Volmer—Weber model

Gonzalez et al. first reported CoSn2 on metal foam obtained by electrodeposition of amorphous Co-Sn alloy and subsequent annealing [77]. It was observed that low current densities and short electrodeposition times favor the formation of discrete submicrometric particles (Volmer-Weber model] and the electrochemical behavior in lithium cell was very good, while the capacity in sodium cell was lower. 

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.

From an experimental point of view, however, it seems that little progress has been made since the evaluation of the Volmer-Weber [4.11] equation in 1926. The experimentalist is bound to use eqs. (4.32) and (4.33), disregarding the small uninformative dependence of A on 77 derived from the Zeldovich factor F or the attachment probability Watt.yVcnt More significant progress seems to have been made with the development of the small cluster model based on the atomistic approach of Becker and Doering. 

The pre-exponential factor A 1p is independent of potential as long as Ncrjt is potential independent, and the factor 3 depends on the mechanism of attachment. Equation [7] reduces to a classical Volmer-Weber type model for nucleation if Ncrjt 3- The total potential dependence of the nucleation rate in an overpotential range where Ncrit is constant according to the atomistic model is thus given by ... 

Figure 2.4 Models of deposition showing layer-by-layer deposition (Frank—van der Merwe), island growth (Volmer—Weber) and mixed (Stranski-Krastanov).

Stranski-Krastanov (SK) model (film growth) Nucleation on a surface that changes structure during deposition (layer-plus-island growth). See Volmer-Weber growth Frank van der Merwe growth. 

Theoretical approaches to nucleation go back almost 80 years to the development of Classical Nucleation Theory (CNT) by Volmer and Weber, Becker and Doring and Zeldovich [9,10,17-20]. CNT is an approximate nucleation model based on continuum thermodynamics, which views nucleation embryos as tiny liquid drops of molecular dimension. In CNT, the steady-state nucleation rate /, can be written in the form / a where jS, is the monomer condensation... 

Careful examination reveals that the modified Stem-Volmer equation is mathematically identical to the original nonlinear model developed by Ryan and Weber (22). Fluorescence quenching curves for Cu -FA and application of the modified Stem-Volmer data treatment to the experimental information are shown in figure 2. Since the nonlinear data treatment and the modified Stem-Volmer equations are algebraically identical, their ability to fit experimental data and provide meaningful parameters is the same. 

The experimentally accessible quantity in crystallization processes is the nucleation rate. The first proposed kinetic model of nucleation by Volmer and Weber [2] estimated it to be the product of the equilibrium cluster size distribution, (N), and... 

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