Nucleation nonclassical

The classical nucleation theory itself is inadequate. Hence, effort has been made to develop nonclassical theories of nucleation, often by... 

Jones et al. (1999) made a classification of the broad range of nucleation likely to be encoimtered in liquids supersaturated with dissolved gas molecules (Jones et al., 1999). Bubble formation from preexisting gas cavities larger than the critical size is referred to as nonclassical heterogeneous bubble nucleation (type TV bubble nucleation, following their... 

An extensive formulation of classical and nonclassical models for homogeneous nucleation, as well as experimental tests of their validity, have been carried out for the Co-Cu precipitation system in which coherent Co-rich nuclei form [15]. 

One of the motivations for undertaking this calculation was the fact that the interfacial widths calculated for the planar interface in Section III D were broad enough that the classical nucleation theory predicted a critical droplet that was almost all interface, calling into question the assumption that it could be treated as a bulk crystal with a sharp surface layer. In this nonclassical theory, the properties of the nucleus at the center are not imposed as in the classical theory the system variationally selects the optimal form. It is... 

Recently Klein and Leyvraz considered nonclassical nucleation near a spinodal using a model with weak long-range repulsive potentials, and showed that it differed substantially from the classical picture, as expected from the considerations of Harrowell and Oxtoby. However, it is unclear whether real systems behave in such a way as to show the influence of a metastability limit for the undercooled liquid. 

Classical nucleation theory may be not well suited to describe the nucleation kinetics of diamond in CVD, since the critical nucleus size under the typical CVD conditions may be on the order of a few atoms. The surface energy contribution may cause a reverse effect on the phase stability and the GFobs free-energy of the formation of a critical nucleus may be negative, a case referred to as nonclassical nucleation. In such a case, atomistic theory should be employed as the starting point of theoretical analyses. 

Oxtoby, D.W., and Evans, R. (1988) Nonclassical nucleation theory for the gas-liquid transition, J. Chem. Phys. 99,151. ... 

Figure 7 Schematic representation of classical and nonclassical crystallization. Pathway (a) the classical crystallization pathway where nucleation clusters grow to a primary nanoparticle, which is amplified to a single crystal. Pathway (b) the primary nanoparticles form an iso-oriented crystal, which can fuse to form a single crystal. Pathway (c) the primary nanoparticles can be stabilized by an additive and can form a mesocrystal. Pathway (d) amorphous particles or liquid droplets are formed, which can transform to complicated morphologies. (Reproduced from Ref. 7. John Wiley Sons, Ltd, 2008.)...

To these could be added the absorption of an additive to a crystal face of a single crystal resulting in a change of growth rate, and incorporation of an additive molecule into the bulk crystal structure. It has been proposed that a single additive can be involved in a number of these modes of action simultaneously. Clearly, additives and impurities can have a complex interplay with crystal nucleation and growth, and there remains much to be understood in this area, particularly with respect to nonclassical crystal growth. 

In addition to the classical theory of the equilibrium for the glass-crystal transition, nonclassical theories were developed by including irreversible thermodynamics (Cahn 1969 and Charles 1973). These theories take into account nonspherical nuclei, high degrees of supercooling, and small interfacial energies. An attempt has been made here to consider a theory of three-dimensional nucleation. 

Fig. 2 a Classical and b, c nonclassical crystallization mechanisms via self-assembly. Crystallization starts from nucleation clusters upper left), d The primary nanoparticles can also grow by ion attachment, but they then aggregate uncontrollably at a certain stage, forming undefined polycrystalline aggregates. (Reproduced from [35], 2005, MRS)... 

These observations form the basis of a new approach to nucleation theory built on density flmctional methods of statistical mechanics. The predictions and results of this nonclassical theory are described in greater detail in Ref 1. The starting point is the observation that the average density of a crystal can be written as a sum over Fourier components ... 

This is a much more flexible theory than classical nucleation theory (which allows the free energy to depend only on a single quantity, the crystallite radius). Here, the interface can be diffuse instead of sharp, the crystallite can be strongly curved, and the order parameters can attain values different from the bulk at the center. At the same time, the nonclassical density functional approach goes over smoothly to the classical theory for large enough crystallites. Comparisons of the predictions of the classical... 

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