Critical radius for nucleation

Here R is a critical radius for nucleation [20,56] on a faceted surface... 

It is evident from Equation 7.114 that in the case when G > 1, nanoshell formation is impossible (taking into account that x and y start from almost 1). This means that, in very small particles, Tba < 2yS2/Ag, the reaction with void formation is impossible. It is interesting that this critical condition coincides with the critical radius for nucleation of a new phase. 

The effect of decreasing temperature on the critical radius for nucleation and on the work of nudeadon. 

The nucleation rate is, in fact, critically dependent on temperature, as Fig. 8.3 shows. To see why, let us look at the heterogeneous nucleation of b.c.c. crystals at grain boundaries. We have already looked at grain boundary nucleation in Problems 7.2 and 7.3. Problem 7.2 showed that the critical radius for grain boundary nucleation is given by... 

Nucleation of solids from liquids critical radius for homogeneous and heterogeneous nucleation... 

The critical radius given by Eq. 19.97 is equal to the critical radius for homogeneous nucleation in the bulk liquid. This result is similar to that obtained in Exercise 19.7... 

It appears that both compatibilization and the nanostructure formation at the interface play a key role for nucleation. The supposed heterogeneous nucleation activity will therefore be discussed in more detail. Heterogeneous nucleation in general is strongly affected by the particle size and the interfacial properties [79, 80], As the particle size of the PPE phase is well above the critical radius of nucleation of several nanometers [80], the interface demands closer examination. 

This radius is called the critical radius, for which for nucleation, AG, is... 

Klausner [34] studied bubble nucleation in stratified flow of refrigerant R113 in a horizontal rectangular channel. The nucleation site density decreased with increasing vapor velocity as illustrated in Fig. 15.15 at a velocity of around 5 m/s, nucleation was totally supressed. Klausner et al. interpreted their data in terms of the relationship between critical radius of nucleation site rc and number density the data from this interpretation are shown in Fig. 15.16 and it will be seen, that for these particular conditions, a rather narrow range of site radius applied. The question of suppression of nucleate boiling is discussed further later in this chapter. 

Sketch the curves of nucleation and crystal growth rate. Label all important features. Explain how the nucleation rate curve represents a competition between kinetic and thermodynamic factors. Explain why the nucleation curve will always occur at temperatures below the crystal growth curve. Discuss the concept of a critical radius for a nucleus. 

It has been observed that very pure gold can be supercooled well below its normal melting point without freezing. Consider a bath of Au(l) that has been supercooled to 1,200 K. Calculate the critical radius for the nucleation of solid in the liquid. 

Critical radius for stable sohd particle (heterogeneous nucleation)... 

Nucleation energy barriers depend upon the surface and volume energies associated with the reaction. A critical radius for the nucleus exists beyond which the new phase may grow spontaneously. 

When the nucleus is a liquid, the angle 6 is called tire wetting angle. It can be seen that the critical radius in heterogeneous nucleation is given by the same equation as tlrat for homogeneous nucleation, but the radius now refers... 

If we compare eqns (7.11) and (7.3) we see that the expressions for the critical radius are identical for both homogeneous and heterogeneous nucleation. But the expressions for the volume of the critical nucleus are not volume is... 

Figure 17. Energy for the nucleation of a surface film on metal electrode. M, metal OX, oxide film EL, electrolyte solution. Aj is the activation barrier for the formation of an oxide-film nucleus and rj is its critical radius. 7 a is the interfacial tension of the metal-electrolyte interface, a is the interfacial tension of the film-electrolyte interface. (From N. Sato, J. Electro-chem. Soc. 129, 255, 1982, Fig. 5. Reproduced by permission of The Electrochemical Society, Inc.)...

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