In surface nucleation

As shown in 4.4.1., two stages usually occur in surface nucleation, nucleation and then nuclei growth. If surface nucleation is fast (Model C) it is likely due to reaction of a gas with the solid particle. The reaction of a liquid is the other possibility, i.e.-... 

When the attachment of the substrate to the precipitate to be formed is strong, the clusters tend to spread themselves out on the substrate and form thin surface islands. A special limiting case is the formation of a surface nucleus on a seed crystal of the same mineral (as in surface nucleation crystal growth). As the cohesive bonding within the cluster becomes stronger relative to the bonding between the cluster and the substrate, the cluster will tend to grow three-dimensionally (Steefel and Van Cappellen, 1990). 

Further investigations on the kinetics of cordierite nucleation revealed that the elastic strain term (AGg) in Eq. 1-1, could also be of significance in surface nucleation. In a specialized experiment,... 

Impurities usually cause a reduction in the growth rates of crystalline materials due to blocking of kink sites, thereby leading to smaller crystals than required. This is a common problem, which is often related to contamination of the feed solution. In some other cases, however, impurities can enhance growth rates, thought to be due to a reduction in interfacial tension and hence increase in surface nucleation rates. 

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. 

As mentioned in Section IX-2A, binary systems are more complicated since the composition of the nuclei differ from that of the bulk. In the case of sulfuric acid and water vapor mixtures only some 10 ° molecules of sulfuric acid are needed for water oplet nucleation that may occur at less than 100% relative humidity [38]. A rather different effect is that of passivation of water nuclei by long-chain alcohols [66] (which would inhibit condensation note Section IV-6). A recent theoretical treatment by Bar-Ziv and Safran [67] of the effect of surface active monolayers, such as alcohols, on surface nucleation of ice shows the link between the inhibition of subcooling (enhanced nucleation) and the strength of the interaction between the monolayer and water. 

Radicals generated from water-soluble initiator might not enter a micelle (14) because of differences in surface-charge density. It is postulated that radical entry is preceded by some polymerization of the monomer in the aqueous phase. The very short oligomer chains are less soluble in the aqueous phase and readily enter the micelles. Other theories exist to explain how water-soluble radicals enter micelles (15). The micelles are presumed to be the principal locus of particle nucleation (16) because of the large surface area of micelles relative to the monomer droplets. 

A number of theories have been put forth to explain the mechanism of polytype formation (30—36), such as the generation of steps by screw dislocations on single-crystal surfaces that could account for the large number of polytypes formed (30,35,36). The growth of crystals via the vapor phase is beheved to occur by surface nucleation and ledge movement by face specific reactions (37). The soHd-state transformation from one polytype to another is beheved to occur by a layer-displacement mechanism (38) caused by nucleation and expansion of stacking faults in close-packed double layers of Si and C. 

Models used to describe the growth of crystals by layers call for a two-step process (/) formation of a two-dimensional nucleus on the surface and (2) spreading of the solute from the two-dimensional nucleus across the surface. The relative rates at which these two steps occur give rise to the mononuclear two-dimensional nucleation theory and the polynuclear two-dimensional nucleation theory. In the mononuclear two-dimensional nucleation theory, the surface nucleation step occurs at a finite rate, whereas the spreading across the surface is assumed to occur at an infinite rate. The reverse is tme for the polynuclear two-dimensional nucleation theory. Erom the mononuclear two-dimensional nucleation theory, growth is related to supersaturation by the equation. 

Introduction of the surface-nucleation mechanism in numerical computation of elastic-plastic wave evolution leads to enhanced precursor attenuation in thin specimens, but not in thicker ones. Inclusion of dislocation nucleation at subgrain boundaries indicates that a relatively low concentration of subgrain boundaries ( 2/mm) and nucleation density (10"-10 m ) is sufficient to obtain predicted precursor decay rates which are comparable to those obtained from the experiments. These experiments are only slightly above the threshold necessary to produce enhanced elastic-precursor decay. 

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. 

Purely physical laws mainly control the behaviour of very large particles. Further down the particle size range, however, specific surface area, i.e. surface area per unit mass, increases rapidly. Chemical effects then become important, as in the nucleation and growth of crystals. Thus, a study of particulate systems within this size range of interest has become very much within the ambit of chemical engineering, physical chemistry and materials science. 

It has been shown that an increase in crystallizer residence time, or decrease in feed concentration, reduces the working level of supersaturation. This decrease in supersaturation results in a decrease in both nucleation and crystal growth. This in turn leads to a decrease in crystal surface area. By mass balance, this then causes an increase in the working solute concentration and hence an increase in the working level of supersaturation and so on. There is thus a complex feedback loop within a continuous crystallizer, illustrated in Figure 7.11. 

J. W. Evans, T. R. Ray. Interface propagation and nucleation phenomena for discontinuous poisoning transitions in surface reaction models. Phys Rev E 50 4302 314, 1994. 

In the secondary nucleation stage, the remaining amorphous portions of the molecule begin to grow in the chain direction. This is schematically shown in Fig. 16. At first, nucleation with the nucleus thickness /i takes place in the chain direction and after completion of the lateral deposition, the next nucleation with the thickness k takes place, and this process is repeated over and over. The same surface nucleation rate equation as the primary stage can be used to describe these nucleation processes. 

One of the more important uses of OM is the study of crystallization growth rates. K. Cermak constructed an interference microscope with which measurements can be taken to 50° (Ref 31). This app allows for study of the decompn of the solution concentrated in close proximity to the growing crystal of material such as Amm nitrate or K chlorate. In connection with this technique, Stein and Powers (Ref 30) derived equations for growth rate data which allow for correct prediction of the effects of surface nucleation, surface truncation in thin films, and truncation by neighboring spherulites... 

If point F in Fig. 2 is reached without physical burn-out occurring, then, as shown by Nukiyama, a further increase in heat flux will raise the surface temperature in the direction of E until physical burn-out does occur. If, however, the heat flux at point F is decreased, the surface temperature does not revert to the value at C, but moves along the curve towards D. On reaching D, it was observed by Nukiyama that the surface temperature undergoes another jump discontinuity along the dotted line DG, and stabilizes at G in the nucleate-boiling region. Both the transition lines CF and DG can be passed only in the direction shown by the arrows in Fig. 2. 

Finally we would like to draw attention to low molecular weight results and their analysis on the basis of surface nucleation theory. The theory was originally developed for infinitely long chains and cannot easily be applied to extended or once-folded chain crystallization. Therefore any discrepancies in this area would not be surprising and would not discredit the theory at higher molecular weights. 

Topley and Hume [453], in a study of the dehydration of CaC03 6 H20, assumed the rapid initial formation of (on average) a single nucleus on the surface of each particle of reactant, represented as a sphere of radius a. In the absence of preferential surface development, the reaction interface penetrates the reactant at equal rates in all inward directions (kG = dr/df) and the volume of material reacted at time t is that volume of a sphere, having its centre at the site of surface nucleation and of radius kGt, which falls within the reactant. The fractional reaction, the zone of interpenetrating spheres, at time t is... 

If we are interested in the nucleation of apeu-ticle prior to completing the solid state reaction, we need to distinguish between surface and volume nucleation of the particle, since these are the major methods of which we can perceive. Several cases are shown in the following diagram. 

To begin, we know that a ehange in free energy must occur simultaneously as a change in phase (nucleation) occurs. This will be related to the total volume, V, and the total surface area of both nuclei and particles, 2, vis-... 

Mendez-Villuendas, E. and Bowles, R.K. (2007) Surface Nucleation in the Freezing of Gold Nanoparticles. Physical Review Letters, 98, 185503-1-185503-4. 

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