Growth of precipitates

Two other factors could contribute to the observed departure of the growth thickness at long times from that predicted by equation 17. First, homogeneous nucleation in the melt and the subsequent growth of precipitates will act as sinks for solute atoms, just as film growth does. The exact location in the melt where homogeneous nucleation will occur depends on the melt compositional and thermal profiles (96). The precipitates are less dense than the melt and will rise to the top of the melt. Such precipitates... 

Figure 5. Qualitative comparison of the dependency of the rates of nucleation and growth of precipitate particle as a function of the solubility parameter (increasing from left to right) or T (opposite direction).

Kolthoff proposed the concept that entrapment of foreign ions, involving growth of precipitate around adsorbed ions, is an important source of contamination, particularly of crystalline precipitates such as barium sulfate and calcium oxalate. Essential to this concept is that occlusion is not an equilibrium process and that recrystaUization during aging can effect purification. The foreign ions represent lattice imperfections unless they are actually held in solid solution. 

The formation and growth of precipitates and crystals are very important in analytical chemistry and in other areas of science. Shown in the photo is the growth of sodium acetate crystals from a supersaturated solution. Because supersaturation leads to small particles that are difficult to filter, it is desirable in gravimetric analysis to minimize the supersaturation and thus increase the particle size of the solid that is formed. 

The simplified overall (total, integral) material balance of the batch precipitation states that the mass increase due to the growth of precipitate crystals of the molecular weight M from the initial size Lo to an arbitrary size L, in an arbitrary time t, is equal to the mass of the solute of volume V delivered by the equimolar doublejet whose molar concentration Cr... 

The significance of Eq. (6.56) lies in the fact that it prescribes the reactant flow rate at any moment of the growth of precipitate crystals, provided that the number and size of the seeds used are known or alternatively, that the number and size of stable nuclei population at the beginning of the growth stage of precipitation are known from the previous experiments. In the latter case, by knowing the size of the final precipitate and the number of moles... 

In conclusion, we reiterate that the growth of precipitation tubes is readily affected by buoyant gas bubbles. In such situations, the tube radius is selected by the radius of the bubble and its growth velocity follows from simple volume conservation of the injected solution. Clearly, additional work is needed to unravel the detailed mechanism of bubble pinning to the nonequilibrium but steady reaction zone at the top region of the growing tube. 

Nano-oxide particles precipitate from the ferritic matrix, maintaining crystalline coherency or partial coherency with a ferritic matrix. In general, the nucleation and growth of precipitates proceed, as both interfacial and strain energies become minimal. In the case of ODS steels, interfacial coherency or partial coherency could be maintained between thermodynamically stable nanoparticle precipitates and the ferritic matrix in order to decrease the free energy in the system from the extremely high-energy state induced by MA. 

In this volume discussions are presented on a variety of aspects of ionic solid systems kinetics of reaction, of diffusion and sintering, of crystallization, of nucleation and crystal growth, of precipitation, and of the destruction of crystals by evaporation or by thermal decomposition of a solution. Unquestionably such studies will provide valuable aid in furthering the practical utilization of reactions in ionic systems. However, as pointed out in the chapter by Stringer et al % theoretical models are still, in general, inadequate for... 

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