Interfaces substrate/nucleus

When the nucleus is formed on a solid substrate by heterogeneous nucleation the above equations must be modified because of the nucleus-substrate interactions. These are reflected in the balance of the interfacial energies between the substrate and the environment, usually a vacuum, and the nucleus-vacuum and the nucleus-substrate interface energies. The effect of these terms is usually to reduce the critical size of the nucleus, to an extent dependent on... 

The carbon atoms arriving at the substrate surface must exceed a certain concentration at the solid-gas interface to reach and exceed the critical nucleus size. Therefore the diamond nucleation density as well as the growth rate are dependent on the relative rates of bulk and surface diffusion of carbon atoms. ° These are different for different substrates. Thus, the nucleation process needs a temperature dependent incubation time which is related to the time required to form critical size diamond clusters on the substrate surface. The nucleation rate, which is initially negligible, reaches a maximum after a certain time period and tends to zero for longer deposition times. ... 

When nucleation occurs on a foreign surface a modification of the surface energy term takes place in equation (4). The surface tension at the interface between the substrate and the nucleus has to be considered. Assuming for example a flat rectangular nucleus as shown in figure 2, equation (4) is replaced by ... 

An epitaxial effect based on similar lattice parameters (McMillan 1979) presented a theoretical explanation for the favorable nucleating action of metals. Furthermore, mechanical strain was present at the substrate-glass interface, producing a high interfacial energy, as the coefficients of thermal expansion of the metal and the new nucleus were substantially different. As a result, catalyzation of nucleation could also be expected. 

Aoki also considers the stochastic aspects of phase propagation mechanism and relates his analysis to the theory of percolation and the fractal dimension of the system. In this approach the Nemst equation for charge transfer at the substrate/film interface is used to compute the probability of the presence of a conductive seed or nucleus. When the potential is incremented, this seed can then grow in a one-dimensional manner governed by the propagation rate constant kp or the kinetic parameter to form a conductive pillar of a definite length. New nuclei can also form at the support electrode/film interface during the potential... 

When a nucleus of a crystalline film F is formed from atoms leaving a nutrient phase N and depositing onto a substrate S, volume of F and two new interfaces, those between the film and the nutrient and the film and the substrate, are formed, while the area of another one, that between the substrate and the nutrient, diminishes. Consequently, the associated total change in free energy is given by... 

With an increase in temperature, these complexes will be dehydrated. The ZnO crystal forms a heterogeneous nucleus at the interface between substrate and solution. After that, the crystals begin to grow into the nanorods. 

It is 0 (n) that accounts for the energy contribution of the nucleus-substrate and the nucleus-solution interface boundaries and has the physical meaning ofthe concept surface free energy defined in this general form by Stranski in 1936 [1.12, 1.13]. 

The situation is more complex if crystalline nuclei are formed not on structureless but on foreign crystalline substrates. In that case it is necessary to take into consideration both the orientation effect of the substrate and the crystallographic lattice mismatch at the nucleus-substrate interface boundary. Such phenomena are known as epitaxial crystal growth and for more information on this important subject the readers are referred to [1.72, 1.82-1.86]. Here we shall present oidy the widely used classification of the different modes of epitaxial crystal growth proposed by Bauer [1.77] in 1958 (Figure 1.18). 

Studying the spontaneous appearance of two-dimensional clusters on the electrode surface one obtains direct information on the average time f] needed to form a 2D nucleus at a given overpotential 7. As we have seen in Chapter 3 (equations (3.8) and (3.10)), in the case of negligible non-stationary effects the time /, equals the reciprocal stationary nucleation rate. This has been used by Budevski et al. [4.16, 4.17] to examine the overpotential dependence of the stationary rate of two-dimensional nucleation. The obtained results confirm the validity of the classical theory of nucleation on a like substrate and provide the possibility to determine the nucleation work, the size of the two-dimensional critical nucleus and the specific free edge energy at the nucleus-solution interface boundary. 

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