Nucleation thermal activation

The decomposition of a solution with composition outside the spinodal region but within the metastable region can be analyzed in a similar way. Let us assume that a sample with composition in this region is cooled to low temperatures. Small fluctuations in composition now initially lead to an increase in the Gibbs energy and the separation of the original homogeneous solution must occur by nucleation of a new phase. The formation of this phase is thermally activated. Two solutions with different composition appear, but in this case the composition of the nucleated phase is well defined at all times and only the relative amount of the two phases varies with time. 

At a microscopic scale, a single coalescence event proceeds through the nucleation of a thermally activated hole that reaches a critical size, above which it becomes unstable and grows [29]. We shall term E(r) the energy cost for reaching a hole of size r. A maximum of E occurs at a critical size r, E r ) = Ea being the activation energy of the hole nucleation process (Fig. 5.2). 

We have mentioned above the tendency of atoms to preserve their coordination in solid state processes. This suggests that the diffusionless transformation tries to preserve close-packed planes and close-packed directions in both the parent and the martensite structure. For the example of the Bain-transformation this then means that 111) -> 011). (J = martensite) and <111> -. Obviously, the main question in this context is how to conduct the transformation (= advancement of the p/P boundary) and ensure that on a macroscopic scale the growth (habit) plane is undistorted (invariant). In addition, once nucleation has occurred, the observed high transformation velocity (nearly sound velocity) has to be explained. Isothermal martensitic transformations may well need a long time before significant volume fractions of P are transformed into / . This does not contradict the high interface velocity, but merely stresses the sluggish nucleation kinetics. The interface velocity is essentially temperature-independent since no thermal activation is necessary. 

Single-Component System with Isotropic Interfaces and No Strain Energy. This relatively simple case could, for example, correspond to the nucleation of a pure solid in a liquid during solidification. For steady-state nucleation, Eq. 19.16 applies with AQC given by Eq. 19.4 and it is necessary only to develop an expression for /3C. In a condensed system, atoms generally must execute a thermally activated jump over a... 

As with other thermally activated processes, the rate of nucleation, N, can be expressed by an Arrhenius equation with AG as the activation energy,... 

A rep < 1, Des < 1, the nucleation dynamics is stochastic in nature as a critical fluctuation in one, or more, order parameters is required for the development of a nucleus. For DeYep > 1, Des < 1 the chains become more uniformly oriented in the flow direction but the conformation remains unaffected. Hence a thermally activated fluctuation in the conformation can be sufficient for the development of a nucleus. For a number of polymers, for example PET and PEEK, the Kuhn length is larger than the distance between two entanglements. For this class of polymers, the nucleation dynamics is very similar to the phase transition observed in liquid crystalline polymers under quiescent [8], and flow conditions [21]. In fast flows, Derep > 1, Des > 1, A > A (T), one reaches the condition where the chains are fully oriented and the chain conformation becomes similar to that of the crystalline state. Critical fluctuations in the orientation and conformation of the chain are therefore no longer needed, as these requirements are fulfilled, in a more deterministic manner, by the applied flow field. Hence, an increase of the parameters Deiep, Des and A results into a shift of the nucleation dynamics from a stochastic to a more deterministic process, resulting into an increase of the nucleation rate. 

In this section, we concentrate on the fundamental impact of particle size reduction on magnetization processes in individual particles. Although not directly related to coercivity, the classical effect of single domain particle formation is described. At small particle size, reversal by coherent rotation tends to be favoured with respect to nucleation/pinning-depinning finally thermal activation effects and macroscopic quantum tunnelling are discussed. 

The growth kinetics describes the nucleation processes on the atomic scale. Thermally activated processes as adsorption, desorption, and diffusion at the surface and in the volume, nucleation, and crystallization/ recrystallization determine the film structure and can be controlled by the substrate temperature and the growth rate. Using a diagram ln(J ) over 1/ T, R being the deposition rate and T the growth temperature, three different growth modes (epitaxial, polycrystalline, and amorphous) can be... 

The analysis of the effect of temperature on the mean lifetime of foam bilayers provides further evidence for the applicability of the theory of bilayer rupture by hole nucleation [399,402,403]. The experiments show that the foam bilayers become less stable with increasing temperature, due both to the Boltzmann-type thermal activation of the hole nucleation and to the decreasing work of a nucleus hole formation. 

In Fig. 21 DCH crystals are shown before polymerization and at an intermediate conversion. It is typical for the thermal reaction that more perfect monomer crystals require longer reaction times than defect-rich crystals. There is evidence that in the radiation polymerization of DCH the polymer crystal perfection increases with decreasing temperature, i.e., the nucleation process requires a rather high thermal activation energy. 

Ceramics obtained from polymeric precursors are usually amorphous. Since substantial thermal activation is required for nucleation and crystallization, precursor-derived ceramics (PDCs) frequently remain amorphous or nanocrystalUne up to rather high temperatures. For example, crystallization of a number of quaternary Si-B-C-N ceramics is retarded even up to 1800°C, resulting in excellent thermomechanical properties. Nevertheless, crystalline materials are of great interest because their microstructure formation can be controlled during devitrification, providing a means for stabilizing nanosized morphologies. 

The nature of boiling heat transfer in a channel with the gap less than the capillary is also studied and presented. The condensation flow mechanisms, pressure drop and heat transfer in microchannels, role of microscale heat transfer in augmentation of nucleate boiling and flow boiling heat transfer, binary-fluid heat and mass transfers in microchannel geometries for miniaturized thermally activated absorption heat pumps, evaporation heat... 

Brown s statistical theory [30] of annihilation of screw dislocation dipoles by thermally activated jog migration determines the PSB nanostructure and the saturation stress. The statistical theory is compatible with the nanotheory and the required activation energies are available for both cross-slip and jog motion in copper, as described in 2.2 and 2.3. What remains is to combine and quantify the above theories of thermally activated fatigue hardening, PSB nucleation, cyclic saturation and PSB surface damage to test their quantitative predictions against experimental data. 

On the other hand, the initial nucleation rate which can be evaluated from the number density at the lowest irradiation level in Fig.3 reveals a unique feature of the nucleation of photo-CVD a-Si. One can clearly recognize two different regions of substrate temperature characterized by the opposite temperature dependences. It seems quite rare that such a minimum shows up in the relation between reaction rate and temperature. It is strongly suggested that a different nucleation mechanism begins to work in the high temperature region assisted by thermal activation. 

Figure 5 shows the potential dependence of the nucleus density obtained from analysis of the current transients according to equation (7). The exponential dependence of the nucleus density on potential suggests thermal activation of nucleation sites, consistent with classical nucleation models [5,8] where N0 °= exp(-eAU/kT). 

The rate of nucleation, /, e.g. the number of nuclei formed per unit time per unit volume, can be expressed in the form of the Arrhenius reaction velocity equation commonly used for the rate of a thermally activated process ... 

Since the atomic motion associated with the nucleation is thermally activated one has... 

Reduction of oxides or hydroxides can be used to obtain nanopowders of ferromagnetic metals like iron, cobalt and nickel [314]. Reduction in hydrogen is one of the thermally activated processes where nucleation and nuclei growth compete. Investigation of transformation mechanisms and their competition has been carried out under nonisothermal conditions. The nickel oxide powders with specific surface areas of 11 and 40 m /g were examined in Ref. [315] (Fig. 5.22). 

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