Crystal growth cluster

The dominant crystal size, is most often used as a representation of the product size, because it represents the size about which most of the mass in the distribution is clustered. If the mass density function defined in equation 33 is plotted for a set of hypothetical data as shown in Figure 10, it would typically be observed to have a maximum at the dominant crystal size. In other words, the dominant crystal size is that characteristic crystal dimension at which drajdL = 0. Also shown in Figure 10 is the theoretical result obtained when the mass density is determined for a perfectiy mixed, continuous crystallizer within which invariant crystal growth occurs. That is, mass density is found for such systems to foUow a relationship of the form m = aL exp —bL where a and b are system-dependent parameters. 

A normal diffusion process, however, runs at a finite concentration of particles different from zero. In this situation it was found [101] that a fractal character (73) of the resulting structure is restricted to an interval a < R < if), where d is the diffusion length (67). Larger clusters have a constant density on a length scale larger than They are no longer fractal there. These observations have various consequences for crystal growth, and will be discussed in the next section. 

Typical surfaces observed in Ising model simulations are illustrated in Fig. 2. The size and extent of adatom and vacancy clusters increases with the temperature. Above a transition temperature (T. 62 for the surface illustrated), the clusters percolate. That is, some of the clusters link up to produce a connected network over the entire surface. Above Tj, crystal growth can proceed without two-dimensional nucleation, since large clusters are an inherent part of the interface structure. Finite growth rates are expected at arbitrarily small values of the supersaturation. 

A comment regarding the dispersion of the Ru-Rh/Si02 and the Ru-Ir/Si02 is in order. For the case of the supported Pt-Ru catalysts. Increases in dispersion as a result of clustering were very large ( ). This effect was particularly noticeable for bimetallic particles which conform to the cherry model. Evidently, the formation of an inner core enriched in one of the two metals, followed by an outer layer enriched in the other metal, inhibits further crystal growth. For the alumina-supported Pt-Ru bimetallic clusters, the effect, although present, is considerably smaller. 

The hypothesis was extended to nucleation of hydrates from liquid water. An alternative hypothesis was proposed by Rodger [1516]. The main difference between these two sets of theories is that Rodger s hypothesis relates the initial formation process to the surface of the water, whereas the theory of Sloan and coworkers considers clusters related to soluted hydrate formers in liquid water as the primary start for joining, agglomeration, and crystal growth. The theories of Sloan and coworkers have been discussed and related to elements of the hypothesis proposed by Rodger [1043]. 

Nucleation is defined as the point where the protonucleus is sufficiently large that its surface area to volume ratio exceeds a critical point, and further growth results in a reduction in global free energy surface effects are now small compared to the inside of the crystal. This is the point where enthalpy dominates over entropy. Subsequent crystal growth and further nucleation events will occur until thermodynamic equilibria is reached, as defined by Eq. 3. The rate of nucleation is defined as the rate at which clusters grow through this critical point. 

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). 

Complete clustering, or segregation, of tautomers may occur during crystal growth. This can lead, for example, to crystals that consist of two tautomers in equal proportions and located at crystallographically independent sites. This is the case for isocytosine, 47 (104). Similarly, in crystalline anthranilic acid the neutral molecule and the zwitterion coexist (10S). Another example, 39, has been mentioned already (82). 

Reductive nitrosylation, transition metal nitrosyl complexes, 34 296-297 ReFejSj cluster, 38 41-43 self-assembly system, 38 41-42 Refining, of actinide metals, see Actinide, metals, purification Refractory compounds heat treatment of solids, 17 105-110 crystal growth, 17 105, 106 decomposition, 17 107,-110 spheroidization, 17 106, 107 preparation of, using radio-frequency plasma, 17 99-102... 

Interface reaction is another necessary step for crystal growth and dissolution. After formation of crystal embryos, their growth requires attachment of molecules to the interface. The attachment and detachment of molecules and ions to and from the interface are referred to as interface reaction. (During nucleation, the attachment and detachment of molecules to and from clusters are similar to interface reaction.) For an existing crystal to dissolve in an existing melt. 

An expected difference between ion-by-ion and hydroxide (or any other cluster) mechanisms is that in the latter, since colloids from the solution stick to the snbstrate snrface, the crystal size is not expected to change greatly with film thickness (it may increase to some extent, since the colloids themselves can grow via an ion-by-ion process on the crystals). For ion-by-ion growth, it is likely that crystal growth occnrs on nncleii already present on the substrate, and therefore crystal size can increase with increasing deposition. 

For the ion-by-ion reaction, nucleation is generally slower and the density of nuclei smaller. Additionally, growth occurs (ideally) only at a solid surface therefore nucleation is confined to two dimensions, in contrast to three dimensions for the cluster mechanism. The crystal growth may terminate when adjacent crystals touch each other or by some other termination mechanism, e.g., adsorption of a surface-active species. These factors should be valid regardless of whether the mechanism proceeds via free chalcogenide ions or by a complex-decomposition mechanism. 

These interactions are vital to understanding the dynamics of many surface phenomena, such as cluster formation and diffusion, crystal growth, surface reactivity, adsorption and desorption, and many others. 

A hypothesis picture of hydrate growth at a crystal is shown in Figure 3.21, modified from Elwell and Scheel (1975). This conceptual picture for crystal growth may be combined with either the labile cluster or local structuring hypotheses for nucleation. 

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