Nucleation and Growth Combined

1 Effect of Nucleation Rate versus Growth Rate on Microstructure 

FIGURE 6.25 For a phase transformation that occurs on cooling a system helow Tg, the overall transformation rate F is a nonlinear product of the nucleation rate N and the growth rate G. Because both N and G obtain a peak at intermediate temperatures, so does F. 

Geology of Ingenous Rocks Natural Case Study in Nucleation and Growth 

LIQUID-SOLID AND SOLID-SOLID PHASE TRANSFORMATIONS 

Slow cooling underground Fast cooling on surface Coarse microstructure Fine microstructure 

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In spite of these obstacles, crystallization does occur and the rate at which it develops can be measured. The following derivation will illustrate how the rates of nucleation and growth combine to give the net rate of crystallization. The theory we shall develop assumes a specific picture of the crystallization process. The assumptions of the model and some comments on their applicability follow ... 

Precipitatioa (2,13—17) techniques employ a combination of nucleation and growth iaduced by adding a chemical precipitant, or by changing the temperature and/or pressure of the solution. Chemical homogeneity is controlled by controlling the rate of precipitation. FFeterogeneous precipitation iavolves the precipitation of a soHd of different composition from the solution, and the composition of the precipitate may change as precipitation continues. Coprecipitation iavolves the simultaneous precipitation of similar size cations ia a salt as a soHd solutioa. 

The complexity of these chemical and mechanical interactions is such that each metal-environment system must be examined on an individual basis to determine the important processes influencing corrosion fatigue crack nucleation and growth rates. Thus, in the ensuing sections, examples are quoted to illustrate commonly occurring phenomena or establish more general principles with reasonably wide applicability for particular classes of metal/environment combinations. It should be noted, however, that when... 

Measurements of the kinetics of the individual nucleation and growth steps in the reactions of several hydrated sulphates have been referred to in Sect. 1.2 though, perhaps surprisingly, these data were not combined in a kinetic analysis for the overall reaction in studies of the alums [51,431, 586] or NiS04 7 H20 [50]. Indeed, Lyakhov and Boldyrev [81], in one of the few reviews of the field, maintain that the satisfactory topochemi-cal description of dehydrations is a problem which at present remains... 

Thus, ellipsometry gives direct evidence for a model of the initial stages of polythiophene growth, disproving the conclusions based purely on coulo-metry. In the same paper, Hamnett and Hillman were able to obtain valuable and complementary information not just on the initial stages of the polymerisation but also on the mechanism of the subsequent nucleation and growth. The unique piece of information that the ellipsometer was able to extract, the changes in film thickness (in real time), when combined with coulometric data allowed a wealth of information to be deduced, e.g. with respect to the film composition, and ably showed the power of the technique. 

The kinetics of CO oxidation from HClOi, solutions on the (100), (111) and (311) single crystal planes of platinum has been investigated. Electrochemical oxidation of CO involves a surface reaction between adsorbed CO molecules and a surface oxide of Pt. To determine the rate of this reaction the electrode was first covered by a monolayer of CO and subsequently exposed to anodic potentials at which Pt oxide is formed. Under these conditions the rate of CO oxidation is controlled by the rate of nucleation and growth of the oxide islands in the CO monolayer. By combination of the single and double potential step techniques the rates of the nucleation and the island growth have been determined independently. The results show that the rate of the two processes significantly depend on the crystallography of the Pt surfaces. 

The Cu adsorbate structure was studied using STM and EXAFS (extended x-ray absorption fine structure) techniques, but it is not yet well understood. UPD-OPD transition is in the range —82 to —71 mV. Bulk fee Cu spacing is reached after deposition of about lOCu monolayers. Holzle et al. (72) have shown that UPD Cu deposition on Au(l 11) is a combined adsorption-nucleation and growth process. 

Computer simulations combined with experiments have also shown that one can deduce from the fractal dimension the nature of nucleation and growth of particles and what chemical and physical mechanisms control the formation of particle aggregates. We consider this briefly before proceeding to other topics. 

Holze et al. (42) have shown that UPD Cu deposition on Au(l 11) is a combined adsorption-nucleation and growth process. 

Glass-ceramics can also be made starting from a powdered glass followed by a single step combined sintering and controlled crystal nucleation and growth steps. This route is the one most relevant to the electroceramics context. 

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