Surface nucleus

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). 

Application of the Mossbauer effect, which is essentially a bulk phenomenon, to the study of surfaces has received significant attention in recent years. The usefulness of this technique lies in its ability to determine the electronic environment and symmetry of the surface nucleus, and it offers a method of investigation that is clearly complementary to other physical methods for the characterization of solid surfaces. Mossbauer spectroscopy has the attractive advantage that it may be used at a variety of pressures and can be applied to the study of heterogeneous catalysis and adsorption processes to probe the nature of the solid surface and its electronic modification when holding adsorbed species. 

The incorporation of the growth unit(s) into a kink on a step. This process may be accompanied by further dehydration either at the time of incorporation or later. The step may be on a two-dimensional surface nucleus or a dislocation growth spiral. 

The growth of a surface nucleus is achieved by either surface or bulk diffusion to the step or kink site at the edge of the growing nucleus. For the liquid phase, bulk diffusion is more important [3], giving a surface growth rate,... 

In the case of homopolymers, the growth rate of a lamellar crystal is controlled by two processes on the one hand by the abihty of forming a surface nucleus (as determined by the degree of undercooling, AT = - T, and on the... 

In the case of homopolymers, the growth rate of a lamellar crystal is controlled by two processes on the rme hand by the ability of forming a surface nucleus (determined by the degree of imdercooUng, AT = T —T and on the other hand by the ability of diffusion of the chain molecules toward the crystal growth front (determined by the difference between the crystallization temperature, Tc, and the glass-transition temperature, T. Both processes are inversely dependent on temperature a maximum rate of crystal growth is usually observed at temperatures close to Tmax (Jg + 7) )/2. 

Based on observations from our simulations, we can make several conclusions about the natme of the surface nucleus during crystal gr owth. We... 

After completion of a layer on the surface of the crystal, a new surface nucleus must be created for the formation of a new layer. This is called a secondary nucleation process. The growth of the crystal is then a series of secondary nucleation events and completions of new layers. The most widely accepted expression for the secondary nucleation rate is given by... 

Figure 4 A three-dimensional spherical nucleus of radius r compared with a two-dimensional surface nucleus with the same radius.

Regime I. One surface nucleus causes the completion of the entire substrate of length L (see Figure 6.30) (77) that is, one chain is crystallizing at a time. Many molecules may be required to complete L. The term surface nucleus refers to a segment of a chain sitting down on a preexisting crystalline lamellar structure, as opposed to the nucleus, which initiates the lamellae from the melt in the first place. 

These nuclei are deposited sporadically in time on the substrate at a rate i per unit length in a manner that is highly dependent on the temperature. Substrate completion at a rate g begins at the energetically favorable niche that occurs on either side of the surface nucleus, chain folding assumed. 

Figure 6.30 Surface nucleation and substrate completion with reptation in regime I. where one surface nucleus deposited at rate /causes completion of substrate of length L, giving overaii growth rate G, = b iL Multiple surface nuclei occur in regime II (not shown) and lead to Gn = lo(2/g) where g is the substarte completion rate. The substrate completion rate, g, is associated with a "reeling in rate r= (l /ao)g for the case of adjacent reentry (77).

When nuclei are formed only on the surface nucleus growth and overlap lead to the formation of a coherent interface between the undecomposed reactant in the interior of the particles and the product layer outside this. If this interface propagates inward at a constant rate, as it will if every molecule of reactant in the interface has the same probability of decomposing, then it follows that... 

Figure 3.25 Polygonal spiral growth from the giant screw dislocation in Fignre 3.24. Arrows on the side snrface indicate the initial advance directions of the two steps. Each layer of the spiral has a thickness b = 4- Other dimensions are the terrace width y and the size of the smallest surface nucleus...

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