Critical radius for

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... 

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

The critical radius given by Eq. 19.92 is equal to the critical radius for homogeneous nudeation in the bulk liquid. This is the expected result because 7LM = ySM (so that the liquid/solid interface makes an angle of 90° with the mold) and the inward pressure on the interface due to curvature, AP = 2-yLS/R (Eq. 12.4), is then exactly balanced by the change in bulk free energy across the interface, jjphase trans — gB (Eq. 12.1). Substitution of Eq. 19.92 into Eq. 19.91 yields the critical free energy for nudeation ... 

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... 

Calcns of the critical radius for Tetryl, based on the Merzhanov Friedman treatments are compared in Table 2. Agreement is quite good. However, note that, as expected, critical radii based on the Frank-Kamenetskii-Chambre treatment (steady-state conditions) are considerably smaller than those computed via the hot spot approach. For comparison, Eq 14 (based on Ref 7) gives a r = 2.76 x 10"3cm for a Tetryl sphere at 700 K, and acr = 2.37cm at 445°K, in close agreement with Merzhanov... 

This book contains a number of papers published by Ruckenstein and coworkers on the topic of nanodispersions. Aerosols are the focus of the first chapter which features a model for the sticking probability as the main contribution. One concludes that, when the particles are small enough, the dissociation rate can become sufficiently large for doublets to reach equilibrium with single particles. However, above a critical radius for the particles, the doublets become stable and their concentration increases with time, providing nuclei for aerosol growth. 

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

The same is true of the critical radius for the spontaneous ignition, r,., of a similar body of a gas-pormcablc oxidatively-heating substance, having a definite shape, placed in the atmosphere maintained at an arbitrary temperature, T,.. 

Figure 1. Free energy required for the stability of a critical nucleus. At the lowest temperature both the energy barrier and the critical radius for a nucleus is the smallest, and both increase with increasing temperatme. At some temperature To, the critical radius is too large for a stable nucleus to form. This corresponds to a system that is not supersaturated. After Raghaven and Cohen (1975).

CRITICAL RADIUS FOR ENERGY TRANSFER FROM SPHERICAL... 

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