Critical island size

Recall that, in nucleation theory [125-134], the size at which for the first time an island becomes more stable with the addition of just one more atom is defined as the critical island size i. In describing the statistical consequences of continuing this process of sequential trapping, in effect i = 1 in this calculation. 

This makes it possible for clusters below some critical size to be energetically unfavorable and hence unstable with respect to disassociation. Depending on the shape of the crystal, the surface energy terms, and the supersaturation, there exists a value of j for which the free energy is at maximum and therefore the attachment of one more molecule will make the crystal stable. The size of the island corresponding to this maximum is known as the critical island size, denoted by i. The value of is determined by the relevant interaction potentials between the molecules and the substrate. The details ai e worked out explicitly in Markov [3] and Taylor et al. [16]. 

The temperature dependence of the critical island size for pentacene on Si02 was explored by Tejima et al. [44] and the results are displayed in Figure 5.1.11. The same scaled island size distributions are shown in Figure 5.1.11a for four different substrate temperatures at a constant thickness of -0.2 ML. The curves corresponding to critical island sizes of one, two, and three are shown and it is clear that the different substrate temperatures used result in different critical island sizes. The scaled island densities for thick pentacene layers are plotted as a function of... 

FIGURE 5.1.10 (a) Island size distribution at different submonolayer coverages (b) the scaled island-size distributions implying a critical island size of three molecules. (Ruiz, R. et al., Phys. Rev. Lett., 91, 136102, 2003.)... 

FIGURE 5.1.11 Effects of temperature on the scaling and the critical island size for pentacene films (a) suhmonolayer (h) multilayer. (Tejima, M. et al., Appl. Phys. Lett., 85, 3746, 2004.)... 

Tersoff J, Denier van der Gon A, Tromp R. (1994) Critical island size for layer-by-layer growth. Phys Rev Lett 72 266-269. 

In InAs/GaAs multilayers, Nakata et al. [7] have shown, from RHEED, that the InAs critical thickness in upper layers was smaller than that of the first layer. However, these authors have not clearly established whether such a decrease of the InAs critical thickness was due to the strain induced by underlying layers or surface migration of In atoms. Similar results have been observed in the Ge/Si system by Schmidt et al. [9, 10]. However, as such measurements were done by means of TEM microanalysis in postgrown samples, no proposal to improve the island size homogeneity has been submitted. 

We now turn our attention to steady states of reaction-transport systems. We focus first on steady states that arise in RD models on finite domains. Such models are important from an ecological point of view, since they describe population dynamics in island habitats. The main problem consists in determining the critical patch size, i.e., the smallest patch that can minimally sustain a population. As expected intuitively, the critical patch size depends on a number of factors, such as the population dynamics in the patch, on the nature of the boundaries, the patch geometry, and the reproduction kinetics of the population. The first critical patch model was studied by Kierstead and Slobodkin [228] and Skellam [414] and is now called the KISS problem. A significant amount of work has focused on systems with partially hostile boundaries, where individuals can cross the boundary at some times but not at others, or systems where individuals readily cross the boundary but the region outside the patch is partially hostile, or a combination of the above. In this chapter we deal with completely hostile boundaries and calculate the critical patch size for different geometries, reproduction processes, and dynamics. 

Growth of polycrystalline films generally begins with the thermally activated nucleation of islands or clusters of film material on the growth surface this was described in atomistic terms in Section 1.3.2 and in terms of more macroscopic quantities in Section 1.3.5. The activation energy JG and critical cluster size, represented in terms of number n of film atoms... 

A different view of CO oxidation comes from computational studies of extended Au(l 11). Steps and kinks play a critical role in reducing the activation energy for O2 dissociation. The enhanced activity of thin islands may be related to step density (geometric effects) rather than to quantum size effects. The literature suggests a key role for such defects. Gold is an effective catalyst because it can bind CO and O2 but weakly enough so that subsequent processes have achievable activation barriers. 

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