Crystal kink, density

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... 

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. 

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. 

Primary structure sensitivity resulting from the effect of changing particle size on step and kink density appears therefore to be present here at short reaction times. Secondary structure sensitivity (including the effect of carbonaceous poisoning on the reaction rate) appears not to be present here. Thus Somorjai has reported that the dehydrogenation reaction of cyclohexane to cyclohexane is insensitive to both structural featureSt whereas the dehydrogenation of cyclohexene to benzene la very sensitive to the densities of atomic steps and kinks and the order of the carbonaceous overlayer on the platinum crystal surface. 

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... 

In the perfectly ordered crystalline ground state, all polymer bonds are parallel and no solvent-polymer contacts are present. If we ignore disorder (vacancies, kinks) in the polymer crystal at finite temperatures, the free-energy density of the crystalline state is zero. 

We can create surfaces from the fee, hep and bcc crystals by cutting them along a plane. There are many ways to do this Fig. A. 1 shows how one obtains the low-index surfaces. Depending on the orientation of the cutting plane we obtain atomically flat surfaces with a high density of atoms per unit area or more open surfaces with steps, terraces and kinks (often referred to as corrugated or vicinal surfaces). Thus, the surface of a metal does not exist one must specify its coordinates. 

From the results of Pt(lll). water can be used as an oxs gen source for COad oxidation even on a smooth single crystal surface. This path is available in a dilute add as infrared measurements show that CO2 buildup starts at very low potential like 300 mV. Probably because the niunber of the sites for this reaction is limited, so is the reaction. When the add is concentrated, this path seems only available when CO is adsorbed on spedal sites (probably defects, kinks or edges) at a low potential such as 50 mV. On high area platinum, this path is more likely to occur because the density of those sites is higher. 

We have been able to identify two types of structural features of platinum surfaces that influence the catalytic surface reactions (a) atomic steps and kinks, i.e., sites of low metal coordination number, and (b) carbonaceous overlayers, ordered or disordered. The surface reaction may be sensitive to both or just one of these structural features or it may be totally insensitive to the surface structure, The dehydrogenation of cyclohexane to cyclohexene appears to be a structure-insensitive reaction. It takes place even on the Pt(l 11) crystal face, which has a very low density of steps, and proceeds even in the presence of a disordered overlayer. The dehydrogenation of cyclohexene to benzene is very structure sensitive. It requires the presence of atomic steps [i.e., does not occur on the Pt(l 11) crystal face] and an ordered overlayer (it is poisoned by disorder). Others have found the dehydrogenation of cyclohexane to benzene to be structure insensitive (42, 43) on dispersed-metal catalysts. On our catalyst, surfaces that contain steps, this is also true, but on the Pt(lll) catalyst surface, benzene formation is much slower. Dispersed particles of any size will always contain many steplike atoms of low coordination, and therefore the reaction will display structure insensitivity. Based on our findings, we may write a mechanism for these reactions by identifying the sequence of reaction steps ... 

For a crystal in contact with a supersaturated solution, the kink site density is expected to be larger than at equilibrium. Since the movement of kinks along a step is energetically neutral, the kinks may be regarded as analogous to a one-dimensional gas. Hence, the density of kinks along a step is... 

From viewpoint of the process of deposition or growth, it would be of interest to make an assessment of the step roughness as defined by the density of kink atoms per unit step length, because it would give an important kinetic parameter of growth. The step roughness can be given as the reciprocal of a normalized mean distance parameter Aink /do,Me, where ink is the mean distance between kink atoms and do,Me is the atomic diameter. For the most dense step [110] on a cubic (100) face of a fee crystal, the mean distance parameter is [2.1, 2.15]... 

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