Nucleation, homogeneous and

Homogeneous and Heterogeneous Nucleation. Homogeneous and heterogeneous nucleation occur at very high levels of supersaturation, either in the solution, or in the case of heterogeneous nucleation, on other inert particles that are present in the form of crystals or as amorphous solid material. Most industrial crystallizers of the types in commercial use operate at levels of supersaturation far below those at which these types of seeding are expected, except under startup conditions. 

As described in Chapter 2, new crystals may be formed by primary nucleation (homogeneous and heterogeneous), secondary nucle-... 

As a general concept of nucleation of crystals, there are two types of nucleation homogeneous and heterogeneous. Both are critically important for fat crystallization in O/W emulsions [7], It is considered that heterogeneous nucleation contributes more to crystallization in O/W emulsions however, some workers in a recent study [43] assumed that homogeneous nucleation contributes more. 

An interesting result obtained by the simulations is that the hard confined nanospheres nucleate homogeneously and crystallize with a first-order kinetics at high temperatures with an Avrami index close to one. As the crystallization temperature was decreased, the Avrami index dropped to 0.5. Several experimental results on diblock copolymers have reported qualitatively similar trends (see Table 12.3). In more complex systems such as triblock terpolymers with two crystallizing blocks, Avrami indices of 0.5 and lower have also been experimentally determined [316]. 

Both homogeneous and heterogeneous mechanisms requite relatively high supersaturation, and they exhibit a high order dependence on supersaturation. These factors often lead to production of excessive fines ia systems where primary aucleatioa mechanisms are important. The classical theoretical treatment of primary nucleation results ia the expressioa (5) ... 

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... 

The maximum statistical fluctuation of 10 atoms is the same in both homogeneous and heterogeneous nucleation. If Q is the volume occupied by one atom in the nucleus then we can easily see that... 

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

Gibbs considered the change of free energy during homogeneous nucleation, which leads to the classical nucleation theory and to the Gibbs-Tliompson relationship (Mullin, 2001). 

Thermodynamic and mechanical equilibrium on a curved vapor-liquid interface requires a certain degree of superheat in order to maintain a given curvature. Characteristics of homogeneous and heterogeneous nucleation can be estimated in the frame of classical theory of kinetics of nucleation (Volmer and Weber 1926 Earkas 1927 Becker and Doring 1935 Zel dovich 1943). The vapor temperature in the bubble Ts.b can be computed from equations (Bankoff and Flaute 1957 Cole 1974 Blander and Katz 1975 Li and Cheng 2004) for homogeneous nucleation in superheated liquids... 

Using the properties of water Li and Cheng (2004) computed from the classical kinetics of nucleation the homogeneous nucleation temperature and the critical nu-cleation radius ra. The values are 7s,b = 303.7 °C and r nt = 3.5 nm. However, the nucleation temperatures of water in heat transfer experiments in micro-channels carried out by Qu and Mudawar (2002), and Hetsroni et al. (2002b, 2003, 2005) were considerably less that the homogeneous nucleation temperature of 7s,b = 303.7 °C. The nucleation temperature of a liquid may be considerably decreased because of the following effects dissolved gas in liquid, existence of corners in a micro-channel, surface roughness. 

Our group has recently observed (ref. 10) that often synthesis time of zeolites can be substantially shortened when microwave radiation is applied instead of conventional heating. Table 3 gives some examples. Also a narrow crystal size distribution is obtained in this way. The crystallization temperature is rapidly (1 min) reached by microwave heating, this may be a factor in homogeneous and essentially simultaneous nucleation. 

Fig. 18 Simulation of 8 chains of L = 250 near a fixed crystalline surface, a-e show simultaneous homogeneous and heterogeneous nucleation and subsequent interaction of the two nuclei, f is the end-view of e showing arrangement of stems on the surface. The values of time t are indicated in each frame... 

Hence, the decision to use a heated substrate with simultaneous evaporation of the component metals as an aid to homogenization requires consideration of whether or not it might have an adverse effect, i.e., causing preferential nucleation of one component, which interdiffusion may not be able to remedy. It was believed (60) that in preparing Pd-Rh alloys by simultaneous deposition on a substrate at 400°C, rhodium nucleated preferentially and that crystallites grew by the addition of palladium (and rhodium) atoms. The diffusion of palladium atoms into this kernel formed a phase with 88 =t 5% Rh (phase II). The outer shell of the crystallite, phase I, was in effect a solid solution deficient in rhodium compared with the overall film composition, and the Rh content of phase I therefore increased as the Rh flux was increased. 

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