Temperature dependence of nucleation

The preexponential. A, is related to the movement of atoms or molecules to and from the nucleus. This expression does not account for diffusion effects in transporting atoms across the nucleus-liquid interface. To explain the observed temperature dependence of nucleation rate (Fig. 1), we include an energy barrier for diffusion, Q ... 

Figure 2 Temperature dependence of nucleation density measured with an ellipsometric monitor. Closed circles and solid line show values for 1000 W microwave power, open, circles and broken line show values for 1400 W microwave power. Other deposition conditions 5 vol.% CO/Hj, flow rate of 100 seem, and pressure of 50 torr. Using CO as reactive gas led to diamond films containing hardly any non-diamond phases.1 1 (Reproduced with permission.)...

Temperature dependence of nucleation rate and of crystal growth rate. 

Fig. 19.12. Temperature dependence of nucleation rate for PESU with M = 9,150 [59]. Open circle is the nominal nucleation rate reduced by the initial view area and open triangle is the real nucleation rate reduced by the real effective area during crystallization. Solid line is the best fitting by Arrhenius expression of the molecular transport term, respectively...

Figure 2-5 The temperature dependency of nucleation speed I and crystal growth speed U [(a) Vitrification occurs readily, (b) Crystals are formed readily] [Ref. 17].

In this way, the heat treatment temperature dependency of nucleation speed can be expressed with variations of [1/Tp - 1/T°p],... 

The previous discussion of this section centered on the temperature dependences of nucleation, growth, and transformation rates. The time dependence of rate (which is often termed the kinetics of a transformation) is also an important consideration, especially in the heat treatment of materials. Also, because many transformations of interest to materials scientists and engineers involve only solid phases, we devote the following discussion to the kinetics of solid-state transformations. 

The temperature dependence of the spreading rate is generally small and can often be neglected against that of the nucleation rate (but see Sect. 3.6.3). 

A more detailed picture of the temperature dependence of the growth is given in Figure 2.4, where the island density is plotted as a function of temperature. It can be seen that only in the temperature range from 207 to 288 K the growth is perfectly template controlled and the number of islands matches the number of available nucleation sites. This illustrates the importance of kinetic control for the creation of ordered model catalysts by a template-controlled process. Obviously, there has to be a subtle balance between the adatom mobility on the surface and the density of template sites (traps) to allow a template-controlled growth. We will show more examples of this phenomenon below. 

The temperature dependence of the reaction was studied, and the activation energy of the reaction was calculated to be approximately 100 kj mol The exponent n was found to lie in the range 1-2, which is consistent with a 2D diffusion controlled reaction mechanism with deceleratory nucleation. The rate of reaction increases markedly with the amount of water added to the LDH with very small amounts of water added, the deintercalation process does not go to completion. This effect is a result of the LiCl being leached into solution. An equilibrium exists between the LDH and gibbsite/LiCl in solution. The greater [LiCl], the further to the LDH side this lies. 

It is remarkable that the predictions of classical nucleation theory without any consideration of polymer connectivity are borne out in experiments. At higher supercooling, deviations are expected because of temperature dependence of the nucleation rate prefactor. 

The temperature dependence of the nucleation rate allows many critical nuclei to be formed on a time scale that is small relative to the growth time when the difference between the actual solution and equilibrium temperatures is greater than a critical value, ATc. If the temperature variations of liquid density are neglected, the critical super saturation, A Tc, will vary with... 

Summary. On the basis of phenomenological Ginzburg-Landau approach we investigate the problem of order parameter nucleation in a ferromagnetic superconductor and hybrid superconductor - ferromagnetic (S/F) systems with a domain structure in an applied external magnetic field H. We study the interplay between the superconductivity localized at the domain walls and between the domain walls and show that such interplay determines a peculiar nonlinear temperature dependence of the upper critical field. For hybrid S/F systems we also study the possible oscillatory behavior of the critical temperature TC(H) similar to the Little-Parks effect. 

Temperature dependence of pearlite nucleation and growth rates in a 0.78% C, 0.63% Mn steel of ASTM grain size 5.25. Data from R. F. Mehl and A. Dube, Phase Transformations in Solids (New York Wiley, 1951), 545. Reprinted with permission of John Wiley Sons, Inc. 

At co-deposition of dielectric and M/SC the structure of a nanocomposite film depends on a relationship between the rate of formation of M/SC particles and the rate of making of a solid dielectric matrix. Models of such deposition are discussed. The special attention is paid to new low-temperature processes of nucleating and growth of nanoparticles in a solid polymeric matrix containing the inclusions of... 

The theory shows that the most important variables affecting the rates at which primary nucleation occur are interfacial energy esurf, temperature T, and supersaturation a. The high-order dependence of nucleation rate on these three variables, especially supersaturation, is important because, as shown by an examination of Eq. (16), a small change in any of the three variables could produce an enormous change in nucleation rate. Such behavior gives rise to the often observed phenomenon of having a clear... 

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