Cluster growth, mechanism

FIGURE 3.10 Hydrate labile cluster growth mechanism imposed on a pressure-temperature trace. (Reproduced from Christiansen, R.L., Sloan, E.D., in Proc. First International Conference on Natural Gas Hydrates (1994) New York Academy of Sciences. With permission.)... 

But also the other coinage elements have been studied intensively, although here the results depend much less sensitively on the approximate or exact description that is used for the interatomic interactions. Among those is Ag. Clusters of Ag were studied by Baletto et alP who used a molecular-dynamics method to determine the stable structures for selected cluster sizes with up to almost 600 atoms. In order to identify the crystal-growth modes, they used the common-neighbour analysis (Section 3.5) in distinguishing between icosahe-dral, decahedral, and fcc-like motifs. From their analysis they were also able to propose a cluster-growth mechanism. 

Rotational convection and angular Brownian motion of clusters, as well as ather-mal nucleation resulting from transient free energy of the system are considered. One concludes that the cluster growth mechanism dominates the other mechanisms of oriented nucleation in the systems with transient chain deformation and orientation. Example computations illustrating transient effects in oriented nucleation are presented for the case of uniaxial elongational flow. 

II. The change of the sign between these two models may be also important for clustering and the surface growth mechanism. In the selfconsistent theory, the silver atoms tend to establish bonds with palladium atoms, while in the non-selfconsistent theory, the Ag-Ag bonds are favored. This explains the differences between the concentration profiles calculated within the models I and II and the fact that they do not simply follow the variations of the on-site terms. 

Fig. 3.15 Representation of the structure of the CdS fihn. It is suggested that the compact inner layer is deposited by an ion-by-ion mechanism whUe the porous outer layer is due to a cluster growth. (Reproduced with permission from [245], Copyright 2009, The Electrochemical Society)...

Figure 2. Evidence for an atom addition mechanism of cluster growth is provided by analysis of the Ni Cry cluster distribution produced by vaporization of a nichrome surface. The simulated distribution below assumes that the probability of Ni or Cr occurring in a cluster is related only to its composition in the source material. Reproduced from Ref. 8, Copyright 1985, American Chemical Society.

The two current transients are shown in Fig. 10.6. The curve for progressive nucleation rises faster at the beginning because not only the perimeter of the clusters increases but also their number it drops off faster after the maximum. Such dimensionless plots are particularly useful as a diagnostic criterion to determine the growth mechanism. Real current transients may fit neither of these curves for a number of reasons, for example, if the growth starts from steps rather than from circular clusters. 

Despite the vast quantity of data on electropolymerization, relatively little is known about the processes involved in the deposition of oligomers (polymers) on the electrode, that is, the heterogeneous phase transition. Research - voltammetric, potential, and current step experiments - has concentrated largely on the induction stage of film formation of PPy [6, 51], PTh [21, 52], and PANI [53]. In all these studies, it has been overlooked that electropolymerization is not comparable with the electrocrystallization of inorganic metallic phases and oxide films [54]. Thus, two-or three-dimensional growth mechanisms have been postulated on the basis that the initial deposition steps involve one- or two-electron transfers of a soluted species and the subsequent formation of ad-molecules at the electrode surface, which may form clusters and nuclei through surface diffusion. These phenomena are still unresolved. 

The mechanisms of the crystal-building process of Cu on Fe and A1 substrates were studied employing transmission and scanning electron microscopy (1). These studies showed that a nucleation-coalescence growth mechanism (Section 7.10) holds for the Cu/Fe system and that a displacement deposition of Cu on Fe results in a continuous deposit. A different nucleation-growth model was observed for the Cu/Al system. Displacement deposition of Cu on A1 substrate starts with formation of isolated nuclei and clusters of Cu. This mechanism results in the development of dendritic structures. 

Apart from the development in photography, most of nucleation and growth mechanisms based on a chemical reduction (Section 20.4.4) behave as development processes, and are likewise controlled by the nuclearity dependence of the cluster redox potential and by the potential of the electron donor. 

Si(lll) plane [300]. Because the redox potential of the Cd +/Cd couple is much lower than the flat band potential of Si substrate, the surface electron concentration is sufficiently high. Thus the process occurs similarly as on a metal surface at relatively low cathodic overpotentials. The initial stages of Cd deposition were explained by progressive nucleation and cluster growth controlled by hemispherical diffusion. CdTe deposition on Si was also studied due to interest in application in IR radiation detectors. Mechanisms of this process on different planes of n-Si(lOO) was also discussed ([203, 301, 302] and references given therein). 

Absorption Growth Mechanism. Here we assume that a nucleus collides with a single atom at each time. This is equivalent to assuming that there are many free atoms in the gas phase and less opportunity for clusters to meet each other. This is a step-by-step reaction. The rate equation for y th step is then expressed as... 

Nucleation of two-dimensional clusters mechanism. In cases where the crystal face is smooth, growth can occur by either a two-dimensional nucleation mechanism or by a spiral-growth mechanism. For two-dimensional nucleation, growth occurs by attachment of molecules to the edge of a nucleus on the surface. Under ideal conditions, the growing step on a crystal surface will advance across the crystal face until that particular layer is complete. Before another layer starts, a center of crystallization has to form via surface nucleation. The growth rate forthis mechanism is exponentially dependent on the driving force ... 

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