Defect Nucleation

Physically, the onset of instabihty at the point is interpreted as the formation of crystal defect there. It should be noted that local instability does not imply global instability of the configuration. If angle between the vectors k and w established in this way is larger than 60°, then the nucleated defect is expected to be a dislocation with slip plane normal k and Burgers vector approximately along w. On the other hand, if the angle between k and w and instability is less than 30°, the nucleated defect would likely be a microcrack or a void. 

For pit nucleation, defects within the metal surface also have to be considered. Inclusions like MnS may prevent the formation of a continuous, protecting passive film locally. They are preferential sites for a breakdown of passivity. Even in this situation, the special chemical properties of aggressive anions to start corrosion pits and to cause their continuous growth have to be included in the proposed mechanisms. These properties should be explained along with the ability of halides to form stable and fast-dissolving complexes of the cations of the metals under study with the related breakdown of their passive layers. 

Dislocation theory as a portion of the subject of solid-state physics is somewhat beyond the scope of this book, but it is desirable to examine the subject briefly in terms of its implications in surface chemistry. Perhaps the most elementary type of defect is that of an extra or interstitial atom—Frenkel defect [110]—or a missing atom or vacancy—Schottky defect [111]. Such point defects play an important role in the treatment of diffusion and electrical conductivities in solids and the solubility of a salt in the host lattice of another or different valence type [112]. Point defects have a thermodynamic basis for their existence in terms of the energy and entropy of their formation, the situation is similar to the formation of isolated holes and erratic atoms on a surface. Dislocations, on the other hand, may be viewed as an organized concentration of point defects they are lattice defects and play an important role in the mechanism of the plastic deformation of solids. Lattice defects or dislocations are not thermodynamic in the sense of the point defects their formation is intimately connected with the mechanism of nucleation and crystal growth (see Section IX-4), and they constitute an important source of surface imperfection. 

Qualitative examples abound. Perfect crystals of sodium carbonate, sulfate, or phosphate may be kept for years without efflorescing, although if scratched, they begin to do so immediately. Too strongly heated or burned lime or plaster of Paris takes up the first traces of water only with difficulty. Reactions of this type tend to be autocat-alytic. The initial rate is slow, due to the absence of the necessary linear interface, but the rate accelerates as more and more product is formed. See Refs. 147-153 for other examples. Ruckenstein [154] has discussed a kinetic model based on nucleation theory. There is certainly evidence that patches of product may be present, as in the oxidation of Mo(lOO) surfaces [155], and that surface defects are important [156]. There may be catalysis thus reaction VII-27 is catalyzed by water vapor [157]. A topotactic reaction is one where the product or products retain the external crystalline shape of the reactant crystal [158]. More often, however, there is a complicated morphology with pitting, cracking, and pore formation, as with calcium carbonate [159]. 

Lutsko J F ef a/1989 Molecular-dynamic study of lattice-defect-nucleated melting in metals using an embedded-atom-method potential Phys. Rev. B 40 2841... 

Nucleation in solids is very similar to nucleation in liquids. Because solids usually contain high-energy defects (like dislocations, grain boundaries and surfaces) new phases usually nucleate heterogeneously homogeneous nucleation, which occurs in defect-free regions, is rare. Figure 7.5 summarises the various ways in which nucleation can take place in a typical polycrystalline solid and Problems 7.2 and 7.3 illustrate how nucleation theory can be applied to a solid-state situation. 

Fig. 7.5. Nucleation in solids. Heterogeneous nucleotion con take place at defects like dislocations, grain boundaries, interphase interfaces and free surfaces. Homogeneous nucleation, in defect-free regions, is rare.

We can anticipate that the highly defective lattice and heterogeneities within which the transformations are nucleated and grow will play a dominant role. We expect that nucleation will occur at localized defect sites. If the nucleation site density is high (which we expect) the bulk sample will transform rapidly. Furthermore, as Dremin and Breusov have pointed out [68D01], the relative material motion of lattice defects and nucleation sites provides an environment in which material is mechanically forced to the nucleus at high velocity. Such behavior was termed a roller model and is depicted in Fig. 2.14. In these catastrophic shock situations, the transformation kinetics and perhaps structure must be controlled by the defective solid considerations. In this case perhaps the best published succinct statement... 

Soapless seeded emulsion copolymerization has been proposed as an alternative method for the preparation of uniform copolymer microspheres in the submicron-size range [115-117]. In this process, a small part of the total monomer-comonomer mixture is added into the water phase to start the copolymerization with a lower monomer phase-water ratio relative to the conventional direct process to prevent the coagulation and monodispersity defects. The functional comonomer concentration in the monomer-comonomer mixture is also kept below 10% (by mole). The water phase including the initiator is kept at the polymerization temperature during and after the addition of initial monomer mixture. The nucleation takes place by the precipitation of copolymer macromolecules, and initially formed copolymer nuclei collide and form larger particles. After particle formation with the initial lower organic phase-water ratio, an oligomer initiated in the continuous phase is... 

Although specific calculations for i and g are not made until Sect. 3.5 onwards, the mere postulate of nucleation controlled growth predicts certain qualitative features of behaviour, which we now investigate further. First the effect of the concentration of the polymer in solution is addressed - apparently the theory above fails to predict the observed concentration dependence. Several modifications of the model allow agreement to be reached. There should also be some effect of the crystal size on the observed growth rates because of the factor L in Eq. (3.17). This size dependence is not seen and we discuss the validity of the explanations to account for this defect. Next we look at twin crystals and any implications that their behaviour contain for the applicability of nucleation theories. Finally we briefly discuss the role of fluctuations in the spreading process which, as mentioned above, are neglected by the present treatment. 

The way in which the physical results rely so strongly on the choice of apportioning is peculiar to this particular nucleation theory and increases the number of adjustable parameters — this may be regarded as either an asset or a defect. 

While it is possible that surface defects may be preferentially involved in initial product formation, this has not been experimentally verified for most systems of interest. Such zones of preferred reactivity would, however, be of limited significance as they would soon be covered with the coherent product layer developed by reaction proceeding at all reactant surfaces. The higher temperatures usually employed in kinetic studies of diffusion-controlled reactions do not usually permit the measurements of rates of the initial adsorption and nucleation steps. 

The dependence on film thickness is attributed to the dewetting nucleation, which occurs in the 2.5-4.5 nm thickness range via the formation of randomly distributed droplets rather than the formation of holes. When the initial film thickness exceeds 4.5 nm, dewetting is trigged via nucleation of holes instead of droplets, and for film thickness above 10 nm, dewetting develops slowly via hole nucleation at defects. The different dewetting processes observed for different initial film thicknesses can be explained in terms of the variation of disjoining pressure and the inability of the polymer to spread on its own monolayer. 

If an elastomer is bonded to a substrate such as steel, it is usual for the bond to have small areas of imperfection where the adhesive or the chemical preparation of the surface is defective. Such areas are known as holidays. In high-pressure gas environments, these holidays form nucleation sites for the growth of half-bubbles or domes, under conditions where gas has been dissolved in the elastomer and the pressure has subsequently been reduced. Gas collecting at the imperfection at the interface will inflate the mbber layer, and domes will show as bumps on the surface of the mbber-coating layer—just as a paint layer bubbles up in domes when the wood underneath gives off moisrnre or solvents in particular areas. 

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