Nucleation scaling theory

The comparison of curves in Figures 21.8 and 21.9 shows that the kinetically consistent classical nucleation theory corrected using quantum data successfully predicts nucleation rates in nearly all the cases studied here. The accuracy of its model predictions is higher than that of the (self-consistency corrected) SCC CNT and the best molecular-based nucleation studies, and stays in line with the best up-to-date empirical scaling theories. As seen from the comparison of curves rep-... 

Fig. 58. Confinement nucleation of adatom islands on a dislocation network, (a) Ordered (25 X 25) dislocation network formed by the second Ag monolayer on Pt( 111) on deposition at 400 K and subsequent annealing to 800 K. The inset shows a model of this trigonal strain relief pattern, (b) A superlattice of islands is formed on Ag deposition onto this network at 110 K (coverage = 0.10 monolayers). The inset shows the Fourier transform of the STM image, (c) Island size distributions for random and ordered nucleation. The curve for ordered nucleation is a binominal fit. The curve labeled i = 1 shows the size distribution from scaling theory for random nucleation on an isotropic substrate. Size distributions were normalized according to scaling theory (5 is the island size in atoms, (S) its mean value, and Ns the density of islands with size s per substrate atom), (d) Zoom into image (b) [198]. Reprinted with permission from H. Brune et al.. Nature 344, 451 (1998), 1998, Macmillan Magazines Ltd.

It is possible that this theory can be adapted to explain molten metal-water thermal explosions although many needed data are still unavailable. One might presume that, at the molten metal-wet surface interface, there is some chemical reaction. Possibly that of the metal plus water or metal plus surface to lead to localized formation of salt solutions. These may then superheat until homogeneous nucleation occurs. The local temperature and pressure would then be predicted to be far in excess of the critical point of pure water (220 bar, 647 K) and a sharp, local explosion could then result. Fragmentation or subsequent other superheat explosions would then lead to the full-scale event. 

As will be described later in this section, for several types of small-scale tests where RFTs would be expected, an increase in the absolute system pressure had a profound effect in suppressing such incidents. As often noted in previous sections, one current theory to explain RPTs invokes the concept of the colder liquid attaining its superheat-limit temperature and nucleating spontaneously. In an attempt to explain the pressure effect on the superheating model, a brief analysis is presented on the dynamics of bubble growth and how this process is affected by pressure. The analysis is due largely to the work of Henry and Fauske, as attested to by the literature citations. 

Solids undergoing martensitic phase transformations are currently a subject of intense interest in mechanics. In spite of recent progress in understanding the absolute stability of elastic phases under applied loads, the presence of metastable configurations remains a major puzzle. In this overview we presented the simplest possible discussion of nucleation and growth phenomena in the framework of the dynamical theory of elastic rods. We argue that the resolution of an apparent nonuniqueness at the continuum level requires "dehomogenization" of the main system of equations and the detailed description of the processes at micro scale. 

In order to start the multiscale modeling, internal state variables were adopted to reflect void/crack nucleation, void growth, and void coalescence from the casting microstructural features (porosity and particles) under different temperatures, strain rates, and deformation paths [115, 116, 221, 283]. Furthermore, internal state variables were used to reflect the dislocation density evolution that affects the work hardening rate and, thus, stress state under different temperatures and strain rates [25, 283-285]. In order to determine the pertinent effects of the microstructural features to be admitted into the internal state variable theory, several different length scale analyses were performed. Once the pertinent microstructural features were determined and included in the macroscale internal state variable model, notch tests [216, 286] and control arm tests were performed to validate the model s precision. After the validation process, optimization studies were performed to reduce the weight of the control arm [287-289]. 

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