Volmer-Weber

Figure 10.5. The three modes of growth of films (a) Frank and van der Merwe s monolayer (two-dimensional) mode (b) the Volmer-Weber three-dimensional mode (c) the Stranski-Krastanov mode involving two-dimensional growth followed by three-dimensional growth.

In practice, uniform films are obtained for only a limited number of film-substrate material combinations (17). The more common experience is that the deposited material forms 3D clusters. The clusters may form directly on the bare substrate, in the Volmer-Weber growth mode, or on top of a very thin but uniform film of the deposit, the Stranski-Krastanov growth mode. We now discuss a method for determining the equilibrium configuration of the deposited material. 

Therefore, we predict that for a system with any finite misfit, a uniform film with a thickness greater than several monolayers is not the equilibrium state the system can lower the chemical potential by the formation of clusters. Clusters will form on either the bare substrate (Volmer-Weber mode any finite misfit with WKl and large misfits if W >1) or on a few layers of uniform film (Stranski-Krastanov mode up to moderate misfits with W>1). This will be true for any system without long-range (e.g. electrostatic) forces. 

The nucleation rate constant (Eq. (5.8.5)) k depends on the size of the critical crystallization nucleus according to the Volmer-Weber equation... 

The first in situ STM study of metal deposition was for Ag on HOPG [430], which is representative of the Volmer-Weber growth mode. Since that time several other studies of metal deposition on HOPG have been reported Ag [393,431-433], Pb [129], Pt [434,435], Au [436], and Ni [437]. In these studies examining the small metal particles proved to be... 

On highly ordered pyrolytic graphite, HOPG(OOOl) electrodes, no UPD has been detected owing to weak carbon-lead interactions [311]. Deposition occurs by three-dimensional island growth according to Volmer-Weber mechanism. Initial steps are controlled by progressive nucleation on active sites and hemispherical diffusion. 

Mechanism by three-dimensional nucleation on a host crystal. This is called the Volmer-Weber mechanism. 

Volmer-Weber (weak adsorption) three-dimensional nucleation Aa > 0 or 2a > a A/j,>0... 

Vii ial equation of state in two dimensions, 931 Virial isotherm, 936 Visible radiation, 797 Volcanoes, in electrocatalysis, 1284 Volmcr, Max, 1048,1474 Volmer. Weber, electrodeposition. 1303. 1306 Volta, 1423, 1455 Volta potential difference, 822 Voltammetry. 1432 1434 cyclic, 1422 1423 diffusion control reactions, 1426 electron transfer reaction, 1424... 

Figure 3. Crystal growth modes (a) three-dimensional island (Volmer-Weber) growth, (b) layer-plus-island (Stranski-Kastanov) growth, and (c) layer-by-layer (Franck-van der Merwe) growth.

If the mutual interaction of adsorbed particles is strong enough the surface diffusion can become organized and leads to a formation of islets of adsorbed molecules in the sense of the Volmer-Weber drop mechanism, or to a layer association, parallel to the crystalline surface, according to the Frank-van der Merve s mechanism. Alternatively, it can form a tridimensional organized region (Stranski-Krastanow s mechanism) similar to that of adsorption mixed crystals74). 

Figure 3.7 Three models of film growth (a) Frank-van der Merwe, layer by layer (b) Volmer-Weber, islands (c) Stranski-Krastanov, combination of layer by layer and islands.

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