Crystal nucleus growing model

The formation of reduction product ce-Fe of ammonia synthesis catalyst is a crystal growth process, which follows the principle and law of crystallography. The basic requirement for this process is that it should form the small a-Fe crystal without growth or conglutination. This requirement is related with the reaction rate, particularly temperature and the concentration of another product H2O, in particular reoxidation of a-Fe should be avoided. Thus, reduction conditions with low-temperatures, high-space velocities and low-water vapor concentrations are required in actual operation. 

The solid state reaction kinetic model mentioned above is based on such an assumption that the rate determined step in chemical interaction between solid states is the formation and growth of crystal nucleus of products on the active sites. The active site can be the defects of surface and point or the outcrop moved to the crystal surface. As the volume of the original material and products varies, the generation process of crystal nuclei will be accompanied by the lattice deformation, that is, the speed of the process depends not only on chemical factor but also depends on the nucleation chemistry. 

There are several solid state kinetic models related to nucleation and growth processes. One of the most commonly used is the equation proposed by 

Kolmogorov proposed two equations after he studied the crystallization process. 

Polycrystalline change, nucleus grow up by controlling of boundary 

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The thermodynamic model presented above only predicts when phase separation will occur. There are, however, two mechanisms by which phase separation can actually occur. The first mechanism is similar to that discussed in an earlier chapter for precipitation of crystals from a melt, where a nucleus is formed and then grows with time. By analogy, this mechanism is termed nucleation and growth. Many of the same factors which control crystal formation also affect phase separation by this mechanism. The second mechanism is termed spinodal decomposition. This mechanism involves a gradual change in composition of the two phases until they reach the immiscibility boundary. 

Similar MC calculations were used by Trout s group to study the carbon dioxide-liquid water interface at 220 K and 4 MPa near the phase boundary of a carbon dioxide hydrate (273 K and 4MPa). Nucleation was achieved by seeding the system with a cluster of carbon dioxide hydrate. It was found that a small cluster with diameter <9.6 A dissolved into the solution readily. A hydrate crystal started to grow, however, when a hydrate cluster twice that size (19.3 A) was implanted into the system. The crystal eventually spanned the whole system (Figure 22). Thus the critical nucleus size for hydrate nucleation is estimated to be about 19 A consisting of approximately 200 water molecules. This is a considerably smaller number than that estimated from the local harmonic model of around 600 molecules. The theoretical results refuted the labile cluster hypothesis.This hypothesis speculates the agglomeration... 

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