Barrier nucleation

From Equation 11.9, for an embryonic nucleus of radius r to coexist with its melt, the melt must be undercooled by an amount equal to ATm- Or the critical size for a viable nucleus for a given imdercooling is given by 

The total Gibbs energy difference between the solid with radius r and its melt is 

Barrier to nudeation. Embryonic nuclei with r r iticai decrease their free energy by melting hence are not viable. Nudei with r rcriscai decrease their free energy by growing hence become stable. 

The peak AG at critical is the barrier to nucleation. An embryonic nucleus with r r mcai can reduce its free energy by dissolving, hence it is not viable. On the other hand, if r r nticau the embryonic nucleus can reduce its free energy by growing and becomes a stable nucleus. Differentiating Equation 11.11 with respect to r to find yields 

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Here the nucleation barrier AO is the excess thermodynamic potential needed to form the critical embryo within the uniform metastable state, while the prefactor Jq is determined by the kinetic characteristics for the embryo diffusion in the space of its size a. Expressions for both AO and Jo given by Zeldovich include a number of phenomenological parameters. 

In contrast, there is no nucleation barrier for rough surface growth at any supercooling. The growth rate is then simply proportional to v as given by Eq. (3.4), and hence is expected to be linear in AT for small undercoolings. 

A drastic departure from nucleation theory was made by Sadler [44] who proposed that the crystal surface was thermodynamically rough and a barrier term arises from the possible paths a polymer may take before crystallizing in a favourable configuration. His simulation and models have shown that this would give results consistent with experiments. The two-dimensional row model is not far removed from Point s initial nucleation barrier, and is practically identical to a model investigated by Dupire [35]. Further comparison between the two theories would be beneficial. 

From comparison with Eqn (3.44) we can see immediately that there is no nucleation barrier in place of a. Alternatively, we can calculate the free energy difference made by the deposition of v stems (cf. Eqn (3.60)) ... 

Figure 4.11 Variation of nucleation barrier, AG, with the radius, r, of the nucleus at various temperatures.

Spinodal decompositions, often observed in binary solid solutions of metals and in glasses, on the other hand, arise from thermodynamic instabilities caused by composition (Cahn, 1968). A special feature of this type of solid state transformation is the absence of any nucleation barrier. There is a class of transformation called eutectoid decomposition in which a single phase decomposes into two coupled phases of different compositions, the morphology generally consisting of parallel lamellae or of rods of one phase in the matrix of the other. 

If the anodic potential of the polarized electrode is now increased until a (h -Ag ) junction zone is formed in the interior of the electrolyte, AgBr will decompose internally provided the nucleation barrier can be overcome. This is shown... 

NiO is a cation deficient semiconductor. The fraction of its cation vacancies and compensating electron holes depends on the oxygen potential as discussed in Section 2.3. The isovalent Ca2+ ions can replace Ni2+ ions in the cationic sublattice of the fee matrix by chemical interdiffusion. TiOz and NiO form NiTi03 which dissolves to some extent in the fee matrix of NiO as Ti and Vmc. The counterdiffusion of Ti02 and CaO in the NiO solvent leads to the encounter of the different solute cations (Fig. 9-12a). With increasing overlap of their concentration profiles, the concentration of the product will eventually surpass the solubility limit (and the nucleation barrier). Precipitation of the rather stable CaTi03 compound as an internal reaction product in the NiO matrix is the result. 

The nucleation barrier for the lenticular particle shown in Fig. 19.12 can be derived using the geometric relations for its volume V and interfacial area A ... 

Both of these polymers do not have any reported mesophase. Since the glass transition is a freezing process on a 3 to 10 mobile unit (bead) scale, there are neither phase boundaries nor nucleation barriers for the process. 

Surface defects always involve local variations in electronic states and binding energies. Therefore, surface defects are crucial in processes such as adsorption, nucleation, and surface reactions. For example, the step of a screw dislocation can eliminate the nucleation barrier for crystal growth. 

Auer, S., Dobson, C.M., and Venndruscolo, M. "Characterisation of the nucleation barriers for protein aggregation and amyloid formation". Hum. Front. Sci. Program J. 1,137146 (2007). 

Assuming Hq. (1), it is then a simple matter to show that there is indeed a critical undersaturation beyond which no nucleation barrier exists at the dislocation. Considering in particular a crystal in contact with a dilute solution, with a saturation concentration cg, this critical undersaturation c0/ce is determined by... 

Furthemiore, a kinetics trace obtained at the hehx wavelength indicates that the helix is completely formed within the time resolution of the pH-jump measurement (100 ns) This result not only demonstrates the efficacy of the laser-induced pH-jump but also has important implications for the dynamics of helix formation. The polyglutamic acid refolds from a highly disordered state and hence must cross the helix nucleation barrier, which it does on a very short timescale (<100 ns). 

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