are single crystals. Researchers have done many experiments with metal single crystals in ultrahigh vacuum chambers so that unimpeded beams of particles and radiation can be used to probe them. These surface science experiments have led to fundamental understanding of the stmctures of simple adsorbed species, such as CO, H, and small hydrocarbons, and the mechanisms of their reactions (42) they indicate that catalytic activity is often sensitive to small changes in surface stmcture. For example, paraffin hydrogenolysis reactions take place rapidly on steps and kinks of platinum surfaces but only very slowly on flat planes however, hydrogenation of olefins takes place at approximately the same rate on each kind of surface site. 

This is the Wilson-Frenkel rate. With that rate an individual kink moves along a step by adsorbing more atoms from the vapour phase than desorbing. The growth rate of the step is then simply obtained as a multiple of Zd vF and the kink density. For small A/i the exponential function can be hnearized so that the step on a crystal surface follows a linear growth law... 

Miyashita et al. [102] have proposed a possible model for the hexagonal-orthorhombic phase transition (Fig. 10). They proposed that since the hexagonal crystal contains many defects along the chain axis, such as kinks and jogs, on its phase transition to the orthorhombic phase, these defects are excluded from the crystal... 

By their nature, dislocations cannot end suddenly in the interior of a crystal a dislocation line can only end at a free surface or a grain boundary (or form a closed loop). Where a screw dislocation intersects a free surface there is inevitably a step or ledge in the surface, one atomic layer high, as shown in Fig. 20.30c. Furthermore, the step need not necessarily be straight and will, in fact, almost certainly contain kinks. 

Growth theories of surfaces have received considerable attention over the last sixty years as summarized by Laudise et al. [53] and Jackson [54]. The well-known model of the crystal surface incorporating adatoms, ledges and kinks was first introduced by Kossel [55] and Stranski [56]. Becker and Doring [57] calculated the rates of nucleation of new layers of atoms, and Papapetrou [58] investigated dendritic crystallization. 

The structure of growing crystal faces is inhomogeneous (Fig. 14.11a). In addition to the lattice planes (1), it featnres steps (2) of a growing new two-dimensional metal layer (of atomic thickness), as well as kinks (3) formed by the one-dimensional row of metal atoms growing along the step. Lattice plane holes (4) and edge vacancies (5) can develop when nniform nucleus growth is disrupted. 

As the crystal surface exposed to the atmosphere is usually not ideal, specific sites exist with even much lower co-ordination numbers. This is shown schematically in Fig. 3.5, which gives a model comprising so-called step, kink and terrace sites (Morrison, 1982). This analysis suggests that even pure metal surfaces contain a wide variety of active sites, which indeed has been confirmed by surface science studies. Nevertheless, catalytic surfaces often behave rather homogeneously. Later it will be discussed why this is the case. In short, the most active sites deactivate easiest and the poorest active sites do not contribute much to the catalytic activity, leaving the average activity sites to play the major role. 

It has been often stressed that low eoordinated atoms (defeets, steps, and kink sites) play an important role in surfaee ehemistry. The existenee of dangling bonds makes steps and kinks espeeially reaetive, favoring the adsorption of intermediate species on these sites. Moreover, smdies of single-crystal surfaces with a eomplex geometry have been demonstrated very valuable to link the gap between fundamental studies of the basal planes [Pt( 111), Pt( 100), and Pt(l 10)] and applied studies of nanoparticle eatalysts and polycrystalline materials. In this context, it is relevant to mention results obtained with adatom-modified Pt stepped surfaces, prior to discussing the effect of adatom modification on electrocatalysis. 

Last, but not least, one must not forget that steps and kinks appear as structural defects on atomically flat surfaces of single crystals, while edges and vertices are inherent structural elements of metal nanoparticles. 

Solid metal electrodes with a crystalline structure are different. The crystal faces forming the surface of these electrodes are not ideal planes but always contain steps (Fig. 5.24). Although equilibrium thermal roughening corresponds to temperatures relatively close to the melting point, steps are a common phenomenon, even at room temperature. A kink half-crystal position—Fig. 5.24c) is formed at the point where one step ends and the... 

Fig. 5.24 Crystalline metal face (a) ad-atom, (b) ad-atom cluster, (c) a kink (half-crystal position), (d) atom at the step, (e) atom in the kink, (f) vacancy, (g) vacancy cluster. (According to E. Budevski)... 

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 important feature is the formation of a coordinatively unsaturated site (cus), permitting the reaction to occur in the coordinative sphere of the metal cation. The cus is a metal cationic site that is able to present at least three vacancies permitting, in the DeNOx process, to insert ligands such as NO, CO, H20, and any olefin or CxHyOz species that is able to behave like ligands in its coordinative environment. A cus can be located on kinks, ledges or corners of crystals [16] in such a location, they are unsaturated. This situation is quite comparable to an exchanged cation in a zeolite, as studied by Iizuka and Lundsford [17] or to a transition metal complex in solution, as studied by Hendriksen et al. [18] for NO reduction in the presence of CO. 

Such a possibility has been recognized by early workers,9 but in spite of this intriguing possibility, only recently has such a metal surface been created. Chiral kink sites were created on Ag single crystal surfaces to produce the enantiomeric surfaces Ag(643)s and Ag(643)R however, no differences between (R)- and (S)-2-butanol were observed for either the temperature-programmed desorption from the clean surfaces or the dehydrogenation (to 2-butanone) from preoxidized surfaces.10 Unfortunately, Ag exhibits few catalytic properties, so only a limited array of test reactions is available to probe enantioselectivity over this metal. It would be good if this technique were applied to a more catalytically active metal such as Pt. 

PM. The intense three peaks indicated by the grey in the top trace are ascribed to three Ala residues in the a-helix (helix G in this figure) protruding from the cytoplasmic membrane surface and four Ala residue in the C-terminal. (C) Schematic representation of the dynamic structure of bR in 2D crystal. The interfacial and kinked portions are illustrated by the shade and belts, respectively. From Refs. 22 and 179 with permission. 

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